Basic structure and formation mechanism of Ti-Si-N superhard nanocomposite coatings Von der Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik der Universität Stuttgart zur Erlangung der Würde eines Doktor-Ingenieurs (Dr.-Ing.) genehmigte Abhandlung Vorgelegt von M. Eng. Xuejie Liu aus Baotou, Inner Mongolia, PR China Hauptberichter: Univ.-Prof. Dr.-Ing. Prof. E.h. Dr.-Ing. E.h. Dr. h.c. mult. Engelbert Westkämper Mitberichter: Prof. Dr.-Ing. Dr. h. c. mult. Uwe Heisel Tag der Einreichung: 15. 01. 2008 Tag der mündlichen Prüfung: 17. 02. 2009 Institut für Industrielle Fertigung und Fabrikbetrieb (IFF) der Universität Stuttgart 2009 Berichte aus dem Fraunhofer-Institut für Produktionstechnik und Automatisierung (IPA), Stuttgart, Fraunhofer-Institut für Arbeitswirtschaft und Organisation (IAO), Stuttgart, Institut für Industrielle Fertigung und Fabrikbetrieb (IFF), Universität Stuttgart und Institut für Arbeitswissenschaft und Technologiemanagement (IAT), Universität Stuttgart Herausgeber: Univ.-Prof. Dr.-Ing. Prof. e.h. Dr.-Ing. e.h. Dr. h.c. mult. Engelbert Westkämper und Univ.-Prof. Dr.-Ing. habil. Prof. E.h. mult. Dr. h.c. mult. Hans-Jörg Bullinger und Univ.-Prof. Dr.-Ing. Dr.-Ing. E.h. Dieter Spath IPA-IAO Forschung und Praxis Innenteil IPA 02.03.09 13:26 Seite 1 Fachverlag · 71296 Heimsheim Institut für Industrielle Fertigung und Fabrikbetrieb Basic structure and formation mechanism of Ti-Si-N superhard nanocomposite coatings Nr. 481 Xuejie Liu Innenteil IPA 02.03.09 13:26 Seite 3 D 93 ISBN (10) 3-939890-42-1, ISBN (13) 978-3-939890-42-3 Jost Jetter Verlag, Heimsheim Dieses Werk ist urheberrechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die der Übersetzung, des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tabellen, der Funksendung, der Mikroverfilmung oder der Vervielfältigung auf anderen Wegen und der Speicherung in Datenverarbeitungsanlagen, bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. Eine Vervielfältigung dieses Werkes oder von Teilen dieses Werkes ist auch im Einzelfall nur in den Grenzen der gesetzlichen Bestimmungen des Urheber- rechtsgesetzes der Bundesrepublik Deutschland vom 9. 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Xuejie Liu Institut für Industrielle Fertigung und Fabrikbetrieb (IFF), Universität Stuttgart Fraunhofer Institut für Produktionstechnik und Automatisierung (IPA), Stuttgart Univ.-Prof. Dr.-Ing. habil. Prof. E.h. mult. Dr. h.c. mult. Hans-Jörg Bullinger ord. Professor an der Universität Stuttgart Präsident der Fraunhofer-Gesellschaft, München Univ.-Prof. Dr.-Ing. Dieter Spath ord. Professor an der Universität Stuttgart Fraunhofer-Institut für Arbeitswirtschaft und Organisation (IAO), Stuttgart Univ.-Prof. Dr.-Ing. Prof. E.h. Dr.-Ing. E.h. Dr. h.c. mult. Engelbert Westkämper ord. Professor an der Universität Stuttgart Fraunhofer-Institut für Produktionstechnik und Automatisierung (IPA), Stuttgart Innenteil IPA 02.03.09 13:26 Seite 4 Geleitwort der Herausgeber Über den Erfolg und das Bestehen von Unternehmen in einer marktwirtschaftlichen Ordnung entscheidet letztendlich der Absatzmarkt. Das bedeutet, möglichst frühzeitig absatz marktorientierte Anforderungen sowie deren Veränderungen zu erkennen und darauf zu reagieren. Neue Technologien und Werkstoffe ermöglichen neue Produkte und eröffnen neue Märkte. Die neuen Produktions- und Informationstechnologien verwandeln signifikant und nachhaltig unsere industrielle Arbeitswelt. Politische und gesellschaftliche Ver ände - rungen signalisieren und begleiten dabei einen Wertewandel, der auch in unseren Indu - striebetrieben deutlichen Niederschlag findet. Die Aufgaben des Produktionsmanagements sind vielfältiger und anspruchsvoller ge - worden. Die Integration des europäischen Marktes, die Globalisierung vieler Industrien, die zunehmende Innovationsgeschwindigkeit, die Entwicklung zur Freizeitgesellschaft und die übergreifenden ökologischen und sozialen Probleme, zu deren Lösung die Wirt- schaft ihren Beitrag leisten muss, erfordern von den Führungskräften erweiterte Perspek - tiven und Antworten, die über den Fokus traditionellen Produktionsmanagements deutlich hinausgehen. Neue Formen der Arbeitsorganisation im indirekten und direkten Bereich sind heute schon feste Bestandteile innovativer Unternehmen. Die Entkopplung der Arbeitszeit von der Betriebszeit, integrierte Planungsansätze sowie der Aufbau dezentraler Strukturen sind nur einige der Konzepte, welche die aktuellen Entwicklungsrichtungen kennzeich- nen. Erfreulich ist der Trend, immer mehr den Menschen in den Mittelpunkt der Arbeits- gestaltung zu stellen - die traditionell eher technokratisch akzentuierten Ansätze weichen einer stärkeren Human- und Organisationsorientierung. Qualifizierungspro - gramme, Training und andere Formen der Mitarbeiterentwicklung gewinnen als Diffe - renzierungsmerkmal und als Zukunftsinvestition in Human Resources an strategischer Bedeutung. Von wissenschaftlicher Seite muss dieses Bemühen durch die Entwicklung von Methoden und Vorgehensweisen zur systematischen Analyse und Verbesserung des Systems Pro- duktionsbetrieb einschließlich der erforderlichen Dienstleistungsfunktionen unterstützt werden. Die Ingenieure sind hier gefordert, in enger Zusammenarbeit mit anderen Disziplinen, z. B. der Informatik, der Wirtschaftswissenschaften und der Arbeitswissen - schaft, Lösungen zu erarbeiten, die den veränderten Randbedingungen Rechnung tragen. Die von den Herausgebern langjährig geleiteten Institute, das - Fraunhofer-Institut für Produktionstechnik und Automatisierung (IPA), - Fraunhofer-Institut für Arbeitswirtschaft und Organisation (IAO), - Institut für Industrielle Fertigung und Fabrikbetrieb (IFF), Universität Stuttgart, - Institut für Arbeitswissenschaft und Technologiemanagement (IAT), Universität Stuttgart Innenteil IPA 02.03.09 13:26 Seite 5 arbeiten in grundlegender und angewandter Forschung intensiv an den oben aufgezeig- ten Entwicklungen mit. Die Ausstattung der Labors und die Qualifikation der Mitarbeiter haben bereits in der Vergangenheit zu Forschungsergebnissen geführt, die für die Praxis von großem Wert waren. Zur Umsetzung gewonnener Erkenntnisse wird die Schriften - reihe „IPA-IAO - Forschung und Praxis“ herausgegeben. Der vorliegende Band setzt diese Reihe fort. Eine Übersicht über bisher erschienene Titel wird am Schluss dieses Buches gegeben. Dem Verfasser sei für die geleistete Arbeit gedankt, dem Jost Jetter Verlag für die Auf- nahme dieser Schriftenreihe in seine Angebotspalette und der Druckerei für saubere und zügige Ausführung. Möge das Buch von der Fachwelt gut aufgenommen werden. Engelbert Westkämper Hans-Jörg Bullinger Dieter Spath Innenteil IPA 02.03.09 13:26 Seite 6 Acknowledgements This Ph. D work has been carried out in the period from April 2001 to January 2008 under supervision of Univ.-Prof. Dr.-Ing. Prof. E.h. Dr.-Ing. E.h. Dr. h.c. mult. Engelbert Westkaemper at the Institute of Industrial Manufacturing & Management (Institut für Industrielle Fertigung und Fabrikbetrieb, IFF) of Universitaet Stuttgart in Germany. Many thanks to Professor Westkaemper for giving me the opportunity to work on this interesting research project: digital factory. Without the kindness, the encouragement, the supervision, and the continual support of Professor Westkaemper, this work would not have been possible. During this period of research here, I have learnt a lot from professor Westkaemper‘s character. His passion for science and innovation and his pure-heartedness toward people have impressed me very much. Many thanks to Professor Hans-Juergen Warnecke for his kindness and for providing me two-year scholarship at the beginning of this research project. And many thanks to Professor Uwe Heisel for his support, for agreeing to be my co-supervisor, and for his advices to my thesis. Many thanks to Professor Hermann Sandmaier and Professor Alexander Verl for accepting the work as doctoral examination chairman. I would like to thank Inner Mongolia University of Science and Technology for sending me to Germany and continually supporting me to work on this research project. This research was initially supported by project CHN01/203 from the Fraunhofer Gesellschaft (FhG), then by Deutsches Bundesprojekt, under Grant iff12807 through HLRS of Universitaet Stuttgart, and also by Inner Mongolia Education and Research Foundation, under Grant NJ06077 through Inner Mongolia University of Science and Technology, PR China. I am very grateful for the supports of all these institutions. I am very grateful to my colleagues Dr. Bernhard Gottwald, Dr. Silvana Sommadossi, Mr. Andreas Meyke, Mr. Frank Herbrig, Mr. Jens Schoebel, Dr. Matthias ii Schneider, Mr. Mehran Ghahremanpour, Dr. Joerg Niemann, Mr. Daniel Tolksdorf, Dr. Birgit Spaeth, Dr. Andreas Scheibe, Dr. Qiaoyan Ye, Mr. Matthias Staufer, Mr. Joerg Siegert, Mr. Ronny Egeler, and Mr. Heiko Herrmann for their hospitality and help. I would like to thank Professor Di Tang, Mr. Zhi Lin, Dr. Gerhard Bilger, Dr. Viktor Laptev, Ms. Andrea Ziegler, Mrs. Xuefen Wang, for their help by measuring Ti-Si- N samples using the Nano Indenter, XRD, EDS, and SEM. I would like to thank my student Miss Xinmeng Wang and Mr. Guangxin Wu for their help and the cooperation on the development of KMC codes. I would like to thank Professor Yu Jia, Mr. Changqing Wang, Mr. Stefan Haberhauer, Dr. Shengfa Ye, and Dr. Wenhui Xie for their help and advices in the ab initio calculations. Many thanks to Professor Graeme Henkelman, Dr. Arthur F. Voter, Professor Peter Kratzer, Dr. Denis Music, and Professor Ole Krogh Andersen for their help and the helpful discussions. I am very grateful to Mrs. Marianne Korell, Mrs. Eva Hestermann-Beyerle, Mrs. Melanie Pfefferle, Mr. Guenter Pavel, Mrs. Gisela Barger, Mr. Zhichun Li, and Mrs. Cornelia Schott for their hospitality and help. A special thank to my cousin Dr. Dongying Wu for her kind help. And I would like also thank my friends Dr. Jianqiang Peng, Dr. Hua Yuan, Mrs. Maria Gottendieck, and their families for their support and help during my stay in Stuttgart. This work is dedicated to my wife Chunyan Wei, my daughter Wei Liu, and my parents Zhanyao Liu and Lijun Li, who are very important in my life and give me the biggest support. My daughter Wei Liu gave me much help with preparing this thesis. I am very proud of her talent. Xuejie Liu In Stuttgart, Germany January 2008 Table of contents Acknowledgements…...….………………………………………………………………i Table of contents……...….……..…………………………………………………………9 Abstract……….......….…………..………………………………………………………12 1. Introduction…...….…………………………………...………………………………14 2. Literature review…….……………………………………………………………….18 2.1. Ti-Si-N superhard nano-composite coatings………………………….………….18 2.1.1. Experimental explorations………………………………………………….18 2.1.2. The hypothesis of Ti-Si-N structure and hardness enhancement…..……….24 2.1.3. The modeling of Ti-Si-N film formation……...…………….……………...25 2.1.4. Discussion.………………………………………………………………….25 2.2. Sputtering physical vapor deposition (PVD) and process simulation.…………...27 2.3. Atomic simulation methods..……………………………………………………..30 2.3.1. Kinetic Monte Carlo method.……………………………………………....31 2.3.2. Ab initio method and density functional theory (DFT).…………………….33 2.3.2.1. Ab initio method with wave function..……………………………….34 2.3.2.2. Density functional theory (DFT) ……………………………………36 3. Experiments on sputtering PVD and Ti-Si-N deposition…….……………………40 3.1. The sputtering PVD system……………………………………………………...40 3.2. The experiments on sputtering PVD process……………….……..…………….42 3.2.1. The ion mass spectra and deposition rates of Ti in RF/DC sputtering…....43 3.2.2. The ion mass spectra and deposition rates of TiN in sputtering PVD...…..45 3.3. The experiments on Ti-Si-N deposition…………………………………………52 3.4. The summary of experiment researches…………………………………………57 4. The kinetic Monte Carlo simulation of Ti-Si-N film growth….…….……………59 4.1. The lattice KMC simulation of film growth…………..…………….…………...60 4.2. The off-lattice KMC simulation of Ti-Si-N film growth………………..……....65 4.3. The summary of the KMC simulation……………..……………………………73 Table of contents 10 5. The atomic calculations with the ab initio method……………..…..……………….75 5.1. VASP and the pre-calculation…………………………………………………...76 5.2. The basic structure of Ti-Si-N superhard coating………………………….........77 5.2.1. Introduction……………………………………………………………......77 5.2.2. A Si atom in the TiN crystallite...……………………………………........78 5.2.3. A Si atom in the boundary of TiN.......………………………………........81 5.2.4. The property of the interface and the Ti-Si-N coating……………….........85 5.2.5. Si atoms distribution in TiN……………………………………………….89 5.2.6. The interface formation on the TiN(001) surface……………………........92 5.2.7. The atomic percent of Ti: N: Si……………………………………………96 5.2.8. The section summary………………………………………………………97 5.3. The basic diffusion behaviors of Ti, N and Si on the TiN (001) surface………...98 5.3.1. Introduction………………………………………………………….….....98 5.3.2. The PES and the diffusion of a Ti, N, and Si adatom………………....…100 5.3.2.1. Adatom‘s PES and diffusion path on the TiN(001) surface….…….100 5.3.2.2. Adatom diffusion around the TiN island……………………….......107 5.3.2.3. Adatom diffusion along the TiN island………………………...…..111 5.3.2.4. Adatom diffusion down the TiN island…………………………….114 5.3.3. The Ti-N addimer and the Si-N addimer diffusion………...…………….116 5.3.3.1. Addimer diffusion on the TiN(001) surface…………….……........116 5.3.3.2. Addimer diffusion around the TiN island……………………..…...119 5.3.3.3. Addimer diffusion along the TiN island……………………….......127 5.3.3.4. Addimer diffusion down the TiN island……………………….......130 5.3.4. The cluster diffusion on the TiN(001) surface…………………….…......133 5.3.4.1. Ti-N-Ti diffusion………………………………………….….........133 5.3.4.2. N-Ti-N diffusion…………………………………………...…........134 5.3.4.3. Ti-N-Si diffusion……………………………………………....…...135 5.3.4.4. 2Ti-2N diffusion…………………………………………….……..137 5.3.5. The inter diffusion in the TiN crystallite or in the TiN(001) surface…….139 5.3.5.1. Ti, Si, N atom inter diffusion in crystalline TiN…………………...139 5.3.5.2. Ti, Si, N adatom inter diffusion in the TiN(001) surface……….....141 5.3.6. The influence of Si adatoms on the Ti and N diffusion………………….142 5.3.7. The section summary and the process parameter……………….…..……144 5.4. The summary of the ab inito calculations……………………..……………….149 Table of contents 11 6. Conclusion and outlook….………………………………………….………………151 Zusammenfassung (Extended Abstract in German)….….…………………..…………159 Appendix A: The calculation of the atomic percent of Ti: N: Si….………….…………168 Appendix B: The Nudged Elastic Band (NEB) method….……………….……………170 References….……………………………………………………………………………172 List of figures.……………….………………………………..…………………………186 List of tables.……………...……………………………..………………………………194 List of symbols and glossary……….…………………………………..………………198 Xuejie Liu Basic structure and formation mechanism of Ti-Si-N superhard nanocomposite coatings Supervisor: Professor Engelbert Westkämper Institute of Industrial Manufacturing and Management, (Institut für Industrielle Fertigung und Fabrikbetrieb, IFF) University of Stuttgart 2008 196 pages, 85 figures, 50 tables Abstract With the concept of digital factory, a research including experiment, kinetic Monte Carlo simulation, and ab initio calculation has been conducted to investigate the basic structure and the formation mechanism of Ti-Si-N superhard nanocomposite coatings. In sputtering PVD process, ion mass spectra and deposition rates have been measured. The measurement results show that the Ti-Si-N deposition in the sputtering PVD is a complicated process and it is difficult to obtain the stoichiometry of TiN without the measurement in situ. The experiments of the Ti-Si-N deposition demonstrate that Si addition obviously influences the film microstructure and hardness. But the atomic structure and the formation mechanism of the Ti-Si-N coatings have not been identified by the experiments. This indicates that the atomic simulation and calculation is necessary. Two kinetic Monte Carlo (KMC) simulation codes with the lattice model and with the off-lattice model have been developed. In the off-lattice KMC simulation, the dimer method was used to search the saddle points on the potential energy surface (PES), which provided the direct calculation method of activation energy and the relaxation algorithm of adatoms, so that this off-lattice KMC simulation is much closer to the real situation. But by the off-lattice KMC simulation, the basic structure and the formation mechanism of Ti- Si-N films have not been found out due to the inaccurate potential algorithm. Therefore, the ab inito calculation is needed. The ab inito calculations have been performed with VASP code which is based on density functional theory.The basic structure and the formation mechanism of the Ti-Si-N composite coating have been identified through the ab intio calculations. The total energy calculation results of the configurations of Si addition into the TiN crystallite or into the boundary of TiN show that (a) there is no silicon interstitial solid solution in the TiN crystallite under the thermal equilibrium condition; (b) if a Abstract 13 titanium atom or a nitrogen atom is missing in the TiN crystallite, a silicon atom is possible to occupy the vacant site and to form the substitutional solid solution; (c) in the lowest-energy structure of the Ti-Si-N composite, Si is in the form of a double cross tetrahedron Si-4N-4Ti and/or a fourfold coordinated plane unit Si-2N-2Ti in boundaries, i.e. the basic structure of the Ti-Si-N superhard composite coatings is the TiN crystallites with Si-4N-4Ti and Si-2N-2Ti in the boundaries. The covalent combination of Si-4N-4Ti and Si-2N-2Ti strengthens the boundary of TiN. The ab initio calculations have been also carried out to investigate (a) the PES and the diffusion path of Ti, N, and Si adatom on the Ti(001) surface; (b) the activation energy for the diffusion of a single adatom or an addimer on the TiN(001) surface, around the TiN island, along the TiN island, and down the TiN island; (c) the activation energy for the diffusion of some clusters on the TiN(001) surface; (d) the activation energy for the inter-diffusion of Ti, N, and Si. The calculation results show the following two points about formation mechanism. (1) Ti adatoms are possible to form the (111) nuclei on the TiN(001) surface, which may lead to the preferred orientation transformation of the TiN crystallite from (001) into (111). Due to high activation energy, the inter diffusion of Ti and N atom/adatom are very difficult. The diffusion of Ti adatom, N adatom, and Ti-N addimer around and along the TiN island are also difficult. This may result in the insufficient diffusion in the TiN film growth process. That is why the TiN films have many voids and a columnar structure. (2) The Si addition could change the formation mechanism of the TiN film. Si adatoms are combined with N adatoms to form the Si-N addimers. The Si-N configuration changes the diffusion mode of the N adatom. The diffusion of the Si-N addimers and the Si adatoms are relatively easy during the Ti-Si-N film growth, which can adjust the PES of Ti adatoms and promote the Ti diffusion. Since the N and Ti diffusion is increased and the inter diffusion of Si is relatively easy, the Ti-Si-N film has dense structure. Put the results of the atomic structure and the formation mechanism together, the Si adatom and atoms could simultaneously promote the diffusion of N and Ti adatoms and restrict the increase of the grain size of TiN in the Ti-Si-N film growth. Because of the effect of Si addition, the Ti-Si-N coating has dense structure and strong boundary, which leads to its hardness enhancement. This research indicates that the technical specification design and the design for manufacture are crucial to the design of nano-composite. The ab initio calculations and the KMC simulations are very helpful to the design. Now the general who wins a battle makes many calculations in his temple ere the battle is fought. The general who loses a battle makes but few calculations beforehand. Thus do many calculations lead to victory and few calculations to defeat: how much more no calculation at all! It is by attention to this point that I can foresee who is likely to win or lose. The Art of War, by Sun Tzu (535-? BC) 1. Introduction One important development today is digitalization, for example, digital earth, digital world, digital life, digital human, digital library, digital hospital, and so on. Digital factory is one of them. These digital X are promoted by a huge market requirment and based on three powerful developments: computers, the internet, and simulation techniques. The mode of our life has been already and will be changed more and more by these digital X. On the digital factory platform, production organizations or manufacture issues are dealt with through calculations, simulations or visualizations [VDI-R4499]. Under the concept of digital factory, process simulations should be performed before the production and even before the production experiment to provide safe and optimal plans for the production or the production experiment and hence to reduce the cost and time of the productions [Westkaemper06]. It is beyond doubt that digital factory will bring a revolution in production system. Another important development today is nano-structured composite materials. The nano-composite materials demonstrate unconventional properties because the size effect and/or the quantum effect come into play if the nanometer size range is reached. This kind of materials is considered as new solutions to energy source, environmental protection, human health improvement, and so on [NNI-web]. However, there are two difficulties in the experimental exploration of nano-composite: (1) the identification of the atomic position relationship and the relevant electronic structure of nanocomposites, (2) the recognition of the formation mechanism, i.e. exact self-assembly process and its causes, of nanocomposite. These two difficulties have led to some problems of the preparation of nano-composite materials. A serious problem is the unreproduction of the nano-composite which has unique property. An example, we will see below, is the Introduction 15 unreproduction of the Ti-Si-N nano-composite coating with 100GPa hardness. In fact, these two difficulties imply (a) the limitation of the present-day characterization methods and the present-day measurement methods in situ, and (b) the incompleteness of the design system of nano-composite materials. In this case, using calculation or simulation as a supplementary method might be very helpful to overcome the difficulties. The research reported in this thesis is a practice under the concept of digital factory to seek a simulation way to promote the development of nano-composite film. The research focuses on the Ti-Si-N superhard nano-composite coating. The search for and the design of superhard materials are a topic of much interest to scientists because superhardness has great meaning to science and technical application [Kaner05] [Haines01]. In recent years, a lot of research interest is attracted to superhard nanocomposite coatings, e.g., nc-TiN/a-Si3N4, nc-W2N/a- Si3N4, nc-TiN/a-TiB2, and so on [Lu06] [Zhang03] [Andrievski01] [Musil00] [Veprek99]. Among these superhard composites, the Ti-Si-N nano-composite coating is a special one. Its hardness was reported to be above 100 GPa, reaching the hardness of diamond [Veprek00-1]. Normally, its hardness is in the range of 30-60 GPa [Patscheider03]. In addition, it has high thermal stability and high oxidation resistance [Veprek00-2]. Unfortunately, this composite coating with 100 GPa hardness is not reproduced, although many research efforts have contributed to synthensize it. Certainly, it is necessary to investigate its structure and formation mechanism carefully. Since 1992, a lot of researches have been carried out on the Ti-Si-N hard composite coatings. Almost all of them are experimental explorations. Through them, a conceptual hypothesis has been presented, that the Ti-Si-N structure is TiN crystallite embedded in amorphous Si3N4 matrix, expressed as nc-TiN/a-Si3N4 [Veprek95-2]. But until now, the atomic structure and the formation mechanism of Ti-Si- N superhard nano-composite coating are not clear. Without the understanding of the atomic structure of Ti-Si-N composite, the accurate analysis of its properties and the numerical design of this kind of composite cannot be conducted. And without the understanding of its formation mechanism, the numerical planning for its fabrication is impossible. Therefore, the goal of this research is to find out the atomic structure and the formation mechanism of the Ti-Si-N superhard composite coating by means of simulation and calculation. And based on the atomic structure and formation mechanism of Ti-Si-N superhard composite coating, we try to provide the process plan, including process condition and process parameters, for the Ti-Si-N manufacture. This research includes Introduction 16 three kinds of investigations: experiments, kinetic Monte Carlo simulations, and ab inito calculations. In the experiment on the sputtering PVD process, the influence factors of the Ti-Si- N deposition were investigated, the deposition and the characterization of Ti-Si-N coatings were performed, and the necessary of atomic simulation was recognized. In order to simulate the film growth of Ti-Si-N, two kinetic Monte Carlo (KMC) simulation code with lattice model and with off-lattice model were developed. In off- lattice KMC simulation of Ti-Si-N film growth, there are two crucial factors, namely the potential energy surface (PES) and the combination of TiN and Si3N4. Both of them depend on the accurate calculation of atomic interaction. An interface structure Si-4N-4Ti was proposed but could not be identified due to the inaccurate potential algorithm. Therefore, the ab initio calculation is necessary. With the ab initio method, total energies of the configurations, in which a Si atom was added into the TiN crystallite or into the TiN boundary, were calculated. Through the comparison of the total energies and the cohesive energies of these configurations, the exact interface form and the basic structure of Ti-Si-N superhard composite coating have been identified. In addition, the potential energy surface (PES), the diffusion paths, and the activation energy for the basic diffusion of Ti, Si, and N on the TiN (001) surface were also investigated through the ab initio calculations. The formation mechanism of the Ti- Si-N coatings has also been recognized. The identification of the basic structure and the formation mechanism of Ti-Si-N superhard composite coatings in this research is meaningful for the further research and development. (1) It provides a basis for the accurate analysis of the property of the composite coating, especially for studying the causes of super or ultra hardness. This basis could also be used in the numerical design of the nano-composite coating and in the numerical planning of its preparation process. (2) A new interface structure and a new kind of self-organization and self-assembly mode have been identified. The interface structure of Ti-Si-N, the double cross tetrahedron or the fourfold coordinated plane unit, can be used in the production of nanometer patterns or quantum dots. A new kind of self- organization and self-assembly mode shows the importance of bond combinations in the fabrication of nanostructure composite coatings. (3) This research indicates that the design method of nanocomposite coating should be improved. The technical specification design, the product evaluation for performance, and the design for manufacture should be added Introduction 17 into the design. This research presents a way for the research and development of nano- structured composite. Before the experimental exploration of a new nanostructured composite, atomic calculations or simulations should be conducted through the ab initio and KMC methods in order to obtain an optimal experiment plan. The emphasis of ab initio calculations and KMC simulations should be on the atomic structure and the formation mechanism of the nano-composite. The outline of this thesis is as followings. In Chapter 2, the development of Ti-Si- N composite coatings are reviewed. And the sputtering PVD process and atomic simulation method are briefly introduced. In Chapter 3, the experiments on the sputtering PVD process and the deposition of Ti-Si-N coatings are presented. In Chapter 4, the development of KMC simulation codes and the KMC simulation of the Ti-Si-N film growth are introduced. In Chapter 5, it is reported the investigations through ab inito calculations into the basic structure of Ti-Si-N superhard composite and into the basic diffusion behaviors of Ti, Si, and N on the TiN(001) surface. 2. Literature review In this chapter, some background information is introduced, including the research of Ti- Si-N nano-composite coatings, the sputtering PVD process, and the atomic simulation methods. And we discuss what should be simulated, why it must be simulated, and how it can be simulated. 2.1. Ti-Si-N superhard nano-composite coatings The exploration of the Ti-Si-N nano-composite coatings is reviewed in this subsection. The emphasis is on the research methodology, the special phenomena in the experiment, the problem in the research, and the reason why the atomic structure and the formation mechanism were not found out. 2.1.1. Experimental explorations The research on the combination of Si3N4 and TiN has a long history. In the beginning, the research focused on electrical conductivity and resistivity [Samsonov60] [Wasa73] [Posad78] [Beensh-M81]. Between 1982 and 1983, Hirai and his coworkers had reported their research results of Si3N4-TiN coatings [Hirai82-1] [Hirai82-2] [Hirai83-1] [Hirai83-2]. The purpose of their research was to improve Si3N4 and to explore new composite materials. The chemical vapor deposition (CVD) of SiCl4-NH3-H2-TiCl4 was used in their researches. The deposition temperature was from 1050°C to 1450°C and the thickness of deposited coatings was of 1.9 mm. The X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray (EDX), electron microscopy, and a laser flash method for the thermal diffusivity measurement were conducted to investigate the microstructure, density, and thermal conductivity of Si3N4-TiN. Literature review 19 There are two interesting points in their research results. The first one is that Si3N4 and TiN are immiscible. Ti and N are bonded together and form crystallites as shown in Fig.3 in Reference [Hirai82-2]. This reveals that the bond of TiN is stronger than the bond of Si-N. The second one is that the thermal conductivity of the composite decreases drastically with increasing of the TiN content [Hirai83-2]. This is an interesting phenomenon. The immiscibility of TiN and Si3N4 has attracted a lot of attention of the following researchers. But the property of thermal conductivity decreasing has not thoughtfully been discussed so far. In 1988, Posadowski deposited Ti-Si-N film with a triode sputtering system for studying the resistivity and the temperature coefficient of resistance (TCR) [Posad88]. The deposition temperature was between 300K and 573K. The film thickness was between 60 nm and 180nm. The TiN content was in the range of 69-87% in the film. The film structure was characterized by X-ray spectrograph and that the nanostructure had been recognized, ―The structure of the Ti-Si-N film is typical of cermet films, in which agglomerates of the conductive phase TiN are suspended in the dielectric matrix‖ [Posad88]. In 1992, the first and also very important research of Ti-Si-N hard coatings had been reported by Li and his coworkers [Li92]. The purpose of their research was to improve TiN coatings. The plasma enhanced CVD of SiCl4-NH3-H2-TiCl4 was used in the deposition of Ti-Si-N coatings. The HSS substrate was heated by the ion bombardment to 560°C and the thickness of the Ti-Si-N coatings was about five micrometer. The investigation was performed through the micro-hardness measurement, XRD, SEM, electron probe micro-analysis (EPMA) for compositional analysis, and X-ray photoelectron spectra (XPS). By XRD, the structure of TiN was identified to be mostly (200) oriented crystallite and the lattice constant was 0.214 nm. But there was no Si3N4 peak in the XRD pattern. In the Ti-Si-N film with 25 % Si, the Si3N4 binding energy was recognized by XPS. Therefore, the Ti-Si-N film was proposed to be a multiphase composite consisting of crystalline TiN, amorphous Si3N4 and a small amount of free Si. Li-group gave a hypothesis that Si3N4 nano-particle in TiN matrix as ―particle hardening‖ made the composite strengthen. Literature review 20 A highlight in this research was that the micro-hardness of the Ti-Si-N film reached a maximum value of about 6350 kgf/mm² (~ 62GPa) at a Si content of 10-15%. This hardness is higher than that of cubic BN. And in this research, a typical feature curve of superhard nano-composite coatings was obtained, which presented the correlation between the micro-hardness and the Si content as shown in Fig. 2.1. The most important point in this research was an interesting phenomenon that addition of Si to a mount higher than 5% changed the TiN columnar structure to a dense and glasslike Ti-Si-N structure which was characterized by SEM. This research puts forward two questions. (1) Why does the film structure be changed so much by Si addition or what is the formation mechanism of the Ti-Si-N composite coating? (2) What is the exact structure of the Ti-Si-N composite coating and why does this composite coating has so high hardness? Fig. 2.1: The microhardness vs. the Si content in the Ti-Si-N films, from [Li92]. Since then the research of Ti-Si-N film has two branches. One is of the electrical property of the diffusion barriers films and the other is of the mechanical property of hard coatings. We pay our attention only on the hard coatings. Shortly after the research of Li group, some research groups began to work on the study of Ti-Si-N hard composite coatings [HeJL95] [HeJW95] [Veprek95-1] [Veprek95- 2]. The researches of Veprek-group (Li joined in this group) are well worth discussing. The plasma CVD of SiH4-H2-N2-TiCl4 was used by Veprek-group for the deposition of Ti-Si-N coatings. The silicon wafer or stainless steel substrates were heated Literature review 21 with controlled hot air through the substrate holder to the temperature of 550°C. The investigations of EDX, XRD, XPS, and Fischer-scope 100 for hardness measurement were conducted. The hardness of the Ti-Si-N coating reached 5000 gkf/mm² [Veprek95-2]. Having studied the deposition process and the characterization of the coatings, Veprek-group modified the estimation of ―particle-hardening‖ from Li-group and presented their hypothesis that the Ti-Si-N composite structure is the nano crystallite of TiN embedded in amorphous Si3N4 matrix, noted as nc-TiN/a-Si3N4 (nc- means nano crystallite and a- means amorphous). Veprek et al. reported their research results and meanwhile gave some concepts for the design of novel superhard coatings [Veprek95-1] [Veprek95-2]. In 1996, Veprek et al. presented some assumptions, including no dislocation in 2- 5nm nanocrystal, the blockings of the crack propagation in a 0.3-0.5 nm thin amorphous tissue as shown in Fig. 2.2, and the percolation threshold of the Si3N4 amorphous phase in the TiN crystalline matrix. According to these assumptions and the correlation between the grain size and the hardness of the nc-TiN/a-Si3N4, it was predicted that the hardness of diamond should be reached if crystallite size in such nano-composite is less 2 nm [Veprek96]. Fig. 2.2: Structure of a nano-crystallite/amorphous composite in which the growth of micro-crack is limited due to the small thickness of the amorphous tissue, from [Veprek96]. In 1999, Veprek group reported an exciting result that the hardness of the Ti-Si-N nano-composite coating was 105GPa, reaching the hardness of diamond [Nied-Vep99] [Veprek00-1]. The deposition parameters and conditions were almost the same as those in their previous research of nc-TiN/a-Si3N4 deposition. The only different parameter was the Literature review 22 discharge current density. Before this research, the discharge current density in their experiments was in the range of 2.5-3 mA/cm². In this research, the discharge current density was of 1.0 mA/cm². Note that the current density in Li‘s research is 1.2 mA/cm². The pattern of TiSi2 was found by XRD and the binding energy of TiSi2 by XPS. Therefore, the nc-TiN/a-SiNx/a- and nc-TiSi2 nano-composite was suggested to be a major cause of the hardness above 80GPa or to 105GPa. A conceptual model of the nc-TiN/a- SiNx /a- and nc-TiSi2 nano-composite was presented [Veprek00-1]. Unlike their prediction in [Veprek96], the grain size was not under 2 nm, seeing Fig. 3 in [Veprek00-1]. And the hardness lost the correlation with the Si content, seeing Fig. 5 in [Veprek00-1]. After this research, the Ti-Si-N nano-composite coatings have never reached the ultra high hardness (>80GPa). This un-reproduction implies the difficulty of the fabrication of nano-structure composites and the limitation of present-day characterization method. Table 2.1: The results of Ti-Si-N superhard nanocomposite coatings from some research groups. Research group Li Veprek Rebouta Patscheider Veprek Hu Kim Method PE-CVD PE-CVD PVD PVD PE-CVD PVD AIP-S Si (at %) 15 % 8-10 at% 7.5 at% 5 at% 5-20 at% 4.14 at% 7.7 at% Micro hardness 6350kgf/cm² 5000kgf/cm² 47GPa 38GPa 80-105GPa 36GPa 45GPa Grain size - 3-5nm 6nm 5nm 3-8nm 20nm - Year 1992 1995 1998 1999 2000 2002 2002 Reference [Li92] [Veprek95-1] [Vaz-Reb98] [Dis-Pats99] [Veprek00-1] [Hu02] [Kim02] Research group Nose Kaufmann Shen Ding Ma Mayan Ma Mayan Bendavid Method PVD PVD IBAD PVD P-CVD P-CVD HCA-CVD Si (at %) 3-8 at% 2-5% 11.4 at% 8 at% 5 at% 8 at% 5 at% Micro hardness 41GPa 45GPa 42GPa 41GPa 75GPa 45GPa 41GPa Grain size 23nm 20nm 3.0nm 10nm 10nm 4 nm 7-8nm Year 2003 2003 2004 2004 2004 2004 2005 Reference [Nose03] [Kaufm03] [Zh-Sh04] [Ding04] [Ma04] [Ma04] [Bendavid05] Literature review 23 The result of 100 GPa hardness stimulates the research on the synthesis of such superhard materials. More and more research groups began to work on the Ti-Si-N superhard nano-composite coatings and the like. Some research results of the Ti-Si-N coatings as examples are listed in Table 2.1. The different deposition methods were used in these researches, such as P-CVD [Li92] [Veprek00-1], sputtering-PVD [Vaz-Reb98] [Dis-Pats99], ion beam aided deposition [Zh-Sh04], arc ion plating and sputtering [Kim02], and hybrid cathodic arc-CVD [Bendavid05]. The deposition film were charachterized by EDX, XRD, XPS, SEM, atomic force microscopy (AFM), high resolution transmission electron microscopy (HRTEM), and selected area diffraction (SAD). The research results are concluded as follows. (1) With Si addition, the Ti-Si-N coatings have dense structure which is recognized by SEM. And the grain size is in the range of nanometers which is calculated with the full width at half maximum (FWHM) value of the XRD peaks. (2) The crystalline TiN is identified by XRD or SAD in TEM. The preferred orientation (PO) of TiN crystallite tends to be (200) [Li92] [Bendavid05]. If a bonding layer was deposited before Ti-Si-N deposition, the PO of TiN crystallite tends to be (111) [Hu02]. (3) The silicon nitride cannot be identified by XRD and the SAD in TEM. By XPS investigation, the binding energy of Si3N4 could be identified, so that Veprek-group presented the hypothesis of nc-TiN/a-Si3N4. This hypothesis is accepted by all the following researchers. (4) The Ti-Si-N composite coating has very good structure stability which include the long-term stability at room temperature in air (no decomposition and hardness reduce for several years) and the thermal stability (no grain size and hardness changes until 800 °C). Additionally, it also has high oxidation resistance until 800 °C [Veprek05]. (5) As Si content increases, the hardness of the Ti-Si-N coating first increases up to the maximum value and then decreases down. The typical curve is shown in Fig. 2.1. (6) The maximum hardness of Ti-Si-N coatings is normally in the range of 30 to 50 GPa. Two special results reported in [Veprek00-1] and [Ma04]. The ultrahigh hardness resulted from the structure of the nc-TiN/a-SiNx /a- and nc-TiSi2 which was reported not stable [Veprek05]. Literature review 24 In these researches, the microstructure results are not quantitative and there is no result about the formation mechanism. The researches on the Ti-Si-N hard coating are continual but the new information is little. What is the problem? 2.1.2. The hypothesis of Ti-Si-N structure and hardness enhancement At beginning, Li-group proposed a hypothesis that the structure of Ti-Si-N composite coating was the nano Si3N4 particle in the TiN matrix [Li92]. Veprek group modified this estimation and presented a structure hypothesis of nc-TiN/a-Si3N4. It should be noted that these two hypotheses are based on the same analysis and characterization of the film. The hardness enhancement of Ti-Si-N coating was explained by Veprek-group with the Hall-Petch law [Hall51] [Petch53] and the design concept of Koehler [Koehler70]. The explanation about the hardness enhancement of Ti-Si-N coatings emphasizes three points: (a) a dislocation source cannot operate within small 2-5 nm nano-crystals of TiN; (b) a dislocation formed under the external applied stress cannot cross through the amorphous grain boundary; (c) the amorphous boundary tissue is very thin (about 0.3~0.6 nm) so that the critical stress which causes the growth of micro-crack in the boundary is much higher [Veprek95-1] [Veprek95-2] [Veprek99]. This is a very good conceptual explanation. But, there is still a question here. Which bond is stronger, the Ti-N bond or the Si-N bond? If the Si-N bond is stronger than the Ti-N bond, it will lead to the formation of the crystalline Si3N4 instead of the formation of amorphous Si3N4 in boundaries. If the Si-N bond is weaker than the Ti-N bond, how can the boundary be strengthened by this weaker amorphous Si3N4? Obviously, the exact atomic structure of the Ti-Si-N composite, in particular, the interface structure, becomes a key point. If the atomic structure description cannot be provided by the structure model, the quantitative analysis is impossible. So far, almost all investigations on the Ti-Si-N nano-composite have been implemented through experiments. Only a few studies on the simulation or calculation of the Ti-Si-N composite have been undertaken and reported. For example, Liu and his coworkers used the Monte Carlo method to investigate the crystalline size transition [Liu04]. The atomic structure of Ti-Si-N was not studied in their research. Recently, Hao and his coworkers have published three papers on the first principle studies of the Literature review 25 structure and properties of TiN(111)/SixNy/ TiN(111) interfaces and the role of oxygen in the interfaces [Hao06-1] [Hao06-2] [Hao06-3]. This is a good beginning. In their investigations, a lot of ab initio calculations were performed for 55 possible configurations of the Ti-Si-N interface and many interesting results were obtained. Their result is that the interface of Ti-Si-N composite is a purely nitrogen coordinated Si-4N tetrahedron structure. Similarly, Hultman et al. studied the interface of TiN-SiN nano-laminates and nano-composites [Hultman07] with experiment and ab initio calculation. They conclude that the interfacial tissue phase can be crystalline, and even epitaxial with complex surface reconstructions. The results of Hao and Hultmen will be discussed in Chapter 5. 2.1.3. The modeling of Ti-Si-N film formation The only effort to explain the formation of the nc-TiN/a-Si3N4 composite coating was also from Veprek-group. The concept of the spinodal phase segregation was used to explain the formation of the nc-TiN/a-Si3N4 composite [Veprek05] [Zh-Vep06]. It is known that if there is a binodal between the phase A and the phase B, the spinodal method can be used to describe the phase instability and the phase segregation with the negative value of the second derivative. However, the formation of the Ti-Si-N film is not in a two-phase situation. In the co-deposition of Ti, Si, and N, many phases such as Ti-N, Ti-Si, Si-N, Ti- Ti, N-N, and Si-Si are on the substrate at the same time. Additionally, the evolution of film structure depends on many factors such as crystallographic orientation, values of the surface diffusion rates and of the specific surface free energies dynamics, the properties of the impinging atoms, and so on [Huang98]. Therefore, it might be difficult to explain the formation of the Ti-Si-N composite coatings with the spinodal method. With regard to the simulation of film growth, molecular dynamics (MD) and kinetic Monte Carlo (KMC) are very popular methods [Westkaemper05] [Voter02] [Yang00D]. By far, no atomic calculation or simulation on the formation of the Ti-Si-N composite coating is reported yet. But, an ab initio study of pathway of atomic process on TiN(001) and (111) surface during film growth [Gall03] reminds us that the film growth of a compound can be simulated by such method. 2.1.4. Discussion Almost all researches on the Ti-Si-N composite coatings were conducted through experiments. In the experiment exploration, deposition experiments provided the samples Literature review 26 of the Ti-Si-N composite coating. Then, the samples were characterized through micro- or nano indentation measurement, EDX, XRD, SEM, HRTEM, XPS and AFM in order to identify their hardness, elementary concentration, crystalline phase and orientation, grain size, binding energy, and surface morphology. Finally, the hypothesis of the Ti-Si-N structure is concluded according to the characterization and the knowledge and experience of researchers. The structure hypothesis of nc-TiN/a-Si3N4 includes neither the description of the atomic position relationship of Ti-Si-N nor the illustration of the connection of TiN-Si3N4. This indicates two points: (a) there is a limitation of present-day characterization method which cannot provide exact information about the atomic structure; (b) the researchers did not know what should be found out from the characterization and where should be searched, so that the clues in the characterization was not be found out. Recently, there are some controversies about the 100GPa hardness of Ti-Si-N coatings [Musil03] [Veprek03][Veprek05]. But the discussion is not concentrating on the common interesting question: whether or how the composite with 100GPa hardness can be prepared. In fact, without the exact atomic structure description, the analysis of property cannot be conducted quantitatively. As a result, the development of Ti-Si-N composite coatings is in the difficult situation. In General, such kind of difficulties is also in other preparations and fabrications of nano-structured materials because the characterization methods and equipments are almost the same and in most cases researchers don‘t know the atomic structure of nano-structured materials beforehand. In the deposition experiments, there is no measurement in situ during the film growth. Therefore, so far there is no discussion about the question why the structure of TiN is changed so much by the Si addition. The formation mechanism of the Ti-Si-N composite coating is not clear. Why do researchers insist on doing research with experimental method instead of with simulation or calculation method? The reason seems to be the incompleteness of the design system of nano-structured materials, comparing with the mechanical product design. The design of mechanical product includes all details such as structure, property, and manufacture, especially process simulation [Heisel06-1] [Heisel06-2] [Heisel99] [Ullman97]. But, in the design of Ti-Si-N superhard composite coating, there is only a conceptual design for a local part, but no technical specification design for accurate atomic connecting relationship, no general design for different layers and the pattern of the layer Literature review 27 (the film may consist of different structure), no product evaluation for performance, and no design for manufacture. Objectively, no detail design here is due to no suitable calculation and simulation method. The simulation and calculation methods have not been widely accepted by researchers. The modeling and simulation regarding crystalline thin film growth has a long history [Yang00D]. Since the vapor deposition technique was applied in microelectronic industry, more and more simulations have been performed to investigate the film growth. But the simulation results which have practical meaning for the research and development of coatings are not many. To summarize above reviews and analysis, it is clear that the experiment exploration of Ti-Si-N nano-composite walks with difficulty and the problem is due to (a) the limitation of present-day characterization method and the measurement in situ and (b) no design system of nanocomposite coatings. In order to solve the problem and establish the design system, atomic calculations and simulations should be used. The question is just how to obtain the useful result with the simulation. 2.2. Sputtering physical vapor deposition (PVD) and process simulation In order to obtain meaningful simulation results for the production of nanocomposite coatings, two points are crucial: (a) to understand the preparation process, the sputtering PVD process in our research, in detail and (b) to develop/select a suitable simulation method. The processes in the sputtering PVD process are discussed in this subsection and the simulation methods are introduced in the next subsection. Preprocess Substrate processing cleaning etching designed dangling bond designed pattern Target processing designed sputtering particle distribution Sputtering process Individual process ion bombardment cascade collision sputtering (TRIM) Stochastic process sputtering flux (CFD) Transport process Individual process 1) interaction (electron/atom) excitation ionization 2) vibration of electron Stochastic process plasma field distribution of ions & electron Deposition process Individual process deposition adsorption reaction diffusion Stochastic process nucleation island growth coalescence film growth Postprocess Annealing: Individual process inter diffusion Stochastic process phase transition Plasma/Surface interaction Fig. 2.3: The sub-processes in the sputtering PVD process. Literature review 28 Structure Post- process Pre-process Deposition processSputtering process Plasma gas: ion materials partial pressure incidence angle Targets: materials microstructur/lattice position Plasma electr. Volt / current incidence energy Reaction gas Composition partial pressure Sputtering method: DC/RF/ MicroW/ Pulsed Transport process Pressure in chamber Distance between target and substrate Plasma: electron vibration and temperature; density Sputtered species2 Flux Energy/ momentum Trajectory State: excitated? Reaction gas Composition partial pressure Probability of collidation: in transport or on the substrate Decline angle to substrate Probability of reaction Sputtering yield Sputtered species1 Flux & state of atom,ion, ... Energy & momentum Trajectory substrate materials microstructure temperature position movement Addition energies Bias: volt/current ...... Deposition process Physical process Adsorption & deadsorption Diffusion & aggregation Resputtering Depositon rate Distribution of the elements and their energies nucleation Phase type & orietation Growths of multiphases Phases separation Influence of energy and temperature Target poison Composites Surface of coating (working layer) Coating (support layers) Interface between substrate and coating Properties Hardness Strength Facture toughness Thermal conductivity Resistivity Reaction activity Interaction between the coating and the counterpart or environment Adherence Interaction Thermal expansion Mismatch Performances Wear resistance Stability High temperature oxidation resistance Withstanding to force Corrosion resistance ....... Friction coefficient Corrosion Phases Vacuum Remains gas Inert gas Remains gas Chemical process Reactions Adsorption & deadsorption Free energy Entropy competition Structuren of phases Composite Size Shape Orientation Nano- & microstructure of film Distribution of phases (texture/ pattern) Defects Microstructure Stress Coupling of crystallization Self- organization /assembly Nanograins & intergranular phases Stress Density Annealing Coupling reaction Temperature Pressure Fields of plasma(electron, ion), magnetron, photons 1 2 3 4 5 Processes of targets and substrates Fig. 2.4: The sputtering and deposition process of the multiphase nanostructure coating and the relationship of the process - structure - property – performance. Literature review 29 Molecular Dynamics Simulation Individual process 1. dopesition & resputtering 2. adsorption &desorption 3. chemical reaction intermediate step 4. diffusion Stochastic process nucleation island growth coalescence film growth Where or position When & how long Which & how many participants In what conditions: temperature pressure How interact How long? 10 -3 second Potential energy surface PES How long? o.5 - n hour How many particles? Composite & structure composites phases/texture grain(size, shape) boundary defects stress distribution Properties and performances Deposition process on the substrate surface: What is the elemental process? What should be simulated, and how? Atom vibration 1012~1014 /second ~ some fs Atomistic trajectory Electronic structure Electron density < 50 psab initio Simulation Wave function/DFT Infrequent events Transition State Theory TST KMC simulation Fig. 2.5: The deposition and the film growth process and the process simulation. As the development of the microelectronics, nano-structured materials, MEMS, and NEMS, the vapor fabrication becomes very important. In our research, the sputtering physical vapor deposition (PVD) process is studied. The sputtering PVD is the most widely-used method of thin film deposition in the fabrication of very-large-scale integration (VLSI) and nano-structured coatings [ThnGrne94]. The sputtering PVD is a process by which a thin film of material is deposited on a substrate according to following sequence of steps: (1) the material to be deposited is sputtered into vapor by collision with high-energy particles in plasma condition; (2) the vapor is transported across a region of low pressure from its source to the substrate; and (3) the vapor undergoes condensation on the substrate to from the thin film. There are two types of processes, namely, individual process and stochastic process in the sputtering process, the transport process, and the deposition process as shown in Fig. 2.3. The behavior of single particle is described in the individual process and the behavior of collective particles in the stochastic process. Literature review 30 It is well known that the deposition film in the sputtering PVD process is very complicated [Lieberman05] [ThnGrne94] [Gottwald06D]. The sputtering PVD process of multiphase nanostructure coating and the relationship of process-structure-property- performance are presented in Fig. 2.4. In the relationship of process-structure-property- performance, the structure is in a center position. There are two models related to the structure. One is about the relationship between the film structure and the formation process, which can be used to the design for manufacture. The other is about the relationship between the film structure and the property, which can be used to the product evaluation for performance. In our research, the emphasis is on the relationship between the film structure and the formation process. Fig. 2.4 shows that deposition process dominates the structure formation of deposited film. Therefore, the deposition process or the film growth process should be simulated. The deposition process includes also two kinds of process, namely individual process and stochastic process. Every individual process could be influenced by the other individual process randomly. The stochastic process depends largely on all the individual processes. Since there are more than 20 orders of magnitude individual processes in the deposition, the film growth process is difficult to be described with an analytical method. Therefore, the process is normally simulated with atomic methods, such as molecular dynamics (MD) or kinetic Monte Carlo (KMC). The simulation of deposition or film growth is shown in Fig. 2.5. The deposition, the adsorption, the reaction, and the diffusion of individual particle are directly simulated by molecular dynamics or kinetic Monte Carlo method. The accumulated simulation result of the individual process presents gradually collective phenomena, such as nucleation, island growth, coalescence, and film growth. The key points of the simulation are the achievable length scale and the achievable time scale, i.e. how many atoms can be simulated and how long process can be simulated. This depends on the simulation method and the calculation algorithm of the atomic interaction, which are discussed in the next section. 2.3. Atomic calculation and simulation methods For process simulation, the selection of calculation and simulation method is crucial. Generally speaking, there are two kinds of modeling method. One is deterministic approch. The molecular dynamics (MD) method is a typical one. The other is stochastic modeling, Literature review 31 e.g. the Monte Carlo method. For both methods, the algorithm of atomic interaction is important, because it has strong influence on calculation accuracy and calculation cost. There are three kinds of algorithms to deal with the interaction among atoms. The first one is ab initio algorithm which includes the wave function method and the density functional theory (DFT). The second one is the tight-binding method. The last one is the force-field algorithm which is also called empirical or semi-empirical algorithm. Reuter et al. concludes achievable length scale, achievable time scale, and provide information of some kinds of simulation or calculation method in Table 2.2, [Reuter05]. For the simulation of the deposited film which consists of 3 nm-sized crystallites, the length scale requirement is more than 20000 atoms, i.e. about 6 6 6 nm³. If deposition rate is 0.8 nm/s, the relevant time scale requirement is more than 7 seconds. The information interested is in scale of nanometer or micrometer. According to the data of Table 2.2, the kinetic Monte Carlo (KMC) method is suitable for the simulation of this film growth. Table 2.2: The time and length scale typically handled by different theoretical approaches to study the chemical reaction and crystal growth, from [Reuter05]. Information Time scale Length scale Density functional theory Microscopic - ≤ 10³ atoms Ab inito molecular dynamics Microscopic t ≤ 50 ps ≤ 10³ atoms Semi-empirical molecular dynamics Microscopic t ≤ 1ns ≤ 10³ atoms Kinetic Monte Carlo simulations Micro- to mesoscopic 1ps ≤ t ≤ 1 hour ≤ 1µm Ab inito atomistic thermodynamics Meso- to macroscopic Average ≥ 10 nm Rate equations Average 0.1 s ≤ t ≤ ∞ ≥ 10 nm Continuum equations Macroscopic 1 s ≤ t ≤ ∞ ≥ 10 nm 2.3.1. Kinetic Monte Carlo method In fact, the molecular dynamics (MD) method is a premiere tool for simulating the dynamical evolution of systems of atoms. The trajectory of each atom in the system could be tracked by calculating the atomic interaction and hence the evolution of the system state is followed. But a limitation of MD method is the achievable time scale. Atoms vibrate in solid materials with a typical frequency of 10 13 Hz and a amplitude of 10 -11 m Literature review 32 [Levitin04]. The accurate trajectory tracking requires the time steps short enough (about 10 -15 s) to resolve the atomic vibration. Then the total simulation time is limited to less than one microsecond [Voter05]. But chemical reactions or diffusion events in solids take place on a much longer time scale, on the order of milliseconds or more [Henkelman03]. This is the ―time scale problem‖ of MD method. The kinetic Monte Carlo (KMC) method follows the concept of the transition state theory (TST) [Voter02] [Voter05] [Henkelman03]. With the TST concept, it is not necessary to track atomic vibration because the system state is not changed during atomic vibration. The really important event is the transition of system state. Based on this idea, the KMC method overcomes the ―time scale problem‖ which the MD method faces. The basic work of KMC is to establish a transition event list and to estimate the rate of state transition. Comparing with atomic vibration, the state transition event is an infrequent- event, e.g., the chemical reaction or the diffusion of atom or cluster. The rate of a chemical reaction or a diffusion event is estimated by identifying the most difficult region of the configuration space which the system must reach during transition – so called ―transition state‖. In the solid systems, the atomic vibration is confined to rather small regions around well defined average position. In this case, the harmonic form of TST (HTST) is a good approximation and the rate constant is given by  TkEEk BIntSad hTST /)(exp0  (2.1) where SadE is the saddle point energy, IntE is the system energy of the initial state, Bk is the Boltzmann constant, and T is the temperature [Voter02] [Henkelman03]. Since the pre-factor 0 is often in the range of 10 12 to 10 13 per second, a common approximation is to choose a fixed value in this range to save the computational work [Voter05]. The implementation steps of the KMC simulation is as followings. (1) All state transition events of the system should be found out and filled in an event list. (2) For the rate calculation, the searching on the potential energy surface (PES) is performed to find out all the neighboring basins and the relevant saddle points. The transition probability or the rate for each transition state is calculated with the equation 2.1. (3) All transition rates are summed up to calculate the residual time which is a period until the first escape happening. Literature review 33 (4) The event from the event list is selected randomly, weighting by the individual rate. (5) The selected event is conducted and the time shift advance. (6) The step (1) to the step (5) is iterated until designed number of atoms is deposited. Kinetic Monte Carlo method is used now more and more to simulate the evolution process such as film growth, radiation, and so on [Voter05] [Amar06]. In the most of KMC simulation today, the lattice model is used. With the lattice model, an atom can diffuse only from one lattice site to another. This lattice model is only suitable to simulate epitaxial deposition. In order to simulate the complicated deposition, the off-lattice KMC method should combine with the ab inito method, e.g., the simulations of Scheffler group [Reuter05] and Jonsson-Henkelman group [Henkelman01]. This combination provides an accurate and relatively long time scale KMC simulation mode. Its limitation is an achievable length scale. Normally, it is limited in a scale less than 1000 atoms. The only KMC simulation of TiN film growth is reported by Huang et al. They investigated the competitive texture formation in TiN film growth process [Huang98]. In this simulation, the lattice model was used, so that it is difficult to describe the real film growth. The complicated potential energy surface of TiN (001) is illustrated in Chapter 5. In our research, two KMC codes, one with lattice model and the other with off-lattice model, have been developed by ourselves, which is reported in Chapter 4. 2.3.2. Ab initio method and density functional theory (DFT) Fig. 2.6: The outline of ab initio methods. Ab initio / First principle Density Functional Theory Schrödinger Equation: Wave Function (1926) Born-Oppenheimer approximation (1927) Idea: Thomas-Fermi (1927) Implementation: Hohenberg-Kohn- Sham Hohenberg-Kohn theorem (1964) Kohn-Sham equation (1965) Hartree-Fock‘s self-consistent field method SCF and Slater determinant with the treatment of electron exchange (1927-1930) Post Hartree-Fock: correlation interaction CI Literature review 34 Ab initio method and density functional theory (DFT) are the most important and the most accurate algorithm to calculate the atomic interaction. Ab initio method and DFT are briefly introduced in this subsection. 2.3.2.1. Ab initio method with wave function With ab initio method, the many-atom systems composed of electrons and nuclei will be treated on the basis of first principle of quantum mechanics without introducing any empirical parameters. The ab initio calculation begins with the Schrödinger equation [Schroedinger26]:  EH  (2.2) where H is the Hamiltonian which describes the total energy of a system, ψ is the wave function of the system, E is the energy of the system. The Hamiltonian of the coupled electron-ion system could be written as           N I Ii iI I JI JI JI ji ji N i i I I rR eZ RR eZZ rr e m p M P H e 1 , 222 1 22 22 (2.3)      rRVRVrVTTH NeNNeeeN , (2.4) here N is the number of ions, RRR N ,...,1 is coordinates of ions, PPP N ,...,1 is moment of ions, NZZ ,...,1 are charges of ions, NMM ,...,1 are the masse of ions; Ne is the number of electrons, rrr eN ,...,1 is coordinates of electrons, ppp eN ,...,1 is moment of electron, m is mass of electron. The TN and Te are the kinetic energy of ion and electron, respectively; eeV is Coulomb potential, NNV is the interaction between ions, and NeV is the interaction between the ion and the electron. Therefore, the Schrödinger equation can be expressed as:           RxERxRrVRVrVTT NeNNeeeN ,,,  (2.5) Literature review 35 After verifying the Schrödinger equation with the calculation of hydrogen, P. Dirac remarked in 1929, ―The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved‖ [Dirac29]. Since 1926, enormous efforts devoted to overcome this difficulty. Some important points are Born-Oppenheimer approximation, Hartree-Fock (HF) self-consistent field (SCF) with Slater determinant, post-HF with the configuration interaction (CI), and Hohenberg-Kohn-Sham density functional theorem (DFT) [Ohno99]. According to the difference in the time scales of nuclear and electronic motions, Born-Oppenheimer approximation separates Schrödinger equation [BornOpp26]. The decoupled adiabatic Schrödinger equation of electrons and nuclei are           RxRRxRrVrVT nnneNeee ,,,   (2.6)         RERRRVT NNN   (2.7) The starting point for the Hartree-Fock method is a set of approximate one-electron wave functions known as orbital for atomic calculation. For a molecular or crystallite calculation, the initial approximate one-electron wave function is typically a linear combination of atomic orbital (LCAO). The trial wave function and the iteration method are used in HF numerical calculation which brings in the name "self-consistent field (SCF) method". The Slater determinant is very helpful to HF method, because in the Slater determinant [Slater29], the electron exchange is treated carefully in order to prevent two parallel-spin electrons from being found at the same point in space. The Slater determinant is an expression for the wave function of a many-fermion system, by which construction satisfies the Pauli-principle. Nevertheless, in HF method, the electron correlation (Coulomb correlation) is neglected. The electron correlation describes the correlation between the spatial positions of electrons with opposite spin due to their Coulomb repulsion. Some methods such as the Literature review 36 configuration interaction (CI) [Loewdin55] are added to improve HF, i.e. the post-HF. 2.3.2.2. Density functional theory (DFT) In 1927, Thomas and Fermi introduced the electron density function with which they calculated the energy of atom. But their density functional theory was inaccurate because there was an error of kinetic energy in their calculation and the electron exchange and the electron correlation were not seriously treated. Thus DFT was largely ignored until 1965 when Kohn and Sham introduced a method which treated the majority of the kinetic energy exactly [Kohn98]. In 1964, Hohenberg and Kohn gave their theorem with which the density functional theory (DFT) is on a firm theoretical basis [HohKoh64]. The Hohenberg-Kohn theorems are expressed as (1) The ground-state energy of a many-body system is a unique functional of the particle density   rEE 0 . (2) The functional   rE has its minimum relative to variation  rn of the particle density at the equilibrium density  rn0 ,       rErnEE min0  (2.8)          0 0  rnrn rn rnE   (2.9) Therefore, the total-energy functional is             rdrnrVnEnEnTnE xcH 3 (2.10) where  nT is the kinetic energy,  nEH is the Hartree energy (electron-electron repulsion),  nExc is the exchange and correlation energy,  rV is the external potential. Literature review 37 In 1965 Kohn and Sham gave their Kohn-Sham equation [KoSh65]. They introduce the particle density     2  rrn i (2.11) And the non-interaction kinetic energy in terms of the  ri is     iinT  2 2 1 (2.12) The Kohn-Sham one-electron equation is           rrrnVrd rr rn erV iiixc                322 2 1 (2.13) where the exchange-correlation potential                rn rnrn rn rnE rnV xcxcxc      (2.14) with the exchange-correlation energy         rdrnrnrnE xcxc 3 (2.15) where   rnxc is the exchange-correlation energy of a homogeneous electron gas with the local density  rn . The equation (2.15) is under the local density approximation (LDA). The total energy functional is             rdrnrVnEnEnTnE xcH 3 (2.16) Obviously, the DFT method possesses some advantages. In DFT the kinetic energy Literature review 38 is treated exactly, both the electron exchange energy and the electron correlation energy are taken into account, especially the variants are much less than that in the wave function method. The wave function is in 3N-dimension, but the density function is only in 3- dimension. Therefore, short after the publication of Hohenberg-Kohn-Sham theorem, DFT quickly became a popular method which is widely used as a quantitative predictive tool. Since the interaction of atoms can be accurately calculated by the ab initio method, the ab initio and DFT are considered as a powerful tool to investigate the structure, the property, the reaction, and the formation of various kinds of materials. In recent years, more and more ab initio calculations have been performed on the investigation of transition metal nitrides, such as on the bonding [Blaha85] [Haeglund93], on the electronic structure and physical property [Ahuja96] [Grossman99] [Marlo00] [Stampfl01] [Jhi01] [Wu05], on the elastic constant [Zh-He01] [Nagao06], and on the surface properties [Marlo00] [Kobayashi01] [Gall03] [Ciobanu05]. According to the total energy calculations of ab initio and DFT, the lattice constant of TiN were studied by some research groups. The calculation result of the lattice constant is very close to the experiment value [Marlo00] [Stampfl01] [Kobayashi01] [Gall03]. These calculations show that the ab initio method is a reliable method to investigate the structure of TiN. Therefore, in our research, the Ti-Si-N composite structure is studied with the ab initio method, which is reported in Chapter 5. The surface energy and the atom arrangement on the surface can also be investigated with ab inito method [Marlo00] [Gall03] [Ciobanu05] [Hao06-1]. The research of Greene group [Gall03] is very helpful to our research. This research shows that the activation energy of atomic diffusion can be calculated through the ab initio method and the nudged elastic band method [Mills95] [Henkelman00]. In our research, these algorithms were used to investigate the basic diffusion behaviors of Ti, N and Si on the TiN (001) surface. The calculation detail is also reported in Chapter 5. From the above review and discussion, it is clear that in the development of Ti-Si- N nanocomposite coatings, the identification of the atomic structure and the formation mechanism becomes very crucial to further progress. Because the atomic structure and the formation mechanism of Ti-Si-N superhard nano-composite coatings cannot be identified through the experiment method, the atomic simulation and calculation should or must be carried out to overcome the difficulty and promote the development. Considering the Literature review 39 complication of deposition film in the sputtering PVD process, we try to use kinetic Monte Carlo and the ab initio method to obtain meaningful result for the fabrication of Ti-Si-N superhard nano-composite coating. In fact, this is an effort to improve the design method of nano-composite materials, exactly, to develop the design for manufacturing. 3. Experiments of sputtering PVD and Ti-Si-N deposition The experiments of sputtering physical vapor deposition (PVD) and Ti-Si-N deposition are a very important step for our process simulations, because we have no experience of the study of sputtering PVD process before this research. In order to simulate the formation process of Ti-Si-N coatings, we should obtain basic understanding about sputtering PVD through experiments. The data in Table 2.1 shows that there is a large difference in the microstructures and the hardness among those Ti-Si-N films. Comparing with the case of TiN coatings [Sundgren85], this large difference might come from various deposition techniques and different process parameters. Therefore, our experiment focuses on the correlation between the particle state in plasma and sputtering process parameters and the correlation between film structure and deposition process parameters. In this chapter we report our experiment exploration which includes two parts, i.e. the experiments on sputtering PVD process and the experiments on the deposition of Ti- Si-N coatings. 3.1. The sputtering PVD system Our experiments have been performed with a sputtering PVD system LS 450 S from Von Ardenne Anlagentechnik GmbH [VonArd]. This is a complete integrated sputtering PVD system to meet the specific deposition requirements of researches [Gottwald06D]. The photo and the framework of LS 450 S are shown in Fig. 3.1. This Sputtering PVD system consists of six subsystems: 1) a vacuum system including vacuum pumps, a pressure control device and a vacuum chamber; 2) a gas flow supply and control system; 3) a sputtering system, including plasma sources, power system, switching network, and targets; 4) a substrate holder and a driving system; 5) a cooling system; and 6) a computer operating system. Experiments of sputtering PVD and Ti-Si-N deposition 41 (a) N2 Ar Vacuum system and pressure controlling system Computer operating system Water cooling system Gas controlling system Substrate ho lder and driv ing system Vacuum chamber P las m a m on it or Sputtering system (b) Fig. 3.1: The sputtering PVD equipment in IFF, University Stuttgart: (a) LS 450S from Von Ardenne Anlagentechnik GmbH [VonArd], (b) the framework of LS 450S. Experiments of sputtering PVD and Ti-Si-N deposition 42 The deposition chamber is a cylindrical room with 480 mm diameter and 180 mm high. The base pressure to 510 -6 Pa can be reached using the pump system that consists of a turbo drag pump and a turbo molecular pump. The process pressure is measured by vacuum gauges and controlled through a valve that connects with the chamber and the vacuum pump system. The valve is controlled by a servo motor system with PID algorithm. The process gas Ar flow rate and the reaction gas N2 flow rate are controlled by two electro-pneumatic valves, respectively. Two balance magnetron-cathodes are used as the plasma sources which can be installed either at the bottom or on the side of the chamber. These two plasma sources are connected with a DC power system and a RF power system through a switching network. The targets mounted on the plasma sources can be sputtered with either DC or RF power. The vacuum chamber and the targets are cooled with a water cooling system. Eight substrates can be fixed on substrate holders which are mounted on a turnplate. The turning direction and speed of the turnplate can be controlled by a step motor driving system. The heating and the temperature control of substrates have not been carried out because of the short circuit problem in plasma. It imposes a limitation on our experiments. This sputtering PVD system can be operated manually or operated via computer control. In addition, an energy-resolved mass spectrometer, namely a plasma-monitor (EQP1000 Hiden Analytical Ltd, EQP- electrostatic quadrupole plasma) [Hiden], is installed on the cover board of the chamber for the measurement of mass spectra. 3.2. The experiments on sputtering PVD process In order to determine the process parameters of the Ti-Si-N film deposition, the ion mass spectra and the deposition rates in sputtering PVD process were investigated. The ion flux, namely the count per second (c/s), and the ion energy were measured by the quadrupole mass spectrometer [Gross04]. The deposition rate was measured by the quartz crystal microbalance QCM method [Lu84]. In this part of research, first the ion mass spectra of plasma and the deposition rates of titanium in the sputtering process were measured in order to study the ion flux, the ion energy distribution, and the deposition rate in the DC and RF sputtering; second the ion mass spectra of plasma and the deposition rates of TiN in the sputtering process were Experiments of sputtering PVD and Ti-Si-N deposition 43 measured to investigate the correlation between the stoicheiometry of TiN and process parameters. 3.2.1. The ion mass spectra and the deposition rate of Ti in RF/DC sputtering Table 3.1: Total ion count per second (c/s) and mean ion energy vs. sputtering powers. The experiment condition: Ar flow rate = 7.0 sccm, process pressure = 0.08 Pa, distance = 55mm. Power (W) 50 100 200 300 400 500 c/s RF(Ti) 1.42E+06 4.80E+06 1.41E+07 2.39E+07 3.29E+07 DC(Ti) 3.32E+05 1.24E+06 2.47E+06 3.68E+06 5.89E+06 eV/c RF(Ti) 35.84 37.17 39.31 40.85 42.05 DC(Ti) 5.87 5.84 5.95 6.10 6.17 (a) (b) Fig. 3.2: The total ion count per second (c/s) and the mean ion energy (eV/c) vs. the RF and DC sputtering power: (a) total ion count vs. sputtering power, (b) mean ion energy vs. sputtering power. The energy resolved ion mass spectrometry is very helpful to investigate the plasma of sputtering PVD in situ [Misina01] [Roth95] [Zeuner98]. In our experiment for the co- deposition of Ti-Si-N, a Ti target and a Si target would be bombarded simultaneously under the RF and DC sputtering, respectively. Therefore, we measured the ion mass spectra of plasma and the deposition rate of Ti in the RF and DC sputtering to investigate the particle state in the plasma. In the process chamber, the base pressure was 10 -5 Pa. Argon with a purity of 99.999% was used as the process gas. Ar flow rate was 7.0 sccm. The process pressure was 0.08 Pa. In the research, a titanium target with a purity of 99.6% was used in LS 450S system and was bombarded in DC or RF sputtering process. The target was installed opposite the plasma monitor EQP1000. The distance between the measurement head of EQP1000 and the Ti target surface was 55 mm. The count of ion per second (c/s) and the energy per ion (eV/c) in plasma were measured through EQP1000. Experiments of sputtering PVD and Ti-Si-N deposition 44 The statistical results are listed in Table 3.1 and presented in Fig. 3.2. The state of Ti ions under the RF sputtering condition is obviously different from that under the DC sputtering condition. For example, the ion flux is 1.41×10 7 c/s under the 200W RF sputtering power, whereas it is only 1.24×10 6 c/s under the 200W DC sputtering power. And the mean ion energy is 39.31 eV under the 200W RF power, while it is only 5.84 eV under the 200W DC power. This means that the ionization is very strong under the RF sputtering condition. However, it does not mean that the deposition rate under the RF sputtering is higher than that under the DC sputtering. Table 3.2: The deposition rate RD (Å/s) vs. the sputtering power measured by the quartz crystal method. The experiment condition: Ar flow rate = 7.0 sccm, process pressure = 0.08 Pa, distance=105mm. Power (W) 100 150 200 300 350 RF (Ti) 0.3161 0.5754 1.0028 1.8056 2.1951 DC (Ti) 1.0634 1.6678 2.1357 3.2228 3.7228 Fig. 3.3: The deposition rate RD (Å/s) vs. the RF and DC sputtering power. The deposition rate under the RF and DC sputtering condition were measured by the quartz crystal method with SCT-200/SQ Deposition Rate Controller from SYCON Instruments [Sycon] and the 6MHz quartz crystal from INFICON [INFICON]. The base pressure and the process pressure were of 10 -5 Pa and 0.08 Pa, respectively. The Ar flow rate was 7.0 sccm. The distance between the quartz crystal measurement head and the Ti target was 105 mm. The Ti was sputtered under RF and DC sputtering power, respectively. The deposition rates are listed in Table 3.2 and presented in Fig. 3.3. The results show that the deposition rate under the DC sputtering condition is manifestly higher than that under the RF sputtering condition. Therefore, the TiN deposition needs relatively Experiments of sputtering PVD and Ti-Si-N deposition 45 more reaction gas of N2 under the DC sputtering condition. According to the above measuement results of the mass spectra and the deposition rate, in our experiment of the Ti-Si-N deposition, Ti was sputtered with DC power to acquire high deposition rate and Si was sputtered with RF power to provide a high ionization condition for TiN and Si-N reactions. 3.2.2. The ion mass spectra and the deposition rate of TiN in sputtering PVD 0,00E+00 4,00E+06 8,00E+06 1,20E+07 1,60E+07 10 20 30 40 50 60 70 Energy (eV) A r (c /s ) 50w 100w 200w 300w 400w (a) 0,00E+00 5,00E+04 1,00E+05 1,50E+05 2,00E+05 2,50E+05 0 20 40 60 80 Energy (eV) N 2 ( c /s ) 50w 100w 200w 300w 400w (b) 0,00E+00 2,00E+04 4,00E+04 6,00E+04 8,00E+04 1,00E+05 1,20E+05 10 20 30 40 50 60 70 Energy (eV) T i ( c /s ) 50w 100w 200w 300w 400w (C) Fig. 3.4: The ion energy distribution dependent on various RF sputtering powers: (a) for Ar + , (b) for N2 + , and (c) for Ti + . The experiment condition: Ar flow rate = 7.0 sccm, N2 flow rate = 0.8 sccm, the process pressure = 0.08 Pa, and the distance = 55 mm. Experiments of sputtering PVD and Ti-Si-N deposition 46 In the Ti-Si-N deposition, the stoichiometry of TiN is one important factor. With the stoichiometry of TiN, i.e. the proportion of Ti atom and N atom is 1: 1, both the lattice constant and the density of TiN film reach to the maximum value [Sundgren85]. And the hardness of TiN film is also influenced by the stoichiometry of TiN [Sundgren85]. In this subsection, we report the investigation into the correlation between the stoichiometry of TiN and process parameters. A titanium target with a purity of 99.6% was used in LS 450S system. The base pressure and the process pressure were 10 -5 Pa and 0.08 Pa, respectively. The Ar flow rate was 7.0 sccm. The N2 flow rate was 0.8 sccm. The distance between the EQP1000 measure head and the target was 55mm. The RF powers were 50W, 100W, 200W, 300W, and 400W, respectively. Table 3.3: The statistical result of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. RF sputtering powers. RF power (W) 50 100 200 300 400 (c/s) Ar 1.90E+09 2.16E+09 2.44E+09 2.51E+09 2.55E+09 N2 5.07E+07 4.06E+07 2.40E+06 1.11E+06 9.08E+05 Ti 4.19E+04 7.44E+05 1.22E+07 2.32E+07 3.26E+07 (eV/c) Ar 33.00 35.00 38.70 40.60 41.50 N2 33.50 35.50 39.30 40.10 42.10 Ti 33.70 35.50 38.90 40.50 41.70 (a) (b) Fig. 3.5: The Statistical result of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. RF sputtering powers: (a) the total ion count per second, (b) the mean ion energy. The measurement results in the Fig. 3.4 show the energy distributions of Ar + , N2 + , and Ti + ion and their corresponding change to the power alteration. The statistical results are listed in Table 3.3 and presented in Fig. 3.5. The statistical data in Table 3.3 indicate Experiments of sputtering PVD and Ti-Si-N deposition 47 three important results. (1) The flux of Ar + is about two to three order of magnitude larger than those of N2 + and Ti + . (2) The energy of Ar + , N2 + , and Ti + are almost same. The energies of these ions increase as the RF power increases. Between the sputtering power 100W and 200W, the ion energy increases relatively large. (3) The curve of N2 + flux and the curve of Ti + flux have an intersection as the RF power changes. If the RF power is lower than 180W, the flux of N2 + is larger than that of Ti + . The low-energy and the small flux of Ti + imply that the Ti target is under the contamination condition, namely the target poisoning [Sundgren83]. If the RF power is higher than 180W, the flux of N2 + decreases to a very low level. This may lead to an over stoichiometry of Ti. Therefore, the stoicheiometry point may be near the RF power 180W. This means that the deposition of Ti-Si-N should be conducted under the condition near the intersection point of Ti + flux curve and N2 + flux curve. Table 3.4: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the N2-flow rate. The experiment condition: RF power=200W, Ar flow rate = 7.0 sccm, the process pressure = 0.08 Pa, the distance = 55mm. N-flow (sccm) 0.6 0.7 0.8 0.9 1 (c/s) Ar 2.53E+09 2.65E+09 2.58E+09 2.63E+09 2.61E+09 N2 3.19E+06 6.55E+06 8.40E+06 4.12E+07 9.98E+07 Ti 1.20E+07 1.20E+07 1.08E+07 6.11E+06 3.34E+06 (eV/c) Ar 38.47 38.52 38.48 38.11 37.77 N2 38.56 38.78 38.69 38.35 37.98 Ti 38.58 38.83 38.61 38.13 37.72 (a) (b) Fig. 3.6: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the N2-flow rate: (a) the total ion count per second, (b) the mean ion energy. The correlation of the ion flux and ion energy with the N2 flow rate was also studied. The RF power was 200W. All of the base pressure, the process pressure, the Ar Experiments of sputtering PVD and Ti-Si-N deposition 48 flow rate, and the measure distance were as same as those in the experiment above. The statistical results are listed in Table 3.4 and presented in Fig. 3.6. Under the RF power 200W sputtering, the curves of Ti + flux and N2 + flux has a intersection at about the N2 flow rate = 0.8 sccm. If the N2 flow rate is higher than 0.806 sccm, the flux of N2 + increases sharply but the energies of all the ions decrease greatly. This shows the situation of Ti target poisoning. Table 3.5: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the Ar flow rate (sccm). The experiment condition: RF power = 200W, the process pressure = 0.08 Pa, N2 flow rate = 0.8sccm, the distance = 55mm. Ar-flow/sccm 3.0 5.0 7.0 9.0 (c/s) Ar 2.67E+09 2.65E+09 2.60E+09 2.45E+09 N2 1.67E+07 1.19E+07 9.55E+06 8.33E+06 Ti 9.32E+06 1.01E+07 1.04E+07 1.03E+07 (eV/c) Ar 38.44 38.39 38.36 38.35 N2 38.73 38.74 38.74 38.80 Ti 38.57 38.52 38.49 38.32 Table 3.6: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the process pressures (Pa). The experiment condition: RF power = 200W, Ar flow rate = 7.0 sccm, N2 flow rate = 0.8 sccm, the distance = 55mm. Pressure (Pa) 0.08 0.2 0.4 0.6 (c/s) Ar 2.57E+09 2.54E+09 2.47E+09 2.43E+09 N2 8.87E+06 6.58E+06 4.20E+06 3.14E+06 Ti 1.10E+07 1.27E+07 2.11E+07 3.23E+07 (eV/c) Ar 38.36 35.14 32.88 31.86 N2 38.69 35.73 33.53 32.70 Ti 38.51 35.41 33.22 32.33 Table 3.7: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the distance (mm) between the target and the substrate. The experiment condition: RF power = 200W, Ar flow rate = 7.0 sccm, N2 flow rate = 0.8sccm, the process pressure = 0.08 Pa. D(mm) 55 65 75 85 95 105 115 125 135 (c/s) Ar 2.66E+09 2.67E+09 2.63E+09 2.66E+09 2.70E+09 2.76E+09 2.80E+09 2.82E+09 2.81E+09 N 9.58E+06 9.60E+06 1.02E+07 1.02E+07 1.07E+07 1.07E+07 1.02E+07 1.04E+07 1.00E+07 Ti 1.10E+07 1.30E+07 1.36E+07 1.46E+07 1.49E+07 1.52E+07 1.53E+07 1.53E+07 1.54E+07 (eV/c) Ar 38.32 36.47 35.23 34.28 33.40 32.70 32.21 31.85 31.53 N2 38.72 36.75 35.53 34.60 33.79 33.20 32.66 32.52 32.29 Ti 38.50 37.05 36.23 35.67 35.23 34.94 34.85 34.88 34.95 Experiments of sputtering PVD and Ti-Si-N deposition 49 In the RF sputtering, the Ar flow rate, the process pressure, and the distance between target and substrate have also influences on the intersection of the Ti flux and the N2 + flux, i.e. the influences on the target poisoning and the stoichiometery of the TiN film. The experimental conditions and the statistical results from EQP measurement are listed in Table 3.5, Table 3.6, and Table 3.7. 0,00E+00 4,00E+06 8,00E+06 1,20E+07 1,60E+07 0 5 10 15 Energy (eV) A r (c /s ) 100W 200W 300W 400W 500W (a) 0,00E+00 2,00E+05 4,00E+05 6,00E+05 8,00E+05 0 5 10 15 Energy (eV) N 2 ( c /s ) 100W 200W 300W 400W 500W (b) 0,00E+00 6,00E+04 1,20E+05 1,80E+05 2,40E+05 0 5 10 15 Energy (eV) T i ( c /s ) 100W 200W 300W 400W 500W (c) Fig. 3.7: The ion energy distribution dependent on various DC sputtering powers: (a) for Ar + , (b) for N2 + , and (c) for Ti + . The experiment condition: Ar flow rate = 7.0 sccm, N2 flow rate = 2.0 sccm, the process pressure = 0.08 Pa, the distance = 55 mm. In the DC sputtering, the similar measurements of the ion mass spectra were conducted. In the research, the Ti target was bombarded under DC sputtering power. The base pressure and the process pressure were 10 -5 Pa and 0.08 Pa, respectively. The Ar flow Experiments of sputtering PVD and Ti-Si-N deposition 50 rate was 7.0 sccm. The N2 flow rate was 2.0 sccm. The measurements were conducted with EQP1000. The distance between the measurement head of EQP and the Ti target surface was 55 mm. Table 3.8: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the DC power. The experiment condition: Ar flow rate = 7.0 sccm, N2 flow rate = 2.0 sccm, the process pressure = 0.08 Pa, the distance = 55 mm. DC power (W) 100W 200W 300W 400W 500W (c/s) Ar 6.01E+07 1.46E+08 2.34E+08 3.39E+08 4.10E+08 N2 7.13E+06 1.27E+07 1.80E+06 1.35E+06 1.10E+06 Ti 4.72E+04 5.05E+05 3.51E+06 6.97E+06 1.19E+07 (eV/c) Ar 3.00 3.26 4.62 4.48 4.51 N2 3.18 3.45 4.77 4.57 4.59 Ti 4.36 4.69 6.30 6.14 6.13 (a) (b) Fig. 3.8: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the DC power: (a) the total ion count per second, (b) the mean ion energy. The EQP measurement results are shown in Fig. 3.7. The statistical results are listed in Table 3.8 and presented in Fig. 3.8. Comparing the ion energy distribution in Fig. 3.7 with that in Fig. 3.4, it is clear that the ion energy distribution under DC sputtering is different from that under RF sputtering. And the mean energy of Ti + is obviously larger than that of Ar + and N2 + under DC sputtering, while the mean energies of Ti + , N + , and Ar + are almost same under RF sputtering. There is a similar feature under DC and RF sputtering cases, i.e. under the DC sputtering, the curves of N2 + flux and Ti + flux have also an intersection as the DC power changes. And the mean ion energy jumps up at the point that the flux of Ti + is higher than that of N2 + . This implies that the system overcomes the target poisoning point. Experiments of sputtering PVD and Ti-Si-N deposition 51 It should be noted that near the intersection point (Fi. 3.5 and Fig. 3.8), the proportion of Ti + flux and N2 + flux has a large change. This large change could give rise to a large scatter in the microstructures and in the properties of TiN coatings [Sandgren85]. This indicates that to maintain the stoichiometry of TiN is crucial in the TiN deposition. The deposition rates of TiN under the DC sputtering condition were measured through the quartz crystal method. The sputtering condition was the same as that of the above EQP measurement. The Ti target with the purity of 99.6% was used under DC sputtering. The base pressure and the process pressure were 10 -5 Pa and 0.08 Pa, respectively. The Ar flow rate was 7.0 sccm. The N2 flow rate was 2.0 sccm. The distance between the quartz crystal measurement head and the Ti target surface was 55 mm. The measurement results, the deposition rates, are listed in Table 3.9 and presented in Fig. 3.9. If the DC power is 290W, the deposition rate decreases abruptly to 5.24 Å/s. This implies that the Ti target is poisoned near the DC power 290W. This result is consistent with the EQP result in Fig. 3.8. Table 3.9: The deposition rate (Å/s) of TiN under the DC power sputtering. The experiment condition: Ar flow rate = 7.0 sccm, N2 flow rate = 2.0 sccm, the process pressure = 0.08 Pa, the distance = 55 mm. DC Power (W) 290 320 350 400 RD (Å/s) 5.24 8.97 9.51 10.68 Fig. 3.9: The deposition rate (Å/s) of TiN under the DC power sputtering. The above results of the EQP measurements and the deposition rate measurements indicate that the TiN stoichiometery point might be just over the Ti target poisoning point. Experiments of sputtering PVD and Ti-Si-N deposition 52 With a given sputtering power, the stoichiometry point could be reached by adjusting the N2 flow rate. Because the Ar flow rate, the process pressure, and the distance between the substrate and the target have also influence on the stoichiometry of TiN, the process parameters should be adjusted relevantly in order to maintain the stoichiometry of TiN. But in the practical preparation of the Ti-Si-N coatings, to reach the exact stoichiometry point is not easy, if there is no measurement in situ. In our deposition experiment of Ti-Si-N film, the process parameters were selected in following way. First a substrate was placed 110 mm against Ti and Si targets, in order to deposit Ti and Si on a substrate at the same time if the substrate did not move. Then the process pressure was set to 0.08 Pa to maintain the mean free path of sputtered atoms on the order of 100 mm. To match this process pressure, the Ar flow rate was set of 7.0 sccm. The DC sputtering power on Ti target and the RF sputtering power on Si target were assigned according to the atomic percent of Ti: N: Si. Finally, the N2 flow rate was adjusted to avoid the target poisoning and to obtain the stoichiometry of TiN. 3.3. The experiments on Ti-Si-N deposition and the characterization The deposition of the Ti-Si-N coating is aimed to two points: (a) to study the microstructure or atomic structure of the Ti-Si-N coatings and (b) to investigate the formation mechanism of the microstructure. Ti-target Si-target Substrate holder Chamber S1 S2 S3 Fig. 3.10: The Ti target and the Si target were mounted on the side of the vacuum chamber and adjoined each other. Three silicon wafer substrates were fixed on the substrate holder which was rotated during the deposition process. Experiments of sputtering PVD and Ti-Si-N deposition 53 The experiment 04030202 is reported here because one probe of this experiment has a chance to be characterized with XRD and the nano-indentation measurement. In this experiment, the thin films of Ti-Si-N were deposited on three unheated Si (111) substrates with the equipment of LS 450S. A Ti target with the purity of 99.6% and a Si target with the purity of 99.999% were both installed on the side of the chamber and adjoined each other as shown in Fig 3.10. In the deposition process, 350 W DC sputtering power added on the Ti target and 100W RF sputtering power added on the Si target. Three substrates were fixed on the substrate holder which rotated 10 rpm during the deposition process. The distances between the target and three substrates were 40 mm for the substrates 04030202-1 (S1), 80mm for the substrates 04030202-2 (S2), and 120 mm for the substrates 04030202-3 (S3), respectively. Before the deposition, three substrates were cleaned with acetone in an ultrasonic bath. The base pressure was 4.8×10 -5 Pa and the process pressure was 0.08 Pa. The Ar flow rate was 7.0 sccm. The N2 flow rate was 2.4 sccm. The elemental concentration of the films was analyzed through QUEST energy dispersive spectroscopy (EDS). The thickness of the films was measured by SEM of FEI Quanta400. The concentration and the thickness of three probes are listed in Table 3.10. The result of the thickness is reasonable because the deposition rate decreases as the distance between the target and the substrate increases. But the concentration of nitrogen seems strangely high. The explanation from the operator is that the concentration of light element like nitrogen cannot be identified precisely with EDS. Table 3.10: Elemental concentrations and film thickness of the Ti-Si-N films (04030202). Concentration (at.%) Thickness (μm) Ti Si N 04030202-1(S1) 18.69 3.44 77.86 1.470 04030202-2(S2) 17.81 4.02 78.17 1.090 04030202-3(S3) 16.98 4.40 78.62 0.7069 Microstructure of the films was investigated by the cross-sectional scanning electron microscopy (SEM) and the X-ray diffraction (XRD). The cross-sectional SEM images from 04030202-1 (S1) and 04030202-3 (S3) are shown in Fig. 3.11(a) and (b), respectively. The S1 film contains a columnar microstructure with uniform columns from substrate to the top of the film [Fig. 3-11(a)]. This is a symbol that the deposited atoms diffuse insufficiently in the film growth process. The distance between the target and S1 Experiments of sputtering PVD and Ti-Si-N deposition 54 was 40 mm. In the deposition process, S1 rotated through two targets and the time of S1 facing the targets was about 13.4% of one revolution time. This unheated S1 was facing the cool chamber wall in the rest time so that the deposited atoms may have not enough energy to diffuse. The distance between target and S3 was 120mm. The time of S3 facing the targets was more than 25% of one revolution time. In this case, the deposited atoms had a better condition to diffusion. A dense structure of S3 is exhibited in Fig. 3.11(b). This indicates that the sufficient diffusion of the adatoms is important for the formation of film structure and thus it is necessary to control the substrate temperature. (a) (b) Fig. 3.11: Cross-sectional images of (a) 04030202-1 and (b) 04030202-3 show the influence of the facing target time on the film microstructure. Experiments of sputtering PVD and Ti-Si-N deposition 55 The XRD characterization was performed with D8 ADVANCE from Bruker AXS GmbH. The X-ray diffraction pattern of the Ti-Si-N film of 04030202-1 probe is shown in Fig. 3.12. There are three diffraction peaks at the positions 2θ = 36.60°, 42.20°, and 61.80° which correspond to the TiN orientation (111), (200), and (220), respectively. There is no diffraction peak for Si3N4. This XRD characterization result is consistent with those of the other researches on Ti-Si-N coatings [Li92] [Moto01]. Normally, the preferred orientation of TiN thick film is (111) [Kajikawa03] [Sundgren85]. The thickness of 04030202-1 probe is 1.470 μm and the main preferred orientation of TiN maintains (200). This shows clearly that the Si addition has an obvious effect on the preferred orientation of TiN crystallite. 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 TiN(220) TiN(111) TiN(200) XRD-5°: 04030202-1 Ti-Si-N In te n si ty defraction angle (°) Fig. 3.12: The XRD pattern for the Ti-Si-N film of the probe 04030202-1. The surface morphology was measured through atomic force microscopy (AFM) with Dimension TM 3000 from Digital Instruments. Fig. 3.13 shows the surface image of Ti-Si-N film 04030202-1. The AFM image was analyzed with an analysis code of scanning probe image processor (SPIP) [SPIP]. The analysis result indicates that the root mean square (rms) roughness is 3.74 nm and the mean diameter of grain is 36.4 nm. To compare with the grain size in Table 2.1, the grain size identified by SPIP is too large. It is possible that some grain boundaries have not been identified through AFM and SPIP. Nano-indentation is a powerful technique for analyzing the mechanical properties of the thin films. The hardness of the probe 04030202-1 was measured through MTS‘s Experiments of sputtering PVD and Ti-Si-N deposition 56 Nano Indenter TM II. Fig. 3.14(a) shows the load-displacement curve of the nano- indentation measurement with a maximum displacement of 40nm, which corresponds to the hardness of 43.14 GPa. The load-displacement curve in Fig. 3.14(b) is from the nanoindentation measurement with a maximum displacement of 100nm. This result corresponds to the harness of 32.19 GPa. Clearly, the hardness of this Ti-Si-N coating is much higher than that of normal TiN coatings [Lengauer00] [Pierson96]. And the elastic recovery of this Ti-Si-N coating is relatively large, about 70%. These results are similar to those reported by other groups [ZhSh04] [Barshilia06]. Fig. 3.13: The AFM image (2µm×2µm) of the Ti-Si-N film 04030202-1. Through above investigations, some information about microstructure of Ti-Si-N films is obtained, e.g. the columnar structure or the dense structure, the orientation of TiN crystallites, the grain size, and surface morphology. These results reflect the collative phenomina. The atomic structure of Ti-Si-N composite, especially the interface of TiN and Si-N cannot be identified or analyzed through these characterizations. This implies that the atomic structure of Ti-Si-N composite is difficult to be found out through the experiment method. But, it does not mean that this identification is impossible with Experiments of sputtering PVD and Ti-Si-N deposition 57 present day characterization means. If the atomic structure of Ti-Si-N composite is known, it might be found out from HRTEM image. (a) (b) Fig. 3.14: Nanoindentation load-displacement curve from the Ti-Si-N cating 04030202-1: (a) the hardness = 43.14 GPa under the condition of indentation depth = 40nm, (b) the hardness = 32.19 GPa under the condition of the indentation depth = 100nm. Linking the microstructure and the deposition process condition in the experiment, some clues about the film formation can be found out. For example, the relatively sufficient diffusion of deposited atoms during the deposition may lead to a denser microstructure of the film. But the formation mechanism of microstructure cannot be identified by these characterizations. Therefore, the atomic simulation or calculation is very necessary to investigate the atomic structure and the formation mechanism of Ti-Si-N composite film. 3.4. The summary of experiment researches Our experiments on the plasma measurement and on the Ti-Si-N deposition reveal that the TiN deposition and the Ti-Si-N deposition are complicated processes. (1) The ion flux and the ion energy are relatively high under the RF sputtering and the deposition rate is relatively high under the DC sputtering. (2) The experiment result shows that near the stoichiometry point of TiN, there is a large change of the proportion of Ti + flux and the N2 + flux. In addition, all the process Experiments of sputtering PVD and Ti-Si-N deposition 58 parameters such as sputtering power, N2 flow rate, Ar flow rate, the process pressure, and the distance between the target and the substrate have influence on the stoichiometry of TiN and these influences are interrelated. This means that it is difficult to obtain and maintain the stoichiometry of TiN in the deposition process. The measurement in situ is necessary to obtain the stoichiometry of TiN. (3) The experiment on the Ti-Si-N deposition shows that the Si addition has obvious influence on the preferred orientation of TiN crystallite and the hardness of Ti-Si- N coatings. However, the exact atomic structure of Ti-Si-N composite film, especially the interface structure of TiN and Si-N, have not been identified by characterizations of SEM, XRD, and AFM. The experiment result indicates that the increase of diffusion of adatoms may lead to a dense microstructure of the film. Thus, it is important to control the deposition temperature. But, the formation mechanism of Ti-Si-N composite film has not been found out by the characterizations. For the identification of the atomic structure and the formation mechanism of Ti-Si-N superhard composite coating, atomic simulations and calculations are necessary. 4. The kinetic Monte Carlo simulation of Ti-Si-N film growth The literature review in Section 2.1 and the experimental results in Chapter 3 show that it is difficult to find out the atomic structure and the formation mechanism of Ti-Si-N superhard nano-composite coatings through experiment method. Therefore, atomic simulations and calculations should be used for this kind of basic investigation. The experiments in Chapter 3 reveal that the Ti-Si-N deposition is a complicated process. The analysis of sputtering PVD process in Section 2.2 shows that the structure of deposited film depends on both individual atomic processes and collective stochastic process in film growth. In the deposition process, main individual atomic events include atom deposition, adsorption, desorption, and adatom diffusion; and main stochastic processes include nucleation, island growth, island coalescence, and film growth. As indicated in Section 2.3, for simulating such evolution of film growth, kinetic Monte Carlo (KMC) is a suitable method. In our research, two 3D KMC codes have been developed to simulate the film growth of Ti-Si-N. The principle and the implementation of KMC are very clear, which has been introduced in Section 2.3. But it is not easy to develop the KMC code. Our development of KMC simulation code was in stages. In the beginning, our first KMC simulation code was developed with the lattice model. The lattice KMC is relatively simple and very popular to be used in various kinds of film growth simulation [Voter02] [Amar06]. But the lattice model is not suitable for the simulation of Ti-Si-N composite because the TiN crystal structure is different from the Si3N4 crystal structure. Therefore, our emphasis shifted quickly on the development of the second KMC simulation code with the off- lattice model. The challenge of the off-lattice KMC is finding the saddle points on the potential energy surface (PES). After resolving the problem of searching on PES, we face another challenge, accurate calculation of atomic interaction. In this chapter, we report these two kinds of KMC simulations. The kinetic Monte Carlo simulation of Ti-Si-N film growth 60 4.1. The lattice KMC simulation of film growth Start Set total deposition particle number N, substrate temperature T, deposition rate RD Calculate the lapse time (Δt) between two arrivals Set the random coordination (x, y) and the new particle is deposited The number of particle deposited n=n+1, ti =0 ** Adjust the table of moveable particles, search their diffusible lattice sites, and calculate the activation energies Ea Σ ti ≤ Δt ? Calculate jump rate for every path ri and for every particle pi, accumulate system rates P = Σ pi , and calculate residence time of the system ti = 1/P Selecte Randomly a particle and its jump path weighted by rate Make a jump, update the coordination of the particle, accumulate the time Σ ti n > N? Stop No Yes Yes No Determining particle color Fig. 4.1: The main flow chart of the KMC simulation of the film growth process. In the epitaxial film growth, the low-energy basin of adatoms is normally at the The kinetic Monte Carlo simulation of Ti-Si-N film growth 61 lattice site of the substrate, so that the lattice model is suitable for the simulation of epitaxial film growth. With the lattice model, all the lattice sites are fixed before the simulation. And an adatom can only diffuse from one lattice site to another lattice site in the simulation. Therefore, transition event list can be built easily and hence calculation cost is relatively low. This is why the KMC with the lattice model is so popular in the film growth simulation. The main flow chart of our first KMC simulation code with the lattice model is shown in Fig. 4.1. The implementation of the lattice KMC simulation in this research included following sequence of steps. (1) The simulation parameters such as the total deposition particle number N, the substrate temperature T, and the deposition rate RD were set up. (2) The lapse time t was calculated with the deposition rate RD: MMR a t D   0 (s) (4.1) where 0a is the lattice constant, MM  is the simulation substrate with simple cubic structure, including MM  lattice sites. The periodic condition was employed for this simulation substrate as shown in Fig. 4.2. Under the periodic condition, if an adatom diffuses out of the boundary, then it will come back into the substrate from the relevant opposite boundary. For example, if an adatom diffuses out of the right side of the region 6, it will come back into the substrate from the link side of the region 5 as shown in Fig. 4.2. 12 2 3 3 4 4 56 6 7 8 8 Fig. 4.2: The periodic condition of the simulation substrate. (3) A new particle was deposited on a random site (x, y). The kinetic Monte Carlo simulation of Ti-Si-N film growth 62 (4) The diffusion rate or the diffusion coefficient iD along each diffusion path of each moveable particle was calculated with following equation [Oura03]:         Tk E z a D B a i exp0 2  (4.2) sIntFina eEEE  (4.3) where 0 is the atomic vibration frequency which is in the range of 10 12 to 10 13 , Bk is the Boltzmann constant, T is deposition temperature, aE is activation energy, a is the jump distance, z is the number of neighboring sites which the adatom can hop to, IntE is the system energy in the initial state, FinE is the system energy in the final state, and se is the activation energy for the particle diffuse on the clean substrate which equates ~5-20% of desorption energy. The diffusion rate of each moveable particle  ij Dp is sum of the diffusion rates along all of its possible diffusion paths. The transition event list consists of the diffusion rates of all the moveable particles. The system rate  jpP is sum of the diffusion rates of all the moveable particles. The residence time of the system is Pt i /1 . This residence time of the system is deduced from the probability distribution function for the time of first escape [Voter05]. Therefore, the real evolution of a system can be simulated by KMC method. For the calculation of IntE and FinE , the Morse potential was used [Morse29]. The Morse potential energy function is of the form     00 2)( 20 rrrrM eeDrV    (4.4) where r is the distance between the atoms, 0r is the equilibrium bond distance, 0D is the ―equilibrium" dissociation energy of the molecule (measured from the potential minimum), and  controls the ―width‖ of the potential. The kinetic Monte Carlo simulation of Ti-Si-N film growth 63 (5) After the calculation of the step 4, the diffusion event could be selected with random number from the transition event list, weighting by the diffusion rate of the particle and the rate of the diffusion path. Then the diffusion event was conducted and the system state was changed. After the transition of the system state, the diffusion rates which related to the diffusion event should be updated and the system time shifted in advance. (6) The step 4 to 5 was iterated until the time summation  it to the lapse time t and then a new particle was deposited. The step 3 to 5 was iterated until all the atoms of designated number were deposited. Fig. 4.3: The grain size vs. the deposition temperature: a) 100K; b) 200K; c) 300K; d) 400K, [Wang05]. A feature of our first KMC code is that different clusters or grains can be presented with different colors, Fig. 4.3. As a result, the statistic analysis can be conducted straight- forwardly with this color presentation method. With this lattice model KMC code, the deposition of 10000 adatoms was simulated (a) (b) (c) (d) The kinetic Monte Carlo simulation of Ti-Si-N film growth 64 and the evolution of deposited film was studied [Wang05]. The influence of deposition temperature on the grain size in the film was investigated. The statistical curve of the number of atoms in the largest cluster versus the deposition temperature in Fig. 4.4 shows that the cluster size or the grain size increases, if the deposition temperature rises. And in this case, the relevant number of the cluster decreases, Fig. 4.5. Fig. 4.4: The number of atoms in the largest cluster vs. the deposition temperature (N=10000, RD=0.5nm/s). Fig. 4.5: The number of the cluster vs. the deposition temperature (N = 10000, RD = 0.5nm/s). Basically, this simulation result is in agreement with the experimental result and the Thornton model [Thornton77], because the diffusion length of adatoms increases as the deposition temperature rises and hence more adatoms can come together to build a relatively large island. As remarked above, in the lattice model KMC simulation, all the lattice sites are The kinetic Monte Carlo simulation of Ti-Si-N film growth 65 fixed before the simulation. But, the crystalline structure of TiN is different from that of Si3N4, so that the film growth of co-deposited Ti-Si-N cannot be simulated with the lattice model KMC. Therefore, we develop our second KMC code with off-lattice model. 4.2. The off-lattice KMC simulation of Ti-Si-N film growth With the off-lattice model, the limitation that an adatom diffuses only from one lattice site to another lattice site is eliminated. Adatoms can diffuse on the potential energy surface (PES) from a basin through a saddle point to another basin. Obviously, the simulation of non-epitaxial film growth should be performed with the off-lattice model. However, the simulation with the off-lattice model faces a big challenge, namely, the PES searching. PES is a hyper-surface which is the interaction result of an adatom and the surface atoms. The PES searching is aimed to the identification of saddle points and basins. Some PES searching methods, including the nudged elastic band (NEB) method and the dimer method, have been developed by Jónsson‘s group [Henkelmen00]. For the PES searching, we had tried to develop the fine lattice method and the geometry method, but our development of new searching method was not successful yet. The fine lattice method is similar to the lattice model. Considering that a basin may be at the site between the lattices, the lattice is further devided into fine grids. If the grid is very fine, the difference between the lattice model and the off-lattice model will be very small. Since the system energy of all configurations, i.e. the adatom is at every grid point, should be calculated, the finer grid means the exponential increase of calculation cost. This implies that a simple fine grid method is not practical. A possible solution is the combination of coarse grids and fine grids according to the concrete situation. This is the way used by Scheffler group for mapping PES [Kley97]. The design of the geometry method is based on a fact that a basin of PES is a point where the sum of the interactions between some surface atoms and an adatom reaches its maximum value. The interaction maximum value of a surface atom and an adatom is on a spherical surface. The spherical radius is the bond length between the surface atom and the adatom. The spherical center is at the site of the surface atom. A basin should be at the intersection of some spherical surfaces. If a new basin for an adatom is found by the solution of equations of these spherical surface, the nudged elastic band method could be used between the initial basin and the final basin to search the saddle point and hence to obtain the activation energy for the diffusion rate calculation. However, this geometry The kinetic Monte Carlo simulation of Ti-Si-N film growth 66 algorithm has a difficulty if there is no intersection of these spherical surfaces. After those efforts, we decide to use the dimer method in our off-lattice KMC simulation. The design of the dimer method is excellent [Henkelman99]. Henkelman indicates that the dimer method uses a finite difference method to sense the lowest curvature direction, and follows it to the saddle point. For an adatom which locates at R , a pair of images is set to form a dimer as shown in Fig. 4.6. The forces acting on two images are normally different in the potential field. The first step of the dimer method is rotating two images around the adatom. The goal of the rotation is to make the perpendicular force on two images to zero, namely that the forces on two images is directly through the line connected two images, along the dimer orientation direction Nˆ . As an analogy, the dimer is just like a magnetic needle in the magnetic field. Under the action of magnetic force, the needle will rotate until it is along the magnetic line. The magnet force is now just through the line which is connected two end points of the magnetic needle. Fig. 4.6: Definition of the various position and force vectors of the dimer. R is the coordinate of adatom, 1R and 2R are the coordinates of the image 1 and the image 2. The rotational force on the dimer,   21 FFF , is the net force acting on image 1 perpendicular to the direction of the dimer. From [Henkelman99]. The second step of the dimer method is translating the dimer to the saddle point. If the force on two images is through the dimer orientation direction, the difference of the forces which are on two images will push the dimer directly to a basin. Since the goal of employing the dimer method is to search the saddle point, translating the dimer is conducted against this direction, i.e. pushing the dimer to the higher energy direction. To avoid translating the dimer to the summit of PES, the dimer is pulled along the perpendicular direction of the dimer orientation direction, if the dimer goes through the The kinetic Monte Carlo simulation of Ti-Si-N film growth 67 inflection point of the PES curve. Under alternatively rotating and translating, the dimer is pulled to the saddle point of the PES. In the rotating dimer and the translating dimer, the Newton‘s method is used to calculate the rotating angle and the translating length, and the conjugate gradient method is used to choice the rotating plane and the translating direction. According to the algorithm in Ref. [Henkelman99] [Osen04], in our KMC code, the implementation of the saddle point searching with the dimer method is follows. First, the potential curvature C along the dimer is of the form: 2 012 )(2 )( R EE R NFF C dd       （4.5） where 1F and 2F are the forces on the image 1 and the image 2; the vector N is a unit vector which defines the dimer direction; R is the direction from the adatom to the image; the energy of the dimer 21 EEEd  is the sum of the energy of the images. The energy 0dE at the fixed midpoint of the dimer is constant during dimer rotation. 0dE can be isolated from equation (4.5) in terms of the known forces on the images, NFF RE E dd    )( 42 210 . Minimizing the dimer energy Ed is equivalent to finding the lowest curvature mode at R . Second, the dimer is rotated with the calculation of the modified Newton algorithm, i.e. finding a rotation angle  to bring the rotation force to zero. A unit vector  is defined which is perpendicular to N within the plan of rotation. Given an angle d of rotation, image 1 moves from 1R to * 1R , as shown in Fig. 4.7. As the dimer rotates through the angle d , a finite difference approximation to the change in the rotational force  RFFF   /)( 21 is given by 2/ **   d d FF d dF F    (4.6) The kinetic Monte Carlo simulation of Ti-Si-N film growth 68 A reasonable estimate of the rotation that is required to bring F to zero can be obtained from Newton‘s method   F FF    2 **  (4.7) or from the modified Newton‘s method         0 02arctan 2 1 F F  (4.8) where 0F and 0F  are the values of F and F  evaluated at 0 . Fig. 4.7: Definition of the various quantities involved in rotating the dimer. All the vectors are in the plane of rotation. The dimer is first rotated about a small angle d to give a finite difference estimate of F  given by Eq. (4.6). The dimer is then rotated by a calculated angle  given by Eq. (4.8) to zero the force within the plane of rotation. Third, the rotation plan is found out with the conjugated gradient method. For the first rotation, the direction of descent   FG . For the ith rotation, ** 11      iiiii GFG  (4.9) where          ii iii i FF FFF 1 (4.10) The kinetic Monte Carlo simulation of Ti-Si-N film growth 69 is the weighting factor between the rotational force iF and the old modified force vector  1iG ; ** is shown in Fig. 4.7. Fourth, the dimer is translated to the saddle point. If the potential curvature C > 0, the translation is under the force //F . The definition of the parallel force is //2 // 1 // FFF  . If the potential curvature C < 0, the translation is under a force to be perpendicular to the unit vector N . Like the calculation of dimer rotating, the Newton method and the conjugated gradient method are also used for the calculation of dimer translating. ** Relax all adatoms deposited, adjust the table of moveable particles, search all diffusion path, relevant basins, and saddle points for every particle, and calculate the activation energies Σ ti ≤ Δt ? No Yes Fig. 4.8: The part flow chart of the KMC simulation with off-lattice model. The flow chart of the KMC code with the off-lattice model is similar to that of the KMC code with the lattice model. The procedure to be changed is in the section with the mark of two stars, Fig. 4.8. With the off-lattice model, the dimer method is used first to relax all the adatoms and the relevant surface atoms circularly until all the adatoms and surface atoms are in the relatively stable basins. Then, a group of dimer will be sent to search the saddle points and the neighboring basins for each moveable particle. Finally, the activation energy for each diffusion path can be calculated with the saddle point energy and the initial basin energy, namely the system energies of the configurations, in which the moveable particle is at the saddle point or at the initial basin. Obviously, there are two advantages of this off-lattice KMC simulation with dimer method. (a) The activation energy can be calculated directly with the system energy difference between the saddle point and the initial basin, which is more accurate than the The kinetic Monte Carlo simulation of Ti-Si-N film growth 70 assumed activation energy in the lattice-model KMC. (b) The relaxation of the atomic arrangement can be conducted by circularly searching the basin position for all the adatoms and surface atoms. This relaxation may make the adatom at a shallow basin [Voter05] slide down to a stable deep basin. With this kind of relaxation, the atoms are just like under the atomic vibration. Therefore, this off-lattice KMC simulation result could be much closer to the real situation, in particular, in the case of multi-elements co- deposition process, like the Ti-Si-N composite film growth in this research. 0 0.5 0 0.5 -0.6 -0.4 -0.2 X(nm) R.TiTi=0.3nm R.NN=0.15nm Y(nm) E (e V ) 0 0.5 0 0.5 -1 -0.5 0 X(nm) R.TiTi=0.3nm R.NN=0.2nm Y(nm) E (e V ) 0 0.5 0 0.5 -1 -0.5 0 X(nm) R.TiTi=0.3nm R.NN=0.25nm Y(nm) E (e V ) 0 0.5 0 0.5 -2 -1 0 X(nm) R.TiTi=0.3nm R.NN=0.3nm Y(nm) E (e V ) Fig. 4.9: The influence of the potential parameters on the PES: the bond length of N-N changing from 0.15nm to 0.30nm. But, there are still three problems in this off-lattice KMC simulation of Ti-Si-N composite film growth. First, it is difficult to determine the potential parameters. The Morse potential was used in this off-lattice KMC simulation. Two important parameters in the Morse potential are the equilibrium bond distance (the bond length) and the ―equilibrium‖ dissociation energy (the binding energy), seeing quation (4.4). Without the ab initio calculation, it is L(TiTi)=0.3nm L(NN) 0.3n L(TiTi)=0.3nm L(NN)=0.25nm L(Ti i) . L( )=0.2nm L(TiTi)=0.3nm L( N)=0.15nm The kinetic Monte Carlo simulation of Ti-Si-N film growth 71 difficult to determine the binding energy and the bond length of N-N, Ti-Ti, Si-Si, Ti-N, Ti-Si, or Si-N. For example, the covalent bond length of N-N is 1.10 Å in the Lang‘s Handbook of Chemistry [Dean99]. The result of ab inito calculation for the bond length N-N is 1.41 Å [Gall03]. But the distance between N-N in the TiN crystallite is ~3.00Å. PES can be greatly changed by the different potential parameters. An example is shown in Fig. 4.9, i.e. the PES with the different bond length of N-N. It is even more difficult to determine the binding energy and the bond length of Ti-Si, because there are few referent data from handbooks and research literatures. Evidently, the ab initio calculations should be performed in order to obtain the information of the theoretical PES. (a) (b) Fig. 4.10: The structure of TiN crystallite and Si3N4 crystallite: (a) TiN, (b) β-Si3N4. （a） (b) (c) Fig. 4.11: The combination of TiN and Si3N4: (a) the cell of TiN, (b) the tetrahedron of Si-4N, (c) the structure of Si-4N-4Ti suggested in this research. Second, the combination detail of the TiN crystallite and the Si3N4 crystallite, i.e. the exact atomic positional relationship of Ti, Si, and N on the interface, is not clear. The structure of the crystalline TiN is different from that of the crystalline Si3N4, as shown in Fig. 4.10. The crystalline TiN has B1 NaCl structure, in which every titanium atom connects with six nitrogen atoms and every nitrogen atom connects with six titanium atoms, Fig. 4.10(a). The typical structure of silicon nitride is α-Si3N4 and β-Si3N4, in which every silicon atom connects with four nitrogen atoms and every nitrogen atom The kinetic Monte Carlo simulation of Ti-Si-N film growth 72 connects with three silicon atoms, Fig. 4.10(b). The interesting point here is that a similar structure can be found out from them, if these two structures are analyzed carefully, (Fig. 4.11). The cell of TiN is a simple cubic structure which consists of four nitrogen atoms and four titanium atoms, Fig. 4.11(a). The side length is 2.12 Å. A tetrahedron Si-4N in the silicon nitride contains also four nitrogen atoms, Fig. 4.11(b). The side length of the cube connected the four nitrogen atoms of the tetrahedron Si-4N is 2.01 Å. Therefore, it is very possible for a silicon atom to move into the center of the TiN cell and to form a Si- 4N-4Ti structure, Fig. 4.11(c). This Si-4N-4Ti is an interesting structure. If a Si atom moves into the cell of TiN, the balance of the interaction of Si-4Ti, Si-4N, and 4Ti-4N must be taken into account. However, since the interactions of Ti-N, Ti-Si, and Si-N are calculated by the Morse potential in this KMC simulation and the parameters of potential are difficult to be determined, it is very difficult to estimate whether Si atom can move into the cell of TiN or not. Obviously, the key point is the accurate calculation of interactionof atoms. This indicates again that the ab initio calculation is necessary. Fig. 4.12: The Ti-Si-N composite film simulated through the off-lattice KMC: the figure above is on plan view and the bottom one is on the section view. The red sphere is Si atom, the green is Ti, and blue is N [Wu06]. Third, the calculation speed is a big problem. With the lattice KMC code, it costed about 20 hours to simulate the deposition of 10000 atoms on our PC computer (1.7 GHz main frequency of CPU and 2.0 GB memory of CPU). The Ti-Si-N co-deposited has been simulated with the off-lattice KMC code [Wu06]. On the same PC computer, the simulation of ~2000 particles (Fig. 4.12) costed over six days, about 150 hours. The simulation speed was very slow. We studied the details of the calculation. It was found that searching for the saddle point with the dimer method costed over ninety percent calculation time. Therefore, the improvement of the PES searching method is very crucial. There are some possible solutions to increase the calculation speed. (a) For the diffusion The kinetic Monte Carlo simulation of Ti-Si-N film growth 73 modes of typical atom arrangements, the activation energy should be calculated by the ab initio method and saved in a database in order to make rearrangement of atoms without calculation in the simulation. (b) The parallel calculation method could be used to search the saddle points because the search of saddle point with dimer method is independent. (c) The geometry method, the dimer method, and the nudged elastic band method could be combined to decreases the calculation time. The new basin positions is estimated roughly by geometry method and then identified by dimer method. The nudged elastic band method is used between the initial basin and the final basin to search the saddle point. The off-lattice KMC simulation indicates clearly that the accurate calculation of atomic interaction is crucial. Therefore, the ab initio calculation is very necessary or even unavoidable. 4.3. The summary of KMC simulation The KMC code with the lattice model has been developed in this research. An epitaxial film growth can be simulated by this lattice KMC. The simulation result is basically in agreement with the experimental result. The KMC code with the off-lattice model has been developed to simulate the non- epitaxial film growth. For the PES searching, the dimer method was used in our off-lattice KMC code. The advantages of this off-lattice KMC simulation are the relaxation algorithm of atoms and the direct calculation method of activation energy, which make the simulation very close to the real situation. The Ti-Si-N film growth was simulated by this off-lattice KMC code, which reveals two limitaions of this off-lattice KMC simulation: inaccurate potential algorithm and low calculation speed. In preparing the Ti-Si-N film growth simulation, the atomic positional relationship of Ti, Si, and N was analyzed carefully. A combination structure, namely the Si-4N-4Ti structure, was suggested but it could be identified due to the inaccurate potential algorithm. And hence the basic structure and the formation mechanism of Ti-Si-N superhard composite coating have not identified yet by the KMC simulation. To obtain the accurate description of atomic interaction of Ti, Si, and N, the ab inito calculation is necessary. Although the KMC simulation of Ti-Si-N film growth was not successful, the development of the off-lattice KMC code has already established a basis. Once the The kinetic Monte Carlo simulation of Ti-Si-N film growth 74 interaction of atoms can accurately be calculated, the evolution simulation of system with large number of atoms can be performed by the off-lattice KMC. For the simulation of system with large number of atoms, it is necessary to improve the PES searching method and to develop a method for the rearrangement without calculations. 5. The atomic calculations with the ab initio method In Chapter 4, the KMC simulation result points out that a key point to the atomic simulation is the accurate calculation of interaction of atoms, so that the ab initio calculation is necessary. As indicated in Section 2.3.2, the ab initio calculation is based on the electronic structure that is described by the Schrödinger‘s wave function or the density functional theory (DFT). Therefore, the atomic structure or the atomic positional relationship of composite material which is identified by the ab initio method is of high accuracy and relatively reliable [Ohno99]. In this chapter, the first goal of the ab initio calculation is to identify the basic structure of Ti-Si-N superhard composite coating. In Chapter 4, the combination of TiN and Si3N4 has been analyzed and it has been suggested that a Si atom may move into the center of the TiN cell and form a Si-4N-4Ti structure. However, by the Morse potential, the accurately positional relationship of Ti, N, and Si atom in the structure could not be identified. And the condition that Si atom could move into the center of the TiN cell is also unclear. In this chapter, the ab initio calculation provides the exact result that is more than what can be analyzed. The way to identify the basic structure with the ab initio method is that first the total energies and the cohesive energies of all the possible atomic arrangements are calculated and then the lowest-energy structure is identified with the comparison of these total energies and cohesive energies [Liu07]. The second goal of the ab initio calculation is to identify the basic diffusion behaviors of the Ti, N, and Si adatom and the ad-cluster (addimer, adtrimer, adtetramer) in the film formation process. These basic diffusion behaviors will provide some clues to the formation mechanism of Ti-Si-N composite coatings. It is known that the achievable time scale of molecular dynamics simulations with ab inito MD is on the order of picoseconds [Reuter05]. Normally, the time for a diffusion event is on the order of milliseconds or more [Henkelman03]. The time disparity is so huge. How can the diffusion events be investigated by the ab intio method? The off-lattice KMC simulation of Chapter 4 shows The atomic calculations with ab initio method 76 that the potential energy surface (PES) plays an important role in the diffusion of adatoms. A key factor is the activation energy that is the energy difference introduced by adatom‘s diffusion from the initial basin to the saddle point on PES. The research of Greene‘s group [Gall03] reminds us that the ab initio method and the nudged elastic band method can be used to identify the basin and the saddle point of PES. And then the activation energy can be claculated. Once the activation energy of basic diffusion is obtained, the diffusion behaviors could be evaluated with the comparison of all the activation energy. This is our research mode for investigating the formation mechanism of Ti-Si-N composite coatings. 5.1. VASP and the pre-calculation The ab initio calculations in this chapter have been carried out with the Vienna ab initio simulation package (VASP) [Kresse93] [Kresse94-1] [Kresse96-1] [Kresse96-2] [Kresse99] that is based on the density functional theory (DFT). It employs pseudo- potentials, a plane-wave basis set and the periodic boundary conditions to determine the Kohn-Sham ground state. In this research, we used the generalized gradient approximation (GGA) of Perdew-Wang‘91[Perdew92] for exchange correlation functional and the ultrasoft pseudopotentials [Vanderbilt90] [Kresse94-2] for ionic potential interaction. A cutoff energy of 348 eV was used for the expansion of the plane-wave basis set in the calculation. The Ti 2p electron was considered as valence electron in the calculations of the TiN and the Ti-Si-N structures. The criteria for terminating the electronic and ionic iterations were an energy difference of 10 -3 or 10 -4 eV according to the atom numbers in the supercell to balance the calculation accuracy and the calculation cost. To obtain the theoretical equilibrium lattice constant of TiN, a series of total energy calculations for various lattice constants were performed. Our calculation result is 4.262 Å, which agrees well with the experimental value of 4.242 Å [Lengauer00] and is very close to the result obtained by the full-potential linear augmented plane wave (FLAPW) method of 4.26 Å [Stampfl01]. For the investigation of the cohesive energy and the adsorption energy of Ti-Si-N structures, the single atom energy of N, Si, and Ti were calculated. The energy of a N atom is -3.27eV and the energy of N2 is -16.49eV. Then a N2 dissociation energy is 9.95eV which is in good agreement with the experimental value of 9.80eV [Dean99]. The energy of a Si atom is -0.77eV and the energy of the Si crystallite consisting of 64 atoms The atomic calculations with ab initio method 77 with the diamond structure is -346.30eV, which corresponds to the Si cohesive energy of 4.64eV/atom. This cohesive energy is in excellent agreement with the value of 4.63eV/atom in the reference [Kittel05]. The energy of Ti atom is -2.32eV and the energy of the Ti crystallite consisting of 2 atoms with the hcp structure is -15.45eV. It leads to the Ti cohesive energy of 5.40 eV/atom which is close to the value of 4.85 eV/atom in the reference [Kittel05]. Therefore, the result of single atom energy of N, Si, and Ti is acceptable for the below calculations of cohesive energy and adsorption energy. 5.2. The basic structure of Ti-Si-N superhard coating 5.2.1. Introduction The identification of the atomic structure is crucial to develop the nano-structured materials because the atomic structure can provide a basis for the analysis of material property, the design of new materials, and the calculation of atomic percent of composite, e.g. the atomic percent of Ti: N: Si in our research. According to this atomic percent, the process parameters such as the sputtering power on the Ti and Si targets as well as the reaction gas N2 flow rate can be determined. In this section, the investigation of the basic structure of Ti-Si-N superhard composite coatings with the ab initio calculation is reported. The investigation includes following items. (1) It is known that the TiN coatings have a polycrystalline structure that consists of crystallites and boundaries, so that a Si atom added into the TiN coating may be in the crystallite, or in the boundary, or in both of them. Thus, the total energies of all possible low-energy configurations, in which a Si atom was set at a high symmetry site in TiN crystallite or in TiN boundary, were calculated with VASP and then the cohesive energies were computed in order to identify the lowest-energy structure of Ti-Si-N composite coating. (2) The properties of the interface structure Si-4N-4Ti and Si-2N-2Ti were studied. The electronic structures of Si-4N-4Ti and Si-2N-2Ti reveal the bond relationships and the properties of Ti-Si-N composite coatings. In addition, it presents a clue for the improvement of Ti-Si-N hardness and a hint for the potential value of the Ti-Si-N composite structure. The atomic calculations with ab initio method 78 (3) The distribution of Si atoms in the TiN boundary was investigated. The emphasis is on the strain introduced by the Si distributions. (4) The formation of Si-4N-4Ti or Si-2N-2Ti on the TiN(001) surface is studied. The calculation for the arrangement of a Si atom, two Ti atoms, and two N atoms were performed to obtain the information about the formation mechanism. (5) The atomic percent of Ti: N: Si was calculated according to the basic structure model, the Si distribution in boundary, and the grain size. This atomic percent is important for setting up the process parameter. 5.2.2. A Si atom in the crystalline TiN (a) (b) (c) (d) Fig. 5.1: The configuration of a Si atom in the TiN crystallite: (a) a Si atom is at a eightfold coordinated hollow site (~Si-HL), the figure above is front view and the bottom one is top view; (b) a Si atom is at a fourfold coordinated hollow site or a plane hollow site (~Si-PHL), the figure above is front view and the bottom one is top view; (c) a Si atom occupies a Ti position (~Si-OCP-Ti); (d) a Si atom occupies a N position (~Si-OCP-N). The square stands for Si, the triangle for Ti, and the circle for N. In order to investigate whether a Si atom could be added into the TiN crystallite, a group of calculations were performed. The total energies and the cohesive energies of seven configurations were calculated. To make the energies of the seven configurations comparable, supercells of TiN used for the calculations of seven configurations had the same volume. The supercell consisted of four layers of atoms, 8 N and 8 Ti per layer. The supercell is termed as 444 model. In this TiN crystallite model, the lattice constant of the supercell was 4.262 Å in three directions (x, y, z). According to the method of Monkhorst-Pack [Monk-Pack], a grid of 555 k-points was used. Three of the seven The atomic calculations with ab initio method 79 configurations had no Si addition: the first one was a perfect TiN crystallite supercell; the second one was the TiN crystallite supercell in which a Ti atom was missing (TiN-1Ti); and the third one was the TiN crystallite supercell in which a N atom was missing (TiN- 1N). In the other four of the seven configurations, a Si atom was added into the supercell. The Si atom was set at a high symmetry site in the TiN crystallite supercell, including at a eightfold coordinated hollow site (HL) in Fig. 5.1(a) connected with 4 N and 4 Ti, or at a fourfold coordinated hollow site (a plane hollow site, PHL) in Fig. 5.1(b) connected with 2 N and 2 Ti, or at a Ti position (replacing a Ti atom) in Fig. 5.1(c), or at a N position (replacing a N atom) in Fig. 5.1(d). The data in Table 5.1 are the ab initio calculation results, the total energies and the cohesive energies of the seven configurations above. In the table, the cohesive energy Ecoh is defined as 0ElEmEnEE SiTiNcoh  (5.1) 0E is total energy of the configuration concerned, EN, ETi, ESi are the energies of a N atom, a Ti atom, and a Si atom in vacuum, respectively. And n, m and l are the number of N, Ti, Si atoms contained in the supercell investigated. Table 5.1: The total energy and the cohesive energy of the configurations investigated. The values are in electron volts (eV). E0 is the total energy; Ecoh is the cohesive energy; and dEcoh is the cohesive energy difference between the TiN crystallite and the other configurations. The configurations of ~Si-HL, ~Si-PHL, Si-OCP-Ti, and ~Si-OCP-N are shown in Fig. 5.1. TiN-1N means that a N atom is missing in the TiN supercell, and TiN-1Ti means that a Ti atom is missing in the TiN supercell. TiN TiN-1Ti TiN-1N ~Si-HL ~Si-PHL ~Si-OCP-Ti ~Si-OCP-N E0 -629.98 -618.94 -618.98 -627.44 -624.55 -623.80 -620.60 Ecoh 451.13 442.41 443.39 447.81 444.93 446.49 444.25 dEcoh 0.00 -8.72 -7.74 -3.31 -6.20 -4.63 -6.88 Since the supercells used for the seven configurations had the same volume, their total energies or cohesive energies can be directly compared with one to another. Through the comparison of the data in Table 5.1, some important results of Si added into the TiN The atomic calculations with ab initio method 80 crystallite can be obtained. If there is no defect in the TiN crystallite, the Si addition is possible in the form of ~Si-HL or of ~Si-PHL. Since both cohesive energies of the ~Si-HL structure and the ~Si-PHL structure are smaller than that of the TiN structure, the Si atom cannot be added into the interstice of the TiN crystallite. This means that there is no silicon interstitial solid solution in the TiN crystallite in the thermal equilibrium condition. Fig. 5.2: The configuration of a Si atom added into a TiN crystallite supercell. A Si atom is at an eightfold coordinated hollow site in the TiN cell, noted ~Si-HL. A double cross tetrahedron Si-4N-4Ti is in the supercell center. The Si atom is shown on the red point. Fig. 5.3: The double cross tetrahedron Si-4N-4Ti consists of a small tetrahedron Si-4N and a large tetrahedron Si-4Ti with the same Si in the center of the TiN cell. The tetrahedron Si-4N is smaller than the TiN cell and the tetrahedron Si-4Ti is larger than the TiN cell. Therefore, the double cross tetrahedron Si-4N-4Ti is an intrinsic mismatch to the B1 NaCl structure TiN. If a Ti atom is missing in the TiN crystallite configuration, i.e. the configuration of TiN-1Ti, it is possible for a Si atom to occupy this vacant site and to form the configuration of ~Si-OCP-Ti because the cohesive energy of ~Si-OCP-Ti is larger than that of TiN-1Ti. The ~Si-OCP-Ti structure is a substitutional solid solution of Si in the TiN crystallite. The configurations of TiN-1N and ~Si-OCP-N can be analyzed in the The atomic calculations with ab initio method 81 same way. The structures of ~Si-OCP-Ti and ~Si-OCP-N are the crystalline structures proposed in the reference [Hultman07]. These structures could appear in the Ti-Si-N film with high propabobility because there are many voids in the TiN film [Sundgren85] and the inter diffusion of Si is easy, seeing Section 5.3. But since the cohesive energies of these two kinds of structures are smaller than that of the TiN crystallite and of the ~Si-HL structure, these two kinds of structures can exist in the Ti-Si-N composite only under the condition that Ti atoms or N atoms are missing. The configuration of ~Si-HL in Fig. 5.2 should be noted. It contains a new structure Si-4N-4Ti that the Si atom is connected with 4 N and 4 Ti. This is a double cross tetrahedron, a small tetrahedron Si-4N and a large tetrahedron Si-4Ti with the same Si atom in the center of TiN cell as shown in Fig. 5.3. This double cross tetrahedron leads to a relatively large distortion of the TiN cell so that the total energy of this configuration is higher and the cohesive energy is smaller than that of the TiN crystallite. The details of this double cross tetrahedron will be discussed below. The investigation in this subsection presents two important results: (1) there is no silicon interstitial solid solution in the TiN crystallite under the thermal equilibrium conditions; (2) if a Ti atom or a N atom is missing in the TiN crystallite, a Si atom is possible to occupy the vacant site to form the substitutional solid solution. 5.2.3. A Si atom in the boundary of TiN In this subsection, it is investigated whether a Si atom can be added into the TiN boundary. Generally, the boundary structure is very complex and it is difficult to create a boundary in the supercell. But, it is known that in the normal direction of the boundary plane, the distance between atoms in or near the boundary is a bit larger or smaller than that in the crystallite. Therefore, the lattice of the supercell may be changed a bit in one direction to mimic a boundary in the calculations. We define D as the boundary distance between the Ti atom and the N atom. It should be noted that a boundary is under non-equilibrium conditions. Thus, to investigate the system states in a given boundary situation, the cohesive energies of all the configurations should be compared with one to another in the same distance D condition. In total energy calculations, the supercell of 4  4  4 model was used, which contained four layers of atoms, 8 N and 8 Ti per layer. The k-points setting was also the The atomic calculations with ab initio method 82 same as that in the subsection above, a grid of 5 5 5. But at this time, the supercell was a boundary supercell. The lattice constant of the supercell was 4.262 Å in two directions, while the lattice constant equated (D2) Å in the third direction to produce a boundary situation. Six groups of calculations were performed. In every group of calculations, the distance D was same. In the six groups, D equated 1.90 Å, 2.00 Å, 2.131 Å, 2.35 Å, 2.55 Å, and 2.75 Å, respectively. And in every group of studies, the cohesive energies of the five configurations i.e. TiN, ~Si-HL, ~Si-PHL, ~Si-OCP-Ti, and ~Si-OCP-N, were calculated. Since the supercells used in every group had the same volume, the cohesive energies of the five configurations within the group could be directly compared with one to another. Table 5.2: The cohesive energies (eV) of TiN and Ti-Si-N configurations under the boundary condition. D is the distance of Ti-N in the boundary. 415 420 425 430 435 440 445 450 455 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 D (Å) C o h e s iv e e n e rg y ( e V ) TiN ~Si-HL ~Si-PHL ~Si-OCP-Ti ~Si-OCP-N Fig. 5.4: The cohesive energies (eV) of TiN and Ti-Si-N configurations under the boundary condition. D is the distance of Ti-N in the boundary. The lattice constant 4.262 Å corresponds to D= 2.131 Å. D (Å) TiN ~Si-HL ~Si-PHL ~Si-OCP-Ti ~Si-OCP-N 1.900 430.19 424.25 420.30 426.86 420.08 2.000 445.47 440.46 436.84 441.37 436.81 2.131 451.13 447.81 444.93 446.49 444.25 2.350 442.92 443.74 443.19 438.31 437.88 2.550 430.51 439.49 439.43 427.55 428.67 2.750 419.77 435.73 434.84 423.00 423.74 The atomic calculations with ab initio method 83 (a) (b) Fig. 5.5: The configurations of a Si atom added into the TiN boundary (A change of lattice constant is in the vertical direction, a0 = 4.700 Å, corresponding to D = 2.35 Å): (a) the structure of ~Si-HL, (b) the structure of ~Si-PHL. The Si atom is shown with the red point. A relaxation effect is obvious. The distances between Ti-N are large in the middle row, but they are relatively small in the top and bottom rows. The cohesive energies were calculated with the equation (5.1). The cohesive energies of the five configurations in the six groups above are listed in Table 5.2 and also presented in Fig. 5.4 which shows the trends clearly. Our emphasis places on the comparison of the cohesive energies within the group, i.e. under the same boundary distance D condition. If the distance D is smaller than 2.35 Å, the cohesive energies of the TiN configurations are larger than those of the other configurations with Si addition within the relevant groups. Evidently, the Si atom cannot be added into the crystallite of TiN or into the narrow boundary of TiN. Nevertheless, if the distance D is larger than 2.35 Å, the cohesive energy of the TiN boundary configuration decreases sharply and both cohesive energies of ~Si-HL and ~Si-PHL are larger than that of the TiN boundary configuration within the relevant groups. This indicates that the Si atom may move into the TiN boundaries, if the distance between the boundary atoms is larger than 2.35 Å. In order to understand the structure ~Si-HL and ~Si-PHL, we analyze the effect of Si addition in the TiN boundary. Two structures are shown in Fig. 5.5, which are the calculation results with D = 2.35 Å in the vertical direction. First, we discuss the configuration of ~Si-HL, namely the supercell with Si-4N-4Ti, [Fig. 5.5(a)]. It is known that if the boundary distance is large, the attractive force between the boundary atoms of different crystallites will increase. This attractive force will make the distance between The atomic calculations with ab initio method 84 atoms near the boundary increase. Thus, the stress becomes higher in the boundary local region. In this case, a Si atom moves into the boundary, it will bond itself with the boundary atoms Ti and N and form the double cross tetrahedron Si-4N-4Ti. This bonding will change the interaction relationship in the local region, weaken the effect of the attractive force between Ti and N atoms that belong to different crystallites, and reduce the changes of the distance near the boundary. In other words, this bonding relaxes the stress and reduces the strain of the crystallite near the boundary. The bond length of Si-Ti is 2.442 Å and the bond length of Si-N is 1.768 Å, as shown in Fig. 5.5(a). Both bond lengths are near the total relaxation state. It means that there is relatively little stress in the double cross tetrahedron Si-4N-4Ti, so that there is little stress in this boundary local region. Clearly, the Si addition in the boundary leads to a stress relaxation and a strain reduction in both of the boundary and the crystallite nearby. This should be the reason why the residual stress was very small [Bendavid05] and the morphology was improved significantly [Li92] in the experiments. Now, we consider the ~Si-PHL structure or the structure with Si-2N-2Ti, [Fig. 5.5(b)]. From the data in Table 5.2, we can see that the cohesive energy of the ~Si-PHL structure is very close to that of the ~Si-HL structure if D is larger than 2.35 Å. This means that the structure with Si-2N-2Ti has almost the same relaxation effect in the boundary as the structure with Si-4N-4Ti although these two structures are different from each other. Therefore, the structure with Si-2N-2Ti is also a favorable form in the TiN boundary. The Si atom can bond not only with 4N-4Ti but also with 2N-2Ti in almost the same level of energy in the boundary, which implies that Si can adapt well to the complex boundary situation. In Fig. 5.5(b), it is shown that the Si-Ti bond is largely compressed. Therefore, if D is smaller than 2.35 Å, the Si-2N-2Ti structure tends to transform to the form of Si-4N-4Ti. A purely nitrogen coordinated Si-4N tetrahedron was suggested to be an interface form in the Ti-Si-N composite coating [Hao06-3]. We calculated the cohesive energies of this Si-4N tetrahedron with the crystallite supercell (no lattice changing) or with the boundary supercell (the lattice changing in one direction), respectively. The calculation results show that there is no distortion problem of Si addition in the crystallite model [Fig 5.6(a)] and there is no relaxation function of Si addition in the boundary model [Fig 5.6(a)]. In the crystallite model, the cohesive energies of the configuration with the Si-4N tetrahedron is 16.33 eV smaller than that of the configuration with the Si-4N-4Ti double cross tetrahedron; and in the boundary model, it is 20.54 eV smaller than that of the configuration with Si-4N-4Ti. Therefore, the interface in the Ti-Si-N composite coating is more likely to be in the form of Si-4N-4Ti or Si-2N-2Ti. The atomic calculations with ab initio method 85 (a) (b) Fig. 5.6: The configuration of the Si-4N tetrahedron in the crystalline TiN with the absence of four Ti atoms: (a) in the crystallite model, there is no distortion with Si addition; (b) in the boundary model i.e. under the lattice change to 4.700 Å in the vertical direction, there is no relaxation effect with Si addition. The double cross tetrahedron Si-4N-4Ti or the fourfold coordinated plane unit Si- 2N-2Ti has not been identified through the characterization of Ti-Si-N probes yet. This ab initio calculation result indicates what and where should be searched in the characteriza- tion of Ti-Si-N film. It should be noted that our search for the basic structure of Ti-Si-N superhard coatings is under the condition of a clear and neat boundary. But, the real boundary may be much more complex. Generally, the complexity makes the boundary energy increase. In other words, we search the lowest-energy structure in some relatively low-energy arrangements. Therefore, our research result is acceptable. To summarize the above calculations and analysis, in the lowest-energy structure of Ti-Si-N superhard coating, Si atom is in the form of a double cross tetrahedron Si-4N- 4Ti and/or a fourfold coordinated plane unit Si-2N-2Ti in the boundary, i.e. the basic structure of Ti-Si-N superhard composite coating is the TiN crystallites with Si-4N-4Ti and/or Si-2N-2Ti in the boundaries. 5.2.4. The property of the interface and the Ti-Si-N coating From the above description, it is obvious that the double cross tetrahedron Si-4N-4Ti is The atomic calculations with ab initio method 86 different from the B1- NaCl structure of TiN. The Si-4Ti tetrahedron is larger than the TiN cell and the Si-4N tetrahedron is smaller than the TiN cell. Thus, there is an intrinsic mismatch between the Si-4N-4Ti structure and the TiN structure. This is one characteristic of Si-4N-4Ti. This intrinsic mismatch, as we will see below, leads to some covalent combinations. (a) (b) (c) (d) Fig. 5.7: The charge density distribution for the double cross tetrahedron Si-4N-4Ti under D = 2.35 Å condition: (a) the charge transfer is in a TiN(110) plane (full curve: charge increase and dot- dashed curve: charge decrease); (b) the charge density in a TiN(110) plane shows the covalent bond of Si-N1; (c) the local charge density in a TiN(110) plane shows the covalent bond of Si-N1; (d) the charge density in a TiN(001) plane shows the charge density mix of Ti1-N2. Another property of Si-4N-4Ti is the covalent combination. For ease of explanation, we name the atoms connected with Si atom as Ti1 and N1 and name those not connected with Si atom as Ti2 and N2. The Si addition leads to a transfer of the electron charge density as shown in Fig. 5.7(a). The charge density increases in the The atomic calculations with ab initio method 87 direction of Si-N1 as well as in the direction of Si-Ti1. The charge density in Fig. 5.7(b) and in Fig. 5.7(c) shows that the bond of Si-N1 is a strong covalent bond. The combination between Si and Ti1 is also a covalent bond which is not very strong. Since the bond of Si-Ti1 is relatively long, the covalent bonds of Si-Ti1 push the Ti1 atoms close to the N2 atoms and make their charge densities overlap, as shown in Fig. 5.7(d). The mix of the charge density increases the covalent constituent of the combination and strengthens the bonding of Ti1 and N2 which belong to the same crystallite. Similarly, there is also an intrinsic mismatch between the Si-2N-2Ti structure and the TiN structure, as shown in Fig. 5.5(b). The charge density image in Fig. 5.8 shows that in the Si-2N-2Ti structure, both the bonds of Si-N1 and Si-Ti1 are strong covalent bonds, and the Si-Ti1 bonds push the Ti1 atoms close to the N2 atoms, which leads to a mix of their charge density. In sum, in the middle of the boundary, there is a group of covalent bonds of Si-N1 and Si-Ti1; on both sides of the boundary, there are the covalent combinations from the charge density mix of Ti1 and N2. The boundary that is full of the covalent combinations certainly has great influence on the properties of the Ti-Si-N coatings. Fig.5.8: The charge density distribution for the parallelogram Si-2N-2Ti in a TiN(001) plane under D = 2.35 Å condition shows the covalent bond of Si-N1 and Si-Ti1 as well as the charge density mix of Ti1-N2 . A direct effect is that the covalent combination of Si-N1 and Si-Ti1 in the TiN boundary could strengthen the boundary, thus the hardness of the Ti-Si-N coatings is enhanced. This is one of the causes for the hardness enhancement of Ti-Si-N coatings. The atomic calculations with ab initio method 88 According to the properties of Si-4N-4Ti and Si-2N-2Ti, we can analyze the hardness enhancement. On the one hand, since the TiN boundary can be strengthened by Si addition, there are the more Si-4N-4Ti and Si-2N-2Ti structures in the boundary, the boundary is stronger. If the density of Si in the boundary is constant, the large-sized crystallite has larger boundary area, contains more Si-4N-4Ti and Si-2N-2Ti in the boundary, and hence is stronger than the small-sized crystallite with respect to restricting the grain boundary sliding. On the other hand, the material with small-sized crystallites has fewer dislocation sources in the crystallite and more boundaries to restrict the movement of the dislocation than the same material with large-sized crystallites. The material with small-sized crystallites, therefore, is harder than the same material with the large-sized crystallites in terms of resisting the dislocation movement and the deformation. Since the Si addition into TiN strengthens the boundary, the decrease of the crystallite size can at first lead to the increase of the hardness. On some crystallite size, the hardness reaches its maximum. If the crystallite size is reduced continually, the boundary becomes relatively weak, the grain boundary sliding begins to occur, and the hardness begins to decrease. This situation is showed in the experimental results of the Ti-Si-N coatings [Patscheider03] [Li92]. Here is an important hint. It implies that the hardness of Ti-Si-N nano-composite coating could continually be improved if the arrangement of different sized crystallites in the coating is carefully designed and prepared. For example, using some layers of the large-sized crystallites restricts the grain boundary sliding, and using some layers of the small-sized crystallites resists the dislocation movement and deformation. It alternatively repeats this arrangement in the film growth direction, like a multilayer. In the same layer, the arrangement of different sized-grain can also be made in any style. This means that the Ti-Si-N composite coatings should be not only a composition of different phases, TiN and Si-4N-4Ti, but also a composition of different sized crystallites, large- and small-sized crystallites. Note that this is just a qualitative analysis. To prove the 100 GPa hardness, further calculations and quantitative analysis are needed. Another obvious effect is that the covalent combination of Si-N1, Si-Ti, and Ti1- N2 restrict the inter diffusion through the boundary. It seems likely that Si-4N-4Ti and Si- 2N-2Ti locks the boundary region and leads to the absence of Ostwald ripening. Therefore, the Ti-Si-N coatings have very good thermal stability [Veprek00-2] [Veprek05]. The atomic calculations with ab initio method 89 With the properties of intrinsic mismatch and covalent combination, as well as the effects of the boundary enhancement and the inter-diffusion restriction, the interface Si- 4N-4Ti and Si-2N-2Ti work like a separation and fixation element in the rocksalt polycrystalline structure, i.e. they separate the crystallites and fix the boundary in the rocksalt polycrystalline structure. Most early transition metal nitrides and carbides have the rocksalt polycrystalline structure. Therefore, the interface structures, the double cross tetrahedron and/or the parallelogram, could be used to prepare nano-composites of transition metal nitrides and carbides with the addition of Si, Ge, or the like. The early transition metal nitrides and carbides combine three types of bonding: ionic, covalent, and metallic [Pieson96]. All of them have good conductivity. If the nanometer-sized (2-10 nm) crystallite of the transition metal nitrides and carbides is surrounded completely by the covalent boundary, their band structure may be changed. And then their electrical properties, optical properties and other properties could be engineered in a controlled way. The Fermi energy EF of TiN is 9.26 eV and the Fermi wavelength F is 0.40 nm. This Fermi wavelength is in atomic dimension, but the beat frequency with the lattice can be an order of magnitude larger. Thus, quantum effects may come into play if the crystallite size in the Ti-Si-N composite is smaller than 4 nm. However, in order to adjust the band structure and hence to tailor the electrical and optical properties, it is necessary to have a very precise control of the size and the shape of the nano-crystallite. And for obtaining the quantum effects, the crystallite size should be smaller than 4 nm, the difference in size should be very small, and the patterns should be very orderly. This is a big challenge of the fabrication. The interface structure Si-4N-4Ti and Si-2N-2Ti as a separation and fixation element will be very helpful to produce nanostructures, nano-patterns, or quantum dots. This is the potential value of the double cross tetrahedron interface structures. It paves the way for the further research. 5.2.5. Si atoms distribution in TiN The double cross tetrahedron Si-4N-4Ti is an intrinsic mismatch to the TiN structure, so that the Si distribution in the TiN boundary could have an influence on the strain, the stress, and the cohesive energy of the system. If some Si atoms are in the adjoined TiN cells, i.e. some Si atoms connect with the same Ti atom or N atom, the interaction of the distortions could lead to increase in strain and decrease in cohesive energy. To confirm this, the total energies and cohesive energies of the seven configurations were calculated. The atomic calculations with ab initio method 90 (a) (b) (c) (d) (e) (f) (g) Fig. 5.9: The distribution configurations of two Si atoms in the TiN: (a) two Si atoms are at the eightfold coordinated hollow sites of two parallel cells adjoined in the same layer, PA; (b) two Si atoms are at parallel cells separated in the same layer, PS; (c) two Si atoms are at the eightfold coordinated hollow sites of two diagonal cells adjoined in the same layer, DA; (d) two Si atoms are at two diagonal cells separated in the same layer, DS; (e) two Si atoms are at the eightfold coordinated hollow sitets of two spatially diagonal cells adjoined, SDA; (f) two Si atoms are at two spatially diagonal cells separated, SDS; (g) two Si atoms are at the eightfold coordinated hollow sites of two cells separated in a slope form in the same layer, SS. The square stands for Si, the triangle for Ti, and the circle for N. The supercell for this group of calculations contained six layers of atoms, 18 Ti and 18 N atoms per layer, for which a 333 Monkhorst-Pack k-points mesh was used. Two Si atoms were set at the eightfold coordinated hollow sites. The seven configurations were shown in Fig. 5.9: two Si atoms were in the parallel cells in the same layer - adjoined (PA) [Fig. 5.9(a)] or separated (PS) [Fig. 5.9(b)]; two Si atoms were in the diagonal cells in the same layer - adjoined (DA) [Fig. 5.9(c)] or separated (DS) [Fig. 5.9(d)]; two Si atoms were in the spatially diagonal cells, i.e. in different layers, - adjoined (SDA) [Fig. 5.9(e)] and separated (SDS) [Fig. 5.9(f)]; and two Si atoms were separated in a slope form in the same layer (SS) [Fig. 5.9(g)]. Because the supercells used in this group of calculations had the same volume, the cohesive energies of the seven configurations above could be directly compared with one to another. With the equation (5.1), the cohesive energies were calculated. The calculation The atomic calculations with ab initio method 91 results, the cohesive energies of the seven configurations above, are listed in Table 5.3. We can see that all the cohesive energies of two Si atoms distributions in TiN in the separated form are larger than those in the adjoined form. This means that the separation of the Si atoms in TiN is stabler. The distribution of the parallel-adjoined (PA) form is shown in Fig. 5.10(a) and the distribution of the parallel-separated (PS) form is shown in Fig. 5.10(b). It is clear that the distortions of two cells against each other in the PA form leads to a change in the distance between the Ti atom and the N atom on the adjoined face, which are 1.917 Å, 2.491 Å, and 2.304 Å as shown in Fig. 5.10(a), whereas the structure in PS form is in a relatively low strain situation. Table 5.3: The total energies and the cohesive energies of different Si distributions in TiN. The meaning of the abbreviations PA, PS, and so on are shown in Fig. 5.9. E0 is the total energy, Ecoh is the cohesive energy. PA PS DA DS SDA SDS SS E0 -2118.98 -2120.28 -2119.19 -2119.80 -2117.40 -2120.22 -2120.12 Ecoh 1513.80 1515.10 1514.01 1514.62 1512.23 1515.04 1514.94 The result here shows an effect of the distortion interaction introduced by the Si distribution. As mentioned above, Si has the other effect, namely, the strain relaxation in boundary region. The supercell used here is a crystallite supercell. Actually, the boundary supercell should be used to investigate the whole result of two effects, the strain increase with the TiN cell distortion confliction and the strain decrease with the relaxation in boundary region. However, with the large boundary supercells (6 6 6), the calculation of some Si distributions was very complicated, e.g. some holes appeared due to maintaining the volume of the supercell. It needs further research, how to investigate the Si distribution with a large boundary supercell. In the experiments with Ti-Si-N coatings, there is an interesting phenomena called ―self-hardening‖. The hardness of some Ti-Si-N coatings can increase upon annealing [Veprek05]. Since the separation of the Si atoms can cause to decrease the strain and to increase the cohesive energy of the system, the self-hardening may be an effect of the separation of collective Si atoms. The requirements that the TiN crystallite is completely surrounded by the Si-4N- The atomic calculations with ab initio method 92 4Ti and at the same time no Si-4N-4Ti is adjoined with one another impose a very strict demand on the preparation process. It is no doubt that the diffusion behavior of the adatom Si, Ti, and N during the formation process of Ti-Si-N coating is an important topic. Our relevant research results are reported in Section 5.3. (a) (b) Fig. 5.10: The distribution of Si in TiN: (a) two Si atoms in the parallel adjoined cells, (PA); (b) two Si atoms in the parallel separated cell, (PS). The two Si atoms are in the adjoin cell make the strain increase. Above investigation of Si distribution in TiN boundary is aimed to reduce the strain, seek largest cohesive energy, and improve the mechanical property of the Ti-Si-N composite. If the goal is to adjust the electronic band structure of the Ti-Si-N composite, the Si distribution in the TiN boundary is a total different topic. It needs further research. 5.2.6. The interface formation on the TiN(001) surface In this subsection, we report about the investigation into the formation of Si-4N-4Ti or Si- 2N-2Ti on the TiN(001) surface. In the investigation, two groups of calculations were conducted with the ab initio method. One group of calculation was to study the low- energy arrangement of Si adatom and a TiN island on the TiN(001) surface. The other one was to investigate whether a Si adatom could drop into the boundary on the TiN(001) surface or not. In both groups of investigations, the structure stability was evaluated with the comparison of the adsorption energies of different configurations. The atomic calculations with ab initio method 93 (a) (b) (c) (d) Fig. 5.11: The configurations of a Si atom and a 2N2Ti island on the TiN(001) surface. (a) a Si atom in the TiN island, Si-in-2N2Ti; (b) a Si adatom is beside the TiN island, Si-by-2N2Ti; (c) a Ti adatom is beside the island and Si occupies the Ti position of the island, Ti-by-2N1Ti1Si; (d) a N adatom is beside the island and Si occupies the N position of the island, N-by-2Ti1N1Si. The square stands for Si, the triangle for Ti, and the circle for N. In the first group of calculations, the arrangement of a Si adatom and a 2N2Ti island on a TiN(001) surface was studied. A TiN surface slab for this group of calculations was used which contained five layers of atoms, 8 Ti and 8 N atoms per layer, and seven layers (about 14.8 Å) of vacuum space. The two bottom layers of the five layers of atoms were fixed to mimic the confining effect of deeper layers, while the other three top layers were relaxed. The k-points setting was 5  5  1. The adsorption energies of the five configurations were calculated with this slab. One of the five configurations was an island of 2N2Ti on the TiN(001) surface. The other four configurations were the arrangements of a Si adatom and an island of 2N2Ti on the TiN(001) surface. The 2N2Ti island was in the center of the layer on the surface and a Si atom was set at the eightfold coordinated hollow site in the island [Fig. 5.11(a), noted Si-in-2N2Ti] or at the site beside the N of the island [Fig. 5.11(b), noted Si-by-2N2Ti]. The other two configurations were that (1) Si takes the Ti position of the island and Ti is at the site beside the N of the island [Fig. 5.11(c), Ti-by- 2N1Ti1Si]; (2) Si takes the N position of the island and N is at the site beside the Ti of the island [Fig. 5.11(d), N-by-2Ti1N1Si]. All the four configurations had five adatoms (a Si adatom, two Ti adatoms, and two N adatoms) on the TiN(001) surface, so that the adsorption energies of them could directly be compared with one to another. The calculation results, adsorption energies of the five configurations above, are listed in Table 5.4 and the Table 5.5, where the adsorption energy Ead is defined as configsSiaTiaNaad EEElEmEnE  (5.2) Econfig is the total energy of the configuration concerned; Es is the energy of the relaxed surface; EN, ETi, ESi are the energies of an N atom, a Ti atom, and a Si atom in vacuum, while na, ma and la are the numbers of N, Ti, Si adatom under the investigation. The atomic calculations with ab initio method 94 Table 5.4: The total energies Econfig and the adsorption energies Ead (eV) of a 2N2Ti island on the TiN(001) surface and of the configuration with a Si atom in or by the island. 2N2Ti Si-by-2N2Ti Si-in-2N2Ti Econfig -809.24 -814.52 -808.17 Ead 23.26 27.76 21.42 Table 5.5: The total energies Econfig and the adsorption energies Ead (eV) of different configurations of a Si atom, two N atoms and two Ti atoms on the TiN(001) surface. Si-by-2N2Ti Ti-by-2N1Ti1Si N-by-2Ti1N1Si Econfig -814.52 -813.80 -813.18 Ead 27.76 27.05 26.42 With these adsorption energy calculations, we want to know whether it is possible to build a Si-4N-4Ti structure on a TiN(001) surface in the full relaxation situation. The adsorption energy data in Table 5.4 show that this is impossible. The adsorption energy of Si-in-2N2Ti is much smaller than that of Si-by-2N2Ti, so that the Si adatom cannot move into the island of 2N2Ti and form the Si-4N-4Ti structure in this case. On the contrary, the arrangement of the Si adatom by the island of 2N2Ti as shown in Fig. 5.12(b) is a relatively stable structure. The double cross tetrahedron in Fig. 5.12(a) is already in the relaxation state, but the TiN cell is under large distortion. Thus, this structure is under larger stress and has smaller adsorption energy than that of the Si outside the island. This fact indicates that the relaxation of the double cross tetrahedron itself could not reduce the energy of the system. Only if it leads to a stress relaxation and a strain reduction in the cells nearby could the double cross tetrahedron have a positive effect on the system energy reduction. The data in Table 5.5 presents a clear picture. According to the comparison of adsorption energy, a Si adatom is more likely to take the place beside N of the island if it hits the island of TiN in the formation process. If a Ti adatom comes by, Si may give the place to the Ti adatom to continually decrease the system energy or increase the adsorption energy of the whole cluster, because the bond energy of Ti-N is larger than that of Si-N. Therefore, it is possible for the Si adatom to be always outside the TiN island in the island growth phase. The atomic calculations with ab initio method 95 (a) (b) Fig. 5.12: The configuration of a Si atom with a 2N2Ti island on the TiN(001) surface: (a) a Si atom is in the eightfold coordinated hollow site of the 2N2Ti island; (b) a Si atom is beside the 2N2Ti island. The Si atom in the island of 2N2Ti makes a large distortion of the TiN cell. In the second group of calculations, it was investigated whether a Si adatom on the surface could move into a boundary or not. The slab used in the this group of calculations contained five layers of atoms, 8 Ti and 8 N atoms per layer, and about 14.8 Å of vacuum space. The two bottom layers of the five atom layers were fixed, while the other three top layers were relaxed. The k-points setting is 5 5 1. This slab was a surface boundary slab. The lattice constant was 4.242 Å in two directions (X, Z). The direction Z was the normal direction of the surface and the direction X was parallel with the surface. To produce a boundary situation, the lattice constant was 5.100 Å in the direction Y that was parallel with the surface and perpendicular to the direction X. This lattice constant corresponded to the boundary distance D = 2.55 Å. The total energies of two configurations were calculated with this slab. One configuration was a Si adatom on the surface, exactly, on the top of a surface N atom. The other configuration was a Si atom into the boundary. Since the slabs had the same volume and both of the configurations contained the same number of atoms, the total energies of two configurations could directly be compared with each other. The total energy of a Si adatom on the surface is -751.392 eV, corresponding to the adsorption energy is 6.378 eV. The total energy of a Si into the boundary is -755.801 eV, corresponding to the adsorption energy is 10.787 eV. Obviously, the configuration of a Si into the boundary is a relatively stable structure. Therefore, Si The atomic calculations with ab initio method 96 adatom can drop into the boundary if it hit a boundary whose distance is larger than 2.55 Å. The calculation result shows the Si-2N-2Ti structure is formed in the boundary. The adsorption energy calculations in this subsection indicate that (1) the Si-4N- 4Ti structure cannot be built directly in the TiN island on the TiN(001) surface, (2) the Si adatom tends to stay outside the island of TiN in the film growth process, and (3) a Si adatom will drop into a boundary if it hits a boundary whose distance is larger than 2.55 Å. 5.2.7. The atomic percent of Ti: N: Si Fig. 5.13: The numerical description of Ti-Si-N hard composite structure: (a) the section view, (b) the axonometric draw of equiaxial crystal. After the identification of atomic structure of the Ti-Si-N superhard composite coating and the recognition of the Si distribution in the TiN boundary, the numerical description of Ti- Si-N composite structure can be obtained, Fig. 5.13. And then it is possible to calculate the atomic percent of Ti: N: Si, according to the grain size and the grain shape. In a perfect crystal, there are 52.4 nitrogen atoms and 52.4 titanium atoms in one nanometer cube of TiN. Since the distribution of silicon should be in a separating form, Si atoms are in one fourth of the total boundary cells. In this case, there are 26.2 silicon atoms, 52.4 nitrogen atoms, and 52.4 titanium atoms in one nanometer cube of boundary. If the size of an equiaxial crystallite is 2.94 nm with monolayer boundary (thickness = 0.235 or 0.255 nm), the atomic percent of Ti: N: Si should be 47.35 at%: 47.35 at%: 5.30 at%, seeing Appendix A. This atomic percent provides a basis to determine the process parameters and to analysis the experiment results. Comparing with the data in Table 2.1, this theoretical atomic percent of Si is low. Since there are many voids in TiN [Sundgren85], some Si The atomic calculations with ab initio method 97 may be in the form of substitutional solid solution in the experiment result. 5.2.8. The section summary In this section we have reported on the identification of the basic structure of Ti-Si-N superhard nano-composite coatings with the ab initio method. The conclusions are as follows. (1) The total energy calculations for all the possible stable configurations, in which a Si atom is added into the TiN crystallite or into the TiN boundary supercell, have been performed. The results show that (a) there is no silicon interstitial solid solution in the TiN crystallite under the thermal equilibrium conditions; (b) if a titanium atom or a nitrogen atom is missing in the TiN crystallite, a silicon atom is possible to occupy the vacant site and to form the substitutional solid solution; (c) in the lowest-energy structure of Ti-Si-N superhard coatings, Si atom is in the form of the double cross tetrahedron Si- 4N-4Ti and/or the fourfold coordinated plane unit Si-2N-2Ti in boundary, i.e. the basic structure of Ti-Si-N superhard composite coatings is the TiN crystallites with Si-4N-4Ti and/or Si-2N-2Ti in the boundaries. (2) A new kind of interface structure, the double cross tetrahedron Si-4N-4Ti and the the fourfold coordinated plane unit Si-2N-2Ti, is one of important discoveries in this research. The interface structures Si-4N-4Ti and Si-2N-2Ti are an intrinsic mismatch to the B1 NaCl structure TiN and their bonding type is different from that of TiN. The silicon atoms in the boundaries can relax the stress, reduce the strain, make the boundary stable, and separate the TiN crystallites. The covalent bonding of the interface structures Si-4N- 4Ti and Si-2N-2Ti could strengthen the boundary and restricts the inter diffusion through the boundary, so that the hardness and the thermal stability of Ti-Si-N nano-composite coatings are enhanced. According to our analysis, the hardness of Ti-Si-N coatings can continually be improved with the careful design and preparation of the arrangement of the different sized crystallites in the coating. Moreover, as a separation and fixation element, the double cross tetrahedron and the parallelogram may be very helpful to produce nano- composites of the early transition metal nitrides and carbides. This kind of interface can be used to control the grain size to improve not only the mechanical properties, but also the other properties such as the electrical, optical, superconductive properties, etc. The potential value of this interface lies in the production of nanometer patterns or quantum dots. The atomic calculations with ab initio method 98 (3) The investigation of silicon distribution in the TiN boundary demonstrates that the interaction of distortion can be avoided through the separation of silicon atoms in the TiN boundary and hence the strain becomes relatively small. According to the results of Ti-Si-N basic structure and the silicon distribution in the boundary, the atomic percent of Ti: N: Si can be calculated. For example, if the size of the TiN equiaxial crystallite is 2.94 nm, the boundary thickness is 0.235 nm, and Si atoms are in one fourth of the total boundary cells, the atomic percent of Ti: N: Si is 47.35%: 47.35%: 5.30% in the Ti-Si-N composite coating. (4) The formation of the double cross tetrahedron Si-4N-4Ti in the film growth process has also been studied. The result indicates that (a) the Si-4N-4Ti structure cannot be built directly in the island of TiN on the TiN(001) surface, (b) Si adatoms tends to stay outside the island of TiN in the film growth process, and (c) Si adatoms will drop into a boundary if it hits a boundary whose distance is larger than 2.55 Å. (5) The above research result reminds us that the numerical design is crucial to the development of nano-composites. The interface should be calculated with ab inito method because an atomic structure description of the interface is very important for analyzing the property of nano-composite. Since the super hardness of Ti-Si-N coatings has been identified, a lot of effort has gone into investigating some similar structures, such as nc- VN/a-Si3N4, Ti-B-N [Veprek99-2], nc-MeN/soft phase [Musil00], nc-TiC/a-C [Pascheider03], or M-X-N [Sandu06] in order to find out other nano-composite structures which have even higher hardness. For all research of this kind, the atomic calculations and the process simulation had better be performed before the experiment. 5.3. The basic diffusion behaviors of Ti, Si, N on the TiN (001) surface 5.3.1. Introduction In this section, we report on the investigations of the basic diffusion behaviors of Ti, Si, and N on the TiN (001) surface. The goals of the investigation are: (1) to recognize the formation mechanism of the Ti-Si-N hard coatings; (2) to build a theoretical basis to determine the process condition and parameters, such as the deposition temperature, the deposition rate, and so on; (3) to obtain the reference of activation energy Ea for the improvement of the off-lattice KMC simulation code. The atomic calculations with ab initio method 99 The investigation focuses on the basic diffusion, namely the diffusion of a single Ti, Si, N adatom and their cluster (the addimer, the adtrimer, the adtetramer) on the TiN(001) surface, around the TiN island, along the TiN island, and down the TiN island. These diffusion events are elementary events and very important for the evolution of the Ti-Si-N film growth. The diffusion behaviors depend largely on the activation energy of the diffusion. Therefore, the research mode is to investigate the potential energy surface (PES), to map the diffusion paths, and to calculate the activation energies. In the TiN film growth process, there is a preferred orientation (PO) transformation, i.e. the texture changes from amorphous to TiN(001) and to TiN(111) [Kajikawa03] [Li03] [Je97]. Studies report that the PO (002) of TiN film changed into (111) with increasing film thickness [Kajikawa03]. But, the some researches show that under the N2 + ion irradiation during the TiN deposition or with high N2 partial pressure, the TiN film maintained PO (002) [Petrov92] [Greene95] [Hultman95] [Gall03] [Beensh-M81] [Li02]. It is interesting that the preferred orientation of the TiN crystallite in the Ti-Si-N superhard coatings is also TiN(002) [Li92] [Chandra06]. In this research, the diffusion behaviors on the TiN(001) surface were investigated, undertaking the hope that the understanding of it might provide a insight on the texture evolution of this kind of coating. The ab initio method and the nudged elastic band method were used in the investigation. First, the adsorption energies of configurations, in which an adatom was set at the high symmetry sites on the TiN(001) surface, were calculated with ab initio method. According to the calculation results, a rough potential energy surface (PES) was obtained. The diffusion path of the adatom could be mapped through analyzing this rough PES. Then, along the diffusion path, the calculation was performed with the nudged elastic band method in order to obtain the curve of the energy difference along the diffusion path (E- Path), to search the saddle point, and to calculate the activation energy Ea. According to the activation energy Ea, the diffusion probability of the adatom could be evaluated. Finally, the formation mechanism of the Ti-Si-N composite coatings could be analyzed with the comparison of all the activation energies in the different diffusion. Since all the possible basic diffusion on the TiN(001) surface in the Ti-Si-N film growth should be calculated, the calculation quantity is very large. The investigation outline is as follows. (1) The PES of a single Ti, N, or Si adatom on the TiN(001) surface has been investigated. And then the diffusion paths have been mapped. Finally, the diffusion The atomic calculations with ab initio method 100 activation energies of the single adatom have been calculated. With the comparison of the PES and activation energies, the diffusion property and influence factors are discussed. The diffusion of a single Ti, N or Si adatom around the TiN island, along the TiN island, and down the TiN island have been also investigated. (2) Since TiN is a binary element alloy, the diffusion of the Ti-N and the Si-N addimer are important diffusion events. The diffusion modes and the activation energy of the Ti-N and the Si-N addimer on the TiN(001) surface, around the TiN island, along the TiN island, or down the TiN island have been investigated in detail. (3) The diffusion of the Ti-N-Ti, the N-Ti-N, the Ti-N-Si adtrimer and the diffusion of the 2N2Ti adtetramer on the TiN(001) surface have been studied to investigate their diffusion mode and diffusion behavious. (4) The inter diffusion is also very important events which influence the defect in the film structure. The activation energies of the inter diffusion of a Ti, N, and Si atom in the TiN crystallite and in the TiN(001) surface have been calculated. (5) The influence of Si addition on the N or Ti adatom diffusion is discussed. 5.3.2. The PES and the diffusion of a Ti, N, and Si adatom 5.3.2.1. The adatom’s PES and diffusion path on the TiN(001) surface In this part investigation, a surface slab of TiN(001) was used, which consisted of five layers of atoms, 8 Ti and 8 N atoms per layer, and seven layers (about 14.8 Å) of vacuum space. The two bottom layers of five atom layers were fixed to mimic the confining effect of deeper layers and the other three top layers were relaxed. This slab was termed 4  4  (5+7) model which was used in the calculations of diffusion on the TiN(001) surface. According to the method of Monkhorst-Pack, a grid of 5 5 1 k-points was employed. A single Ti adatom was set at the high symmetry site such as the top of a surface Ti (Top-Ti), the top of a surface N (Top N), the fourfold coordinated hollow site (HL), or the bridge site (BR), as shown in Fig. 5.14. The total energies of these configurations were The atomic calculations with ab initio method 101 calculated with the ab initio method and then the adsorption energies were computed with the equation (5.2). HL BR Top N Top Ti Fig. 5.14: The high symmetry points on the TiN(001) surface. Table 5.6: The total energies and adsorption energies of a single Ti, Si, or N adatom at some high symmetry sites on the TiN(001) surface. Ti Si N E0(eV) Ead(eV) E0(eV) Ead(eV) E0(eV) Ead(eV) HL -780.18 3.05 -778.75 3.17 -781.38 3.30 Top-Ti//HL -779.25 2.13 - - - - Top-Ti -777.58 0.45 -776.92 1.35 -780.86 2.78 BR -779.39 2.26 -778.31 2.74 -781.67 3.59 Top-N -780.02 2.89 -779.36 3.78 -781.56 3.49 Top-N//HL -779.90 2.77 -778.95 3.37 -781.96 3.88 HL -780.18 3.05 -778.75 3.17 -781.38 3.30 0.25 0.30 0.35 0.40 0.45 0.50 0.40 0.45 0.50 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Ead (eV) BR Top-Ti Top-N HL 0.25 0.30 0.35 0.40 0.45 0.50 0.40 0.45 0.50 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Ead (eV) BR Top-Ti Top-N HL 0.25 0.30 0.35 0.40 0.45 0.50 0.40 0.45 0.50 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Ead (eV) Top-Ti Top-N HL BR (a) (b) (c) Fig. 5.15: The rough potential energy surface (PES) of a Ti, Si, and N adatom on the TiN(001) surface: (a) the PES of a Ti adatom, (b) the PES of a Si adatom, and (c) the PES of a N adatom. The atomic calculations with ab initio method 102 Table 5.7: The adsorption energies, the bond lengths and the reference covalent radii [Dean99] of some combinations. The nearest neighbor The second near neighbor Ead (eV) Bond length (Å) Covalent bond (Å) Bond length (Å) Covalent bond (Å) Ti-TopTi 0.45 Ti-Ti = 2.489 Ti-Ti = 1.32 + 1.32 (4) Ti-N =3.162 Ti-N = 1.32 + 0.70 Ti-TopN 2.89 Ti-N = 1.837 Ti-N = 1.32 + 0.70 (4) Ti-Ti = 2.932 Ti-Ti = 1.32 + 1.32 N-TopTi 2.78 Ti-N = 1.694 Ti-N = 1.32 + 0.70 (4) N-N = 3.113 N-N = 0.70 + 0.70 N-TopN 3.49 N-N = 1.335 N-N = 0.70 + 0.70 (4) N-Ti = 2.516 N-Ti = 0.70 + 1.32 N-DBasin 3.88 N-N = 1.398 N-N = 0.70 +0.70 (2) N-Ti = 2.043 (2) N-Ti = 3.132 N-Ti = 0.70 + 1.32 Si-TopTi 1.35 Si-Ti = 2.511 Si-Ti = 1.17 + 1.32 (4) Si-N = 3.368 Si-N = 1.17 + 0.70 Si-TopN 3.78 Si-N = 1.796 Si-N = 1.17 + 0.70 (4) Si-Ti = 2.818 Si-Ti = 1.17 + 1.32 Si-HL 3.17 (2) Si-N = 2.043 Si-N = 1.17 +0.70 (2) Si-Ti = 2.450 Si-Ti = 1.17 + 1.32 (a) (b) (c) (d) (e) (f) Fig. 5.16: The charge density of some configurations: (a) a Ti adatom on the top of a surface Ti, (b) a Ti adatom on the top of a surface N, (c) a N adatom on the top of a surface Ti, (d) a N adatom on the top of a surface N, (e) a Si adatom on the top of a surface Ti, (f) a Si adatom on the top of a surface N. The adsorption energies are listed in Table 5.6 and also presented in Fig. 5.15(a) which is the rough PES of a Ti on the TiN(001) surface. In similar way, the total energy and the adsorption energy of the configurations for a Si adatom and a N adatom were also calculated. The adsorption energies results are also listed in Table 5.6 and the rough PES of a Si adatom and of a N adatom on the TiN(001) surface are presented in Fig. 5.15(b) and Fig. 5.15(c), respectively. Some bond lengths and the reference covalent radii are listed in Table 5.7. And The atomic calculations with ab initio method 103 some charge density figures are presented in Fig. 5.16. The properties of the PES and the diffusion paths of a single Ti, N, and Si adatom on TiN(001) are discussed as follows. (1) One of the important points here is a clue to the preferred orientation transformation from TiN(001) to TiN(111). The basin sites of the PES of a Ti adatom on the TiN(001) surface are at the fourfold coordinated hollow site and on the top of N. The diffusion path of a Ti adatom is from a hollow site through the top of N to next hollow site. At the hollow site and on the top of N, Ti adatom has almost the same adsorption energy, the difference between them is only 0.16 eV. And at these two basin sites, the distance between the Ti adatom and the TiN(001) surface is also almost same. If two Ti adatoms are above the surface N and one Ti adatom is at a hollow site or two Ti adatoms are at hollow sites and one Ti adatom is on one top of N, these three Ti adatoms will form a TiN(111) nucleus on the TiN(001) surface. To confirm this, the total energies of some (111) and (001) configurations with three Ti atoms, four Ti atoms or five Ti atoms were calculated. The calculation results indicate that (a) the (001) configuration is more stable than the (111) configuration; (b) the total energy difference between (001) and (111) configurations is very small, 0.013 eV/adatom for three Ti adatoms configurations, 0.090 eV/adatom for four Ti configurations, and 0.213 eV/adatom for five Ti configurations. This means that the (111) nuclei of Ti atoms is possible to be built on TiN(001) surafec. This might be a cause of the preferred orientation transformation from TiN(001) into TiN(111). The PO transformation from (001) into (111) also depends on the diffusion of N adatom. If a Ti adatom is above a surface Ti, the adsorption energy of the Ti adatom is down to the minimum, of 0.45 eV. This reflects that (i) the bond of Ti-Ti is weak; and (ii) the interaction of Ti-N is relatively weak if the distance between the Ti adatom and surface N atoms is large to 3.162 Å. The weak bond of Ti-Ti has large influence on the diffusion of a Ti adatom along the TiN island. (2) The PES of the N adatom on the TiN(001) surface is very interest. The deepest basin is between the top of N and the fourfold coordinated hollow site, noted D-Basin. At D-Basin, the largest adsorption results from the strong covalent bond of N-N and the interaction between this N adatom and two surface Ti atoms, the second nearest neighbors. Symmetrically, there are four D-Basin positions around a surface N atom. One diffusion path of the N adatom is from a D-Basin through a bridge (BR) site to the next D-Basin, namely the N adatom diffuses around the surface atom N. Another diffusion path of the N adatom is from a D-Basin through a hollow site to the next D-Basin. The atomic calculations with ab initio method 104 If a N adatom is on the top of a surface N atom, the bond length of N-N is 1.335 Å, short than 1.400 Å, which results from the four Ti-N interactions. This shows that the force of Ti atom has a long range effect. On the TiN(001) surface, the smallest adsorption energy of a N adatom is above a surface Ti. It is not beneficial to the TiN(001) film growth. This smallest adsorption energy, actually, is not very small, of 2.78 eV. Comparing with the adsorption energy of the Ti adatom on the top of N which is of 2.89 eV, the difference between them shows that the interaction of Ti-Ti has a long range effect and the interaction of N-N has a short range effect. Both of the long range effect and the short range effect have a strong influence on the diffusion behaviors. (3) On the PES of a Si adatom, the adsorption energy reaches the maximum if the Si adatom is on the top of a surface N atom. This means that the Si-N binding energy is relative large and the interaction between Si and Ti has a long range effect. The adsorption energy goes to the minimum if Si adatom is on the top of a surface Ti. The bond length of a Si adatom and a surface Ti atom, of 2.511 Å, reveals a strange phenomenon that the surface atoms N might repel the Si adatom as shown in Fig. 5.16(e). The diffusion path of a Si adatom on the TiN(001) surface is from the top of a surface N through a hollow site to the next top of a surface N. (4) The surface Ti atoms as the second near neighbors attract the adatom as shown in Fig. 5-3-3(b), (d), and (f). But the surface N atoms repel the covalent bonded pair atoms shown in Fig. 5-3-3(c) and (e). This repulsive effect is very strong if a N2 molecular is deposited on the TiN(001) surface. The N2 molecular cannot adsorb on the top of a surface N and can only adsorb on the top of surface Ti with very small adsorption energy, 0.380 eV. This means that N2 molecular may very easily desorbs from the TiN(001) surface. (5) The bond lengths and the binding energies have crucial influence on the PES of a Ti, Si and N adatom. The bond lengths of Ti-Si-N, from short to long, are N-N, N-Si, N-Ti, Si-Si, Si-Ti, and Ti-Ti. The binding energies of Ti-Si-N, from strong to weak, are N- N, N-Ti, N-Si, Si-Si, Si-Ti, and Ti-Ti. The bond lengths and the binding energies of Si-N and Si-Ti are just between the bond lengths and the binding energies of N-N, N-Ti and that of Ti-Ti. This is an important factor for the Si addition to change the formation mechanism of TiN. The atomic calculations with ab initio method 105 Table 5.8: The energy difference along the diffusion path of a Ti, N, and Si adatom on TiN(001). E0 is the total energy of the configuration investigated and Ediff is the energy difference between the energy of the initial point and that at the sites along the diffusion path. The unit of E0 and Ediff is eV and the unit of the path is nm. The unit is the same in this section. Ti: Top-N to HL Si: Top-N to HL N: D-Basin to HL N: D-Basin to BR Path E0 Ediff Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.00 -780.02 0.16 0.00 -779.36 0.00 0.81 -781.96 0.00 0.08 -781.96 0.00 0.03 -779.61 0.57 0.03 -778.93 0.43 0.98 -781.47 0.48 0.07 -781.56 0.40 0.05 -779.56 0.62 0.05 -778.74 0.62 1.04 -781.14 0.82 0.06 -781.51 0.44 0.08 -779.59 0.59 0.09 -778.53 0.83 1.23 -780.89 1.06 0.05 -781.42 0.54 0.12 -779.78 0.40 0.12 -778.43 0.93 1.39 -780.98 0.97 0.05 -781.34 0.62 0.15 -780.18 0.00 0.15 -778.75 0.61 1.50 -781.38 0.58 0.04 -781.67 0.29 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.04 0.08 0.12 0.16 Path(nm) (e V ) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.04 0.08 0.12 0.16 Path(nm) (e V ) (a) (b) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.04 0.08 0.12 0.16 Path (nm) (e V ) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.04 0.08 0.12 0.16 Path (nm) (e V ) (c) (d) Fig. 5.17: The energy difference along the diffusion path (E-Path) of a Ti, Si, and N adatom on the TiN(001) surface: (a) the diffusion of a Ti adatom from Top-N to a hollow site; (b) the diffusion of a Si adatom from Top-N to a hollow site; (c) the diffusion of a N adatom from the site of D-Basin to a hollow site; and (d) the diffusion of a N adatom from the BR site to the site of D-Basin. In order to obtain the diffusion activation energy, the nudged elastic band NEB method [Mills95] [Henkelman00] was used to calculate total energies of a set of configurations along the diffusion path of Ti adatom. In the NEB calculations, the adatom The atomic calculations with ab initio method 106 relaxation is limited to a plane perpendicular to the diffusion path between initial and final positions while the surface atom relaxation is unconstrained, seeing Appendix B. The calculation results are listed in Table 5.8. The energy differences were obtained through subtracting the total energy at the initial position from those at a series of sites along the diffusion path. The curve of E-Path, which is a section of the PES along the diffusion path, is presented in Fig. 5.17(a). It should be noted that the E-Path curve is a bi-direction curve, which shows the system energy change during the diffusion of the Ti adatom between the top of a surface N and the hollow site. From the curve, the activation energy Ea from the hollow site to the top of a surface N can be obtained, of 0.62 eV which is underlined in Table 5.8, whereas the activation energy from the top of a surface N to the hollow site could be calculated. It is 0.46 eV. Similarly, the calculations along the diffusion path of a Si adatom and two diffusion paths of a N adatom were also performed with the nudged elastic band method. The results are listed in Table 5.8 and the E-Path curves are presented in Fig. 5.17(b), (c), and (d), respectively. The activation energy Ea for the diffusion of a Ti adatom is relatively small, of 0.62 eV, so that a Ti adatom may diffuse easily on the TiN(001) surface. With Ea = 0.62 eV, a N adatom diffuses easily around a surface N atom, whereas a N adatom is relatively difficult to diffuse from a D-Basin site through a hollow site to the next D-Basin site, because the relevant activation energy Ea is 1.06 eV. And the E-Path curve in Fig. 5-3-4(c) shows the short range effect of the interaction of N-N. The diffusion probability of a Si adatom on the TiN(001) surface is relatively low due to the activation energy Ea = 0.93 eV. But a Si adatom above a surface N has the largest adsorption energy, of 3.78 eV, so that the nucleation may easily occur beside the Si adatom. The calculations and analysis above provide the clue to the preferred orientation transformation from (001) to (111). This transformation is based on three points: (a) Ti adatoms diffuse much more easily than N adatoms on the TiN(001) surface; (b) Ti adatoms are possible to create the nucleus of TiN(111) on the TiN(001) surface; (c) N adatoms diffuse mostly around the local surface N atom. Therefore, the transformation from (001) to (111) may be restricted by preventing Ti adatoms from the collection. As the mention above, under the N2 + ion irradiation during TiN deposition or with increasing N2 partial pressure, the TiN film will maintain the preferred orientation (002). With the N2 + ion irradiation and the N2 partial pressure increasing, N2 + ions have more chance to combine with Ti adatoms [Gall03], so that the formation of (111) nuclei of Ti adatoms is The atomic calculations with ab initio method 107 restricted. In fact, this equals to using more N2 + ions deposition to replace the diffusion of N adatoms. On the other side, since the adsorption energy of N2 is very small on the TiN(001) surface, if the N2 + ion hits the N adatom, they will form a N2 molecular and easily desorbs from the surface. Thus, to a certain extent, the more N2 + ion deposition cannot lead to the N content increase in the TiN film. In the Ti-Si-N deposition, since the basin and the diffusion path of a Si adatom are as same as those of a Ti adatom, Si adatom will influence the diffusion of Ti adatoms. Therefore, more Si difusion could restrict the collection of Ti adatoms and hence maintain the preferred ornietation of TiN (001) [Chandra06]. 5.3.2.2. Adatom diffusion around the TiN island P1 P2 P3 P4 P5 P6 Fig. 5.18: The single adatom diffuses around the island of 2Ti2N In order to precisely control the grain size and the grain shape in film growth process, it is necessary to investigate the diffusion of a single adatom around an island, along an island, and down an island. In this subsection, we introduce the investigation into the adatom diffusion around an island. In the investigation, a surface slab of TiN(001) was used which consisted of five layers of atoms, 18 Ti and 18 N atoms per layer, and seven layers (about 14.8 Å) of vacuum space. The two bottom layers of five atom layers were fixed and the other three top layers were relaxed. This slab is termed as 6 6 (5+7) model which was used in all the calculations for the diffusion around the TiN island, along the TiN island, and down the TiN island. A Monkhorst-Pack k-points mesh 3 3 1 was used. An island of 2N2Ti was built in the center of the TiN(001) surface. The 2N2Ti island and relevant five positions beside the island were marked in the Fig. 5.18 which was used to explain the diffusion path of an adatom. Because the binding energies of Ti-Ti and that of Ti-Si are small and their bond lengths are long, the total energies of the configurations with a Ti adatom or a Si adatom at the site P2 are very high. Under the relaxation, the Ti adatom or the Si adatom will slide to the site P5, a basin site. The atomic calculations with ab initio method 108 First, a Si adatom diffusing around this 2N2Ti island was investigated. The total energies of the configurations with a Si adatom at the site P1, the site P5, the site P3, or the site P4 were calculated. After that, the nudged elastic band method was used to calculate total energies along the diffusion path of the Si adatom, i.e. from the site P3 to the site P4, from the site P3 to the site P5, and from the site P5 to the site P1. The calculation results of the Si adatom diffusing around the island are listed in Table 5.9 and the E-Path curves are presented in Fig. 5.19. Table 5.9: The total energy and the different energy of a Si adatom diffusing around the island of 2N2Ti. Si: P3 - P4 Si: P3 - P5 Si: P5 - P1 Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.03 -1782.76 0.00 -0.03 -1782.76 0.00 0.00 -1782.17 1.07 0.03 -1782.70 0.06 0.05 -1782.20 0.56 0.07 -1781.91 1.33 0.05 -1782.49 0.27 0.11 -1781.90 0.86 0.12 -1781.70 1.54 0.08 -1782.14 0.62 0.17 -1781.71 1.05 0.19 -1782.10 1.14 0.12 -1781.73 1.03 0.23 -1781.92 0.84 0.24 -1782.93 0.31 0.15 -1781.51 1.25 0.30 -1782.17 0.59 0.28 -1783.24 0.00 0.0 0.5 1.0 1.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 0.5 1.0 1.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.19: The E-Path of a Si adatom diffusing around the island of 2N2Ti: (a) between the site P3 and the site P4, (b) between the site P3 and the site P5, (c) between the site P5 and the site P1. The atomic calculations with ab initio method 109 Table 5.10: The total energy and the different energy of a Ti adatom diffusing around the island of 2N2Ti. Ti: P3 - P4 Ti: P3 - P5 Ti: P5 - P1 Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.02 -1784.90 0.00 0.02 -1784.90 0.00 0.30 -1783.83 0.00 0.04 -1784.84 0.06 0.05 -1784.65 0.25 0.25 -1783.71 0.11 0.06 -1784.59 0.31 0.09 -1783.75 1.15 0.19 -1783.57 0.26 0.09 -1784.11 0.79 0.14 -1783.38 1.52 0.14 -1783.38 0.45 0.12 -1783.76 1.14 0.21 -1782.95 1.95 0.09 -1783.01 0.82 0.15 -1783.78 1.12 0.27 -1782.94 1.97 0.04 -1782.94 0.89 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.20: The E-Path of a Ti adatom diffusing around the island of 2N2Ti: (a) between the site P3 and the site P4, (b) between the site P3 and the site P5, (c) between the site P5 and the site P1. The calculations for a Ti adatom diffusing around the 2N2Ti island are the same as those of a Si adatom diffusion. The calculation method for a N adatom diffusing around the 2N2Ti island is similar. The four basin sites for a N adatom are the site P1, the site P2, the site P3, and the site P4, respectively. The results of a Ti adatom diffusing around the island are in Table 5.10 and in Fig. 5.20. The results of a N diffusing adatom around the island are in Table 5.11 and shown in The atomic calculations with ab initio method 110 Fig. 5-3-7. A low-energy basin of a Si adatom is beside the N atom of the island, namely at the site P3. From the site P3, a Si adatom can diffuse to the site P4 (the corner N of the island) or to the site P5. The activation energy along the diffusion path of P3-P4 or along P3-P5 is Ea =1.25 eV or Ea =1.05 eV. The lowest-energy basin for a Si adatom is at the site P1 (the Ti corner of the island). The activation energy Ea for a Si adatom to diffuse out from the site P1 to the site P5 is 1.54 eV. This highest activation energy is the activation energy for a Si abatom to diffuse around the island. Clearly, the total energies of the configurations and the energy differences along the diffusion path disclose the diffusion behaviors of a Si adatom. According to the activation energies, a Si adatom seems like to diffuse from the site P3 to the site P5, then to fall into the site P1 and to be fixed there. Only if it obtains enough energy, larger than 1.54 eV, can it jump out the site P1 and diffuse around the island. This example shows the way that the diffusion behaviors can be revealed by the ab initio calculation results. In comparison with the Si adatom diffusion, the Ti adatom diffusion around the island is relatively difficult. The lowest-energy basin for a Ti adatom is at the site P3, beside the N atom of the island. The activation energy Ea for a Ti adatom to jump out this basin to the site P5 is 1.97 eV. This is the activation energy for a Ti adatom around the island. The Ti adatom bonds itself with two N atoms and five Ti atoms at the site P3, while it bonds itself with one N atom and four Ti atoms at the site P5. This combination difference leads to the high activation energy. The diffusion behaviors of Ti adatom around the island is that Ti adatom diffuses easily from the site P1 to the site P5, then to fall into the site P3 and to swing around the N corner of the island; only if its energy is larger than 1.97 eV can it diffuse around the island. Table 5.11: The total energy and the different energy of a N adatom diffusing around the island of 2N2Ti. N: P2 - P1 N: P2 - P3 N: P3 - P6 Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.03 -1786.95 0.00 0.03 -1786.95 0.00 0.09 -1784.96 0.00 0.06 -1786.90 0.04 0.04 -1786.56 0.39 0.08 -1784.76 0.20 0.08 -1786.74 0.21 0.09 -1785.17 1.78 0.07 -1784.42 0.54 0.10 -1786.47 0.47 0.16 -1783.92 3.02 0.06 -1784.42 0.54 0.13 -1786.24 0.70 0.20 -1784.83 2.12 0.05 -1784.77 0.19 0.15 -1786.15 0.79 0.24 -1786.15 0.79 0.05 -1784.95 0.01 The atomic calculations with ab initio method 111 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.21: The E-Path of the N adatom diffusing around the island of 2N2Ti: (a) between the site P2 and the site P1, (b) between the site P2 and the site P3, (c) between the site P3 and the site P6. The N adatom diffusing around the island is even more difficult. The activation energy Ea for the N adatom to diffuse around the island is high to 3.02 eV. Therefore, the N adatom might stay at the site P2 or swing around the Ti corner of the island. The high activation energy will be analyzed in Section 5.3.2.3. Obviously, the Si adatom diffusing around the island is relatively easy. The Si adatom diffusion around the TiN island could help the diffusion of Ti adatoms and N adatoms. This is a positive effect of the Si adatom in the Ti-Si-N formation. 5.3.2.3. Adatom diffusion along the TiN island In this part of the research, the slab of 66 (5+7) model and the k-points setting 3 3 1 were used. An island of 6N6Ti was built on the TiN(001) surface, (Fig. 5.22). The low- energy basin of a Ti adatom or a Si adatom was at the site P2. The diffusion path of a Ti adatom or a Si adatom along the island was from the site P2 through the site P3 to the site P4. The low-energy basin of a N adatom was at the site P1. The diffusion path of a N adatom along the island was from the site P1 to the site P2. The calculation results are listed in Table 5.12 and the E-Path curves are presented in Fig. 5.23. The atomic calculations with ab initio method 112 P1 P2 P3 P4 P5 1 2 3 4 Fig. 5.22: The single adatom diffusion along the TiN island. Table 5.12: The total energy and the different energy of a single adatom diffusing along the island. Ti N Si Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.01 -1862.62 0.00 0.02 -1863.67 0.00 0.02 -1860.37 0.00 0.04 -1862.10 0.52 0.06 -1863.18 0.49 0.05 -1859.66 0.70 0.09 -1860.91 1.71 0.09 -1862.01 1.66 0.10 -1858.97 1.39 0.15 -1860.42 2.19 0.14 -1861.62 2.04 0.17 -1858.70 1.67 0.21 -1859.94 2.67 0.18 -1861.78 1.89 0.23 -1858.93 1.43 0.28 -1859.91 2.71 0.24 -1861.77 1.90 0.30 -1859.27 1.10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.23: The E-Path of the single adatom diffusing along the island of 6N6Ti: (a) a Ti adatom diffusing between the site P2 and the site P3, (b) a N adatom diffusing between the site P1 and the site P2, and (c) a Si adatom diffusing between the site P2 and the site P3. The atomic calculations with ab initio method 113 Comparing with the diffusion around the island, the Ti adatom diffusing along the island is even more difficult because the activation energy is high to 2.71 eV. The E-Path curve shows that the high activation energy results from the energy difference of the initial site and the final site, Fig. 5.23(a). At the site P2, the Ti adatom connects with two N atoms and six Ti atoms. But at the site P3, the Ti adatom combines with only one N atom and four Ti atoms. Therefore, as the Ti adatom diffuses from the site P2 to the site P3, the system loses one Ti-N binding and two Ti-Ti bindings. Comparing with the activation energy of the Ti adatom diffusion around the island, it is strange that one weak Ti-Ti binding has so large influence on the configuration energy. If a N adatom diffuses from the site P1 to the site P2, a bond of N-N is built between the N adatom and the N atom of the island. The activation enrgy for the N adatom diffusing around the TiN island is to 2.04 eV. It is interesting to compare the E- Path curve of N adatom along the island with that around the island. In both cases, the energy difference between the initial site and the final site is same. But in the case of around the island, the activation energy is very large, high to 3.20 eV. Where does this large energy difference come from? The difference of the two cases is that the N atom of 6N6Ti island is fixed by the Ti atoms nearby and it cannot move. Therefore, this large energy difference implies that N-N bond may be built very difficultly if the N atom of the island is not fixed. The activation energy of the Si adatom diffusing along the island is relatively small, of 1.67 eV, so that the Si adatom can easily diffuse along the island. It should be noted that the island of 2N2Ti can be seen as an island with the shortest side and the island of 6N6Ti is an island with the longest side. The activation energy of the Ti adatom diffusing around the island of 2N2Ti is of 1.97 eV, whereas the activation energy of the Ti adatom diffusing along the island of 6N6Ti is of 2.71 eV. This means that the diffusion of the Ti adatom along the long side island is more difficult than along the short side island. In contrary, the diffusion of the N adatom along the short side island is more difficult than along the long side island. Obviously, the diffusion of Ti adatoms and N adatoms around and along the island are main difficulty in the TiN film growth process. The atomic calculations with ab initio method 114 5.3.2.4. Adatom diffusion down the TiN island P1 P2 P3 P4 P5 1 2 P3 P4 P3 P5 Fig. 5.24: The single adatom diffusion down the TiN island. In the calculations of this investigation, the slab of 6 6 (5+7) model and the k-points setting 331 were employed. To study a single adatom diffusing down the TiN island, an island of 12N12Ti was built on the surface. First, the total energies of some configuration, in which an adatom was set at the high symmetry sites on the island and nearby the island, were calculated. On the island, the low-energy basins of a Ti adatom are at the site P5, at the site P3, and at the site P4, (Fig. 5.24). Due to the relaxation effect, the lowest-energy basin is at the site P4, namely the edge of the island. The lowest-energy basin for a Si adatom on the island is also at the site P4. Both the low-energy basins of Ti and Si adatom beside the island on the surface are at the site P2. The diffusion path of a Ti adatom or a Si adatom down the island is from the site P5 through the site P4 to the site P2. Both the low-energy basins of a N adatom on the island are at the deep basin near the site P5 and near the site P4, and the low-energy basin beside the island on the surface is at the site P1. The diffusion path of a N adatom down the island is from the deep basin near the site P5 through the deep basin near the site P4 to the site P1. The calculations along the diffusion path were conducted with the nudged elastic band method. The calculation results are listed in Table 5.13 and the E-Path curves are presented in Fig. 5.25. Table 5.13: The total energy and the different energy of a single adatom diffusing down the island. Ti N Si Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.03 -1978.69 0.00 0.10 -1980.73 0.00 0.04 -1978.06 0.00 0.08 -1978.74 -0.05 0.14 -1980.61 0.12 0.07 -1977.96 0.10 0.14 -1979.02 -0.33 0.20 -1980.65 0.08 0.13 -1977.86 0.20 0.20 -1979.61 -0.93 0.28 -1980.20 0.53 0.18 -1978.10 -0.04 0.24 -1980.60 -1.92 0.34 -1980.73 0.00 0.23 -1978.44 -0.38 0.29 -1981.09 -2.41 0.38 -1981.86 -1.13 0.28 -1978.71 -0.65 The atomic calculations with ab initio method 115 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.00 0.10 0.20 0.30 Path (nm) (e V ) -2.50 -1.50 -0.50 0.50 1.50 0.00 0.20 0.40 Path (nm) (e V ) (a) (b) -2.50 -1.50 -0.50 0.50 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.25: The E-Path of the single adatom diffusing down the island of 6N6Ti: (a) an adatom Ti from the site P4 to the site P2, (b) an adatom N from the site P3 to the site P1, and (c) an adatom Si from the site P4 to the site P2. The activation energy of a Ti adatom diffusing from the site P5 to the site P4 is very low, of 0.10 eV and for diffusing down the island is 0.00 eV. The activation energy of a Si adatom diffusing from the site P5 to the site P4 is lower than that of its diffusion on surface, of 0.79 eV and for diffusing down the island is 0.20 eV. The activation energy of a N adatom diffusing from the deep basin near the site P5 to the deep basin near the site P4 is 0.51 eV and for diffusing down the island is also small, of 0.53 eV. Therefore, the growth mode of the Ti-Si-N film on TiN(001) could be in the Frank-van der Merwe (FM) mode, i.e. the layer-by-layer mode. The short summary of the diffusion behaviors of the single Ti, N, or Si adatom on TiN(001) are follows. (1) The activation energy of the Ti adatom diffusing on the TiN(001) surface is relatively small so that Ti adatoms could diffuse easily on the surface. However, both the activation energies of the Ti adatom diffusing around the TiN island or along the TiN island are very large, namely, 1.97 eV and 2.71 eV. Therefore, the Ti adatoms diffuses The atomic calculations with ab initio method 116 difficultly around or along the island. (2) The combination of N-N is a strong covalent bond and has a short range effect. As the result, the lowest-energy basins of a N adatom are around a surface N atom. The most diffusion of N adatoms on the TiN(001) surface is to run around the surface N atom. The activation energies of N adatoms diffusing around and along the TiN island are also very large, i.e. 3.20 eV and 2.04 eV, so that N adatoms diffusing around or along the island is difficult, too. The above two points leads to insufficient diffusion of Ti adatoms and N adatoms in the TiN film growth process. Therefore, the TiN coating has normally many voids and the columnar structure. The PES of a Ti adatom and the difference of diffusion behaviors between Ti adatoms and N adatoms on the TiN(001) surface may lead to the preferred orientation transformation from (001) to (111). (3) Relatively, the activation energies of the diffusion of Si adatoms are small, especially in the case of diffusing around and along the TiN island. The easy diffusion of Si adatoms could promote the diffusion of N and Ti adatoms. (4) All the activation energies of Ti, Si, and N adatoms diffusing down the TiN island are very small, so that the Ti-Si-N film growth is in a layer-by-layer mode, namely the Frank-van der Merwe (FM) mode. 5.3.3. The Ti-N addimer and the Si-N addimer diffusion 5.3.3.1. Addimer diffusion on the TiN(001) surface (a) (b) (c) (d) Fig. 5.26: The diffusion of an Ti-N addimer on the TiN(001) surface: (a) an Ti-N addimer is at the initial position, (b) the N diffuses around its partner Ti, (c) the Ti diffuses around its partner N, (d) the Ti-N addimer is at the final position. The atomic calculations with ab initio method 117 The diffusion difficulty of an N adatom is illustrated in Section 5.3.2. This difficulty is due to the combination of N adatom and N atom as well as the dissociation of this strong covalent bond of N-N. Since TiN is a binary alloy, the addimer on the TiN(001) surface may change the diffusion mode of N adatoms. On the TiN(001) surface, a Ti adatom and a N adatom may hit each other, bond together, and form the Ti-N addimer. The lowest-energy configuration of the Ti-N addimer is that the Ti of the addimer is on the top of a surface N atom and the N of the addimer is on the top of a surface Ti atom. With this configuration, the combination of N- N and the (111) nucleus of Ti adatoms could be avoided. Thus, it is helpful to the film growth of TiN(001). This configuration leads to a rotation diffusion mode [Gall03]. Table 5.14: The total energy and the different energy of a Ti-N addimer diffusing on the TiN(001) surface. N around Ti Ti around N Path E0 Ediff Path E0 Ediff 0.03 -790.35 0.00 0.01 -790.35 0.00 0.07 -789.73 0.62 0.06 -789.69 0.66 0.12 -789.22 1.14 0.11 -789.06 1.29 0.18 -789.21 1.14 0.18 -789.06 1.29 0.23 -789.72 0.63 0.23 -789.66 0.70 0.28 -790.35 0.00 0.29 -790.35 0.00 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) Fig. 5.27: The E-Path curves for the diffusion of an addimer Ti-N on the TiN(001) surface: (a) the N of the addimer diffuses around its partner Ti, (b) the Ti of the addimer diffuses around its partner N. The diffusion mode of the Ti-N addimer is a two-step 90° rotation as shown in Fig. 5.26. First, the N atom of the addimer diffuses around its partner Ti atom and the Ti atom remains at its original site. Then, the Ti atom of the addimer diffuses around its partner N atom that stays at its actual position. The atomic calculations with ab initio method 118 This two-step 90° rotation diffusion was calculated with the nudged elastic band method. The surface slab used in the calculation was the 4 4 (5+7) model and the k- points setting was 551. The calculation results are listed in Table 5.14 and the E-Path curves are presented in Fig. 5.27. The E-Path curves show that this rotating diffusion is very smooth. The activation energy of the N rotation is 1.20 eV and the activation energy of the Ti rotation is 1.35 eV. The difference of these two activation energies is relatively small, so that the N atom and the Ti atom of the addimer can diffuse consecutively. The activation energy of the Ti-N addimer diffusing on the Ti (001) surface is 1.35 eV. Table 5.15: The total energy and the different energy of a Si-N addimer diffusing on the TiN(001) surface. N around Si Si around N Path E0 Ediff Path E0 Ediff 0.04 -787.92 0.00 0.00 -787.92 0.00 0.08 -787.33 0.59 0.06 -787.37 0.54 0.12 -786.95 0.97 0.12 -787.21 0.71 0.18 -786.95 0.96 0.19 -787.21 0.71 0.22 -787.33 0.59 0.24 -787.37 0.54 0.27 -787.92 0.00 0.30 -787.92 0.00 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) Fig. 5.28: The E-Path curves of a Si-N addimer diffusing on the TiN(001) surface: (a) the N of the addimer diffuses around its partner Si, (b) the Si of the addimer diffuses around its partner N. In the co-deposition of Ti, N, and Si, Si adatoms are also possible to bond with N adatoms and to form Si-N addimers. The lowest-energy configuration of a Si-N addimer is just the same as that of a Ti-N addimer, i.e. the Si atom of the addimer is above a surface N atom and the N atom of the addimer is above a surface Ti atom. The diffusion mode of a Si-N addimer is also the two-step 90° rotation. The similar calculations for this rotating The atomic calculations with ab initio method 119 diffusion were performed. The results are listed in Table 5.15 and the relevant E-Path curves are presented in Fig. 5.28. The diffusion of a Si-N addimer is also smooth. The activation energy of the N rotating diffusion reduces to about 1.00 eV. The activation energy of the Si rotating diffusion is only of 0.75 eV. The activation energy of the diffusion of the Si-N addimer is 1.00 eV which is smaller than that of the Ti-N addimer. This is one of the effects of Si adatom in the Ti-Si-N deposition, i.e. to form Si-N addimers and to promote the diffusion of N adatoms. 5.3.3.2. Addimer diffusion around the TiN island The investigations in Section 5.3.2 show that the adatom diffusion around or along the TiN island is crucial for the TiN and Ti-Si-N film growth. In this subsection, we discuss the investigation into the addimer diffusion around the TiN island. In the following subsection, we introduce the study of the addimer diffudion along the TiN island. P1 P2 P3 P4 P5 P1 2 4 5 P6 P7 P8 A B C D P9 P1 P2 P3 P4 P5 P1 2 4 5 P6 P7 P8 A B C D P9 (a) (b) Fig. 5.29: The diffusion of the addimer around the island: (a) the addimer diffuse along the down-path (from P3-P4 to P5-P8) or along the up-path (from P4-P3 to P2-P7), (b) the Si of the addimer diffuses alone firstly around the corner N of the island to the site P7, then the island N jumps to the site P9, finally, the N of the addimer takes the corner place of the island. The surface slab used in the calculations of this investigation was the 6 6 (5+7) model and the k-points setting was 331. An island of 2N2Ti was built on the TiN(001) surface. In the lowest-energy configuration of the Ti-N addmier beside the island, the Ti atom of the addimer is at the site P3 and the N atom of the addmier is at the site P4, [Fig. 5.29(a)]. The atomic calculations with ab initio method 120 Table 5.16: The total energy and the different energy of a Ti-N addimer diffusing around the island along the down-path (1): Ti-P3-C-P5 and then N-P4-P8. Ti from P2 to C Ti from C to P5 N from P4 to P8 Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.02 -1795.93 0.00 0.03 -1794.72 0.00 0.03 -1795.14 0.00 0.06 -1795.29 0.64 0.08 -1794.46 0.26 0.07 -1794.85 0.29 0.09 -1794.24 1.69 0.13 -1793.95 0.77 0.12 -1794.62 0.52 0.16 -1794.18 1.75 0.20 -1794.06 0.66 0.18 -1794.62 0.52 0.22 -1794.32 1.61 0.25 -1794.78 -0.06 0.23 -1794.86 0.28 0.28 -1794.72 1.21 0.30 -1795.14 -0.42 0.27 -1795.14 0.00 Table 5.16: Continued N from P4 to D N from D to P6 Path E0 Ediff Path E0 Ediff 0.03 -1795.14 0.00 0.03 -1794.00 0.00 0.06 -1794.54 0.60 0.07 -1793.74 0.26 0.10 -1793.69 1.45 0.12 -1793.13 0.87 0.16 -1793.28 1.86 0.18 -1793.13 0.87 0.22 -1793.72 1.42 0.23 -1793.73 0.26 0.27 -1794.00 1.14 0.28 -1794.00 0.00 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) The atomic calculations with ab initio method 121 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (d) (e) Fig. 5.30: The E-Path of a Ti-N addimer diffusion around the island along the down-path (1): (a) the Ti of the addimer from site P3 to site C, (b) Ti from site C to site P5, (c) the N of the addimer from site P4 to site P8, (d) N from site P4 to site D, (e) N from site D to site P8. First, the diffusion of the Ti-N addimer along the down-path was studied [Fig. 5.29(a)]. The Ti atom of the addimer diffused around its partner N atom from the site P3 through the site C to the site P5. After that the N atom of the addimer could jump over through two Ti atoms directly from the site P4 to the site P8 or could diffuse around its partner Ti atom from the site P4 through the site D, the site P6, and to the site P8. The calculation for every sub path was performed with the nudged elastic band method. The results are listed in Table 5.16 and the E-Path curves are shown in Fig. 5.30. The activation energy for the Ti atom of the Ti-N addimer diffusing from the site P3 to the site C is of 1.75 eV which is smaller than that of the Ti adatom diffusing alone around the island (of 1.97 eV). This shows a positive effect of its partner N. After the Ti atom of the addimer reaches the site P5, the N atom of the addimer can diffuse directly from the site P4 to the site P8, for which the activation energy Ea is about 0.55 eV, or diffuse around its partner Ti from the site P4 through the site D, the site P6 and to the site P8, for which the activation energy Ea is about 1.86 eV. Comparing these two activation energies, it is clear that the N atom of the addimer will diffuse directly from the site P4 to the site P8 instead of diffusing around its partner Ti atom. The jumping over through two support partners is also a typical diffusion mode in the Ti-Si-N formation process. Then, the diffusion of the Ti-N addimer along the up-path was investigated [Fig. 5.29(a)]. The N atom of the addimer diffused around its partner Ti atom from the site P4 through the site B to the site P2. After that, the Ti of the addimer could jump over through two N atoms from the site P3 to the site P7 or diffused around its partner N atom from the site P3 through the site A, the site P1 and to the site P7. Similar to the down-path diffusion, the jumping diffusion is easier. The similar calculation for every sub path was also The atomic calculations with ab initio method 122 performed with the nudged elastic band method. The calculation results are listed in Table 5.17 and presented in Fig. 5.31. Table 5.17: The total energy and the different energy of a Ti-N addimer diffusing around the island along the up-path (2): N-P4-B-P2 and then Ti-P3-P7. N from P4 to B N from B to P2 Ti from P3 to P7 Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.03 -1795.93 0.00 0.04 -1794.67 0.00 0.02 -1794.59 0.00 0.06 -1795.42 0.51 0.07 -1794.43 0.24 0.07 -1794.01 0.58 0.09 -1794.30 1.63 0.12 -1793.90 0.78 0.10 -1793.09 1.50 0.16 -1793.73 2.20 0.17 -1793.93 0.75 0.20 -1793.08 1.51 0.22 -1794.31 1.61 0.22 -1794.38 0.30 0.23 -1793.98 0.61 0.28 -1794.67 1.26 0.27 -1794.59 0.08 0.28 -1794.59 0.00 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.31: The E-Path of the Ti-N addimer diffusion around the island (2): (a) the N of the addimer from the site P4 to the site B, (b) N from the site B to the site P2, (c) the Ti of the addimer from the site P3 to the site P7. The atomic calculations with ab initio method 123 Table 5.18: The total energy and the different energy for the Ti of a Ti-N addimer diffusing alone around the corner N of the island 2N2Ti. The Ti of the addimer around corner N alone Path E0 Ediff 0.02 -1795.93 0.00 0.07 -1794.89 1.04 0.10 -1793.67 2.26 0.18 -1793.39 2.54 0.23 -1794.00 1.93 0.29 -1794.48 1.45 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) Fig. 5.32: The E-Path of the Ti of a Ti-N addimer diffuses alone around the island N corner. The activation energy Ea for the N atom of the Ti-N addimer to diffuse from the site P4 to the site B is of 2.20 eV and from the site B to the site P2 is of 0.82 eV. For the Ti atom of the addimer to jump from the site P3 to the site P7, the activation energy Ea is about 1.60 eV. Because the activation energy Ea =2.20 eV is relatively high, a calculation was performed to investigate another possible diffusion mode, i.e. the Ti atom of the Ti-N addimer diffusing alone around the corner N atom of the island from the P3 to the site P7, whereas the N atom of the addimer remains its origin position P4, [Fig. 5.29(b)]. The calculation result is listed in Table 5.18 and the E-Path curve presented in Fig. 5.32. The activation energy is of 2.54 eV. With so high activation energy, the probability of this diffusion is very little. Checking all the activation energies of a Ti-N addimer diffusing around the island of 2N2Ti from Table 5.16 to Table 5.18, it can be identified that the activation energy of a Ti-N addimer diffusing around the island is 2.20 eV. This means that the diffusion of a Ti- N addmier around the TiN island is also very difficult. The atomic calculations with ab initio method 124 Following this, we discuss the diffusion of the Si-N addimer around the TiN island, which is somewhat different from that of the Ti-N addimer. The lowest-energy configuration of the Si-N addimer was similar to that of the Ti- N addimer, i.e. the Si atom of the Si-N addimer was at the site P3 and the N atom of the addimer was at the site P4, [Fig. 5.29(a)]. Table 5.19: The total energy and the different energy of a Si-N addimer diffusing around the island along the down-path (1): Si-P3-C-P5 and then N-P4-P8. Si around N (P3-C) Si from C to P5 N jump (P4-P8) Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.03 -1792.76 0.00 0.06 -1792.44 0.00 0.04 -1792.83 0.00 0.05 -1792.30 0.46 0.11 -1792.34 0.11 0.08 -1792.70 0.12 0.12 -1792.12 0.63 0.16 -1792.29 0.15 0.13 -1792.52 0.30 0.19 -1792.22 0.54 0.21 -1792.38 0.06 0.18 -1792.52 0.30 0.25 -1792.40 0.36 0.25 -1792.71 -0.27 0.23 -1792.70 0.12 0.30 -1792.44 0.32 0.30 -1792.83 -0.38 0.26 -1792.83 0.00 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.10 0.20 0.30 0.40 Path (nm) (e V ) (a) (b) 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.33: The E-Path of a Si-N addimer diffusing around the island along the down-path (1): (a) Si from the site P3 to the site C, (b) Si from the site C to the site P5, (c) N from the site P4 to the site P8. The atomic calculations with ab initio method 125 Along the down-path, the Si atom of the Si-N addimer diffused from its initial site P3 through the site C to the site P5 and then the N atom of the addimer jumped over through its supporters Si and Ti atoms from the site P4 to the site P8. The calculation results of the diffusion along this down-path are listed Table 5.19 and the E-Path curves are presented in Fig. 5.33. The activation energies for this series diffusion are very small, less than 0.63 eV, so that the diffusion along this down-path is very easy. Table 5.20: The total energy and the different energy of a Si-N addimer diffusing around the island along the up-path (2): N-P4-B-P2 and then Ti-P3-P7. N around Si (P4-B) N from B to P2 Si jump (P3-P7) Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.03 -1792.79 0.00 0.04 -1791.02 0.00 0.03 -1791.34 0.00 0.06 -1792.36 0.43 0.07 -1791.24 -0.23 0.06 -1791.13 0.20 0.11 -1790.77 2.02 0.11 -1790.93 0.09 0.11 -1790.84 0.50 0.18 -1789.90 2.89 0.16 -1790.79 0.22 0.19 -1790.85 0.49 0.22 -1790.44 2.35 0.20 -1791.14 -0.12 0.24 -1791.14 0.20 0.28 -1791.02 1.77 0.25 -1791.34 -0.32 0.28 -1791.34 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) -1.0 0.0 1.0 2.0 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 1.0 2.0 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.34: The E-Path of a Si-N addimer diffusing around the island along the up-path (2): (a) N from the site P4 to the site B, (b) N from the site B to the site P2, (c) Si from the site P3 to the site P7. The atomic calculations with ab initio method 126 Table 5.21: The total energy and the different energy for Si of a Si-N addimer alone diffusing around the corner N of the island 2N2Ti, the corner N atom diffusing, and the N of the addimer moving to the corner site. Si round N corner N corner diffusion N to corner site Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.03 -1792.76 0.00 0.02 -1792.42 0.00 0.03 -1791.37 0.00 0.06 -1791.92 0.84 0.06 -1791.76 0.66 0.07 -1791.11 0.26 0.10 -1791.48 1.28 0.10 -1790.84 1.58 0.13 -1790.50 0.87 0.16 -1791.27 1.49 0.17 -1790.70 1.72 0.20 -1790.70 0.67 0.23 -1792.05 0.71 0.23 -1791.13 1.29 0.24 -1791.44 -0.08 0.29 -1792.42 0.34 0.26 -1791.37 1.05 0.31 -1792.76 -1.39 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) -2.2 -1.2 -0.2 0.8 1.8 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.35: The E-Path of a addimer Si-N diffusion around the island (3): (a) the Si of the addimer alone diffuses around the corner N of the island 2N2Ti from the site P3 to the site P7, (b) the corner atom N jumps from the corner site of the island to the site P9, (c) the N of the origin addimer diffuses from the site P4 to corner site of the island. However, the situation along the up-path was totally different. Along the up-path, the N atom of the Si-N addimer diffused from its origin site P4 through the site B to the site P2, and then the Si atom of the addimer jumped over from the site P3 to the site P7. The atomic calculations with ab initio method 127 The calculation results for the diffusion are listed in Table 5.20 and the E-Path curves are presented in Fig. 5.34. A special point in the results is that the activation energy for the N atom of the addimer to diffuse around its partner Si atom from the site P3 to the site B is high to 2.89 eV. This very high activation energy would restrict the diffusion of the Si-N addimer around the TiN island, although all the activation energies of the other sub- diffusion along the down-path and along the up-path are very small. Therefore, the calculations were conducted for another diffusion mode of the Si-N addimer around the island [Fig. 5.29(b)]. First, the Si atom of the Si-N addimer diffused alone around the corner N atom of the island 2N2Ti from the site P3 to the site P7. Then, the island corner N atom jumped over through Si and Ti atoms from the corner site to the site P9. Finally, the N atom of the origin Si-N addimer diffused from the site P4 to the corner site of the island. The calculation results of the diffusion are listed in Table 5.21 and the E-Path curves are shown in Fig. 5.35. The activation energy of the Si atom of the addimer alone diffusing around the corner N atom of the island is of 1.49 eV which is slightly larger than the activation energy of a Si adatom diffusing around the corner N atom of the island, of 1.25 eV. The activation energy for the corner N atom to jump over from the corner site to the site P9 is of 1.72 eV which is the activation energy of the Si-N addimer diffusing around the island of 2N2Ti. The activation energy 1.72 eV is much smaller than that of the Ti-N addimer diffusing around the island, so that the diffusion of the Si-N addimer around the island is relatively easy. The easy diffusion of the Si-N addimer around the island has a very positive effect to the Ti-Si-N formation, about which we will discuss in Section 5.3.6. 5.3.3.3. Addimer diffusion along the TiN island P1 P2 P3 P4 P5 1 2 3 4 A B Fig. 5.36: The addimer diffusion along the TiN island. In this subsection, we discuss the addimer diffusion along the TiN island. In the calculations, a slab with 6 6 (5+7) model was used and the k-points setting was 3 3 1. An island of 6N6Ti was built on the surface. In the lowest-energy configuration of the Ti- The atomic calculations with ab initio method 128 N addimer beside the island, the Ti atom of the addimer was at the site P2 and its partner N atom was at the site P3, (Fig. 5.36). The diffusion path of the Ti atom of the addimer along the island was from the site P2 through the site B to the site P4. The diffusion path of the N atom of the addimer along the island was from the site P3 through the site A to the site P1. Because of the symmetry, we need only to calculate the Ti diffusion along the path from the site P2 to the site B and the N diffusion along the path from the site P3 to the site A. The calculation results are listed in Table 5.22 and the E-Path curves are presented in Fig. 5.37. The activation energy of the N of a Ti-N addimer diffusing along the island is 1.93 eV and the activation energy of the Ti diffusion is 2.59 eV. Both of the activation energies are slightly smaller than that of a N adatom and a Ti adatom diffusing along the island, i.e. 2.04 eV and 2.71 eV. This shows the positive effect of the addimer partner on the diffusion. But the effect is not very significant. The diffusion of the Ti-N addimer along the TiN island is still difficult. Similarly, the Si-N addimer diffusing along this 6N6Ti island was studied. Both the lowest-energy configuration and the diffusion path of the Si-N addimer are as same as that of the Ti-N addimer, (Fig. 5.36). The calculation results of the Si-N addimer diffusing along the island are listed in Table 5.23 and the E-Path curve are shown in Fig. 5.38. The activation energy of the N atom of the Si-N addimer diffusing along the island is 1.67 eV and the activation energy of the Si of the addimer diffusing along the island is about 1.00 eV. Both activation energies are much smaller than that of theTi-N addimer diffusing along the island. Therefore, the Si-N addimer diffuse much easier than theTi-N addimer along the island. The activation energy of the Si-N addimer diffusing along the island is 1.67 eV. Table 5.22: The total energies and different energies of a Ti-N addimer diffusing along the island. Ti around N N around Ti Path E0 Ediff Path E0 Ediff 0.02 -1873.36 0.00 0.02 -1873.36 0.00 0.05 -1872.49 0.87 0.06 -1872.64 0.72 0.10 -1871.06 2.30 0.11 -1871.68 1.68 0.16 -1870.77 2.59 0.17 -1871.43 1.93 0.22 -1871.12 2.24 0.23 -1872.07 1.29 0.28 -1871.49 1.88 0.28 -1872.39 0.98 The atomic calculations with ab initio method 129 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) Fig. 5.37: The E-Path of a Ti-N addimer diffusing along the island: (a) the Ti of the addimer diffuses from the site P2 to the site B; (b) the N of the addimer diffuses from the site P3 to the site A. Table 5.23: The total energies and different energies of a Si-N addimer diffusing along the island. N around Si Si around N Path E0 Ediff Path E0 Ediff 0.04 -1869.91 0.00 -0.03 -1869.91 0.00 0.07 -1869.36 0.55 0.04 -1869.33 0.59 0.12 -1868.47 1.44 0.10 -1868.98 0.93 0.19 -1868.30 1.61 0.16 -1869.00 0.91 0.25 -1868.56 1.35 0.22 -1869.18 0.73 0.28 -1868.24 1.67 0.27 -1869.25 0.66 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -0.10 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) Fig. 5.38: The E-Path of a Si-N addimer diffusing along the island: (a) the N of the addimer diffuses from the site P3 to the site A, (b) The Si of the addimer diffuses from the site P2 to the site B. The atomic calculations with ab initio method 130 5.3.3.4. Addimer diffusion down the TiN island P1 P2 P3 P4 P5 1 P3 P4 P5 P6 P7 P8 2 Fig. 5.39: The diffusion of a Ti-N or Si-N addimer down the island. In this subsection, we introduce the diffusion of the Ti-N or the Si-N addimer down the TiN island. The surface slab used in the calculations was the 6 6 (5+7) model and the k- points setting was 3  3  1. For studying the addimer down the island, an island of 12N12Ti was built on the TiN(001) surface. In the lowest-energy configuration of the Ti- N addmier beside the island, the Ti atom of the addimer was at the site P2 and the N atom of the addmier was at the site P1, (Fig. 5.39). And some low-energy configurations of the Ti-N addmier on the island were at the P5-P6 sites, the P6-P3 sites, and the P3-P4 sites, respectively. The diffusion paths were first the N atom of the addimer from the site P5 to the site P3, then the Ti atom of the addimer from the site P6 to the site P4, finally the addimer from the P3-P4 sites to the P1-P2 sites. The Ti and N atoms of the addimer diffused together down the island. Both the lowest-energy configurations and the diffusion paths of the Si-N addimer were similar to those of the Ti-N addimer. The difference is that the Si atom of the Si-N addimer diffuses easier than the N atom. Therefore, the diffusion paths were first the Si atom of the Si-N addimer from the site P8 to the site P4, then the N atom of the addimer from the site P7 to the site P3, finally the Si-N addimer from the P3- P4 sites to the P1-P2 sites. The Si and N atoms of the Si-N addimer diffused together down the island. The calculations along the diffusion paths were carried out with the nudged elastic band method. The calculation results of the diffusion down the island are listed in Table 5.24 and Table 5.25 and the E-Path curves are presented in the Fig. 5.40 and Fig. 5.41. The activation energies of the Ti-N addimer are 0.67 eV for the N atom from P5 to P3, 0.97 eV for the Ti atom from P6 to P4, and 0.00 eV for the Ti-N addimer down the island. The activation energies of the Si-N addimer are 0.07 eV for the Si atom from P8 to P4, 0.36 eV for the N atom from P7 to P3, and 0.00 eV for the Si-N addimer down the island. Together with the fact that the activation energies of Ti, Si, and N adatoms diffusing down the island are almost of 0.00 eV, it disclosed that the film formation of the The atomic calculations with ab initio method 131 Ti-Si-N on the TiN(001) surface is in the layer-by-layer mode, namely the Frank-van der Merwe (FM) mode. Table 5.24: The total energies and the different energies of a Ti-N addimer diffusing down the island. N-path Ti-path Path E0 Ediff Path E0 Ediff 0.03 -1989.39 0.00 0.02 -1989.39 0.00 0.07 -1989.53 -0.14 0.06 -1989.53 -0.14 0.11 -1989.71 -0.32 0.15 -1989.71 -0.32 0.14 -1990.18 -0.79 0.22 -1990.18 -0.79 0.21 -1991.04 -1.66 0.26 -1991.04 -1.66 0.29 -1991.77 -2.38 0.29 -1991.77 -2.38 -3.0 -2.0 -1.0 0.0 0.00 0.10 0.20 0.30 N-Path (nm) (e V ) -3.0 -2.0 -1.0 0.0 0.00 0.10 0.20 0.30 Path(nm) (e V ) (a) (b) Fig. 5.40: The E-Path curves of a Ti-N addimer diffusing down the island: (a) the N of the addimer diffuses from the site P3 to the site P1, (b) the Ti of the addimer diffuses from the site P4 to the site P2. Table 5.25: The total energies and the different energies of a Si-N addimer diffusing down the island. N-path Si-path Path E0 Ediff Path E0 Ediff 0.05 -1987.00 0.00 0.03 -1987.00 0.00 0.07 -1987.20 -0.20 0.08 -1987.20 -0.20 0.13 -1987.29 -0.29 0.14 -1987.29 -0.29 0.20 -1987.44 -0.44 0.19 -1987.44 -0.44 0.27 -1987.95 -0.95 0.20 -1987.95 -0.95 0.29 -1988.28 -1.28 0.28 -1988.28 -1.28 The atomic calculations with ab initio method 132 -1.5 -1.0 -0.5 0.0 0.00 0.10 0.20 0.30 N-Path (nm) (e V ) -1.5 -1.0 -0.5 0.0 0.00 0.10 0.20 0.30 Si-Path (nm) (e V ) (a) (b) Fig. 5.41: The E-Path curves of a Si-N addimer diffusing down the island: (a) the N of the addimer diffusing from the site P3 to the site P1, (b) the Si of the addimer diffusing from the site P4 to the site P2. A summary of the diffusion behaviors of the Ti-N addimer and the Si-N addimer are follows. (1) In the lowest-energy arrangement of the Ti-N addimer or the Si-N addimer on the TiN(001) surface, the Ti or Si atom of the addimer is on the top of a surface N atom and the N atom of the addimer is on the top of a surface Ti atom. These configurations prevent the N adatom from connecting with the surface N atom, so that the diffusion of the addimer on TiN(001) are relatively smooth. The diffusion mode of the Ti-N or the Si-N addimer on the TiN(001) surface is the two-step 90° rotation. The activation energies of the Ti rotating diffusion and the N rotating diffusion are 1.35 eV and 1.20 eV, respectively. And the activation energies of the Si rotating diffusion and the N rotating diffusion are 0.75 eV and 1.00 eV, respectively. Manifestly, the diffusion of the Si-N addimer is easier than that of the Ti-N addimer. This is a positive effect of the Si addition, namely, to promote the diffusion of N adatoms. (2) With the addimer partnership, the activation energies of the Ti-N addimer diffusion around or along the TiN island are slightly lower than those of the adatoms. However, the activation energies are still high to 2.20 eV or 2.50 eV, so that Ti-N addimer diffusion around or along the TiN island are still very difficult. The activation energies of the Si-N addimer diffusion around the TiN island or along the TiN island are 1.72 eV or 1.67 eV, respectively. Clearly, the Si-N addimer diffusion around or along the island are easier than the Ti-N addimer. (3) Both the activation energies of the Ti-N and the Si-N addimer diffusion down the TiN island are of 0.00 eV, so that the Ti-Si-N film growth is in a layer-by-layer mode, namely the Frank-van der Merwe (FM) mode. The atomic calculations with ab initio method 133 5.3.4. The cluster diffusion on the TiN(001) surface 5.3.4.1. Ti-N-Ti diffusion (a) (b) (c) Fig. 5.42: The low-energy configurations of a Ti-N-Ti adtrimer on the TiN(001) surface and its diffusion mode: (a) the line configuration, LINE; (b) the corner configuration, CORNER; (c) the N of adtrimer jumps over through two Ti supporters. An Ti-N-Ti adtrimer has two stable configurations on the TiN(001) surface, one is a line configuration, noted LINE [Fig. 5.42(a)] and the other is a corner arrangement, noted CORNER [Fig. 5.42(b)]. With the 90° rotating diffusion mode, the LINE configuration can transform into the CORNER arrangement, or inversely. The other diffusion mode is that the N atom of the adtrimer jumps over through two Ti supporters. [Fig. 5.42(c)]. The slab used in the calculations of these two diffusion modes was the 4 4 (5+7) model and the k-points setting was 5 5 1. The calculations were performed with the nudged elastic band method. The calculation results are listed in Table 5.26 and the E-Path curves are presented in Fig. 5.43. Table 5.26: The total energies and the different energies of the Ti-N-Ti diffusion. Ti: CORNER - LINE N: jumping diffusion Path E0 Ediff Path E0 Ediff 0.01 -797.83 0.00 0.03 -798.09 0.00 0.06 -797.39 0.44 0.07 -797.39 0.70 0.12 -796.96 0.87 0.12 -797.03 1.06 0.18 -796.87 0.96 0.18 -797.05 1.04 0.23 -797.22 0.61 0.23 -797.40 0.68 0.28 -798.09 -0.26 0.27 -798.09 0.00 The atomic calculations with ab initio method 134 -0.5 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) Fig. 5.43: The E-Path curves of the Ti-N-Ti diffusion: (a) the Ti rotating diffusion from the CORNER configuration to the LINE one, or inversely, (b) the N jumping diffusion over through two Ti partners. The activation energy for the Ti rotating diffusion from the CORNER configuration to the LINE one is 0.96 eV. And inversely, from the LINE configuration to the CORNER arrangement, the activation energy is 1.22 eV. The activation energy for the N jumping diffusion is 1.10 eV. The difference of these three activation energies is very small, so that the Ti-N-Ti cluster can diffuse smoothly on the TiN(001) surface. The activation energy for this cluster diffusion is 1.22 eV. 5.3.4.2. N-Ti-N diffusion The low-energy configurations of N-Ti-N on the TiN(001) surface are similar to those of Ti-N-Ti, also with the LINE configuration or the CORNER arrangement, [Fig. 5.42(a) and (b)]. The diffusion modes are the rotating diffusion and the jumping diffusion. The surface slab used in the calculation, the k-points setting, and the calculation method are the same as those for the Ti-N-Ti diffusion. The calculation results are listed in Table 5.27 and the E-Path curves are presented in Fig. 5.44. The activation energy for the N rotating diffusion from the CORNER configuration to the LINE arrangement is 1.25 eV; and inversely, from LINE to CORNER, the activation energy is 0.66 eV. The activation energy for the Ti jumping diffusion is of 1.70 eV. The difference of these three activation energies is relatively large, so that the diffusion of N-Ti-N is not easy comparing with those of Ti-N-Ti. The activation energy for this adtrimer diffusion is 1.70 eV. The atomic calculations with ab initio method 135 Table 5.27: The total energies and different energies of the N-Ti-N diffusion. N: CORNER - LINE Ti: jumping diffusion Path E0 Ediff Path E0 Ediff 0.02 -799.89 0.00 0.02 -799.89 0.00 0.07 -799.26 0.62 0.07 -799.20 0.69 0.13 -798.80 1.09 0.10 -798.28 1.60 0.19 -798.64 1.25 0.20 -798.29 1.60 0.24 -799.08 0.80 0.23 -799.20 0.69 0.28 -799.30 0.59 0.28 -799.89 0.00 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.5 1.0 1.5 2.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) Fig. 5.44: The E-Path curves of the N-Ti-N diffusion: (a) the N of N-Ti-N rotates from the CORNER arrangement to the LINE one, or inversely, (b) the Ti of N-Ti-N jumps over through two N partners. 5.3.4.3. Ti-N-Si diffusion The low-energy configurations of Ti-N-Si on the TiN(001) surface are similar to those of Ti-N-Ti, also with the LINE configuration or the CORNER arrangement, [Fig. 5.42(a) and (b)]. The diffusion modes are also the rotating diffusion and the jumping diffusion. The surface slab used in the calculation, the k-points setting, and the calculation method are the same as those for the Ti-N-Ti diffusion. The calculation results are listed in Table 5.28 and the E-Path curves are presented in Fig. 5.45. The activation energy for the Ti rotating diffusion of Ti-N-Si from the CORNER configuration to the LINE arrangement is of 1.43 eV; and inversely from LINE to CORNER, the activation energy is of 0.85 eV. The activation energy for the Si rotating diffusion from CORNER to LINE is of 1.40 eV; and inversely from LINE to CORNER, The atomic calculations with ab initio method 136 the activation energy is of 0.85 eV. The activation energy for the N jumping diffusion is of 1.10 eV. Therefore, the activation energy for the Ti-N-Si diffusion is of 1.43 eV. Table 5.28: The total energies and the different energies of the Ti-N-Si diffusion. Ti: CORNER - LINE Si: CORNER - LINE N: jumping diffusion Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.02 -796.11 0.00 0.01 -796.11 0.00 0.03 -796.11 0.00 0.05 -795.41 0.69 0.05 -795.50 0.61 0.08 -795.35 0.76 0.10 -794.78 1.33 0.11 -794.81 1.30 0.13 -795.02 1.09 0.17 -794.68 1.43 0.17 -794.74 1.36 0.20 -795.09 1.02 0.23 -794.92 1.19 0.23 -795.08 1.03 0.23 -795.45 0.66 0.28 -795.53 0.58 0.28 -795.53 0.58 0.27 -796.11 0.00 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.45: The E-Path curves of the Ti-N-Si diffusion: (a) the Ti of Ti-N-Si rotates from the CORNER arrangement to the LINE one, or inversely; (b) the Si of Ti-N-Si rotates from the CORNER arrangement to the LINE one, or inversely; (c) the N of Ti-N-Si jumps over through its partners Ti and Si. The atomic calculations with ab initio method 137 5.3.4.4. 2Ti-2N diffusion P1 P2 P3 P4 P5 P1 P2 P3 P4 P1 P2 P3 P4 P5 P1 P2 P3 P4 P1 P2 P3 P4 P5 P1P4 5 P6 5 P6 (a) (b) (c) Fig. 5.46: The low-energy configurations and the diffusion mode of 2N2Ti: (a) the lowest-energy configuration of 2N2Ti; (b) the Ti of 2N2Ti diffuses from P1 through P2 to P3, or inversely; (c) the N of 2N2Ti diffuses from P4 through P5 to P6, or inversely. The lowest-energy configuration of 2N2Ti on the TiN(001) surface is shown in Fig. 5.46(a), every Ti atom of 2N2Ti connected with three N atoms ( two N adatoms and one surface N atom) and every N atom of 2N2Ti connected with three Ti atoms. The diffusion mode is the rotating diffusion. The Ti atom of 2N2Ti diffused firstly from its origin site P1 through the site P2 to the site P3, [Fig. 5.46(b)]. And this diffusion could also be taken as the Ti diffusing from the site P3 through the site P2 to the site P1 after the N diffusion. The N atom of 2N2Ti diffusion is in the same mode, i.e. the N atom diffusing from the site P4 through the site P5 to the site P6, or inversely, as shown in Fig. 5.46(c). The slab used in the calculation for the diffusion of 2N2Ti is the 6 6 (5+7) model and the k-points setting is 3 3 1. The calculation results for the Ti diffusion are listed in Table 5.29 and the E-Path curves are presented in Fig. 5.47. The results for the N diffusion are listed in Table 5.30 and the E-Path curves are shown in Fig. 5.48. The activation energy for the Ti diffusion from the site P1 to the site P3 is 2.22eV; and inversely, from the site P3 to the site P1, the activation energy is of 1.16 eV. The activation energy for the N diffusion from the site P4 to the site P6 is 2.18 eV; and inversely, from the site P6 to the site P4, the activation energy is 0.90 eV. Clearly, whether the Ti atom or the N atom of the 2N2Ti adtetramer diffuses firstly, the activation energy is above 2.18 eV. Therefore, the 2N2Ti adtetramer is relatively stable arrangement on TiN(001) and difficult to diffuse. The atomic calculations with ab initio method 138 Table 5.29: The total energies and the different energies for the Ti diffusion of 2N2Ti : P1-P2-P3. Ti: P1-P2 Ti: P2-P3 Path E0 Ediff Path E0 Ediff 0.01 -1777.41 0.00 0.02 -1775.81 0.00 0.05 -1777.02 0.38 0.07 -1775.54 0.26 0.10 -1775.60 1.80 0.12 -1774.99 0.82 0.17 -1775.19 2.22 0.19 -1775.11 0.70 0.22 -1775.38 2.03 0.24 -1775.79 0.01 0.28 -1775.81 1.60 0.29 -1776.15 -0.34 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 0.40 Path (nm) (e V ) (a) (b) Fig. 5.47: The E-Path curve of the Ti diffusion of 2N2Ti: (a) the Ti atom diffuses from the site P1 to the site P2, or inversely; (b) the Ti atom diffuses from the site P2 to the site P3, or inversely. Table 5.30: The total energies and the different energies for the N diffusion of 2N2Ti: P4-P5-P6. N: P4-P5 N: P5-P6 Path E0 Ediff Path E0 Ediff 0.02 -1777.39 0.00 0.04 -1776.11 0.00 0.06 -1776.86 0.53 0.07 -1775.85 0.26 0.08 -1775.75 1.64 0.12 -1775.31 0.80 0.15 -1775.20 2.18 0.17 -1775.39 0.72 0.21 -1775.72 1.67 0.22 -1775.91 0.20 0.27 -1776.11 1.28 0.28 -1776.15 -0.04 The atomic calculations with ab initio method 139 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) Fig. 5.48: The E-Path curve of the N diffusion of 2N2Ti: (a) the N atom diffuses from the site P4 to the site P5, or inversely; (b) the N atom diffuses from the site P5 to the site P6, or inversely. To summarize above investigations, on the TiN(001) surface, the 2N2Ti cluster is a stable configuration because the activation energy for its diffusion is higher than 2.18 eV. Comparing with the 2N2Ti cluster, the Ti-N-Ti, N-Ti-N, and Ti-N-Si adtrimer are relatively easy to diffuse because the activation energies of their diffusion are lower than 1.60 eV. Comparing with addimer, the diffusion of N-Ti-N, and Ti-N-Si adtrimers are difficult than those of the Ti-N and the SiN addimers; the diffusion of Ti-N-Ti is easier than that of the Ti-N addimer but difficult than that of the Si-N addimer on the TiN(001) surface. 5.3.5. The inter diffusion in the TiN crystallite or in the TiN(001) surface 5.3.5.1. Ti, Si, N atom inter diffusion in crystalline TiN (a) (b) Fig. 5.49: The inter diffusion of a Ti atom in the crystalline TiN: (a) the initial arrangement, (b) a Ti atom diffuses to a vacant site. In this subsection, the investigation of the inter diffusion in crystalline TiN is discussed. In an inter diffusion, a Ti atom or a Si atom diffuses from its initial site to a Ti vacancy, (Fig. 5.49), while a N atom diffuses from its initial site to a N vacancy. The atomic calculations with ab initio method 140 For the calculations, a supercell with 4 4 4 model was used and the k-points setting was 555. The calculations were performed with the nudged elastic band method. The calculation results are listed in Table 5.31 and the E-Path curves are presented in Fig. 5.50. Table 5.31: The total energy and the different energy of Ti, N, and Si inter diffusion in the crystalline TiN. Ti N Si Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.07 -618.96 0.00 0.07 -618.96 0.00 0.07 -612.76 0.00 0.09 -617.83 1.13 0.09 -617.67 1.29 0.10 -612.59 0.17 0.13 -615.36 3.60 0.14 -615.70 3.27 0.14 -611.29 1.47 0.20 -615.32 3.64 0.20 -615.70 3.27 0.20 -611.31 1.45 0.25 -617.84 1.12 0.25 -617.67 1.29 0.24 -612.63 0.14 0.30 -618.96 0.00 0.31 -618.96 0.00 0.29 -612.76 0.00 0.0 1.0 2.0 3.0 4.0 0.00 0.20 Path (nm) (e V ) 0.0 1.0 2.0 3.0 4.0 0.00 0.20 Path (nm) (e V ) (a) (b) 0.0 1.0 2.0 3.0 4.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.50: The E-Path curve for the inter diffusion of an atom in the crystalline TiN: (a) for a Ti atom inter diffusion, (b) for a N atom inter diffusion, (c) for a Si atom inter diffusion. The activation energies of the Ti inter diffusion and the N inter diffusion in the TiN crystallite are very high, of 3.90 eV and 3.50 eV, respectively. These high activation energies show that the inter diffusion of the Ti atom and the N atom in the TiN crystallite The atomic calculations with ab initio method 141 are very difficult. According to this high actication energy, the voids in theTiN crystallite are not easy to move into the boundary. The activation energy of the Si atom inter diffusion in the TiN crystallite is relatively low, of 1.60 eV. This indicates that the Si inter diffusion in the TiN crystallite is relatively easy. 5.3.5.2. Ti, Si, N adatom inter diffusion in the TiN(001) surface Table 5.32: The total energies and the different energies of the Ti, N, and Si adatom inter diffusion in the TiN(001) surface. Ti N Si Path E0 Ediff Path E0 Ediff Path E0 Ediff 0.01 -763.35 0.00 0.01 -763.53 0.00 0.02 -757.45 0.00 0.07 -761.82 1.54 0.06 -762.45 1.08 0.06 -757.01 0.43 0.11 -759.81 3.54 0.11 -761.51 2.02 0.11 -757.32 0.13 0.20 -759.86 3.49 0.20 -761.51 2.02 0.19 -757.32 0.12 0.24 -761.89 1.46 0.24 -762.45 1.08 0.24 -757.02 0.43 0.29 -763.35 0.00 0.30 -763.53 0.00 0.28 -757.45 0.00 0.0 1.0 2.0 3.0 4.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) 0.0 1.0 2.0 3.0 4.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) 0.0 1.0 2.0 3.0 4.0 0.00 0.10 0.20 0.30 Path (nm) (e V ) (c) Fig. 5.51: The E-Path curve for the inter diffusion of an adatom in the first layer of the TiN(001) surface: (a) a Ti adatom diffuses in the TiN surface, (b) a N adatom diffuses in the TiN surface, (c) a Si adatom diffuses in the TiN surface. The atomic calculations with ab initio method 142 In the final phase of island growth, the deposition film is in the channels form or the holes form [Warrender04]. In this phase, the adatom inter diffusion in the surface layer is very important for the formation of dense structure. From the results of Section 5.3.5.1, it is known that the inter diffusion of the Ti atom and the N atom in the TiN crystallite is very difficult. In this case, the adatom inter diffusion in the surface is even more important. In this subsection, we introduce the study on the inter diffusion of a Ti adatom, a N adatom, and a Si adatom in the TiN(001) surface, i.e. a adatom in the surface diffuses to a vacant site that is also in the surafec. The surface slab used in the calculation was the 4 4 (5+7) model and the k- points setting was 551. The calculation results are listed in Table 5.32 and the E-Path curves are presented in Fig. 5.51. The activation energy of the Ti adatom diffusion in the TiN surface is still very high, of 3.76 eV, so that the inter diffusion of the Ti adatom in the TiN(001) surface is also very difficult. The activation energy for the N adatom diffusion in the TiN surface is 2.15 eV. With this activation energy, the N adatom inter diffusion in the TiN(001) surface also belongs to the difficult diffusion. This difficulty of the inter-diffusion of the Ti and N adatom may lead to many voids near the boundaries in the TiN coatings [Sungren85]. The activation energy for the Si adatom diffusion in the TiN surface is very low, of 0.43 eV so that the inter diffusion of the Si adatom in the TiN(001) surface is very easy. 5.3.6. The influence of Si adatoms on the Ti and N diffusion P1 P2 P3 P4 P5 P1 P2 P3 P4 P5 4 1 1 2 P3 2 P3 4 (a) (b) Fig. 5.52: The influence of a Si adatom and a Si-N addimer on the Ti diffusion of a Ti-N addimer along the TiN island: (a) the Ti diffusion from the site P1 to the site P2 is influenced by a Si adatom, (b) the Ti diffusion from the site P1 to the site P2 is influenced by a Si-N addimer. The atomic calculations with ab initio method 143 Since the Ti and N inter diffusion in the TiN crystallite and in the TiN surface are very difficult, the formation of the TiN film depends largely on the diffusion of the Ti and N adatom on the surface. But the diffusion of the Ti adatom, the N adatom, and the Ti-N addimer around and along the TiN island are also not easy. Therefore, the promotion effect of the Si addition is crucial to the evolution of the Ti-Si-N structure. In this section we discuss the influence of Si adatoms on the Ti and N diffusion. From above investigations, it is known that the Si adatom can combine with the N adatom and form the Si-N addimer. In this direct mode, the diffusion of the N adatom could be promoted by the Si addition, as indicated in Section 5.3.3. However, in the lowest-energy configuration, a Si adatom cannot combine with a Ti adatom to form an addimer like the Si-N addimer. Could the diffusion of the Ti adatom be promoted by the Si adatom in the other mode? All the diffusions of the Si adatom and the Si-N addimer around and along the island are relatively easy, see Section 5.3.2 and Section 5.3.3. If the Si adatom and the Si- N addimer diffuse nearby the Ti adatom, the PES of the Ti adatom could be changed and the activation energy of the Ti diffusion may decrease. Thus, the the diffusion of the Ti adatom becomes easier. To confirm this, two calculations were performed to study the activation energy of the Ti atom of the Ti-N addimer. In the first case, during the Ti atom of the Ti-N addimer diffuses along the TiN island from the site P1 to the site P2, a Si adatom is just at the site P4, as shown in Fig. 5.52(a). In the second case, during the Ti atom of the Ti-N addimer diffuses from P1 to P2, an addimer Si-N are just on the site P4 and the site P3, respectively [Fig. 5.52(b)]. Table 5.33: The total energies and the different energies of the Ti diffusion along the TiN island under the influence of a Si adatom or a Si-N addimer. Ti-N-Si Ti-N-Si-N Path E0 Ediff Path E0 Ediff 0.03 -1878.79 0.00 0.03 -1887.00 0.00 0.06 -1878.20 0.59 0.07 -1886.31 0.69 0.10 -1876.92 1.87 0.12 -1885.07 1.93 0.18 -1876.58 2.21 0.20 -1885.31 1.69 0.24 -1876.95 1.84 0.25 -1887.06 -0.06 0.30 -1877.42 1.37 0.30 -1887.55 -0.55 The atomic calculations with ab initio method 144 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.00 0.10 0.20 0.30 Path (nm) (e V ) (a) (b) Fig. 5.53: The E-Path curves of the Ti diffusion along the TiN island under the influence of a Si adatom or a Si-N addimer: (a) under the Si adatom influence, (b) under the influence of a Si-N addimer. In the calculation, the surface slab of 6 6 (5+7) was used and the k-points setting was 331. The calculations were conducted with the nudged elastic band method. The calculation results are listed in Table 5.33 and the E-Path curves are presented in Fig. 5.53. The calculation result of Section 5.3.3.3 shows that the activation energy for the diffusion of the Ti of the Ti-N addimer around its partner N is of 2.59 eV. Here, with a Si adatom nearby the site P1, the activation energy of the Ti diffusion decreases to 2.21 eV. And with a Si-N addimer at the nearest neighboring site and the second nearest neighboring site, the activation energy reduces to 1.93 eV. Theoretically, this activation energy decrease could make the Ti diffusion from the site P1 to the site P2 relatively easier. Comparing Fig. 5.23(a), Fig. 5.37(a), and Fig. 5.53(a) (b), the change of PES is obvious. It is clear that the effect of the Si adatom and the Si-N addimer is to change the PES nearby the Ti adatoms or the Ti-N addimers and hence to promote the Ti diffusion. 5.3.7. The section summary and the process parameter estimation After the investigation of above basic diffusion modes, all the activation energies of the diffusion are collected and listed in five tables, Table 5.34 to Table 5.38. These activation energies have a very large difference in value. In fact, a small difference in value of activation energies could lead to a very large influence on the diffusion. For example, on the TiN(001) surface, the activation energy of a Ti adatom is 0.62 eV. If the deposition rate is 0.64nm per second and the deposition temperature is 100 C°, the diffusion coefficient calculated with equation (4.2) is (5.2)² nm². The activation energy of a N The atomic calculations with ab initio method 145 adatom is 1.06 eV. Under the same condition, the diffusion coefficient for a N adatom is only (0.0041)² nm². So we can image that the diffusion depended on the activation energies in the five tables are some total different events in the film growth process. In addition, in the film growth process, there are over 20 orders of magnitude such diffusion events and they influence on one and another. On the whole, it is like a chaos or a symphony. Therefore, the numerical analysis of the film growth process is very difficult. Nevertherless, through analyzing the activation energies in the five tables, we can draw some qualitative conclusions which reveal the formation mechanism of the TiN coatings and the Ti-Si-N coatings. (1) About the formation mechanism of the TiN film. The activation energy calculations for the diffusion of Ti and N adatom on the TiN (001) surface provide a clue to the preferred orientation transformation from (001) to (111). This transformation is based on three points: (a) Ti adatoms diffuse much more quickly than N adatoms on the TiN(001) surface; (b) Ti adatoms are possible to create the nuclei of TiN(111) on the TiN(001) surface; (c) N adatoms diffuse mostly around the local surface N atom. The transformation could be hindered by the restriction on the collection of Ti adatoms. The inter diffusion of Ti and N atoms in the TiN crystallite or in the TiN(001) surface are very difficult, because the activation energies are high to 3.90 eV and 3.76 eV for the inter diffusion of Ti; and 3.50 eV and 2.15 eV for the inter diffusion of N, (Table 5.38). Additionally, the diffusion of Ti adatoms, N adatoms, and Ti-N addimers around and along the TiN island on the TiN(001) surface are also difficult, the activation energies from 1.97 eV to 3.02 eV, (Table 5.34 and Table 5.35). These high activation energies lead to the insufficient diffusion in the TiN film growth process. This is why the TiN films have many voids [Sundgren85] and a columnar structure [Li92]. (2) About the formation mechanism of the Ti-Si-N coating. Si adatoms could promote the Ti and N diffusion in the Ti-Si-N film growth process. First, Si adatoms combine with N adatoms and forms Si-N addimers. The Si-N configuration changes the diffusion mode of the N adatom. All the activation energies for the diffusion of the Si-N addimers on the TiN(001) surface, around the TiN island, and along the TiN island are relatively low, lower than 1.72 eV (Table 5.35), so that the Si-N addimers diffuse straight- forwardly during the Ti-Si-N film growth. Second, both the activation energies for the diffusion of Si adatoms around and along the TiN island are also low, lower than 1.67 eV (Table 5.34), so that during the Ti-Si-N film growth process, Si adatoms can diffuse easily, too. Third, Si can always stay outside the TiN island because the Si-Ti bond and the Si-N The atomic calculations with ab initio method 146 bond are weaker than the Ti-N bond (This conclusion is from Section 5.2). The frequent diffusion of the Si adatoms and the Si-N addimers around the island could change the potential energy surface (PES) of the Ti adatom and promote the Ti diffusion, as illustrated in Section 5.3.6. Under the promotion of Si adatoms, the diffusion of the Ti and N adatom are increased. And the Si atoms and adatoms can diffuse easily in the TiN crsystallite and in the TiN(001) surface because the activation energies are low, 1.60 eV and 0.43 eV. These two points could make the voids in the film decrease. Thus, the Ti-Si-N film has a dense structure [Li92]. With the increase of N2 partial pressure and the frequent diffusion of the Si-N addimers and the Si adatoms, the (111) nuclei of the Ti adatoms on the TiN(001) surface may be restricted. Therefore, the TiN crystallite in Ti-Si-N coating maintains the preferred orientation (002) [Chandra06]. Table 5.34: The activation energies (eV) for the adatom diffusion. On surface Around island Along island Down island 1 2 3 Ti 0.62 1.14 1.97 0.89 2.71 0.00 N 1.06 0.62 0.79 3.02 0.54 2.04 0.66 Si 0.93 1.25 1.05 1.54 1.67 0.00 Table 5.35: The activation energies (eV) for addimer diffusion. Ti or Si around N N around Ti or Si Around island (1) Around island (2) Ti: P3-C Ti: C-P5 N: P4-P8 N: P4-B N: B-P2 Ti: P3-P7 Ti-N 1.35 1.20 1.75 0.77 0.52 2.20 0.82 1.60 Si-N 0.75 1.00 0.63 0.15 0.30 (2.89) 0.22 0.50 Around island (3) Along island Down island Around corner N Corner N jumping N to the corner site Ti or Si around N N around Ti or Si Ti-N 2.54 - - 2.59 1.93 0.00 Si-N 1.49 1.72 0.87 1.67 0.95 0.00 The atomic calculations with ab initio method 147 Table 5.36: The activation energies (eV) for adtrimer diffusion. Corner-Line Line-Corner Jump Ti-N-Ti 0.96 1.22 1.06 N-Ti-N 1.25 0.66 1.60 Ti-N-Si Ti moving Si moving Ti moving Si moving 1.09 1.43 1.36 0.85 0.78 Table 5.37: The activation energies (eV) for the diffusion of adtetramer 2N2Ti. P1 to P2 P2 to P3 P3 to P2 P2 to P1 Ti moving 2.22 0.82 1.16 0.62 P4 to P5 P5 to P6 P6 to P5 P5 to P4 N moving 2.18 0.80 0.84 0.51 Table 5.38: The activation energies (eV) for inter diffusion. Ti N Si In the crystallite 3.90 3.50 1.60 In the surface 3.76 2.15 0.43 (3) On the TiN(001) surface, the diffusion of the Ti adatom, the N adatom, the Ti- N addimer, and the Ti-N-Ti, N-Ti-N, and Ti-N-Si adtrimer are not difficult because the activation energies are lower than 1.60 eV. However, the 2N2Ti adtetramer is a stable structure on the TiN(001) surface and it is not easy to diffuse, (Table 5.37). (4) All the activation energies for the diffusion of the Ti, N, and Si adatom, the Ti- N addimer, and the Si-N addimer down the TiN island are very small or of 0.00 eV, so that the film growth of TiN and Ti-Si-N on the TiN(001) surface is the layer-by-layer mode or the Frank-van der Merwe (FM) mode. Comparing with the AFM measurement result in our experiment (Chapter 3), we know that the layer-by-layer growth mode does not equal to the surface of the film to be in form of atomic-level plane. According the above analysis, the Si adatoms play a very special role during the deposition process of Ti-Si-N. The micro- and nano-structure of Ti-Si-N depends largely on the diffusion behaviors of the Si adatom. With the above activation energies, we tried to estimate the process condition and parameters, such as the deposition temperature and the deposition rate. In this estimation, the ab initio calculation result was used as the The atomic calculations with ab initio method 148 activation energy Ea in the equation (4.2).         Tk E z a D B a i exp0 2  (4.2) In order to form the Ti-Si-N structure with the 3-nanometer-diameter sized TiN crystallite and the nano-crystallite surrounded by monolayer Si, Si adatoms must diffuse sufficiently quick to reach in time the place where two TiN islands hit each other and the boundary distance is larger than 2.55 Å. The activation energy for the Si-N addimer around or along the island is 1.72 eV. If the deposition rate is 0.64 nm per second, the time for a monolayer (ML) deposition is 0.33 s. The maximum mean free time td for the diffusion of the Si-N addimer around the TiN island is expected to be at least one order of magnitude less than the time required to form a monolayer, i.e. td = 0.033 s. The diffusion length is a half of the circumference of the 3 nanometer island, (3 3.1416)/2 nm. With the activation energy, the maximum mean free time td, the diffusion length, a = 0.3 nm, z = 2 (around the island), and atomic vibration frequency ν0 of 1013 per second, we can calculate the corresponding temperature for the diffusion, i.e. T = 861.0 K or about 588 °C. If we use the diffusion activation energy of the Si adatom around the TiN island, of 1.67 eV, the corresponding temperature T is 836.0 K or about the 563 °C. This means that under the above process condition and parameter, namely the deposition rate 0.64 nm/s and the deposition temperature 563 °C or 588 °C, the Si adatom may separate two TiN island in time and hence lead to the formation of the 3 nm grain in the Ti-Si-N film growth process. This example indicates that the effect of the Si addition relys largely on the process condition and parameters. The above calculation results of 563 °C and 588 °C are very close to the deposition temperature 560° which were used in the experiments [Li92]. Therefore, we can believe that the ab initio method is really useful for the activation energy calculation. Especially now we have no other method which can calculate the activation energy so accurately. However, this does not mean that these activation energies have practical meanings for the production. Objectively, these activation energies obtained by the ab initio calculations have just the relative meanings, i.e. they could be used to analyze the diffusion probability of the different adatoms or ad-clusters. For being used in the production, these activation energies should be calibrated through the experiments. In fact, the whole diffusion event in film growth process is just like a symphony. On the one side, the diffusion events which related to the underlined activation energies in The atomic calculations with ab initio method 149 the Table 5.34 to Table 5.38 dominate the formation process. On the other side, the diffusion events related to the low activation energies have also large influence on the local atomic arrangement. The whole stochastic formation process should be simulated with the KMC method. 5.4. The summary of the ab inito calculations Through the ab initio calculations, the basic structure and the formation mechanism of the Ti-Si-N superhard nanocomposite coatings have been identified. The relevant results are presented in the summaries of Section 5.2 and Section 5.3. Together these two summaries, we come to the following conclusions. (1) The ab initio calculation result shows a picture about the self-organization and self-assembly of the Ti-Si-N nanostructure. In the self-organization and self-assembly, the Si adatom and atom play an interesting and important role. In the formation process of the nanostructure, the Si adatoms work like an organizer, i.e. they could promote the diffusion of the Ti and N adatoms. In the self-assembly process, the Si atoms move into the boundary of TiN, separate the TiN crystallites, and fix the boundary. With these two effects, the Si adatoms and atoms simultaneously promote the diffusion of the Ti and N adatoms and restrict the increase of the TiN grain size. This is a very special function in the Ti-Si-N film growth process. (2) The hardness enhancement of Ti-Si-N results also from these two effects. Under the Si promotion, the diffusion of Ti and N increases and hence the voids in film decrease. The substitutional solid solution of Si can also make the voids decrease. The TiN coating with few voids has relatively high hardness [Jhi01]. In addition, with Si in the boundary, the strain and stress in boundary region are decreased and the combination of boundary atoms is enhanced. Therefore, the hardness of Ti-Si-N coatings could increase due to the dense structure and the strong boundary. (3) The Ti-Si-N superhard nanocomposite coatings provide a good example for the bond combination. Actually, all the Si effects come from the difference of the bond types, bond energies and bond lengths. The bond energies of N-N and Ti-N are relatively strong and their bond lengths are relatively short, while the bond energy of Ti-Ti is weak and its bond length is long. This leads to the diffusion difficulty of Ti and N. The bond energies of Si-N and Si-Ti are weaker than those of N-N and Ti-N, but stronger than that of Ti-Ti. The bond length of Si-N is longer than that of N-N but shorter than those of Ti-N The atomic calculations with ab initio method 150 and Ti-Ti; the bond length of Si-Ti is longer than those of N-N and Ti-N but shorter than that of Ti-Ti. Therefore, the Si adatom and the Si-N addimer can diffuse easily in the formation process and hence promote the N and Ti diffusion. As the self-assembly result, the covalent bonds of Si-N and Si-Ti in the TiN boundary have large influence on the property of the Ti-Si-N composite. This reminds us that the design of the bond relationship and combination is very crucial to the nanostructure development. The design of the bond combination should focus not only on the property of nanostructure materials but also on the self-organization and self-assembly process. (4) The effect of Si addition on the self-organization and self-assembly in the film growth process depends heavily on the process conditions and parameters. Under different process conditions and parameters, the Si diffusion behaviors is different, self-assembly is different, and then the nanostructure is different. This means that apart from the design of bond combination and the nanostructure, the numerical design of process is also very important to the nanostructure development. This numerical design of process should provide the accurate correlation between nanostructure (composite, phase, texture, grain size and shape, interface, and pattern) and the process condition and parameters. The designed nanostructure could be prepared only by a precise combination of the atomic percent of Ti, Si, N, the deposition temperature T, and the deposition rate Rd. Certainly, the research focus will be on the statistical process. Based on the activation energies obtained with the ab initio method, the KMC simulation will play a key role for this kind of research. (5) The research results show that the ab initio method is powerful which can provide the insight of the atomic structure and the formation mechanism of nanostructure materials and hence provide a basis to determine the process condition and parameters. 6. Conclusion and outlook This research is a practice of the digital factory. The goal of this research is to seek for a simulation way to solve the problems in the development of nanostructured composite coatings. In this research, the simulation and the calculation methods have been used to identify the atomic structure and the formation mechanism of the Ti-Si-N superhard nanocomposite coatings. The research includes three kinds of investigations: experiments, kinetic Monte Carlo simulations, and ab initio calculations. In the sputtering PVD process, the ion mass spectra and the deposition rates have been measured. The measurement results show that the Ti-Si-N deposition in the sputtering PVD is a complicated process and it is difficult to obtain the stoichiometry of TiN without the relevant measurement in situ, because (a) there is a large change of the proportion of the Ti + ion flux to the N2 + ion flux near the stoichiometry point of TiN; (b) all the process parameters such as the sputtering power, the N2 flow rate, the Ar flow rate, the process pressure, and the distance between target and substrate have the influence on the stoichiometry of TiN and these influences are interrelated. The experiment of the Ti- Si-N depositions and relevant characterizations with SEM, XRD, AFM, and nanoindenta- tion measurement have been carried out. The experiment results show that the Si addition has obvious influence on the microstructure and the hardness of Ti-Si-N coatings. But the atomic structure and the formation mechanism of Ti-Si-N coatings have not been identified through the experiments. This reveals the limitation of the present-day experimental method and indicates that the atomic simulation and calculation are necessary. Two kinetic Monte Carlo (KMC) simulation codes, namely the KMC simulation code with the lattice model and with the off-lattice model, have been developed. Both of them are in 3D model. With the lattice model KMC code, the deposition process simulations of over 10000 atoms have been conducted. The simulation result is basically The conclusion and the outlook 152 in agreement with the experiment result. In the off-lattice KMC simulation, the dimer method has been used to search the saddle points on the potential energy surface (PES), which provided the direct calculation method of activation energy and the relaxation algorithm of adatoms. Therefore, this KMC simulation is relatively close to the real situation. The Ti-Si-N deposition of 2000 atoms has been simulated with this off-lattice KMC code. But the basic structure and the formation mechanism of the Ti-Si-N film have not been found out due to the inaccurate potential algorithm. In order to obtain the accurate description of atomic interaction, the ab inito calculation should be conducted. The ab inito calculations have been performed with VASP code which is based on density functional theory (DFT). The basic structure of the Ti-Si-N superhard composite coating has been identified with the ab intio calculations [Liu07]. (1) The total energy and cohesive energy calculations for the configurations, in which a Si atom is added into the TiN crystallite or into the TiN boundary, have been performed. The calculation results show that (a) there is no silicon interstitial solid solution in the TiN crystallite under the thermal equilibrium condition; (b) if a titanium atom or a nitrogen atom is missing in the TiN crystallite, a silicon atom is possible to occupy the vacant site and to form the substitutional solid solution; (c) in the lowest-energy structure of Ti-Si-N composite, Si atom is in the form of a double cross tetrahedron Si-4N-4Ti and/or a fourfold coordinated plane structure Si-2N-2Ti in the boundary of TiN, i.e. the basic structure of Ti-Si-N superhard composite coatings is TiN crystallites with Si-4N-4Ti and/or Si-2N-2Ti in the boundaries. (2) A new kind of interface structure, Si-4N-4Ti and Si-2N-2Ti, is a discovery in this research. The properties of the interface structures Si-4N-4Ti and Si-2N-2Ti are: (a) Si-4N-4Ti or Si-2N-2Ti is an intergranular phase; (b) the crystal structure of Si-4N- 4Ti or Si-2N-2Ti is total different from that of the TiN structure, i.e. there is an intrinsic mismatch between the structure Si-4N-4Ti (or Si-2N-2Ti) and the B1 NaCl structure TiN; (c) the bonding type of Si-4N-4Ti or Si-2N-2Ti is different from that of the TiN structure. With the covalent bonding of Si-4N-4Ti and Si-2N-2Ti in the boundary, the boundary is strengthened and the inter diffusion through the boundary is restricted. Thus, the hardness and the thermal stability of Ti-Si-N nano-composite coatings are enhanced. The hardness of Ti-Si-N coatings could further be improved if the arrangement of different sized crystallites is carefully designed and prepared. The conclusion and the outlook 153 The interface structure, the double cross tetrahedron or the fourfold coordinated plane unit, can separate the crystallites and fix the boundaries in the polycrystalline materials of rocksalt structure. Therefore, the interface structure will be very helpful to prepare the nano-composites of the early transition metal nitrides and carbides. The interface structure could be used to control the size of the crystallite and to improve not only the mechanical properties, but also the other properties such as the electrical, optical, superconductive properties, and so on. The potential value of this interface lies in the production of nanometer patterns or quantum dots. (3) The investigation of Si distribution in the TiN boundary of Ti-Si-N composites demonstrates that the interaction of the distortion introduced by Si-4N-4Ti can be avoided through the separation of Si atoms in the TiN boundary and hence the strain in the structure is reduced. According to the results of Ti-Si-N basic structure and the Si distribution in the boundary, the atomic percent of Ti: N: Si can be calculated. For example, if the grain size of the TiN equiaxial crystallite is 2.94 nm, the boundary thickness is 0.235 nm, and Si atoms are in one fourth of the total boundary cells, the atomic percent of Ti: N: Si is 47.35 at%: 47.35 at%: 5.30 at% in the Ti-Si- N coating. (4) The study on the formation of the interface Si-4N-4Ti indicates that (a) Si adatoms tend to stay outside the TiN island because the Si-N and Si-Ti bonds are weaker than the Ti-N bond and (b) Si atom may drop into the boundary if it hits a wide boundary whose distance is larger than 0.255 nm. The ab initio calculations have been also carried out to study the formation mechanism of Ti-Si-N superhard composite coatings. The investigation includes (a) the PES and the diffusion paths of Ti, N, and Si adatom on the TiN(001) surface; (b) the activation energy for the diffusion of Ti, N, and Si adatom on the TiN(001) surface, around the TiN island, along the TiN island, and down the TiN island; (c) the activation energy for the diffusion of the Ti-N or Si-N addimer on the TiN(001) surface, around the TiN island, along the TiN island, and down the TiN island; (d) the activation energy for the diffusion of the Ti-N-Ti, N-Ti-N, and Ti-N-Si adtrimer and the 2Ti2N adtetramer on the TiN(001) surface; (e) the activation energy for the inter-diffusion of Ti, N, and Si atom in the TiN crystallite and in the TiN(001) surface. By these investigations, the formation mechanism of the film growth of TiN and Ti-Si-N have been recognized. The conclusion and the outlook 154 (1) About the formation mechanism of TiN film. The activation energy calculations for the diffusion of Ti and N adatom on the TiN (001) surface provide a clue to the preferred orientation transformation from (001) to (111). This transformation is based on three points: (a) Ti adatoms diffuse much more quickly than N adatoms on the TiN(001) surface; (b) Ti adatoms are possible to create the nuclei of (111) on the TiN(001) surface; (c) N adatoms diffuse mostly around the local surface N atom. The transformation could be hindered by the restriction on the collection of Ti adatoms. The inter diffusion of Ti and N atoms in the TiN crystallite or in the TiN(001) surface are very difficult, because the activation energies are high to 3.90 eV and 3.76 eV for the inter diffusion of Ti; and 3.50 eV and 2.15 eV for the inter diffusion of N, (Table 5.38). Additionally, the diffusion of Ti adatoms, N adatoms, and Ti-N addimers around and along the TiN island are also difficult, the activation energies from 1.97 eV to 3.02 eV, (Table 5.34 and Table 5.35). These high activation energies may result in the insufficient diffusion in TiN film growth process. Thus, the TiN films have many voids [Sundgren85] and a columnar structure [Li92]. (2) About the formation mechanism of the Ti-Si-N coating. The Si addition could change the TiN film growth. (a) Si adatoms combines with N adatoms and forms the Si-N addimers. The configuration of Si-N changes the diffusion mode of N adatom. All the activation energies for the diffusion of the Si-N addimers on the TiN(001) surface, around the TiN island, and along the TiN island are relatively low, lower than 1.72 eV (Table 5.35), so that the Si-N addimers diffuse straightforwardly during the Ti-Si-N film growth. (b) The activation energies for the diffusion of Si adatoms around and along the TiN island are also low, lower than 1.67 eV (Table 5.34), so that the Si adatoms can also diffuse easily during the Ti-Si-N film growth process. (c) Si adatoms tend to stay outside the TiN island. The frequent diffusion of the Si adatoms and the Si-N addimers around the island could change the potential energy surface (PES) of the Ti adatom and to promote the Ti diffusion, as illustrated in Section 5.3.6. Under the influence of Si adatoms, the diffusion of N and Ti adatoms are increased. And since the activation energies are low, 1.60 eV and 0.43 eV, the inter diffusion of Si atoms and adatoms are easy in the TiN crsystallite and in the TiN(001) surface. These two points could make the voids in the film decrease. Therefore, the Ti-Si-N The conclusion and the outlook 155 film has a dense structure. With the increase of N2 partial pressure and the frequent diffusion of the Si-N addimers and the Si adatoms, the (111) nuclei of Ti adatoms on TiN(001) surface may be restricted. This makes the TiN crystallite in Ti-Si-N coating maintain the preferred orientation (002). (3) The diffusion promotion effect of Si adatom depends on the process parameters. For example, if the deposition rate is 0.64 nm per second, the deposition temperature should be at least in the range of 563 °C to 588 °C in order to maintain the sufficient diffusion of the Si-N addimers and the Si adatoms, and hence the formation of 3 nm sized TiN crystallites in Ti-Si-N film. Together with the identification results of the atomic structure and the formation mechanism of Ti-Si-N, the effects of the Si addition have been found out. In the self- organization and self-assembly, the Si adatoms and atoms play an interesting and important role. In the formation process of the Ti-Si-N composite, the Si adatoms promote the diffusion of the N and Ti adatoms. In the self-assembly process, the Si atoms move into the boundary of TiN, separate the TiN crystallites, and fix the boundary. With these two effects, Si adatoms and atoms can simultaneously promote the diffusion of the N and Ti adatom and restrict the increase of grain size of TiN. This is a very special mechanism in the Ti-Si-N film growth process. The hardness enhancement of Ti-Si-N results also from these two effects. Under the Si promotion, the Ti and N diffusion increases and the voids in film decrease. The substitutional solid solution of Si can also make the voids decrease. The TiN coating with few voids has relatively high shear modulus [Jhi01]. In addition, with the Si atoms in the boundary, the strain and the stress in boundary region are decreased and the combination of boundary atoms is enhanced. With the dense structure and strong boundary, the hardness of Ti-Si-N coatings is increased. Actually, the Si effects come from the difference of the bond types, bond energies and bond lengths of Ti, N, and Si combinations. Comparing with the Ti-N bond, the bond energy of N-N is relatively strong and the bond length is relatively short, while the bond energy of Ti-Ti is weak and the bond length is long. This leads to the diffusion difficulty of Ti and N. The bond energies of Si-N and Si-Ti are weaker than those of N-N and Ti-N, but stronger than that of Ti-Ti. The bond length of Si-N is longer than those of N-N but shorter than those of Ti-N and Ti-Ti. The bond length of Si-Ti is longer than those of N-N and Ti-N but shorter than that of Ti-Ti. Therefore, the diffusion of Si adatom and Si-N The conclusion and the outlook 156 addimer is relatively easy during the film growth process. As the self-assembly result, the covalent bonds of Si-N and Si-Ti in the TiN boundary have a major influence on the property of the Ti-Si-N composite. This reminds us that the design of bond combination is very crucial to the development of nanostructured materials. The bond combination design should focus not only on the property of the nanostructured material but also on the self- organization and self-assembly process. And the numerical design of manufacturing process is also very important to the nanostructure development. The designed nanostructure could be prepared only by a precise combination of the atomic percent of Ti, Si, N, the deposition temperature T, and the deposition rate Rd. Another important result of this research is a hint for a simulation way, namely the design method for the nano-composite. In order to develop new nano-composites film, atomic calculation, simulation, and the experiment could be conducted in following sequence of steps. Firstly, the ab initio calculation should be carried out in order to investigate the atomic structure and the activation energies for the basic diffusion. Secondly, the result of the atomic structure can be used to the technical specification design for the pattern in different layers. And then the KMC simulation or the ab initio calculation could be performed in the product evaluation for performance. Thirdly, the activation energies for the basic diffusion could be used in the design for manufacture. For example, based on the ab initio results, the calculation algorithm of simple potentials could be improved. And then the off-lattice KMC simulation with improved algorithm of simple potentials can be conducted to study the stochastic process of a large sized system, which can present the experiment plan for film preparation. Finally, experiments may be carried out to check the simulation results. In return, the experiments can provide the suggestion for improving simulation method. Objectively, the identification of the atomic structure and the formation mechanism of Ti-Si-N in this research is still at the first stage and all the results should be verified by experiments and the off-lattice KMC simulations. Additionally, the basic diffusion of Ti, N, and Si on the TiN(111) surface should also be investigated in next step. After the above researche, now we come to a new starting point and face many new questions that provide the subjects for the further research. (1) How could the hardness of Ti-Si-N be improved by the arrangement of the different The conclusion and the outlook 157 sized crystallites or how should the different sized crystallites and the interface elements be arranged in Ti-Si-N film to restrict the boundary crack, the grain boundary sliding, and the dislocation operation and movement? Does the hardness relate with the phonon frequency? What is the correlation between the phonon frequency of the interface structure and the TiN crystallite size? Could the Ti-Si-N composite be prepared in form of a phonon crystal to resist some phonon dispersion, especially to resist the high frequency phonon dispersion? (2) If the TiN crystallite is completely surrounded with the covalent bond interface, will the electronic band structure of TiN be changed? Does the change of the electronic band structure relate with the crystallite size? Is it possible to obtain the quantum effect with the Ti-Si-N composite? (3) What are the differences in the structure and the formation process between Ti-Si-N and the other transition metal nitrides with Si addition? What are the differences in the structure and the formation process between Ti-Si-N and the titanium nitride with the addition of C, Ge? Could the mechanism of self-organization and self- assembly of nanostructured composites be identified through the comparison with these different formation processes? (4) How could the Si addition be use to accurately control the size and shape of the TiN crystallite and to produce the designed pattern in the Ti-Si-N film growth process? How can this process be simulated with the off-lattice KMC code? The questions of group (1) to (3) regard to the design of new structures and the evaluation their properties. The questions of group (3) and (4) are about the preparation of the nano structured composites, namely the design for manufacturing. Facing these questions, how should we do the researches, with the experiment or with the simulation? This research shows clearly that the simulations should be performed before the experiments and the ab initio calculations should be conducted before the other simulations. Our experience in this research also indicates that based on the ab initio calculation, the steady improvement of the simulation algorithm may be a appreciate way to provide a meaningful information for the practical project. This research shows the importance of the digital factory and the digital laboratory, i.e. the atomic calculation and the process simulation is necessary, worthwhile, and unavoidable for the development of the nano-composites. Although the results are far The conclusion and the outlook 158 from perfect yet, this research has already presented enough evidence that it is impossible to develop the nanocomposites like Ti-Si-N without the ab initio calculations. Certainly, the ab initio calculation and the simulation will become the most important method for the design of nanostructured materials. This research is only a start. The task of next step is based on the ab initio calculation and the off-lattice KMC simulation, gradually to develop a whole design method of nano-composite materials, which includes the concept design, the technical specification design, the evaluation for performance, and the design for manufacture, i.e. progressively closs to the strict design of mechanical product [Heisel06- 2] [Ullman97]. On the platform of the digital factory or the digital laboratory, every detail of the nanocomposite and its manufacture process will be described with accurate numbers and images. With the purposeful combination of the simulation and the physical experiments, we can not only steadily promote the development of the nano-composite coatings but also speed up the transition from the art to the science [Greene03] and from the science to the art. Zusammenfassung ( Extended Abstract in German) Einführung In der vorliegenden Arbeit werden unterschiedliche Methoden und Simulationsmodelle zur Beschreibung und Charakterisierung der Bildungsmechanismen von superharten Ti- Si-N Nanokomposites entwickelt und beschrieben. Das Hauptziel der Forschungsarbeiten besteht in der Identifizierung und Modellierung spezifischer atomarer Strukturen und Bildungsmechanismen. Die langfristigen Ziele solcher Prozessimulationen liegen in der Vorhersage des Schichtwachstums sowie der makroskopischen mechanischen und optischen Schichteigenschaften. Zudem stellen Prozessimulationen eine solide Basis für die weiterführenden Betrachtungen innerhalb der Digitalen Fabrik dar. In den letzten Jahren sind Untersuchungen und Designsstudien der superharten Nanokompositeschichten ins Blickfeld vieler Wissenschaftler gerückt [Veprek99] [Andrievski01] [Musil00] [Zhang03] [Lu06]. Insbesondere interessieren viele Forscher die Ti-Si-N Nanokompositschichten, weil mit diesen Kompositschichten breits eine maximale Härte von über 100 GPa erreicht wurde. Das übersteigt sogar die Härte von Diamanten [Niederhofer99] [Veprek00-1]. Dieser Sachverhalt verdeutlicht den hohen Stellenwert, die den Nanokompositschichten in der Wissenschaft und in der technischen Anwendung zugeschrieben werden. Leider konnten Nanokompositschichten mit dieser Härte nicht wieder produziert werden, obwohl viel Forschungsarbeit in die Reproduktion dieser Schichten gesteckt wurde. Zur systematischen Weiterentwicklung dieser Schichten ist es zwingend notwendig, die atomare Struktur und die Bildungsmechanismen mit Hilfe geeigneter Simulationsmethoden zu identifizieren und zu modellieren. Unter Zuhilfenahme der Charakterisierung und Analyse der Messverfahren XRD, SEM, HRTEM, und XPS wurde bereits ein Strukturmodell der Ti-Si-N Nanokomposit- schicht entwickelt [Veprek95-1]. Mit diesem ist die Einbettung nanokristalliner TiN- Teilchen in einer amorphen Si3N4-Matrix darstellbar. Das Modell wird als nc-TiN/a-Si3N4 ausgedrückt. Dieses Modell liefert jedoch keine atomistische Beschreibung. Hierbei Zusammenfassung 160 werden die Grenzen gegenwärtiger Möglichkeiten der Charakterisierung deutlich gezeigt. Deshalb sind die atomistsche Berechnung und die Simulation für diese Strukturen notwendig. Vor kurzem führten Hao et al. und Hultman et al. unabhängig voneinander Ab-initio-Berechnungen zur atomaren Struktur durch und erzielten dabei einige interessante Ergebnisse [Hao06-1] [Hao06-2] [Hao06-3] [Hultman07]. Für die Identifizierung der Bildungsmechanismen von Ti-Si-N Nanokomposite- schichten sind bisher jedoch noch keine Messung in situ gemacht worden. Veprek et al. versucht die Separation der Phasen TiN und Si3N4 mit der Spinodal Methode zu erklären [Veprek05] [Zh-Vep06]. Bisher ist dies die einzige Forschungsarbeit, die über den Bildungsprozess der Ti-Si-N Nanokompositschichten veröffentlicht wurde. Im Gegensatz zu den obigen Ausführungen liegen die Schwerpunkte dieser Forschungsarbeit in der Weiterentwicklung der kinetischen Monte Carlo Simulations- methode, der quantenmechanischen Ab-initio-Berechnungen sowie der experimentellen Erfassung benötigter Randbedingungen. Experimentelle Untersuchungen zur Ermittlung de r Simulationsrandbedingungen In dem Sputter-PVD-Prozess wurden Messungen mit einem Plasmamonitor und einem Schwingquarz durchgeführt. Das Messsergebnis mit dem Plasmamonitor zeigt, dass die Abscheidung von Ti-Si-N ein sehr komplizierter Prozess ist und die Stöchiometrie von TiN sehr schwer zu ermitteln ist, weil (a) die Proportionalität des Ti+ Ion Flusses und des N2+ Ion Flusses einen großen Wechsel hat; (b) die Prozessparameter wie Sputterleistung, Abscheidungsrate, N-Fluss, Prozessdruck, Ar-Fluss, und Abstand zwischen Target und Substrat auf die Stöchiometrie von TiN einwirken. Außerdem stehen die Einflüsse dieser Parameter in einer Wechselbeziehung zueinander. Viele Experimente wurden zur Abscheidung von Ti-Si-N Nanokompositschichten und zu relevanten Charakterisierungen wie SEM, XRD, AFM und Nanoindentation durchgeführt. Dabei wurde festgestellt, dass der Zusatz von Si einen deutlichen Einfluss auf die Mikrostruktur und die Härte der Ti-Si-N Schicht hat (vgl. Kap. 3.3). Leider sind die atomare Struktur und die Bildungssmechanismen der Ti-Si-N Nanokompositschicht jedoch experimentell mit den heute zur Verfügung stehenden Methoden nicht auflösbar. Dieser Umstand verdeutlicht noch einmal die Notwendigkeit für theoretische Lösungs- ansätze und praktische Simulationsmethoden. Zusammenfassung 161 Kinetische Monte Carlo Simulation In dieser Forschungsarbeit wurden zwei erweiterte kinetische Monte Carlo (KMC) Simulationsmodelle entwickelt und programmiert. Der erste KMC-Ansatz basiert auf dem Gitter-Modell. Mit diesem Code können Simulationen von mehr als 10.000 Atomen durchgeführt werden. Abbildung 1 zeigt das Feature dieses Codes durch die farbliche Kennzeichnung verschiedener Kristalle. Der zweite KMC-Ansatz beruht auf dem dem „Ohne-festes-Gitter-Modell―. In diesem Modell diffundieren die Atome oder Teilchen nicht mehr von einem Gitter zum anderen, sondern hängen von der Potential der Oberflächenenergie (PES: potential energy surface) ab. Abbildung 1: Die Korngröße in Abhängigkeit von der Temperatur: a) 100K; b) 200K; c) 300K; d) 400K. Die Dimer Methode [Henkelman99] wird in den Porgrammcode implementiert, um den Sattelpunkt auf PES zu finden. Diese Methode liefert einen direkten Algorithmus für die Aktivierungsenergie und hat eine Entspannungsfunktion für die abscheidenden Atome. (a) (b) (c) (d) Zusammenfassung 162 Mit dem Ohne-festes-Gitter-Modell ist die Simulation weit realer als mit dem Gitter- Modell. Mit diesem Code wird die Simulation der gleichzeitigen Abscheidung von über 2000 Ti-, N-, und Si-Atomen durchgeführt, siehe Abbildung 2. Die atomare Struktur und der Bildungsmechanismus der Ti-Si-N Schicht sind mit diesen Simulationsansätzen jedoch nicht eindeutig darstellbar. Die Ursache liegt unter anderem im ungenauen Algorithmus der Interaktion zwischen den Atomen. Aus diesem Grund sind wesentlich genauere Simulationsansätze, die auf quantenmechanischen Berechnungen wie der Ab- initio-Berechnung beruhen, notwendig. Abbildung 2: Die KMC Simulation des Schichtwachsen der Ti-Si-N Komposite mit Ohne-festes-Gitter- Modell. Ab-initio-Berechnungen Die Ab-initio-Berechnungen basieren auf der elektronischen Struktur, die durch Schrödingers Wellenfunktion oder die Dichtefunktionaltheorie (DFT) beschrieben werden können (vgl. Kap. 2.3). Mit der Ab-initio-Methode kann das genaue Potenzial zwischen den Atomen berechnet werden. Deshalb ist die Struktur, die von den Ab-initio- Berechnungen simuliert wird, relativ zuverlässig. In dieser Forschungsarbeit wurden die Ab-initio-Berechnungen mit dem VASP Code, der auf der Dichtefunktionaltheorie (DFT) beruht, durchgeführt. Die Grundstruktur von Ti-Si-N Hartschichten wird durch eine Reihe von Berechnungen identifiziert. Die Berechnungen der Gesamtenergie und der kohäsiven Energie wurden für Konfigurationen durchgeführt, in denen ein Si-Atom im TiN-Kristallit oder an der TiN- Grenze an den hohen Symmetriepunkten dargestellt ist. Die Ergebnisse führen zu folgenden Erkenntnissen: (1) Die Grundstruktur von Ti-Si-N Kompositechichten. (a) Es existieren keine interstitiellen Mischkristalle von Si in perfektem TiN-Kristall im thermischen Zusammenfassung 163 Gleichgewicht; (b) Wenn ein Ti-Atom oder ein N-Atom im TiN Kristall fehlt, kann ein Si-Atom diese freie Lage besetzen und bildet ein Substitutions- mischkristall; (c) Die Grundstruktur von Ti-Si-N Kompositschichten ist das TiN- Kristall mit einem doppelt gekreuzten Tetraeder Si-4N-4Ti oder Si-2N-2Ti an der Grenze (siehe Abbildung 3). (a) (b) Abbildung 3: Die Interface-Struktur: (a) Si-4N-4Ti, (b) Si-2N-2Ti. (2) Die Struktur des neuen Interface, (doppelt gekreuzter Tetraeder Si-4N-4Ti und Si- 2N-2Ti) ist ein wichtiges Ergebnis dieser Forschungsarbeit. Die Interface- strukturen von Si-4N-4Ti und Si-2N-2Ti besitzen drei Eigenschaften: (a) Si-4N- 4Ti oder Si-2N-2Ti sind interkristalline Phasen; (b) Die Kristallstruktur von Si-4N- 4Ti oder Si-2N-2Ti unterscheidet sich von der TiN Struktur, da es eine intrinsische Fehlanpassung zwischen der Struktur Si-4N-4Ti (oder Si-2N-2Ti) und der TiN- Struktur gibt; (c) Der Verbindungstyp von Si-4N-4Ti oder Si-2N-2Ti unterscheidet sich auch von der TiN Struktur. Durch die kovalente Bindung von Si-4N-4Ti und Si-2N-2Ti an der Grenze ist die Grenze der TiN-Struktur gestärkt und dadurch wird die interne Diffusion beschränkt. Die Härte und die thermische Stabilität von den Ti-Si-N Nano- kompositschichten können somit verbessert werden. Weiter kann die Härte von Ti- Si-N-Schichten weiter verbessert werden, indem die Anordnung verschiedener Kristalle sorgfältig entworfen und vorbereitet wird. In der Ti-Si-N Kompositschicht kann die Interfacestruktur (doppelt gekreuzter Tetraeder) die TiN-Körner trennen und die TiN-Grenzen verfestigen, was für die Herstellung von Nanokomposites der Übergangsmetalle Nitrid und Karbid bedeutsam ist. Dies kann zur Kontrolle der Korngröße eingesetzt werden. Dies trägt somit sowohl zur Verbesserung der mechanischen Eigenschaften als auch der elektrischen, optischen oder supraleitenden Eigenschaften bei. Der potenzielle Zusammenfassung 164 Wert dieses Interfaces liegt in der Produktion von Nanometerstrukturen oder Quantenpunkte. (a) (b) Abbildung 4: Die Elektron Dichtung des Interfaces: (a) Si-4N-4Ti, (b) Si-2N-2Ti (3) Die Untersuchung der Si-Distribution an der TiN-Grenze zeigt, dass das Zusammenspiel von Verzerrungen vermieden werden kann, indem Si-Teilchen an der TiN-Grenze getrennt und damit die Belastungen in der Struktur relativ klein gehalten werden. Aufgrund der Ergebnisse bezüglich der Ti-Si-N Grundstruktur und der Distribution von Si-Teilchen an der Grenze, kann der Anteil der Ti: N: Si in den Kompositen berechnet werden. Zum Beispiel betragen die atomaren Prozentsätze von Ti:N:Si in der Ti-Si-N Schicht 47,35%: 47,35%: 5,30 % , wenn die Korngröße des äquiaxialen TiN-Kristallit 2,94 nm und die Grenzdicke 0,235 nm entsprechen (vgl. Kap. 5.2). (4) Die Untersuchung der Interfacebildung deutet darauf hin, dass ein abscheidendes Si-Atom zum Verbleib außerhalb der TiN-Insel neigt und auf die Grenze, in der der Abstand zwischen Atomen größer als 0,255 nm ist, trifft. Die Ab-initio-Berechnungen wurden zudem aus folgenden Gründen durchgeführt: (a) Untersuchung der PES und der Diffusionswege der adsorbierten Ti-, N- und Si-Atome auf der TiN(001)-Oberfläche; (b) Bestimmung der Aktivierungsenergie für die Diffusion der abscheidenden Ti-, N- und Si-Atome auf der TiN(001)-Oberfläche und der peripheren Umgebung der TiN-Insel, (c) Untersuchung der Aktivierungsenergie für die Diffusion der abscheidenden Ti-N und Si-N Dimere auf der TiN(001)-Oberfläche und der peripheren Umgebung der TiN-Insel; (d) Bestimmung der Aktivierungsenergie für die Diffusion der abscheidenden Ti-N-Ti, N-Ti-N, und Ti-N-Si Trimer und die Diffusion der abscheidenden 2Ti2N Tetramere auf der TiN(001) Oberfläche; (e) Untersuchung der Aktivierungsenergie Zusammenfassung 165 für die interne Diffusion von Ti-, N- und Si-Atomen im TiN-Kristallit und in der TiN(001) Oberfläche. 0.25 0.30 0.35 0.40 0.45 0.50 0.40 0.45 0.50 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Ead (eV) BR Top-Ti Top-N HL 0.25 0.30 0.35 0.40 0.45 0.50 0.40 0.45 0.50 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Ead (eV) BR Top-Ti Top-N HL 0.25 0.30 0.35 0.40 0.45 0.50 0.40 0.45 0.50 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Ead (eV) Top-Ti Top-N HL BR (a) (b) (c) Abbildung 5: Die überschlägige Potenzial-Energie-Oberfläche (PES) von Ti, Si, und N auf TiN (001)-Oberflächen: (a) PES für das abscheidende Atom Ti, (b) PES für Si, (c) PES für N. Die Ergebnisse zum Bildungsmechanismus der Ti-Si-N Schicht lassen sich durch folgende drei Punkte zusammenfassen. (1) Der Bildungsmechanismus der TiN-Schicht. Ti Adatome können die (111) Keime auf der TiN (001) Oberfläche formieren. Darüber hinaus kann es im TiN- Filmwachstum dazu führen, die präferierte Orientierung von TiN Kristallen aus (001) in (111) umzuwandeln. Die interne Diffusion des Ti-Atoms und des N-Atoms im Kristallit TiN oder in der TiN (001) Oberfläche erweist sich als schwierig, weil die Aktivierungsenergien sehr hoch sind. So betragen die Aktivierungsenergien 3,90 eV und 3,76 eV für Ti, und 3,50 eV und 2,15 eV für N (siehe Tabelle 5.38). Die Diffusion der abscheidenden Ti-Atome, der abscheidenden N-Atome und der abscheidenden Ti- N-Dimere in der Umgebung der TiN-Insel erweisen sich ebenfalls als schwierig (siehe Tabelle 5.34 und Tabelle 5.35). Die unzureichende Diffusion im TiN- Filmwachstum führt zu einer Säulenstruktur. (2) Der Bildungsmechanismus der Ti-Si-N Schicht. Die abscheidenden Ti, N, und Si Atome haben verschiedene PES auf den TiN(001) Oberflächen, (siehe Abbildung 5). Aus diesem Grund weisen sie verschiedenes Diffusionsverhalten auf. Der Hauptaugenmerk liegt in dem großen Unterschied der Aktivierungsenergien Zusammenfassung 166 zwischen der Diffusion der Ti Atome, der Diffusion der N Atome und der der Diffusion der Si Atome auf den TiN(001) Oberflächen und auch in der Umgebung der TiN-Insel (siehe Tabelle 5.34). Der Zusatz von Si-Atomen ändert den Bildungsmechanismus der TiN-Schicht. Zunächst wird ein abscheidendes Si-Atom mit einem abscheidenden N-Atom kombiniert und ein abscheidendes Si-N Dimer wird gebildet. Die Aktivierungs- energien für die Diffusion des abscheidenden Si-N Dimers auf der TiN (001) Oberfläche, entlang der TiN-Insel und in deren Umgebung sind relativ gering (Tabelle 5.35), so dass ein abscheidendes Si-N Dimer während des Schicht- wachstums von Ti-Si-N leicht diffundieren kann. Zweitens findet die Diffusion eines abscheidenden Si-Atoms entlang der TiN-Insel oder in deren Umgebung aufgrund der geringen Aktivierungsenergien leicht statt (siehe Tabelle 5.34). Drittens befindet sich ein abscheidendes Si-Atom im Gegensatz dazu außerhalb der TiN-Insel, weil die Si-Ti Bindungen und die Si-N Bindungen schwächer als die Ti- N Bindungen sind (Tabelle 5.5). Durch die häufige Diffusion der absorbierten Si- Atome und der abscheidenden Si-N Dimere können die PES eines Ti-Atoms verändert werden und deshalb kann die Ti-Diffusion dadurch gefördert werden. Die Diffusion von abscheidenden Ti- und N-Atomen wird durch den Zusatz von Si-Atomen gefördert. Daher ergibt sich eine dichte Struktur in der Ti-Si-N Schicht. (3) Die Wirkung von Si-Zusätzen zur Fördeung der Diffusion hängt von den Prozess- parametern ab. So sollte zum Beispiel die Abscheidungstemperatur zwischen 563°C und 588°C liegen, wenn die Abscheidungsrate 0,64 nm pro Sekunde beträgt, damit eine ausreichende Diffusion des abscheidenden Si-Atoms für die Bildung von 3nm großen Kristallen während des Ti-Si-N Schichtwachstums anhalten kann (vgl. Kap 5.3). Abschluss In dieser Forschungsarbeit wurde die Grundstruktur und der Bildungsmechanismus von superharten Ti-Si-N Nano-Komposit-Schichten durch atomistische Berechnungen identifiziert. In dem Schichtwachstum kann die Diffusion von abscheidenden N- und Ti- Atomen durch den Zusatz von Si-Atomen gefördert werden. In der Ti-Si-N Komposit- Struktur sind an der Grenze Si-Atome enthalten. Sie trennen die TiN-Kristalle und verfestigen die Grenze. Deshalb können Si-Atome gleichzeitig die Diffusion von Zusammenfassung 167 abscheidenden N- und Ti-Atomen fördern und die Vergrößerung von TiN Kristallen vermeiden. Von großer Wichtigkeit ist zudem die Berücksichtigung des Simulationsverfahrens. Zur Entwicklung der neuen Nanokomposite müssen zuerst Ab-initio-Berechnungen durchgeführt werden, um die atomare Struktur und die Aktivierungsenergien für die grundlegende Diffusion zu bestimmen. Auf der Grundlage dieser Ergebnisse wird der Algorithmus für die einfache Potenzial-Berechnung verbessert. Danach können das Ohne- festes-Gitter-Modell angewendet und die KMC-Simulation durchgeführt werden, um die stochastischen Prozesse zu simulieren und die Planung für Experimente voranzutreiben. Schließlich wurden experimentelle Arbeiten durchgeführt, um die Ergebnisse der Simulation zu validieren. Diese Forschungsarbeit zeigt, dass die hier vorgestllten Simulationen und Berechnungen eine leistungsfähige Methode zur Ermittlung der atomaren Struktur und des Bildungs- smechanismus von Nanokompositen darstellen. Da diese Simulationsarbeiten erst am Anfang stehen und die Nanotechnologie generell einen sehr starken Trend verzeichnet, wird für derartige Modellierungsansätze auch zukünftig ein sehr hoher Bedarf in der Forschungs- und Entwicklungsarbeit bestehen. Appendix A: The calculation of the atomic percent of Ti: N: Si Fig. A-1: The axonometric draw of equiaxial crystal of Ti-Si-N. B1 B2 R3 R1 H1 φ δ2 (C) (D) H30 R H3 H0 (A) (B) δ Fig. A-1: The section of the equiaxial crystallite of Ti-Si-N: (A) the front view; (B) the top view; (C) the side section; (D) the cross section. Appendix A 169 The structure of equiaxial crystallite of TiN and the monolayer boundary is shown in Fig. A-1 and its figures of the view and the section is presented in Fig. A-2. The δ is the half of the boundary thickness; the δ2 is the relevant thickness at the hexagon corner. The φ is the angle between the top surface and the horizontal surface, here φ equals 45°. The numbers of atoms in a TiN cell are 0.5 Ti atom and 0.5 N atom. With this count the number of atoms per nanometer cube (nm³) could be calculated, i.e. there are 52.4 nitrogen atoms/ nm³ and 52.4 titanium atoms/nm³ in the TiN crystallite. Since the distribution of silicon should be in a separating form, Si atoms are in one fourth of the total boundary cells. In this case, there are 26.2 silicon atoms, 52.4 nitrogen atoms, and 52.4 titanium atoms in one nanometer cube of boundary. Then, we need just calculate the volume of TiN crystallite and the boundary to obtain the atomic percent of Ti: N: Si. The volume of the equiaxial crystallite without the boundary is 1]30cos)1[(30]30cos)1[( 2 3 22 1 HRHRVcrt  (A.1) The volume with the boundary is 3]30cos)3[(330]30cos)3[( 2 3 22 3 HRHRVcrt  (A.2) And the volume of the boundary is 13 crtcrtbd VVV  (A.3) Here )90sin( 1    B ,  tgBB  212 , 213  RR , 21130 BBHH  , and 2213 BHH  . If we take H1=H0 = R1=14.69, δ=1.06, which corresponds to the 3 nm sized crystallite with monolayer boundary, the atomic percent of Ti: N: Si is 47.35 at%: 47.35 at%: 5.30 at%. Appendix B 170 Appendix B: The Nudged Elastic Band (NEB) method The Nudged Elastic Band (NEB) method is an algorithm to identify the ―minimum energy path‖ (MEP) between two basins. The MEP is a lowest energy path for a rearrangement of a group of atoms from one stable configuration to another. The NEB method was developed in the Jonsson group several years ago [Jonsson98] [Henkelman00] [Henkelman01D]. In the Nudged Elastic Band (NEB) method, a string of images of the system are created and connected together with springs and the images are relaxed by the spring force and the perpendicular force down toward the MEP, i.e. the distance between the images are maintained by the spring force and the images are pushed by the perpendicular force to the low energy region. A string of images or an elastic band with 1N images can be denoted by [ 0R , 1R , 2R , . . . , NR ], where the end points, 0R and NR , are fixed and given by the energy minima corresponding to the initial and final states. The 1N intermediate images are adjusted by the optimization algorithm. The tangent at an image i is estimated from two adjacent images along the path, 1iR and 1iR . ii ii ii ii i RR RR RR RR           1 1 1 1 (B.1) And then normalize  / . The force on each image should only contain the parallel component of the spring force, and perpendicular component of the true force ii S iii FREF   )( (B.2) where )( iRE is the gradient of the energy with respect to the atomic coordinates in the system at image i , and SiF is the spring force acting on image i . The perpendicular component of the gradient is obtained by subtracting out the parallel component ////)()()(   iii RERERE (B.3) Appendix B 171 The spring force should be evaluated as iiiii S i RRRRkF )( 11   (B.4) here k is spring constant. If the perpendicular component of the true force is too weak, it may leads to the problem of ‗kinky‘ and convergence to the MEP may never be reached. In this case, it needs a better estimate of the tangent.            11 11 iiii iiii i EEEif EEEif    (B.5) where iii RR    1 , 1   iii RR , and )( ii REE  (B.6) If image i is at a minimum 11   iii EEE or at a maximum 11   iii EEE , the tangent estimate become            11 maxmin, 11 minmax iiiiii iiiiii i EEifEE EEifEE    (B.7) where ),max( 11 max iiiii EEEEE   , and ),min( 11 min iiiii EEEEE   . Finally, the tangent vector needs to be normalized. In a modification of the NEB method, one of the images, which has the highest energy after a few relaxation steps, is made to move uphill in energy along the elastic band. This method is called the Climbing Image –NEB [Henkelman01D]. References [Ahuja96] R. Ahuja, O. Eriksson, J. M. Wills, and B. Johansson, Structural, elastic, and high-pressure properties of cubic TiC, TiN, and TiO, Phys. Rev. B 53(6), 3072-3079 (1996) [Amar06] J. G. 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Westkämper, Digitale Produktion – Herausforderung und Nutzen, FtK2006 - Fertigungstechnisches Kolloquium Stuttgarter Impulse. in Stuttgart, 469-490 (2006) [Wu05] Z. G. Wu, X. J. Chen, V. V. Struzhkin, and R. E. Cohen, Trends in elasticity and electronic structure of transition-metal nitrides and carbides from first principles, Phys. Rev. B 71, 214103-5p (2005) References 185 [Wu06] G. X. Wu, X. J. Liu, E. Westkämper and X. M. Wang, Off-lattice kinetic Monte Carlo simulation of initial stage of TiN film growth. Chinese Journal of Vacuum Science and Technology 26(4), 299-302 (2006) [Yang00D] Y.G. Yang, The Monte Carlo simulation of physical vapor deposition, Dissertation of University of Virginia, AAT 9975457 (2000) [Zeuner98] M. Zeuner, H. Neumann, J. Zalman, D. Slavínská, and H. Biederman, Characterization of DC unbalanced magnetron deposition of Ni C : H composite films, Vacuum 51(3), 417-426 (1998) [Zhang03] S. Zhang, D. Sun, Y Fu, and H. Du, Recent advances of superhard nanocomposite coatings: a review, Surf. Coat. Technol. 167(2-3), 113-119 (2003) [Zh-He01] M. Zhang and J. He, Ab-initio calculation of elastic constants of TiN, Surf. Coat. Technol. 142-144, 125-131 (2001) [Zh-Sh04] C.H. Zhang, Z.J. Liu, K.Y. Li, Y.G. Shen, and J.B. Luo, Microstructure, surface morphology, and mechanical properties of nanocrystalline TiN/amorphous Si3N4 composite films synthesized by ion beam assisted deposition, J. Appl. Phys. 95(3), 1460-1467 (2004) [Zh-Vep06] R.F. Zhang and S. Veprek, On the spinodal nature of the phase segregation and formation of stable nanostructure in the Ti–Si–N system, Mater. Sci. Eng. A 424(1-2), 128-137 (2006) List of figures Fig. 2.1: The micro-hardness vs. the Si content in the Ti-Si-N films, from [Li92]. Fig. 2.2 Structure of a nano-crystallite/amorphous composite in which the growth of micro-crack is limited due to the small thickness of the amorphous tissue, from [Veprek96]. Fig. 2.3: The sub-processes in the sputtering PVD process. Fig. 2.4: The sputtering and deposition process of the multiphase nanostructure coating and the relationship of the process - structure - property – performance. Fig. 2.5: The deposition and the film growth process and the process simulation. Fig. 2.6: The outline of the ab initio methods. Fig. 3.1: The sputtering PVD equipment: (a) LS 450S from Von Ardenne Anlagentechnik GmbH [VonArd], (b) the framework of LS 450S. Fig. 3.2: The total ion count per second (c/s) and the mean ion energy (eV/c) vs. the sputtering RF and DC power: (a) total ion count vs. sputtering power, (b) mean ion energy vs. sputtering power. Fig. 3.3: The deposition rate RD (Å/s) vs. the RF and DC sputtering power. Fig. 3.4: The ion energy distribution dependent on various RF sputtering powers: (a) for Ar + , (b) for N2 + , and (c) for Ti + . The experiment condition: Ar flow rate = 7.0 sccm, N2 flow rate = 0.8 sccm, the process pressure = 0.08 Pa, and the distance = 55 mm. Fig. 3.5: The Statistical result of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. RF sputtering powers: (a) the total ion count per second, (b) the mean ion energy. Fig. 3.6: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the N2-flow rate: (a) the total ion count per second, (b) the mean ion energy. List of figures 187 Fig. 3.7: The ion energy distribution dependent on various DC sputtering powers: (a) for Ar + , (b) for N2 + , and (c) for Ti + . The experiment condition: Ar flow rate = 7.0 sccm, N2 flow rate = 2.0 sccm, the process pressure = 0.08 Pa, the distance = 55 mm. Fig. 3.8: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the DC power: (a) the total ion count per second, (b) the mean ion energy. Fig. 3.9: The deposition rate (Å/s) of TiN under the DC power sputtering. Fig. 3.10: The Ti target and the Si target were mounted on the side of the vacuum chamber and adjoined each other. Three silicon wafer substrates were fixed on the substrate holder which was rotated during the deposition process. Fig. 3.11: Cross-sectional images of (a) 04030202-1 and (b) 04030202-3 showing the influence of the facing target time on the film microstructure. Fig. 3.12: The XRD pattern for the Ti-Si-N film of the probe 04030202-1. Fig. 3.13: The AFM image (2µm×2µm) of the Ti-Si-N film 04030202-1. Fig. 3.14: Nanoindentation load-displacement curve from the Ti-Si-N cating 04030202-1: (a) the hardness = 43.14 GPa under the condition of indentation limit = 40nm, (b) the hardness = 32.19 GPa under the condition of the indentation limit = 100nm. Fig. 4.1: The main flow chart of the KMC simulation of the film growth process. Fig. 4.2: The periodic condition of the simulation substrate. Fig. 4.3: The grain size vs. the deposition temperature: a) 100K; b) 200K; c) 300K; d) 400K. Fig. 4.4: The particle number of the largest cluster vs. the deposition temperature (N=10000, RD=0.5nm/s). Fig. 4.5: The number of the cluster vs. the deposition temperature (N = 10000, RD = 0.5nm/s). Fig. 4.6: Definition of the various position and force vectors of the dimer. R is the coordinate of adatom, 1R and 2R are the coordinates of the image 1 and the image 2. The rotational force on the dimer,   21 FFF , is the net force acting on image 1 perpendicular to the direction of the dimer. From [Henkelman99]. List of figures 188 Fig. 4.7: Definition of the various quantities involved in rotating the dimer. All the vectors are in the plane of rotation. The dimer is first rotated about a small angle d to give a finite difference estimate of F  given by Eq. (4.6). The dimer is then rotated by a calculated angle  given by Eq. (4.8) to zero the force within the plane of rotation. Fig. 4.8: The part flow chart of the KMC simulation with off-lattice model. Fig. 4.9: The influence of the potential parameters on the PES: the bond length of N-N changing from 0.15nm to 0.30nm. Fig. 4.10: The structure of TiN crystalline and Si3N4 crystalline: (a) TiN, (b) Si3N4. Fig. 4.11: The combination of TiN and Si3N4: (a) the cell of TiN, (b) the tetrahedron of Si-4N, (c) the structure of Si-4N-4Ti suggested in this research. Fig. 4.12: The Ti-Si-N composite film simulated through the off-lattice KMC: the figure above is on plan view and the bottom one is on the section view. The red sphere is Si atom, the green is Ti, and blue is N [Wu06]. Fig. 5.1: The configuration of a Si atom in the TiN crystallite: (a) a Si atom is at a eightfold coordinated hollow site (~Si-HL), the figure above is front view and the bottom one is top view; (b) a Si atom is at a fourfold coordinated hollow site or a plane hollow site (~Si-PHL), the figure above is front view and the bottom one is top view; (c) a Si atom occupies a Ti position (~Si- OCP-Ti); (d) a Si atom occupies a N position (~Si-OCP-N). The square stands for Si, the triangle for Ti, and the circle for N. Fig. 5.2: The configuration of a Si atom added into a TiN crystallite supercell. A Si atom is at an eightfold coordinated hollow site in the TiN cell, noted ~Si-HL. A double cross tetrahedron Si-4N-4Ti is in the supercell center. The Si atom is shown on the red point. Fig. 5.3: The double cross tetrahedron Si-4N-4Ti consists of a small tetrahedron Si- 4N and a large tetrahedron Si-4Ti with the same Si in the center of the TiN cell. The tetrahedron Si-4N is smaller than the TiN cell and the tetrahedron Si-4Ti is larger than the TiN cell. Therefore, the double cross tetrahedron Si- 4N-4Ti is an intrinsic mismatch with the B1 NaCl structure TiN. Fig. 5.4: The cohesive energies of the TiN and the configurations of the TiN with Si addition as the lattice changes in one direction. D is the distance of Ti-N in the boundary. The lattice constant 4.242 Å corresponds to D= 2.131 Å. List of figures 189 Fig. 5.5: The configurations of a Si atom added into the TiN boundary (A change of lattice constant is in the vertical direction, a0 = 4.700 Å, corresponding to D = 2.35 Å): (a) the structure of ~Si-HL, (b) the structure of ~Si-PHL. The Si atom is shown on the red point. A relaxation effect is obvious. The distances between Ti-N are large in the middle row, but they are relatively small in the top and bottom rows. Fig. 5.6: The configuration of the Si-4N tetrahedron in the crystalline TiN with the absence of four Ti atoms: (a) in the crystallite model, there is no distortion with Si addition; (b) in the boundary model i.e. under the lattice change to 4.700 Å in the vertical direction, there is no relaxation effect with Si addition. Fig. 5.7: The charge density distribution for the double cross tetrahedron Si-4N-4Ti under D = 2.35 Å condition: (a) the charge transfer is in a TiN(110) plane (full curve: charge increase and dot-dashed curve: charge decrease); (b) the charge density in a TiN(110) plane shows the covalent bond of Si-N1; (c) the local charge density in a TiN(110) plane shows the covalent bond of Si-N1; (d) the charge density in a TiN(100) plane shows the charge density mix of Ti1-N2. Fig.5.8: The charge density distribution for Si-2N-2Ti in a TiN(100) plane under D = 2.35 Å condition shows the covalent bond of Si-N1 and Si-Ti1 as well as the charge density mix of Ti1-N2 . Fig. 5.9: The distribution configurations of two Si atoms in TiN: (a) two Si atoms are at the eightfold coordinated hollow sites of two parallel cells adjoined in the same layer, PA; (b) two Si atoms are at parallel cells separated in the same layer, PS; (c) two Si atoms are at the eightfold coordinated hollow sites of two diagonal cells adjoined in the same layer, DA; (d) two Si atoms are at two diagonal cells separated in the same layer, DS; (e) two Si atoms are at the eightfold coordinated hollow sitets of two spatially diagonal cells adjoined, SDA; (f) two Si atoms are at two spatially diagonal cells separated, SDS; (g) two Si atoms are at the eightfold coordinated hollow sites of two cells separated in a slope form in the same layer, SS. The square stands for Si, the triangle for Ti, and the circle for N. Fig. 5.10: The distribution of Si in TiN: (a) two Si atoms in the parallel adjoined cells, (PA); (b) two Si atoms in the parallel separated cell, (PS). The two Si atoms are in the adjoin cell make the strain increase. List of figures 190 Fig. 5.11: The configurations of a Si atom and a 2N2Ti island on TiN(001) surface. (a) a Si atom in the TiN island, Si-in-2N2Ti; (b) a Si adatom is beside the TiN island, Si-by-2N2Ti; (c) an adatom Ti is beside the island and Si occupies the Ti position of the island, Ti-by-2N1Ti1Si; (d) a N adatom is beside the island and Si occupies the N position of the island, N-by-2Ti1N1Si. The square stands for Si, the triangle for Ti, and the circle for N. Fig. 5.12: The configuration of a Si atom with a 2N2Ti island on the TiN(001) surface: (a) a Si atom is in the eightfold coordinated hollow site of the 2N2Ti island; (b) a Si atom is beside the 2N2Ti island. The Si atom in the island of 2N2Ti makes a large distortion of the TiN cell. Fig. 5.13: The numerical description of Ti-Si-N composite structure: (a) the cross section view, (b) the axonometric draw of equiaxial crystal. Fig. 5.14: The high symmetry points on the TiN(001) surface. Fig. 5.15: The rough potential energy surface (PES) of a Ti, Si, and N adatom on the TiN(001) surface: (a) the PES of a Ti adatom, (b) the PES of a Si adatom, and (c) the PES of a N adatom. Fig. 5.16: The charge density of some configurations: (a) a Ti adatom on the top of a surface Ti, (b) a Ti adatom on the top of a surface N, (c) a N adatom on the top of a surface Ti, (d) a N adatom on the top of a surface N, (e) a Si adatom on the top of a surface Ti, (f) a Si adatom on the top of a surface N. Fig. 5.17: The energy difference along the diffusion path of a Ti, Si, and N adatom on the TiN(001) surface: (a) the diffusion of a Ti adatom from Top-N to the hollow site; (b) the diffusion of a Si adatom from Top-N to the hollow site; (c) the diffusion of a N adatom from the site of D-Basin to the hollow site; and (d) the diffusion of a N adatom from the BR site to the site of D-Basin. Fig. 5.18: The single adatom diffuses around the island of 2Ti2N Fig. 5.19: The E-Path of a Si adatom diffusing around the island of 2N2Ti: (a) between the site P3 and the site P4, (b) between the site P3 and the site P5, (c) between the site P5 and the site P1. Fig. 5.20: The E-Path of a Ti adatom diffusing around the island of 2N2Ti: (a) between the site P3 and the site P4, (b) between the site P3 and the site P5, (c) between the site P5 and the site P1. List of figures 191 Fig. 5.21: The E-Path of the N adatom diffusing around the island of 2N2Ti: (a) between the site P2 and the site P1, (b) between the site P2 and the site P3, (c) between the site P3 and the site P6. Fig. 5.22: The single adatom diffuses along the island. Fig. 5.23: The E-Path of the single adatom diffusing along the island of 6N6Ti: (a) the Ti adatom diffuses between the site P2 and the site P3, (b) the N adatom diffuses between the site P1 and the site P2, and (c) the Si adatom diffuses between the site P2 and the site P3. Fig. 5.24: The single adatom diffuses down the island. Fig. 5.25: The E-Path of the single adatom diffusing downs the island of 6N6Ti: (a) an adatom Ti from P4 to P2, (b) an adatom N from P3 to P1, and (c) an adatom Si from P4 to P2. Fig. 5.26: The diffusion of a Ti-N addimer on the TiN(001) surface: (a) a Ti-N addimer is at the initial position, (b) the N diffuses around its partner Ti, (c) the Ti diffuses around its partner N, (d) the addimer Ti-N is at the final position. Fig. 5.27: The E-Path curves for the diffusion of Ti-N addimer on TiN (001) surface: (a) the N diffuses around its partner Ti, (b) the Ti diffuses around the N. Fig. 5.28: The E-Path of a Si-N addimer diffusion on the TiN(001) surface: (a) the N diffuses around its partner Si, (b) the Si diffuses around its partner N. Fig. 5.29: The diffusion of an Ti-N or Si-N addimer around the island: (a) the addimer diffuse along the down-path (P3-P4 to P5-P8) or along the up-path (P4-P3 to P2-P7), (b) the Si of the addimer diffuses alone firstly around the corner N of the island to the site P7, then the island N jumps to the site P9, finally, the N of the addimer takes the corner place of the island. Fig. 5.30: The E-Path of a Ti-N addimer diffusion around the island along the down- path (1): (a) the Ti of the addimer from site P3 to site C, (b) Ti from site C to site P5, (c) the N of the addimer from site P4 to site P8, (d) N from site P4 to site D, (e) N from site D to site P8. Fig. 5.31: The E-Path of a Ti-N addimer diffusion around the island (2): (a) the N of adaimer Ti-N from the site P4 to the site B, (b) N from the site B to the site P2, (c) the Ti of addimer Ti-N from the site P3 to the site P7. Fig. 5.32: The E-Path of the Ti of Ti-N addimer diffuses alone around the corner N of the island. List of figures 192 Fig. 5.33: The E-Path of addimer Si-N diffusion around the island (1): (a) the Si of Si- N addimer from the site P3 to the site C, (b) Si from the site C to the site P5, (c) the N of addimer Si-N from the site P4 to the site P8. Fig. 5.34: The E-Path of a Si-N addimer diffusion around the island (2): (a) the N of addimer Si-N from the site P4 to the site B, (b) N from the site B to the site P2, (c) the Si of addimer Si-N from the site P3 to the site P7. Fig. 5.35: The E-Path of a Si-N addimer diffusion around the island (3): (a) the Si of addimer Si-N alone diffuses around the corner N of the island 2N2Ti from the site P3 to the site P7, (b) the corner atom N jumps from the corner site of the island to the site P9, (c) the N of the origin addimer diffuses from the site P4 to corner site of the island. Fig. 5.36: The addimer diffusion along the island of TiN. Fig. 5.37: The E-Path of the Ti-N addimer diffusion along the island: (a) the Ti of the addimer diffuses from the site P2 to the site B; (b) the N of the addimer diffuses from the site P3 to the site A. Fig. 5.38: The E-Path of the Si-N addimer diffusion along the island: (a) the N of the addimer diffuses from the site P3 to the site A, (b) The Si of the addimer diffuses from the site P2 to the site B. Fig. 5.39: The diffusion of Ti-N or Si-N addimer down the island. Fig. 5.40: The E-Path curves of the Ti-N addimer diffusing down the island: (a) the N of the addimer diffuses from the site P3 to the site P1, (b) the Ti of the addimer diffuses from the site P4 to the site P2. Fig. 5.41: The E-Path curves of the Si-N addimer diffusing down the island: (a) the N of the addimer diffusing from the site P3 to the site P1, (b) the Si of the addimer diffusing from the site P4 to the site P2. Fig. 5.42: The low-energy configuration of a Ti-N-Ti adtrimer on the TiN(001) surface and its diffusion mode: (a) the line configuration- LINE, (b) the corner configuration-CORNER, (c) the N of adtrimer jumps over through two supporters Ti. Fig. 5.43: The E-Path curves of the Ti-N-Ti adtrimer diffusion: (a) the Ti rotating diffusion from the CORNER configuration to the LINE one, or inversely, (b) the N of the adtrimer jumping over through two Ti of the adtrimer. List of figures 193 Fig. 5.44: The E-Path curves of the diffusion of N-Ti-N adtrimer: (a) the N of adtimer rotates from the CORNER arrangement to the LINE one or inversely, (b) the Ti of the adtrimer jumps over through two N of the adtrimer. Fig. 5.45: The E-Path curves of an Ti-N-Si adtrimer diffusion: (a) the Ti of the adtrimer rotates from the CORNER arrangement to the LINE one or inversely, (b) the Si of the adtrimer rotates from the CORNER arrangement to the LINE one or inversley, (c) the N of the adtrimer jumps over through the Ti and the Si of the adtrimer. Fig. 5.46: The low-energy configuration and the diffusion mode of a 2N2Ti adtetramer: (a) the low-energy configuration of a 2N2Ti adtetramer, (b) the Ti of the adtetramer diffuses from P1 through P2 to P3 or inversely, (c) the N of the adtetramer diffuses from P4 through P5 to P6, or inversely. Fig. 5.47: The E-Path curve of the Ti diffusion of a 2N2Ti adtetramer: (a) the Ti atom diffuses from the site P1 to the site P2 or inversely, (b) the Ti atom diffuses from the site P2 to the site P3, or inversely. Fig. 5.48: The E-Path curve of the N diffusion of a 2N2Ti adtetramer: (a) the N atom diffuses from the site P4 to the site P5 or inversely, (b) the N atom diffuses from the site P5 to the site P6 or inversely. Fig. 5.49: The inter diffusion of a Ti atom in the crystallite of TiN: (a) the initial arrangement, (b) the Ti atom diffusing to a vacant site. Fig. 5.50: The E-path curve for the inter diffusion of an atom in the crystalline TiN: (a) a Ti atom diffuses in TiN, (b) a N atom diffuses in TiN, (c) a Si atom diffuses in TiN. Fig. 5.51: The E-path curve for the inter diffusion of an atom in the first layer of the TiN (001) substrate: (a) a Ti atom diffuses in TiN surface, (b) a N atom diffuses in TiN surface, (c) a Si atom diffuses in TiN surface. Fig. 5.52: The influence of a Si adatom and a Si-N addimer on the Ti diffusion of Ti-N addimer along the island of TiN: (a) the Ti diffusion from the site P1 to the site P2 is influenced by a Si adatom, (b) the Ti diffusion from the site P1 to the site P2 is influenced by a Si-N addimer. Fig. 5.53: The E-Path curves of the Ti of Ti-N addimer diffuses along the island with the promotion of a Si adatom or a Si-N addimer: (a) under the promotion of a Si adatom, (b) under the promotion of a Si-N addimer. List of tables Table 2.1: The results of Ti-Si-N superhard nanocomposite coatings from some research groups. Table 2.2: The time and length scale typically handled by different theoretical approaches to study the chemical reaction and crystal growth, from [Reuter05]. Table 3.1: The total ion count per second (c/s) and the mean ion energy vs. the sputtering powers. The experiment condition: Ar flow rate = 7.0 sccm, pressure = 0.08 Pa, Distance = 55mm. Table 3.2: The deposition rate RD (Å/s) vs. the sputtering power measured by the quartz crystal method. The experiment condition is: Ar flow rate = 7.0 sccm, pressure = 0.08 Pa, Distance=105mm. Table 3.3: The statistical result of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. RF sputtering powers. Table 3.4: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the N2-flow rate. The experiment condition: RF power=200W, Ar flow rate = 7.0 sccm, the process pressure = 0.08 Pa, the distance = 55mm. Table 3.5: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the Ar flow rate (sccm). The experiment condition: RF power = 200W, the process pressure = 0.08 Pa, N2 flow rate = 0.8sccm, the distance = 55mm. Table 3.6: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the process pressures (Pa). The experiment condition: RF power = 200W, Ar flow rate = 7.0 sccm, N2 flow rate = 0.8 sccm, the distance = 55mm. Table 3.7: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the distance (mm) between the target and the substrate. The experiment condition: RF power = 200W, Ar flow rate = 7.0 sccm, N2 flow rate = 0.8sccm, the process pressure = 0.08 Pa. List of tables 195 Table 3.8: The statistical results of the total ion count per second (c/s) and the mean ion energy (eV/c) in plasma vs. the DC power. The experiment condition: Ar flow rate = 7.0 sccm, N2 flow rate = 2.0 sccm, the process pressure = 0.08 Pa, the distance = 55 mm. Table 3.9: The deposition rate (Å/s) of TiN under the DC power sputtering. The experiment condition: Ar flow rate = 7.0 sccm, N2 flow rate = 2.0 sccm, the process pressure = 0.08 Pa, the distance = 55 mm. Table 3.10: Elemental concentrations and film thickness of the Ti-Si-N films (04030202). Table 5.1: The total energy and the cohesive energy of the configurations investigated. The values are in electron volts (eV). E0 is the total energy; Ecoh is the cohesive energy; and dEcoh is the cohesive energy difference between the TiN crystallite and the other configurations. The configurations of ~Si-HL, ~Si- PHL, Si-OCP-Ti, and ~Si-OCP-N are shown in Fig. 5.1. TiN-1N means that a N atom is missing in the TiN supercell, and TiN-1Ti means that a Ti atom is missing in the TiN supercell. Table 5.2: The cohesive energies (eV) of TiN and configurations with Si addition under the boundary condition. D is the distance of Ti-N in the boundary. Table 5.3: The total energies and the cohesive energies of different Si distributions in TiN. The meaning of the abbreviations PA, PS, and so on are shown in Fig. 5.9. E0 is the total energy, Ecoh is the cohesive energy. Table 5.4: The total energies Econfig and the adsorption energies Ead (eV) of a 2N2Ti island on the TiN(001) surface and of the configuration with a Si atom in or by the island. Table 5.5: The total energies Econfig and the adsorption energies Ead (eV) of different configurations of a Si atom, two N atoms and two Ti atoms on TiN(001) surface. Table 5.6: The total energies and adsorption energies of a single Ti, Si, and N adatom at some high symmetry points on the TiN(001) surface. Table 5.7: The adsorption energies, the bond lengths and the reference covalent radii [Dean99] of some combinations. Table 5.8: The energy difference along the diffusion path of a Ti, N, and Si adatom on TiN(001). E0 is the total energy of the configuration investigated and Ediff is the List of tables 196 energy difference between the energy of the initial point and that at the sites along the diffusion path. The unit of E0 and Ediff is eV and the unit of the path is nm. The unit is the same in this section. Table 5.9: The total energy and the different energy of a Si adatom diffusing around the island of 2N2Ti. Table 5.10: The total energy and the different energy of a Ti adatom diffusing around the island of 2N2Ti. Table 5.11: The total energy and the different energy of a N adatom diffusing around the island of 2N2Ti. Table 5.12: The total energy and the different energy of a single adatom diffusing along the island. Table 5.13: The total energy and the different energy of a single adatom diffusing down the island. Table 5.14: The total energy and the different energy of an Ti-N addimer diffusing on TiN(001) surface. Table 5.15: The total energy and the different energy of an Si-N addimer diffusing on TiN(001) surface. Table 5.16: The total energy and the different energy of a Ti-N addimer diffusing around the island along the down-path (1): Ti-P3-C-P5 and then N-P4-P8. Table 5.17: The total energy and the different energy of a Ti-N addimer diffusing around the island along the up-path (2): N-P4-B-P2 and then Ti-P3-P7. Table 5.18: The total energy and the different energy of the Ti of addimer Ti-N diffusing alone around the corner N of the island of 2N2Ti. Table 5.19: The total energy and the different energy of Si-N addimer diffusing around the island (1): Si-P3-C-P5 and then N-P4-P8. Table 5.20: The total energy and the different energy of Si-N addimer diffusing around the island (2): N-P4-B-P2 and then Ti-P3-P7. Table 5.21: The total energy and the different energy for Si of an addimer diffusing alone around the corner N of 2N2Ti island, the corner atom N diffusing, and the N of the addimer moving to corner site. Table 5.22: The total energies and different energies of Ti-N addimer diffusing along the island. List of tables 197 Table 5.23: The total energies and different energies of Si-N addimer diffusing along the island. Table 5.24: The total energies and the different energies of the Ti-N addimer diffusing down the island. Table 5.25: The total energies and the different energies of the Si-N addimer diffusing down the island. Table 5.26: The total energies and the different energies of the Ti-N-Ti adtrimer diffusion. Table 5.27: The total energies and different energies of the N-Ti-N adtrimer diffusion. Table 5.28: The total energies and the different energies of the Ti-N-Si adtrimer diffusion. Table 5.29: The total energies and the different energies for the Ti diffusion of the adtetramer: P1-P2-P3. Table 5.30: The total energies and the different energies for the N diffusion of the adtetramer: P4-P5-P6. Table 5.31: The total energy and the different energy of Ti, N, and Si inter diffusion in the TiN crystalline. Table 5.32: The total energies and the different energies for Ti, N, and Si inter diffusion in TiN(001) surface. Table 5.33: The total energies and the different energies of the Ti diffusion along the island by the promotion of a Si adatom or a Si-N addimer. Table 5.34: The activation energies (eV) for the adatom diffusion. Table 5.35: The activation energies (eV) for addimer diffusion. Table 5.36: The activation energies (eV) for adtrimer diffusion. Table 5.37: The activation energies (eV) for the diffusion of 2N2Ti adtetramer. Table 5.38: The activation energies (eV) for inter diffusion. List of symbols and glossary 2N2Ti an island that consists of two N atoms and two Ti atoms 3D three dimensional 44 (5+7) model a surface slab of the TiN(001) that consisted of five layers of atoms, 8 Ti and 8 N atoms per layer, and seven layers, about 14.8 Å, of vacuum space. 66 (5+7) model a surface slab of the TiN (001) that consisted of five layers of atoms, 18 Ti and 18 N atoms per layer, and seven layers, about 14.8 Å, of vacuum space.  the coefficient of the ―width‖ of the potential i the weighting factor between the rotational force  iF and the old modified force vector 1iG  a rotation angle to bring the rotation force to zero R the direction from the adatom to the image t the lapse time  rn the variation of the particle density   rnxc the exchange-correlation energy of a homogeneous electron gas with local density F Fermi wavelength 0 the atomic vibration frequency which is in the range of 10 12 to 10 13 Ψ, Φ, n , or χ the wave function of the system  a unit vector which is perpendicular to N within the plan of rotation a the jump distance 0a the lattice constant List of symbols and glossary 199 Ab initio (From first principles). This expression can mean different things in different fields. In the field of quantum chemistry, it means that a calculation was done by solving Schroedinger‘s equation for the electrons in the system without using any empirical data. In solid state physics the term also includes methods such as density functional theory, which contains approximations that have been fit to experiment. [Henkelman01D] AFM atomic force microscopy BN boron nitride BR the bridge site that is between the top of Ti and the top of N C the potential curvature c/s ion count per second CFD Computational fluid dynamics CI configuration interaction CORNER the configuration of three adatom which is in a form of CORNER CPU central processing unit CVD chemical vapor deposition d an given angle of rotation, with which the image 1 moves from 1R to * 1R 0D the ―equilibrium" dissociation energy of the molecule (measured from the potential minimum) iD the diffusion rate diffusion coefficient for every diffusion path of every moveable particle DA two cells which are plane diagonal adjoined in the same layer D-Basin the deepest basin is between the top of N and the hollow site DC direct current dEcoh the cohesive energy difference between the TiN crystallite and the other configurations DFT: Density functional theory that is an approximate method of solving Schroedinger‘s equation for a system of electrons. The energy and force of the system is calculated from the electron density. DFT List of symbols and glossary 200 scales better than many-body orbital based quantum chemistry methods and can be used with larger systems. [Henkelman01D] Digtal factory a software platform with which production organizations or manufacture issues are dealt with through calculations, simulations or visualizations. Dimer method: A method for finding saddle points that requires energy and force but not second derivatives. The dimer method can be used to find many different saddle points on the potential energy rim surrounding a potential minimum. [Henkelman01D] DS two cells which are plane diagonal separated in the same layer E the energy of the system E0 total energy of the configuration concerned aE the activation energy Ead the adsorption energy Ecoh the cohesive energy Econfig the total energy of the configuration concerned Ed the energy of the dimer 21 EEEd  is the sum of the energy of the images. 0dE the energy at the fixed midpoint of the dimer which is constant during the dimer rotation EF Fermi energy FinE the system energy of the final state IntE the system energy of the initial state SadE the saddle point energy EN, ETi, ESi the energies of a N atom, a Ti atom, and a Si atom in vacuum Es the energy of the relaxed surface se the activation energy for the particle diffuse on the clean substrate which equates ~5-20% of desorption energy.   rE the functional of the particle density  nEH the Hartree energy (electron-electron repulsion) List of symbols and glossary 201  nExc the exchange and correlation energies EDS energy dispersive spectroscopy EDX energy dispersive X-ray E-Path the curve of the energy difference along the diffusion path EPMA electron probe micro-analysis EQP electrostatic quadrupole plasma. A quadrupole mass spectrometer equipment from Hiden Analytical Ltd eV electron Volt F the rotational force F  a finite difference approximation to the change in the rotational force F 0F the value of F evaluated at 0 0F  the value of F evaluated at 0 1F the force on the image 1 in the dimer method 2F the force on the image 2 in the dimer method F the net force acting on image 1 perpendicular to the direction of the dimer,   21 FFF  1F the force acting on image 1 perpendicular to the direction of the dimer  2F the force acting on image 2 perpendicular to the direction of the dimer //F the net force acting on adatom parallel to the direction of the dimer, // 2 // 1 // FFF  // 1F the force acting on image 1 parallel to the direction of the dimer // 2F the force acting on image 2 parallel to the direction of the dimer FM the Frank-van der Merwe mode FWHM full width at half maximum  iG the direction of descent for the ith rotation List of symbols and glossary 202 GPa giga pascal (1 Pa = 1 N/m 2 = 10 −5 bar = 10.197×10 −6 at = 9.8692×10 −6 atm) H the Hamiltonian which describes the total energy of a system hcp the hexagonal close-packed crystal structure Hessian matrix: The matrix of force constants (second derivatives of the potential energy). When this matrix is divided by the masses of the atoms, the eigenvectors are the normal modes, and the eigenvalues are the square of the normalmode frequencies. [Henkelman01D] HK Hartree-Fock HL the hollow site HRTEM high resolution transmission electron microscopy HTST: Harmonic transition state theory. A simplified form of transition state theory in which the potential is assumed to be of harmonic form both at the minimum and at the saddle point. This is a good approximation at low enough temperature, unless quantum effects become important. It typically works well for metals at room temperature. [Henkelman01D] Bk the Boltzmann constant k hTST the rate constant of the harmonic form of TST (HTST) KMC kinetic Monte Carlo k-points the k-points at which the Brillouin zone is to be sampled during a self consistent calculation to find the electronic ground state may be defined either by specifying a list of k-points or a Monkhorst-Pack grid in terms of the dimensions of the k-point mesh or a minimum k- point density. The origin of the Monkhorst-Pack grid may be offset by a vector from the origin of the Brillouin zone. L(NN) the bond length of N-N L(TiTi) the bond length of Ti-Ti LCAO a linear combination of atomic orbital LDA local density approximation LINE the configuration of three adatom which is in a form of LINE List of symbols and glossary 203 LS 450 S a sputtering PVD equipment from Von Ardenne Anlagentechnik GmbH MM  the simulation substrate with the simple cubic structure, including MM  lattice sites. NMM ,...,1 the masse of ions m the mass of electron MD molecular dynamics ML monolayer N the number of ions, N a unit vector which defines the dimer direction n, m and l the number of N, Ti, Si atoms contained in the supercell investigated na, ma and la the numbers of N, Ti, Si adatom under the investigation  rn local density  rn0 equilibrium density Ne the number of electrons NEB Nudged elastic band method which is a method for finding the minimum energy paths between two points on a potential surface. A path of discrete images of a system are connected by springs (elastic band) and allowed to collectively relax. The ‗nudging‘ refers to the fact that the spring forces act only along the band, and the potential forces act only perpendicular to the band. Typically this method is used to find the MEP and saddle point(s) between two potential minima. [Henkelman01D] nc-TiN/a-Si3N4 nanocrystallite TiN embedded in amorphous Si3N4 matrix N-by-2Ti1N1Si a N adatom is beside an island that consists of two Ti atoms, a N atom and a Si atom. NNI National Nanotechnology Initiative of USA P the system rate  jpP jp the diffusion rate of every moveable particle  ij Dp List of symbols and glossary 204 PPP N ,...,1 the moment of ions ppp eN ,...,1 the moment of electron P1, P2, … … the position1, the position2, …… PA two cells which are parallel adjoined in the same layer PC personal computer PES the potential energy surface on which each point in configuration space represents one configuration or position of the atoms in the system. For this position, there is a potential energy. The potential energy surface is the surface defined by the value of the potential energy at each point in configuration space. [Henkelman01D] PHL the plane hollow site PID a control algorithm with the Proportional, the Integral and Derivative values PO preferred orientation PS two cells which are parallel separated in the same layer PVD physical vapor deposition QCM the quartz crystal microbalance r the distance between the atoms r0 the equilibrium bond distance R the coordinate of adatom RRR N ,...,1 the coordinates of ions rrr eN ,...,1 the coordinates of electrons RD the deposition rate 1R ( * 1R ) the coordinate of the image 1 2R the coordinate of the image 2 RF radio frequency SAD selected area diffraction List of symbols and glossary 205 Saddle point: A point on a potential surface at which the force is zero and at which there is one negative curvature or unstable mode in the Hessian matrix. [Henkelman01D] SDA two cells which are spatially diagonal adjoined SDS two cells which are spatially diagonal separated SCF self-consistent field SEM scanning electron microscopy Si-2N-2Ti a interface structure, the parallelogram structure in the TiN boundary in which Si is connected with two N atoms and two Ti atoms Si-4N-4Ti a interface structure, the double cross tetrahedron structure which consists of a small tetrahedron Si-4N and a large tetrahedron Si-4Ti with the same Si in the center of the TiN cell Si-by-2N2Ti a Si adatom is beside the 2N2Ti island Si-in-2N2Ti a Si atom is in the 2N2Ti island ~Si-HL a configuration in which a Si atom is at the hollow site of TiN cell ~Si-OCP-N a configuration in which a Si atom occupies a N position ~Si-OCP-Ti a configuration in which a Si atom occupies a Ti position ~Si-PHL a configuration in which a Si atom is at the plane hollow site SPIP scanning probe image processor SS two cells which are separated in a slope form in the same layer Supercell a special cell used in atomic calculation or simulation which contain some basic cell of the crystal investigated T the substrate temperature during the deposition Te the kinetic energy of electron TN the kinetic energy of ion  nT the kinetic energy td the maximum mean free time it the residence time of the system Pt i /1 TCR temperature coefficient of resistance List of symbols and glossary 206 TEM transmission electron microscopy Ti-Si-N the composite that consist of Ti, Si and N Ti-by-2N1Ti1Si a Ti adatom is beside an island that consists of two N atoms, a Ti atom and a Si atom. Ti1, N1 the atom Ti or N which is connected with Si atom Ti2, N2 the atom Ti or N which is not connected with Si atom TiN titanium nitride TiN-1N a TiN configuration in which a N atom was missing TiN-1Ti a TiN configuration in which a Ti atom was missing Top N a site on the top of surface atom N on the TiN (001) surface Top-Ti a site on the top of surface atom Ti on the TiN (001) surface Top-N//HL a site between the top of N and the hollow site Top-Ti//HL a site between the top of Ti and the hollow site Transition state: A bottle neck region which a system must cross in order to undergo a transition from a given initial state. The transition state has dimension one less than the full system. [Henkelman01D] TST Transition state theory which is a theory for calculating the rate at which a system leaves a given initial state (potential energy basin) though a bottle neck region. [Henkelman01D] TRIM a Monte Carlo program for simulating the sputtering process eeV the columbo potential NeV the interaction between the ion and the electron NNV the interaction between ions  rV the external potential )(rVM the Morse potential energy VASP the Vienna ab initio simulation package VDI Verein Deutscher Ingenierue VLSI very-large-scale integration XPS X-ray photoelectron spectra List of symbols and glossary 207 XRD X-ray diffraction z the number of neighboring sites which the atom can hop to NZZ ,...,1 the charges of ions