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Item Open Access Spectroscopic study of CaMnO3/CaRuO3 superlattices and YTiO3 single crystals(2009) Yordanov, Petar; Keimer, Bernhard (Prof. Dr.)The first two sections of Chapter 1 give a general overview of the research topics and experimental methods discussed in the thesis. Further on, in Chapter 2, some of the most important characteristics and mechanisms underlying the physics of transition metal oxides are presented. As the experimental part of the thesis includes studies on manganites and titanates, these two classes of compounds are exemplified in the exposition of Chapter 2. Several recent works in the emerging research field of transition metal oxide interfaces and superlattices are also discussed along with a brief introduction in x-ray spectroscopic methods with synchrotron radiation. Chapter 3 introduces the principles of optical spectroscopy and the simplest models for dielectric function, i.e., Lorentz oscillator and Drude dielectric function. The following Chapter 4 introduces two of the experimental techniques in optical spectroscopy, reflectance and spectroscopic ellipsometry. Further on, we describe the design of a new home-built apparatus for near-normal reflectance with high magnetic fields. Several critical technical details and findings during the assembling process are also discussed. Chapter 5 represents a comprehensive experimental spectroscopic study of a prototypical superlattice system made from an antiferromagnetic insulator CaMnO3 and a paramagnetic metal CaRuO3. The resulting interface ferromagnetic state was closely investigated by means of optical spectroscopy as well as by soft x-ray scattering and absorption methods. This study led us to the conclusion that magnetic bound states, i.e. magnetic polarons, have to be considered in the description of this SL system. Chapter 6 describes a polarized far infrared reflectance study with high magnetic field on the ferromagnetic Mott insulator YTiO3, single crystals. All 25 infrared-active phonon modes were observed. The temperature and magnetic-field dependence of the phonon modes revealed a weak spin-phonon coupling in YTiO3 and largely extended temperature range (up to TM ~ 80 - 100K), for the field-induced effects on the oscillator parameters. This later observation, uncovered short-range magnetic order state which remains even at temperatures as high as three times the temperature of the actual ferromagnetic transition of Tc ~ 30K. While a quantitative theoretical description of these data is thus far not available, they point to a complex interplay between spin, orbital, and lattice degrees of freedom due to the near-degeneracy of the Ti t2g orbitals in YTiO3.Item Open Access Resonant X-ray scattering studies of ruthenium oxides and ruthenocuprates(2009) Bohnenbuck, Britta; Keimer, Bernhard (Prof. Dr.)The magnetic and orbital properties of the ruthenium oxides Ca3Ru2O7 and Mn doped Sr3Ru2O7 and the ruthenocuprate RuSr2GdCu2O8 were investigated using resonant and high-energy x-ray diffraction. Bilayered Ca3Ru2O7 is a paramagnetic metal at high temperatures and orders antiferromagnetically at T_N=56K. A second phase transition to a less conductive state is observed at T_MI=48K. This transition is accompanied by abrupt structural changes and a reorientation of the magnetic moment. In addition, there is experimental evidence for the existence of orbital order below T_MI. Our resonant x-ray diffraction studies at the Ru L-absorption edges were focused on the investigation of the magnetic reflections (001) and (110). The observation of a magnetic signal at these reciprocal space positions is in full agreement with an A-type antiferromagnetic structure, consisting of ferromagnetic bilayers coupled antiferromagnetically along the c-axis. Based on the azimuthal angle dependence of the signals, the direction of the magnetic moment was determined to lie along the b-axis below T_MI and along the $a$-axis between T_MI and T_N. The origin of the reorientation of the magnetic moment at T_MI is not yet completely understood. However, it might result from the strong spin-orbit coupling which presumably causes an unquenched orbital magnetization. The latter might then induce additional terms in the spin Hamiltonian that are responsible for the reorientation of the magnetic moment. Although various experiments have given indirect evidence of orbital order below T_MI, we did not detect any orbital signal within the experimental sensitivity. This indicates that the orbital ordering parameter is significantly weaker than in the single layered counterpart Ca2RuO4, which is presumably due to residual charge or orbital fluctuations in the insulating state. RuSr2GdCu2O8 exhibits long range magnetic order and superconductivity within a broad coexistence range. Only limited information about the magnetic structure has been available so far, as most studies were performed on powder samples due to the small size of available crystals. In this situation, resonant x-ray diffraction at the Ru L-absorption edges has turned out to be the ideal tool for the investigation of RuSr2GdCu2O8 since it is sensitive to magnetism, but does not depend on a large crystal mass. Our single crystal studies of the magnetic reflections (1/2 1/2 1/2) and (1/2 1/2 3/2) indicate a G-type antiferromagnetic structure, characterized by a doubling of the unit cell along all three crystallographic directions. From the azimuthal angle dependence of the magnetic signal, we deduced a magnetic moment direction along a low symmetry axis with substantial components parallel and perpendicular to the RuO2 planes. These findings are consistent with previous neutron powder diffraction results and magnetization data. A symmetry analysis in conjunction with a recent crystallographic study revealed that the experimentally observed G-type antiferromagnetic structure needs to be accompanied by an additional ferromagnetic in-plane component, which alternates between neighboring RuO2 layers. This ferromagnetic mode corresponds exactly to the one deduced from nuclear and ferromagnetic resonance experiments. Therefore, our resonant x-ray diffraction data reconcile a variety of apparently contradictory results on the magnetic structure of RuSr2GdCu2O8 and thus resolve a big controversy in the experimental literature. Bilayered Sr3Ru2O7 has attracted a lot of interest in the past years due to the observation of the quantum critical behavior which is related to a metamagnetic transition. In the ground state, the material is a paramagnetic metal and shows Fermi liquid behavior below 10K. Upon substituting Mn for Ru, an insulating antiferromagnetic state is induced; its transition temperature varies with the Mn concentration. Using resonant x-ray diffraction at the Ru L-absorption edges, we investigated the antiferromagnetic structure of 10 Mn substituted Sr3Ru2O7. Our studies of the superstructure reflections (1/4 1/4 0) and (3/4 3/4 0) indicate that the magnetic order is essentially two dimensional and that the magnetic moments are aligned along the c-axis. In combination with a previous neutron powder diffraction study, which was carried out on 5% Mn substituted Sr3Ru2O7, our results suggest an up-up-down-down spin arrangement in the RuO2 planes, which is independent of the Mn concentration. This implies that an antiferromagnetic instability is already present in the parent compound Sr3Ru2O7. Interestingly, the anisotropic resistivity behavior, observed in the nematic phase of Sr3Ru2O7, could be explained assuming the same up-up-down-down spin arrangement as in Mn substituted Sr3Ru2O7. If the two phases are in fact identical, has to be checked by a detailed single crystal neutron diffraction study including a complete structure refinement.Item Open Access Investigation of the effect of Zn impurities and magnetic field on the spin dynamics in underdoped YBa2(Cu1-yZny)3Ox(2009) Suchaneck, Anton; Keimer, Bernhard (Prof. Dr.)This work employs neutron scattering to examine the changes in the spin excitation spectrum of the underdoped high-temperature superconductor YBa2Cu3Ox which is doped with zinc or subject to a strong magnetic field. Doping levels of x=6.6 and x=6.45 are used with an optional zinc substitution of 2% zinc per copper atom. A detwinning procedure is an important factor in order to reorient all twinning domains of the orthorhombic crystal cell in the same direction. Numerous single crystals were oriented and assembled to create a sample of total mass 2g neccessary for neutron scattering experiments. The experiments were performed on triple axis neutron scattering spectrometers to measure spin excitations around the antiferromagnetic wave vector at energies up to 50meV. Zinc substitution and magnetic field influence the spin excitations, which in the pure compound feature the resonance mode, a spin gap and an hour-glass dispersion. Upon zinc substition the spectrum of YBa2(Cu0.98Zn0.02)3O6.6 is quantitatively unchanged around the resonance energy, however its marked temperature onset disappears. At lower energies new induced quasi-static exitations emerge. Similar finding have been observed in other cuprate compounds. The induced excitation exhibit a strong anisotropy in the copper planes. All these results are compared to other experimental techniques which provide comparable experimental evidence. Another compounds examined in this work is the more strongly oxygen underdoped YBa2(Cu0.98Zn0.02)3O6.45. The common bilayer related signal remains unchanged with zinc substitution, however a new inter-plane correlated signal is induced indicating ordering between copper planes. A comparison with other experimental techniques indicated that the superconducting critical temperature is the sole determining factor of the qualitative spin excitation spectrum, no matter what factor are responsible for it. Additional examinations have been devoted to the magnetic field effect on YBa2Cu3O6.45. Similar to other cuprate families, a magnetic-field induced enhancement of the low-energy excitations has been observed. Both the static and the inelastic excitations around 4meV are enhanced. The latter could indicate remains of the resonance mode, which is not detected by common techniques otherwise. Finally, at results on the zinc substitution and magnetic field effect are compared with complementary experimental measurements to deduce many similarities.Item Open Access Electron-phonon interaction in conventional and unconventional superconductors(2009) Aynajian, Pegor; Keimer, Bernhard (Prof. Dr.)Asking most scientists if it is worth to have a closer look at the phonon spectra of conventional superconductors like niobium and lead using inelastic neutron scattering, the answers would be quite discouraging. First of all, there exists the famous microscopic theory of Bardeen, Cooper, and Schrieffer (1957) known as the BCS theory, which explains nearly all aspects of conventional superconductivity. Second, the worldwide interest is oriented towards high temperature superconductivity in cuprates and heavy fermion systems. Thus the first experiments of this thesis, which addressed the phonon linewidths of superconducting niobium and lead, were only intended as a short testbed of the resolution properties of a new high-resolution neutron spectrometer at the research reactor FRM II. This new generation spectrometer, TRISP (triple axis spin echo), allows us to measure phonon linewidths over large parts of the momentum space, with a resolution in the sub micro-eV range, i.e., two orders of magnitude better than what is achieved by conventional triple-axis neutron spectrometers. It was pointed out by Philip Allen that the phonon linewidth is proportional to the electron-phonon coupling parameter, which is an essential parameter describing the formation of Cooper pairs in phonon mediated superconductors. The superconducting energy gap, whose magnitude, symmetry, and temperature dependence are intimately related to Cooper pairing, can also be directly determined in phonon linewidth measurements. The opening of the gap results in a redistribution of electronic states and excitations in the immediate vicinity of the Fermi surface. Electron-phonon scattering is suppressed for phonon energies below the gap 2D due to the stability of the Cooper pairs below Tc. Discontinuities in the phonon linewidths are thus expected when the phonon energy exceeds 2D. Consequently, the gap and its momentum dependent anisotropy (and also the pairing symmetry) can be accurately resolved from a map of these discontinuities in different crystallographic directions. While phonon energies are highly sensitive to the superconducting energy gap, their momenta can serve as a similarly comprehensive probe of the geometry of the Fermi surface, which also leaves an imprint on the phonon linewidth. Phonons which connect nearly parallel segments of the Fermi surface exhibit an enhanced electron-phonon scattering probability, and thus linewidth extrema (termed Kohn anomalies) are expected. A full image of the underlying Fermi surface is contained in a map of these Kohn anomalies. The phonon-linewidth spectra of these long-known superconductors presented in this thesis showed new and unexpected features that were not visible in previous low resolution experiments. Anomalies were observed at phonon energies corresponding to the magnitude of the superconducting gap, 2D, in the electron spectrum. These features were not only visible, as expected, below the superconducting transition temperature Tc, but persist to much higher temperatures. A detailed analysis showed that these features originate from previously unknown Kohn anomalies. As these anomalies were observed both in niobium and lead, which have different crystal structures (BCC and FCC), Fermi surfaces, and energy gaps, it is likely that this link between 2D and the Kohn anomalies is more a general phenomenon. Thus the question arose whether the Kohn anomalies impose a limit on the magnitude of the 2D gap. The major part of this thesis was accordingly concentrated on the relation between Kohn anomalies and 2D. First, similar measurements were carried out along different high symmetry directions. Yet in all cases, the 2D gap was found to coincide with the lowest-energy Kohn anomaly indicating that this phenomenon can not be attributed to an accident. Since the energies of the Kohn anomalies vary (within 10%) for different crystallographic directions, this "locking" of 2D to the Kohn anomaly provides a simple explanation to the long quest for the origin of the gap anisotropy, which was already inferred from tunneling experiments in the 1960's and intensively discussed in the following decades. To shed more light on this lock-in mechanism, other metallic superconductors were explored. A key candidate was the Pb-Bi alloy. Bi adds electrons and increases the radius of the Fermi surface. It was known from previous tunneling experiments that both the gap magnitude 2D and Tc increase with Bi concentration. Inelastic neutron spectroscopy on different Pb-Bi alloys revealed a shift of the Kohn anomalies to higher energies with increasing Bi content in lockstep with 2D, supporting the lock-in hypothesis. Phonon linewidth experiments were also performed on the high temperature superconductor LSCO, whose understanding is still in its infancy. The electron-phonon linewidths of transverse acoustic phonon branches in underdoped, optimally doped, and overdoped samples were extracted from the data.Item Open Access Renormalization group theory for fermions and order parameter fluctuations in interacting Fermi systems(2009) Strack, Philipp; Metzner, Walter (Prof. Dr.)The physics of interacting Fermi systems is extremely sensitive to the energy scale. Of particular interest is the low energy regime where correlation induced collective behavior emerges. The theory of interacting Fermi systems is confronted with the occurrence of very different phenomena along a continuum of scales calling for methods capable of computing physical observables as a function of energy scale. In this thesis, we perform a comprehensive renormalization group analysis of two and three-dimensional Fermi systems at low and zero temperature. We examine systems with spontaneous symmetry-breaking and quantum critical behavior by deriving and solving flow equations within the functional renormalization group framework. We extend the Hertz-Millis theory of quantumphase transitions in itinerant fermion systems to phases with discrete and continuous symmetry-breaking, and to quantum critical points where the zero temperature theory is associated with a non-Gaussian fixed point. The order parameter is implemented by a bosonic Hubbard-Stratonovich field, which - for continuous symmetry-breaking - splits into two components corresponding to longitudinal and transversal Goldstone fluctuations. We compute the finite temperature phase boundary near the quantum critical point explicitly including non-Gaussian fluctuations. We then set up a coupled fermion-boson renormalization group theory that captures the mutual interplay of gapless fermions with massless order parameter fluctuations when approaching a quantum critical point. As a first application, we compute the complete set of quantum critical exponents at the semimetal-to-superfluid quantum phase transition of attractively interacting Dirac fermions in two dimensions. Both, the order parameter propagator and the fermion propagator become nonanalytic functions of momenta destroying the Fermi liquid behavior. We finally compute the effects of quantum fluctuations in the superfluid ground state of an attractively interacting Fermi system, employing the attractive Hubbard model as a prototype. The flow equations capture the influence of longitudinal and Goldstone order parameter fluctuations on non-universal quantities such as the fermionic gap and the fermion-boson vertex, as well as the exact universal infrared asymptotics present in every fermionic superfluid.Item Open Access Magneto-electrical transport through MBE-grown III-V semiconductor nanostructures: from zero- to one-dimensional type of transport(2009) Storace , Eleonora; von Klitzing, Klaus (Prof. Dr.)From the development of the first transistor in 1947, great interest has been directed towards the technological development of semiconducting devices and the investigation of their physical properties. A very vital field within this topic focuses on the electrical transport through low-dimensional structures, where the quantum confinement of charge carriers leads to the observation of a wide variety of phenomena that, in their turn, can give an interesting insight on the fundamental properties of the structures under examination. In the present thesis, we will start analyzing zero-dimensional systems, focusing on how electrons localized onto an island can take part in the transport through the whole system; by precisely tuning the tunnel coupling strength between this island and its surroundings, we will then show how it is possible to move from a zero- to a one-dimensional system. Afterwards, the inverse path will be studied: a one-dimensional system is electrically characterized, proving itself to split up due to disorder into several zero-dimensional structures.Item Open Access Small alloyed ohmic contacts to 2DES and submicron scale corbino devices in strong magnetic fields : observation of a zero bias anomaly and single electron charging(2009) Göktas, Oktay; von Klitzing, Klaus (Prof. Dr.)The Quantum Hall Effect (QHE) was a big surprise discovered on a two-dimensional electron system (2DES) in 1980. The surprising result was that the Hall resistance develops plateaus with simultaneously vanishing longitudinal resistance for a certain range of magnetic field. The value of Hall resistance is quantized at h/(ie2) where i is an integer number. The accuracy of the quantization made the possibility of defining an international resistance standard. Klaus von Klitzing was honored by the physics Nobel prize in 1985 for his discovery. The original discovery was made on a 2DES at the Si-SiO2 interface in a metal-oxide-semiconductor field effect transistor. However, 2DES realized in molecular beam epitaxy grown modulation doped GaAs/AlGaAs heterostructures become the base system for the investigation of the QHE due to their superior electron mobility. The 2DES forms at the GaAs/AlGaAs heterojunction which lies typically 35 nm to 200 nm below the surface. Making a reliable, reproducible and low resistive ohmic contacts to the 2DES in these heterostructures is an important issue. Alloyed Indium ohmic contacts have been used to contact the 2DES on these heterostructures. Since, Indium is not a suitable material for lithographic purposes - it is hard to evaporate - Au/Ge/Ni contacts, which are used to contact n-GaAs, have been adopted to contact the 2DES in GaAs/AlGaAs heterostructures. However, every group developed and used its own recipe and there are not much systematic studies available in the literature. A detailed study of alloyed ohmic contacts to 2DES is necessary since they become an important ingredient of the QHE for the microscopic understanding of the phenomena. The present understanding of QHE is still under debate. Several theories has been developed to explain the effect. Of them the edge state picture was very successful to account for most of the experimental findings. However, recent experiments on the Hall potential profiles in quantum Hall samples by scanning force microscopes reveal convincing evidences for the existence of compressible and incompressible stripes in the depletion region at the sample edges supporting the theories that take screening effects into account. Moreover, these experiments have shown that compressible and incompressible stripes also exist at the border between ohmic contacts and the 2DES. Based on the fact that incompressible stripes have insulating properties, we propose a submicron Corbino devices as a new type of single electron-charging device in this work. Single-electron charging is a phenomena that is observable when the electrostatic charging energy for adding an electron to a conducting island becomes larger than the thermal energy. The effect is observable for the devices in micron or submicron size at temperatures in the range of one Kelvin or below. The basic ingredients of a single-electron charging device is a small island coupled to the leads via tunneling barriers. When Fermi wavelength of electrons become comparable to the island size, which is the case for electrons in a 2DES in GaAs/AlGaAs heterostructures with a few hundred nanometer device size, the effect of the size confinement starts to play a role and one speaks of quantum dot systems. In a Corbino device, at low temperatures and under strong magnetic field, there are incompressible stripes isolating the main compressible bulk from the ohmic contacts for certain magnetic field range. When the size of Corbino device is small enough - in submicron scale - single-electron charging should be observable. This makes the base of our proposal. During this work we have investigated electrical and structural properties of alloyed Au/Ge/Ni contacts to the 2DES in GaAs/AlGaAs heterostructures in great detail and developed a model for the ohmic contact formation on these systems based on the experimental findings. We have focused on contacting the 2DES in GaAs/AlGaAs heterostructures on submicron scale and succeeded to make successfully working contacts down to a diameter of 0.2 µm. Using these small contacts we have prepared successfully working Corbino devices in submicron scale. As characterizing the devices at low temperatures we have observed a zero bias anomaly - a differential conductance dip at zero bias. Applying a small magnetic field partly suppress the zero bias anomaly. This zero bias anomaly seems to be an interference effect with some unusual properties. Under strong magnetic field we have observed magnetic field periodic oscillations and signature of single-electron charging. We propose models for the explanation of the observed phenomena based on compressible and incompressible stripes.Item Open Access Herstellung und Eigenschaften von Metall/Halbleiter-Übergittern und Mikroringresonatoren : zwei Anwendungen aus der Nanotechnologie(2009) Zander, Tim; Schmidt, O. G. (Prof. Dr.)Diese Arbeit behandelt die Herstellung und Charakterisierung von planaren Metall-Halbleiter-Übergittern (MeSSL), bestehend aus einer Abfolge von ultradünnen InGaAs/GaAs/Cr-Schichten. Weiterhin wird die Änderung der Emissionsenergie in Abhängigkeit einer äußeren Verspannung von Mikroringresonatormoden sowie die darin enthaltenen selbstorganisiert gewachsenen InAs-Quantenpunkte (QP) untersucht. Die Herstellung der planaren MeSSLs wird durch Aufrollen einer Schichtfolge von epitaktisch gewachsenen InGaAs/GaAs und einer thermisch aufgedampften Cr realisiert. Die Verspannung in der Bischicht resultierte in der Formierung eines Röllchen, das abhängig von der Ätzzeit bis zu 17 Umdrehung ausführte. Durch Zusammendrücken dieses radialen Übergitters entstand eine Abfolge InGaAs/GaAs/Cr, die durch eine sogenannte Spiegelebene separiert war. Diese Spiegelebene besteht aus Cr und entstand durch das Zusammendrücken der beiden im Röllchen diametral gegenüberliegenden Metallschichten. Mittels FIB wurde aus diesem MeSSL eine 200nm dünne Lamelle herauspräpariert. Dabei wurde durch Ausmessen der Schichtdicken die Existenz zweier Schichten nachgewiesen, die nicht dem Halbleiter oder dem Metall entsprach. Eine Elementanalyse mit EDX bestätigte das Vorhandensein von Sauerstoff an den zwei Grenzflächen zwischen Metall und Halbleiter. Daraus wurde geschlossen, daß es sich um die jeweiligen Oxide handelte. Reflektivitätsmessungen unter flachem Winkel mit hochenergetischer Synchrotonstrahlung werden diskutiert. Es konnten in den Reflektivitätsmessungen Signalanteile nachgewiesen werden, die dem Multilagensytem des MeSSLs zugeschrieben werden konnten. Dies fiel jedoch nicht so eindeutig aus wie erwartet. Zum einen wurden unter diesem enorm flachen Winkel, und dem entsprechend langen Ausleuchtwinkel des Röntgenstrahls, nicht nur an dem im Vergleich zum Strahl klein bemessenen MeSSL reflektiert, sondern auch von Verunreinigungen auf der Probe und von den Bereichen nebem dem MeSSL. Die Phasenköhärenz wurde auch dadurch stark reduziert, daß sich Oxide gebildet haben, oder noch wahrscheinlicher, durch die Beleuchtung von Falten und Hohlräumen, die durch das Pressen verursacht wurden, was sich auch in den TEM-Aufnahmen nachwiesen ließ. Mikroringresonatoren sind eine konsequente Fortführung des Konzepts der Mikroscheiben. Emitter, in diesem Fall QPe, die sich in der Mitte der Scheibe befinden und demnach weit weg von den am Rand der Scheibe lokalisierten Resonatormoden, erzeugen in Photolumineszenz-(PL)Messungen ungünstige Hintergrundsignale. Durch Entfernen der Scheibenmitte, also der Herstellung von Ringen, hat man sich dieses Problems entledigt. Die Ringe wurden durch komplettes Entfernen der Opferschicht gelöst und auf einem Saphir geklebt. Als Haftschicht kam konventioneller PMMA-Lack zum Einsatz. AFM-Messungen zeigten, daß der Ring nicht im Lack versinkt, sondern auf der Oberfläche bleibt. Anhand von temperaturabhängigen PL-Messungen wurde die Emissionsenergie der im Mikroring befindlichen QPe durch die Abnahme von E_g=E_g(T) um etwa 2,4meV rotverschoben, während die Resonatormoden nur um etwa 0,6eV zu kleineren Energien schoben, da die Änderung des effektiven Brechungsindexes n_eff nur sehr gering ist. Der Nachteil dieser Methode ist die Zunahme von Elektronen-Phononen-Wechselwirkung mit zunehmender Temperatur sowie eine wachsende Emission von Ladungsträgern in die Barriere aus dem QP heraus. Unter Verwendung von Gaskondensation besteht die Möglichkeit, die Modenenergie durch die Zunahme des Volumens und eine damit einhergehende Veränderung von n_eff blauzuverschieben, die Energie der QPe bleibt hierbei unberührt. Wünschenswert war also eine Technik, mit der eine große Verschiebung in beide spektrale Bereiche ohne Verbreiterung der Emissionslinien möglich ist. Zu diesem Zweck wurden die Ringe auf einem piezoelektrischen Kristall, bestehend aus PMN-PT, transferiert. Vermittels Anlegen einer Spannung wird dieser Kristall abhängig vom Vorzeichen der Spannung verformt. Dadurch ließ sich die Energie der QPe als auch der Resonatormoden in spannungsabhängigen Messungen ändern. Während die QP-Energie durch Änderung der Bandlückenenergie zustande kam, ändert sich sowohl die Energie der Mode aufgrund der Änderung von n_eff als auch durch den photoelastischen Effekt. Es konnte über einen Spannungsbereich von -1,1 bis +1,1kV eine maximale Verschiebung der QP-Energie von fast 4meV nachgewiesen werden, die Modenenergie änderte sich dabei um etwa die Hälfte. Eine Zunahme und zudem eine gleichmäßigere Verschiebung wird durch eine vollständige Einbettung der Ringe in PMMA erwirkt. Während sie für Ringe auf dem Lack liegend (1,29+/-0,22)meV betrug, konnte man eine Zunahme auf (2,19+/-0,13)meV mit einer geringeren Streuung beobachten. Oft konnte eine Drift in den Messungen beobachten werden, d.h. die Verspannung wurde zeitlich verzögert an den Ring übertragen, da dieser durch die Lackschicht und einer 1µm dicken SiOx Schicht vom Piezo separiert war. Die Drift ließ sich in einem Mehrfachdurchlauf (2,5 Durchläufe von 0 bis 1kV) zu 130 µeV bestimmen. Zudem konnte mit ortsaufgelöster PL-Spektroskopie gezeigt werden, daß die Verspannung innerhalb des Rings nicht gleichmäßig ist. Dadurch werden QP-Energien an unterschiedlichen Orten im Ring unterschiedlich geändert. Eine Verkippung des Rings konnte jedoch ausgeschlossen werden. In Simulation anhand von Finite-Elemente-Analyse konnten die experimentellen Beobachtungen erklärt werden. Es wurde gezeigt, daß die Verspannung durch die Einbettung in Lack um einen Faktor von 2,2 erhöht war gegenüber den Fall des auf dem Lack liegenden Rings. Das Verspannungsprofil im Querschnitt unterschied sich deutlich für die beiden Fälle und wies auch leichte Unterschiede für verschiedene Kristallrichtungen auf. Weiterhin ließ sich nachweisen, daß kleinere Ringe eine größere Steifigkeit zeigen, die Energieverschiebung in der QP-Ebene war in beiden untersuchten Kristallorientierungen um 0,3meV kleiner. Auch die Verschiebung der Modenenergie wurde durch Simulationen untersucht und ergab einen 0,5meV kleineren Wert als im Experiment. Hier wurde nur die Verkleinerung des Ringdurchmessers um 1nm berücksichtigt. Unter Einbeziehung des photoelastischen Effekts erhöht sich dieser Wert um 0,3meV. Hiermit wurde bestätigt, daß beide Effekte verantwortlich für die Energieverschiebung sind.