Barrier properties and analysis of defects of plasma polymerized hexamethyldisilazane-based films Von der Fakultät Energie-, Verfahrens- und Biotechnik der Universität Stuttgart zur Erlangung der Würde eines Doktors der Naturwissenschaften (Dr. rer. nat) genehmigte Abhandlung Vorgelegt von Mariagrazia Troia aus Andria, Italien Hauptberichter: Prof. Dr. Thomas Hirth Mitberichter: Prof. Dr. Marc Kreutzbruck Tag der mündlichen Prüfung: 26th November 2019 Institut für Grenzflächenverfahrenstechnik und Plasmatechnologie der Universität Stuttgart 2019 "おめでとう" 庵野 秀明 Contents Index of figures ix Index of tables xvii Index of symbols xix Abstract 1 Kurzfassung 3 1 Introduction and statement of the objectives 5 2 State of the art of oxygen barrier layers 9 2.1 Organic light emitting devices and their encapsulation.............................................. 10 2.2 Plasma-polymerized barrier layers .............................................................................. 12 3 Permeation theory 15 3.1 Permeation process ...................................................................................................... 15 3.2 Fick’s laws of diffusion .................................................................................................. 16 3.3 Fickian diffusion through multilayer systems .............................................................. 19 3.4 Dependence of the diffusion coefficient on temperature and activation energy ...... 21 3.5 Limits of the Fickian approach ..................................................................................... 23 3.6 Permeation through defects in barrier layers ............................................................. 24 3.7 Effects of defects on barrier layers’ properties ........................................................... 26 3.8 Effects of defects on activation energies .................................................................... 28 4 Plasma fundamentals 31 4.1 Plasma properties and classification ........................................................................... 31 4.2 Electron cyclotron resonance (ECR) plasmas .............................................................. 35 4.3 Plasmochemical processes for surface modifications ................................................ 38 4.4 Plasma-enhanced-chemical-vapor-deposition (PEVCD) ........................................... 41 Contents vi 5 Experimental setup 45 5.1 Plasma reactor and experimental conditions ............................................................. 45 5.2 Substrates ................................................................................................................... 48 5.3 Monomers as plasma feed gases ................................................................................ 52 6 Diagnostic methods 59 6.1 Profile measurements ................................................................................................. 59 6.2 Chemical analyses.........................................................................................................61 6.2.1 Fourier-transform infrared (FTIR) spectroscopy..........................................61 6.2.2 X-ray photoelectron spectroscopy (XPS) ................................................... 65 6.3 Microscopy .................................................................................................................. 66 6.3.1 Optical microscopy ...................................................................................... 66 6.3.2 Scanning electron microscopy (SEM) .......................................................... 67 6.4 Permeation measurements ......................................................................................... 71 6.4.1 Experimental set-up ..................................................................................... 71 6.4.2 Instruments cross-calibration ...................................................................... 76 6.5 CO2 test for the localization of defects in barrier layers .............................................. 79 6.5.1 State of the art for defect detection methods ............................................. 79 6.5.2 Pinhole test – chemical principles and processes ........................................ 83 6.5.3 Sample-holding cell and experimental set-up ............................................ 86 6.5.2 Evaluation of the pinhole test ..................................................................... 90 7 Single barrier films – Results and discussion 101 7.1 Study of the variation of the O2/HMDSN feed ratio ................................................. 101 7.1.1 Deposition rates ..........................................................................................102 7.1.2 IR analyses of the barrier films................................................................... 106 7.1.3 Morphology of the barrier films .................................................................. 119 7.1.4 Permeation curves of the barrier films .......................................................120 7.1.5 Pinhole test for the barrier films ................................................................. 127 7.1.6 Effect of temperature on permeation curves and diffusion coefficients . 140 7.2 Study of the operating power .................................................................................... 158 7.2.1 Effects on the chemical composition ......................................................... 158 7.2.2 Effects on films transmission rates ........................................................... 162 7.2.3 Ranges of operationality ............................................................................ 165 7.3 Study on barrier thickness ......................................................................................... 168 7.3.1 Deposition rates of barrier films with different thicknesses ..................... 169 7.3.2 IR analyses of barrier films with different thicknesses ............................... 170 7.3.3 Oxygen permeation curves of barrier films with different thicknesses ..... 177 7.3.4 Morphology at different thicknesses and growth mechanisms ................ 181 7.4 Barrier films flexibility and resilience ........................................................................ 188 vii 7.4.1 Bending cycles ............................................................................................ 188 7.4.2 Deposition on substrates with various roughnesses ................................. 194 7.5 Comparison of HMDSN- and HMDSO-based films .................................................. 198 7.5.1 Barrier properties and film morphology ..................................................... 199 7.5.2 FTIR and XPS chemical analyses of HMDSN- and HMDSO-based films ....................................................................................................... 204 7.5.3 Deposition rates of HMDSN- and HMDSO-based films ............................ 217 7.5.4 Polymerization reactions and pathways for HMDSN and HMDSO ................................................................................................. 218 8 Multilayer barriers and encapsulation of OLEDs prototypes 227 8.1 Multilayer coatings ..................................................................................................... 227 8.2 OLED prototypes ....................................................................................................... 238 8.3 Building and connection of a glovebox to the ECR reactor ...................................... 240 8.4 Encapsulation of OLEDs ........................................................................................... 242 9 Summary and outlook 247 9.1 Summary .................................................................................................................... 247 9.2 Outlook ......................................................................................................................250 Appendix A1 253 Appendix A2 267 Bibliography 279 Acknowledgements 295 Eidesstattliche Erklärung 297 Contents viii Index of figures 1.1 Overview of the current work ................................................................................................ 7 2.1 Oxygen transmission rates for commercially available products ....................................... 10 2.2 OLEDs encapsulation strategies ......................................................................................... 11 2.3 Schematic structure of a multilayer system ........................................................................ 13 3.1 Concentration profile at the boundary for a one-dimensional case ................................... 18 3.2 Permeation curve as a function of time .............................................................................. 19 3.3 Schematic representation of possible gas-solid diffusion mechanisms ........................... 26 3.4 Simplified permeant transport modes for mono- and bi-layers ........................................ 29 4.1 Plasmas as a function of their electron density and temperature ...................................... 32 4.2 Electron gyration motion in a magnetic field ...................................................................... 36 4.3 Drift motion of an electron trapped in a magnetic field ..................................................... 36 4.4 Simplified representation of the processes in PECVD ....................................................... 42 4.5 Internal structure of a PECVD silica-like film with an organic component ........................ 42 4.6 Interface between substrate and PECVD thin coating ...................................................... 44 5.1 Schematic of the electron cyclotron resonance reactor .................................................... 46 5.2 Front and back view of the ECR reactor .............................................................................. 47 5.3 Array of 48 permanent cobalt-samarium magnets ............................................................ 47 5.4 Plasmas seen from the side window port of the ECR vessel ............................................. 48 5.5 Repetitive unit of polyethylene terephthalate (PET) ......................................................... 49 5.6 Schematic representation of a section of the Hostaphan PET foil ..................................... 50 5.7 Normalized oxygen transmission rates for uncoated Hostaphan PET .............................. 51 5.8 AFM scan of Melinex foils .................................................................................................... 51 5.10 Normalized oxygen transmission rates for uncoated Melinex PET foils ............................ 52 5.11 Molecular formula and bond energies of hexamethyldisilazane........................................ 53 5.12 Absorption infrared spectrum of gaseous HMDSN ............................................................ 53 5.13 Molecular formula and bond energies of hexamethyldisiloxane ....................................... 54 Index of pictures x 5.14 Absorption infrared spectrum of gaseous HMDSO ........................................................... 54 6.1 Profile measurement for the determination of the thickness of thin films ....................... 60 6.2 Schematic representation of a Michelson interferometer ................................................ 62 6.3 Attenuated total reflectance unit ........................................................................................63 6.4 High refractive index crystal in the sample holding cell ..................................................... 64 6.5 Schematic representation of the SEM column and beam focusing .................................. 69 6.6 Signals produced by an accelerated electron beam at the end of a SEM column ............. 70 6.7 Sample-holding cell for the carrier gas method .................................................................. 71 6.8 Systems for the measurements of the oxygen transmission rates .................................... 72 6.9 Open sample-holding cells .................................................................................................. 73 6.10 Galvanic cell for the determination of the oxygen concentration ...................................... 74 6.11 Schematic representation of steps in the permeation measurement routine ................... 75 6.12 Delay time and line length for the permeation systems ..................................................... 77 6.13 Curves of the same coated sample tested in both systems ................................................ 78 6.14 Oxygen transmission rate values for the measurements in the two systems of the sample coated foil. ............................................................................................................ 78 6.15 Sheaf of wheat precursor for a spherulite .......................................................................... 85 6.16 Schematic section of the sample-holding cell for the pinhole test .................................... 87 6.17 Sample holding cell opened and mounted during a pinhole test ...................................... 88 6.18 Details of an optical microscope frame at different times of a pinhole test .......................91 6.19 SEM picture of an uncoated PET foil after the pinhole test ............................................... 92 6.20 SEM pictures of uncoated PET tested with an underlying aluminum foil ......................... 92 6.21 Schematic representation of the increased CO2 concentration at the edges of a droplet .............................................................................................................................. 94 6.22 SEM pictures of crystals at the edges of a droplet ............................................................. 94 6.23 Detail of the smaller crystallites at the edge of a lime water drop .................................... 95 6.24 Detail of an uncoated patch of polymer substrate during a pinhole test .......................... 96 6.25 PET foil coated with a good barrier layer damaged during its handling ............................ 97 6.26 Uncoated PET foil purposefully scratched before the pinhole test ................................... 98 6.27 Damages on the barrier layer caused by folding of the substrate foil ............................... 98 6.28 Microscope and SEM pictures of the same area investigated via pinhole test ................. 99 7.1 Thickness of HMDSN-based films at different compositions versus their deposition time .................................................................................................................................. 103 7.2 Normalized thickness vs. deposition time for films with different oxygen-to- monomer ratios ............................................................................................................... 103 7.3 Normalized deposition rates for different oxygen-to-monomer ratios .......................... 104 7.4 Errors caused by sensitivity limits and overall errors affecting HMDSN fluxes ................ 105 xi 7.5 ATR FTIR spectra for films with different O2/HMDSN plasma feed ................................ 107 7.6 Peak intensity of the methyl band compared to the Si-O-Si band and methyl peak position ............................................................................................................................ 110 7.7 Water droplets sitting on glass substrates coated with films with different oxygen content ............................................................................................................................ 112 7.8 Si-O-Si main band position and its half widths at half maximum as function of the oxygen-to-monomer ratio ................................................................................................. 113 7.9 Details of the IR -OH band from Figure 7.5 ....................................................................... 115 7.10 -OH stretching sub-bands for an O2/HMDSN=70 sample ................................................ 116 7.11 Schematic of the condensation process of vicinal hydroxils groups on a surface ex- posed to oxygen radicals ................................................................................................. 117 7.12 Spectra of repeated depositions of 100 nm thick films with an oxygen-to-monomer ratio of 15 ......................................................................................................................... 118 7.13 Infrared spectra of 100 nm films deposited at the extremities of the area covered by the ECR magnet movement ........................................................................................... 118 7.14 Scanning electron microscope pictures for HMDSN-based films at different plasma feed dilutions ................................................................................................................... 119 7.15 Oxygen transmission rates as a function of the oxygen-to-monomer ratios .................. 121 7.16 Oxygen transmission rates as a function of the IR methyl band ...................................... 122 7.17 Normalized oxygen transmission rates as a function of time for uncoated PET and three coated samples ...................................................................................................... 123 7.18 Diffusion coefficient of the substrate plus barrier system calculated from the record- ed permeation curves ...................................................................................................... 124 7.19 Curves of the concentration of oxygen in the carrier gas versus time for a selection of four coated samples ........................................................................................................ 125 7.20 Diffusion coefficient as a function of the oxygen-to-monomer ratio in the plasma phase for the substrate plus barrier and for the 100 nm barriers alone ......................... 126 7.21 Details of optical microscope pictures for uncoated PET and a selection of thin films.... 128 7.22 SEM pictures of the calcium carbonate crystals formed on the surface of the uncoat- ed polymer reference and for three barriers................................................................... 129 7.23 Overview of CaCO3 crystals found on the surface of uncoated PET foil .......................... 129 7.24 Overview of CaCO3 crystals found on the surface of a thin film with a 10/1 oxygen-to- monomer ratio ................................................................................................................ 130 7.25 Overview of CaCO3 crystals found on the surface of a thin film with a 40/1 oxygen-to- monomer ratio ................................................................................................................ 130 7.26 Overview of CaCO3 crystals found on the surface of a thin film with a 70/1 oxygen-to- monomer ratio ................................................................................................................ 131 7.27 Details of crystals upturned or displaced during the sample handling ............................. 133 7.28 Oxygen transmission rates before and after the pinhole test .......................................... 134 Index of pictures xii 7.29 CaCO3 crystals number in a fixed frame of the investigated barrier surface as a func- tion of time ...................................................................................................................... 136 7.30 Numerical defect density for barriers as a function of the oxygen-to-monomer ratio in the plasma feed ........................................................................................................... 137 7.31 Uncoated PET sample after being subjected twice at the pinhole test............................ 139 7.32 OTRs measured at 35°C for a 40/1 barrier, before and after the sample has been heated up to 60°C........................................................................................................... 140 7.33 OTRs as a function of the temperature for the uncoated PET and three coated sam- ples ................................................................................................................................... 141 7.34 Fit of the uncoated PET data with an Arrhenius-like equation .........................................142 7.35 Barrier improvement factors as a function of the temperature for three investigated thin films ..........................................................................................................................142 7.36 Oxygen transmission rates of the isolated thin films as a function of the temperature .. 143 7.37 Relative variations in the OTRs for the isolated barriers alone with respect to the measured values pertinent to the substrate plus barrier system .................................. 144 7.38 Box-and-whisker chart for the whole 10/1 sample measurements, and them after being split in two subset .................................................................................................. 145 7.39 Logarithmic Arrhenius-like plots for the substrate plus barrier and the isolated barri- er contributions for the three investigated plasma-feed compositions ....................... 146 7.40 Activation energies calculated by means of the Arrhenius plots and the associated coefficient of determination R2 for the substrate plus thin film system and the iso- lated barrier contributions alone ..................................................................................... 147 7.41 Arrhenius plots for the 40/1 sample ‘as measured’ and isolated with two separate fittings .............................................................................................................................. 150 7.42 Activation energies for the 40/1 samples set of data, split in two segments, and the associated coefficient of determinationR2 for the substrate plus barrier system and the isolated barrier contributions alone .......................................................................... 151 7.43 Oxygen transmission rates as a function of the temperature according to the free diffusion model for the uncoated PET reference and the three investigated films ....... 155 7.44 Oxygen transmission rates as a function of the temperature according to the Knud- sen diffusion model for the uncoated PET reference and the three investigated films ................................................................................................................................. 156 7.45 Calculated activation energies for the investigated bilayers and uncoated PET as a function of their normalized OTRs at 35°C ..................................................................... 157 7.46 Deposition rates vs. operating power for an oxygen-to-monomer ratio of 13/1, 40/1 and 70/1 ............................................................................................................................ 159 7.47 ATR FTIR absorption spectra for different operating powers and different oxygen- to-monomer ratios ......................................................................................................... 160 7.48 Si-O-Si main band position and ratio between the intensities of the methyl band and xiii main band for all investigated conditions ....................................................................... 161 7.49 OTRs as function of the operating power for a 13/1, 40/1 and 70/1 oxygen-to- monomer ratios ............................................................................................................... 163 7.50 Optical microscope pictures taken after the pinhole test for films deposited with an average operating power of 520 W, 580 W and 660 W .................................................. 164 7.51 Methyl-to-Si-O-Si bands intensity ratio and OTRs displayed as BiFs of the PET sub- strate plotted as function of different gas feed ratios and operating powers ............... 167 7.52 Range in which thin films with barrier improvement factors equal to or higher than 20 are attained, with highlighted the two best pair of conditions ................................. 168 7.53 Rates for films deposited with an oxygen-to-monomer ratio of 40 and a thickness over almost two order of magnitude .............................................................................. 169 7.54 Normalized infrared spectra for films with different thicknesses at a constant oxy- gen-to-monomer ratio of 40/1 ........................................................................................ 171 7.55 Proposed LO mode peaks arising from the splitting of the four TO components pro- posed for the main Si-O-Si band ..................................................................................... 174 7.56 Half width at half maximum for different film thicknesses .............................................. 175 7.57 Peak positions of the main Si-O-Si band as a function of the film thickness and corre- sponding oxygen fraction ............................................................................................... 176 7.58 Detail of the –OH stretching band for all spectra displayed in Figure 7.54....................... 176 7.59 Normalized oxygen transmission rates as a function of thickness for samples depos- ited out of a 40/1 oxygen-to-monomer plasma feed ..................................................... 178 7.60 Recorded curve of the concentration of oxygen in the carrier gas versus time for a 40/1 barrier with a thickness of 570 nm ........................................................................... 179 7.61 Numerical defect density for 40/1 barriers as a function of their thickness. .................... 179 7.62 CaCO3 crystals number in a fixed frame of the investigated barriers with different thickness as a function of time ........................................................................................ 180 7.63 Diffusion coefficients as a function of the thickness of 40/1 films for the substrate plus barrier and for the barriers alone ............................................................................. 181 7.64 Detail of calcium carbonate crystals and other aggregates spotted on the surface of barriers with various thicknesses at a 40/1 oxygen-to-monomer ratio ......................... 182 7.65 Frames of the surface of 40/1 inorganic barriers with different thickness after one hour of pinhole test ......................................................................................................... 183 7.66 SEM pictures of a section of a 40/1 barrier layer deposited on glass ................................ 184 7.67 Detail of a shard of barrier being dislodged during the clipping of the glass substrate, and the underlying still attached film ............................................................................. 185 7.68 Proposed structure for a 40/1 barrier film with a thickness higher than 0.5 micron ........ 187 7.69 Step-by-step bending cycle for a coated PET sample ...................................................... 189 7.70 Oxygen transmission rates for an uncoated PET foil after being subjected to cycles of bendings at different radii ........................................................................................... 190 Index of pictures xiv 7.71 Normalized oxygen transmission rates for 0 – 50 bending cycles and two curvature radii for 40/1 samples. ..................................................................................................... 191 7.72 Normalized oxygen transmission rates for 0 – 50 bending cycles and two curvature radii for 70/1 samples ...................................................................................................... 192 7.73 Normalized oxygen transmission rates for a 1.8 cm curvature radius over 50 bending cycles for 40/1 oxygen-to-monomer ratio samples with different thicknesses ............. 193 7.74 OTRs after 50 bending cycles compared to the unbent OTRs versus film thickness ...... 194 7.75 Antiblock particles on PET foils before and after plasma exposure and their role as defects initiatiors in the thin films ................................................................................... 195 7.76 Scanning electron microscope pictures for polymer foils uncoated and with 100 nm thick inorganic film ......................................................................................................... 196 7.77 Oxygen transmission rates for barriers deposited on both sides of Melinex foils and reference values for barriers on Hostaphan .................................................................... 197 7.78 Optical microscope pictures for a 100 nm, 40/1 barrier layer deposited on Hostaphan foil and on the rough side of a Melinex .......................................................................... 198 7.79 Oxygen transmission rates normalized to the uncoated PET reference for HMDSN- and HMDSO- based films 100 nm thick ......................................................................... 200 7.80 Defect densities calculated by means of the pinhole test for 100 nm thick films de- posited via HMDSN and HMDSO ...................................................................................201 7.81 Summary of the measured OTRs and defect densities for HMDSN and HMDSO sample with 10/1, 40/1 and 70/1 oxygen-to-monomer ratios ........................................ 202 7.82 Normalized oxygen transmission rates before and after the pinhole test for HMDSO- based films with different oxygen-to-monomer ratios ................................................. 202 7.83 Scanning electron microscope pictures for HMDSN- and HMDSO-based films at three different plasma feed dilutions ............................................................................. 203 7.84 ATR FTIR normalized spectra for films deposited via different O2/HMDSO plasma feed ................................................................................................................................. 205 7.85 Relative peak intensity of the methyl band with respect to the main Si-O-Si band and position of the main Si-O-Si peak for HMDSN- and HMDSO-based films ............ 206 7.86 Normalized single-reflection absorption IR spectra for a selection of HMDSN-based samples ............................................................................................................................ 207 7.87 Normalized single-reflection absorption IR spectra for a selection of HMDSO-based samples ........................................................................................................................... 208 7.88 Superimposed FTIR spectra for the 40/1 and the 70/1 oxygen-to-monomer ratios ........ 209 7.89 XPS atomic ratios as a function of the oxygen-to-monomer ratio for HMDSN and HMDSO as precursors .....................................................................................................210 7.90 High resolution C1s spectra and relative fitting for HMDSN and HMDSO as precur- sors at different dilutions ................................................................................................212 7.91 Fitted high resolution N1s spectra for HMDSN-based films up to a dilution of 10/1 ........ 213 xv 7.92 High resolution Si2p spectra and relative fitting for HMDSN and HMDSO as precur- sors at different dilutions ................................................................................................ 214 7.93 Peak positions for the experimental O1s and Si2p overall signals and their corre- spondent full width at half maximum, for both precursors ........................................... 215 7.94 Normalized deposition rates as a function of the oxygen-to-monomer ratio for both precursors ........................................................................................................................ 218 7.95 Proposed reaction pathways for the Si-NH-Si backbone of HMDSN .............................. 221 7.96 Proposed reaction pathways for the Si-O-Si backbone of HMDSO and for the result- ing fragments ................................................................................................................. 222 7.97 Summary of the simplified reaction pathways involving the backbones of HMDSN and HMDSO .................................................................................................................... 223 8.1 OTRs and corresponding BiFs for two sets of single barrier layers on PET and double- sided coated samples ..................................................................................................... 228 8.2 Pictures at the optical microscope for the double-sided sample before and after the pinhole test ..................................................................................................................... 229 8.3 Diffusion coefficients for the first set of samples, calculated for the PET plus barri- er(s) system from the recorded permeation curved, and extrapolated for the barri- ers alone .......................................................................................................................... 230 8.4 Multilayers on glass consisting of a pair of dyads ............................................................. 231 8.5 Normalized oxygen transmission rates for the first batch of multilayers ........................ 232 8.6 Optical microscope pictures of a selection of samples after the pinhole test .................. 233 8.7 Absorbance FTIR ATR spectra of a selection of multilayers ............................................. 233 8.8 SEM pictures of the section of a stacked multilayer on glass ........................................... 235 8.9 SEM pictures of the section of a gradient multilayer on glass .......................................... 236 8.10 Normalized oxygen transmission rates for multilayer systems ....................................... 238 8.11 Schematic representation of the two types of BEOLEDs employed in the multilayer encapsulations ................................................................................................................. 239 8.12 Structure of larger BEOLEDs with a total thickness of less than 500 nm ........................ 239 8.13 OLEDs prototypes on glass and on PET ........................................................................... 240 8.14 Smaller prototypes on PET tested one week after being printed and immediately before the encapsulation process .................................................................................. 240 8.15 Schematic representation of the glovebox employed for handling of uncoated OLEDs .............................................................................................................................. 241 8.16 Glovebox and relative flushing system and sensors connected to the ECR reactor, and details of the suction cap for the insertion of samples in the vessel ...................... 242 8.17 Oxygen fraction in the glovebox atmosphere as a function of time ............................... 242 8.18 Schematics of the encapsulation strategy for OLED prototypes on PET ........................ 243 8.19 Glass substrates left uncoated for reference and coated with different sets of dyads ... 244 Index of pictures xvi 8.20 OLEDs prototypes inside the glovebox being tested before and after the two-step encapsulation ................................................................................................................. 245 8.21 Large OLED on PET at different stages of the encapsulation and post-encapsulation process ............................................................................................................................ 246 A1.1 FTIR spectra of untreated PET Hostaphan and PET Melinex on the smooth and rough side ....................................................................................................................... 254 A1.2 Rotational isomers of the glycolic group in PET ............................................................... 257 A1.3 Absorbance spectra for annealed and native Hostaphan, and for annealed, native smooth and native rough Melinex ................................................................................. 261 A1.4 Highlights from the absorbance spectra of Figure A.3 .................................................... 262 A1.5 Ethylene gauche and trans bands for native and annealed PET foils .............................. 263 A1.6 Trans-to-gauche ratios for native and annealed PET foils ............................................... 263 A1.7 Areas of the trans and gauche ethylene wagging peaks for Hostaphan and Melinex .... 265 A2.1 Measured thickness as a function of the deposition time for different hydrogen-to- monomer ratios .............................................................................................................. 268 A2.2 Normalized deposition rates as a function of the hydrogen-to-monomer ratio ............ 268 A2.3 ATR infrared spectra for different hydrogen-to-monomer ratios ................................... 269 A2.4 Relative intensity of the methyl peak compared to the main band and main position of the methyl band as a function of the hydrogen-to-monomer ratio .......................... 271 A2.5 Fitted methyl bands for a hydrogen-to-monomer ratio equal to 70/1, 40/1 and 10/1 ...... 272 A2.6 Silyl band position as a function of the hydrogen-to-monomer ratio .............................. 273 A2.7 Oxygen transmission rates as a function of the hydrogen-to-monomer ratio ................ 274 A2.8 100 nm films deposited with HMDSN as precursor and nitrogen, hydrogen and oxy- gen ................................................................................................................................... 275 A2.9 Residual thickness of organic layers with a hydrogen-to-monomer ratio of 10, 40 and 70 after being etched in an oxygen plasma .................................................................... 276 Index of tables Table 4.1 List of internal and external parameters for plasmo-chemical processes ............ 40 Table 5.1 Main physical properties of polyethylene terephthalate ...................................... 49 Table 5.2 Physical properties of precursors and co-gases for PECVD ................................... 55 Table 6.1 Peak positions and attributed chemical bonds of the components employed for the curve fitting of high resolution C1s, N1s and Si2p spectra ....................... 67 Table 6.2 Specifics of the two permeation measurement systems employed ..................... 76 Table 6.3 Tabulation of defect densities for single-layer inorganic barrier films depos- ited on polymeric substrates by means of different techniques ........................ 82 Table 7.1 Peak positions and vibrational mode assignments for the main absorption infrared bands ..................................................................................................... 109 Table 7.2 [Si-O]-related vibration modes in the 1150-970 cm-1 range for thin silicon oxi- de films ............................................................................................................... 112 Table 7.3 Activation energies for uncoated PET foils calculated via an Arrhenius-like plot ...................................................................................................................... 147 Table 7.4 Average size of a monodisperse population of square defects and area frac- tions covered by them ........................................................................................ 152 Table 7.5 Peak positions and vibrational mode assignments for the main absorption infrared bands for Fig. 7.15 spectra .................................................................... 172 Table 7.6 Position and assignment of TO and proposed (*) LO modes for the investi- gated bands ........................................................................................................ 173 Table 7.7 Operating conditions employed for the deposition of the HMDSN and HMDSO samples ................................................................................................ 199 Table 7.8 Bond energies for HMDSN and HMDSO precursor molecules ........................... 219 Table 8.1 Operating conditions and thicknesses for the films employed in multilayer systems .............................................................................................................. 228 Table 8.2 Labels for the deposited multilayer samples ....................................................... 234 Index of tables xviii Table A1.1 Peak positions and vibrational mode assignments for the main absorption bands of PET. ......................................................................................................255 Table A2.1 Peak positions and vibrational mode assignments for the main absorption bands in the infrared spectra displayed in Figure A2.1. ..................................... 270 Table A2.2 Peak positions and band intervals for the sub-components of the methyl and silyl band. ............................................................................................................ 273 Table A2.3 Calculated residual thicknesses as absolute and relative values for the three etched films. ....................................................................................................... 276 Index of symbols Symbol Description A Area (Chapter 6), integrated area of absorbance peaks (Appendix A1) Acceleration B Magnetic field CSu Sutherland constant c Speed of light (Chapter 6), concentration (elsewhere) [c] Concentration D Diffusion coefficient dp Diameter of the permeated pore (Chapter 3), penetration depth (Chapter 6) E Electric field EB Binding energy Ek Kinetic energy e Elementary charge (Chapter 3), Euler's number (elsewhere) f Frequency F Faraday constant Lorentz force h Lateral size of a defect along the y-axis k Elastic constant (Section 6.2.1), equilibrium constant (elsewhere) kB Boltzmann constant Kn Knudsen number j Electron current (Chapter 4), flux in [mol s-1 m-2] (elsewhere) L Plasma dimension (Chapter 4), defects separation (Chapter 7) M Molecular weight m Mass N Number of atoms in a molecule n Defect density (Chapter 3), Planck constant (Chapter 4), refractive index (Chapter 6) Index of symbols xx Symbol Description nc Cut-off electron density ni Density of particles i P Pressure (Chapter 6), permeability coefficient (elsewhere) p Partial pressure q Electric charge (Chapter 4) R Ideal gas constant R2 Coefficient of determination r Radius rL Larmor radius S Oversaturation (Chapter 6), solubility (elsewhere) s Defects elongation (Chapter 7), solubility coefficient (elsewhere) T Temperature t Time U Electrolytic cell potential Velocity vD Drift velocity w Lateral size of a defect along the x-axis X Ionization degree (Chapter 4), concentration in [ppm] (Chapter 6) y0 Initial film thickness Z Number of vibration for a molecular bond Zi Electric charge of particle i G Gibbs free energy variation H Enthalpy variation S Entropy variation y Variation of film thickness o Vacuum permittivity p Effective porosity  Viscosity  Tilting angle  Wavelength D Debye length f Mean free path between collisions  Permeand mobility (Chapter 3), reduced mass (Chapter 6) p Defect tortuosity  Frequency of electromagnetic radiation Wavenumber xxi Symbol Description  Archimedes' constant  Cross section (Chapter 3), standard deviation (elsewhere)  Thickness fraction (Chapter 3), work function (Chapter 6)  Volume fraction  Gas flow  Fraction of trans isomers  Angular frequency c Cyclotron frequency AMOLED Active Matrix Organic Light Emitting Device ATR Attenuated Total Reflectance BEOLED Bottom Emitting Organic Light Emitting Device DSC Differential Scanning Calorimetry ESCA Electron Spectroscopy for Chemical Analyses FOLED Flexible Organic Light Emitting Device FTIR Fourier Transform InfraRed FWHM Full Width at Half Maximum HMDSN HexaMethylDiSilazaNe HMDSO HexaMethylDiSilOxane ILT Ideal Laminate Theory IR InfraRed LED Light Emitting Device MFC Mass Flow Controller OLED Organic Light Emitting Diode OTR Oxygen Transmission Rate PECVD Plasma Enhanced Chemical Vapor Deposition PET Polyethylene terephthalate SEM Scanning Electron Microscopy UV UltraViolet VUV Vacuum UltraViolet XPS X-ray Photoelectron Spectroscopy Index of symbols xx Abstract A great variety of commercially available goods, e. g. food products, require a degree of protec- tion against gases and vapors. Electronic devices whose active layers are based on organic mate- rials in particular demand extremely low oxygen transmission rates in order to attain adequate lifetimes. In order to do so, an encapsulation of the device by means of a barrier becomes neces- sary. In case of flexible devices, such as organic light emitting devices (OLEDs), conventional en- capsulation methods relying on stiff glass lids cannot be employed. Plasma-enhanced chemical vapor deposition (PECVD) methods on the other hand have been proven to be successful in ob- taining thin films (in the range of tens or hundreds of nanometers) which combine good barrier performances with flexibility and other favorable mechanical properties. In the current work, thin silica-like (SiOx) films have been deposited on polyethylene tereph- thalate (PET) through a low-pressure microwave plasma and a gaseous feed consisting of hexa- methyldisilazane (HMDSN) and oxygen, with the aim of providing flexible oxygen barrier layers with additional properties as transparency, colorlessness, good adhesion to the substrate and resilience. Operational parameters such as the gas feed composition, microwave power and deposition time have been investigated and optimized, thus obtaining inorganic barriers with an optimal thickness in the 50 to 100 nm range and with a barrier improvement, when compared to the uncoated substrates, up to a factor of 100. The defects in the barriers have been investigated by means of a concurrently developed non-destructive method for their localization and identifi- cation, based on the precipitation of calcium carbonate crystallites on top of them, which allows the defect to be later retrieved and investigated by means of microscopy methods. Further anal- yses of the transmission rates have been carried out at different temperatures in order to investi- gate the permeation mechanisms through the bulk and the defects. The films, when compared to barriers deposited via the common precursor hexamethyldisiloxane (HMDSO), obtained in the same experimental setup, showed consistently better properties in a wider range of conditions, proving HMDSN to be a better precursor for thin films with barrier applications. Multilayer systems, based on the combination of SiOx films and an intermediate organic layer optimized in parallel to the barriers, have been developed, tested and used successfully for the encapsulation of flexible Organic Light Emitting Device (OLED) prototypes printed on poly- mers. Chapter 1. Introduction and statement of the objectives 2 Kurzfassung Zahlreiche im Handel erhältliche Produkte wie z.B. Nahrungsmmittel müssen vor Gasen und Dämpfen geschützt werden. Um speziell bei elektronischen Bauteilen, deren aktive Schichten aus empfindlichen organischen Materialien bestehen, eine ausreichende Lebensdauer zu gewährleisten, muss die Sauerstoffdurchlässigkeit stark reduziert werden. Zu diesem Zweck wird eine Verkapselung der Bauteile durch eine Barriereschicht erforderlich. Insbesondere bei flexiblen organischen Leuchtdioden (OLEDs) können konventionelle Verkapselungsmethoden wie z.B. das Aufbringen einer dünnen steifen Glasplatte nicht verwendet werden, ohne die Flexibilität dieser Geräte stark zu beeinträchtigen. Die Plasma Enhanced Chemical Vapor Deposition (PECVD)-Methode hat sich bereits als erfolgreich erwiesen, um dünne Schichten im Bereich von einigen Nanometern bis zu einigen 100 nm herzustellen. Diese Schichten besitzen sehr gute Barriereeigenschaften und weisen weitere vorteilhafte mechanische Eigenschaften wie eine hohe Flexibilität auf. In der aktuellen Arbeit wurden dünne quarzähnliche (SiOx) Schichten mittels eines Nieder- druck-Mikrowellen-Plasmaverfahren aus einer Gasmischung von Hexamethyldisilazan (HMDSN) und Sauerstoff auf Polyethylenterephtalate (PET)-Folien mit einer Dicke von 23 µm abgeschieden. Ziel war es, flexible Sauerstoffbarrierenschichten mit zusätzlichen Eigenschaften wie Transparenz, Farblosigkeit, gute Haftung und Stabilität, zu erhalten. Die Betriebsparameter wie Gasmischungsverhältnis, Mikrowellenleistung und Abscheidungsdauer wurden untersucht und optimiert. Es konnten anorganische Barrierenschichten mit einer optimalen Schichtdicke von 50 bis 100 nm abgeschieden werden, die gegenüber dem unbeschichteten PET eine um den Faktor 100 niedrigere Sauerstoffdurchlässigkeit aufweisen. Die Defekte (Pinholes) in den Barriereschichten wurden mittels einer im Rahmen der Arbeit entwickelten zerstörungsfreien Lokalisierungs- und Identifizierungsmethode untersucht. Sie basiert auf der Ausfällung von Kalziumkarbonatkristallen auf den Defekten. Diese Methode ermöglicht ebenfalls das nachfolgende Wiederauffinden und die detaillierte Untersuchung der Defekte durch optische Mikroskopie und Rasterelektronenmikroskopie. Weitere Perme- ationsanalysen bei verschiedenen Temperaturen wurden durchgeführt, um die Permeationsmechanismen durch die PET-Folie und die Defekte zu untersuchen. Im Vergleich mit dem weit verbreiteten Precursor Hexamethyldisiloxan (HMDSO) zeigten die HMDSN- basierten Schichten wesentlich bessere Barriereeigenschaften über einen weiten Bereich von Kurzfassung 4 von experimentellen Betriebsparametern. Mehrschichtsbarrieresysteme basierend auf SiOx-Schichten und organischen Pufferschichten wurden entwickelt, getestet und für die Verkapselung von flexiblen, auf Polymeren gedruckten OLED Prototypen erfolgreich eingesetzt. Chapter 1 Introduction and statement of the objec- tives A great variety of commercially available products require a degree of protection against external gases and liquids, chiefly among them oxygen and water vapor. Electronic devices whose active layers are based on organic materials in particular demand extremely low oxygen transmission rates in order to attain adequate lifetimes. In order to do so, an encapsulation of the device by means of a barrier layer becomes necessary. Glass lids several times thicker than such devices, sealed with epoxy resins, are widely employed for this purpose. This kind of encapsulation cannot however be applied if the aim is also to retain the inherent flexibility, lightness and thinness that organic devices like organic LEDs can offer when compared to their inorganic counterparts. The relative harshness of the epoxy resin curing step alone, and the resulting ultraviolet irradiation, are enough to destroy the active layer of the devices. Thin inorganic films deposited from volatile precursors by means of plasma-aided processes, on the other hand, have been widely investigated and already employed as barriers in food pack- aging and other similar fields. Such layers combine transparency, thinness, lightness, and superi- or adhesion and flexibility, when compared to films obtained by conventional deposition meth- ods, all of which is also desirable for the encapsulation of organic devices. The deposition process itself, being carried out through low-temperature plasmas, is ‘mild’ enough not to endanger the substrates, quick, efficient, reproducible, tunable and easily up-scalable in case of large-area in- dustrial applications. For the latter, the reduced amount of reagents required makes it also envi- ronment-friendly and cost-effective, too. The capacity of films in the sub-micrometric scale to mimic their macroscopic counterparts, their related oxygen barrier properties included, is however limited by the presence of defects extending along their entire bulk. Through such nanometric spaces the permeand molecules can travel almost unhindered and, provided the density of such defects to be high enough, the barrier properties of the whole thin film result to be severely compromised or, at worst, almost com- pletely nullified. Chapter 1. Introduction and statement of the objectives 6 Hence in the current work a low-pressure, microwave-based plasma reactor has been em- ployed for the deposition of silica-like (SiOx) films with the principal aim to obtain thin barrier lay- ers against oxygen. The reactor employed and its configuration allow areas much larger than the proper plasma to be treated, while at the same time providing mild operating conditions suited for the encapsulation of sensitive electronic devices even in case of prolonged deposition steps. The main aim is therefore that the thusly obtained films must first and foremost present a suitable chemical composition that allows them to act as barriers against oxygen, but also pos- sess, when possible, further favorable properties that would make an encapsulation of flexible light-emitting devices feasible: they need to be transparent and colorless, to exhibit good adhe- sion to their substrate and to be able to undergo repeated bending without compromising their mechanical stability. In order to meet the above-mentioned requirements, an optimization of a wide range of operating parameters, including the composition of the plasma feed, the operating power and the duration of the deposition step, has been performed. Furthermore, for the purposes of encapsulating very sensitive devices, the precursor for the polymerization of the barriers should not contain oxygen atoms. In the current work the mono- mer of choice has been therefore the organosilicone hexamethyldisilazane (HMDSN), which is relatively seldom used in plasma-assisted processes for the purpose of obtaining silica-like films. Another aim of the work has therefore been to compare the deposited films and their barrier per- formances with those produced by means of more widespread, conventional and oxygen- containing organosilicone precursors, in order to ascertain whether and to what extent silazanes may prove to be more suitable for the intended encapsulation purposes. The comparison has been focused in particular on the commonly-used hexamethyldisiloxane (HMDSO) monomer, whose similar molecular structure differs only in an oxygen atom in lieu of an amino group. As part of the aforementioned optimization process of the oxygen barriers, moreover, a simultaneous and thorough investigation of the presence of defects, their nature, size and spac- ing in the thin layers, their density and most importantly the effect they have in limiting the bar- rier performances has been rendered necessary. In order to do so, a method for the localization and identification of such defects, that at the same time preserves the integrity of the investigat- ed barriers and allows them to be further tested afterwards, has become necessary. Since most of the currently available defects localization methods are destructive in nature, an entirely new, non-destructive test has been designed and developed. The aim in this case has been to first veri- fy its feasibility, validity and reproducibility, and then later to successfully employ it for the analy- sis of the plasma-deposited barriers in order to further characterize them. Once a set of optimized operating conditions leading to the best possible barriers have been reached, the aim has been to first develop and investigate a multilayer system incorporating sev- eral of the single optimized barriers, in order to further abate the amount of permeated oxygen, and then later to test whether it would be possible to successfully treat and encapsulate sensitive electronic devices in the current reactor set-up without destroying their integrity in the process. 7 The layout and general structure of the current work is better detailed in the following. Fur- thermore, a schematic representation of it, explicitly referencing the chapters in which the single sub-sections of the work have been investigated, is presented below in Figure 1.1. The conventional encapsulation strategies for a variety of stiff and flexible substrates are presented in Chapter 2, together with an overview of plasma-polymerized films that can act as Figure 1.1: Overview of the current work. In round brackets, the chapters and sub-chapters in which the different work packages are respectively presented and discussed. Chapter 1. Introduction and statement of the objectives 8 barrier layers. The theoretical fundamentals of the permeation processes in a solid are thorough- ly presented in Chapter 4. The plasma fundamentals, together with the operating principles on which the plasma reactor employed in the current work is based, are shown in Chapter 3. An overview of the chemo-physical processes taking place inside a plasma, with a focus in particular on the plasma-enhanced deposition processes from a gaseous phase, is also included. The exper- imental setup for the plasma reactor and the operating conditions, the employed substrates and the monomers acting as precursors for the deposited films are detailed in Chapter 5. Chapter 6 deals with the diagnostic methods employed for the investigations on the properties of the thin barriers. The chapter also includes a thorough discussion regarding the method, developed in the current work, for the identification of defects in the film, including a short overview on the state of the art, the fundamentals and the assumptions on which the test relies on, and an evaluation on its validity and effectiveness. Chapter 7 extensively presents and discusses the results regarding single layer barriers, including the optimization of several operating parameters related to their deposition process and the characterization of their properties, particularly those connected to their performances as barriers against oxygen. Chapter 8 on the other hand focusses on multilayer systems, their properties, and their application as barriers on OLED prototypes. The changes in the experi- mental setup and in the reactor preparatory to the handling of such devices are also here includ- ed. A summary of the current work and a brief outlook are finally offered in Chapter 9. Chapter 2 State of the art of oxygen barrier layers Some degree of protection against external gases, mostly oxygen and water vapor, is prefer- able, and sometimes required, for countless commercially available goods and products. Sensitive food products may extend their shelf life when sealed with appropriate barrier packaging. Liquid crystals displays and light emitting devices, if left unprotected against at- mosphere, would quickly cease to function. The organic counterparts of the latter possess even stricter requirements, in order for them to be commercially viable [1-4]. Some of the lower limits in oxygen transmission rates required for a small collection of products are of- fered in Figure 2.1. Other times, not a complete barrier, but rather a partial one that can act as a release regulator, becomes necessary: such is the case for example for drugs and medicaments, or for organs-on-a-chip which must remain at least partially permeable and allow the human cells inside them the necessary amount of oxygen. In all such cases, a solid barrier must be applied on the product of interest or on its casing. Inorganic coatings acting as such, for example, have been commercially employed since the 1960s for the reduction of the permeation rates of polymer foils [5,6]. The physical and mechanical properties of such barriers will then determine the amount of gas per square meter per day allowed to perme- ate through them. In order to be commercially suitable, moreover, the production of such barriers must be quick, and inexpensive, i.e. the barriers must be as thin as possible and be deposited preferably on large areas in quick steps [7]. Last but not least, a progressive switch from glass and metal oxides packaging to lighter, cheaper and more functional systems con- sisting of a combination of polymer plus a barrier is also becoming increasingly supported by the current European legislation [8]. A further advantage of such almost completely organic systems, moreover, is their inherent recyclability. In the following sections, a more in-depth overview on organic light emitting devices (Section 2.1) and their conventional encapsulation methods is presented. In Section 2.2, a Chapter 2. State of the art of oxygen barrier layers 10 brief overview on barrier systems based on plasma-polymerized thin films will be given. 2.1 Organic light emitting devices and their encapsulation Organic Light Emitting Devices (OLEDs), as the name suggests, are optoelectronic light sources in which the injection of charge carriers (electrons and electron holes) at a material junction and their later recombination produce the emission of photons in the visible range (electrolumines- cence). Contrary to conventional LEDs, based on appropriately doped semiconductors, the active layer in OLEDs is organic and polymeric, often constituted by long -conjugated hydrocarbon chains acting as chromophore, or by saturated chains with isolated lateral groups containing irid- ium or other rare earths complexes [10] which are responsible for the emission of light. The de- vice is completed by means of a pair of electrodes, one of them transparent in order to ensure the transmission of the produced photons, and several intermediate layers that help maximize the charge transport and injection efficiency. Contrary to inorganic LED, they are much cheaper to produce, ensure very high efficiencies and operate at considerably lower voltages, down to few mV [11]. Since the first operative prototypes, emitting in the green spectrum range, were reported in 1987 [11, 12], OLEDs for general illumination purposes became available on the market only in 2009, distributed by Philips and Osram [13]. Nowadays, Active Matrix OLEDs (AMOLEDs) are widely employed in large scale and high resolution displays, for TVs and smartphones, among many other applications [14, 15]. Figure 2.1: Oxygen transmission rates required for commercially available products. Data taken from [9]. 11 2.1 Organic light emitting devices and their encapsulation Organic LEDs principally require protection against oxygen and water vapor, too. In both cases, in fact, oxygen atoms quickly react with the unsaturated sites or other high-energy bonds in the active matrix, destroying the conjugation that causes the electroluminescence or other- wise compromising the emitting layer’s integrity and conductivity. The otherwise unprotected devices can operate in air for few hours at best, before catastrophic failures. By contrast, in order to be suitable for commercialization and large-scale use, a light device should possess a guaran- teed lifetime of at least 10000 hours [16, 17]. If the device is built onto some rigid substrate that also possesses suitable barrier properties against such gases, as for example glass, then only a top encapsulation is required. Vice versa, a back encapsulation becomes mandatory, too. The top encapsulation is usually carried out in inert atmosphere, like nitrogen or argon, by means of a glass or metallic lid [18]. The lid is glued to the substrate by means of beads of epoxy resin, to be later hardened in an UV-curing step – keeping in mind that UV can promptly destroy the aforementioned emitting layer –. As the resin vapors thus developed are also extremely detrimental to the OLEDs functioning, a sufficient amount of Figure 2.2: Schematic sections of OLEDs encapsulation strategies: (a) on glass substrate, (b) on polymeric substrate with a top polymeric lid, and (c) on polymeric substrate with an upper thin barrier layer. Picture from [5]. Chapter 2. State of the art of oxygen barrier layers 12 a getter substance, usually elemental calcium and barium to be later oxidized to CaO and BaO [18, 5], must also be deposited beneath the lid. Such additional layers are usually fractions of mil- limeters thick [5] and tend to swell upon contact with water vapor, thus stressing the device and accelerating its eventual degradation. The encapsulation process must be carried out at low temperatures, care must be taken so that no solvent comes in direct contact with the emitting layer or cathode of the device, and finally the resin sealing requires substrates much larger than the actual dimensions of the to-be-encapsulated OLED [19, 5]. The lid must however still allow stable electric contacts to be established with the device within. The resulting structure is always several times, or even a few orders of magnitude, thicker than the proper OLED alone, as shown schematically in Figure 2.2a and 2.2b. Such end product, moreover, is extremely stiff and both the lid and the now-hardened epoxy resin are brittle and prone to fail in case of applied mechani- cal stresses. Therefore, the approach is not suitable for Flexible OLEDs (FOLEDs), which can be produced on polymer substrates [20-23]. A similarly polymeric lid provides flexibility and resili- ence, but the brittle epoxy resin is still required in order to successfully glue together the two halves. Thin barriers laying in intimate contact with the OLED, on the other hand, can reduce the overall thickness by a factor of two and ensure mechanical robustness, good adhesion and stabil- ity [5]. They would also render superfluous both the resin and the getter, and are therefore par- ticularly suitable also for large scale production of flexible, cheap OLEDs with short-lived applica- tions. Their thinness compared to traditional methods is exemplified in Figure 2.2c. 2.2 Plasma-polymerized barrier layers A wide variety of materials obtained by means of Plasma Enhanced Chemical Vapor Deposition (PECVD) processes has shown good barrier properties against oxygen: a short, partial list include aluminum and thallium oxides and silicon nitrides and oxides [18]. The silicon-based films in par- ticular also possess good dielectric properties [7], which render them microwaveable and particu- larly suited for the food packaging industry [24], also thanks to their atoxicity. This, together with a more retortability, flexibility and recyclability [25], and in the case of SiOx transparency and col- orlessness [26], render them perfect candidates for the encapsulation of light emitting devices, among others. Their deposition process, on the other hand, is operationally easy, tunable, cost effective [24], up-scalable [27] and can be carried out at very low temperatures [25], without be- ing limited by the size and shape of the substrates [24]. It also often shows better results when compared to other deposition techniques such as sputtering, thermal evaporation or chemical vapor deposition [18, 28, 29]. For a more detailed overview of the polymerization processes tak- ing place in the plasma phase and how they differ from more conventional chemical reactions, see also Chapter 4.3 and 4.4. 13 2.1 Plasma-polymerized barrier layers Single SiOx thin layers deposited by means of radiofrequency and microwave plasmas alike have shown to possess good barrier properties [25, 30-35], with normalized values down to 10-1 cm3/m2·day·bar and more, when coupled with adequately poorly permeable substrates [36]. This proves more than enough for food packaging [34], but it is still several orders of magnitude too high to meet the requirements for organic devices [5], as previously shown in Fig. 2.1. Micro- and submicro-scopic defects extending for the whole length of the plasma-polymerized barriers cause their performances to be far from those of their silica counterpart, which is often assumed to be completely impervious to oxygen [7, 37]. Along such defects, the gas can permeate freely or scarcely unhindered [38]. In order to further improve the performances of such barriers, then a multilayer system consisting of alternated inorganic and organic dyads must be employed [4, 9, 19, 30, 39, 40], similar to the Barix© sputtered encapsulation multilayer developed by Vitex Sys- tem [3]. The structure of such systems is illustrated in Figure 2.3. The insertion of a layer with a completely different chemistry between the barriers decouples the defects and prevents them to propagate through the whole structure. The effective, tortuous length that the permeand parti- cles have to travel before reaching the substrate, therefore, becomes much longer than the nom- inal thickness of the multilayer, improving the overall barrier performances [41, 42]. The number of dyads in a system and the average defect densities and transmission rates of the barriers em- bedded in it become then the limiting factors that determine a multilayer’s effectiveness. Thin- ner barriers, when possible, are favored as they retain a higher intrinsic resilience, flexibility and integrity [27, 31], and also result in shorter deposition steps suitable for large-scale applications. Figure 2.3: Schematic structure of a multilayer system on a substrate (left), and representation of the increase in the diffusion length caused by defects decoupling. Based on [18]. Chapter 2. State of the art of oxygen barrier layers 14 Chapter 3 Permeation theory 3.1 Permeation process The permeation is a physico-chemical process in which a liquid or gaseous species, called permeant, moves through a solid medium under the effect of a spatial and temporal concen- tration gradient of the former. For most solids, and for organic polymers in particular, the process can be envisioned after the free volume theory [43, 44]: such theory states that the permeant atoms or molecules can move through the bulk of a solid material thanks to the small free spaces inside it caused by thermal movement of its molecules or polymeric chains. As a consequence, such process is directly dependant on the temperature, as an increase in the mobility of polymers chains induced by the temperature, for example, results in an in- creased density and frequency of free spaces through which the permeant can move. For a quantitative description of the dependence on temperature, also refer to Section 3.4. The overall diffusion process in a homogeneous solid can be split schematically into three steps: i. adsorption of the permeant gas or liquid on the surface of the solid to be per- meated; ii. dissolution of the permeant in the solid and diffusion through it; iii. desorption of the permeant upon reaching the back interface of the solid. The second step is often the rate-determining one in the overall process and is strongly af- fected by the solubility and the diffusivity of the permeant in the solid phase. Such depend- ence is better illustrated through the permeation coefficient P, defined as [45]: where D is the diffusion coefficient and S the solubility of the permeant species. The solubility of the permeant in the permeate depends on their mutual interactions, as Chapter 3. Permeation process 16 for example dipole-dipole and van der Waals forces [45]. Assuming that no chemical reaction takes place between them, that the concentration of the permeant molecules in the perme- ated solid is low and that the former are homogeneously distributed, then the solubility can be rewritten by means of Henry’s law as [46, 47]: where c is the concentration of the permeant in the solid and pg is its partial pressure outside the solid. The diffusion coefficient is a measure of the speed of the permeation process and, ac- cording to the Einstein–Smoluchowski relation, can be expressed as [48-50]: where  is the mobility of the permeant molecules in the solid, kB is the Boltzmann constant and T is the temperature. Knowing that the mobility can be written as: then Eq. 3.3 can be rewritten as: r is the radius of the permeant species and is the viscosity of the permeated solid, which as hinted before is also dependent on the temperature. The diffusion coefficient for a fixed permeant-permeated pair will therefore increase with the temperature (see also Section 3.3). The dependence of the diffusion coefficient on the concentration gradient inside the solid has to be made explicit by means of mathematical models as the one in the following sec- tion. 3.2 Fick’s laws of diffusion The diffusion process can be treated mathematically by means of the Fick’s equations, which describe the spatial and temporal variation of the permeant concentration in the solid. For the most general case the two Fick’s laws can be written as [46]: ⃗ ⃗⃗⃗ 17 3.2 Fick’s laws of diffusion ⃗⃗⃗ ( ⃗⃗⃗ ) j is the diffusion flux and is expressed as [mol m−2 s−1], i.e. the amount of permeant per unit area in unit of time, and ⃗⃗⃗ is the concentration gradient. Here, the diffusion coefficient is a function of the concentration, the spatial coordinates in the solid, and the temperature, or: ⃗ Both Fick’s laws can be reduced to a one-dimensional case, assuming the solid to be isotropic regarding diffusion (more on this in section 3.4), and D to be independent from the concen- tration. Eq. 3.6 and 3.7 become then: ⃗ in order to obtain analytical solutions for both equations, a system of boundary conditions is to be provided. By considering a solid with a thickness d which separates two gaseous phas- es, so that the permeating gas is initially the sole component of the first and is completely absent from the second, as well as from the solid, i.e. there is an initial concentration gradi- ent at the two interfaces of the solid, and considering how for longer times the permeant molecules will diffuse through the solid acting upon such gradient, until they reach the se- cond gaseous phase and they are continuously removed from here, so that their concentra- tion is zero, the following set of boundary conditions can be proposed [44]: { By means of the Fourier method for separating variables it is then possible to obtain a solu- tion for the temporal differential equation, and moreover to calculate, for t , the steady- state concentration value cs for the whole solid thickness: ( ) the concentration inside the solid therefore decreases linearly the further away from the permeant-rich gaseous phase. A representation of such trend is reported in Figure 3.1. By substituting the solution to the second Fickian law in the first one, and by solving the differ- ential equation with x=d, i.e. in correspondence of the second solid-gas interface, it is possi- Chapter 3. Permeation process 18 ble also in this case to obtain a steady-state value for the permeant flow, equal to: The non-steady-state flow can then be expressed as an approximated function of the previ- ous value [51]: √ A typical time value , corresponding to the following conditions: can be introduced, the value of which can be expressed as [43, 46]: so that: Figure 3.1: Concentration profile in the one-dimensional case for a solid with thickness d, with an initial concentration on its first interface (left) equal to co that linearly decreases to zero on its second interface (right). The picture refers to the boundary conditions reported in Eq. 3.11. [52]. 19 3.3 Fickian diffusion through multilayer systems An instrument that allows the record of a permeant flux vs. time permeation curve, as the one displayed in Figure 3.2, will therefore enable the calculation of the diffusion coeffi- cient of the solid film under investigation by means of the aforementioned equation. For fur- ther informations on the experimental setup and how it obeys the boundary conditions em- ployed for the analytical solution of the Fick’s laws, see also Chapter 6.4. 3.3 Fickian diffusion through multilayer systems In case of systems consisting of several solid layers, each one of them still obeying the Ficki- an laws for diffusion of gases (under the assumption that the diffusion coefficient is again independent from the concentration), their overall permeability and, consequently, their dif- fusion coefficient, can be described by the ideal laminate theory (ILT), i.e. a series resistance type equation [30, 38, 54, 55]: ( ∑ ) where PTOT is the total permeability of the system, i refers to the number of layers of which the latter consists, with Pi being their respective permeabilities. , the thickness fraction, is thus defined [38]: Figure 3.2: Permeation curve as a function of time, with js as the steady state permeand flux and  the typical time at which j = 0.616 js. Picture based on [53]. Chapter 3. Permeation process 20 such that: ∑ ∑ By substituting Eq. 3.1 in 3.13, and by then using Eq. 3.2: so that the previous equations for a multilayer can be rewritten in terms of the permeant flux at the steady-state, the physical quantity that can be experimentally measured as seen in Chapter 6.4. It is noteworthy to stress that Eq. 3.18 shows how, in case of layers with severely differ- ent permeabilities, the composite system is overall characterized, or better limited, mainly by the layer with the smallest value of P [55], so that the overall flux could be reduced to: where k is the index referring to the permeation-limiting layer. For a bilayer system, as the majority of cases in the current work, consisting of a poly- meric substrate and a thin barrier on top of it, therefore, the total permeant flux can be writ- ten as: where the subscripts bar and pol refer to the barrier and the polymeric film, respectively. Besides the assumptions made ab initio in order to apply a Fickian approach to the diffu- sion process, in this case a further assumption is made necessary: that the interfaces be- tween the layers in the system are no low-energy conduits to transport [30] (on the subject, see also Section 3.5 and 3.6). In practice, especially in case of plasma-deposited thin films, however, the presence of an interface with unknown thickness, chemical composition and 21 3.4 Dependence of the diffusion coefficient on temperature and activation energy barrier properties induced by the plasma itself [36, 56, 57], which may not necessarily fulfill the assumptions for a Fickian diffusion, introduces errors hard to precisely quantify. Finally, recent work in literature [58, 59] provide an even more simplified relation, by not accounting for the layers thickness when splitting the single contributions, so that: ∑ and for a bilayer: 3.4 Dependence of the diffusion coefficient on temperature and activation energy As already stated in Sections 3.1 and 3.2, diffusion processes modeled after the free volume theory and obeying Fick’s laws are dependent on the temperature, more specifically they are thermally activated, i.e. facilitated by its increase. The permeation through polymeric mate- rials can then be modeled after the solid diffusion model, or Arrhenius model [39, 54], and the dependence of the permeation coefficient on the temperature can be expressed through an Arrhenius-like equation [38, 54, 60] that is found to be valid both for inorganic, silicon- based [61] and organic polymeric materials [62]: [ ] where R is the ideal gas constant, P0 is the maximal permeation coefficient typical of the sol- id, and Ep is the apparent activation energy for the process, being related, also but not only, to the energy necessary to a permeant particle to squeeze through the empty spaces in the lattice / amidst the polymer chains [54]. Such quantity can be also written as [35]: i.e. the thermal activation energy or the variation of Gibbs energy associated with the overall process. For an isothermal process, the latter can be rewritten as: Chapter 3. Permeation process 22 where H is the enthalpic variation for the permeation process, i.e. it includes both the ef- fects of the dissolution of the permeant and its diffusion in the solid [35], and S is the varia- tion of entropy. The latter depends on the disorder in the lattice or more generally in the structure of the permeated solid [63]. By substituting Eq. 3.30 in Eq. 3.28: [ ] [ ] the exponential growth of the permeation process is mediated by the enthalpic contribution alone, while the entropic one can be included in the pre-exponential factor. Knowing that both S and D exhibit in turn an Arrhenius-like dependence on temperature [46, 47, 64], then: [ ] [ ] where S0 and D0 are the typical pre-exponential coefficients, Hs is the enthalpy of solution and Ea the diffusion activation energy. By substituting Eq. 3.1 in Eq. 3.28, then: [ ] [ ] with, comparing Eq. 3.34 with Eq. 3.31: A further simplification may at this point be made: the coefficient of solubility S, on which the solubility depends [65], depends in turn linearly on the temperature, but changes less than 1 % in the 0-100 °C temperature range [54, 66], so that the solubility may therefore be assumed to be constant. The variation in enthalpy for the overall permeation process then coincides with the activation energy of the diffusion process alone, the latter becoming then the rate-limiting step [54, 59]: The activation energy may be experimentally obtained by taking again into account Eq. 3.23, so that in a steady-state condition: [ ] and, turning the previous equation in its logarithmic version: 23 3.5 Limits of the Fickian approach with the last equation bearing the following structure: where the line gradient is equal to the activation energy over the gas constant and the inter- cept still contains an entrophy-related term inside it, as already shown in Eq. 3.31. A fitting procedure of a set of data for the same sample tested at different temperatures will then provide the activation energy of the latter [67]. The fitting procedure will remain valid pro- vided that the investigated temperature range is reasonably small. 3.5 Limits of the Fickian approach As already mentioned in Section 3.2, several assumptions have been made in order to obtain an analytical solution for the two Fickian laws. As a consequence, several limitations apply to solid whose permeation mechanism is to be considered Fickian. Firstly, in order to reduce the differential equation to a one-dimensional case, such solid has been considered isotropic and non-porous, while the diffusion coefficient has been assumed to be independent on the per- meant concentration [55]. The latter condition is valid only for extremely diluted ‘solutions’ (Henry’s law limit), i.e. small amounts of permeant dissolved in the solid bulk [68], and in case of non-condensable gases: this can only be for temperatures above the permeand criti- cal values, which in most cases lie well outside the normally investigated ranges [68]. Moreover, the diffusion coefficient being independent on the concentration bars inter- actions, especially chemical, between the solid and the permeant particles. Such is, for ex- ample, not the case when the latter are water vapor [69], which in polymeric solids results in swelling and poorly understood permeation mechanisms, with memory and hysteresis ef- fects [30, 68]. For polymeric materials, in particular, most of the commonly investigated temperature ranges lie below their glass transition temperature, with the possibility of resulting at best in non-Fickian diffusion and dual-mode sorption [68, 70]. In this case, a second term for the sol- ubility appears, depending on the density of microcavities in the bulk of the polymer in the glassy state, their size and their affinity with the permeant particles that can be housed in them and remain stuck. For a more in-depth analysis of the model, see also [48, 71-73]. Even neglecting the aforementioned deviations, the biggest limitation to the Fickian Chapter 3. Permeation process 24 approach is the intrinsic anisotropy of the solid bulk, both for an organic polymer and an in- organic barrier. The former unavoidably, even in a glassy state, possesses a certain crystallin- ity degree, with the presence of randomly scattered and oriented sub-domains in its bulk. The relative diffusion coefficient can at best be simplified in some sort of ‘average’ value. For a much more thorough overview and description of crystallinity in commercially available polymers employed in the current work, refer to Appendix A1. For inorganic thin films acting as barriers, on the other hand, the Fickian model com- pletely fails to take into account the presence of macro- and micro-scopic defects in their bulk, which cause small volume fractions to present severely different permeation proper- ties. Such defects, moreover, are often strongly oriented, further invalidating the premise of a homogeneous, isotropic solid. The following two paragraphs will deal in great detail about the type and size of defects, the permeation processes through them, their activation energy and dependence on the temperature. 3.6 Permeation through defects in barrier layers Permeation through defects follows usually completely different pathways when com- pared to the passage of a permeant in a defect-free solid bulk. Moreover, such pathways de- pend on the lateral size of the defects selves, particularly when compared to the radius of the permeant particles [54, 74]. A classification of defects based on such mechanisms can be made by introducing the Knudsen number Kn, a dimensionless quantity that can be thus de- fined [75]: with f as the mean free path of a permeant particle in the defect between collisions against the walls, and dp as the diameter of the defect or pore being permeated. For Kn < 1, the amount of particle-walls collisions is negligible when compared to the particle-particle ones: the transport can then take place freely inside the defect, without be- ing hindered by the latter’s lateral size. This regime is called free diffusion and can be as- sumed to be dominant already for diameters of 1 nm [54], while at the same time becoming independent of the permeated solid thickness [70]. The defects fulfilling the condition of such transport mechanism are called, somewhat improperly, ‘macro’-defects, as their size is several times, and often several order of magnitudes, bigger than the permeant particles. In case of thin coatings, this ranges from pinholes still invisible to optical microscopy up to mac- roscopic uncoated areas which leave the underlying substrate exposed, cracks, delamination 25 3.6 Permeation through defects in barrier layers and otherwise damages to the film integrity. A diffusion coefficient pertaining such permea- tion mechanism can be defined as [76]: √ where p is the permeant partial pressure,  its cross section, M its molecular weight, and Csu, the Sutherland constant, is typical for each gas and takes into account the effects of temper- ature on its cross section [55]. In a steady-state condition then, similarly to Fickian diffusion, the flux of permeant through such defects will then be proportional to T2.5/(T+Csu). When the lateral size of the defect becomes comparable or slightly smaller than the free path of the permeant, the particles collisions against the walls are not anymore negligible. In standard conditions, this happens for defects with a diameter in the 0.3 ÷ 1 nm range [54]. In this case, Kn is greater than one and the regime is called Knudsen diffusion [75]. The corre- sponding diffusion coefficient DKn can be written as [77, 78]: √ withp the effective porosity of the medium, i.e. considering only defects/pore extending fully between the two solid interfaces, and p the tortuosity of the defects. In this case the diffusion coefficient loses its dependence upon the pressure but becomes related not only to the dimension of the defects, but also on their tortuosity, since at such nano- and subnano- metrical ranges they cannot be equated anymore to straight channels [78]. The steady-state flow is now linearly dependent on the square root of the temperature. Finally, for Kn ≫ 1, the defects size become equal to the interstices in a crystalline lattice or to the small free volumes in an amorphous solid, and the diffusion coefficient becomes much more strongly dependent on the temperature, as the latter now increases not only the mobility of the permeant by avoiding its condensation in the small volumes, but has also an effect on the volume of the cavities. In this case then the whole model goes back to the solid diffusion model and Fickian diffusion described in Sections 3.1 and 3.2. The three simplified regimes here described are schematically depicted in Figure 3.3. Further possible effects as surface diffusion or capillary condensation [55, 70] have been here overlooked. In a practical case, most if not all of these permeation pathways are to be found in a solid barrier on a substrate: as a consequence, the overall process won’t exh