RUBY THIN FILM PRESS URE SENSORS By Eric M Straley A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Chemical Engineering Master of Science 2018 ABSTRACT RUBY THIN FILM PRESSURE SENSORS By Eric M Straley As the population rises, it is important that society adopts a more environmentally friendly energy landscape. Currently, solid oxide fuel cells (SOFCs) are a promising technolog y due to high ener gy efficiency, power density, and fuel flexibility. However, SOFCs are held back by high costs which are due, in part, to high operating temperatures. It is the principle research goal in the SOFC community to decrease these operating temperatures and curr ent research studies suggest that strain engineering SOFC materials can help. Current studies are hamstrung by the lack of ability to determine stress in - situ thus performance improvements due to strain cannot be isolated. A method to easily measure non - hy drostatic stress is needed to make strain engineered SOFCs a reality. Fluorescent stress sensors have been used to measure non - hydrostatic stress, but the accuracy of these measurements have never been evaluated. The work here uses ruby thin films as non - h ydrostatic, fluorescent stress sensors and uses curvature - determined stress to evaluate the accuracy of these new sensors. Highly oriented ruby thin films were deposited onto single crystal sapphire and yttria - stabilized zirconia (YSZ) substrates using pulsed - laser deposition. The resulting ruby/YSZ samples achieved a fluorescence determined stress of ~ 1.9 GPa while the ruby/sapphire samples achieved ~0. 0 5 GPa. Stress determination from sample curvature measurements confirmed the r esults of the fluorescence stress measurements , indicating that the ruby piezospectroscopic tensor, which had previously been experimentally validated up to 0.9 GPa, is accurate up to nearly 2 GPa. This work concludes that ruby thin films are an effective sensor for measuring biaxial stress; t hus, strain engineer ing a variety of thin film devices is now a possibility . iii ACKNOWLEDGEMENTS This work was financially supported by National Science Foundation (NSF) Award Number CBET - 1254453 There are many people who I would like to thank for their help and support along the way. First, I d like to thank my graduate committee members. To my advis or, Dr. Jason Nicholas, thank you for your guidance and support throughout my time at MSU, I truly appreciate the opportunity that you gave me. To Dr. Tim Hogan, thank you for your guidance and expertise in teaching me pulsed - laser deposition and thin - film growth. Dr. Susannah Dorfman, I am grateful for your expertise in all - things fluorescence spectroscopy related. Finally, thank you to Dr. Yue Qi for your support. I have also received help in my experiments from Karl Dersch and Dr. Per Askeland. Without t hem, none of this would have been possible. I would like to thank my past and present research - group mates: Dr. Ted Burye, Yuxi Ma, Quan Zhou, Yubo Zhang, Brandon Bocklund, and Lindsay Fricano. I truly appreciate all the recommendations and friendly conve rsations along the way. Finally , I would like to thank my friends and family. I am forever grateful to my parents and sister for their unwavering support in these last 4 years. To the wonderful friends that I ve met at MSU: thank you for all the amazing m emories and for keeping me sane during my time in East Lansing. iv TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ............... v LIST OF FIGURES ................................ ................................ ................................ ............ vi KEY TO ABBRE VIATIONS ................................ ................................ ............................ vii CHAPTER 1 MOTIVATION AND OVERVIEW ................................ ........................... 1 1.1 SOLID OXIDE FUEL CELLS ................................ ................................ ................... 1 1.2 STRAIN ENGINEERING ................................ ................................ .......................... 2 1.3 STRESS MEASUREMENT ................................ ................................ ....................... 3 1.4 HY POTHESIS AND AIM OF THIS WORK ................................ ............................ 4 CHAPTER 2 LITERATURE REVIEW ................................ ................................ .......... 5 2.1 FILM/SUBSTRATE STRESS FROM CURVATURE ................................ .............. 5 2.2 FLUORESCENT PRESSURE SENSORS ................................ ................................ . 7 CHAPTER 3 EXPERIMENTAL TECHNIQUES ................................ .......................... 13 3.1 SAMPLE PREPARATION AND CHARACTERIZATION ................................ .... 13 3.2 STRESS DETERMINATION FROM FLUORESCENCE ................................ ...... 16 3.3 STRESS DETERMINATION FROM CURVATURE ................................ ............. 18 CHAPTER 4 - EVALUATION OF RUBY THIN FILM PRESSURE SENSORS ............. 20 4.1 INTRODUCTION ................................ ................................ ................................ .... 20 4.2 EXPERIMENTAL METHODS ................................ ................................ ................ 20 4.3 RESULTS AND DISCUSSION ................................ ................................ ................ 23 4. 4 CONCLUSIONS ................................ ................................ ................................ ....... 35 CHAPTER 5 - CONCLUSIONS ................................ ................................ ......................... 36 APPENDIX ................................ ................................ ................................ ........................ 37 BIBLIOGRAPHY ................................ ................................ ................................ .............. 41 v LIST OF TABLES Table 1: Summary table of pressure sensor metrics for materials considered for this work, adapted from Raju et al [38] ................................ ................................ ................................ 9 Table 2: Piezospectroscopic coefficients of ruby fluorescence peaks [32] ............................ 11 Table 3: Separate PLD conditions for the 5 ruby thin film samples [82] ........................... 21 Table 4: Average and standard deviation of contour plots. Positive stress is compressive. Error bars are standard deviation of the stress contour plot or the manufacturer reported er ror the spectrometer used in this work, whichever number was greater. ........................ 30 Table 5: Average curvature values for all samples. Error is standard deviation of the curvature measurements ................................ ................................ ................................ .... 32 Table 6: Curvature - determined stress values (MPa) for all samples. Error is from propagation of uncertainty in film thickness and curvature measurements ....................... 33 vi LIST OF FIGURES Figure 1: Solid oxide fuel cell schematic ................................ ................................ .............. 1 Figure 2: Diagrams of the five d - electron orbitals [36] ................................ ......................... 8 Figure 3: Labeled image of PLD chamber ................................ ................................ .......... 14 Figure 4: Labeled image of automated fluorescence test rig ................................ .............. 16 Figure 5: Schematic of multi - beam optical stress sensor. Adapted from [23]. ................... 19 Figure 6: XRD data for ruby on a) sapphire substrate samples, and b) YSZ substrate samples. A= - Al 2 O 3 . Y =YSZ peak. AS=Sillimanite (Al 2 SiO 5 ) Peaks indexed for - Al 2 O 3 , YSZ, and Sillimanite using JCPDS card numbers 74 - 582, 70 - 4436, and 70 - 7052, respectively. Asterisks in 6a denote impurity phases present in the bare wafer [82] .............................. 24 Figure 7: Representative backscatter SEM image of ruby on YSZ [82] ............................. 25 Figure 8: Sample film thickness distributions, from SEM analysis [82] ............................. 26 Figure 9: SEM cross - sections of a) RY2 and b) RY3 film thickness abnormalities ........... 27 Figure 10: ToF - SIMS depth profile of Cr through sample RS1 [82] ................................ .. 28 Figure 11: R 1 Stress contour plots for a) RS1, b) RS2, c) RY1, d) RY2, and e) RY3. All stress values are in MPa. Compressive stress is positive ................................ ................... 29 Figure 12: Representative profilometry of bare wafers and film/substrate samples for a) ruby/sapphire and b) ruby/YSZ samples ................................ ................................ .......... 31 Figure 13: Comparison plot of a) R1 fluorescence - determined stress with MOSS - determined stress b) R1 fluorescence stress with profilometry determined stress c) R2 fluorescence - determined stress with MOSS stress and d) R2 fluorescence - determined stress with profilometry stress. The dashed 45 - degree line is added to aid the eye [82] ...................... 34 vii KEY TO ABBREVIATIONS CCD Charge - coupled device CTE Coefficient of thermal expansion DAC Diamond anvil cell MOSS Multi - beam optical stress sensor PLD Pulsed laser deposition RS Ruby on sapphire sample (usually followed by a number to identify the sample) RY Ruby on YSZ sample (usually followed by a number to identify the sample) SEM Scanning electron microscope SFP Stress free position, referring to ruby fluorescence peak position Sm:YAG Samarium doped yttria aluminum garnet SOFC ( s ) Solid oxide fuel cell ( s ) ToF - SIMS Time of flight secondary ion mass spectrometry XRD X - ray diffraction YSZ Yttria - stabilized zirconia 1 CHAPTER 1 MOTIVATION AND OVERVIEW 1.1 SOLID OXIDE FUEL CELLS As the world s population continues to rise, reducing dependence on fossil fuels is critical to preventing further environmental damage. Solid oxide fuel cells (SOFCs) are an enticing technology as they can achieve efficiencies in excess of 85% in combined heat and pow er applications [ 1 ] . SOFCs also offer the highest volumetric power density and the second highest gravimetric power density, second only to large scale gas turbines, of any energy generation technology [ 2 ] . As such, SOFCs are a good technology to help improve efficiency of processes that consume fossil - fuels. SOFCs running on a variety of fuels have also been demonstrated [ 3 ] which suggests that SOFCs could remain an import energy generation technology in the future as natural gas and biofuels become more prevalent. A solid oxide fuel cell is composed of three components: a cathode, an electrolyte, and an anode. A schematic of an SOFC can be seen in Figure 1, below. Hydrocarbon fuel is continuously fed to the anode side of the cell where the fuel is oxidize d, pull ing oxygen from the lattice of the anode. This reaction forms an oxygen vacancy, V O ** , water, and electrons which flow through an external circuit. The oxygen vacancy migrates through the e lectrolyte into the cathode where it is consumed at the surface of the cathode and replaced by an oxygen ion. In Kroger - Vink notation these half - reactions look like: Figure 1 : Solid oxide fuel cell schematic 2 Anode: (1) Cathode: (2) These surface reactions and the diffusion of charged species through a solid electrolyte require high temperatures to operate efficiently which contributes to industrial SOFCs having operating temperatures of 700 - 1000 o C [ 1 ] . Such high operating temperatures necessitate the use of durable , expensive materials and reduce SOFC operating lifetimes. Therefore, the focus of much SOFC research is in reducing the operating temperatures in the hope of reducing cost and improving lifetime, thus gaining more industrial traction for SOFCs. 1.2 STRAIN ENGINEERING Applying strain to functional materials has been shown to improve performance in catalysts [ 4 - 8 ] and semiconductors [ 9 , 10 ] . Similar experiments have been performed on SOFC materials and suggest that applying strain can improve the speed of both oxygen transport through the electrolyte [ 11 - 15 ] and surface exchange at the cathode surface [ 16 - 21 ] resulting in 100 o C operating temperature re ductions . Such a decrease is a huge step in the right direction, but the method these studies use to apply strain renders the results inconclusive. These studies deposit thin films on different substrate materials to induce various levels of lattice - mismat ch strain s on the films. This technique has several drawbacks: 1) depositing on different substrates can affect the film stress and/or structure which can have an impact on performance [ 22 ] , thus the reported performance improvements may not only be due to strain, 2) many of these studies perform no in - situ measurement of stress on performance so the reported strains due to lattice mismatch may not accurately depict the stress that the film experiences, and 3) all of these studies are done on epitaxial thin films while real world SOFCs use polycrystalline el ectrodes; thus the strain effects on real SOFC materials cannot be examined using this technique. For these reasons, a new method of measuring 3 stress in - situ is needed so that stress and performance of SOFC materials can be properly studied. 1.3 STRESS M EASUREMENT Measuring the stress of a thin film can be easily accomplished by measuring sample curvature, a simple experiment that can be done in - situ [ 23 - 25 ] , and using Stoney s Equation [ 26 ] to calculate film st ress. However, determining stress in this fashion can only be done on circular samples with a thin film deposited on a thick substrate which drastically limits the applicability of such experiments in the real - world where films are not always thin and abnormal geometries are commonly observed . Stress measurement using fluorescent stress - sensors is an alternative method to measuring stress that has been commonly employed in the mineral physics and geology communities since the first calibration of rub y fluorescence peak shift in 1978 [ 27 ] . Since then, different materials like diamond [ 28 ] , Samarium doped yttria - aluminum garnet (Sm:YAG) [ 29 ] , and doped tetraborate [ 30 , 31 ] have all been calibrated as fluorescent pressure sensors. Each of these materials uses the same fundamental principle to measure stress : As stress is applied, the fluorescence peak position(s) of the material changes in a reproducible way. Once the change in peak position with stress is calibrated, fluorescence spectroscopy can be used to measure the peak position, and therefore stress, during experiments. Thes e fluorescence sensors are typically utilized in diamond anvil cells (DACs) under hydrostatic stress. For nonhydrostatic stresses, the usual peak shift - stress calibrations are not valid and the piezospectroscopic tensor of the stress sensing material must be used . For ruby, the piezospectroscopic tensor has been evaluated up to 0.9 GPa [ 32 ] which allows stresses applied in non - hydrostatic environments to be determined from fluorescen ce peak shift. However, the accuracy of stress measurements from this piezospectroscopic tensor 4 have not been evaluated so there remains a knowledge gap in measuring non - hydrostatic stress using fluorescen t stress sensors. 1.4 HYPOTHESIS AND AIM OF THIS WORK To improve SOFC performance through strain engineering, there is dire need for a way to measure non - hydrostatic film stress in - situ without relying on curvature measurements which are limited by the system geometry. Using ruby thin films as a fluores cent pressure sensor offers a promising option for measuring non - hydrostatic stress, but the accuracy of such measurements needs to be confirmed at stresses higher than 0.9 GPa in order to enable strain engineering experiments at higher stresses . The hypot hesis of this work is : D eposit ing ruby thin films onto thick substrates will allow wafer curvature determined stress measurements to confirm biaxial fluorescence stress measurements; thus, validating the ruby piezospectroscopic tensor to higher stress and enabling ruby thin films to be used as a novel in - situ stress sensor. Of the following chapters, Chapter 2 will outline the relevant literature of stress measurements from curvature and fluorescence, Chapter 3 will explain in detail the experimental techn iques used in this work, Chapter 4 will use fluorescence and curvature measurements to study the stress of ruby thin films, and Chapter 5 will summarize the conclusions and future possibilities of this work. 5 CHAPTER 2 LITERATURE REVIEW 2.1 FILM/SUBSTRATE STRESS FROM CURVATURE 2.1.1 Stoney s Equation For a thin film deposited on to a thick circular substrate, the famous Stoney Equation can be used to determine the average film stress [ 26 ] . The equation is as follows: ( 3 ) f is the average film stress (GPa), h s is the substrate thickness (m), M s is the substrate biaxial modulus (GPa), is sample curvature (m - 1 ), and h f is the film thickness (m). Stoney s equation assumes that both film and substrate exhibit linear - elastic deformation, stress in the sample plane is biaxial (i.e. stress in both x and y directions are equal ) and the stress out - of - plane (denoted as z) is 0, and sample curvature is uniform. In circumstances where these assumptions are met, film stress can be easily calculated from film thickness, curvature, substrate thickness, and known substrate material prop erties. For discussions on film thickness and curvature measurements, see Chapters 3.1.2 and 3.2, respectively. 2.1.2 Single Crystal Material Properties As noted above in equation 3 , the substrate biaxial modulus must be known in order to determine film stress. In general, b iaxial modulus is calculated as: ( 4 ) E is the Young s Modulus (GPa) and is the Poisson s ratio. For single crystals E and , and therefore M, are dependent upon the direction which the stress is applied relative to the crystal orientation. This is shown in the generic form of Hooke s law: ( 5 ) 6 ij is the stress acting in the j direction on the plane with normal direction i, is the strain in the j direction acting on the plane with normal direction i, and C ik is the elastic constant matrix. For a cubic material, like yttria - stabilized zirconi a, the elastic constant matrix is: For a trigonal material, like Al 2 O 3 , the matrix is: In a cubic material, Young s modulus and Poisson s ratio can be determined as a function of direction using the following equations [ 33 ] : ( 6 ) ( 7 ) S ij is a compliance value (the compliance matrix is calculated as the inverse of the elastic constant matrix: [S ij ]=[C ij - 1 ]), E hkl is the Young s modulus in the hkl direction (indicated by the plane of the single - crystal substrate), and , , and are angles between the direction of the stress and the principle directions, x, y, and z. For a trigonal material, calculating Young s modulus and Poisson s ratio is slightly more complicated [ 33 , 34 ] . The quantities are calculated as: ( 8 ) ( 9 ) 7 In this case, S 11 and S 1 2 are calculated as: ( 10 ) ( 11 ) The values of S are again compliances and a ij is a directional cosine, calculated as: , , and have their previously defined meanings. Combining the definition of the directional cosine above with equati ons 10 and 11 , then plugging into equations 8 and 9 will give the biaxial modulus of a trigonal crystal. 2.2 FLUORESCENT PRESSURE SENSORS As the name implies, the operating principle of fluorescent pressure sensors relies upon the phenomenon of fluorescence. Excitation, in this case caused by an incoming laser pulse, promotes electrons into higher energy shells. When the laser is turned off, the electrons collapse back into lower energy shells which causes the emissi on of a photon. Different materials have different characteristic wavelengths at which the fluorescent light is emitted , which is caused by crystal field splitting of d or f electron orbitals. For d electrons there are 5 possible electron orbitals, as show n in Figure 2 [ 35 ] . When a dopant atom exists on an atomic site , like Cr on an Al site in the Al 2 O 3 lattice or Sm on the Y site of YAG, the bond lengths between the central metal atom and surrounding oxygen atoms is distor ted. This distortion creates some higher energy d orbitals (those that have become closer to an O atom due to distortion, and thus have higher electron - electron repulsions) 8 and some with lower energy d orbitals (those that have become further from the neig hboring O atom). As stress is applied bond distances within the material change which results in a change of the energy levels of the electron shells. Thus, as stress is applied the characteristic wavelengths changes. Calibrating the change in wavelength with stress is typ ically done using a diamond anvil cell (DAC). Fluorescence spectra are collected as hydrostatic pressure is applied to the stress sensing material, so the change in characteristic wavelength can be observed. Within the DAC is a standard, typically a simple metal. The specific volume of the standard is measured using X - ray diffraction (XRD) and equations of state are used to determine the pressure from the specific volume. Therefore, the change in characteristic wavelength of the fluorescent sensor is measur ed at the same time as the stress is determined from the standard , effectively calibrating the change in wavelength with stress in the fluorescent material . After calibrating a material, subsequent experiments only need the fluorescent sensor to be placed in the DAC and the stress can then be determined from the characteristic wavelength measured via fluorescence spectroscopy. As alluded to in section 1.3, there are several different fluorescent pressure sensors that have been considered over the years. Ruby was the first fluorescent pressure sensor to be calibrated [ 27 ] , followed by Sm:YAG [ 29 ] , Sm d oped strontium tetraborate [ 31 , 36 ] , Figure 2 : Diagrams of the five d - electron orbitals [36] 9 Alexandrite [ 37 ] and d iamond [ 28 ] . The ideal fluorescence sensor for this work must possess several desired characte ristics: 1) high sensitivity of the characteristic wavelength to pressure changes, so that stresses down to 10 or 100 MPa can be resolved, 2) distinctive fluorescence peaks with high intensity so that peak fits give accurate positions, 3) the fluorescence sensor must be able to be deposited as a thin film, and 4) the sensor must have a known piezospectroscopic tensor in order to measure non - hydrostatic stresses ( since a thin film sensor on a substrate will be subject to biaxial stress ) . A final criterion to be considered , especially for future work , is that the pressure sensor should be able to accurately measure pressure at high temperatures since future strain engineering experiments will need to be conducted at SOFC operating temperatures which can exceed 700 o C. Table 1 : Summary table of pressure sensor metrics for materials considered for this work, adapted from Raju et al [ 38 ] Sample 0 (nm) d /dP (nm/GPa) d /dT*10 - 3 (nm/K) T - Range: Room T to Reference Ruby R 1 694.25 0.348 7.7 [ 38 ] R 1 694.28 0.365 7.3 [ 27 ] , [ 39 ] R 1 694.05 7.0 600 K [ 37 ] R 2 694.7 7.8 600 K [ 38 ] R 2 692.52 7.3 [ 37 ] Sm 2+ :SrB 4 O 7 S 1 685.38 0.281 ~0 823 K [ 38 ] S 1 685.4 0.255 ~0 [ 39 ] Alexandrite A 1 680.47 0.321 8.9 823 K [ 38 ] A 1 680.2 8.7 500 K [ 37 ] A 2 678.55 0.519 8.1 823 K [ 38 ] A 2 678.6 7.8 500 K [ 37 ] Sm 3+ :YAG Y 1 617.9 0.292 0.55 823 K [ 38 ] Y 1 617.75 0.17 823 K [ 40 ] Y 2 616.47 0.249 - 0.05 823 K [ 38 ] Y 2 616.11 - 0.06 823 K [ 40 ] As seen in Table 1, above , doped tetraborate and Sm:YAG show low sensitivity of the characteristic wavelength to pressure, making them unideal for this work since the resolution of these sensors is not good enough to accurately measure stress in the MPa range. However, both materials show little or no change in peak position with temperature, 10 making them possibilities for strain engineering experiments at SOFC operating temperatures. Ruby exhibits good sensitivity and Alexandrite exhibits excellen t sensitivity, especially for the A 2 peak. However, taking a deeper look at the Alexandrite peaks shows that the peaks are not well resolved, even at room temperature , which indicates that Alexandrite cannot be considered as a thin - film fluorescent stress sensor. This leaves ruby as the optimal stress sensor for the work presented here. 2.2.1 Ruby Pressure Sensors The addition of Cr on an octahedrally - coordinated Al site in an Al 2 O 3 lattice structure causes the 5 d orbitals to split into 2 with higher e nergy ( and orbitals) and 3 with lower energy states (d xy , d xz , and d yz , for images of these orbitals see Figure 2) [ 41 ] . This results in two distinct fluorescence peaks: the R 1 peak located at 694.2 nm resulting from an electron relaxing from the shell to the ground state, 4 A 2 , and the R 2 peak located at 693.0 nm resulting from an electron relaxing from the 2 state to the ground state [ 42 , 43 ] . Pressure calibration of the R 1 and R 2 peaks under hydrostatic stress has been conduc ted from 0 - 1 GPa [ 44 ] up to 150 GPa [ 45 ] . T here have also been studies of ruby under non - hydrostatic [ 46 ] or quasi - hydrostatic conditions [ 47 ] where the pressures within the DAC are so high that the conducting medium cannot support hydrostatic stresses. While ruby remains the gold - sta ndard fluorescent stress sensor, there are some drawbacks. At temperatures above 550K, the R 1 and R 2 peaks have merged so significantly that stress measurements are inaccurate [ 48 ] . The work of Ragan et al reports significant error in pressure measurements above 400K [ 49 ] which suggests that ruby may not be an ideal stress sensor under SOFC operating temperatures. Howeve r, for the work here that is investigating thin film stress sensors , ruby offers advantages over the other stress sensing materials, like Sm:YAG, that perform better at high temperatures . These advantages are : 1) studies have shown that the R 2 peak positio n doesn t change with non - hydrostatic stresses 11 [ 46 ] , 2) under stresses normal to the c - axis, the change in R 1 and R 2 peak split is minimal which suggests that the peaks will not merge under non - hydrostatic stress [ 46 ] , 3) high quality fluorescent ruby thin films have already been deposited on sapphire via PLD [ 50 , 51 ] , and 4) the piezospectroscopic tensor of ruby [ 32 ] has been calibrated , so non - hydrostatic stresses , like the biaxial stresses thin films on substrates are subjected to, can be correlated to changes in fluorescent peak positions, something that cannot be said for any other fluorescent stress sensing ma terial. Therefore, while ruby does have stress - sensing limitations at high temperatures it is the optimal stress sensor to measure biaxial stresses in thin films. 2.2. 2 Piezospectroscopic Stress Sensors In general, the change in fluorescence peak frequen cy (the inverse of wavelength) is related to the change in stress by the following expression: (1 2 ) ij has the same definition as in equation 5, is the change in fluorescence peak frequency (cm - 1 ), and is the piezospectroscopic tensor: Here, the 11 direction is parallel to the a - axis of the Al 2 O 3 lattice , the 22 direction is parallel to the m - axis, and the 33 direction is parallel to the c - axis. The values for the piezospectroscopic coefficients ( , , and ) have been calibrated at room temperature from 0 - 0.9 GPa [ 32 ] . The values are shown in Table 2, below . Table 2 : Piezospectroscopic coefficients of ruby fluorescence peaks [ 32 ] Peak R 1 2.56 3.5 0 1.53 R 2 2.65 2.8 0 2.16 12 Equation 1 2 can be simplified by expanding the right - hand side: (1 3 ) The change in frequency is simply the measured frequency of a sample, (cm - 1 ), minus the frequency at some stress - free position (SFP) , (cm - 1 ) : (1 4 ) Applying the fact that frequency is the inverse of wavelength and converting from cm to nm, we can simpl if y this equation further: (1 5 ) indicates the peak wavelength (nm) and all other variables have their previous definitions . Combining Equation 1 5 with the piezospectroscopic coefficients in Table 2 give s separate equations that relate t he peak position s of the R 1 and R 2 peaks with the stress applied in any direction relative to the Al 2 O 3 lattice : (1 6 ) (1 7 ) Here, a subscript R 1 indicates the variable applies to the R 1 peak, a subscript R 2 indicates the variable applies to the R 2 peak, and all other variables have their previous definitions. Equations 1 6 and 1 7 now give R 1 and R 2 positions for stress in any direction. The effectiveness of using these piezospectroscopic stress tensor relationship s has been demonstrated in literature in studies of fluorescent alumina - containing ceramic materials [ 52 - 63 ] and thermal barrier coatings [ 63 - 73 ] . 13 CHAPTER 3 EXPERIMENTAL TECHNIQUES 3 .1 SAMPLE PREPARATION AND CHARACTERIZATION 3 .1.1 Pulsed Laser Deposition Pulsed laser deposition (PLD) is a physical vapor deposition technique used to deposit thin - film s. Short p ulses from a high - powered laser are focused onto a rotating polycrystalline target held in a vacuum environment. The focu sed laser pulses impact the target material, vaporizing it and creating a plume of particles. A substrate is suspended upside down within the plume several centimeters from the target, and particles from the plume are subsequently deposited onto the subst rate [ 74 , 75 ] . T wo separate PLD targets were created from ruby powder with 0.05% Cr. The powder was synthesized by mixing high purity Al 2 O 3 powder (Sumitomo Chemical, Tokyo, Japan) with 99.99% Chromium Nitrate (Alfa Aesar, Haverhill, MD, USA) and water. This mixture was drie d while stirring in a polyethylene beaker. After the powder dried, half the powder was calcined at 1000 o C for 6 hours to calcine it . Both calcined and uncalcined powders were separately ground in a high purity alumina mortar and pestle, filtered through a 45 - micron stainless steel mesh ( to homogenize particle size ) , and pressed into a target using a uniaxial press. One PLD target was created from the calcined powder and another was created from the uncalcined powder. After pressing , both targets were fired at 1400 o C for 24 hours and then 1700 o C for 2 hours [ 50 ] . The density of the calcined target was 72.8% while the uncalcined target was 93.1% dense, both numbers were determined ge ometrically. To produce ruby films under different stress states two substrate materials were chosen. One substrate material is - Al 2 O 3 , hitherto referred to as sapphire, and the other is yttria stabilized zirconia (YSZ). Depositing ruby on sapphire will p roduce thin films with low stress since ruby and sapphire are so chemically similar (the only difference being the nominal 0.05% Cr present in the ruby) that stresses generated from mismatch in lattice parameter and coefficient of thermal expansion (CTE) w ill be minimal. YSZ and ruby have 14 a larger mismatch in lattice parameter and CTE, therefore depositing ruby on YSZ will generate films under higher stresses. O ne - inch diameter single crystal (0001) Al 2 O 3 , (MTI Corporation, Richmond, CA, USA) and single cry stal (100) 9.5% YSZ (Crystec, Berlin, Germany) substrates were used in this work . The YSZ substrates were annealed at 1450 o C for 20 hours while the sapphire substrates were annealed at 1400 o C for 20 hours since sapphire has a slightly lower melting point t han YSZ. Annealed wafers were then placed in the PLD vacuum chamber. During the thin film deposition , the vacuum chamber was injected with high purity oxygen to achieve an oxygen partial pressure, P O2 , of 1.5 - 1.6*10 - 5 bar. A 248nm excimer laser with a rep rate of 10 Hz and laser fluence of 12 - 17 J/cm 2 was used to deposit the films. The target - substrate distance was 2.12 inches and the substrate temperature was approximately 650 o C. The as - deposited films were amorphous, so after deposition the samples were c rystallized in air at 1400 o C for 2 hours. A picture of the PLD setup is seen in Figure 3, below . 3 .1.2 Scanning Electron Microscopy (SEM) In SEM, high energy electrons are focused onto a sample causing secondary electrons and backscattered electrons to be emitted. These emitted electrons are collected by various detectors and used to image the sample. In this work, a Mira3 SEM (Tescan, Brno, Czech Republic) wit h back - scatter and secondary electron detectors was used on cross - sections of thin film/substrate samples to determine the thickness of the thin film s in the ruby on YSZ Figure 3 : Labeled image of PLD chamber 15 samples. Secondary electron imaging was used to investigate topographical features of the cross - sections while backscattered imaging was used to emphasize the contrast between film and substrate , enabling film thickness determination. For the ruby on sapphire samples, there is little contrast difference between the materials since they are so chemically similar, so SEM cannot be used to determine the thickness of these samples. 3.1.3 Time - of - Flight Secondary Ion Mass Spectro metry (ToF - SIMS) ToF - SIMS is a technique where an ion beam is focused on the sample surface causing ions to be emitted. The ions pass through a detector where the chemical identity is determined from the mass of the ions. By using ToF - SIMS while slowly milling through a surface a depth profile can be determined which shows the concentration of an ion as a function of depth through the sample. In this work, ToF - SIMS was used to obtain the depth profile of Cr + ions in the RS samples in order to determine the thickness of the ruby fi lms deposited on the two sapphire substrates. The film thickness was determined from the depth profile by measuring the depth at which the concentration of Cr + ions started to decrease significantly as this drop in concentration would be located at the interface between the ruby film, which nominally has 0.05 weight % of Cr, and the sapphire substrate, which is Cr free. 3 .1. 4 X - Ray Diffraction (XRD) XRD was used to analyze the crystal structure of film/substrate b ilayer samples ; a necessary analysis step since the film orientation must be known to use the piezospectroscopic tensor equation s (Equation s 1 6 and 17 ) to obtain film stress . In XRD, electrons emitted from a tungsten filament hit a metal target (typically Copper) which causes electrons in the target to excite. As the electrons relax back into their ground state, an X - ray is emitted. The X - rays from the target are directed onto the sample. As the X - 16 rays reflect off planes of atoms in the sample, the reflecte d waves constructively and destructively interfere. This brings about the relationship known as Bragg s Law: (1 8 ) Bragg s Law relates the X - ray wavelength, (nm) , to the spacing between planes of atoms, d (nm) , and the angle between the in cident X - ray and the X - rays reflected off the sample , (degrees ), [ 76 ] . In the work presented, a D2 Phaser (Bruker, Billerica, MA, USA) was used to investigate film orientation by scanning from 20 - 80 o 2 at 0.02 o intervals. 3 .2 STRESS DETERMINATION FROM FLUORESCENCE An Optiprexx PLS (Almax eas y Lab Inc, Cambridge, MA, USA) table - top spectrometer was used to collect fluorescence spectra across the surface of the film/substrate samples. A custom test rig, seen in Figure 4 , was designed and built so that the sample was automatically moved to specified positions and the spectrometer was triggered to collect a spectrum at each position. This test rig was composed of two motorized 2 - inch linear translation stages (Thorlabs, Newton, NJ, USA) to automatically adjust where the fluorescence laser hit the sampl e, a single 1/2 - inch manual translation stage (Thorlabs, Newton, NJ, USA) to make sure the laser was focused on the sample, custom spacers to ensure the sample was at the proper height and that the whole rig was screwed into the Figure 4 : Labeled image of automated fluorescence test rig 17 spectrometer baseplate, a r otation stage (not shown in Figure 4 ) to keep the entire sample perpendicular to the laser, and a right - angle piece to hold one automated stage at 90 o so the sample was held perpendicular to the laser . A custom - made LabView program was used to control the sample movement and fluorescence spectra collection parameters and to record the coordinates where each spectrum was collected . Fluorescence spectra peak positions for R 1 and R 2 were determined using Origin Pro 8.1 (OriginLab Corporation, Northampton, MA, USA). A batch processing template was created in Origin Pro that was used to analyze many spectra at once. The template utilized the following steps: 1. Spectral data in a single spectrum from 690 - 700 nm (an appropriate range to include both R 1 and R 2 peaks without including the excess noise present from 680 - 690nm and 700 - 775nm) were imported. 2. Each spectr um was fit to a Voigt peak shape (a combination of Gaussian and Lorentzian peaks) using no baseline treatment, identifying two peaks by analyzing 5 local poi nts, 500 max iterations, a nd a tolerance of 1E - 15. 3. A summary of key statistics for each spectrum was output to a spreadsheet. The statistics were the R 1 and R 2 peak positions (nm), error on the peak positions (nm), peak heights (counts), and R 2 value of t he peak fit. Once all the spectra for a sample were analyzed in Origin, crystallographic data from XRD was used with the piezospectroscopic tensor (see Equation s 1 6 and 1 7 , for full details see Chapter 4.2.3 ) to determine the film stress at each position across the sample surface. Finally, MATLAB was used to plot contour plots of stress vs. horizontal and vertical position for all points with a peak fit R 2 of 0. 85 or greater. Th is cutoff R 2 was chosen to maxi mize the number of data points across the sample surface while removing points with l ower R 2 values , which indicate poor fits and would result in anomalous stress values. 18 3 . 3 STRESS DETERMINATION FROM CURVATURE One of the primary aims of this work is to calibrate the piezospectroscopic coefficients of ruby to pressures higher than 0.9 GPa , so a second method for measuring stress is needed to confirm the fluorescence - determined stress values and thus the piezospectroscopic coefficie nts . Curvature - determined stress is the second method which will be used validate the accuracy of ruby thin - film stress measurements. As indicated in section 2.1.1 and 2.1.2 , curvature and biaxial modulus must be known in order to determine stress using St oney s equation. To determine biaxial modulus of YSZ, literature values for the elastic constants as a function of temperature of YSZ [ 77 ] were converted to compliances and plugged into equations 6 and 7 before calculating biaxial modulus from equation 4. The result was an equation for single crystal biaxial modulus, in GPa, for (100) YSZ: (1 9 ) T is the temperatu re ( O C). Similarly, the compliances for Al 2 O 3 [ 78 ] were plugged into Equations 10 and 11, then 8 and 9 before calculating the biaxial modulus: ( 20 ) The following subsections outline two separate experimental techniques that were used to measure sample curvature . 3 . 3 .1 Multi - beam Optical Stress Sensor One way to measure sample curvature is by using a multi - beam optical stress sensor (MOSS). MOSS has been used in literature many times to determine film stress of a thin film on a thick circular substrate [ 23 - 25 , 79 - 81 ] . In this technique, a 3x3 grid of laser do ts is deflected off the sample and back into a CCD camera where the spacing between dots in the laser array is measured. A simple geometric relationship between the angle of reflection, , the sample - detector distance, L (m), the original inter - dot spacing , d 0 , and the inter - dot spacing after the grid reflects off the sample, d , gives the curvature, (m): 19 ( 21 ) . A schematic of the MOSS setup can be seen in Figure 5 . 3 . 3 .2 Profilometry Along with MOSS measurements, profilometry was used to measure curvature. Profilometry is a technique where th e displacement (aka height) of a sample is measured across the sample surface. In this work, a NanoMap - 500LS stylus contact surface profilometer (AEP Technology, Santa Clara, CA, USA) was used. In stylus profilometers, a needle , known as a stylus, is dragg ed across the sample surface while a constant force is applied . As the sample height changes due to the displacement of the sample, the profilometer determines the height from Hooke s Law . Displacement profiles across the sample surface were taken in two perpendicular directions. Each profile was fit with a second order polynomial using least - squares regression, and curvature was determined by taking the second derivative of displacement. Figure 5 : Schematic of multi - beam optical stress sensor. Adapted from [2 3 ]. 20 CHAPTER 4 - EVALUATION OF RUBY THIN FILM PRESSURE SENSORS 4.1 INTRODUCTION As outlined in Chapter 1, there is a need for a non - hydrostatic fluorescence stress sensor in order to use strain engineering to improve SOFC performance . In this chapter, ruby thin films will be investigated to fill that need . Thin film data of ruby deposited on sapphire and YSZ substrates is presented . Fluorescence - determined stress will be compared to curvature - determined stress values to see how accurate ly ruby thin films can measure stress at two different stress states (a lower stres s state with the ruby/sapphire samples and a higher stress state with ruby/YSZ samples). Sample manufacturing, characterization, and stress analysis are discussed in detail. The piezospectroscopic stress sensor of ruby has been evaluated from 0 - 0.9 GPa w hich has enabled non - hydrostatic stress measurement using the fluorescence techniques that have long been used in geology and mineral physics [ 32 ] . This has allowed non - hydrostatic stress to be determined in ceramic materials as explained in section 2.2.2. However, all these studies investigate stress in ceramic materials which are fluor escent, and none of the studies confirm the accuracy of determining non - hydrostatic stress using the piezospectroscopic tensor relationship. By comparing the fluorescence - determined stress of ruby thin films to the curvature - determined stress from Stoney s equation, the accuracy of determining stress from the piezospectroscopic tensor will be evaluated for the first time and the piezospectroscopic coefficients will be calibrated beyond 0.9 GPa . 4.2 EXPERIMENTAL METHODS 4.2.1 Ruby thin film sample preparation Ruby thin films were produced using PLD using the procedure in Chapter 3.1.1. Two samples, denoted RS1 and RS2, were deposited onto sapphire while three samples, denoted RY1 , RY2, and RY3, were deposited onto YSZ substrates. The PLD parameters that 21 differed between samples are shown in Table 3 [ 82 ] , below. A ll other parameters are listed in Chapter 3.1.1 . After deposition the ruby films were heated to 1400 o C for 2 hours to produce crystalline films. Table 3 : Separate PLD conditions for the 5 ruby thin film samp les [ 82 ] Sample PLD Target Laser Fluence (J/m 2 ) PLD Duration (min) P O2 (bar) RS1 Calcined 17.0 30 1.49 *10 - 5 RS2 Uncalcined 12.2 45 1.59 *10 - 5 RY1 Calcined 17.4 30 1.54 *10 - 5 RY2 Calcined 17.0 30 1.55 *10 - 5 RY3 Uncalcined 12.2 45 1.55 *10 - 5 4.2.3 Stress measurements from fluorescence Equations 1 6 and 1 7 show the relationship between stress and R 1 and R 2 peak position. These equations are dependent upon the direction, relative to the crystal structure, that the stress is applied. From th e XRD results shown in Chapter 4.3.1, the ruby films in each of the 5 samples were preferentially oriented in the (001) plane. This plane is parallel to the c - axis in ruby. Since the film is oriented parallel to the c - axis and we have a circular sample, th e film is under a biaxial stress. Biaxial stress signifies that the stress in x and y directions, which are in the plane of the sample, are equal in magnitude while the stress in the z - direction, which is out of the plane of the sample, is 0: ( 2 2 ) ( 2 3 ) Since we have (001) oriented films this means that the out - of - plane direction (the z - direction) is the (001) direction. This is the same direction as the 33 direction denoted in the piezospectroscopic tensor while the 11 and 22 directions are the two perpendicular in - plane directions. Applying this fact to equations 2 2 and 2 3 gives: 22 ( 2 4 ) ( 2 5 ) We can plug equations 2 4 and 2 5 into equations 1 6 and 1 7 , with some algebraic manipulation, to obtain: ( 2 6 ) ( 2 7 ) Rearranging, we can solve for the biaxial stress, , in terms of the peak wavelengths: ( 2 8 ) (2 9 ) Here, R1 is the biaxial stress ( G Pa) determined from R 1 peak shift, R2 is the biaxial stress ( G Pa) determined from R 2 peak shift, and all other variables have t heir previous definitions. Measuring a stress - free ruby grain with a calibrated spectrometer gave the stress - free positions of 694 .335 and 693.912nm which are nearly identical to literature room temperature SFPs [ 32 , 64 ] . The fluorescence spectra collection and analysis procedure outlined in Chapter 3.2 was used along with Equations 2 8 and 2 9 to get the fluorescence - determined stress of the ruby thin films. The error analysis procedure for pr opagating the uncertainty in peak positions through to the average stress values is outlined in the Appendix . 4.2. 3 Stress measurements from curvature Curvature values in two perpendicular directions across each sample were determined from both profilome try and MOSS. These curvature measurements were done on the bare, annealed wafers and then on the samples after crystalli zing the ruby film. The difference in 23 curvature between the film/substrate sample and bare wafer was then used in Stoney s Equation, Eq uation 3, to determine film stress. The e rror analysis procedure for propagating the uncertainty in curvature and film thickness through to the average film stress is outlined in the Appendix . 4.2.4 Microstructural characterization XRD was used to determine orientation and phase - purity of ruby thin films and substrates, as outlined in Chapter 3.1.3. SEM was used to determine film thickness for the RY samples as outlined in Chapter 3.1.2. Images were taken at 5 different locations acr oss the sample surface: at both edges, in the middle of the sample, and in between each edge and the middle. The ruler tool in Adobe Illustrator was used to measure the film thickness at 3 different locations in each image. ToF - SIMS performed by EAG Labs ( East Windsor, NJ, USA) was used to determine the film thickness of the RS1 sample. 4.3 RESULTS AND DISCUSSION 4.3.1 Microstructural characterization Figure 6 [ 82 ] , below, shows the XRD for the five ruby thin film samples and representative sca n s of bare, annealed YSZ and sapphire wafers . In Figure 6a, t he bare sapphire wafer has some impurities at approximately 20, 57, and 64 o which also appear in the crystallized thin films , RS1 and RS2. This impurity is likely from the manufacturing process o f the wafers and since it is present in the bare wafer it will likely have no impact on stress measurements . Sample RS1 shows some apparent silicon contamination as indicated by the sillimanite (Al 2 SiO 5 ) phases shown in Figure 6a. This silicon contaminatio n occurs during the deposition and could be from the chamber, or the calcined PLD target. The same sillimanite contamination is not seen in RS2, however, as that sample shows no other impurit y peaks other than those present in the sapphire wafer. RS1 was d eposited 24 after RS2 so it s possible that silicon contamination within the chamber increased during the 4 months between these depositions, causing Si impurities to only be present in RS1. It s also possible that an impurity formed in the calcined powder during formation or use of the calcined target . The sillimanite phase shown in RY1 and RY2 (which were also deposited with the calcined target) in Figure 6b suggest this is a possibility, but t he RY1 and RY2 were deposited shortly after RS1 which means that Si contamination in the chamber could also be the cause of these impurities. The impact of these impurities on fluorescence results will be discussed in Chapter 4.3.2. Figure 6b shows that the bare YSZ wafer has only the (100) family of YSZ peaks indicating a phase - pure, single crystal wafer. As mentioned above, bot h RY1 and RY2 show Figure 6 : XRD data for ruby on a) sapphire substrate samples, and b) YSZ substrate samples. A= - Al 2 O 3 . Y =YSZ peak. AS=Sillimanite (Al 2 SiO 5 ) Peaks indexed for - Al 2 O 3 , YSZ, and Sillimanite using JCPDS card numbers 74 - 582, 70 - 4436, and 70 - 7052, respectively. Asterisks in 6a denote impurity phases present in the bare wafer [82] 25 a small sillimanite peak at ~26 o , but they also show the - Al 2 O 3 (006) peak indicating that there is a crystalline ruby film present. The RY2 sample also shows a very small (116) alumina peak at ~54 o , which is also visible in RY1. From the ratio of peak heights in the JCPDS reference, it was calculated that the (006) r uby phase makes up more than 95% of the ruby film, by volume. This means that while there is a small amount of a second ruby phase, it is unlikely to significantly affect the stress calculated from Equations 28 and 29 which assume the film is (001) oriented. Figure 7 shows a representative SEM image of a ruby/YSZ sample. With the backscatter detector, it is easy to see the interface between the dark gray ruby fil m and the lighter YSZ substrate. The film shows some waviness at the film surface, though this could be due to the titanium conductive coating that was applied to reduce charging. Some dark shading in the YSZ substrate is visible which is likely from fract uring the sample to expose the cross section. Figure 7 : Representative backscatter SEM image of ruby on YSZ [82] 26 As seen in Figure 8 [ 82 ] , the film thickness for the RY samples is relatively consistent across the surface of each of the samples. The average film thicknesses, in nm, are as follows: 331 + 14 for RY1, 348 + 31 for RY2, and 356 + 38 for RY3. It should be noted that , sta tistically speaking, the average film thickness of all the samples is identical . There are two data points that appear as outliers in Figure 8 : The middle of RY3 , which is noticeably higher than the other measurements in that sample and the measurement at 11 mm in RY2 , which is significantly lower than the other measurements. Figure 9 shows those two SEM cross sections. In Figure 9a there is an anomalous darker layer that is too dark to be part of the film and isn t in the other images for RY2. Again , it is possible that this layer is part of the conducting layer, though the deposited conducting layer should be on the order of a few nanometers thick, not close to 200nm. It is also obvious that the RY2 film is noticeably thinner in this image which may indica te that there are some areas of the sample that weren t coated evenly. This appears to be the case in Figure 9b as well. Again , there is a darker layer on top of the ruby film, but the film itself appears thicker than in the other images for sample RY3 . T hese variations in film thickness have been considered in the Figure 8 : Sample film thickness distributions, from SEM analysis [82] 27 error bars for the curvature stress calculations. For full details on how the error was propagated, see the Appendix. The thickness of the ruby on sapphire samples was measured to be 310.0 nm from the ToF - SIMS depth profile of Cr + ions seen in Figure 10. The Cr + concentration increases abruptly at the start of the profile as su rface contamination is milled away and the ions from the film are measured in the spectrometer , therefore the film itself starts at a depth of approximately 10 nm . The concentration then increases from 0.02 to 0.0326 before decreasing. This suggests that t he concentration of Cr + ions is not constant through the film. Since the sapphire initially has no Cr + ions, diffusion of the ions from the film/substrate interface into the sapphire lattice would be expected to show an exponential decay in concentration. Beginning at a depth of ~310 nm is the expected diffusion profile of the Cr + ions meaning that the film/substrate interface is located at a depth of approximately 320 nm, as indicated by the rightmost black bar in Figure 10. This results in a measured fil m thickness of 310 nm for RS1 and RS2. Figure 9 : SEM cross - sections of a) RY2 and b) RY3 film thickness abnormalities 28 Figure 10 : ToF - SIMS depth profile of Cr through sample RS1 [82] 4.3.2 Fluorescence - determined stress The c ontour plots for all 5 samples , seen in Figure 1 1 [ 82 ] , show that each sample has a consistent stress value across the sample surface , as expected [ 83 ] , except for RY3 which shows some area of lower st ress in the middle of the sample . The RS1 and RS2 samples have similar contour plots with most of the surface appearing to be around 5 0 MPa with only sparse isolated data values of darker blue signifying lower stress values. These are likely due to variati ons , such as a piece of dust or a small film defect on the surface, which manifest in abnormal peak intensity and thus decreasing the quality of the fit. For the RY samples, we see similar contour plots with most stress values around 18 00 MPa. Again , there are some points, especially in RY3, that exhibit some lower stress values. RY3 showed a higher film thickness towards the middle of the sample, as seen in Figures 8 and 9, which would suggest from Stoney s Equation that the film stress would be lower in t he center. Given the high density of low stress values in the center of Figure 1 1 e , t his is further evidence that there are indeed some film thickness variations across RY3 . 29 Figure 11 : R 1 Stress contour plots for a) RS1, b) RS2, c) RY1, d) RY2, and e) RY3. All stress values are in MPa. Compressive stress is positive 30 The average stress values shown in Table 4 demonstrate that the fluorescence - determined stress values in the sapphire sample s agree, as do those of the YSZ samples. The standard deviations for the R 1 stress in the RY samples are less than 10% which is an impressive result. For the R 1 stress in the RS samples, the standard deviations of the stress contour plots were smaller tha n the manufacturer reported error for the spectrometer (which was 100 MPa) . It was expected that the R 2 stress values would have higher error s since the R 2 peak height is lower, thus the signal to noise ratio isn t as good, and the peak fits are less preci se. Still, the R 1 and R 2 stress values overlap when the errors are considered . This indicates that either peak can be used to determine stress, but the R 1 peak gives more accurate stress measurements . Table 4 : Average and standard deviation of contour plots . Positive stress is compressive. Error bars are standard deviation of the stress contour plot or the manufacturer reported error the spectrometer used in this work , whichever number was greater . Sample R 1 Stress (MPa) R 2 Stress (MPa) RS1 58 + 100 263 + 461 RS2 27 + 100 197 + 425 RY1 1899 + 117 2128 + 389 RY2 1878 + 109 2109 + 369 RY3 1710 + 133 1696 + 135 Upon peak fitting, each reported peak center also had a reported uncertainty. The error propagation of the peak position uncertainty gave errors of at most 33 MPa which is insignificant considering t he manufacture reported uncertainty for the Optiprexx PLS spectrometer is 100 MPa (see the Appendix for details on error propagation) . Therefore, the error in peak fitting is less significant than the resolution limit of the spectrometer and the deviation in stress across the sample surface. 31 4.3.3 Curvature - determined stress As seen in Figure 1 2 [ 82 ] , which shows representative profilometry results for each sample, t he ruby on sapphire sample s had much less displacement (and therefore curvature) than the YSZ sample s , which is logical since there is less thermal expansion or lattice mismatch between ruby and sapphire than between ruby and YSZ . All profiles are the expected parabolic shape except for the bare YSZ wafer s which show ed areas of higher displacement at the wafer edges . This is likely a result of the crystal polishing from the substrate manufacturer, but it signifies that not all residual stress was removed during annealing. However, upon deposition and crystallization of the ruby film the YSZ samples had the normal parabolic shape. Figure 12 : Representative profilometry of bare wafers and film/substrate samples for a) ruby/sapphire and b) ruby/YSZ samples 32 Ta ble 5 shows a summary of the curvature change between the bare wafers and the film/substrate samples measured using MOSS and profilometry. As expected, the curvature changes of the sapphire samples are much smaller than the curvature changes of the YSZ sam ples. The MOSS measured curvature changes and profilometry measured curvature changes are within the error bars of each other for all samples. The error bars in each measurement come from the fact that each curvature measurement (on bare wafer and film/sub strate sample) was done in two different directions perpendicular to each other, therefore the reported value is an average and the error is the standard deviation of two measurements . Table 5 : Average curvature values for all samp les. Error is standard deviation of the curvature measurements Sample MOSS Curvature (m - 1 ) Profilometry Curvature (m - 1 ) RS1 0.0138 + 0.0069 0.0128 + 0.0054 RS2 0.0014 + 0.0026 - 0.0013 + 0.0065 RY1 0.2906 + 0.0189 0.2927 + 0.0193 RY2 0.2695 + 0.0173 0.2660 + 0.0197 RY3 0.2771 + 0.0112 0.2725 + 0.0205 Taking the values in Table 5 , the film thicknesses from Figure s 8 and 10 , and the room temperature material properties calculated from Equations 19 and 20 and plugging into Stoney s Equation (Equation 3) gives the curvature - determined stress values in Table 6. The error bars are from propagation of uncertainty in the film thic kness and curvature measurements. The procedure for this error analysis is outlined in the Appendix. Table 6 shows that there is very good agreement between the MOSS - determined stress and the profilometry - determined stress values for all samples. The stres s values of the ruby on YSZ samples are statistically similar as the error bars of the 3 samples overlap. Interestingly, the ruby on sapphire samples have statistically different stress values. This is likely due to 33 the fact that slight differences in cur vature or film thickness have large r effects on stress when the magnitude of the stress is low , as is the case for the ruby/sapphire samples . The error in stress for RS1 and RS2 is also lower since the error is proportional to the magnitude of the stress, as seen in Equation A13 . Also, the film thickness of sample RS2 was not measured by ToF - SIMS but was assumed to be identical to RS1 since the samples had identical deposition conditions. Therefore, a slight difference in film thickness between the RS sampl es could be the cause of the different stress values. Table 6 : Curvature - determined stress values (MPa) for all samples. Error is from propagation of uncertainty in film thickness and curvature measurements Sample MOSS Stress (MPa) Profilometry Stress (MPa) RS1 346 + 141 201 + 87 RS2 72 + 48 - 24 + 117 RY1 1802 + 174 1848 + 143 RY2 1534 + 156 1476 + 170 RY3 1711 + 196 1616 + 213 4.3.4 Comparison of fluorescence and curvature - determined stress The stress values of Table 6 and Table 4 are compared in Figure 1 3 , below [ 82 ] , and the results show good precision for the stress measurements in samples of the same substrate . Since the MOSS and profilometry - determined stress values were statistically similar, Figures 1 3 a and 1 3 b are essentially identical as are Figures 1 3 c and 1 3 d. In this plot, a data point that overlaps the 45 o line would represent perfect agreement between the curvature - determined stress and the fluorescence - determined stress. For R 1 fluorescence - determined stress: Samples RY1 and RY3 show agreement between fluorescence and curvature - determined stresses while RY2 is slightly off , and sample RS2 has perfect agreement while RS1 is slightly off the line. For the R 2 fluores cence - determined stress, all samples perfectly agree except for RY2 which is again slightly off the line. While there are the slight differences 34 in stress measured with the two different methods (which likely stems from the sillimanite phase impurities and /or the small fraction of (116) oriented ruby film), the small spread between samples deposited on the same substrate and the effectiveness with which the stress is measured from 50 - 1900 MPa renders this work a success. It is clear that ruby thin films can be used to measure biaxial stress and the piezospectroscopic coefficients are valid up to 1.9 GPa of compressive stress . Figure 13 : Comparison plot of a) R1 fluorescence - determined stress with MOSS - determined stress b) R1 fluorescence stress with profilometry determined stress c) R2 fluorescence - determined stress with MOSS stress and d) R2 fluorescence - determined stress with profilometry stress. The dashed 45 - degree line is added to aid the eye [82] 35 4.4 CONCLUSIONS Oriented, crystalline r uby thin film s deposited via PLD onto sapphire and YSZ substrates have been used as fluorescent stress sensors for the first time . These thin film sensors show incredibly high spatial resolution as they were used to determine differe nces in stress on areas of 0.01 mm 2 . The accuracy of the piezospectroscopic coefficients of ruby was confirmed by measuring thin film biaxial stress using both fluorescence and wafer curvature measurements. The c urvature - determined stress values confirmed that at stress values up to 1.9 GPa, these novel thin film stress sensors provide accurate fluorescence - determined stress measurements indicating that the piezospectroscopic tensor of ruby is accurate up to 1.9 GPa (more than double the previous calibration) . These novel PLD thin film sensors can now be used to measure film stress in real devices which can help to improve performanc e . 36 CHAPTER 5 - CONCLUSIONS Reducing solid oxide fuel cell (SOFC) operating temperatures is of the utmost importance as it would reduce the cost of the technology . Making SOFCs more widespread is critical since SOFCs offer energy density, energy efficiency, an d fuel flexibility that other energy technologies cannot match. Strain engineering has been proposed to help improve SOFC performance, and thus reduce operating temperatures, but few studies have been able to measure stress and performance in - situ or isola te the effect of stress and strain on performance. A thin - film stress sensor that works under non - hydrostatic stress is sorely needed to make strain engineering experiments possible. The work presented here has demonstrated the use of ruby as a thin film fluorescent stress sensor for biaxial stress. These thin films were deposited onto sapphire and YSZ substrates where the measured fluorescence stresses were approximately 0. 0 5 and 1.9 GPa, respectively. The accuracy of fluorescence stress measurements was confirmed by determining stress from curvature using Stoney s Equation with curvature measured using a multi - beam optical stress sensor and a profilomet er . The curvature stress measurements confirmed that the samples reproducibly and accurately measure st ress, even with multiple phases and impurities present. Therefore, at ~ 2 GPa these novel sensors are robust enough to accurately measure stress and the piezospectroscopic coefficients of ruby have been calibrated to more than double the previous stress cal ibrations. All this work establishes PLD ruby thin films as a novel technology that is ready to be implemented to study non - hydrostatic stress effects on thin film performance in real world devices like SOFCs. 37 APPENDI X 38 Fluorescence - Determined Stress Error Analysis As described in the main article, R 1 and R 2 stress of (001) ruby films on substrate can be determined from fluorescence peak position using the piezospectroscopic equations that simplified down to equations 6 - 8 . Equation 6, the general form of equations 7 and 8 is rewritten below ( A 1) denotes stress (GPa), SFP denotes the wavelength of the stress - free fluorescence peak position (nm), and sample denotes the wavelength of the sample fluorescence peak position (nm). This equation, which can be applied for both R 1 and R 2 peaks, is dependent on a single independent variable, the peak position, therefore only the error propagation of the peak position measurements needs to be considered when determining the error in the stress value. For a single variable equation, calculating the propagated error is done with the fo llowing equation [ 84 ] : ( A 2) Where Z is a function of A, is the mean of A, and is the error of the variable denoted by the subscript. Applying this error propagation to equation 1 above, we get: ( A 3) where is the error in an individual stress measu rement, is the recorded peak position, and is the error in the recorded peak position, which is reported by Origin during the peak fitting process. Of course, this error applies to every point on the sample where a fluorescence spectrum was recorded so those errors must be propagated to determine the error in the average stress that is reported. The average stress is calculated as: ( A 4) 39 This equation is dependent upon n variables, the number of fluorescence spectra. To c alculate the error for a multi - variable function, the following equation is used [ 84 ] : ( A 5) Where Z is a function of A, B, and C and and are the change in Z when A, B, and C, respectively, are varied but the other variables are held constant. These are calculated as: ( A 6) ( A 7) ( A 8) Applying equation 5 to equation 4 gives: ( A 9) Combining equations 4 and 6 gives the error in average stress due to the variance of a single measurement: ( A 10) In the work presented, equation 3 was used to calculate the error in every individual measurement, then equations 9 and 10 were used to determine the error in the average stress value. Curvature - Determined Stress Error Analysis Stoney s equa tion was used to determine stress from curvature measurements: ( A 11) Where is stress (GPa), h is layer thickness (m), is sample curvature (m - 1 ), subscript s indicates a substrate property, a subscript f indicates a film property, and M is Biaxial Modulus (GPa). The substrate thickness is a constant, as is the biaxial modulus for 40 measurements taken at constant temperature, so this equation is dependent upon two variables with error: sample curvature and film thickness. 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