Liquid-Phase Processing of Barium Titanate Thin Films.

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Abstract

HARRIS, DAVID THOMAS. Liquid-Phase Processing of Barium Titanate Thin Films. (Under the direction of Jon-Paul Maria.)

Processing of thin films introduces strict limits on the thermal budget due to substrate stability and thermal expansion mismatch stresses. Barium titanate serves as a model system for the difficulty in producing high quality thin films because of sensitivity to stress, scale, and crystal quality. Thermal budget restriction leads to reduced crystal quality, density, and grain growth, depressing ferroelectric and nonlinear dielectric properties. Processing of barium titanate is typically performed at temperatures hundreds of degrees above compatibility with metalized substrates. In particular integration with silicon and other low thermal expansion substrates is desirable for reductions in costs and wider availability of technologies.

In bulk metal and ceramic systems, sintering behavior has been encouraged by the addition of a liquid forming second phase, improving kinetics and promoting densification and grain growth at lower temperatures. This approach is also widespread in the multilayer ceramic capacitor industry. However only limited exploration of flux processing with refractory thin films has been performed despite offering improved dielectric properties for barium titanate films at lower temperatures.

This dissertation explores physical vapor deposition of barium titanate thin films with addition of liquid forming fluxes. Flux systems studied include BaO-B2O3, Bi2O3-BaB2O4,

BaO-V2O5, CuO-BaO-B2O3, and BaO-B2O3 modified by Al, Si, V, and Li.

Additions of BaO-B2O3 leads to densification and an increase in average grain size from 50

nm to over 300 nm after annealing at 900 ◦C. The ability to tune permittivity of the material improved from 20% to 70%. Development of high quality films enables engineering of ferroelectric phase stability using residual thermal expansion mismatch in polycrystalline films. The observed shifts toTC match thermodynamic calculations, expected strain from the thermal expansion

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Our system exhibits flux-film-substrate interactions that can lead to dramatic changes to the microstructure. This effect is especially pronounced onc-sapphire, with Al diffusion from the substrate leading to formation of an epitaxial BaAl2O4 second phase at the substrate-film

interface. The formation of this second phase in the presence of a liquid phase seeds{111}twins that drive abnormal grain growth. The orientation of the sapphire substrate determines the BaAl2O4 morphology, enabling control the abnormal grain growth behavior.

CuO additions leads to significant grain growth at 900◦C, with average grain size approaching 500 nm. The orthorhombic-tetragonal phase transition is clearly observable in temperature dependent measurements and both linear and nonlinear dielectric properties are improved. All films containing CuO are susceptible to aging.

A number of other systems were investigated for efficacy at temperatures below 900 ◦C. Pulsed laser deposition was used to study flux + BaTiO3 targets, layered flux films, and in situ

liquids. RF-magnetron sputtering using a dual-gun approach was used to explore integration on flexible foils with Ba1-xSrxTiO3. Many of these systems were based on the BaO-B2O3 system,

which has proven effective in thin films, multilayer ceramic capacitors, and bulk ceramics. Modifiers allow tailoring of the microstructure at 900◦C, however no compositions were found, and no reports exist in the open literature, that provide significant grain growth or densification below 900◦C.

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Liquid-Phase Processing of Barium Titanate Thin Films

by

David Thomas Harris

A dissertation submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the Degree of

Doctor of Philosophy

Materials Science and Engineering

Raleigh, North Carolina

2015

APPROVED BY:

Elizabeth Dickey

Professor of Materials Science and Engineering

Jacob Jones

Professor of Materials Science and Engineering

James LeBeau

Assistant Professor of Materials Science and Engineering

Lubos Mitas Professor of Physics

Jon-Paul Maria

Professor of Materials Science and Engineering

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Dedication

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Biography

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Acknowledgements

I would first like to thank my advisor Prof. Jon-Paul Maria for both guiding my research and career goals, but also for his instrumental role in convincing me to pursue my doctorate. His engagement with his graduate students has enabled my success, and without his initiative in recruiting I would not have pursued this path.

I would like to thank Dr. Peter Lam for his involvement in the early parts of this work. The Electronic Oxides Group has assisted with equipment, experiments, and fun: Michelle Casper, Nicole Estrich, David Hook, Xiaoyu Kang, Kyle Kelley, John Leonard, William Luke, Ed Mily, Beth Paisley, Bennet Rogers, Tina Rost, Edward Sachet, Chris Shelton, and Alex Smith. I would also like to thank Dr. Jon Ihlefeld, whose 2006 dissertation laid much of the groundwork for my own.

Prof. Beth Dickey, Dr. Jing Li, Matthew Burch, and Ali Moballegh for the close collaboration and electron microscopy work. Prof. Jacob Jones, Dr. Chris Fancher, and Dr. James Tweedie for work with hot-stage x-ray diffraction. Prof. Susan Trolier-McKinstry and Dr. Lauren Garten of Pennsylvania State University for discussions and collaborations. Joe Matthews was especially helpful in troubleshooting problems with photolithography and verifying that I was not insane. My parents, from a young age, have provided the support and intellectual stimulation needed for my growth, even when the schools did not. They encouraged my speculation and pursuits, starting with my inane childhood theories. My successes in life have been in no small part to their hard and caring work.

A number of science and math teachers have shared their love of the world and infected me with curiosity: Mr. Clauset, Mrs. Mowbray, Mr. Ferree, Mrs. Fix, Mrs. McMurray, Prof. Wayne Christiansen, Prof. Sean Washburn, Prof. Hugon Karwowski, Prof. John Engel, and Prof. Lubos Mitas. The importance of their enthusiasm cannot be understated, both in inspiring my interest in science and constantly reminding me of the joy of learning.

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Table of Contents

List of Tables . . . .viii

List of Figures . . . ix

Chapter 1 Introduction . . . 1

1.1 Barium titanate based dielectrics . . . 1

1.2 Outline of work . . . 2

Chapter 2 Ferroelectrics and dielectrics . . . 5

2.1 Ferroelectricity . . . 5

2.1.1 History and definition . . . 5

2.1.2 Perovskites and phase transitions . . . 6

2.1.3 Ferroelectric domains and dielectric properties . . . 16

2.1.4 Stress effects . . . 21

2.2 Barium titanate thin film growth . . . 23

Chapter 3 Scaling effects in barium titanate . . . 24

3.1 Scaling effects in bulk ceramics . . . 25

3.1.1 The micron regime . . . 25

3.1.2 The sub-micron regime . . . 28

3.2 Critical size for ferroelectricity . . . 31

3.2.1 Ferroelectricity in nanoparticles . . . 32

3.2.2 Epitaxial thin films . . . 33

3.3 Scaling effects in polycrystalline thin films . . . 35

3.3.1 The film-substrate system . . . 35

3.3.2 Thickness and grain size effects . . . 37

3.3.3 Influence of processing . . . 40

3.3.4 Outlook on scaling effects . . . 42

Chapter 4 Liquid phase sintering . . . 44

4.1 Overview . . . 44

4.1.1 Capillary forces and rearrangement . . . 45

4.1.2 Reprecipitation and chemical interaction . . . 47

4.1.3 The final sintered product . . . 49

4.2 Liquid-phase sintering in BaTiO3 . . . 49

4.2.1 Twinning and abnormal grain growth in barium titanate . . . 54

4.3 Liquid phase assisted growth of thin films . . . 58

4.4 Flux incorporation in the barium titanate lattice . . . 62

Chapter 5 Common experimental details . . . 66

5.1 Flux powder synthesis . . . 66

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5.2 Film synthesis . . . 70

5.3 Film characterization . . . 73

Chapter 6 Realizing strain enhanced dielectric properties in BaTiO3 films by liquid phase assisted growth . . . 75

6.1 Abstract . . . 76

6.2 Introduction . . . 76

6.3 Experimental details . . . 78

6.4 Results and discussion . . . 78

6.5 Conclusions . . . 85

6.6 Acknowledgements . . . 86

6.7 Supplemental information . . . 86

Chapter 7 Low temperature control of twins and abnormal grain growth in barium titanate . . . 88

7.1 Abstract . . . 88

7.2 Introduction . . . 89

7.3 Experimental . . . 91

7.4 Results and Discussion . . . 92

7.4.1 Microstructure dependence on substrate orientation . . . 92

7.4.2 Controlled atmosphere processing . . . 99

7.4.3 Dielectric properties . . . 102

7.5 Conclusions . . . 104

7.5.1 Acknowledgments . . . 104

Chapter 8 Microstructure and dielectric properties with CuO additions to liquid phase sintered BaTiO3 thin films . . . .106

8.1 Introduction . . . 106

8.2 Experimental . . . 107

8.3 Results and discussion . . . 109

8.3.1 Growth onc-sapphire . . . 109

8.3.2 Microstructure on MgO . . . 117

8.4 Conclusions . . . 120

8.5 Acknowledgements . . . 120

Chapter 9 Bi2O3-BaB2O4 addition for low temperature processing . . . .121

9.1 Bi2O3-BaB2O4 experimental details . . . 123

9.1.1 Bi2O3-BaB2O4 powder and target synthesis . . . 123

9.1.2 Thin film growth . . . 124

9.2 Bi2O3-BaB2O4 results and discussion . . . 126

9.3 Conclusions . . . 130

Chapter 10 BaO-V2O5 flux for low temperature processing . . . .132

10.1 BaO-V2O5 powder and target preparation . . . 132

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10.2.1 BaO-V2O5 films . . . 134

10.2.2 BVO wetting behavior . . . 136

10.3 Changes in texture within situ BVO . . . 137

10.4 Barium vanadate layered growth by PLD . . . 141

10.5 Conclusions . . . 146

Chapter 11 Microstructure of BaTiO3 films with modifiers to the BaO-B2O3 flux . . . .147

11.1 Experimental details . . . 148

11.2 Crystallinity and microstructure . . . 150

11.3 Conclusion . . . 158

Chapter 12 Conclusions and future directions . . . .159

12.1 Conclusions . . . 159

12.2 Future directions . . . 162

References. . . .164

Appendices . . . .190

Appendix A Non-sapphire substrates, buffers, and template layers . . . 191

A.1 Elimination of BaAl2O4 . . . 191

A.2 Template growth layers . . . 198

A.2.1 Ba6Ti17O40 . . . 198

A.2.2 BaAl2O4. . . 201

Appendix B Permittivity extraction from interdigitated contacts using conformal mapping . . . 208

B.1 Conformal mapping and partial capacitance . . . 209

B.1.1 Application to multilayered systems . . . 210

B.1.2 Numerical considerations . . . 213

B.2 Application to barium titanate thin films . . . 215

B.3 Conclusion . . . 216

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List of Tables

Table 2.1 Measured and predicted transition temperatures for the ferroelectric BaTiO3

phases. . . 8

Table 4.1 Reported liquid phase systems and the temperature where densification was observed. . . 51

Table 4.2 Elements with their expected coordination, ionic radii, and reported occu-pancies in the ABO3 perovskite structure of BaTiO3. . . 63

Table 4.3 Elements with their reported changes to the paraelectric-ferroelectric transi-tion temperature. . . 65

Table 5.1 BBO flux compositions designations. . . 67

Table 11.1 The final atomic percents and label designations for the fluxes added. . . 148

Table 11.2 The mass (g) of each source material added for each 10 g of BaTiO3. . . 149

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List of Figures

Figure 1.1 Schematic of a multilayer ceramic capacitor. . . 2

Figure 2.1 The crystal structure of BaTiO3 at room temperature. . . 7

Figure 2.2 The crystal structure of BaTiO3at room temperature with oxygen octahedral and exaggerated distortion . . . 8

Figure 2.3 (Inset)Permittivity-temperature measurements of a BaTiO3 single crystal and the inverse permittivity demonstrate Curie-Weiss behavior. . . 10

Figure 2.4 The resulting minimized phase and polarization magnitude and vector from an 8th order expansion. . . 11

Figure 2.5 Charge distribution in AlAs . . . 13

Figure 2.6 Schematic showing compensation of the depolarizing field by a) polarization gradient, b) surface screening charge, and c) domain wall formation. . . 16

Figure 2.7 Schematic showing the mechanical distortion (exaggerated) at a 90◦ domain wall. . . 18

Figure 2.8 Polarization hysterisis measurement of a PbZrxTi1-xO3 thin film. . . 19

Figure 2.9 Example capacitance-voltage measurement of a ferroelectric. . . 20

Figure 2.10 Schematic of a potential energy landscape for ferroelectric domain wall motion. 21 Figure 3.1 Permittivity and TC as a function of grain size in the micron regime. . . 25

Figure 3.2 Permittivity as a function of grain size in the micron and sub-micron regime. 26 Figure 3.3 Reported sizes where ferroelectricity is observed or predicted. . . 31

Figure 3.4 Permittivity-temperature comparison for single crystal, bulk ceramic, rigid, and flexible thin films. . . 36

Figure 3.5 Experimental permittivities fit with a series capacitor model. . . 40

Figure 3.6 Permittivity with grain size, displayed for films processed above 900◦C and below 800◦C. . . 41

Figure 4.1 Illustration showing how mixed powder liquid phase sintering progresses. . . 45

Figure 5.1 Phase diagram for the BaO-B2O3 system . . . 68

Figure 5.2 Preparation pathway for BBO powder precipitation. . . 69

Figure 5.3 DSC of the final BBO flux powder reveals melting as expected. . . 69

Figure 5.4 XRD of BaTiO3 and a BBO target. . . 70

Figure 5.5 Schematic of PLD system. . . 72

Figure 5.6 Schematic of the interdigitated contacts used. . . 74

Figure 6.1 TEM cross-sections of BaTiO3 and BBO. . . 79

Figure 6.2 HRTEM of BaTiO3 and 3%BBO grain boundaries. . . 80

Figure 6.3 Relative tuning and capacitance-temperature measurements as a function of BBO amount. . . 83

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Figure 7.1 SEM plan view images of etched films grown on a)a-sapphire, b)r-sapphire,

and c) c-sapphire. . . 93

Figure 7.2 Cumulative frequency distribution of grain sizes measured using linear inter-cept from SEM plan-view. . . 94

Figure 7.3 Bragg-Brentano geometry x-ray diffraction scans for samples grown on a-, r-, andc-sapphire. . . 95

Figure 7.4 TEM cross-sections for films grown on a) a-sapphire, b) r-sapphire, and c) c-sapphire. . . 97

Figure 7.5 SEM images showing films processed on c-sapphire with a) Ba6Ti17O40 buffer and b) (002)-BaAl2O4 buffer. . . 100

Figure 7.6 SEM plan view images of films after annealing at 900 ◦C in low oxygen partial pressures. . . 101

Figure 7.7 Capacitance-voltage curves for films grown on a-,r-, andc-sapphire. . . 103

Figure 7.8 Capacitance measurements as a function of temperature for samples on different sapphire cuts. . . 103

Figure 8.1 SEM plan-view micrographs of pure BaTiO3 (a, d, g), BaTiO3 + 8nm CuO (b, e, h), and BaTiO3 + 8 nm CuO + BBO (c, f, i) on c-sapphire annealed at 800, 850, and 900 ◦C. . . 110

Figure 8.2 XRD patterns of BaTiO3 onc-sapphire annealed at 900 ◦C with CuO and CuO + BBO additions. The pure BaTiO3 sample includes Pt top electrodes. Unlabeled peaks are due to substrate reflections. . . 111

Figure 8.3 SEM plan-view micrographs of pure BaTiO3 + BBO on a) 100 nm, b) 1 nm, and c) 0 nm of Cuo annealed at 900◦C onc-sapphire. Example {111}twins are indicated by arrows. . . 113

Figure 8.4 SEM plan-view micrographs of second likely second phasees in a) BaTiO3 + 8 nm CuO + BBO and b) BaTiO3 + 8nm CuO, after annealing at 900◦C . 114 Figure 8.5 a) Capacitance-temperature and b) relative tuning with applied DC field after thermal de-aging for samples onc-sapphire annealed at 900 ◦C. . . 115

Figure 8.6 Capacitance-voltage measurements of a) BaTiO3+ 8 nm CuO and b) BaTiO3 + 8 nm CuO + BaO-B2O3films after aging for 2 months at ambient conditions (Aged), and after de-aging at 250◦C for 30 minutes (Thermal) or 1000 cycles of ±35 V (E-field). . . 116

Figure 8.7 SEM plan-view micrographs of a) BaTiO3, b) BaTiO3 + 8 nm CuO, and c) BaTiO3 + 8 nm CuO + BBO on MgO and annealed at 900◦C. . . 118

Figure 8.8 SEM plan-view micrographs of BaTiO3 + 8 nm CuO + BBO on MgO and annealed at 900◦C showing second phase. . . 119

Figure 8.9 XRD patterns of BaTiO3 on MgO annealed at 900 ◦C with CuO and CuO + BBO additions. . . 120

Figure 9.1 Ellingham diagram for copper and bismuth oxides. . . 123

Figure 9.2 Phase diagram for the Bi2O3-BaB2O4 system . . . 124

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Figure 9.4 Permittivity as a function of annealing oxygen partial pressure for BST films

with BBBO flux. . . 127

Figure 9.5 SEM micrographs of BST and BBBO with varying BBBO volume percent. . 128

Figure 9.6 SEM micrographs of BST and 4% BBBO with varying oxygen partial pressure.129 Figure 9.7 XRD of 4% films processed at different oxygen partial pressures. . . 130

Figure 9.8 SEM micrographs of pure BST deposited at 200 ◦C and 25 ◦C. . . 131

Figure 10.1 Phase diagram for the V2O5-BaO system . . . 133

Figure 10.2 DSC shows 540 ◦C melting point for BVO system. . . 133

Figure 10.3 XRD Bragg-Brentano scan for phase analysis of BVO target. . . 134

Figure 10.4 Optical image of a BVO film deposited at 400◦C . . . 135

Figure 10.5 Optical image of a BVO film after heating to 575 ◦C in air. . . 135

Figure 10.6 XRD of BVO films before and after film melting in air at 575 ◦C. . . 136

Figure 10.7 BVO powder (before and after melt) on sapphire showing the wetting behavior.137 Figure 10.8 Schematic illustrating the film growth steps. . . 138

Figure 10.9 Comparison of BaTiO3 grown without BVO in situ liquid and with BVO deposited at 400 ◦C and room temperature. The BaTiO3 peaks are indexed demonstrating texture development. . . 139

Figure 10.10 Cross-section of the needle-like second phases present in BVO deposited at 400◦C. . . 140

Figure 10.11 SEM plan view image of BaTiO3 grown with in situ BVO. . . 140

Figure 10.12 Schematic of layered BVO and BaTiO3 growth. . . 141

Figure 10.13 AFM micrographs of BaTiO3 and BVO layered films on c-sapphire. . . 142

Figure 10.14 XRD for varying number of BVO layers in BaTiO3 on c-sapphire. . . 143

Figure 10.15 XRD for varying number of BVO layers in BaTiO3 on MgO. . . 143

Figure 10.16 XRD for 5 layers of BVO in BaTiO3 onc-sapphire as a function of annealing temperature. . . 144

Figure 10.17 AFM for 5 layers of BVO in BaTiO3 onc-sapphire at different annealing temperatures. . . 145

Figure 11.1 XRD of BaTiO3+M1 (Ba, B, V, Al) after annealing at the indicated tem-peratures. . . 150

Figure 11.2 XRD of BaTiO3+M2 (Ba, B, V (1.0%), Si, Al) after annealing at the indicated temperatures. . . 151

Figure 11.3 XRD of BaTiO3+M2B (Ba, B, V (0.1%), Si, Al) after annealing at the indicated temperatures. . . 151

Figure 11.4 XRD of BaTiO3+M4 (Ba, B, Si, Al) after annealing at the indicated tem-peratures. . . 152

Figure 11.5 XRD of BaTiO3+M5 (Ba, B, Al) after annealing at the indicated temperatures.152 Figure 11.6 XRD of BaTiO3+M6 (Ba, B, Li) after annealing at the indicated temperatures.153 Figure 11.7 XRD of BaTiO3 + indicated flux after annealing at 900 ◦C. . . 153

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Figure 11.9 SEM plan view micrographs of BaTiO3+ M4 (Ba, B, Si, Al) annealed at 900

C. . . 155

Figure 11.10 SEM plan view micrograph of BaTiO3+M1 (Ba, B, V, Al) annealed at 900◦C.156 Figure 11.11 SEM plan view micrographs of BaTiO3+ M5 (Ba, B, Al) annealed at 900 ◦C.157 Figure 11.12 SEM plan view micrographs of BaTiO3+ M6 (Ba, B, Li) annealed at 900 ◦C.157 Figure 11.13 SEM plan view micrographs of BaTiO3+ a) M1 (Ba, B, V, Al), b) M5 (Ba, B, Al), and c) M6 (Ba, B, Li) annealed at 800 ◦C. . . 158

Figure A.1 SEM micrograph of BaTiO3 with 3% BBO grown on a YSZ substrate. . . . 192

Figure A.2 SEM micrograph of BaTiO3with 3% BBO grown on a hafnium oxide buffered c-sapphire substrate. . . 193

Figure A.3 XRD pattern for BaTiO3 with 3% BBO grown on YSZ and a HfO2 buffer layer. . . 193

Figure A.4 XRD pattern for BaTiO3 with 3% BBO grown on Al2O3. . . 194

Figure A.5 SEM micrograph of BaTiO3 with 3% BBO grown on a) polished alumina substrate and b) ablated alumina on MgO. . . 195

Figure A.6 AFM micrograph of BaTiO3 with 3% BBO grown on a flexible copper substrate. . . 196

Figure A.7 AFM micrograph of BaTiO3 with 3% BBO grown on a flexible nickel substrate.197 Figure A.8 AFM micrograph of BaTiO3 with 3% BBO grown on a flexible palladium substrate. . . 197

Figure A.9 Bragg-Brentano XRD scan of a Ba6Ti17O40 target. . . 199

Figure A.10 SEM micrograph of BaTiO3 with 3% BBO grown on a Ba6Ti17O40 buffer on c-sapphire. . . 200

Figure A.11 SEM micrograph of 200 nm of Ba6Ti17O40 on Cu foil. . . 201

Figure A.12 SEM micrograph of Ba6Ti17O40 on Cu foil. . . 202

Figure A.13 Bragg-Brentano XRD scan of BaAl2O4 target. . . 203

Figure A.14 Bragg-Brentano XRD scan of BaAl2O4 (before and after BaTiO3 deposition) grown onc-sapphire. . . 204

Figure A.15 Phi XRD scan of BaAl2O4 grown onc-sapphire. . . 205

Figure A.16 SEM micrograph of BaTiO3 with 3% BBO grown on a (002) BaAl2O4 buffer on c-sapphire. . . 205

Figure A.17 SIMS depth profiles for Al and Ba of a BaTiO3 film with 3% BBO grown on a c-sapphire after annealing for 1 hour. . . 206

Figure A.18 In situ XRD of annealing a BaTiO3 + 3%BBO film. . . 207

Figure B.1 Layout of IDC for Gevorgian conformal mapping model . . . 210

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Chapter 1

Introduction

1.1

Barium titanate based dielectrics

Barium titanate has been studied extensively since its discovery both because of its prototypic ferroelectric behavior, as well as for its high permittivity. This has generated a tremendous amount of research, both in the open literature and in the form of patents. As of this writing (2014) greater than 10,000 have been published in each category according to Google Scholar. The chief use of BaTiO3 is in capacitive elements and specifically multilayer ceramic capacitors

(MLCCs). In 2010, greater than one trillion BaTiO3 based MLCCs were produced each year for

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Figure 1.1: Schematic of a multilayer ceramic capacitor.

efforts in reducing the processing temperature.

This layered structure maximizes the area of the capacitor while minimizing the the footprint. However, as in all electronic devices, there is a strong trend towards miniaturization with packages 0.254 mm by 0.127 mm fabricated for surface mounting.3 Current generation devices

have thousands of layers below 1 micron in thickness, near the limit of screen printing and thick film technologies. Advances in thin film processing are needed to enable further decreases in capacitor dimensions.

A second class of devices utilizes the nonlinear dielectric properties of ferroelectrics to create tunable elements and circuits.4,5 The desire to integrate these components directly with other elements of the circuits requires reduced processing temperatures while maximizing ferroelectric properties that are suppressed by small scales, rigid substrates, and low processing temperatures.6 Both of these applications require BaTiO3 based materials that can be processed

at low temperates, in varied atmospheres, and on substrates ranging from silicon to flexible foils.

1.2

Outline of work

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work. Chapter 3 discusses the impact of reduced dimensions on the dielectric and ferroelectric properties of BaTiO3. Scaling effects in ceramics and nano-structured systems are introduced

so that the effects of polycrystalline films can be better understood. Chapter 4 introduces the concept of liquid phase sintering and explores the history of sintering in BaTiO3 ceramics. The

role of second phases and non-ferroelectric twins is discussed. Finally the few cases of liquid phase sintering in thin film complex oxides are highlighted and the incorporation of flux components in BaTiO3 are discussed.

Chapter 5 gives experimental details that are common to several experiments. Additional experimental details are given in the appropriate sections.

Chapter 6 discusses the efficacy of a BaO-B2O3 flux in improving non-linear dielectric

properties of laser ablated BaTiO3 films. Engineering of ferroelectric transitions using residual

thermal strain is demonstrated. Chapter 7 extends the study of the BaTiO3-BaO-B2O3 system,

demonstrating control of twinning and abnormal grain growth that is mediated by a second phase. Chapter 8 adds CuO to the BaO-B2O3 flux system, yielding larger grain sizes and

twinning without the previously seen second phases.

Chapter 9 examines the possibility of bismuth oxide additions. Chapter 10 looks at a vanadium oxide flux, both as a typical liquid sintering addition as well as anin situ liquid. The reasons for the unsuitability of these systems in thin films are discussed.

Chapter 11 examines common oxide sintering modifiers in combination with BaO-B2O3 in

an effort to lower processing temperatures below 900 ◦C.

Chapter 12 summarizes the findings and gives concluding remarks on the body of work. Suggestions for further work are given.

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Chapter 2

Ferroelectrics and dielectrics

2.1

Ferroelectricity

2.1.1 History and definition

Ferroelectricity was first recognized in NaKC4H4O6·4H2O, commonly known as Rochelle salt, in

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total electrical polarization was changed.7,8

This new class of materials was termed piezoelectric materials and is characterized by a coupled nature of electric polarization and strain. Of the 32 crystal systems, 11 display a center of symmetry, meaning with applied stress charge distributions in the crystal will move symmetrically about the center, leading to no change in polarization. Of the remaining 21 systems, 20 display piezoelectricity. Of the piezoelectric crystal classes, half possess spontaneous polarization without applied strain, or pyroelectricity. The ability for the spontaneous polarization to be reoriented along different crystal directions separates ferroelectrics from pyroelectrics.

Further advances in ferroelectricity were made through the discovery of KH2PO4 by Busch

and Scherrer in the 1930s.9 To this point all discovered ferroelectrics posses hydrogen bonding, leading Slater to suggest a model that described the phase transition of the much simpler KH2PO4 material.10 This model correctly defined ferroelectrics as possessing a spontaneous

polarization that could be reoriented, however subsequent discoveries of ferroelectrics that were hydrogen free demonstrated the overly simple nature of the model. However it wasn’t until the discovery of ferroelectricity in BaTiO3 that significant interest and progress was made in

understanding and utilizing ferroelectric materials.11The discovery of stable ferroelectricity in the simple perovskite structure enabled a deeper understanding of the origins of ferroelectricity and the application of theories originally developed for ferromagnetic materials.8,12

2.1.2 Perovskites and phase transitions Perovskite crystals

BaTiO3 belongs to a class of materials defined by the perovskite crystal. Figure 2.1 shows

the perovskite structure of BaTiO3 at room temperature. In general the ABO3 structure is

characterized by A2+ on the cube corners and B4+ at the center of an oxygen octahedra (oxygen located on the faces of the cube). Thus the A-site species (Ba) is 12-coordinated and the B-site (Ti) is 6-coordinated.

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Figure 2.1: The crystal structure of BaTiO3 at room temperature. Ba (green) on the corners,

Ti (blue) at the center, and O (red) on the faces.

temperature (ac = 1.01). Figure 2.2 shows an exaggerated view of this distortion with the oxygen octahedral drawn around the central Ti ion. From this view it can clearly be seen that the octahedral has been distorted and is no longer symmetric along the tetragonal (by convention

c-axis or (001)) axis. Due to the ionic nature of the material, this gives rise to an electric dipole that can be oriented along any of the<001>family of directions.

The origins of this distortion are best understand by viewing the perovskite structure as stacking of corner sharing octahedra with A-site ions located at the interstitial 12-coordinated sites. The size of the A-site ion must fit within these interstitial sites, and large cations will displace the octahedra giving rise to polar distortions. Goldschmidt proposed a tolerance factor based on the ionic radii of the A- and B-site cations (RA andRB) to describe if distortions will

occur

t= √rA+rO 2(rB+rO)

(2.1)

where rO is the anion (oxygen) ionic radius.13 Sr results in a tolerance factor of 1, giving a

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Figure 2.2: The crystal structure of BaTiO3 at room temperature with oxygen octahedral and

exaggerated distortion. Ba (green) on the corners, Ti (blue) at the center, and O (red) on the faces.

Perovskite phase transitions

As a function of temperature (from high temperature to low temperatures), BaTiO3 exhibits

hexagonal, cubic, tetragonal, orthorhombic, and rhombohedral distortions from the ideal cubic perovskite.14,15 The cubic and hexagonal phases are non-polar, but below 120 ◦C BaTiO3

exhibits ferroelectricity. Table 2.1 gives experimental and theoretical values for the transitions temperatures. In the tetragonal phase, polarization occurs along the<001>family of directions, while in the orthorhombic and rhombohedral phases spontaneous polarization is along the <011>and <111>directions respectively.8

Table 2.1: Measured (Megaw) and predicted (Li) transition temperatures for the ferroelectric BaTiO3 phases.

Study Rhombohedral to Orthorhombic

Orthorhombic to Tetragonal

Tetragonal to Cubic

Megaw15 183 K 273 K 393 K

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Of particular interest is the cubic (Pm¯3m, paraelectric) to tetragonal (P4mm, ferroelectric) transition. In the paraelectric phase no spontaneous polarization is stable (the cubic phase is centrosymmetric). Cooling towards the transition temperature leads to large increase in permittivity, as seen in the inset of Figure 2.3. This is a first order transition that obeys the Curie-Weiss law,

= C

T −T0

(2.2)

where C is the Curie-constant and T0 is the Curie temperature (typically slightly below the

observed maximum in permittivity or the Curie point). By fitting 1 vs T, these constants can be extracted. From the experimental data, the Curie constant is found to be 4.3E5K−1 and the Curie temperature 378 K.17

In BaTiO3 the maximum in permittivity is observed at TC=120 ◦C. The Currie-Weiss

law describes where the the permittivity of the system will go to infinity. For BaTiO3 T0=105

C, below the transition point from paraelectric to ferroelectric. This trend of T

0 <TC is

characteristic of a first-order transition, where this is a volume change and an abrupt drop in the order parameter (spontaneous polarization for ferroelectrics) atTC.18–20

Much of the understanding of ferroelectrics has been gained through exploration of its coop-erative nature and examining coopcoop-erative lattice vibrations, or phonons. The large permittivities seen near TC can be understood in the context of a soft mode phonon. In particular, the

transverse-optic mode describing vibrations of the Ti (B-site) ions is a function of temperature. The soft mode of the system is described by8

Ω2(k)∼T−TC. (2.3)

As the temperature is lowered towards TC the soft mode will condense at the Brillouin zone

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3 0 0 4 0 0 5 0 0

0

2

4

1 0 0 2 0 0

0

1 0 0 0 0 2 0 0 0 0 3 0 0 0 0

Di

ele

ctr

ic

co

ns

ta

nt

T e m p e r a t u r e ( ° C )

1/

ε

(x

10

-4

)

T e m p ( K )

Figure 2.3: (Inset)Permittivity-temperature measurements of a BaTiO3 single crystal17 and

the inverse permittivity demonstrate Curie-Weiss behavior.

a reduction in the restoring force for the vibration that eventually becomes so weak that a structural distortion is frozen in.18 The condensation of the soft mode leads to stabilization of a spontaneous polarization (degenerate along the three equivalent orientations in the tetragonal structure). The Brillouin zone is understood in reciprocal space, meaning a condensation at the zone centerq0 = 0 corresponds to long wavelengths in real space. Experimental measurements of

soft modes using Raman spectroscopy or neutron scattering find good agreement with soft mode theory for a number of ferroelectrics, however BaTiO3 has an over-damped soft mode which

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0 2 0 0 4 0 0 0 . 0

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5

< 1 1 1 > < 0 1 1 > < 0 0 1 >

Po

la

riz

at

io

n

m

ag

ni

tu

de

(C

/m

2

)

T ( K )

C u b i c

Figure 2.4: The resulting minimized phase and polarization magnitude and vector from an 8th order expansion.

Phenomenological model

Landau phenomenological theory had its start in 1937 in a paper by Landau on second order phase transitions21. The theory was successfully used to describe both ferromagnetism as well as transitions in superconducting materials22,23. Devonshire first applied Landau theory to ferroelectrics in a study of barium titanate in 195012. With advancements in theory as well as new experimental findings, Landau-Devonshire theory has been expanded to describe a diverse set of phenomena including strain24,25 and size effects in different geometries.26–28

Landau theory is based upon the concept of a long range ordering parameter, polarization in the case of ferroelectrics, being used to characterize a phase transition. The free energy of the system is expanded as a function of the order parameter P:

G(P) = 1 2aP

2+1

4bP

4+1

6aP

6 (2.4)

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even terms appear due to the centrosymmetric nature of the paraelectric state.18 Work by the superconducting, ferromagnetic, and ferroelectric communities have crafted models for a wide variety of geometries, domain structures, and time scales. By applying boundary conditions and adding more terms to the free energy expansion, effects such as strain, depolarization field, and size can be studied. Additional terms in the expansion are added to better model real world behavior, resulting in the modern 8th order expansion used today.16 The Landau-Devonshire coefficients are determined through fitting to either experiment or first principle calculations, hence the phenomenological nature of the theory. Figure 2.4 shows the minimized stable polarization vector and corresponding polarization magnitude for a Landau potential for BaTiO3.16 The sharp drop in spontaneous polarization atTC is characteristic of the first order

nature of the BaTiO3 transition.18

A modern view of material polarization

Thermodynamics and phenomenological models describe many experimental results well, but are dependent on significant input from experimental work. First principle based simulations of ferroelectric materials proved difficult, in part because of the generally accepted view of polarization in materials. Polarization as a bulk material property has long been utilized to explain observed properties such as permittivity, piezoelectricity, pyroelectricity, and ferroelectricity. However, theories of polarization using classical treatments have ambiguities stemming from how we terminate our crystal and the introduction of surface charges. By taking a quantum approach to material polarization it is evident that the bulk material polarization arises from the adiabatic change of state of the material and is analogous to the differences in polarization measured in experiments.

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materi-Figure 2.5: Charge distribution in AlAs (110) plane. Al (purple) are in plane while As (yellow) are below the plane. (DFT simulation performed in ABINIT and visualized using XCrySDen.)

als8,18–20,29,30. A localized view of the electrons in materials is not realistic for even partially covalent materials in which the electron is inherently delocalized (see, for example, the electron density for AlAs in Figure 2.5).

Measurements of a polarized material yields a polarization P which has units of electric dipole moment per unit volume. The most obvious interpretation of this is to define

P= 1 Vsample

ˆ

sample

drrρ(r). (2.5)

This definition requires a finite crystal and introduces surface terms and boundary conditions to a phenomenon that we suspect is a bulk property of infinite crystals as well as finite ones.

Another tempting definition for our polarization is to instead integrate over the charge distribution within one interior unit cell

P= 1 Vcell

ˆ

cell

drrρ(r)

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drawn, making the Clausius-Mossotti definition of polarization insufficient. Another suggested definition for bulk polarization is given as

∇ ·P(r) =−ρ(r).

Here we again encounter the problem of needing to account for surface terms in order to describe a bulk property.

From the above arguments it is clear that a bulk polarization cannot be defined based only on the charge distribution within the material and so we must formulate a new modern means of defining polarization. The difficulty of defining a bulk polarization has been known since the 1970s,32 but it was not until geometric phases in quantum mechanics were understood that progress was made on the theory of material polarization.

The geometric phase approach was developed in the early 1990s by Resta33, and Vanderbilt and King-Smith34,35. Resta gives an independent derivation of the macroscopic polarization following a different approach but arriving at the same conclusions.36

When attempting to describe the theory of an experimental observation it is of vital importance to consider the experimental methods and what is actually measured. Experimental methods for polarization do not directly measure the bulk value, but instead probe the derivative or finite difference with respect to some parameter. For example, χαβ = dPdEαβ and Πα = dPdTα

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total change in polarization can be written as

∆P=

ˆ 1

0

dλdP

dλ (2.6)

whereλis a dimensionless adiabatic time. This adiabatic change can be sublattice displacements, strains, electric fields, temperature, etc, that give rise to observable flow of polarization currents. The change in polarization can be due to both ionic contributions, which can be safely treated classically, and electronic contributions, which require a quantum approach. For (Eq. 2.6) to be true the sample must remain insulating at all intermediate λ. If the sample becomes conductive the observed current is no longer uniquely defined from the change in polarization.

The total polarization including both electronic and ionic contributions is34,35

P(λ) = 2ei (2π)3

M X

n

ˆ

BZ

dkhunk| ∇k|unki+ e Ω

X

s

Zsionrs (2.7)

remembering that the actual observed quantity will be the total change in polarization ∆Ptotal =

∆Pel+ ∆Pion due to the adiabatic change in our system fromλ= 0 to λ= 1.

With this quantum approach, another method of treating material polarization is in terms of Wannier functions, where the polarization is now expressed in terms of the displacement of charge centers of the Wannier functions found using a Fourier transform. The classic Clausius-Mossotti picture of polarization does not apply to the delocalized electron distribution. However, the Wannier charge can be used in the classical framework where negative point charges are placed at the Wannier centers building an equivalent cell that works in the familiar polarization framework.

The introduction of the geometric phase approach to material polarization enables first principle studies of ferroelectrics such as BaTiO3, joining theoretical, phenomenological, and

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Figure 2.6: Schematic showing compensation of the depolarizing field by a) polarization gradient, b) surface screening charge, and c) domain wall formation.

2.1.3 Ferroelectric domains and dielectric properties

The boundary conditions of real ferroelectric crystals impose constraints on the systems and complicates the picture of polarization. In particular, the fact that real crystals are not infinite and must terminate at some surface or interface gives rise to a depolarizing electric field that opposes the material spontaneous polarization and can lead to a destabilized ferroelectric state.6,8,37,38 Specifically, the requirement that the displacement be continuous and polarization at the surface normal is zero requires that some manner of compensation must be present for stable ferroelectricity to be observed.

The depolarizing field can be compensated for by a number of different mechanisms (pictured in Figure 2.6)6,38:

1. A polarization gradient that smoothly approaches zero at the surface.

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3. Formation of ferroelectric domains.

4. (Not pictured) Conduction through the ferroelectric.

The effects of the depolarization field can play a large role in thin dielectrics as will be discussed further in Chapter 3. The formation of a domain structure in BaTiO3 is important, both in the

understanding of scaling effects as well as for understanding the origin of desirable dielectric properties.

The domain structure in Figure 2.6 c) shows the existence of three different domains. A ferroelectric domain is defined as a region of the crystal with like spontaneous polarization orientation, with the region between two neighboring domains referred to as the domain wall. In tetragonal BaTiO3 domains can orient along any of the <001>directions. From this it can

be seen that the angle between a [001] and a [00¯1] is 180◦, thus this type of domain wall is referred to as a 180◦ domain wall. Similarly, two neighboring domains with polarization vectors along the [001] and [100] directions form a 90◦ domain wall. The head to tail orientation of the domains minimizes electrostatic contributions to domain wall energy.39

Both domain walls are categorized as ferroelectric in nature. Namely, application of electric fields can cause domain wall motion, growing domains aligned with the applied field at the expense of other domains.8 However, further consideration of the nature of 90◦walls reveals boundary conditions that introduce mechanical stress due to the tetragonal distortion along the polar axis.38 Figure 2.7 shows an exaggerated view of the mechanical boundary condition at a 90◦ wall.

Because of the mechanical discontinuity at 90◦walls, these boundaries are also classified as ferroelastic in nature and can move in response to applied mechanical stress in addition to applied electric field. Furthermore, in polycrystalline or thin film systems, mechanical constraints on the system can lead to preferential formation or suppression of certain domain structures.38,40 Figure 2.8 shows a polarization hystersis loop measured from a PbZrxTi1-xO3 thin film at

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Figure 2.7: Schematic showing the mechanical distortion (exaggerated) at a 90◦ domain wall.

that remains once the applied field is removed, is found from the intersections with the y-axis. The material permittivity r is related to polarization by a derivative with respect to the

electric field. Specifically permittivity describes how an applied field E changes the electric displacement fieldD of a material41

D=r0E=0E+P (2.8)

where Pis the polarization density. From this it can be seen that

r ∼

∂P

∂E, (2.9)

or how polarization of the material changes with electric field.

Contributions to the relative permittivity include space charges, dipoles, ionic motion, and electronic motion. The response of these contributions varies with frequency of the applied field, dropping out above certain frequencies where oscillations of the field are too fast for a particular polarization mechanism to respond. This corresponds to frequencies of approximately 103 Hz (space charges), 107 Hz (dipoles), 1010 Hz (ionic), and 1015 Hz (electronic) for the different

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- 4 0 0 - 2 0 0 0 2 0 0 4 0 0 - 5 0

0

5 0

P

(

µ

c/

cm

2

)

E l e c t r i c F i e l d ( k V / c m )

Figure 2.8: Polarization hysterisis measurement of a PbZrxTi1-xO3 thin film. Sample provided

by Professor Susan Trolier-McKinstry of Pennsylvania State University.

Also of interest is the complex dielectric constant

r=0+i00 (2.10)

where 0 and00 are the real and imaginary parts of the permittivity respectively. In a perfect dielectric material the permittivity will be entirely imaginary (current and field are 90◦out of phase), however in most realistic materials there will be some real part of the permittivity that leads to losses. Losses are characterized by the loss tangent

tanδ = 00

0 (2.11)

which is 0 for a perfect dielectric.19

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Figure 2.9: Example capacitance-voltage measurement of a ferroelectric. In the green (central) region, domain wall motion leads to large extrinsic contributions to permittivity, while this contribution is suppressed at higher fields (yellow)

presented in Figure 2.9. The effect of domain wall contributions to the dielectric properties are immediately visible. At low fields domain wall motion dominates the material permittivity, leading to large dielectric constants that in BaTiO3 can exceed several thousand. However, at

higher applied fields domain wall motion is clamped, suppressing this extrinsic contribution and the total permittivity. The hysteresis due to polarization switching is still clearly visible in these measurements.

This nonlinear dielectric effect can be characterized by the tunability ratio

tuning = max min

(2.12)

for a given applied voltage or field. Commonly this metric is also given as a percentile relative tunability

tuning= 1− min max

. (2.13)

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Figure 2.10: Schematic of a potential energy landscape for ferroelectric domain wall motion.

the operating frequency tuned electronically.

Domain walls in ferroelectrics may encounter obstructions to their motion in the form of pinning centers. This is shown qualitatively in Figure 2.10. Common pinning sites (represented by peaks int he energy landscape) include dopants, defects, and impurities. Motion within a valley is said to be reversible, as when the applied field is removed the domain wall will return to the original location. However, with larger applied fields domain walls can move past pinning sites resulting in irreversible motion. The relative amounts of this motion can be probed using sub-switching applied fields and Rayleigh analysis.38 Large contributions from irreversible domain wall motion is indicative of domain walls that can easily traverse the potential energy landscape and should result in large extrinsic contributions to permittivity and thus high tunability.

2.1.4 Stress effects

The study of hydrostatic pressure on BaTiO3 single crystals was first undertaken in 1950 by

Merz.42 With increasing pressure it was found there was linear dependence ofTC on pressure

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on sample prehistory. Following the same trend in pressure was a slight increase in the peak permittivity. The tetragonal-rhombohedral transition showed less dependence on hydrostatic pressure, first decreasing modestly then increase at pressures above 150 MPa. The dependence ofTC in a single crystal on hydrostatic pressure was confirmed by Samara.43,44 Additionally, at

the permittivity at phase transitions was found to follow the relationship

3=

C∗ p−p0

(2.14)

, analogous to the typical Curie-Weiss behavior with temperature. The lowest temperature orthorhombic-rhombohedral transition was also determined to decrease with increase pressure. Buessem et al. studied the effects of two-dimensional stress on polycrystalline BaTiO3

ceramics.45 For 10 µm ceramics, permittivity was found to decrease with with increasing stress, however for 1µm material increased pressure increased the dielectric constant. The result for the fine grained material was explained as due to the increased internal stress of the system due to the absence of 90◦ domain walls, however later results on size effects show that these domain walls are still present at this scale (See Ch. 3).

Application of a two-dimensional stress, in contrast to a hydrostatic stress, was found to increase TC by stabilizing the tetragonal distortion.46 Forsbergh, in 1954, used a

Landau-Devonshire potential expanded to the second order to model the behavior ofTC and predicted

that the lower temperature tetragonal-orthorhombic transition should be greatly suppressed. Significantly later, Pertsevet al.looked at the effects of an epitaxial misfit strain on the stability of BaTiO3 phases.24 The conclusions were remarkably similar, predicting increases inTC and

decreases in the orthorhombic-tetragonal transition. Pertsev also considered the effects of tensile strain, finding that while compressive strain stabilized out of plane polarization (normal to the film surface), tensile strain stabilized in plane polarization. Experimental work with SrTiO3 and

BaTiO3 confirmed the ability to shift transition temperature hundreds of degrees and increase

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2.2

Barium titanate thin film growth

Barium titanate based materials can be grown using a variety of techniques. Reports exist for chemical solution deposition,48 pulsed laser deposition,49,50 RF-magnetron sputtering,51 molecular beam epitaxy,52,53atomic layer deposition,54,55and metal organic vapor deposition.56 For polycrystalline growth the most common methods are chemical solution deposition, pulsed laser ablation, and sputtering. Chemical solution deposition is desirable for scalability as well as synthesis without the need for a vacuum chamber.

The remaining two techniques are plasma techniques that take place in vacuum chambers with controlled gas flows. In sputtering an Ar plasma is created and Ar ions are accelerated into the target material by a potential bias, ejecting ions of the material of interest. A magnetron behind the target serves to better confine the plasma near the target surface.57 Important parameters include the substrate temperature,51 Ar to O2 gas ratio,58 and the deposition

power.59 In pulsed laser ablation, a UV laser with energy densities on the order of 5 J/cm2 is pulsed through a UV transparent window at a target. The pulse width is typically on the order of tens of nanoseconds, giving power densities at the target surface in the tens of megawatts range.57This leads to local heating of thousands of K, and an energetic plasma of ions, molecules, and particles that is directed towards the substrate.60,61 Under proper conditions laser ablation

can create stoichiometric films. This was studied in BaTiO3 and it was found that below a laser

fluence of approximately 1.25 J/cm2, films were Ba rich, with deviations as large as 10% found for fluence of 0.5 J/cm2.62 The energetics of the plasmas can lead to re-sputtering and damage from ion bombardment of the film surface during deposition.63 The ambient pressure selected must be optimized for the target to substrate distance in order to minimize particulates, insure stoichiometric depositions, and maximize material properties.64,65In both cases a ceramic target of the desired composition is used. Deposition of BaTiO3 films with these techniques are often

followed by a post-deposition anneal in order to crystallize the material, improve crystallinity, or oxygenate the sample.51,65 Sputtering has the advantage of relatively large areas of uniform

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Chapter 3

Scaling effects in barium titanate

The desire for high permittivity material suitable for small form factor capacitors has driven research in reducing the dimensions of ferroelectric materials. Barium titanate, and related ferroelectric materials, posses high permittivity that is desirable for maximizing capacitive density while reducing the overall size of the devices. Additionally, as MEMS devices reach smaller scales maintaining the performance of closely related piezoelectric properties is of interest to the community. However, as the dimensions of ferroelectric devices and materials move to the nano-regime, bulk like properties are severely diminished, and in some cases the spontaneous polarization characteristic of ferroelectricity is lost.

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1 1 0 1 0 0

0

2 0 0 0 4 0 0 0 6 0 0 0

A v e r a g e g r a i n s i z e (

µ

m )

ε

(

25

°C

)

1 1 5 1 2 0 1 2 5 1 3 0

T

C

C)

Figure 3.1: Permittivity andTC as a function of grain size in the micron regime. Adopted from

Kinoshita and Yamaji.68

3.1

Scaling effects in bulk ceramics

3.1.1 The micron regime

The changes to dielectric, ferroelectric, and piezoelectric properties of BaTiO3 ceramics as a

function of grain size has been studied since the 1950s.67 By varying processing conditions, typically sintering temperature and time or milling, the final grain size of the ceramics can be varied over wide ranges. Typical firing conditions result in grains of many microns, however by reducing sintering temperatures finer grained material can be made.

Kinoshita and Yamaji studied the dielectric properties of BaTiO3 ceramics with grain sizes

down to 1 µm. Figure 3.1 shows the room temperature permittivity and the tetragonal-cubic phase transition as measured by temperature-permittivity measurements. The permittivity trends upwards with decreasing grain size, and hints at further increases in the sub-micron scale. Simultaneous with the large increase in , a slight shift downwards inTC was observed, as well

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0 . 1 1 1 0 1 0 0

0

2 0 0 0 4 0 0 0 6 0 0 0

A v e r a g e g r a i n s i z e (

µ

m )

ε

(

25

°C

)

Figure 3.2: Permittivity as a function of grain size in the micron and sub-micron regime. Adopted from Arlt et al.40

engineer materials with enhanced properties and the desire for smaller scale electronics continued to drive research in size effects.

Arlt et al. later studied the BaTiO3 system in-depth, extending the grain size into the

sub-micron sizes and proposing a model for the peak in permittivity observed near 1µm. Figure 3.2 shows the work from Arltet al., confirming a peak in the room temperature permittivity of 5000 for ceramics with an average grain size of ∼1 µm. Using electron microscopy, the width of 90◦ domain walls was studied for each of the grain sizes. It was found that the size of the ferroelectric domains decreased with decreasing grain size. As the motion of domain walls is a major extrinsic contributor to permittivity, a model was sought to explain the trends observed.

Arlt et al.explained the observed increase in dielectric constant using the balance of domain wall energy, ww, electric field energy, we, and mechanical stress energy wm. Specifically, the

quantity

ww+we+wm=W (3.1)

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will be high enough to cause charge separation in defects and fully compensate the system. The domain wall density is given by

ww≈

σ

d (3.2)

where σ is the domain wall energy per unit area and dis the domain width.

The mechanical energy term comes from the tetragonal distortions in neighboring domains and the constraints on the edges of the system. This energy term is of the form

wm=C×

d a ≈

d

a (3.3)

where ais the edge of a cubic grain. The minimization condition can be found from

dW dd =

−σ

d + 1

a = 0 (3.4)

. Solving for dgives the relationship of

d∼√a (3.5)

.

By placing appropriate values for domain wall and elastic energy of the system, Arlt et al.

found good agreement between this model that predicts increasing domain wall density, and thus increasing extrinsic contributions to permittivity, with decreasing grain size. However, below 700 nm this model fails to predict the observed steep decrease in . Recentin situ diffraction measurements of BaTiO3 ceramics shows enhanced 90◦ domain wall motion, confirming this

hypothesis.69

Additionally Arlt et al. made several other observations that were not explained. As the grain sizes became smaller the tetragonal distortion decreased, TC shifted and became diffuse,

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domain walls at ∼400 nm.

3.1.2 The sub-micron regime

The steep decrease in dielectric properties at fine grain sizes poses severe problems for shrinking devices. Fine grained BaTiO3 ceramics were further studied by Freyet al.70,71 Frey confirmed

the suppression of ferroelectric twinning for grains several hundred nm and the tendency for a pseudo-cubic phase consisting of orthorhombic-tetragonal-cubic systems was again seen at room temperature.70 The numerous grain boundaries clamp the grains introducing stress, which can be better accommodated by the orthorhombic system and the increased allowable polarization directions.

Freyet al.considered the effect of a depolarizing field that could arise due to the requirement that polarization must be continuous and surface polarization is zero. This could destabilize the ferroelectric phase, leading to the observed suppression of tetragonal distortion and ferroelectricity. This field is typically compensated for by configuration of domains and surface charges. Frey found that this effect was unlikely to play a large role at the grain sizes studied as the numerous grain boundaries should provide means for easy surface charge compensation and the predicted behavior of TC was not observed.70

In a follow-up study, Frey et al. prepared ceramics with grain sizes down to 40 nm.71 Ferroelectric hysteresis loops were observed even for samples with 40 nm grains, indicating polar phases are still stable even for these small grain sizes. However, permittivities were still reduced with smaller grains (although still above 2000 for grains sub-100 nm) and the remnant polarization and saturation of the loops decreased dramatically with finer grains. The diffusiveness of the TC was also noticeably improved, with a distinct bump observable for

sub-100 nm grains. Also of note was that TC did not shift with reducing grain size.

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Frey et al. explained the sharp decrease in dielectric properties using a brick-wall model. Specifically, the microstructure was treated as a core-shell, with a high permittivity BaTiO3 core

surrounded by a low permittivity, non-ferroelectric shell. In a parallel plate configuration, the field lines will pass through both the core and shell (modified by a geometric factor to account for field lines preferentially avoiding the low permittivity edges) of each grain. This configuration means the total permittivity can be written as a sum of capacitors in series:

1 =

vg

g

+gvd d

(3.6)

where vg andvd are the volume fractions of the grain and dead layer andgis a geometric factor

(26 for cubes, 1 for spheres, and 0.8 for polyhedra).71 Frey and Payne found that assuming a two unit cell dead layer (0.8 nm), a permittivity of 130 was found to model the observed behavior, a reasonable value for TiO2.72 In these polycrystalline ceramic systems the sharp decrease in

permittivity can be modeled by dilution of a non-ferroelectric grain boundary phase whose volume fraction increases with decreasing grain size, rather than an effect intrinsic to BaTiO3.

Additionally, Frey showed that some of the trends ascribed to scaling are likely due to imperfect processing.

The application of spark plasma sintering to BaTiO3 enables finer control of grain sizes

with lower processing temperatures.73–80 Structural studies in the sub-100 nm grain size shows

decreasing tetragonal distortions, with an extrapolated critical grain size of 10-30 nm.73 At these small grain sizes, line broadening and the short coherence length of the crystals can lead to BaTiO3 appearing cubic to x-rays. Measurements such as PFM and Raman spectroscopy allow

local probing of the ferroelectric and bonding structures. For BaTiO3 ceramics that appear cubic

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with movement heavily pinned by the high density of boundaries.76 Additional evidence for the suppression of extrinsic contributions to permittivity can be gleaned from permittivity measurements under applied DC fields. The large decreases in permittivity at low fields is indicative of suppression of domain wall contributions.78

These more recent studies support earlier findings of broadened TC, decreasing permittivity,

and pseudo-cubic structure. All also report depression of the transition temperature, indicating that Freyet al.71 is either an anomalous report or the quality of samples has not been matched.

The changes with decreasing grain size below 1µm in bulk BaTiO3 ceramics can be summarized

as:

ˆ Decreasing dielectric constant

ˆ Decreasing TC, although this may be due to processing71

ˆ Broadening of the ferroelectric-paraelectric phase transition to the point of no discernible

transitions

ˆ Decreasing tetragonal distortion that eventually forms a pseudo-cubic phase consisting of

short range polar phases

ˆ Decreasing saturation and remnant polarization in hysteresis loops

ˆ Decreased dielectric nonlinearities due to suppression of domain wall contributions

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2 0 0 0

2 0 1 0

2 0 2 0

1

1 0

1 0 0

b u l k b u l k

b u l k c o m p o s i t e

c r y s t a l

e p i n a n o

n a n o n a n o

n a n o n a n o

n a n o

n a n o t h e o r y

t h e o r y

f i l m

n a n o b u l k

Re

po

rte

d

siz

e

(n

m

)

Y e a r

Figure 3.3: Reported sizes for ferroelectricity.17,71,73,76,81,84–94

3.2

Critical size for ferroelectricity

Much of the theoretical work performed has focused on isolated particles unsuitable for devices, or on epitaxial films, however an understanding of these systems is an important step towards engineering better polycrystalline devices. Here we examine these two cases in order to better understand any expected intrinsic effects that may play a role in polycrystalline films. These intrinsic effects should arise purely due to changes in the dimension of the system and not due to strain, grain boundaries, defects, interfaces, or other changes that may be introduced during processing of the material.

Figure 3.3 shows reported BaTiO3 critical sizes by year, labeled for the system they were

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3.2.1 Ferroelectricity in nanoparticles

The study of BaTiO3 nanoparticles, while useful from a scientific perspective, does not directly

translate to practical devices due to differences in electromechanical boundary conditions and the difficulty in fabricating actual electronic devices. Nevertheless, these studies can help build an understanding of size effects at extreme scales.

Typically these studies exhibit similar behavior to ceramics work. The main point of agreement is decreasing tetragonal distortions that eventually result in a pseudo-cubic phase. These systems are typically studied by observing the crystal structure.

McCauley et al. studied BaTiO3 nanoparticles (20 - 83 nm) embedded in a glass matrix, a

system that could conceivably be used in devices. The nanoparticle size was varied by changing the sintering time. The composites showed typical broadening and lowering of the cubic-tetragonal phase transition. This system exists as an intermediary between polycrystalline ceramics and isolated nanoparticles. The glass matrix is expected to limit charge compensation and the depolarizing field should play a greater role than in similarly sized ceramics. By extrapolating dielectric measurements, a critical size for polarization stability was predicted as 17 nm.

Numerous other studies have found also found critical sizes below 40 nm.86–89,91,92,95–99 These studies almost exclusively rely on techniques that probe the local polarization or crystal structure. Examples include Raman,86,88,98 x-ray pair distribution function,89,92,95 second har-monic generation,87 and scanning probe microscopy.88,91 Generally these studies support the conclusion that a mix of polar and non-polar phases coexist in these fine particles, as they do for polycrystalline ceramics.

There is one report in the literature by Xu and Gao on the synthesis of tetragonal BaTiO3

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One challenge in nanoparticle systems is synthesizing particles and preventing grain growth. The synthesis often occurs at room temperature or with only minor thermal energy added.87,88,92 Challenges in synthesis of ceramics was previously identified by Freyet al. as responsible for some of the trends observed,70 and it is likely that these complex chemistry and low temperature techniques do not realize consistently high purity and crystallinity necessary for comparison between experiments.

Another key difference between these nano systems and polycrystalline devices is the lack of strain or mechanical clamping. Nanoparticles are typically not clamped by a substrate or surrounding grains, changing the electromechanical boundary conditions of the system in a way that is unrealistic for real devices.

3.2.2 Epitaxial thin films

A second approach to studying size effects is in epitaxial systems. These systems should allow extremely thin, high quality crystals to be grown and enable direct comparison with theory. This work was strongly motivated for the desire of high-K gate dielectrics, ferroelectric memories, and miniaturized MEMS.6 In practice these systems are complicated by the strains inherent in the system and in correct choice of contacts.

In 2003 first principle calculations predicted a critical grain size of 2.4 nm (6 unit cells) for the SrRuO3-BaTiO3-SrRuO3 stack.93 Incomplete screening at the interfaces led to a substantial

depolarization field that eventually destabilizes the ferroelectric phase. This finding was later investigated experimentally and hysteresis loops were demonstrated in 5 nm thick BaTiO3.101–103

As seen in bulk systems, the reduction of ferroelectric properties, such as remnant polarization, occurred smoothly towards zero.

Other ferroelectric systems have been similarly studied using first principles, with lead titanate exhibiting distortion down to 1.2 nm (3 unit cells)104. As seen in most systems, TC

(48)

The strength of the depolarizing field can be changed by adjusting the top contact. Plonkaet al., using epitaxial Ba1-xSrxTiO3 films on SrRuO3 showed changes inTC shifts and permittivity

with thickness by changing the top contact from SrRuO3 to Pt.105 The total device permittivity

was strongly dependent on top metal electrode, with SrRuO3 providing higher permittivities.

First principle studies with Pt and SrRuO3 contacts on SrTiO3 by Stengel and Spaldin showed

decreasing polarization and permittivity extending into films at the contact interfaces due to incomplete screening.106 Pt was found to provide more complete screening, however this finding

did not agree with literature results and was attributed to difficulties in growing high quality SrTiO3 on Pt. Stengel and Spaldin also showed that the dead layer at the contact interface

should lead to noticeable reductions (15%) in permittivity for films 75 nm thick.

This prediction is troubling for devices such as high-K dielectrics where it is desirable to have extremely fine layers, however for most applications polycrystalline films will typically be significantly thicker than this. This theoretical result was true even for the fully relaxed state, a result not found in experiment. Saadet al. fabricated a free-standing BaTiO3 device

by sectioning a 75 nm thick slice from a single crystal and recovered bulk-like properties.17

Dielectric measurements showed an extremely sharp transition at the expected temperature, with typical Curie-Weiss behavior above the transition. The high permittivity (greater than 25000) and lack of TC shifts or broadening seems to indicate that many of the size effects

reported in the literature are not intrinsic to reducing the scale, but rather extrinsic effects due to strain or difficulties in producing high quality material.

In a closely related study, Chang et al. sliced thin sheets of both BaTiO3 and SrTiO3 from

bulk single crystals.107Using Pt contacts no dead layer was observed in the BaTiO3device, while

equivalent SrTiO3 structures did exhibit a dead layer. First principle calculations confirm this

(49)

3.3

Scaling effects in polycrystalline thin films

The body of work on nanoparticles and epitaxial thin films demonstrates that size effects can and do play a role, leading to decreases in and eventual elimination of ferroelectric properties. However, recent theoretical and experimental work has demonstrated that these effects can be avoided by a properly engineered system. Additionally these effects tend to dominate at length scaled below 40-50 nm, length scales not seen in most polycrystalline films. How this translates to polycrystalline systems with multiple grain and mechanical boundaries (both between BaTiO3

grains and the metalization layers) is unclear. In particular, poorly terminated or oriented grains at the metal interface may lead to dead layers that become important as films are made thinner.

The introduction of grain boundaries into films is expected to effect the dielectric properties in a manner similar to those in polycrystalline systems.40,71 However smaller device dimensions, limited thermal budgets, and substrate induced strains will greatly complicate understanding and engineering of these systems. As will become apparent, processing plays an underrated role in determining the final properties. Difficulty in processing these systems leads to misleading reports that confuse the discussion of scaling effects by confounding them with processing.

As a transition, the impact of a single grain boundary in epitaxial Pb(Zr0.45Ti0.55)O3 (PZT)

studied by Marincelet al.is reviewed.112PZT films were grown epitaxially on a SrTiO

3bi-crystal.

Away from the grain boundary films exhibited strong piezoelectric properties with well saturated hysteresis loops. However, within several hundred nm of the boundary the domain structure was changed, domain wall motion was pinned, and nonlinear response was diminished. This study serves as an example of the deleterious effect of grain boundaries.

3.3.1 The film-substrate system

In order to illustrate the various effects acting on thin film BaTiO3 systems, Figure 3.4 shows

Figure

Table 2.1Measured and predicted transition temperatures for the ferroelectric BaTiO3

Table 2.1Measured

and predicted transition temperatures for the ferroelectric BaTiO3 p.10
Figure 2.1:The crystal structure of BaTiO3 at room temperature. Ba (green) on the corners,Ti (blue) at the center, and O (red) on the faces.

Figure 2.1:The

crystal structure of BaTiO3 at room temperature. Ba (green) on the corners,Ti (blue) at the center, and O (red) on the faces. p.21
Table 2.1:Measured (Megaw) and predicted (Li) transition temperatures for the ferroelectricBaTiO3 phases.

Table 2.1:Measured

(Megaw) and predicted (Li) transition temperatures for the ferroelectricBaTiO3 phases. p.22
Figure 2.3: (Inset)Permittivity-temperature measurements of a BaTiO3 single crystal17 andthe inverse permittivity demonstrate Curie-Weiss behavior.

Figure 2.3:

(Inset)Permittivity-temperature measurements of a BaTiO3 single crystal17 andthe inverse permittivity demonstrate Curie-Weiss behavior. p.24
Figure 2.4:The resulting minimized phase and polarization magnitude and vector from an 8thorder expansion.

Figure 2.4:The

resulting minimized phase and polarization magnitude and vector from an 8thorder expansion. p.25
Figure 2.5:Charge distribution in AlAs (110) plane. Al (purple) are in plane while As (yellow)are below the plane

Figure 2.5:Charge

distribution in AlAs (110) plane. Al (purple) are in plane while As (yellow)are below the plane p.27
Figure 2.6:Schematic showing compensation of the depolarizing field by a) polarization gradient,b) surface screening charge, and c) domain wall formation.

Figure 2.6:Schematic

showing compensation of the depolarizing field by a) polarization gradient,b) surface screening charge, and c) domain wall formation. p.30
Figure 2.7:Schematic showing the mechanical distortion (exaggerated) at a 90◦ domain wall.

Figure 2.7:Schematic

showing the mechanical distortion (exaggerated) at a 90◦ domain wall. p.32
Figure 2.9:Example capacitance-voltage measurement of a ferroelectric. In the green (central)region, domain wall motion leads to large extrinsic contributions to permittivity, while thiscontribution is suppressed at higher fields (yellow)

Figure 2.9:Example

capacitance-voltage measurement of a ferroelectric. In the green (central)region, domain wall motion leads to large extrinsic contributions to permittivity, while thiscontribution is suppressed at higher fields (yellow) p.34
Table 4.1:Reported liquid phase systems and the temperature where densification was observed.

Table 4.1:Reported

liquid phase systems and the temperature where densification was observed. p.65
Table 4.2:Elements with their expected coordination, ionic radii, and reported occupancies inthe ABO3 perovskite structure of BaTiO3.

Table 4.2:Elements

with their expected coordination, ionic radii, and reported occupancies inthe ABO3 perovskite structure of BaTiO3. p.77
Table 4.3: Elements with their reported changes to the paraelectric-ferroelectric transitiontemperature

Table 4.3:

Elements with their reported changes to the paraelectric-ferroelectric transitiontemperature p.79
Figure 5.1:Phase diagram for the BaO-B2O3 system.279

Figure 5.1:Phase

diagram for the BaO-B2O3 system.279 p.82
Figure 5.4:XRD of BaTiO3 and a BBO target.

Figure 5.4:XRD

of BaTiO3 and a BBO target. p.84
Figure 5.5:Schematic of PLD system.

Figure 5.5:Schematic

of PLD system. p.86
Figure 5.6:Schematic of the interdigitated contacts used.

Figure 5.6:Schematic

of the interdigitated contacts used. p.88
Figure 6.1:TEM cross-sections of BaTiO3 films containing (a) 0%, (b) 1%, (c) 3% and (d) 5%barium borate flux

Figure 6.1:TEM

cross-sections of BaTiO3 films containing (a) 0%, (b) 1%, (c) 3% and (d) 5%barium borate flux p.93
Figure 6.3: (a-d) Capacitance-voltage curves show tunability is increased to 70% for samplesgrown from the 3% target, a strong indication of increased crystalline quality

Figure 6.3:

(a-d) Capacitance-voltage curves show tunability is increased to 70% for samplesgrown from the 3% target, a strong indication of increased crystalline quality p.97
Figure 6.4:sin2ψ analysis of the BaTiO3 (211) peak reveals residual in-plane tensile strain of0.15% confirming the shift seen in the capacitance-temperature measurements

Figure 6.4:sin2ψ

analysis of the BaTiO3 (211) peak reveals residual in-plane tensile strain of0.15% confirming the shift seen in the capacitance-temperature measurements p.99
Figure 7.1:SEM plan view images of etched films grown on a)c a-sapphire, b) r-sapphire, andc) c-sapphire

Figure 7.1:SEM

plan view images of etched films grown on a)c a-sapphire, b) r-sapphire, andc) c-sapphire p.107
Figure 7.2: Cumulative frequency distribution of grain sizes measured using linear interceptfrom SEM plan-view

Figure 7.2:

Cumulative frequency distribution of grain sizes measured using linear interceptfrom SEM plan-view p.108
Figure 7.3: Bragg-Brentano geometry x-ray diffraction scans for samples grown on a-, r-,and c-sapphire

Figure 7.3:

Bragg-Brentano geometry x-ray diffraction scans for samples grown on a-, r-,and c-sapphire p.109
Figure 7.4:TEM cross-sections for films grown on a) a-sapphire, b) r-sapphire, and c) c-sapphire.BaAl2O4 is outlined in white, and the relative volume fraction of second phase increases from a-to r- to c-plane.

Figure 7.4:TEM

cross-sections for films grown on a) a-sapphire, b) r-sapphire, and c) c-sapphire.BaAl2O4 is outlined in white, and the relative volume fraction of second phase increases from a-to r- to c-plane. p.111
Figure 7.5:SEM images showing films processed on c-sapphire with a) Ba6Ti17O40 buffer andb) (002)-BaAl2O4 buffer.

Figure 7.5:SEM

images showing films processed on c-sapphire with a) Ba6Ti17O40 buffer andb) (002)-BaAl2O4 buffer. p.114
Figure 7.8:Capacitance measurements as a function of temperature reveal similar behavior forfilms on all substrates; however, those on c-sapphire exhibit significantly lower capacitance.

Figure 7.8:Capacitance

measurements as a function of temperature reveal similar behavior forfilms on all substrates; however, those on c-sapphire exhibit significantly lower capacitance. p.117
Figure 8.2:XRD patterns of BaTiO3 on c-sapphire annealed at 900 ◦C with CuO and CuO +BBO additions

Figure 8.2:XRD

patterns of BaTiO3 on c-sapphire annealed at 900 ◦C with CuO and CuO +BBO additions p.125
Figure 8.3:SEM plan-view micrographs of pure BaTiO3 + BBO on a) 100 nm, b) 1 nm, and c)0 nm of Cuo annealed at 900 ◦C on c-sapphire

Figure 8.3:SEM

plan-view micrographs of pure BaTiO3 + BBO on a) 100 nm, b) 1 nm, and c)0 nm of Cuo annealed at 900 ◦C on c-sapphire p.127
Figure 8.6:Capacitance-voltage measurements of a) BaTiO3 + 8 nm CuO and b) BaTiO3 + 8nm CuO + BaO-B2O3 films after aging for 2 months at ambient conditions (Aged), and afterde-aging at 250 ◦C for 30 minutes (Thermal) or 1000 cycles of ±35 V (E-field).

Figure 8.6:Capacitance-voltage

measurements of a) BaTiO3 + 8 nm CuO and b) BaTiO3 + 8nm CuO + BaO-B2O3 films after aging for 2 months at ambient conditions (Aged), and afterde-aging at 250 ◦C for 30 minutes (Thermal) or 1000 cycles of ±35 V (E-field). p.130
Figure 8.8:SEM plan-view micrographs of BaTiO3 + 8 nm CuO + BBO on MgO and annealedat 900 ◦C showing second phase.

Figure 8.8:SEM

plan-view micrographs of BaTiO3 + 8 nm CuO + BBO on MgO and annealedat 900 ◦C showing second phase. p.133
Figure 8.9:XRD patterns of BaTiO3 on MgO annealed at 900 ◦C with CuO and CuO + BBOadditions.

Figure 8.9:XRD

patterns of BaTiO3 on MgO annealed at 900 ◦C with CuO and CuO + BBOadditions. p.134

References