University of Southern California Dissertations and Theses

Phase change heterostructures for electronic and photonic applications

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Phase change heterostructures for electronic and photonic applications

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Content Copyright 2022 Yang Liu

Phase Change Heterostructures for Electronic and Photonic Applications

by

Yang Liu

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATERIALS SCIENCE)

August 2022
ii
Acknowledgments
I enjoyed doing my Ph.D. at the University of Southern California, which I got to know as a
place with excellent opportunities and origination of creative ideas and thinking. Not only because
of the good facilities and creative and beautiful environment, but mainly because of the great
people whom I worked with made the research atmosphere inspiring and motivating. Their insights,
openness, and willingness to share their knowledge helped me a lot throughout my Ph.D. I really
wish to have spent more time on campus and especially in the lab with those great people.
First, I would like to thank my advisor, Professor Jayakanth Ravichandran for his continued
support and guidance over the past six years. In particular, he is the one, who scientifically guided
me through the world of epitaxy and opened so many doors for me. I appreciate his trust in my
work from the beginning and for always backing me up in any situation. I would like to thank my
thesis committee, Prof. Andrea Armani, Prof. Paulo Branicio, Prof. Aiichiro Nakano, and Prof.
Han Wang for taking the time to critically evaluate this dissertation.
I would like to thank the current and former members of the Ravichandran group for their
support over the years. I would like to especially thank Dr. Shanyuan Niu, Dr. Thomas Orvis,
Huandong Chen, Boyang Zhao, Mythili Surendran, and Harish Kumarasubramanian for all the
insightful brainstorms and ideas they shared with me over the years. This work cannot be finished
without your help in all aspects. Many thanks also to Prof. Han Wang and Zhonghao Du for the
collaborations in the oscillator measurements.
There are numerous people outside USC, whom I share the credit for my work with: Prof.
Darrell Schlom and Dr. Zhe Wang for providing the high-quality SrTiO3/Si substrates for the film
iii
growth, Chirag Garg for the early inputs for the oscillator theoretical work. Prof. Asif Khan and
his student Zheng Wang for their quick and brilliant ferroelectric investigations, Prof. Rohan
Mishra and his student Guodong Ren for DFT calculations, and Dr. Arashdeep Thind for the
excellent STEM measurements.
Lastly, I am most thankful to and for my wife Hongmei Guo. Her comfort and company help
me while I was struggling with my research and manuscript. Special thanks to my parents for
endless support throughout my life. Thank you very much!

iv
Table of Contents
Acknowledgments ......................................................................................................................................... ii
List of Tables .............................................................................................................................................. vii
List of Figures ............................................................................................................................................ viii
Abbreviations .............................................................................................................................................. xv
Abstract ..................................................................................................................................................... xvii
Chapter 1. Introduction .................................................................................................................... 1
1.1 Information Age: History and Challenges ..................................................................... 1
1.2 Photonic solution ............................................................................................................ 3
1.2.1 Electro-optic effect ......................................................................................................... 5
1.2.2 Ferroelectric to paraelectric phase transition ................................................................. 7
1.2.3 Propagation loss ........................................................................................................... 10
1.3 Electronic solution ....................................................................................................... 12
1.3.1 Von Neumann vs. Neuromorphic ................................................................................ 13
1.3.2 Oscillatory Neural Network ......................................................................................... 16
1.3.3 Metal-to-Insulator Transition ....................................................................................... 17
Chapter 2. Experimental Methods and Background ...................................................................... 21
2.1 Materials Synthesis ...................................................................................................... 21
2.1.1 Epitaxy ......................................................................................................................... 21
2.1.2 Pulsed Laser Deposition ............................................................................................... 24
2.1.3 Growth Process and Growth Mode .............................................................................. 26
2.2 In Situ Characterization ................................................................................................ 29
2.2.1 Reflection High Energy Electron Diffraction .............................................................. 29
2.3 Ex Situ Characterization ............................................................................................... 31
2.3.1 X-ray Diffraction .......................................................................................................... 31
2.3.2 Atomic Force Microscopy ............................................................................................ 33
2.3.3 Piezo-response Force Microscopy ............................................................................... 34
2.3.4 Transmission Electron Microscopy .............................................................................. 36
2.3.5 Raman Spectroscopy .................................................................................................... 38
Chapter 3. Theoretical Investigation of High electro-optical Materials ........................................ 39
3.1 Background .................................................................................................................. 39
3.2 Method ......................................................................................................................... 42
3.2.1 First-Principles Density-Functional Theory ................................................................. 42
3.2.2 Landau-Devonshire Model ........................................................................................... 43
3.3 Electro-optic Tensor of BaTiO 3 ................................................................................... 44
v
3.4 Model Fitting and Parameters ...................................................................................... 47
3.5 Electro-optic Coefficients of BaTiO 3 ........................................................................... 52
3.6 Factors Affecting the Electro-optic Coefficient ........................................................... 53
3.6.1 Temperature Dependence ............................................................................................. 53
3.6.2 Strain Dependence ....................................................................................................... 55
3.6.3 Modulating Frequency Dependence............................................................................. 56
3.7 Discussion .................................................................................................................... 59
3.7.1 EO Coefficient Prediction of BCZT-50 ....................................................................... 68
3.8 Summary ...................................................................................................................... 69
Chapter 4. Epitaxial Growth of the Electro-optic Thin Film ......................................................... 71
4.1 Background .................................................................................................................. 71
4.2 Epitaxial Growth of Barium Calcium Titanium Zirconium Oxide Thin Film ............. 72
4.2.1 Substrate Selection ....................................................................................................... 72
4.2.2 Effect of Growth Temperature ..................................................................................... 73
4.2.3 Effect of Growth Pressure ............................................................................................ 74
4.2.4 Effect of Cooling Rate ................................................................................................. 75
4.2.5 Effect of Interlayer – SrRuO 3 ....................................................................................... 77
4.3 Surface Characterization of Barium Calcium Titanium Zirconium Oxide Thin Film . 78
4.4 Structural Characterization and Strain Analysis of the Thin Films .............................. 80
4.5 Ferroelectricity and Piezoelectricity Response ............................................................ 85
4.6 Summary ...................................................................................................................... 87
Chapter 5. Electro-optic thin film integration on silicon platform ................................................ 89
5.1 Background .................................................................................................................. 89
5.1.1 Epitaxial Growth of Strontium Titanate on Silicon ..................................................... 90
5.2 Epitaxial Growth of Barium Calcium Titanium Zirconium Oxide on Strontium
Titanate/Silicon Substrate ................................................................................................................... 92
5.3 Alternative Methods of Transfer BCZT Films to Silicon Substrate ............................ 95
5.4 Summary .................................................................................................................... 100
Chapter 6. Modeling of Low-Power and High-Frequency Phase Change Electronic Oscillators102
6.1 Background ................................................................................................................ 102
6.1.1 State-of-the-Art Phase Change Oscillator Devices .................................................... 102
6.2 Theoretical Framework .............................................................................................. 105
6.2.1 The Resistivity Fitting of VO 2 ................................................................................... 105
6.2.2 Device Structure ......................................................................................................... 106
6.2.3 Conservation of Heat.................................................................................................. 107
6.3 Operating Mechanism ................................................................................................ 112
6.4 Factors Influencing the Operation of the Oscillator ................................................... 116
6.4.1 Interfacial Thermal Conductivity ............................................................................... 116
6.4.2 Current and Capacitance ............................................................................................ 117
6.4.3 Effective Volume ....................................................................................................... 118
6.5 Discussion .................................................................................................................. 120
vi
6.6 Summary .................................................................................................................... 122
Chapter 7. Fabrication and Characterization of the Epitaxial SrRuO 3/ VO 2 Heterostructure ...... 124
7.1 Background ................................................................................................................ 124
7.2 Epitaxial Growth of Vanadium Dioxide on (111)-Oriented Perovskite Substrates ... 127
7.2.1 Thin Film Growth ...................................................................................................... 127
7.3 Characterization of Vanadium Dioxide Thin Films ................................................... 127
7.4 Oscillator Characteristics of the Vanadium Dioxide/Strontium Ruthanate Bilayer
Devices 136
7.4.1 Geometry of the Devices ............................................................................................ 136
7.4.2 I-V and Oscillator Characteristics .............................................................................. 137
7.4.3 Applied Current and Tuning of Capacitance .............................................................. 139
7.4.4 Footprint Effect .......................................................................................................... 140
7.5 Summary .................................................................................................................... 141
Chapter 8. Conclusion and Outlook ............................................................................................. 143
Bibliography ............................................................................................................................................. 147
Appendix A ............................................................................................................................................... 166

vii
List of Tables
Table 1 Typical growth parameters used in the experiments. ...................................................... 26
Table 2 Extracted Landau-Devonshire coefficients from the DFT calculated free energy
curves. ............................................................................................................................... 52
Table 3 physical properties summary of ABO3 ferroelectrics. Ps in the unit of C/m
2
and r in
the unit of pm/V ................................................................................................................ 62
Table 4 Physical properties of the BCZT-50 from experiments. (Ref. 50, 173, 188-192) ........... 68
Table 5 Electrical and thermal properties of the materials used in the simulation. .................... 107
Table 6 Simulation data of the maximum frequencies of VO2/SRO bilayer oscillators
depending on the channel size. The current I0 and capacitance Ca is corresponding to
the values optimized for max. frequencies (fmax). The electrical time constant 𝜏𝑒 is
estimated by the Equation 5.6 ......................................................................................... 120
Table 7 Estimation of electrical time constant 𝜏𝑒 and thermal time constant 𝜏𝑡 ℎ for the
VO2/SRO bilayer devices with various channel length L. The estimated frequency 𝑓𝑒𝑠
is calculated by inversion of the lowest time constant which is the 𝜏𝑡 ℎ𝑉𝑂 2−𝑆𝑇𝑂 for
this case. The deviation from the optimized fmax is also listed. ...................................... 121
Table 8 Comparison of the observed Raman modes and the nature of these modes with the
reference report. .............................................................................................................. 134
Table 9 Optimized electrical oscillation frequency summary of various footprints. .................. 141
Table 10 Landau coefficients summary of ABO3 materials ....................................................... 173

viii
List of Figures
Figure 1.1 Comparison of literature values for (a) the linear electro-optic coefficient and (b)
dielectric constant in bulk crystals for various material system. SiO2: Ref. 29, ZnO:
Ref. 32, Strained Si: Ref. 30, LiNbO3, BaTiO3 and PZT: Ref. 29, BCZT: Ref. 47. .......... 6
Figure 1.2 Characteristic P-E hysteresis loop of a ferroelectric material. The Ps is the
spontaneous polarization and Ec is the coercive field ........................................................ 7
Figure 1.3 Ideal cubic perovskite structure ABO3. “A” cation occupies corner sites, “B” cation
occupies cube center, and O anion occupies face centers, forming a BO6 octahedra. ....... 8
Figure 1.4 (a) The schematic of Von Neuman architecture (Adopted from [66]] and (b) a
schematic of a biological neuron network. (Adopted from [67]) ..................................... 13
Figure 1.5 (Top) A schematic atomic model of low temperature monoclinic and high
temperature tetragonal Rutile phases. (Bottom) A schematic of the metal-insulator
transition behavior. The phase change shows hysteretic behavior, and, within this
region, we expect to have phase co-existence. ................................................................. 18
Figure 2.1 Schematic illustration of lattice matched, strained, and relaxed heteroepitaxial
structures. .......................................................................................................................... 22
Figure 2.2 A illustration of a pulsed laser deposition chamber .................................................... 24
Figure 2.3 The picture of experiment set up of (a) pulsed laser deposition chamber and (b) the
KrF excimer laser. Picture credit: Ravichandran group. .................................................. 25
Figure 2.4 A Growth model of the thin film ................................................................................. 27
Figure 2.5 RHEED pattern examples of (a) 2D streak pattern, (b) 2D diffraction pattern when
the coherence is maintained on both directions in-plane, (c) 3D pattern. ........................ 29
Figure 2.6 A illustration of the mechanism and physical setup for the X-ray diffraction ............ 31
Figure 2.7 Schematic diagram for DART. (a) The experimental set-up. (b) Principle of the
dual-frequency excitation. Adopt from Ref 102. .............................................................. 35
Figure 2.8 Illustration of the principles for imaging in (left) TEM and (right) STEM. Image
credit: Edna Vargas in the presentation of “Contrast in TEM and STEM”. .................... 37
Figure 3.1 Change with temperature of the structure and dielectric constant of a BaTiO3 crystal.
The schematics of Ti displacement and the corresponding spontaneous polarization
direction is indicated by the blue arrows. (Adopted from ref. [158]) ............................... 49
Figure 3.2 Energy density as a function of polarization along (a) [001], (b) [011], and (c) [111]
directions in BaTiO3 obtained using DFT calculations. ................................................... 50
Figure 3.3 Theoretical and experimental electro-optic coefficients of tetragonal BaTiO3, a:
Ref. 168, b. Ref. 151 ......................................................................................................... 52
Figure 3.4 Temperature dependence of electro-optic coefficients in BaTiO3. a: Ref. 135, b:
Ref. 171 ............................................................................................................................ 54
ix
Figure 3.5 Evolution of EO coefficients (a) 𝑟 33, (b) 𝑟 42, (c) 𝑟 13 with misfit strain for
BaTiO
3
. The EO coefficients calculated from LD and DFPT are indicated with solid
lines and dotted lines with marker. The blue region and yellow region, respectively,
represent orthorhombic (O) and tetragonal (T) phase. The misfit strain imposed on
coherently strained BaTiO3 films grown on SrTiO3 and GdScO3 substrates are marked
to identify the potentially achievable EO coefficients in strained thin films. .................. 55
Figure 3.6 The electro-optic coefficient r33 of tetragonal BaTiO3 dependence on the frequency
of modulating electric field ranging from 1Hz to 100 THz. The simulation result of
this work is shown as solid line with open circle marker in green and experimental
results from different references are represented by corresponding markers in red. a:
Ref. 116, b: Ref. 180, c: Ref. 125, d: Ref. 123, e. Ref. 122, f: Ref. 175, g: Ref. 179 ...... 57
Figure 3.7(a) The dimensionless Landau energy density with respect to the polarization. The
dependence of dielectric permittivity (b) and spontaneous polarization (c) on the
coefficient a1. The value of a1 in the figure a is +1, 0, and 1. The other fourth and sixth
order parameters are normalized to 1. .............................................................................. 59
Figure 3.8 The plot of effective electro-optic coefficient against the spontaneous polarization.
The simulated materials are indicated by different colors. The values calculated from
first-principle calculation in this work is marked as circles and others values calculated
from Landau coeffcients adopted from literatures are marked as squares, triangle and
hexagonal to refer to different sources. The used Landau coefficients are listed in
Table 10 in Appendix A ................................................................................................... 63
Figure 3.9 Ball stick model of a BaTiO3 spontaneous polarization in the direction of up and
down. The origin of spontaneous polarization is the off center displacement of Ti
4+
at
the center of oxygen octahadral. The arrows indicate the displacement direction which
is opposite to the spontaneous polarization direction. ...................................................... 64
Figure 3.10 The plot of effective electro-optic coefficient against the well depth. The
simulated materials are indicated by different colors. The values calculated from first-
principles calculation in this work is marked with circle and others values calculated
from Landau coeffcients adopted from literatures are marked with square, triangle and
hexagonal to refer to different sources. The used Landau coefficients are listed in
Table 10 in Appendix A ................................................................................................... 66
Figure 3.11 Energy profile evolution as a function of volume fraction L of the ferroelectric
content in the alloy of ferroelectric-paraelectric. .............................................................. 67
Figure 4.1 Illustration of the range of commercially available single crystalline substrate
lattice constants and film lattice constants. Abbreviations: LSAT:
[LaAlO3]0.3[Sr2AlTaO6]0.7. LMSO: La0.7Sr0.3MnO3, BCZT-50: Ba(Zr0.2Ti0.8)O3 – 0.5
(Ba0.7Ca0.3)TiO3 ................................................................................................................ 72
x
Figure 4.2 (a) High resolution, short angular-range XRD plot of BCZT-50 film grown at 650,
750, 800, and 850° C. The dashed lines indicate the position of fully strained and
relaxed BCZT-50, GdScO3 (GSO) 220, and SrRuO3 (SRO) 220 reflections. (b)
Variation of out of plane lattice spacing of the BCZT-50 thin film with the deposition
temperature. (c) Evolution of the full width at half maximum values of rocking curve
with the deposition temperature. ...................................................................................... 73
Figure 4.3 (a) Out of plane XRD plot of BCZT-50 film grown at 1, 10, 20, and 50 mTorr of
oxygen pressure. The dash lines indicate the position of fully strained and relaxed
BCZT-50, GdScO3 (GSO) 220, and SrRuO3 (SRO) 220 reflections. (b) The variation
of full-width at half-maximum values of rocking curve with the oxygen partial
pressure in the deposition chamber. ................................................................................. 75
Figure 4.4 Short angular XRD scans of BCZT on GdScO3 samples with a cooling rate at
10℃/min and (b) 5℃/min. (c) The typical RHEED oscillations for BCZT film directly
grown on GdScO3 substrate. Up to 50 oscillations have been observed. Insert pictures
are the RHEED patterns of GdScO3 substrate and as grown BCZT film at 750 ℃ and
10 mTorr. The abrupt increase and decrease in the RHEED intensity pointed by arrow
is due to manual adjustment of the incident electron beam intensity. .............................. 76
Figure 4.5 High resolution short angular XRD plot of (a) BCZT(100 nm) on GdScO3 and (b)
BCZT (100 nm) / SRO (15 nm) on GdScO3). The thickness fringes are shown near the
002 BCZT diffraction peak for samples with SrRuO3 as bottom electrode. .................... 77
Figure 4.6 Representative reflection high energy electron diffraction patterns of: (a) GdScO3
(GSO) substrate, (b) SrRuO3 (SRO) bottom electrode, and (c) BCZT-50 film. (d)
Specular spot intensity oscillations of SrRuO3 and BCZT-50 film. ................................. 79
Figure 4.7 Representative topography image of (a) annealed GdScO3 substrate, (b) SrRuO3
film, and (c) BCZT-50 film surface. (d) Cross-sectional profile of BCZT-50 film
showing the step height. The distance between two horizontal guidelines is 4 Å, which
corresponds to the lattice spacing expected in single-layer-step. ..................................... 80
Figure 4.8 (a) XRD plot of a representative BCZT-50 thin film. (b) A high-resolution
reciprocal space map of BCZT-50 thin film centered on GdScO3 332 substrate peak.
The map clearly shows the film is coherently strained to the substrate. .......................... 81
Figure 4.9 Short angular range XRD plot of BCZT thin film with thickness of 20 nm, 50 nm,
80nm, 100nm and 200 nm. ............................................................................................... 82
Figure 4.10 Reciprocal space map of (a) 50 nm (b) 100 nm and (c) 200 nm films. The black x
marks indicate the reflection position of the fully strained film and red x mark
indicates the fully relaxed reciprocal lattice constant position. ........................................ 82
Figure 4.11 (a) Cross-sectional low-magnification HAADF image of a
BCZT/SrRuO3/GdScO3 sample. No obvious misfit dislocations were observed in
BCZT thin film. Atomic resolution HAADF images of (b) BCZT/SrRuO 3 and (c)
xi
SrRuO3/GdScO3 interfaces with overlaid atomic models. The brown, blue, green, grey,
purple, and pink atomic symbols correspond to (Ba, Ca), (Ti, Zr), Sr, Ru, Gd and, Sc
elements, respectively. ...................................................................................................... 83
Figure 4.12 Strain analysis of the HAADF image of the BCZT/SRO/GSO sample. The 𝜀𝑥𝑥
and 𝜀𝑦𝑦 are the strain in the lateral and horizontal directions which refer to the lattice
parameters measured in the red square box in the HAADF image. ................................. 84
Figure 4.13 (a) Dielectric constant and (b) impedance angle as a function of DC electric field
at room temperature (solid line and dash line indicate the scans with increasing and
decreasing electric fields) and (c) ferroelectric hysteresis loop of a typical BCZT-50
film. Dash line indicates the build-in electric field. The blue and red lines correspond
to sweeps starting with positive and negative applied electric fields. .............................. 85
Figure 4.14 PFM responses of a BCZT film. (a) the phase and (b) amplitude plot as a function
of electric field. The box-in-box pattern is shown in terms of (c) phase and (d)
amplitude. The corresponding film thickness is 100 nm for this measurement. .............. 86
Figure 5.1 schematic of epitaxial growth of SrTiO3 on Si, summarized from Ref. 119............... 91
Figure 5.2 (a) RHEED patterns at various stages during the growth process of 200 nm BCZT-
50 Film. (b) The intensity of specular spot for BCZT-50 grown on SrRuO3/SrTiO3/Si.
(c) the topography of as-grown BCZT film measured by AFM. The RSM roughness
is 0.4 nm. .......................................................................................................................... 92
Figure 5.3 (a) High resolution, wide angular-range XRD plot of a BCZT-50 film grown on
SRO/STO/Si substrate. The peaks are indexed correspondingly above. The inserted
figure is the short angular-range XRD scan of the film in 40-50 degrees of 2-theta. (b)
the rocking curve scans of BCZT 002 on Si (red line) and on GSO (blue line) 2-theta
peak at 44.7º . The full width at half maximum is 0.205 º and 0.02º for BCZT films on
Si and GSO respectively. .................................................................................................. 94
Figure 5.4 Piezoelectric response of the BCZT50 films on STO/Si substrate. The result of
typical measurements of (a) amplitude and (b) phase signal. ........................................... 95
Figure 5.5 Schematic for epitaxial growth and epitaxial transfer of BCZT thin films to silicon
substrate ............................................................................................................................ 96
Figure 5.6 XRD scan of BCZT film (a) before transfer and (b) after transfer. Each reflection
is indexed with corresponding material. The inserts on the right are the short-angle
XRD scan for 42-49° around the most intense 002 reflection of BCZT. ......................... 98
Figure 5.7 (a) The PFM set up for the BCZT film. The box-in-box pattern is shown in terms
of (b) phase and (c) amplitude. PFM responses of transferred BCZT films. (d) the
amplitude, (e) phase as a function of field. The corresponding film thickness is 100
nm for this measurement. The piezo-response hysteresis loop shown in the phase
indicates a relaxer ferroelectric of BCZT-50 films. ......................................................... 99
xii
Figure 6.1 The resistivity-temperature relationship of VO2. Different transition temperature
is used to differentiate the heating and cooling cycle for first-order phase transition. ... 105
Figure 6.2 The illustration of device structure of (a) VO2 and (b) VO2/SrRuO3 oscillators. ..... 106
Figure 6.3 Temperature profile of typical (a) VO2 and (b) VO2/SRO devices near transition
temperature. The thickness of VO2 layers presented here are 30 nm for both devices.
The SrRuO3 (SRO) thickness is 25 nm for the illustration purpose. .............................. 108
Figure 6.4 Turn-on and turn-off transient at a step voltage input. The comparison of VO2 and
VO2/SRO device of (a) (b) input voltage, (c) (d) average temperature in between the
metal electrodes, and (e) (f) total current across the device, respectively. ..................... 109
Figure 6.5 Voltage forward and backward scan of (a-f) VO2 and (g-l) VO2/SRO devices. (a)
and (g) The applied step voltage to the 30 nm thick VO2 device and 5 nm SrRuO3 /
30nm VO2 bilayer device. The time step is 20ms which could be considered as steady-
state simulation condition. The time domain evolutions of (b) (h) the temperature at
the VO2 layer top surface and (c) (i) corresponding overall resistance of device.
Distinctive two state of VO2 could be observed. (d) (j) characteristic I-V loop and (e)
(k) corresponding temperature and (f) (l) overall resistance as a function of applied
voltage. ........................................................................................................................... 110
Figure 6.6 Circuit schematic for a VO2 -based oscillator. The I0 is applied current delivered
by a current source. The VO2 based device is paralleled with a capacitance. The
voltage oscillation V could be detected by an oscilloscope. .......................................... 112
Figure 6.7 Simulation algorithm of thermoelectrical model of VO2 based oscillator. ............... 112
Figure 6.8 Operation mechanism of the VO2 oscillator. (a) Time-evolution of temperature and
voltage of the VO2 channel for the highest achievable frequency of 20 MHz; the
parallel capacitance used in this simulation is 4 pF and driving current is 0.73 mA.
The operating stage is denoted as A, B, C, and D. (b) Simulated I-V characteristic
curve for an oscillation period corresponding to (a). The four stages of operation of
the oscillation are charging, heating, discharging, and cooling. The A and C points are
the lowest and highest voltage position corresponding to the onset of changing and
discharging stage. The B and D are the transition points of min. and max. temperature
corresponding to the heating and cooling stage, respectively. ....................................... 113
Figure 6.9 Operation mechanism of the VO2/SRO oscillator. (a) Time-evolution of
temperature and voltage for the unoptimized device shows a frequency of 40 MHz;
the simulation condition is used as the same as the previous VO2 device simulation,
I=0.9 mA and C=4 pF. The operating stage is denoted as A, B, C, and D. The four
stages of operation of the oscillation are charging, heating, discharging, and cooling.
The A and C points are the lowest and highest voltage position corresponding to the
onset of changing and discharging stage. The B and D are the transition points of min.
xiii
and max. temperature corresponding to the heating and cooling stage, respectively. (b)
Simulated I-V characteristic curve for an oscillation period corresponding to (a). ....... 115
Figure 6.10 A schematic to demonstrate the heat flow considered in the theoretical model. .... 116
Figure 6.11 Oscillation evolution regarding the interfacial thermal conductivity (ITC). The
ITCs used for the simulation that shows sustain oscillation are 2x10
8
W/m
2
K and
1x10
8
W/m
2
K for SrRuO3/VO2 and VO2/SrTiO3 interface. The ITCs for the damping
oscillation and no oscillation are half and one tenth of that for sustain oscillation. ....... 117
Figure 6.12 The oscillation frequency dependence on applied current and parallel capacitance
map of (a) VO2 and (b) VO2/SRO device. Only the oscillation frequency above 1 MHz
have been shown in the figure. ....................................................................................... 118
Figure 6.13(a) The transition voltage and (b) the optimized frequency as a function of channel
length (L). The yellow marked region refers to the voltage that could generate sustain
oscillation. The insert is the schematic for the channel length. M refers to the metal
contacts. The thicknesses of SrRuO3 (SRO) and VO2 are 5 nm and 30nm, respectively.
........................................................................................................................................ 119
Figure 7.1 V-O phase diagram showing VO2, V2O3 V2O5, Magné li series, VnO2n+1, and the
Wadsley series, VnO2n-1. (Taken from Ref 263) .............................................................. 124
Figure 7.2 Crystal structure illustrations of (a) monoclinic VO2 (010), (b) rutile TiO2 (010),
(c) LSAT (111) and (d) SrTiO3 (111). ............................................................................ 126
Figure 7.3 RHEED diffraction pattern for (a) LSAT, (b) rutile VO2 [100], (c) STO, and (d)
rutile VO2 [001] at 500 C. The primary diffraction spots for VO2 have been indexed
according to the rutile structure symmetry. .................................................................... 128
Figure 7.4 (a). High resolution 2θ-θ XRD pattern of VO2 thin film on LSAT substrate. (b).
Off-axis φ scan of VO2 110 and LSAT 022. .................................................................. 129
Figure 7.5 Thickness dependent (a). 2θ-θ XRD patterns and (b). X-ray reflectivity (XRR) of
VO2 thin film on LSAT substrate and (c) STO substrate. Simulation curves fitting to
XRR data is shown as black line. ................................................................................... 130
Figure 7.6 AFM topography image of (a). annealed LSAT surface, (b). 17 nm, (c). 31 nm, (d).
63 nm as-grown VO2 surface (e). annealed STO surface, and 60nm as-grown VO2
surface. ............................................................................................................................ 131
Figure 7.7 Raman spectra of VO2 thin film on LSAT substrate and LSAT substrate measured
at 350 K (HT) and room temperature (RT) respectively. The 11 Raman active modes
from room temperature VO2 are highlighted by grey triangles. ..................................... 132
Figure 7.8 Temperature-resistivity characteristics for VO2 thin films. (a) Temperature
dependent four probe resistivity of 30, 50, and 100 nm VO2 films on LSAT (111). (b)
Comparison of four probe resistivity of 100 nm VO2 on LSAT and STO substrate. (c)
Four probe resistivity of 30 nm VO2 and 5 nm SRO / 30 nm VO2 bilayer on STO
substrate. ......................................................................................................................... 135
xiv
Figure 7.9 Device structure illustration and photos. (a) the 3D device structure for a 30 nm
VO2 and 5 nm SRO on SrTiO3. Top view photos of (b) head-to-head geometry and (c)
overlap geometry of the Au/Ti electrodes. ..................................................................... 136
Figure 7.10 I-V characteristic scan of (a) VO2 and (b) SRO/VO2 device. A current compliance
of 7 mA has been applied to prevent failure of the SRO/VO2 device. ........................... 137
Figure 7.11 Typical oscillation waveforms for (a) VO2 and (b) SRO/VO2 devices operating at
0.3 mA with a parallel capacitor of 200 nF. ................................................................... 137
Figure 7.12 (a) Characteristic current vs. voltage loop of a head-to-head device with 1 μm x 1
μm dimension, obtained sourcing a current and measuring the voltage for the blue line
and sourcing voltage and measuring current for the yellow line. (b) oscillation
waveform obtains at 1.0 mA applied current and 560 pF parallel capacitor. ................. 138
Figure 7.13 (a) The effect of the oscillation frequency on parallel capacitance for a 1 μm x 1
μm VO2/SRO device. The variation of frequencies under constant parallel capacitance
is due to measurements carried out at different applied current. (b) The dependence of
the electrical oscillation frequency on applied current which is measured with a
capacitance of 1.08 nF. ................................................................................................... 140

xv
Abbreviations
AFM Atomic force microscopy
BCZT-50 or BCZT 0.5 Ba(Zr0.2Ti0.8)O3 – 0.5 (Ba0.7Ca0.3)TiO3
BTO BaTiO3
CMOS Complementary Metal Oxide Semiconductor
CPU Central processing unit
DFT Density-functional theory
DI De-ionized
EO Electro-optic
FET Field-effect transistor
FWHM Full-width at half-maximum
GGA Generalized gradient approximation
GSO GdScO3
HAADF High-angle annular dark-field
HRS High resistant state
HRTEM High resolution transmission electron microscopy
HT High temperature
IMT Insulator-to-metal
LD Landau-Devonshire
LDA Local density approximation
LRS Low resistant state
LSMO (La,Sr)MnO3
MIT Metal-to-insulator transition
xvi
PAW Projector augmented-wave
PBE Perdew-Burke-Ernzerhof
PDMS Polydimethylsiloxane
PLD Pulsed laser deposition
Ps Spontaneous polarization
PVD Physical vapor deposition
RHEED Reflection high energy electron diffraction
RMS Root mean square
RSM Reciprocal space mapping
RT Room temperature
Si
SRO
Silicon
SrRuO3
STEM Scanning transmission electron microscopy
TDGL Time-dependent Ginzburg-Landau
TEM Transmission electron microscopy
VASP Vienna Ab-initio Simulation Package
XRD X-ray diffraction
xvii
Abstract

Phase Change Heterostructures for Electronic and Photonic Applications
by
Yang Liu
Doctor of Philosophy in Materials Science
University of Southern California

Dr. Jayakanth Ravichandran, Chair

Our modern information age and its exponential growth in the use of computing and
communication is prompted by the continuous increase in the number of transistors packed in a
unit area. As transistor feature size approaching the physical limits, it is obvious that room for
future miniaturization has run out. Further, it is unclear whether the current computing and
communication methods are the most efficient in solving emerging needs such as associative
learning. Particularly, there is a need to develop novel hardware capabilities that can be more
effective in solving such problems. As materials underpin the development of most hardware
technologies, it is necessary to discover and develop novel materials to solve such problems. In
this thesis, I address two important materials problems that are critical for next generation
computing and communication technologies. First, I address the modeling of electro-optic
materials with large coefficients and their integration to Silicon photonics platform to achieve
high-speed communication, and the other is the development of alternative computing
architectures such as neuromorphic computing to minimize energy consumption without
sacrificing computing speed.
xviii
Ferroelectric oxides often possess not only large dielectric constants but also electro-optic
responses leveraging the abrupt polarization switching arising from the broken symmetry. A
theoretical pathway for finding ferroelectric oxide materials with large electro-optic (EO) response
has been investigated using the model of Landau-Devonshire phenomenological theory with input
from first-principles density functional theory. The model is first applied to a paradigmatic oxide,
BaTiO3, and find that the predicted electro-optic constants agree well with the experimental results.
The agreement of the temperature dependence of the electro-optic coefficients with the results
from other models also demonstrates the efficacy of the model. Besides, the frequency- and strain-
dependence of the EO response are also established. The model is then applied to six well-known
ferroelectric ABO3-type materials and find that the spontaneous polarization of ferroelectric
materials and well depth in the free energy profile are the keys to designing a material with giant
electro-optic responses. Based on the matrix of spontaneous polarization and the well depth, a
material, 0.5 Ba(Zr0.2Ti0.8)O3 – 0.5 (Ba0.7Ca0.3)TiO3 (BCZT-50), with smaller Ps and well depth
comes into view, and we predict electro-optic coefficients as high as 1880 pm/V for r42 and 399
pm/V for r33 for experimental validation.
High-quality BCZT-50 thin films with atomically flat surface have been epitaxially grown on
single crystalline GdScO3 substrate by pulsed laser deposition. Growth conditions have been
carefully studied with the effect on the crystalline quality and surface condition. With the
optimized growth condition, sustained layer-by-layer growth of up to 100 unit cells has been
observed. Atomic force microscopy investigations show atomically smooth step terrace
morphonology. Transmission electron microscopy results reveal good epitaxial relation between
xix
the film and the substrate without any line defects. High dielectric constant (~1400) and slim
hysteresis loops in polarization-electric field characteristics were observed in BCZT-50 films,
which are characteristic of relaxor-type ferroelectric materials.
Integration to the silicon platform is a critical requirement for the utilization of the EO
materials. Direct deposition and indirect transfer methods are explored in this work. Epitaxial
growth of BCZT-50 films on silicon substrate is performed using thin SrTiO3 as a buffer layer.
The growth results show a similar quality to that of GdScO3 with better lattice matching with
BCZT-50. The preferred orientation of the film is along the c-axis of BCZT-50. The piezoelectric
response is measured to confirm the relaxor-type ferroelectric behavior. Free-standing BCZT-50
films that could be transferred to Si substrate were attempted as an alternative process with a
sacrificial thin layer of (La,Sr)MnO3. The switching behavior of the transferred film was observed
in the piezoelectric force microscopy measurements.
Another aspect of the thesis focuses on VO2, which possesses a reversible metal-to-insulator
transition. This makes it an excellent candidate to realize electrical oscillators for next generation
electronic applications such as hardware implementation of oscillatory neural networks.
Theoretical models based on thermal and electrical transport have been established to understand
the mechanism of VO2-based oscillators operating under the application of constant current. Here,
a bilayer structure of VO2 and SrRuO3 that could potentially have high maximum frequency with
lower power consumption is proposed. The simulation results show high tunability and predict a
high-frequency oscillator could be built with a 100 nm size device. Experiments were carried out
to validate our simulation results. Epitaxial growth of VO2 and VO2/SRO bilayer devices have
xx
been grown on epitaxial oxide substrates. I carefully investigated the structural and surface quality
of the VO2 film and achieved low surface roughness with over 3 orders of magnitude change in
resistance during the transition. The oscillation frequency for a pure VO2 and bilayer SRO/VO2
have been measured under the same conditions, the bilayer device shows a faster voltage waveform
and low operating power, which is indicated by the amplitude of the voltage. A maximum of 1.5
MHz frequency has been achieved for a bilayer device and further investigation on thermal
management, and a smaller footprint to achieving sub-GHz frequency with low power is ongoing.

1
Chapter 1. Introduction
1.1 Information Age: History and Challenges
Semiconductor research made a giant leap forward with the invention of the transistor in
1947.
1
Since then, large numbers of researchers engaged in the study of fundamental physics and
processes of semiconductors.
2,3
The next decade saw the emergence of Si as the leading electronic
material. The invention of the self-aligned planar gate Si metal-oxide-semiconductor field-effect
transistor (FET) in the late 1960s created a solid foundation for the semiconductor integrated
circuit industry.
4
With the introduction of the strained silicon and silicon-germanium channels,
5,6

high-k/metal-gate stack
7
and non-planar fin field-effect transistors,
8
the number of transistors on a
chip doubled about every 18 months with the size of the individual transistors shrinking at the
same pace.
9
However, the speed of the downsizing has slowed down in the recent past and is
grinding to a halt in the near future as we reach the physical limits of scaling. As we achieved
transistors with a channel length below 10 nm, further down-scaling of the critical dimensions
gives rise to two main problems: increasing propagation delay and increased power consumption.
Although the downscaling of the transistor increases the speed, the same is not true for the
downsizing of interconnect.
10
On-chip interconnect is nothing but electrical wiring that distributes
signals, provides power and ground among the various circuits or systems functions. In the early
1980s, the delay in interconnects was limited by the propagation of the electromagnetic waves
associated with SiO2, rather than the RC constant.
11
Naeemi et. al. estimate the delay under various
conditions and finds that the average delay jumped by 21.8% from 22 nm to 11 nm and by 48%
2
from 11 nm to 7 nm technology.
12
In this sense, the CPU only uses a fraction of its computational
power, and the communication speed starts to become the dominant bottleneck.
The second issue with the downscaling is power consumption. There was a time when FET
scaling was governed by Dennard scaling,
13
which says that as transistors get smaller, their power
density stays constant, so that the power use stays in proportion with the area. Historically, the
transistor power reduction allowed manufacturers to drastically raise clock frequencies without
significantly increasing overall circuit power consumption.
13
Since around 2005-2007, Dennard
scaling appears to have broken down.
13
Over the past decade, as the channel length of one transistor
becomes small as few tens of nanometers, the leakage current through the gate has increased
significantly, which leads to not only power leakage but also heat up the chip and therefore further
increases energy costs. Coming back to the interconnects, with the scaling of transistors, the
resistance of the compatible metal wires becomes larger as their dimension gets thinner and longer.
The result is that electronics and communication take around 10% of the global electricity demand
and this number will double by 2030. If we continue at this pace of increasing energy consumption,
by the year 2050, computing and communication will use the majority of the world’s electricity
capacity.
14

To deal with those issues, there is a clear demand for innovative materials to add more
functions to the current device schemes and/or innovate new designs for computing architectures.
I believe the phase change materials will play an important role in the next generation electronic
and photonic devices. I propose to leverage the phase transition in oxide heterostructures for
electronics and photonics applications. The first proposed solution is to enhance the efficiency of
3
the electric signal to optical signal conversion by integrating electro-optic materials with large
coefficients to the Silicon platform to achieve high-speed communication. The second solution is
the development of alternative computing architectures such as neuromorphic computing to
minimize energy consumption without sacrificing computing speed.
1.2 Photonic solution
As the internet explosion has changed the way we go about our everyday lives, the thirst for
information and the need to “be connected always” is spawning a new era of communications. The
new era will continue to spur the need for higher bandwidth technologies to keep pace with
processor performance. One of today’s main challenges lies in the communication for computing
and storage at various levels i.e., from computer to computer, from board to board, from chip to
chip, and within a chip. An intel core i7 operates at 2-5 GHz while the data travels on a bus line
operating at only 400 MHz. The “interconnect bottleneck” will eventually limit the performance
of next generation electronics. There is a clear trend that communication is shifting from
electronics to photonics. Fiber-optic solutions have long replaced copper-based solutions for long-
distance communication, which can no longer meet the bandwidth and distance requirements
needed for worldwide data communications and more recently, a staple in data centers that handles
an enormous amount of data.
Fiber optics have been used world-widely for long-haul communication for decades,
motivated by the negligible heat dissipation in transparent media, low cross talk, and most
importantly, the high carrier frequency of > 100 THz which enables bandwidths of > Tb/s.
15–19

The excellent performance of optical links, the transparency of silicon at important
4
telecommunication wavelengths of 1.3 µ m and 1.55 µ m,
20
and the low-cost fabrication in current
CMOS lines triggered the development of silicon photonics. Indeed, shorter interconnect delay
times, advantages in the total power consumption and increased bandwidth compared to electrical
interconnects have been predicted for integrated photonics.
Despite these great advantages in the field of silicon photonics, many challenges still need to
be solved. The merging of Si-based electronics with photonics has largely required the pursuit of
hybrid technologies of light emitters and modulators.
21
A large community is therefore focused on
combining silicon with new materials to enrich the functionalities and fabricating novel structures
for new device concepts. The main interest is in combining III-V semiconductor laser diodes with
Si circuits for optical fiber communications or optical interconnections. For the modulator part,
typically a silicon-based electro-absorption modulator is used in the state-to-art devices.
22–24
The
intrinsic limitation of electro-absorption modulator is the dissipative loss due to the absorption of
the light. Instead of manipulating the imaginary part of the refractive indices, there are materials
whose real part of the refractive index can be modulated by an applied electric field. These
materials are known as electro-optic materials. However, the integration of electro-optic materials
with silicon is challenging and critical to state-of-art telecommunications. Recently, LiNbO3 has
been integrated to silicon enabling on-chip electro-optic modulation. In line with this development,
there is an urgent need to not only identify materials with much larger electro-optic coefficients
but also integrate these materials to silicon.
5
1.2.1 Electro-optic effect
Electro-optic effect deals with the modulation of refractive index of the media carrying the
electromagnetic wave with an applied external electric field. For an isotropic material, the real part
of the refractive index n is described by:
where 𝑟 is the Pockels coefficient, 𝑅 is the electro-optic Kerr coefficient, and 𝑛 0
is the refractive
index for zero applied electric field. The second-order Kerr coefficient is present in any materials,
while the first-order Pockels effect vanishes in centrosymmetric crystals. Although both effects
can be utilized to modulate light, the Pockels effect is often preferred compared to the Kerr effect
for high-speed communications due to the linear dependence of n on the applied electric field,
which leads to a much larger induced phase shift or amplitude modulation under modest electric
fields. Therefore, the first-order, linear electro-optic effect will be the focus of this work.
The linear electro-optic effect was first observed in quartz by Rontgen and Kundt in 1883.
25

It was not clear whether the electro-optic effect resulted from the directly field-induced change of
refractive indices or the photo-elastic effect due to piezoelectrically induced strain in the first report.
This question was answered by Pockels in 1893
26
when he was studying the electro-optic effect in
quartz, tourmaline, potassium chlorate, and Rochelle salt. In his study, he revealed the existence
of the direct coupling between refractive indices and the electric field and characterized electro-
optic coefficients for various point groups of crystals.
27
The electro-optic coefficient decides the
magnitude of the phase rotation through a material’s length at a certain applied voltage. Increasing
EO coefficients lead to smaller-size and potentially less expensive devices.
𝑛 (𝐸 )=𝑛 0
−
1
2
𝑟 𝑛 0
3
𝐸 −
1
2
𝑅 𝑛 0
3
𝐸 2

(1.1)
6
Pockels in his early research pointed out that Rochelle salt shows some peculiar behavior
upon reversal of the electric field direction, for example, the electro-optic effect was not reversed
by reversion of the field directions as should be the case in piezoelectric non-ferroelectrics. This
observation is certainly connected with ferroelectricity. This interrelationship between
ferroelectricity and electro-optic effect was better demonstrated by Zwicher and Scherrer in
1944.
28
They observed that the electro-optic coefficients of KH2PO4 and KD2PO4 was proportional
to the dielectric constants and showed a Curie-Weiss behavior as a function of temperature. From
the results of Zwicker and Scherrer, one could conclude that large electro-optic effects would be
observed in ferroelectric materials with large dielectric constant and spontaneous polarization. The
summary of the electro-optic coefficient and their corresponding DC dielectric constant is shown
in Figure 1.1.
29–32

Figure 1.1 Comparison of literature values for (a) the linear electro-optic coefficient and (b) dielectric constant in bulk
crystals for various material system. SiO2: Ref. 29, ZnO: Ref. 32, Strained Si: Ref. 30, LiNbO3, BaTiO3 and PZT: Ref.
29, BCZT: Ref. 47.
7
1.2.2 Ferroelectric to paraelectric phase transition
“Ferroelectric” materials are the electrical analogs to ferromagnets, which carry a permanent,
switchable electric dipole moment below a certain temperature called Curie temperature, Tc. The
electrical dipole moment that ferroelectric materials possess without the application of any electric
field is called “spontaneous polarization” Ps. The distinguishing feature of ferroelectrics is that the
polarization can be reversed by applying an external electric field in the opposite direction that
crosses a threshold field called coercive field Ec. Thus, the polarization is dependent not only on
the current electric field but also on its history, yielding a hysteresis loop, analogous to
ferromagnetic materials, as shown in Figure 1.2. Unlike the ferromagnetic materials,
ferroelectricity exists only in materials with non-centrosymmetric symmetry, which allows the
displacing of the positive and negative charge center at zero fields and induces the spontaneous
electric dipole moment. Above the Curie temperature, the spontaneous polarization vanishes, and
the ferroelectric crystals transform into a paraelectric, which usually possess a centrosymmetric
unit cell.
Figure 1.2 Characteristic P-E hysteresis loop of a ferroelectric material. The Ps is the spontaneous polarization and Ec is the
coercive field
8
Barium titanate BaTiO3 is one of the widely studied ferroelectric materials. BaTiO3 is a
member of the perovskite family, of which the parent material is the mineral CaTiO3, named after
a Russian mineralogist Lev Perovski.
33
The General formula of this compound family is ABO3.
The ideal ABO3 perovskite structure consists of a 3D network of corner-shared BO6 octahedra
with a large A cation at the body center. A is typically an alkali or alkaline earth metal and B is a
transition metal. The selection of cationic elements is guided by Goldschmidt’s tolerance factor.
34

With various atomic radius combinations of A and B-site, tetragonal and orthorhombic variances
can be achieved other than ideal cubic perovskite. Besides, other ABO3-related structures, such as
edge- and face-shared BO6 could also be realized in some extreme conditions but they are not
classified as proper perovskite materials. From the point of view of practical applications,
perovskite oxides and halides attract a lot of interest due to their structural and chemical diversity,
stability, and large coupled responses such as ferroelectric, electro-optic, piezoelectric,
photovoltaic, superconducting, and more emergent functional properties.
Figure 1.3 Ideal cubic perovskite structure ABO3. “A” cation
occupies corner sites, “B” cation occupies cube center, and
O anion occupies face centers, forming a BO6 octahedra.
9
Lithium niobate bulk crystals have been used for decades to modulate light at high
frequency.
19,35,36
It is a major component for many of the laser spectroscopy systems to generate
and modulate ultrafast light. More recently, there is a great interest in using LiNbO3 as a modulator
for telecommunication applications. Researchers have achieved operation at CMOS-compatible
drive voltage with up to 210 Gb/s data rates and extended the operating frequency up to 500
GHz.
37–39
Recently, Organic materials with large EO coefficients have been integrated on Si and
show high-speed performance.
40–43
Nevertheless, the operating temperature and the speed of
operation have fundamental limitations in organic materials. Lead titanate zirconate thin films, a
more stable system, have been fabricated actively on the SiN.
44
Recent investigations on solid
solutions of BaTiO3, specifically 0.5 Ba(Zr0.2Ti0.8)O3 – 0.5 (Ba0.7Ca0.3)TiO3 (BCZT-50) – a
composition near the morphotropic phase boundary,
45
has shown a high dielectric constant of 2800,
piezoelectric coefficient d33 of 500 pC/N and, more importantly, a high effective electro-optic
coefficient rc of 530 pm/V.
46–50
However, high-quality single crystal of BCZT is not easy to make
in the bulk form, which limited the measurements of intrinsic EO tensors.
In Chapter 2, the experimental methods which are used in this work are presented. Starting
from the deposition of epitaxial thin films, we discussed the fabrication and characterization
techniques including pulsed laser deposition, reflection high energy electron diffraction, X-ray
diffraction, and transmission electron microscope.
To understand the mechanism and find materials with large EO coefficients, a semi-empirical
method to compute the electro-optic coefficient of ferroelectric materials by combining first-
principles calculations with Landau-Devonshire phenomenological modeling is presented in
10
Chapter 3. This method not only predicts EO coefficients accurately but also can be used to study
the temperature-, frequency- and strain-dependence of EO tensors. Additionally, a figure of merit
is also extracted from the analysis of the external variances to demonstrate a pathway to achieving
large EO coefficient materials. To verify the validation of the figure of merit, the method is applied
to different oxides including LiNbO3, LiTaO3, KNbO3, BaTiO3, BiFeO3, PbTiO3, and BCZT.
1.2.3 Propagation loss
The other limitation in the integration of EO materials is large propagation loss. The loss
mechanisms include absorption, leakage, and scattering from the bulk, surfaces, and interfaces.
Absorption: Optical absorption is an intrinsic property of any material. This can be simply
avoided during the material selection. Choosing a material with low extinction coefficient at the
wavelength of the light transmitting through the EO material ensures low loss by absorption.
Defects will also lead to absorption loss. For example, impurities and oxygen vacancies can cause
absorption. This has been confirmed in potassium niobate films.
51
Hence, high-quality single-
crystalline materials with minimal defects are of essence to prevent losses due to absorption. This
is usually difficult in most ceramic processing methods. The epitaxial thin film can be a viable
solution.
Leakage loss: Cladded semiconductor substrates such as Si do not support true guided modes,
because of the large refractive index of the substrate n ~ 3.8 at 633 nm. This implies that a mode
in the film will eventually leak into the substrate. Good refractive index matching of the film and
substrate is important. Fortunately, the SiO2 layer on the Si substrate could be used for silicon
11
photonics. It has a refractive index of 1.4 at 633 nm, which is smaller than most of the EO materials,
and gives better internal reflection to minimize the loss.
Scattering: Scattering is in essence, the coupling of one mode to other guided modes and/or
radiation modes. Variations in the refractive index either through material inhomogeneities or by
grain misorientation in the material will induce scattering in the waveguide. In all types of films,
inhomogeneities may result from amorphous inclusions or ferroelectric domain formation. BaTiO3,
for example, may unavoidably contain inhomogeneities due to a mixed a/c orientation texture.
52

The interface is typically, but not always, a polished substrate surface, with root mean square
(RMS) roughness less than 1 nm. This loss is generally not a dominant portion of the overall
propagation loss. Film morphology usually creates roughness far larger than that of a polished
substrate. The scattering loss varies quadratically with the roughness. This requires atomically
smooth surface which presents a very difficult challenge.
In Chapter 4, I will discuss the growth and characterization of ferroelectric epitaxial BCZT
films on the GdScO3 substrate.
53
The GdScO3 provides a good lattice match with the BCZT thin
films. This could lead to low density of defects such as threading dislocations and low surface
roughness. Uniform polarization in a single domain system is not stable without an applied field
that can counteract the depolarization field. One of the solutions is to have a metallic layer to
screen the depolarization field from the ferroelectric layer. SrRuO3, a good oxide conductor, is
used as an electrode and also screening layer for this reason. All of this rational design will
contribute to getting high-quality atomic smooth epitaxial BCZT thin films.
12
Due to the numerous properties of perovskite oxides that are absent in silicon such as
ferroelectricity, piezoelectricity, and electro-optic, a large research community explored the
integration path with the vision of enabling new devices and functionalities for silicon-based
electronics and photonics. Silicon photonics also defines the boundary conditions for electro-
optically active oxides to be used in the potential application. Using novel materials in optical
devices is challenging since such devices are extremely sensitive to structural and chemical defects
that might impact light propagation in an undesired way. I will show our effort in the integration
of high-quality BCZT thin films on SrTiO3/Si substrate in Chapter 5.
1.3 Electronic solution
Computers have become of the essence to all aspects of human life i.e., control processing,
communication, entertainment, science, etc. Currently, about 10% of the world’s energy is spent
on the manipulation, transmission, and processing of data.
14
The number will keep increasing in
the foreseeable future.
In the early 1980s, researchers have begun to investigate the idea of “neuromorphic”
computing.
13,54
Brain-inspired computing architectures were envisioned to be a million times more
power-efficient and faster than devices being used at that time. While the conventional computer
had achieved notable feats, they did not do a good job for most of the basic tasks that biological
systems have mastered such as optimization, speech and image recognition, decision making, and
learning.
55–58
Hence, the idea that mimics the biological brain might lead to fundamental
improvements in computational capabilities.
13
Over the years, a number of groups have been working on the direct implementation of deep
neural networks.
59–64
There are two major types of designs that vary from processors specialized
for machine learning to systems that attempt to simulate biological neurons. The former design is
not fundamentally different from existing CPUs but has achieved 120 times lower power than that
of the general-purpose processor. The latter is better known as neuromorphic computing. One of
the latest accomplishments in neuromorphic computing has come from IBM research,
TrueNorth,
65
which implements one million spiking neurons and 256 million synapses on a chip
with 5.5 billion transistors with a typical power draw of 70 milliwatts.
1.3.1 Von Neumann vs. Neuromorphic
Throughout the evolution of traditional computers, von Neumann architecture (Figure 1.4 (a))
has continued to be the standard architecture for computers. The von Neumann architecture is a
multi-modular design based on rigid physically separate functional units.
66
It consists of three
different entities:
(b)
(a)
Figure 1.4 (a) The schematic of Von Neuman architecture (Adopted from [66]] and (b) a schematic of a biological neuron
network. (Adopted from [67])
14
Central processing unit (CPU): The processing unit can be broken into sub-units --
arithmetic and logic unit (ALU) and control unit. The ALU is that part of the CPU that handles all
the calculations needed to run programs. The control unit is used to direct the flow of data through
the processor.
Main memory unit: The memory unit stores anything that the computer would need to store
and retrieve, which includes both volatile and non-volatile memory.
Input/output device (I/O device): Program or data is read into main memory from the input
device under the control of CPU input instruction. Output devices are used to output the
information from a computer.
These units are connected over different buses such as the data bus, address bus, and control
bus. The buses allow data communication between the various logic units. If the speed of
computation is much lower than the speed of communication, the von Neumann architecture
suffers from the bottleneck created due to the constant shuffling of data between the memory unit
and the CPU. Specifically, if the instructions can only be processed one at a time and in a sequential
manner, this issue becomes more acute. Both of these factors hold back the competence of the
CPU. An alternate solution of parallelizing the computers is being practiced where millions of
processors are interconnected. This solution, though, will nevertheless continue to use large
processing power, is still limited by the bottleneck in its core elements.
In contrast, Neuromorphic computing incorporates computation based on biological brain-
inspired mechanisms, where an interconnected network of neurons and synapses
67
(Figure 1.4(b))
are used for computing, learning, memorizing, and distributing information. The advantage of
15
neuromorphic computing is the co-location of the compute and memory operation that
significantly reduces the need to communicate between the memory and computing units, and also
special characteristics associated with learning and memory used in the brain will make it
significantly efficient in associative learning compared to von Neuman architecture. Neurons are
living cells thought to be the main information processing units of the brain. The human brain
contains a network of about 100 billion highly interconnected neurons. Living nerve cells have
major components- synapses, dendrites, soma, and axon.
68

Synapse: Synapse is the connection between neurons. Electrochemical signals enter the
neurons through a tiny interface called the synapse. The synapses are the most advanced element
that has been simulated and constructed, where the memristor is a good model.
62
Memristors are
electrical resistors with memory. They are able to regulate current based on the history of the
voltages applied to them. The implementation of a synapse is frequently accomplished in a two-
terminal device such as a memristor. It mimics the way that the connections between neurons
strengthen or weaken when signals pass through them.
Dendrite/Axon: Input and output. The synapses are scattered over the surfaces of tree-root-
like fibers called dendrites, which reach out into the surrounding nerve tissue, gather signals from
their synapses, and conduct the signals to the heart of the cell, the soma. The outputs are conducted
through the axon, the tree-like fiber, from the cell body (soma) into the nervous tissue, ending at
synapses on other cells’ dendrites, on muscle, or organ synapses. The role of dendrite and axon
are commonly believed to provide signals from multiple neurons into a single neuron and distribute
signals to output devices. They are not designed as what I/O did in the von Neumann architecture.
16
A neuron is usually connected to hundreds of other neurons through dendrites, which emphasizes
the three-dimensional nature of the connectivity of the brain. Pseudo-3D systems have been
implemented in multilayer neuromorphic systems.
55,56,59,69
There is still a long way to make “truly”
3D implementation as a brain does.
Soma: Process the inputs. The soma is a structure that transforms the incoming
electrochemical signals from the synapses to the output pulse train. There are more than 20
different transformations that have been identified in nature, ranging from simple logic functions
to complicated transforms. One of the most widely used in neuromorphic computing is the leaky
integrator: a function that sums up signals as they arrive with the fixed decay rate of the total signal.
If the sum exceeds a threshold, the cell body outputs a pulse.
Artificial neurons will not completely work like the brain. The primary reason is that the
current solid-state implementations cannot fulfill the complex functionality of the brain. Hence,
the research has focused on the use of conventional and emerging solid-state materials and devices
to create simple imitations of the neuron. The following discussion will survey these efforts.
1.3.2 Oscillatory Neural Network
Several mechanisms have been explored to mimic neurons in the solid-state form that can
approach the biological level of performance and energy efficiency. The voltage or current
controlled oscillators are considered one of the important solid-state analogs to the biological
neuron.
70
Hence, over the years, voltage controlled oscillators composed of the CMOS based ring
oscillators have been widely used to simulate solid-state neurons.
71
Besides the CMOS based ring
oscillators, inductor-capacitor circuits, micro-electro-mechanical systems (MEMS) are also used
17
as tunable oscillators today. The key limitation of the existing technologies is the constraints on
scaling the threshold voltage to the biological level of < 200 mV, which is well below the threshold
voltage of CMOS transistors. Other limitations include the scalability to achieve a small footprint
(in micro/nanoscale) for the oscillator device and minimizing the energy consumption per cycle of
operation without compromising the noise characteristics. Emerging oscillator methods based on
the spintronic and phase change materials promise to offer low voltage, power, and more scalable
alternatives to these approaches. These advantages are especially important for the operation of an
oscillator as a solid-state neuron. Among several emerging oscillator mechanisms
72–80
considered
against the above-mentioned methods, we propose electrical oscillators based on phase change
oxides as a candidate for solid-state neurons. Phase change oxide based oscillators possess the
necessary qualities to overcome some of these limitations of current technologies, especially if one
were to implement them as miniaturized micro/nanoscale oscillators with a minimal footprint and
ultra-low power consumption with appropriate phase noise characteristics.
81,82
Hence, such
oscillators can offer a direct path to realize solid-state neurons, an important step towards
neuromorphic architecture, a non-von Neumann computing methodology.
1.3.3 Metal-to-Insulator Transition
VO2 has been widely studied for its sharp metal-to-insulator transition (MIT) over a very
narrow range of temperatures close to room temperature (~ 340 K).
83,84
At this transition
temperature, VO2 undergoes a large change in resistivity, as high as five orders of magnitude, in
high-quality single crystals.
85
This transition is accompanied by a structural transition from
monoclinic (M1) to tetragonal rutile (R) structure. The schematic crystal structures for these phases
18
are shown in Figure 1.5. The role of this structural change, and the strong correlation on the
physical properties and MIT in VO2 remains an important topic of investigation.
86–91

There is still a debate over whether the mechanism of MIT in VO2 is a Mott insulator, Peierls
insulator, or a combination of both.
86–91
The Mott-Hubbard model basically explains the MIT due
to the electron-electron interaction. Mott considers a lattice model with just one electron per site.
Without taking the electron-electron interaction into account, each site could be occupied by two
Monoclinic VO2 Tetragonal VO2
Figure 1.5 (Top) A schematic atomic model of low temperature monoclinic and high temperature
tetragonal Rutile phases. (Bottom) A schematic of the metal-insulator transition behavior. The phase
change shows hysteretic behavior, and, within this region, we expect to have phase co-existence.
19
electrons, one with spin up and one with spin down. Due to the interaction, the electrons could feel
a strong Coulomb repulsion, which Mott argued splits the band into two: the lower band is then
occupied by the one and the upper is empty. If each site is only occupied by a single electron, the
lower band is filled and the upper band completely empty, the system thus a so-called Mott
insulator. The Peierls transition is a distortion of the periodic lattice of a one-dimensional crystal.
From theoretical calculations, people find that the electronic band of a periodic crystal with lattice
spacing a is continuous in E-k diagram and should be half-filled, up to values of 𝑘𝑎 = ±𝜋 /2 in
the ground state. In the distorted crystal, when an ion moves closer to one neighbor and away from
the other creating a dimerized lattice with 2a as the new lattice spacing, a gap opens up at 𝑘𝑎 =
±𝜋 /2. Many studies have investigated the origin of the MIT in VO2. In 1975, Zylbersztejn and
Mott showed that the mechanism of MIT in VO2 was not a simple Mott-Hubbard transition.
84
In
2018, Lee et al. found that VO2 was not a pure Peierls insulator by discovering a monoclinic metal
phase of VO2 in the vicinity of the transition temperature.
92

The bistable nature of the MIT in VO2 allows us an opportunity to use an external stimulus
to switch between the two states, and hence create an oscillator. Current implementations of these
phase change oscillators use a resistor in series with the lateral MIT channel device to induce
electrical self-oscillations across the MIT device. In practice, the power consumption necessary to
achieve this low switching energy has been large, and low voltage (< 1 V) and low power (< 1
mW) switching is challenging to realize in the current configuration.
78
Large parasitic capacitances
and resistances associated with the MIT device channel are the primary cause for this high-power
consumption and low oscillation frequency.
93

20
To overcome these issues, I will present a novel design of the oscillator with single crystalline
layers of phase change oxides VO2 and an epitaxial oxide with metallic conductivity, which allows
high-frequency electrical oscillation with low drive power, in Chapter 6. This design takes
advantage of the relatively low resistance of the metallic layer instead of the high-power demand
of the high resistance state to drive the oscillation in the classic VO2 oscillator device. Furthermore,
this design also minimizes the transition area of the VO2 so that achieves fast cooling -- one fatal
limitation from high-frequency oscillator. In order to demonstrate advantages of this design, an
electrical and thermal simulation study is carried out.
Based on the simulation results, the epitaxial growth of single crystal VO2 is grown on the
LSAT
94
and STO substrate by means of pulsed laser deposition. To demonstrate the quality of the
VO2 single layer device, different characterizations including X-ray diffraction, Raman
spectroscopy, temperature-dependent resistivity measurement are performed. The VO2/SrRuO3
bilayer devices are fabricated, and oscillation behaviors are characterized. (Chapter 7)
21
Chapter 2. Experimental Methods and Background
2.1 Materials Synthesis
2.1.1 Epitaxy
The modern word epitaxy originates from two ancient Greek words, epi (placed or resting
upon) and taxis (arrangement). Epitaxy refers to the growth of crystalline films on a surface of a
substrate, where the substrate and the film possess a structural relationship at the atomic scale.
95–
97
The deposited film is generally referred to as an epitaxial film or epitaxial layer. Compared to
the time intensive process of growing single crystals, deposition of epitaxial films is relatively
faster and is also closely related to manufacturing approaches for device applications. From a
fundamental research point of view, epitaxial growth is widely used to control the strain state of a
material, and hence, its properties. Thus, epitaxial growth enables the design of materials with
precision at atomic level and has spurred research into artificial materials such as heterostructures
and superlattices.
There are two primary types of epitaxy: homoepitaxy and heteroepitaxy. Homoepitaxy is the
growth of thin films of the same material as that of the substrate. Even though homoepitaxy is
conceptually simple, it requires care to ensure the structure and chemical state of the bulk are
identical to the substrate, while the surfaces and interfaces are sharp without any intermixing or
defects. An important example of the application of homoepitaxy is the silicon-based electronic
device technology, where the (001)-oriented silicon wafer surface is usually refined with an
epitaxial Si film, whose quality is better than that of the original substrate.
98

22
In this thesis, I will focus on heteroepitaxy, where the film and substrate materials are
different. Heteroepitaxy is widely employed in several fields such as semiconductor technology
and functional complex-oxides research. The proper choice of the materials for the film and
substrate can lead to artificial structures such as quantum wells and superlattices with emergent
properties.
99–102
An important quantity, which characterizes epitaxy, is the lattice mismatch f which
is defined as
where 𝑎 𝑠 and 𝑎 𝑓 refer to the lattice parameters of the substrate and the film, respectively. When
the lattice parameter of the epitaxial layer is close to the substrate crystal in the in-plane directions,
there is lattice matching with little or no interfacial strain. In heteroepitaxy, the lattice parameters
are usually different, and depending on the extent of the mismatch, we can envision three types of
epitaxial relationships as shown in Figure 2.1. If the lattice mismatch is very small, then the
𝑓 =
𝑎 𝑠 −𝑎 𝑓 𝑎 𝑓 (2.1)
Figure 2.1 Schematic illustration of lattice matched, strained, and relaxed heteroepitaxial structures.
23
heteroepitaxial interfacial structure is essentially similar to that of homoepitaxy. Other factors such
as the chemistry, crystal and electronic structures, and coefficient of thermal expansion could also
play a very important role in the perfection of the interface. Overall, small lattice mismatch is
universally desired and can achieve several practical applications.
When the film and substrate lattice mismatch becomes more substantial, we will end up with
scenarios such as strained and relaxed films. In a strained film, the in-plane lattice parameter of
the film is forced to be the same as that of the substrate’s lattice parameter. At small film
thicknesses, below a threshold thickness known as critical thickness, the film can accommodate
the misfit purely in the form of strain. At thicknesses greater than the critical thickness, the film
cannot accommodate this strain. The film will create (misfit) dislocations or other defects to
accommodate the misfit and leads to relaxation of the film with the film lattice parameter
approaching the bulk values. Strained epitaxy usually occurs between film-substrate pairs
composed of dissimilar chemical compositions but similar crystal structure and relatively small
lattice mismatch and thickness below the critical thickness. Lattice parameter differences between
the film and substrate are generally large and the thicknesses are above the critical thickness for
the case of relaxed films.
24
2.1.2 Pulsed Laser Deposition
The pulsed laser deposition (PLD) is a simple process of ablating materials by a small pulse
width (~10- 30 ns typically) and high energy (~0.5-2 J/pulse) laser that yields high-quality epitaxial
films. In the early days, pulsed laser deposition was believed to be a novelty and never imagined
as a scalable thin film growth method.
103
After D. Dijkkamp, X. Wu and T. Venkatesan
104

published their breakthrough article on PLD of high-temperature superconductor YBa2Cu3O7-x
(YBCO), there has been tremendous attraction and interest in the use of this physical vapor
deposition (PVD) process.
There are four essential components of a PLD system, i.e., a vacuum chamber, high power
laser (often excimer or quadrupled Nd:YAG laser), target and substrate as shown in Figure 2.2.
The vacuum chamber is maintained at a low base pressure ranging from 10
-6
mbar to 10
-10
mbar
to ensure a clean background. The laser and optics in PLD systems are chosen to deliver a laser
fluence of 1-2 J/cm
2
at the target surface. The target is made of materials with the same desired
Figure 2.2 A illustration of a pulsed laser deposition chamber
25
composition in the film, often single-phase and dense target is preferred, and the substrate is
usually a high-quality single crystal with known crystallographic orientation and atomically
smooth surface achieved by a combination of polishing, chemical treatment, and thermal annealing.
The light from the laser enters the vacuum chamber via a special laser entry port, which is
made of UV transparent material such as fused silica or sapphire, and ablates the target. A plasma
plume of the target material leaves the target surface and arrives on the surface of the substrate
which is placed opposite to the target to deposit the film. This process is typically carried out in a
low vacuum (~10
-4
to a fraction of mbar) with background gas flow. The gas is used to regulate
the anionic stoichiometry and/or affect the kinetic energy distribution of the deposited materials.
For example, molecular oxygen is used to establish an oxidizing atmosphere for the growth of
oxides.
In this thesis, a TSST PLD system with a 248 nm KrF excimer laser is used to deposit epitaxial
films. The actual pictures of the experiment set up are presented in Figure 2.3. The vacuum
(a)
Figure 2.3 The picture of experiment set up of (a) pulsed laser deposition chamber and (b) the KrF excimer laser.
Picture credit: Ravichandran group.
(b)
26
chamber is evacuated to a high vacuum with a base pressure of 10
-7
mbar. The GdScO3 (110)
single crystal substrates were pre-annealed in an atmosphere of high purity oxygen at 1100° C for
3 hours and then cleaned sequentially in acetone, and isopropanol alcohol prior to the deposition.
Polycrystalline targets were made in-house by solid-state reaction and pre-ablated for 500 laser
pulses before each growth. Important parameters for the deposition process are given in Table 1.
Table 1 Typical growth parameters used in the experiments.
Deposition Conditions
Film Material
(Ba,Ca)(Ti,Zr)O3 SrRuO3 (La,Sr)MnO3 VO2
Process Pressure (mbar) 1 – 100 1-100 20 5-25
Background Gas Ultra-High Pure O2
Substrate
Temperature ( °C)
600-850 500-850 700-750 500-550
Cooling Rate ( °C/min) 5 10 10 5-10
Spot Size (mm
2
) 2.5 2.5 2.5 3
Spot Shape Rectangular
Target Composition and
Type Sintered Pellet
Isostatic
Pressed
Pellet
Sintered Pellet
V2O5 Sintered
Target
Laser Fluency on Target
(J/cm
2
)
1.5 1.5 1.5 1.5-2
Laser Repeat Rate (Hz) 5-10 5 3 10
2.1.3 Growth Process and Growth Mode
The growth process of an epitaxial film is shown in Figure 2.4, including five process,
incoming vapor flux of atoms, particles from the target, absorption of the incoming atoms to the
substrate surface, re-evaporation of adatoms from the substrate surface, surface diffusion and
nucleation of the film.
The adatom could travel on the surface to the nucleate and join the existing nucleus or attach
to a step edge. When the adatom reaches a step edge or terrace, it might fall or remain above
27
depending on the energy barrier of the transition. (The step edge or terrace on the substrate is
inevitable as all the substrates have a miscut associated with the crystal.) It may even reevaporate
to the vaper form. The most important parameter to determine the possible behavior is the
characteristic diffusion length 𝑙 𝐷 :
𝑙 𝐷 =√𝐷 𝑠 𝜏
(2.2)
where the 𝜏 is the residence time before the adatom reevaporates. The surface diffusion
coefficient Ds is described by
𝐷 𝑠 =𝑣 𝑎 2
𝑒 −
𝐸 𝐴 𝑘 𝐵 𝑇
(2.3)
where EA is the activation energy of diffusion, 𝑣 is the attempt frequency, and a is the
characteristic jump distance. kB and T are the Boltzmann constant and temperature. In the following
Figure 2.4 A Growth model of the thin film
28
discussion, we only consider the adatom staying at the surface when the diffusion time is smaller
than 𝜏 .
Island growth mode: Island growth happens when the diffusion length is very small. Islands
nucleate on the surface and as more influx adatoms, the island grows in three dimensions. The
island growth mode is also called the 3D growth mode. The surface roughens each time a plume
reaches the surface, and this growth mode is not ideal for achieving smooth epitaxial thin films but
is often leveraged to achieve epitaxial quantum dots.
105,106

Layer-by-layer growth: This growth mode is similar to the island growth, except that the
islands grow in a 2D manner. The diffusion length is long enough to let the adatom fall from the
edge of islands and islands continue to grow until they collide with each other. This is known as
coalescence. At this stage, the surface has a large density of pits, and roughness reaches its
maximum. When additional materials come from the vaper, the adatoms diffuse into these pits and
complete the layer. This process is repeated for each subsequent layer.
Step flow growth: Beyond the layer-by-layer growth described above, there is a step flow
growth which is also 2D in nature. The diffusivity is so high that the adatoms migrate freely to the
step edges where the nucleation energy is lowest before they have a chance to nucleate an island.
The growth surface is viewed as steps traveling across the surface. This growth mode is obtained
by depositing at elevated temperatures or the deposited material itself has large diffusivity, such
as SrRuO3.
107
Both the layer-by-layer and step flow growth modes are favorable to get atomically
smooth surface with good crystallinity in epitaxial thin films.

29
2.2 In Situ Characterization
2.2.1 Reflection High Energy Electron Diffraction
To monitor the structure of the film surface during growth, an attached reflection high energy
electron diffraction (RHEED) system from k-space was used. This technique allows us to not only
determine the thickness of the film but also characterize the structure of the sample surface (1-2
atomic layers) in situ and in real-time. A high energy (10-20 keV) electron beam is incident at a
grazing angle on the substrate, and the reflected and diffracted electrons are imaged on a
fluorescent screen at the opposite end. The wavelength of the electron beam is 0.062 to 0.12 nm
comparable to the lattice parameter, i.e., 0.4 nm for perovskite oxides. At small incidence angles,
the penetration depth of electrons is less than 1 nm, which makes RHEED very surface sensitive.
The three common RHEED patterns are shown in Figure 2.5. The reciprocal space of a 2-
dimensional crystalline surface layer consists of infinite rods extending perpendicular to the
sample surface, which create a typically line-shaped streaky diffraction pattern (Figure 2.5 (a)).
This is usually observed on the atomic smooth substrate surface. In practice, the surface of a film
may not maintain the smooth condition as the substrates, the surface becomes rough but within the
Figure 2.5 RHEED pattern examples of (a) 2D streak pattern, (b) 2D diffraction pattern when the coherence is maintained on both
directions in-plane, (c) 3D pattern.
(a) (b) (c)
30
spatial coherence region in both the perpendicular and parallel direction to the incident beam. This
will lead to the broadening of the rods in the reciprocal space which further results in the broad 2D
rod diffraction pattern as shown in Figure 2.5 (b). In the case of an even rougher surface, for
example in island growth mode, however, the electron beam penetrates the islands and RHEED
works in the so-called transmission mode, resulting in the diffraction pattern of a three-
dimensional (3D) crystal as shown in Figure 2.5 (c). This is the same diffraction pattern as would
be observed in transmission electron microscopy.
108
A more informative mathematical and
physical description of RHEED can be found elsewhere.
108

The reflected spot (specular spot) provides insight into the surface smoothness. In the case of
a 2D layer-by-layer growth mode, one can expect the surface to start as atomically smooth, and as
the film is deposited becomes rough as the coverage increases and peaks at half coverage. After
half coverage, the surface becomes gradually smooth again to recover to a nearly atomically
smooth surface at full coverage. In this growth mode, the intensity changes of the specular spot
can be used to monitor the growth rate at the single unit cell level, where the full period of an
oscillation corresponds to the deposition of one unit cell. The minima correspond to a half coverage
and the maxima correspond to a surface with full atomic coverage. However, the growth rate is
difficult to monitor and measure in the island and step flow growth modes. As described earlier,
the surface is so rough in the island growth that diffuse scattering dominates and tracking the
intensity of the specular spot is not meaningful, whereas the smoothness of the surface remains
constant in the step flow growth and therefore the reflection intensity remains unchanged. If we
keep track of the intensity of the specular spot while the deposition starts from the atomically
31
smooth substrate, there are three possibilities, i.e., the intensity remains constant (step flow
growth), oscillates in a regular period (layer-by-layer growth), and decreases (island growth) and
thus different growth modes could be distinguished.
2.3 Ex Situ Characterization
2.3.1 X-ray Diffraction
The crystalline structure of the epitaxial layers is characterized by X-ray diffraction (XRD).
The physical principle of XRD is illustrated in Figure 2.6. The X-ray radiation is generated by a
Cu-anode with K  radiation. ( =0.154 nm). The sample is exposed to X-rays at various incident
angles and the intensity and angles of diffracted X-rays is recorded by a detector. I used three
modes of operation in the following experiments:
⚫ Symmetric 𝜽 −𝟐𝜽 Scan.
In one of the typical configurations, the X-ray source and detector move symmetrically with
respect to the static sample stage. For the diffraction condition to be satisfied, the incident angle
of the beam (with respect to the sample surface) is equal to the angle subtended by the detector
and the sample surface. For the polycrystalline sample, all of the available reflections from each
grain with the same crystallographic planes are received at specific diffraction angles with different
Figure 2.6 A illustration of the mechanism and physical setup for the X-ray diffraction
32
azimuthal angles. The diffraction angle 𝜃 obeys the relationship of Bragg’s Law – 2dsin 𝜃 =λ,
where the d is the spacing between each atomic plane (d-spacing), 𝜃 the angle between the incident
beam and the sample, λ the wavelength of the X-ray. The azimuthal angles are the in-plane
rotational angle on the detector plane. In contrast to polycrystalline samples, epitaxial thin films
satisfy diffraction conditions only along specific azimuthal angles due to the well-defined crystal
orientation.
⚫ Rocking Curve.
The rocking curve is used to determine the crystalline quality of an epitaxial thin film. The
angle between the incident beam and the sample 𝜔 is varied slightly while the angle between the
incident beam and the detector 2𝜃 is fixed at a value corresponding to a certain crystallographic
plane. For an ideal perfect crystal, the full-width-at-half-maximum of the rocking curve should be
very small (~ several arcseconds) since any change in 𝜔 would induce the misalignment to the
crystallographic plane. In practice, any nonidealities such as defects could lead to the broadening
of the rocking curve.
⚫ Reciprocal Space Mapping
The reciprocal space mapping (RSM) measurements distinguish the in-plane and out-of-plane
lattice parameters and thus a tool to define the strain conditions demonstrated in Figure 2.6. The
RSM data are collected with asymmetric 𝜔 −2𝜃 scans each being offset by an angle of Δ𝜔 from
the previous. The beam source and the detector are scanned the same way as in the symmetric 𝜃 −
2𝜃 scan with an offset angle which corresponds to a specific crystallographic plane. Typically, a
reciprocal plane h k l which can be projected to the in-plane and out-of-plane orientation is selected.
33
For the case of pseudo-cubic perovskites, the 103 reciprocal plane is typically used. The
corresponding d-spacing at 2𝜃 angle can therefore be projected onto the in-plane and out-of-plane
reciprocal space lattice parameters given the known offset angles. To monitor the film substrate
relation, a sequence of Δ𝜔 offsets is applied to iterative asymmetric 𝜔 −2𝜃 scans. A 2-D map is
generated including the lattice information of film and substrate. The in-plane lattice parameter of
the film is equal to that of the substrate for the fully strained condition, whereas lattice parameters
of a fully relaxed film coincides with the bulk values of the film material.
2.3.2 Atomic Force Microscopy
The atomic force microscopy (AFM) is among the best techniques for measuring the
nanoscale surface topography at ambient conditions. AFM consists of a sharp tip that is
approximately 10 to 20 nm in diameter, which is attached to a cantilever. The tip/cantilever
assembly is commonly referred to as the probe which is generally micro-fabricated from Si or
Si3N4. The AFM probe interacts with the sample surface through a raster scanning motion. The
up/down and side-to-side motion of the tip as it scans along the surface is monitored through a
laser beam reflected off from the cantilever. The reflected laser beam is tracked by a photodetector
that measures the vertical and lateral motion of the probe.
An AFM is operated in two basic modes, such as contact and tapping modes. In the contact
mode, the AFM tip is in continuous contact with the surface. In contrast, in the tapping mode, the
AFM probe vibrates above the sample surface such that the tip is only in intermittent contact with
the surface. Tapping mode limits the contact between the sample surface and the pit to protect both
34
from damage. Therefore, the tapping mode was exclusively used for all the AFM scan images
throughout this work.
In the tapping mode, the cantilever is caused to vibrate near its resonance frequency (typically
~400 kHz for this work) by a piezoelectric shaker. The tip subsequently moves up and down in a
sinusoidal motion. This motion is reduced by attractive and repulsive interactions as it comes near
the sample surface. The feedback of the oscillation amplitude is traced and converted to the height
information to create the surface topography.
2.3.3 Piezo-response Force Microscopy
AFM microscopes are versatile tools that are not only limited to topographical measurements
and imaging applications but also employed to assess mechanical and electrical material properties,
such as piezoelectric response. Piezo-response force microscope (PFM) is a technique to
characterize the electromechanical coupling of piezo- and ferroelectric materials. It operates on
the same principles of AFM used for topographic analysis. The conductive AFM tip applies a local
voltage in the contact mode to a sample surface which subsequently causes it to deform. This
localized expansion and contraction deflect the cantilever and the mechanical response can be
measured. It is worth mentioning that the magnitude of mechanical response is on the order of
approximately 10 - 100 pm, which is 10000 times smaller than the width of the hair. To measure
such small deformation, the measurement is made at a high frequency where the voltage is applied
as AC and the deflection is measured using a lock-in amplifier at the same frequency. The signal-
to-noise is greatly improved by this approach. Furthermore, a DART technique (Dual AC
35
Resonance Tracking),
109
in our AFM system (Asylum Research), is used to increase the sensitivity
of the measurements in this work.
The schematic of the experimental set-up is shown in Figure 2.7 (a). The applied voltage is
the sum of two AC voltages with frequencies near the resonance frequency of the tip-sample
contact. The resulting cantilever deflection is measured by two separate lock-in amplifier with
frequencies corresponding to the two applied voltages. When the resonance frequency shifts from
the solid curve to the dashed curve due to a change in the contact stiffness of the tip-surface contact
during the scanning shown in Figure 2.7 (b), the amplitude A1 increases to A1’ while the amplitude
A2 decreases to A2’. Hence, the amplitude change is amplified by a factor of two compared to
Figure 2.7 Schematic diagram for DART. (a) The experimental set-up. (b) Principle of the dual-frequency
excitation. Adopt from Ref 102.
36
single frequency tracking. Finally, the amplitude difference is used as an input to the feedback
loop to maintain the two driving frequencies bracketing the resonant frequency, where the A1’ and
A2’ return to the setpoint value A1 and A2 and the amplitude difference maintains zero.
2.3.4 Transmission Electron Microscopy
The smallest object that a human eye can distinguish is about 0.2 mm. Optical microscopes
reveal even smaller objects by magnifying them with a combination of glass lenses. However, the
limitation of a light microscope lies in the wavelength of the visible light (400 nm to 800 nm). In
order to “see” objects at the atomic level (~ sub nanometers), the incident wavelength has to be
much smaller in wavelength, where electron beams with a wavelength of 0.0037 nm to 0.0025 nm
under accelerating voltages at 100 to 200 kV are an attractive option.
In a transmission electron microscope (TEM), the electron beam is generated from the
electron gun, accelerated under high electric field and then passes through a thin slice of sample
to generate diffraction patterns or TEM image collected at the bottom of the TEM column. The
magnification process is similar to that in optical microscopes. The electron beam is focused by
the electromagnetic lenses. Unlike the glass lenses, the strength of the electromagnetic lenses can
be changed by the current through the lens coil and the spatial resolution greatly rely on the
perfectness of the lenses.
37
Scanning transmission electron microscopy (STEM) combines the principles of transmission
electron microscopy and scanning electron microscopy (SEM). Similar to SEM, the STEM
technique scans a very finely focused beam of electrons across the specimen in a raster pattern.
Similar to TEM, the STEM sample requires sufficient thin samples and looks primarily at the beam
transmitted through the sample. One of the advantages over TEM is that STEM enables to use the
signals that are not spatially correlated in TEM, such as scattered beam electrons for high angle
annular dark-field (HAADF) imaging, characteristic X-rays for energy dispersive X-ray (EDX)
and wavelength dispersive X-ray (WDX) spectrometry, and electron energy loss for electron
energy loss spectrometry (EELS).
Figure 2.8 Illustration of the principles for imaging in (left) TEM and (right) STEM. Image credit:
Edna Vargas in the presentation of “Contrast in TEM and STEM”.
38
For this work, the atomic resolution imaging was conducted by collaborators at Washington
University in St.Louis at the Center for Nanophase Materials Sciences, Oak Ridge National
Laboratory. High-resolution transmission electron microscopy (HRTEM) and high-annular dark-
field scanning transmission electron microscopy (HAADF-STEM) experiments were carried out
using the aberration-corrected Nion UltraSTEM
TM
200 (operating at 200 kV) microscope at Oak
Ridge National Laboratory, which is equipped with a fifth-order aberration corrector and a cold
field emission electron gun.
2.3.5 Raman Spectroscopy
Raman spectroscopy is an analytical technique used to measure the vibrational energy modes
of a sample. It is named after Sir C. V. Raman, who first observed Raman scattering in 1928.
110

Raman spectroscopy can provide structural information through their characteristic vibrational
signatures in the Raman spectrum. When light interacts with molecular vibrations, phonons, or
other excitations in the system, the energy of the reemitted photons is shifted up or down in
comparison with incident light frequency by the energy of the interacting vibrational mode. The
shift provides information about vibrational, rotational, and other low-frequency transition of the
phonons in the crystalline system.
A sample is illuminated with a laser beam and the re-emitting light from the sample is
collected by a lens and sent through a monochromator. The elastic or so-called Rayleigh scattering
(the frequency does not change after scattering) is filtered out by filters or a spectrophotometer
while the rest of the light is collected onto a detector.

39
Chapter 3. Theoretical Investigation of High electro-optical
Materials
3.1 Background
AMO3-type ferroelectric oxides offer strong coupling between electrical, thermal, and optical
properties, and enable novel applications that leverage the coupled phenomena. They are currently
used in nonvolatile memories, actuators, transducers, and electro-optic (EO) devices, owing to
their excellent dielectric, piezoelectric and pyroelectric properties, and optical response.
111–114
For
optical applications, ferroelectric oxide perovskites exhibit large EO coefficients with low optical
loss, and are the materials of choice for low-power EO devices. EO modulators based on LiNbO3
have been widely studied for optical communication applications due to its good linear EO or
Pockels effect (𝑟 33
:32 pm/V) and high transparency over a wide range of wavelength.
35
Thin film
deposition of EO oxides, characterization of their optical response,
99
and fabrication of optical
devices have undergone significant refinement since the 1990s.
115–118
In line with this development,
there is a growing interest in achieving epitaxially grown ferroelectric thin films integrated on
silicon-based chips for optical waveguide modulators.
119–124

Among different ferroelectric oxides, BaTiO3 and LiNbO3 have been investigated intensively
for on-chip EO applications due to their sizable linear EO effect (tetragonal BaTiO3 on
Si 𝑟 42
:105 pm/V, 𝑟 𝑒𝑓𝑓 :148 pm/V
125
and LiNbO3 on Si 𝑟 33
: 17.6 pm/V
126
). However, modeling
methods for the EO response of these ferroelectric materials as a function of temperature,
frequency, strain and electric dipole orderings have not been well-established.
127–131
In fact, EO
40
effects are shown to be sensitive to the microstructure, and an accurate assessment of this intrinsic
property requires single crystals or high-quality thin films, which are not easily accessible or
prepared. Therefore, the theoretical prediction of the nonlinear optical properties of crystalline
materials along with the effect of various experimental conditions, such as strain and temperature,
can help to establish performance limits for subsequent experimental verification. In the past
decade, sustained efforts on theoretical investigations of nonlinear optical phenomena in oxide
perovskites have resulted in accurate methods for predicting these properties. DiDomenico and
Wemple revealed the importance of oxygen octahedra in perovskites on their optical
properties.
132,133
Ghosez and co-workers calculated the optical susceptibilities, Raman efficiencies,
and EO tensors based on density functional perturbation theory.
36,134–136
More recently, Hamze et
al., Qiu et al., and Paillard et al. studied the effect of strain on the EO tensor.
127–131,137
Furthermore,
with the ability to prepare atomically precise heterostructures and superlattices, it is of both
scientific and practical importance to understand the mechanism of the EO effect in these complex
systems and predict the EO coefficients reliably.
138,139
While first-principles calculation methods
used in previous studies are effective in predicting the EO effect for single crystals, modeling EO
effects in superlattices and multilayers presents a formidable challenge. The periodicity of the
superlattices and multilayers, which span few nm to few 10s of nm, and breadth of phase space in
terms of materials and periodicities needed to model EO effects and identify high-efficiency
structures make first-principles methods computationally expensive and impractical.
Phenomenological models, such as those based on Landau-Devonshire theory
140
enable fast,
accurate, and highly scalable calculations of the functional properties of complex structures. It is
41
important to note that Landau-Devonshire model uses input from experimental results or first-
principles calculations to fit the coefficients used in the model. Hence, the accuracy of Landau-
Devonshire expansion coefficients in the subsequent estimation of functional properties is
determined by these inputs. For a multicomponent system, such as superlattices and multilayers,
one can simulate their physical properties by summing up the thermodynamic free energies of each
component as a function of strain, electric fields, and their gradients.
141,142
This approach has been
extensively applied for the simulation of dielectric and piezoelectric responses of ferroelectric
materials and multilayer heterostructures.
143–145

The objectives of this study are to establish a semi-empirical model to simulate the EO
behavior of perovskite ferroelectrics, find a pathway to design large EO materials, and predict EO
coefficient values. This work has been published in Journal of Applied Physics.
146
This model uses
the phenomenological Landau-Devonshire model with parameters obtained from either first-
principles calculations or experimental results to improve the scalability of EO calculations for
complex structures without compromising on speed and accuracy. This model is first applied to
prototypical ferroelectric oxide BaTiO3 with first principles input. We obtained the free-energy
landscape associated with the transition between ferroelectric and paraelectric phases using
density-functional theory (DFT) calculations. We extracted Landau-Devonshire coefficients using
a polynomial fitting to the energy landscape and calculated the EO coefficients at room
temperature. We find that our model can predict EO coefficients that have good agreement with
experimental results. Using this model, we have calculated the temperature dependence of the EO
coefficients for BaTiO3 and find them to be within 30% of experimental results for most cases.
42
Moreover, the strain effect on the EO coefficient is discussed in the range of -5 to 5% misfit strain
for BaTiO3. Our model is able to capture the ferroelectric to paraelectric phase transition, which is
associated with a divergence of the EO tensor. Later, a survey among the ABO3 ferroelectrics has
been carried out to find the relation between the individual Landau coefficients and the EO
responses in order to find a guild line for finding strong EO materials in the future. To validate our
hypothesis, the calculation is carried out for BCZT-50 which perfectly fits into the regime where
our hypothesis lies, whereas the clear EO tensors are not available from the experiment.
3.2 Method
3.2.1 First-Principles Density-Functional Theory
The landscapes of free energy for the different AMO3 oxides were computed using DFT as
implemented in Vienna Ab-initio Simulation Package (VASP).
147
The DFT calculation is
performed in collaboration with Guodong Ren and Dr. Rohan Mishra at Washington University at
St. Louis.
146
We used projector augmented-wave (PAW) potentials.
148
In general, the accuracy in
the estimation of ferroelectric properties is sensitive to the adopted exchange-correlation
functionals such as the local density approximation (LDA),
149
and the semi-local generalized
gradient approximation (GGA) in the standard from of Perdew-Burke-Ernzerhof (PBE)
150
. GGA
is known to suffer from the so-called super-tetragonality error, which significantly overestimates
the structural distortion in conventional perovskite ferroelectrics
151
. For the most-studied oxide
ferroelectrics, BaTiO3 and PbTiO3, the lattice distortion, spontaneous polarization, and lattice
dynamics predicted by LDA functional agree well with the experimental results.
152
Therefore, we
chose LDA to describe the electronic exchange-correlation interactions. We have considered three
43
paradigmatic AMO3 oxides, BaTiO3 (P4mm, Amm2, R3m), for determining structural transition
and ferroelectric polarization. A cutoff energy of 700 eV was used to determine the number of
planewave basis sets in the calculations. We used Γ-centered 10× 10× 10 k-points mesh for
sampling the Brillouin zone of BaTiO3. The crystal structures were fully optimized until residual
forces were less than 10
−3
eV/Å. The spontaneous polarization induced by the polar soft-phonon
modes was calculated based on the modern theory of polarization
153
, which is a sum over the
contribution from the ionic and electronic charges. Symmetry and distortion-mode analyses were
conducted using programs from the Bilbao crystallographic server.
154
The intermediate images
corresponding to soft-phonon distortion were interpolated using the ISOTROPY software suite.
155

3.2.2 Landau-Devonshire Model
Landau phenomenological theory is widely used to describe phase transitions and temperature
dependence of physical properties of ferroelectrics.
156
Here, we use Helmholtz free energy to
describe the thermodynamics due to the convenience in choosing the internal variables:
polarization (P) and strain (S) as independent variables, whereas the electric field (E) and the stress
are external applied variables. The free energy and free energy density refer to Helmholtz free
energy and Helmholtz free energy density, unless noted otherwise. The Helmholtz free energy
density (f0) of a ferroelectric system under no external field is written as an expansion of the order
parameter - the polarization (P), as:
157

𝑓 0
=𝑎 1
(𝑃 1
2
+𝑃 2
2
+𝑃 3
2
)+𝑎 11
(𝑃 1
4
+𝑃 2
4
+𝑃 3
4
)+𝑎 12
(𝑃 1
2
𝑃 2
2
+𝑃 1
2
𝑃 3
2
+𝑃 2
2
𝑃 3
2
)+
𝑎 111
(𝑃 1
6
+𝑃 2
6
+𝑃 3
6
)+𝑎 112
(𝑃 1
4
(𝑃 2
2
+𝑃 3
2
)+𝑃 2
4
(𝑃 1
2
+𝑃 3
2
)+𝑃 3
4
(𝑃 1
2
+𝑃 2
2
))+
𝑎 123
𝑃 1
2
𝑃 2
2
𝑃 3
2
,
(3.1)
44
where the subscripts 1,2,3 refer to [100], [010], and [001] directions in the crystal, 𝑎 𝑖,𝑎 𝑖𝑗
,𝑎 𝑖𝑗𝑘
are the phenomenological Landau-Devonshire coefficients, and 𝑃 𝑖 is the polarization along
direction i. The temperature dependence of ferroelectricity is governed by the coefficient 𝑎 1
and it
is defined as
The other coefficients are all assumed to be temperature independent. Here T
0
and C are the
Curie-Weiss temperature and constant above which the system transitions to a paraelectric state,
and 𝜀 0
is the dielectric constant of free space, respectively. We set T
0
to be 388 K in the entire
simulation for BaTiO3 which were observed from experiments.
35,158–160
Classical Landau theory
ignores the temperature effect on the higher-order coefficients in the expansion. Nevertheless, it is
shown that the higher order terms are actually temperature dependent.
161
We include temperature
effects in our calculations, and for simplicity, we only consider the temperature dependent 𝑎 1
in
this work. The effect of temperature-dependent high-order terms, such as 𝑎 11
, on EO responses
will be a target for future work.
3.3 Electro-optic Tensor of BaTiO3
The variation of the free energy density under external electric field is written as:
where E1, E2, and E3 is the applied electric field along x, y, and z principal crystallographic
directions, respectively. The equilibrium configuration is determined by finding the minima of ∆𝑓 ,
where we shall have
𝜕 ∆𝑓 𝜕𝑃
=0. Then, the electric field E as a function of polarization is determined
by:
𝑎 1
=(𝑇 −𝑇 0
)/2𝜀 0
𝐶 . (3.2)
∆𝑓 =𝑓 0
−𝐸 1
𝑃 1
−𝐸 2
𝑃 2
−𝐸 3
𝑃 3
, (3.3)
45
Every time an external electric field is applied, we solve equations (3.4.a-c) to deduce the
field-induced polarizations. Then, the obtained polarization values are applied to solve the
corresponding equations (3.8-3.9) in the following paragraphs. Thus, we will always maintain the
thermodynamic equilibrium:
𝜕 ∆𝑓 𝜕𝑃
=0.
From equation (3.4), we have the electric field as a function of polarization. For the E2 and
E3, we have:
The dielectric tensor 𝜀 𝑖𝑗
is defined in terms of the first-order derivative of polarization with
respect to the external electric field.
Here, we summarize the derived dielectric constants for tetragonal (𝑃 1
=𝑃 2
=0,𝑃 3
≠0) and
orthorhombic (orthorhombic, 𝑃 1
=𝑃 2
≠0,𝑃 3
=0) BaTiO3 phases below. We don’t include the
𝐸 1
=
𝜕 𝑓 0
𝜕 𝑃 1
, (3.4.a)
𝐸 2
=
𝜕 𝑓 0
𝜕 𝑃 2
, (3.4.b)
𝐸 3
=
𝜕 𝑓 0
𝜕 𝑃 3
. (3.4.c)
𝐸 1
=
𝜕𝑓
𝜕 𝑃 1
=2𝑎 1
∗
𝑃 1
+4𝑎 11
∗
𝑃 1
3
+2𝑎 12
∗
𝑃 1
𝑃 2
2
+2𝑎 13
∗
𝑃 1
𝑃 3
2
+6𝑎 111
𝑃 1
5
+𝑎 112
(2𝑃 1
(𝑃 3
4
+𝑃 2
4
)+4𝑃 1
3
(𝑃 2
2
+𝑃 3
2
))+2𝑎 123
𝑃 1
𝑃 2
2
𝑃 3
2

(3.5.a)
𝐸 2
=
𝜕𝑓
𝜕 𝑃 2
=2𝑎 1
∗
𝑃 2
+4𝑎 11
∗
𝑃 2
3
+2𝑎 12
∗
𝑃 1
2
𝑃 2
+2𝑎 13
∗
𝑃 2
𝑃 3
2
+6𝑎 111
𝑃 2
5
+𝑎 112
(2𝑃 2
(𝑃 3
4
+𝑃 1
4
)+4𝑃 2
3
(𝑃 1
2
+𝑃 3
2
))+2𝑎 123
𝑃 1
2
𝑃 2
𝑃 3
2

(3.5.b)
𝐸 3
=
𝜕𝑓
𝜕 𝑃 3
=2𝑎 3
∗
𝑃 3
+4𝑎 33
∗
𝑃 3
3
+2𝑎 13
∗
𝑃 3
(𝑃 1
2
+𝑃 2
2
)+6𝑎 111
𝑃 3
5
+𝑎 112
(2𝑃 3
(𝑃 1
4
+𝑃 2
4
)+4𝑃 3
3
(𝑃 1
2
+𝑃 2
2
))+2𝑎 123
𝑃 1
2
𝑃 2
2
𝑃 3

(3.5.c)
𝜀 𝑖𝑗
𝜀 0
=
𝜕 𝑃 𝑗 𝜕 𝐸 𝑖 (3.6)
46
low-temperature rhombohedral phase since the rhombohedral phase is not accessible in the
experiments though strain engineering at room temperature.
Box I. Expression of spontaneous polarization and dielectric constants for tetragonal BaTiO 3.
Box II. Expression of spontaneous polarization and dielectric constants for orthorhombic BaTiO 3.
The propagation of light in a crystal is determined by the refractive index 𝑛 𝑖𝑗
. The relation
between the dielectric constant and the refractive index is 𝑛 𝑖𝑗
2
=𝜀 𝑖𝑗
/𝜀 0
. The linear EO tensor
𝑟 𝑖𝑗𝑘 describes the change of refractive index of a crystal in response to the applied electric field.
Therefore, we write the linear EO tensor 𝑟 𝑖𝑗𝑘 as first-order dependence of the inverse of refractive
index square when a static or low-frequency modulating electric field 𝐸 𝑘 is applied:
The index ijk refers to the ij component of the refractive index and the dielectric tensor, for
an applied electric field along the k direction.
36,128,162
For the following paragraphs, we denote the
index ij with Voigt notations, i.e. 11→ 1,22→ 2,33→ 3,23→ 4,13→ 5,and 12→ 6.
𝜀 11
=𝜀 22
=
1
2𝑎 1
∗
+2𝑎 13
∗
𝑃 3
2
+2𝑎 112
𝑃 3
4
,
𝜀 33
=
1
2𝑎 3
∗
+12𝑎 33
∗
𝑃 3
2
+30𝑎 111
𝑃 3
4
.
𝑋 11
=2𝑎 1
∗
+12𝑎 12
∗
𝑃 1
2
+2𝑎 12
∗
𝑃 2
2
+30𝑎 111
𝑃 1
4
+𝑎 112
(12𝑃 1
2
𝑃 2
2
+2𝑃 2
4
),
𝑋 22
=2𝑎 1
∗
+12𝑎 12
∗
𝑃 2
2
+2𝑎 12
∗
𝑃 1
2
+30𝑎 111
𝑃 2
4
+𝑎 112
(12𝑃 1
2
𝑃 2
2
+2𝑃 1
4
),
𝑋 12
=4𝑎 12
∗
𝑃 1
𝑃 2
+8𝑎 112
(𝑃 1
3
𝑃 2
+𝑃 1
𝑃 2
3
),
𝑋 33
=2𝑎 3
∗
+2𝑎 13
∗
(𝑃 1
2
+𝑃 2
2
)+8𝑎 112
(𝑃 1
3
𝑃 2
+𝑃 1
𝑃 2
3
),
𝜀 11
=
𝑋 22
𝑋 11
𝑋 22
−𝑋 12
2
, 𝜀 22
=
𝑋 11
𝑋 11
𝑋 22
−𝑋 12
2
, 𝜀 33
=
1
𝑋 33
.
𝛥 (𝑛 𝑖𝑗
−2
)=𝑟 𝑖𝑗𝑘 𝐸 𝑘 (3.7)
47
The equations in the box I and II give the dielectric constant as a function of polarization by
substituting them into equation (3.7). Thus, given all the Landau-Devonshire coefficients obtained
using polynomial fitting, the EO coefficients can be obtained. Here, we consider the case of
tetragonal and orthorhombic phases of BaTiO3 as examples. The EO tensors in the ferroelectric
tetragonal P4mm phase of BaTiO3 have three independent elements (Voigt notations), 𝑟 13
, 𝑟 33
,
and 𝑟 42
.
162

The orthorhombic phase of BaTiO3 is not a thermodynamically stable phase at room
temperature. However, it could be stabilized under tensile strain, such as epitaxially grown
orthorhombic BaTiO3 films on MgO.
115
The EO tensors of orthorhombic BaTiO3 are
3.4 Model Fitting and Parameters
The ferroelectric transition from a centrosymmetric reference can be expressed as the result
of ionic displacements along a specific direction with charge separation leading to a net electrical
dipole moment.
163
By interpolating the ionic displacements from a centrosymmetric structure to a
𝑟 13
=
𝜀 0
(4𝑎 12
∗
𝑃 3
+8𝑎 112
𝑃 3
3
)
2𝑎 1
∗
+12𝑎 11
∗
𝑃 3
2
+30𝑎 111
𝑃 3
4
, (3.8.a)
𝑟 33
=
𝜀 0
(24𝑎 11
∗
𝑃 3
+120𝑎 111
𝑃 3
3
)
2𝑎 1
∗
+12𝑎 11
∗
𝑃 3
2
+30𝑎 111
𝑃 3
4
, (3.8.b)
𝑟 42
=𝜀 0
(
8𝑎 123
𝑃 3
4𝑎 12
∗
+4𝑎 123
𝑃 3
2
+
4𝑎 13
∗
𝑃 3
+8𝑎 112
𝑃 3
3
2𝑎 1
∗
+2𝑎 13
∗
𝑃 3
2
+2𝑎 112
𝑃 3
4
+
4𝑎 13
∗
+24𝑎 112
𝑃 3
2
4𝑎 13
∗
𝑃 3
+8𝑎 112
𝑃 3
3
). (3.8.c)
𝑟 13
=
𝜀 0
(24𝑎 11
∗
𝑃 1
+120𝑎 111
𝑃 1
3
+24𝑎 112
𝑃 1
𝑃 2
2
+4𝑎 12
∗
𝑃 2
+24𝑎 112
𝑃 2
𝑃 1
2
+8𝑎 112
𝑃 2
3
)
(2𝑎 3
∗
+2𝑎 13
∗
(𝑃 1
2
+𝑃 2
2
)+2𝑎 112
(𝑃 1
4
+𝑃 2
4
)+2𝑎 123
(𝑃 1
2
𝑃 2
2
))
, (3.9.a)
𝑟 33
=
𝜀 0
(4𝑎 13
∗
(𝑃 1
+𝑃 2
)+8𝑎 112
(𝑃 1
3
+𝑃 2
3
))
(2𝑎 3
∗
+2𝑎 13
∗
(𝑃 1
2
+𝑃 2
2
)+2𝑎 112
(𝑃 1
4
+𝑃 2
4
)+2𝑎 123
𝑃 1
2
𝑃 2
2
)
, (3.9.b)
𝑟 42
=𝜀 0
(
4𝑎 13
∗
𝑃 1
+8𝑎 112
𝑃 1
3
2𝑎 1
∗
+12𝑎 11
∗
𝑃 1
2
+2𝑎 12
∗
𝑃 2
2
+30𝑎 111
𝑃 1
4
+12𝑎 112
𝑃 1
2
𝑃 2
2
+2𝑎 112
𝑃 2
4
+
4𝑎 13
∗
𝑃 2
+8𝑎 112
𝑃 2
3
4𝑎 12
∗
𝑃 1
𝑃 2
+8𝑎 112
𝑃 1
3
𝑃 2
+8𝑎 112
𝑃 1
𝑃 2
3
).
(3.9.c)
48
polar phase, the energy as a function of ionic displacements can be mapped using DFT calculations.
As has been shown recently by Paoletta and Demkov
127
, phonons causing the ionic displacements
will in turn alter the electronic energy of the system, and this is the origin of electron-phonon
interactions under the adiabatic approximation. That is to say, our DFT calculations for free energy
landscape of each distortion mode also reflects the electron-phonon interactions. For the
subsequent Landau-Devonshire fittings, we have converted the ionic displacements into
spontaneous polarization based on the modern theory of polarization.
164
The landscape of the
change in free energy density (J/m
3
) for the three ferroelectric phase transitions from paraelectric
BaTiO3 (P4/mmm) as a function of the polarization are shown in Figure 3.2. By fitting the Landau-
Devonshire expansion to the change in energy density with polarization, quadratic and higher-
order coefficients of the polynomial can be derived for ferroelectric transition along [001], [011],
and [111] direction for tetragonal (P4mm), orthorhombic (Amm2), and rhombohedral (R3m)
structures, respectively. The free energy density with respect to the polarization 𝑃 001
=𝑃 3
,
𝑃 011
=√𝑃 2
2
+𝑃 3
2
, and 𝑃 111
=√𝑃 1
2
+𝑃 2
2
+𝑃 3
2
can be described by the following equations,
respectively:
165

𝑓 001
=𝑎 1
𝑃 001
2
+𝑎 11
𝑃 001
4
+𝑎 111
𝑃 001
6
, (3.10.a)
𝑓 011
=𝑎 1
𝑃 011
2
+𝑎 11
𝑂 𝑃 011
4
+𝑎 111
𝑂 𝑃 011
6
, (3.10.b)
𝑓 111
=𝑎 1
𝑃 111
2
+𝑎 11
𝑅 𝑃 111
4
+𝑎 111
𝑅 𝑃 111
6
, (3.10.c)
49
where the superscripts O and R indicate the orthorhombic and rhombohedral phase for BaTiO 3,
𝑎 11
𝑂 =
1
2
𝑎 11
+
1
4
𝑎 12
, 𝑎 111
𝑂 =
1
4
(𝑎 111
+𝑎 112
), 𝑎 11
𝑅 =
1
3
(𝑎 11
+𝑎 12
) , and 𝑎 111
𝑅 =
1
27
(3𝑎 111
+
6𝑎 112
+𝑎 123
). We used the “Curve Fitting Toolbox” in MATLAB to fit the free energy density
curves obtained from DFT calculations. We fitted the energy density landscape of tetragonal
BaTiO3 with the equation (2.10.a) to obtain the 𝑎 1
, 𝑎 11
, and 𝑎 111
. To get the 𝑎 12
and 𝑎 112
, the
orthorhombic energy density is fitted to the equation (3.10.b). 𝑎 123
is derived by fitting the energy
density of rhombohedral phase using the equation (3.10.c) using all the other parameters obtained
from the previous steps. Then all the parameters are manually tuned to minimize the coefficients
of determination (R
2
) of three equations (3.10.a-c) by slightly changing only one parameter at a
time while fixing all remaining parameters. Thus, the whole sets of the Landau-Devonshire
coefficients can be derived.
Figure 3.1 Change with temperature of the structure and dielectric constant of a BaTiO3 crystal. The
schematics of Ti displacement and the corresponding spontaneous polarization direction is indicated by
the blue arrows. (Adopted from ref. [158])
50
We have used the LDA functional to calculate the Helmholtz free energy density as a function
of the polarization for LiNbO3, LiTaO3, and BaTiO3. In the case of BaTiO3, the high-temperature
phase has a centrosymmetric cubic structure. However, as the temperature decreases, a sequence
of phase transitions are observed experimentally as follows: cubic
388𝐾 → tetragonal
273𝐾 →
orthorhombic
183𝐾 → rhombohedral.
158,166
These three ferroelectric phase transitions result in a
change in the direction of the spontaneous polarization from the [001] axis (tetragonal, 𝑃 1
=𝑃 2
=
0,𝑃 3
≠0 ), to the [110] axes (orthorhombic, 𝑃 1
=𝑃 2
≠0,𝑃 3
=0 ), and to the [111] axes
(rhombohedral, 𝑃 1
=𝑃 2
=𝑃 3
≠0) as the temperature decreases. In Figure 3.2, the changes in
dielectric constant for the phase transition from the cubic structure directly to tetragonal,
Figure 3.2 Energy density as a function of
polarization along (a) [001], (b) [011], and (c)
[111] directions in BaTiO3 obtained using DFT
calculations.
(a) (b )
(c)
51
orthorhombic, and rhombohedral phase of BaTiO3 are shown. In Figure 3.2, we show the energy
landscape for BaTiO3 for polarization along [001], [011] and [111] directions. The spontaneous
polarization corresponds to the polarization value at which the energy reaches the minima at the
bottom of the double-well. The calculated spontaneous polarization values for tetragonal,
orthorhombic, and rhombohedral BaTiO3 are 0.24 C/m
2
, 0.27 C/m
2
, and 0.32 C/m
2
, respectively.
The Landau-Devonshire coefficients are extracted by fitting the double-well energy curves
obtained from the first-principles calculations to a polynomial expression (Equation (3.1)). Under
rigid symmetry framework, the 6
th
order series expansions are commonly accepted as the basic
free energy format describing the ferroelectric phase transitions in BaTiO3.
165
A polynomial with
higher-order expansion terms will yield better accuracy but the large number of fitting parameters
can also lead to overfitting. Moreover, the higher-order terms require additional information at
high polarization region and their physical meaning still remains unclear.
167
Hence, we performed
the polynomial fitting to the free energy density curves of BaTiO3 up to 6
th
order expansions to
ensure that the critical aspects of the EO phenomena can be sufficiently described without
overfitting. We fit the polynomial of Equations (3.10.a), (3.10.b), and (3.10.c) to free energy
density curves of the three ferroelectric phases: tetragonal, orthorhombic, and rhombohedral,
respectively, by simultaneously and manually adjusting the fitting parameters to find the smallest
𝑅 2
(coefficient of determination). The 𝑅 2
values are 0.998, 0.999, and 0.996 for tetragonal,
orthorhombic, and rhombohedral phase of BaTiO3, respectively.

52
Table 2 Extracted Landau-Devonshire coefficients from the DFT calculated free energy curves.
3.5 Electro-optic Coefficients of BaTiO3
We applied the fitted parameters from DFT and the parameters from Bell et al.
168
to calculate
the EO coefficients using Equations (3.8.a-c). Figure 3.3 shows the comparison between the
experimental results and the calculated values using the model. Overall, our method predicts the
sign of the EO constants correctly and the values of the EO coefficients are in good agreement
with the experimental works. The result of r33 and r13 from our fitted parameters are closer to
Landau-Devonshire Coefficient
BaTiO 3
This work Bell and Cross
168

𝑎 1
(Nm
2
/C
2
) -6.07× 10
8
-2.71× 10
7

𝑎 11
(Nm
6
/C
4
) 4.32× 10
9
-6.38× 10
8

𝑎 12
(Nm
6
/C
4
) 6.29× 10
9
3.23× 10
8

𝑎 111
(Nm
10
/C
6
) 1.29× 10
10
7.89× 10
9

𝑎 112
(Nm
10
/C
6
) -1.44× 10
10
4.47× 10
9
𝑎 123
(Nm
10
/C
6
) -1.67× 10
10
4.91× 10
9

Figure 3.3 Theoretical and experimental electro-optic coefficients of tetragonal BaTiO3,
a: Ref. 168, b. Ref. 151
53
experimental values with deviations of 30% and 10% vs. 100% and -50% for the coefficients from
literature. However, the calculated r42 values are around 55% lower than that from experimental
measurements. The deviation from the experimental values could be due to the extrinsic factor
such as stoichiometry and structural quality of the samples and domain structures, which are not
considered in this method. Moreover, according to Equation (3.8.c), r42 relies more on the off-
diagonal Landau parameters as a12 a13 and a112. The accuracy of the diagonal terms could be
verified by experimental results of the spontaneous polarizations, dielectric constants, and
piezoelectric constants. However, it is hard to identify the accuracy of the other terms and that is
also the reason of off-diagonal terms vary a lot in different reports even for the same materials
BaTiO3.
165,168–170
We will come back to this discussion in the later section 3.7.
3.6 Factors Affecting the Electro-optic Coefficient
3.6.1 Temperature Dependence
To the best of my knowledge, the experimental results of temperature dependency of the EO
coefficients of BaTiO3 have not been reported in the literature, and hence, I am unable to make the
comparison. Nevertheless, two sets of theoretical data are available Veithen et al.
135
and Pietro et
al.
171
for tetragonal BaTiO3, as depicted with red and yellow markers in Figure 3.4, respectively.
The EO coefficient 𝑟 33
increases with temperature below the Curie temperature and shows a
divergent trend close to the Curie temperature, as the spontaneous polarization abruptly drops to
zero at and above the Curie temperature.
54
It is worth reemphasizing that in our model, we assume 𝑎 1
as the only temperature-dependent
term and hence, the temperature dependence of EO response is essentially attributed to it. The
contribution of other terms to EO coefficients in equation (3.8.a) and (3.9.a), such as 𝑎 11
𝑃 3
2
, are
typically much smaller than 𝑎 1
. Hence, we resorted to this simplification. Any corrections to this
simplification will be explored in the future depending on the availability of the experimental
results. EO coefficients tend to be extremely large as the temperature approaches the Curie
temperature, T0. By definition, 𝑎 1
, given in Equation (3.2), converges to 0 as the temperature
reaches 𝑇 0
. This hints that small 𝑎 1
is desirable to achieve a large EO coefficient. To obtain a small
|𝑎 1
|, the energy barrier for switching the polarization from one energy well to the other has to be
low. It indicates that the origin of this EO enhancement is attributed to the ease of the ferroelectric
switching as manifested in the free energy landscape.
Figure 3.4 Temperature dependence of electro-optic coefficients in BaTiO3. a: Ref. 135,
b: Ref. 171
55
3.6.2 Strain Dependence
Figure 3.5 shows the EO tensor as a function of strain with misfit strains ranging from -5%
to 5% along the in-plane a and b axes for BaTiO3, which was obtained using Equations (3.8.a-c)
and (3.9.a-c). The thermodynamically stable phases are obtained by minimizing the total free
energy F under a given misfit strain. The calculation was performed by setting the temperature in
the free energy expansion coefficient, 𝑎 1
, as room temperature. We obtained two stable single-
phase states. The stable strain condition for tetragonal phase is denoted as T with yellow shade
(𝑃 1
=𝑃 2
=0,𝑃 3
≠0) below -1% compressive strain, and for orthorhombic phase, it is denoted as
(b ) (a)
GdScO
3
SrTiO
3

(c)
Figure 3.5 Evolution of EO coefficients (a) 𝑟 33
, (b) 𝑟 42
, (c) 𝑟 13

with misfit strain for BaTiO
3
. The EO coefficients calculated
from LD and DFPT are indicated with solid lines and dotted lines
with marker. The blue region and yellow region, respectively,
represent orthorhombic (O) and tetragonal (T) phase. The misfit
strain imposed on coherently strained BaTiO3 films grown on
SrTiO3 and GdScO3 substrates are marked to identify the
potentially achievable EO coefficients in strained thin films.

56
O with blue shade (𝑃 1
=𝑃 2
≠0,𝑃 3
=0) above ~1.9% tensile strain. For the phase region between
the T and O phase, it contains a two-phase mixture (T+O). At zero strain state, we obtain almost
identical values of electro-optical tensors as bulk values summarized in Figure 3.5. The small
deviation comes from the electrostrictive energy term, which is not included in the previous
calculations. The strain-induced polarization variations under compression and tensile strain have
a large contribution to the relevant EO constants. We predict a surprisingly high value, up to
thousands of pm/V, for 𝑟 42
coefficient of BaTiO3 under ~ −1.3% compressive strain and 𝑟 33
≈
800 pm/V under 1.8% tensile strain, which is 1 – 2 orders of magnitude larger than 𝑟 33
=32 pm/V
for LiNbO3.
172
In this specific case, at the transition region between T and T-O, the sign change of
𝑎 1
∗
leads to a large value of the 𝑟 42
coefficient; similarly, 𝑟 33
is large at the T-O and O phase
boundary due to the vanishingly small 𝑎 3
∗
values. Similar EO coefficient enhancement has been
demonstrated as a function of temperature near a ferroelectric phase transition due to the
divergence of the dielectric constant.
132,171
The polarization rotation at the phase boundary is easier
to achieve than in a single phase region, as the corresponding switching barrier is small. This could
also explain why ferroelectrics at the phase boundary usually have large dielectric, piezoelectric,
and EO responses.
46,50,173

3.6.3 Modulating Frequency Dependence
To investigate the frequency dispersion of the coefficients, we also applied the time-
dependent Ginzburg-Landau (TDGL) equation
99,140
:
𝜕 𝑃 𝑖 (𝑡 )
𝜕𝑡
=−𝐿 𝜕𝐹 (𝑃 𝑖 )
𝜕 𝑃 𝑖 (3.11)
57
where L is the kinetic coefficient (proportional to the dipole motion velocity) and t is time. We
adopted the L = 6000 [A
2
s/(Jm)] from the study of Liu et al. for tetragonal BaTiO3.
174
The energy
function F is Δ𝑓 in equation (5) except the fact that the applied electric field is static but here,
dynamic electric field is used as a triangular wave function:
where E0 is the amplitude of the electric field and f the frequency.
It is not easy to solve TDGL explicitly, as we have done for the static calculations. Therefore,
we performed the calculations using finite element method to obtain the EO coefficients from 10
Hz to 100 THz. In this work, we provide an example of the frequency dependent r33 for the
tetragonal BaTiO3.
𝐸 (𝑡 )=𝐸 0
𝑠𝑖𝑛 −1
[𝑠𝑖𝑛 (𝑓𝜋𝑡 )] (3.12)
Figure 3.6 The electro-optic coefficient r33 of tetragonal BaTiO3 dependence on the frequency of
modulating electric field ranging from 1Hz to 100 THz. The simulation result of this work is shown
as solid line with open circle marker in green and experimental results from different references are
represented by corresponding markers in red. a: Ref. 116, b: Ref. 180, c: Ref. 125, d: Ref. 123, e.
Ref. 122, f: Ref. 175, g: Ref. 179
58
The frequency dispersion of r33 is shown in Figure 3.6. By choosing kinetic coefficient
(proportional to the dipole motion velocity) of 6000 [A
2
s/(Jm)], the absolute value of 𝑟 33
remains
constant for frequencies up to several GHz, and then starts to decrease gradually to nearly zero at
5 THz. It is worth noting that the model predicts significant ionic contributions at frequencies up
to 100 GHz, which is necessary for high-speed optical communication applications. We also note
experimental results from the literature for comparison to validate our simulation. The highest
operating electric field frequency reported in the literature is 40 and 50 GHz demonstrated by
Girouard et al.
175,176
They report effective EO coefficient of 107 pm/V at 30 GHz which is
consistent with our result. Large 𝑟 33
coefficient as high as 342±93 pm/V at high frequency (1 GHz)
is reported by Abel et al. in 2019.
122
EO coefficients measured on high quality single crystal thin
film samples vary from 20-200 pm/V with an average of ~100 pm/V across DC to GHz
frequencies.
96,116,123,125,177–179
There are no experimental reports for electric field modulation in the
THz frequencies to the best of our knowledge but Chen et al. reported a coefficient of 8.27 pm/V
at THz frequency domain.
180
Further, we observe a diverging behavior near 1 THz, which
corresponds to the lowest resonance frequency of the dipole-dipole interaction in BaTiO3.
174
Thus,
the dipole motion is slower compared to electrical field modulations at THz frequencies. This has
been demonstrated in LiNbO3,
181
where the dielectric constants and the birefringence drops
dramatically at ~1-10 THz due to the resonance of the phonon modes corresponding to the
excitation field frequencies. The large EO coefficients of BaTiO3 in the frequency range of 10
MHz to 1 THz would make it a good candidate for use in the EO modulation devices in this
frequency range.
59
3.7 Discussion
From the discussion above, we could find that the first order parameter plays very important
role in determining the temperature and strain-dependence of EO coefficients. To gain more
insights, let us take a step back and get to know what the landau parameters are and why they are
important in general.
The ai, aij, aijk, and aijkl are the landau coefficients corresponding to the second, fourth, sixth,
and eighth order terms of polarization in the free energy expression for the ferroelectrics. The first
order ai determines the phase of the material. The Figure 3.7 (a) indicates the transition through
the ferroelectric phase with a negative a1 parameters to the paraelectric phase with a positive a1
parameter. If a1 is positive, the free energy has a minimum at the origin. In this case, we can ignore
(c)
(b) (a)
Figure 3.7(a) The dimensionless Landau energy density with respect to the polarization. The dependence
of dielectric permittivity (b) and spontaneous polarization (c) on the coefficient a1. The value of a1 in the
figure a is +1, 0, and 1. The other fourth and sixth order parameters are normalized to 1.
60
the terms with higher order than the quadratic term to estimate the dielectric permittivity by using
the simplified equation from Equation (3.6) ：
It describes the relationship between the polarization and modulating electric field in the case
of linear dielectric materials such as SrTiO3 and LaAlO3. Here, the a1 is defined as the inversion
of the dielectric permittivity. We will come to this point later in the following discussion.
On the other hand, if the parameter is smaller than zero, then the free energy profile has two
minima at finite polarizations ± P, indicating a symmetry breaking from non-polar
centrosymmetric phase to anharmonic, non-centrosymmetric phase, i.e., ferroelectric phase. The
finite polarizations correspond to the spontaneous polarization:
where the a11 and a111 is a general form of the fourth and sixth order Landau parameters. The
dependence of spontaneous polarization on the a1 is shown in Figure 3.7 (c). The polarization
decreases with the a1 increase in the region of ferroelectrics and goes to zero at a1=0. At this critical
point, the second order polarization P
2
term vanishes, and the energy profile shows an
extraordinary flat regime near the origin, indicating an infinite coherent length which represents
the natural spatial length scale variation of P.
On the contrary, the dielectric permittivity increases with the increasing of the a1 in the
ferroelectric phase region and reaches the maximum at this critical point a1=0. This is due to the
relationship of the permittivity and the landau parameter a1. Analogy to the non-linear dielectric
𝜒 =
𝑃 𝐸 =
1
𝑎 1
(3.13)
𝑃 𝑠 =
√
−𝑎 11
+√𝑎 11
2
−3𝑎 1
𝑎 111
3𝑎 111

(3.14)
61
susceptibility, the Landau coefficients are called dielectric stiffness – reciprocal of dielectric
permittivity.
The terms with even powers are omitted as they are symmetry forbidden. The function of free
energy must be even function. Hence, the dielectric permittivity and dielectric stiffness are not
one-on-one correspondence. Generally, the smaller the dielectric stiffness, the larger the dielectric
permittivity. To summarize, the sign of a1 determine the phase and the magnitude define the
spontaneous polarization and the dielectric strength.
When it comes to the EO coefficient, the relationship between each component and the
Landau coefficient is not as explicit as in the case of dielectric permittivity. To understand the role
of the Landau coefficients on the EO coefficients, we could differentiate the contributions of
Landau coefficients into two parts. One is the spontaneous polarization and the other the switching
energy barrier.
Spontaneous Polarization: The spontaneous polarization is a characteristic parameter for
each material. It is defined as a polarization state when no external stimulus is applied. It worth to
reminding that the calculations performed in this chapter was done in the thermodynamic
equilibrium by differentiating the free energy near the minima. Therefore, the value of polarization
in the equation is substituted by the spontaneous polarization. In this sense, the spontaneous
polarization exists in both the nominator and denominator but in different order. The terms in the
denominator are always one order higher than those terms in the nominator and thus, the EO
𝑃 =𝜒 (1)
𝐸 +𝜒 (2)
𝐸 2
+⋯ (3.15)
𝐸 =2𝑎 1
𝑃 +4𝑎 11
𝑃 3
+6𝑎 111
𝑃 5
+⋯ (3.16)
62
coefficient is inversely proportional to the spontaneous polarization. In other words, it is preferably
to have smaller spontaneous polarization values in order to obtain large EO coefficients. To
validate the hypothesis, a survey of polarization and EO coefficient relationship has been
performed in ABO3 ferroelectrics.
Table 3 physical properties summary of ABO3 ferroelectrics. Ps in the unit of C/m
2
and r in the unit of pm/V
A list of selected ferroelectric ABO3 materials and their physical properties has been
summarized in Table 3. Not surprisingly, the two materials with the lowest spontaneous
polarization values in the list, BaTiO3 and KNbO3, possess the largest EO coefficients and
extraordinarily high r51 over 1000 pm/V. On the other hand, the EO coefficients for materials with
large spontaneous polarization such as PbTiO3 and BiFeO3 are only 13.8 and 12 pm/V respectively.
We calculated the EO coefficient of selected ferroelectric materials using the Landau model. The
results are shown in Figure 3.8. To make the comparison between materials with different
symmetries possible, I am using the effective rc with the formula:
Materials
Space
Group
Ps r 33 r 13 r 51 r 23 r 42 r eff Remark Ref
BTO P4mm
0.26 105 8

1300 Experi. Zgonik PRB 1994
182

122 25 622 Sim. Veithen PRB 2005
135

PTO P4mm
0.5-
1.0
5.9 13.8

Experi.
Clamp
Handbook of optical
materials
172

5.9 9.0 30.5
Sim.
clamp
Veithen PRL 2004
36

KNO Amm2 0.42 64.0 28.0 380.0 1.3 105 65.0 Experi.
Gunter Optics
Communications
1974
183

BFO R3m
0.9 12.0 2.4

9.7

Sim. Sando PRB 2014
184

4.4 -6.4

10.9
Experi.
Film
Sando PRB 2014
184

LNO R3m
0.71 32.2 10.0

32.0 17.0 Experi.
Handbook of optical
materials
172

27.0 10.5 28.6 Sim. Veithen PRB 2005
136

LTO R3m 0.6 30.5 8.4

22.0 Experi.
Handbook of optical
materials
172

63
as a point of comparison. The effective value is considered important for the performance of
electro-optical devices than the individual components of r13 and r33.
185
The ratio of ordinary no
and extra-ordinary ne is estimated as 1, as the two values are typically similar for perovskite
oxides.
186
For this calculation, we adopted the Landau coefficients from literature reports, listed in
the appendix A. The spontaneous polarization values were calculated using Equation (3.14). These
values correspond to the diagonal terms among all the Landau coefficients and reflect the
contributions of a1, a11, a111 and a1111 as discussed earlier. Overall, the EO coefficient decreases
with the increasing spontaneous polarization across different ferroelectric materials. The largest
EO coefficients are estimated in BaTiO3 and KNbO3 which is consistent with the experimental
𝑟 𝑐 =𝑟 33
−(
𝑛 𝑜 𝑛 𝑒 )
3
𝑟 13
(3.17)
Figure 3.8 The plot of effective electro-optic coefficient against the spontaneous polarization. The simulated materials are
indicated by different colors. The values calculated from first-principle calculation in this work is marked as circles and
others values calculated from Landau coeffcients adopted from literatures are marked as squares, triangle and hexagonal
to refer to different sources. The used Landau coefficients are listed in Table 10 in Appendix A
64
result. As the spontaneous polarization becomes close to 1 C/m
2
, the EO coefficient is smaller than
100 pm/V. The BiFeO3 shows the smallest rc value of 17.9 pm/V which is also agrees with the
experimental result of 10.9 pm/V.
Now, let us look into the contribution of individual Landau coefficient terms to the
spontaneous polarization. As I mentioned earlier, the spontaneous polarization is closely related
to the second order landau coefficients in an inverse proportional manner - the closer the second-
order Landau coefficient is to zero, the smaller the spontaneous polarization. This could explain
the temperature dependence of the spontaneous polarization as shown in Figure 3.4 and also
experimental results where the spontaneous polarization of the KNbO3 decreases to zero and EO
coefficient increases as the temperature is close to Curie temperature.
187
Moreover, from Equation
(3.14), the highest order term a111 plays a more important role, as it is the only term on the
denominator. Further, the magnitude of sixth-order terms are generally 1 to 2 orders higher than
the second-order and fourth-order terms. Therefore, we could conclude that smaller second-order
Figure 3.9 Ball stick model of a BaTiO3 spontaneous polarization in the
direction of up and down. The origin of spontaneous polarization is the off
center displacement of Ti
4+
at the center of oxygen octahadral. The arrows
indicate the displacement direction which is opposite to the spontaneous
polarization direction.
Ba
Ti
O
65
and larger sixth-order terms are favorable for small spontaneous polarizations, resulting in high
EO coefficients.
From the physics point of view, spontaneous polarization is the polarization difference
between two states, namely the centrosymmetric phase to broken-symmetry phase. Here, I take a
tetragonal BaTiO3 as an illustration to the polarization state. The concept for different structures
is equivalent. Microscopically, the formation of the spontaneous polarization arises from the Ti
4+

ion displacement with respect to the oxygen octahedral, causing the net charge shift within a unit
cell. The magnitude of the polarization is determined by the effective charge and displacement of
the ion. In the case of shallow potential and small spontaneous polarization, even modest applied
electric field could lead to large changes in the susceptibility. This is why one can expect a large
change in the refractive index and hence, a large EO coefficient for materials with small
spontaneous polarization.
It is worth noting that EO coefficients calculated for BaTiO3 in this work are much smaller
than the literature values, although the spontaneous polarization simulated are nearly identical and
KNbO3 with a higher spontaneous polarization has a similar effective EO values comparable to
BaTiO3. Thus, it is evident that spontaneous polarization is not the only factor that affects the
magnitude of the EO responses. The switching energy barrier or so-called the well depth in the
energy profile also plays an important role as discussed below.
66
Switching Energy Barrier (Well Depth): Ferroelectric effect is not only characterized by
the spontaneous polarization at zero field, but also the polarization reversal under finite electric
field. Switching energy barrier characterizes the difficulty of switching from one polarization state
to the other. From a free energy point of view, this energy barrier corresponds to difference of the
two minima in the double-well potential curve with respect to the energy at P = 0. The well depth
also plays a minor role in this calculation.
The EO coefficients as a function of the well depth are shown in Figure 3.10. Overall, similar
to the spontaneous polarization analysis above, the EO coefficient decreases with increasing well
depth. It is generally believed that the magnitude of the depth of the double-well scales with the
magnitude of the ferroelectric polarization. It is mostly true for the materials selected except
BaTiO3 in this work, which a relatively smaller polarization but nearly an order larger well depth
Figure 3.10 The plot of effective electro-optic coefficient against the well depth. The simulated materials
are indicated by different colors. The values calculated from first-principles calculation in this work is
marked with circle and others values calculated from Landau coeffcients adopted from literatures are marked
with square, triangle and hexagonal to refer to different sources. The used Landau coefficients are listed in
Table 10 in Appendix A
67
than values from literature, which makes the EO coefficients smaller, but closer to experimental
values.
One way to reduce both the spontaneous polarization and well-depth is by making alloys of
ferroelectric and paraelectric materials. As I introduced earlier, Helmholtz free energy is simply
the sum of all the energy components in Landau-Devonshire theory.
142
The total 𝑎 1
is the sum of
𝑎 1
of the ferroelectric and paraelectric phases weighted according to their respective volume
fraction.
where 𝑎 𝐹 is negative for ferroelectrics and positive 𝑎 𝑃 for paraelectric. L is the ferroelectric
volume fraction. When alloying a ferroelectric with a paraelectric, the corresponding spontaneous
polarization and the well depth both decrease and eventually at a certain volume fraction the alloy
becomes a paraelectric. In the example shown in Figure 3.11, Ps = 0 at L = 0.2.
𝑓 =𝐿 (𝑎 𝐹 𝑃 2
+𝑏 𝐹 𝑃 4
+𝑐 𝐹 𝑃 6
)+(1−𝐿 )𝑎 𝑃 𝑃 2
(3.18)
Figure 3.11 Energy profile evolution as a function of volume fraction L of the ferroelectric content
in the alloy of ferroelectric-paraelectric.
68
3.7.1 EO Coefficient Prediction of BCZT-50
Table 4 Physical properties of the BCZT-50 from experiments. (Ref. 50, 173, 188-192)
To verify the hypothesis, I applied this model to a material which is an alloy derived from
BaTiO3 by substituting the Ba sites with Ca and Ti sites by Zr. The chemical formula is 0.5
Ba(Zr0.2Ti0.8)O3 – 0.5 (Ba0.7Ca0.3)TiO3 (BCZT-50). The spontaneous polarization is reported in the
range of 0.12~0.17 C/m
2
,
173,188–192
much smaller than that of BaTiO3. An effective EO coefficient
as high as 530 pm/V has been measured on polycrystalline samples by Dupuy et al.
50
However,
there are no reports on the individual EO tensor of BCZT-50 to the best of my knowledge. To
calculate the EO coefficients of BCZT-50, we used the Landau coefficients from Bandyopadhyay
et al. (shown in Table 10 in Appendix A)
193

When we compare the Landau coefficients of BCZT-50 with BaTiO3, the a1 coefficient for
BCZT-50 is not as small compared to BaTiO3 but the a111/a1 ratio is smaller, which gives rise to a
smaller spontaneous polarization of 0.14 C/m
2
, which is nearly half of the value of BaTiO3. The
double-well depth of BCZT-50 is 1.3 meV/unit cell which is 35% smaller than that of BaTiO3.
The reduced spontaneous polarization and reduced well depth of ferroelectric BCZT-50 as
compared to ferroelectric BaTiO3 are in good agreement with previous experimental results.
49,194

The EO coefficient r33 and r42 of BCZT-50 were deduced to be 399 pm/V and 1880 pm/V,
respectively, although r13=11.7 pm/V is comparable to BaTiO3. The EO coefficients of BCZT-50
are the highest amongst the materials discussed here, and ~2 times and ~3 times larger than the r33
and r42 of BaTiO3 values simulated in the section 2.7. Enhanced EO responses could be explained
Space Group a(Å) b(Å) c(Å) Ps (C/m
2
) 𝜺 d (pC/N) r (pm/V)
P4mm 3.998 3.998 4.03 0.12-0.17 2800 500 530
69
shallow barrier between the ferroelectric and paraelectric phases or two different ferroelectric
phases such as the O- and T-phases in a mixed-phase BaTiO3 based material.
195
The small barrier
between the two phases makes the polarization switching (between up and down) and/or
polarization rotation (between two ferroelectric states) easier.
3.8 Summary
A methodology to predict the EO coefficients in ferroelectric oxides as a function of strain,
modulation frequency, and temperature is demonstrated here. This method enables highly scalable
calculation of EO coefficients by combining computationally expensive, but accurate, first-
principles calculations with scalable phenomenological Landau-Devonshire theory. We applied
our approach to representative ferroelectric oxides such as BaTiO3. The calculated EO coefficients
are in good agreement with the experimental results. And the relevance of specific model
parameters for EO effect are discussed. In the light of the previous discussion of temperature and
strain effects on the EO responses, we conclude that small 𝑎 1
(𝑎 1
∗
for strained case) is favorable
for high-𝑟 EO materials.
A survey of ferroelectric complex oxides with available Landau coefficients was carried out.
The simulation results agree with the experimental data. A design matrix is established from the
survey that materials with low spontaneous polarization and shallow switching energy barrier are
likely to have larger EO response. To further verify the argument, a material of BCZT-50 with
nearly half the spontaneous polarization and 35% lower switching barrier of BaTiO3 is used in this
simulation and predicted to possess high r33 and r42 of 399 pm/V and 1880 pm/V using our
approach.
70
The method can be also extended to simulate the EO response of FE/DE heterostructures or
film with different phases or domain structure, once the complete set of the bulk, elastic,
electrostrictive and gradient energy terms are available either from first-principles calculations or
from experiments. I expect that this method will pave a way to discover new materials with high
EO performance.
71
Chapter 4. Epitaxial Growth of the Electro-optic Thin Film
4.1 Background
Ferroelectric materials such as LiNbO3 and BaTiO3 show pronounced linear electro-optic
effect (Pockels effect), especially in the telecom to visible energies.
37,126,176,196,197
LiNbO3 has been
used for decades to modulate light at high frequencies for optical spectroscopy studies,
198–200
and
more recently, it is being explored as a platform for optical modulators in communication
applications.
37,201
Recently, BaTiO3 has attracted more attention for its large electro-optic
coefficients ~ 30 times larger than in LiNbO3.
122,202
For communication applications, it is
necessary to grow electro-optic materials with optical transparency and low loss. Various synthesis
routes such as conventional solid-state reaction technique
47,203,204
, sol-gel method
205–207
, chemical
co-precipitation
208–210
, and hydrothermal technique
211
have been used in the fabrication of
ferroelectric ceramics. Among them, the solid-state reaction is the most universal one due to the
cost effectiveness and ease of use.
212
This process results in excellent ferroelectric properties but
does not achieve desired transparency. Ceramics are polycrystalline ionic materials, which is
composed of several extended defects such as grain boundaries, and pores. The opacity of
polycrystalline ceramics is caused by the scattering at the defects, where the disorder leads to
discontinuity of optical properties between the grains and across other extended defects. The use
of high purity, ultra-fine raw materials with ultrafast sintering process has been shown to achieve
a high degree of optical transparency in BCZT-50 ceramics.
50
The semi-transparent samples
produced by this method showed an unprecedented effective electro-optic coefficient of 530 pm/V.
72
Further, single crystalline fully transparent BCZT samples have been grown by flux growth
method, but no electro-optic coefficient was reported.
213
High quality single crystalline samples
with minimal defects and smooth surfaces and interfaces are desirable to measure the intrinsic
electro-optic properties of materials and similar quality manufacturable samples are needed for
applications. In this chapter, I will discuss the growth and characterization of BCZT-50, an EO
material with large EO coefficients, as shown in my earlier calculations in Chapter 3 and also
experiments on polycrystalline ceramic materials.
50

4.2 Epitaxial Growth of Barium Calcium Titanium Zirconium Oxide Thin
Film
4.2.1 Substrate Selection
BCZT-50 is a tetragonal perovskite which share the same space group of P4mm as BaTiO3.
It has lattice parameters of a = b = 3.998 Å and c = 4.013 Å. The available substrate for the BCZT
growth is shown in Figure 4.1. A low lattice mismatch between substrate and the film material is
crucial to achieve high-quality epitaxial films. We selected GdScO3 (GSO) as the substrate to grow
epitaxial BCZT-50 films. GSO is a commercially available substrate and has a pseudo-cubic lattice
Figure 4.1 Illustration of the range of commercially available single crystalline substrate
lattice constants and film lattice constants. Abbreviations: LSAT: [LaAlO3]0.3[Sr2AlTaO6]0.7.
LMSO: La0.7Sr0.3MnO3, BCZT-50: Ba(Zr0.2Ti0.8)O3 – 0.5 (Ba0.7Ca0.3)TiO3
73
parameter of 3.969 Å. The misfit strain calculated from Equation 2.1 is 1%. Next, I will focus on
the effect of various growth parameters on the structural properties of BCZT-50 thin films. To this
end, I studied the effect of parameters such as the growth temperature, pressure, cooling rate and
interlayer of SrRuO3.
4.2.2 Effect of Growth Temperature
We used structural properties derived from X-ray diffraction measurements as the criteria for
understanding the effect of the growth parameters on the structural properties of the BCZT-50 thin
films. We varied the substrate temperature and the oxygen partial pressure to identify the optimized
parameters for improved texture and epitaxial relationship with the substrate. First, we varied the
substrate temperature, Ts from 650 to 850° C with fixed oxygen partial pressure at 10 mTorr. Figure
Figure 4.2 (a) High resolution, short angular-range XRD plot of BCZT-50 film grown at 650, 750, 800, and 850° C. The
dashed lines indicate the position of fully strained and relaxed BCZT-50, GdScO3 (GSO) 220, and SrRuO3 (SRO) 220
reflections. (b) Variation of out of plane lattice spacing of the BCZT-50 thin film with the deposition temperature. (c)
Evolution of the full width at half maximum values of rocking curve with the deposition temperature.
74
4.2 (a) shows the XRD plot of ~100nm BCZT-50 films deposited at Ts = 650, 750, 800, and 850° C.
The BCZT-50 films exhibit a strong c-axis oriented texture with the [110] substrate
crystallographic direction for all temperatures. It is worth noting that we observed thickness fringes
around primary reflection in the XRD curve of 750° C. This indicates that the surface of the samples
grown at this condition tends to be smooth, also confirmed by AFM in Figure 4.7 (c). We observed
a gradual shift in the position of reflections for BCZT-50 thin film as a function of the Ts. We show
the evolution of the BCZT lattice parameter as a function of the growth temperature in Figure 4.2
(b). We observed a clear decrease in the out-of-plane lattice parameter from 4.2 to 4.06 Å as T s
increased from 650 to 850° C. This change in the lattice parameter is ascribed to the relaxation of
the strain induced by lattice mismatch of the substrate and film. We also performed rocking curve
measurements to study the perfection of the out-of-plane texture of BCZT-50 002 reflections at
different growth temperatures. The full width at half-maximum (FWHM) values of those rocking
curves are plotted against the substrate temperature in Figure 4.2 (c). The best FWHM value is
0.036° obtained at Ts = 750° C, indicating good crystallinity with excellent out-of-plane texture of
the as-grown BCZT-50 films.
4.2.3 Effect of Growth Pressure
The oxygen partial pressure was varied from 1 to 50 mTorr with Ts fixed at 750° C to
investigate the effects of oxygen pressure on BCZT-50 films structure. XRD spectra of BCZT-50
films grown at 1, 10, 20, and 50 mTorr are shown in Figure 4.3 (a). Unlike the temperature series,
oxygen pressure plays a lesser role in determining the relaxation state of the film. Instead, it gives
us clear guidance to smooth surface. At lower pressure (1 and 10 mTorr), the presence of
75
Pendellö sung fringes in the  -2 scans indicate a flat surface whereas the high pressures (20 and
50 mTorr) give relatively rough surface. The rocking curve FWHM values of all samples were
summarized in Figure 4.3 (b). The smallest FWHM value obtains at 10 mTorr as 0.036° .
4.2.4 Effect of Cooling Rate
As shown earlier, the growth was carried in a system with an in situ RHEED system. The
deposition started with a single crystalline substrate of GSO, which shows a 2D pattern as shown
in Figure 4.4 (c). Then, the BCZT film was deposited with the growth conditions shown in Table
1. During the deposition, we monitored the intensity of the specular spot and observed a sustained
intensity oscillation indicating a layer-by-layer growth mode. The growth rate is calculated to be
0.16 Å/pulse from the oscillation period and the repetition rate of the laser. The thickness of the
1mTorr
10mTorr
20mTorr
50mTorr
GSO 220
SRO 220
BCZT 002
( )
( ° )
(b)
(a)
θ ( ° )
( )
Strained
Relaxed
1mTorr
10mTorr
20mTorr
50mTorr
GSO 220
SRO 220
BCZT 002
( )
( ° )
(b)
(a)
θ ( ° )
( )
Strained
Relaxed
Figure 4.3 (a) Out of plane XRD plot of BCZT-50 film grown at 1, 10, 20, and 50 mTorr of oxygen
pressure. The dash lines indicate the position of fully strained and relaxed BCZT-50, GdScO3 (GSO) 220,
and SrRuO3 (SRO) 220 reflections. (b) The variation of full-width at half-maximum values of rocking
curve with the oxygen partial pressure in the deposition chamber.
76
film was kept as 100 nm and the 2D streaky pattern retained to the end of the growth, which
indicates a single crystalline film with a smooth surface. However, contrary to the in situ RHEED
results, the XRD scan of the sample display a broad 002 reflection with low intensity as shown in
Figure 4.4 (a). Broadening in the 2θ presumably attributed to the cooling of the as-grown sample
as it is the only process between in situ and ex situ measurements. Typically, the cooling rate is set
at the highest value where the properties of the film do not change upon decreasing the cooling
rate further. A cooling rate of 10-20 ℃/min is used for most of the perovskite thin film.
214,215
In
our case, the cooling rate had significant influence on the texture and crystallinity of the films.
Figure 4.4 (a) and (b) show XRD scans of films deposited at the same condition but cooled at 10
and 5 ℃/min, respectively. The width of the 002 reflection becomes much smaller and the intensity
Figure 4.4 Short angular XRD scans of BCZT on GdScO3 samples with a cooling rate at 10℃/min and (b) 5℃/min. (c) The
typical RHEED oscillations for BCZT film directly grown on GdScO3 substrate. Up to 50 oscillations have been observed.
Insert pictures are the RHEED patterns of GdScO3 substrate and as grown BCZT film at 750 ℃ and 10 mTorr. The abrupt
increase and decrease in the RHEED intensity pointed by arrow is due to manual adjustment of the incident electron beam
intensity.
GdScO 3
77
is 5 times stronger in the films cooled at 5 ℃/min than that of the films cooled at 10 ℃/min. The
BCZT-50 crystal quality is indeed sensitive to the cooling rate.
4.2.5 Effect of Interlayer – SrRuO3
Another important factor affects the texture of ferroelectric films is the ability to minimize
the nucleation of domains due to depolarization field.
216
One solution to this issue is the growth of
a metallic underlayer.
217–220
Strontium ruthenate SrRuO3 (SRO) is one of the conducting materials
among perovskite family that has drawn attention over 40 years. It has a metal behavior at high
temperature
221
, whereas a Fermi liquid behavior at low temperature
222
. Moreover, it becomes a
good candidate for the electrode in ferroelectric measurements because of its good lattice match
with several substrate materials and its nearly ideal growth mode which induces superior
crystallinity and surface smoothness as demonstrated by Eom et al.
107,223

A substantial difference was observed in the BCZT thin films with and without an SRO
buffered layer as shown in Figure 4.5. The angular positions of 002 reflection are the same for the
two films but the sample with a buffer layer of SRO shows well-ordered Pendellö sung fringes
Figure 4.5 High resolution short angular XRD plot of (a) BCZT(100 nm) on GdScO3 and (b) BCZT (100 nm) / SRO (15 nm)
on GdScO3). The thickness fringes are shown near the 002 BCZT diffraction peak for samples with SrRuO3 as bottom
electrode.
78
around the primary reflection at 43.7° in 2𝜃 . The fringes arise from the constructive and
destructive interference between the reflections at top and bottom faces of the BCZT thin film.
The interference is only possible in films with nearly atomically flat surfaces and interfaces. This
is also verified by the AFM results later. The separation of two adjacent fringe includes the
information of film thickness t with a relationship of 𝑡 =
(𝑛 1
−𝑛 2
)𝜆 2(sin𝜔 1
+sin𝜔 2
)
, where the n1 and n2 are
the index of the fringe and 𝜔 1
and 𝜔 2
are the corresponding Omega angle (half of the 2𝜃 in this
case). The total thickness of this BCZT film is calculated to be 108 nm which is close to the
thickness anticipated from RHEED oscillations.
4.3 Surface Characterization of Barium Calcium Titanium Zirconium
Oxide Thin Film
As introduced earlier, the surface and interface conditions are the key factors that affect the
scattering loss in the EO application. A perfect atomically smooth surface is always favorable to
any light modulations with low losses. The characterization of the surface of BCZT-50 films were
carried out using in situ RHEED and ex situ AFM analysis. In Figure 4.6, we present a set of
representative RHEED patterns and intensity oscillations of the specular spot at the optimal
condition of 750 ° C and 10 mTorr. At first, the annealed GSO substrates exhibited a clear 2D
diffraction pattern, which attests to the presence of highly smooth GSO surface. During the
deposition of SRO, well defined diffraction and specular spots with streaky pattern, and RHEED
intensity oscillations were observed. We grew 12 nm thick SRO layer and estimated the growth
rate of SRO to be 0.049 Å/pulse. We followed the SRO deposition with the growth of BCZT-50.
Initially, the 2D diffraction pattern was retained with the subtle change in the diffraction spots
79
corresponding to the larger lattice parameter of BCZT-50. As the growth continued, the diffraction
spots gradually transformed to become streaks. The streaky pattern remained till the end of growth,
which again indicates a relatively smooth surface. The Figure 4.6 (c) shows the RHEED pattern at
the end of the growth of a 100 nm thick BCZT-50 film. As evidence of layer-by-layer growth, we
show the oscillations in the intensity of the specular spot for BCZT-50 in Figure 4.6 (d). The
growth rate of BCZT-50 was estimated as 0.135 Å/pulse. To quantitatively analyze the interface
and surface roughness obtained upon the growth, we preformed AFM studies on three different
samples of annealed GSO substrate, 15 nm SRO on GSO and 100 nm BCZT-50 film on 15 nm
SRO/GSO substrate as shown in Figure 4.7. Overall, all the surfaces have a root mean square
roughness of ~2 Å or less. SRO has a relatively smooth surface while the step feature is not readily
GSO
Substrate
SRO film after growth BCZT film after growth
( )
( )
( )
( )
//
//
( )
( )
(b) (a) (c)
(d)
SRO
BCZT
Figure 4.6 Representative reflection high energy electron diffraction patterns of: (a) GdScO3 (GSO) substrate, (b)
SrRuO3 (SRO) bottom electrode, and (c) BCZT-50 film. (d) Specular spot intensity oscillations of SrRuO3 and
BCZT-50 film.
80
apparent. The annealed substrate and BCZT-50 film exhibit atomically smooth surface with step
terraces. The height of the steps corresponds to single unit cell as shown in Figure 4.7 (d).
4.4 Structural Characterization and Strain Analysis of the Thin Films
To establish the epitaxial relationship between the film and the substrate, we performed high-
resolution XRD, RSM and STEM studies. Figure 4.8 (a) shows a representative XRD pattern from
a 50 nm BCZT-50 thin film grown at 750 ° C and 10 mTorr, where only 00l family of reflections
are visible for the BCZT-50 thin film with the ll0 reflections of the substrate, which correspond
the pseudo-cubic 00l reflections. This indicates that the BCZT-50 is highly oriented along the out-
of-plane direction of GSO substrate. The SRO layer reflections are not readily observed due to
weak reflections arising from its ultrathin nature, but one could clearly observe them in Figure 4.2
Figure 4.
Rq=0.222nm Rq=0.216nm Rq=0.235nm
GdScO
3
SrRuO
3
BCZT-50
1 µm
1 µm 1 µm
0nm
5nm
(a) (b) (c)
(d)
Figure 4.7 Representative topography image of (a) annealed GdScO3 substrate, (b) SrRuO3 film, and (c) BCZT-50 film surface. (d)
Cross-sectional profile of BCZT-50 film showing the step height. The distance between two horizontal guidelines is 4 Å, which
corresponds to the lattice spacing expected in single-layer-step.
81
and Figure 4.3. To further illustrate the in-plane epitaxial relationships, we performed RSM studies
centered on 332 GSO reflection. We observed three reflections corresponding to SRO, GSO and
BCZT-50 in the RSM. All of three reflections possess the same in-plane reciprocal lattice
parameter (qx), which indicates all the layers are fully strained to the substrate with negligible
relaxation. For the out-of-plane (qz) direction, the lattice constants agree well with the out-of-plane
lattice parameters obtained from 2-  scans. Based on these results, we conclude that BCZT films
were epitaxially grown on GSO (110) substrates with the following epitaxial relationship:
BCZT(001)||GSO(110) and BCZT[100]||GSO[001].
Figure 4.8 (a) XRD plot of a representative BCZT-50 thin film. (b) A high-resolution reciprocal space map of BCZT-50 thin film
centered on GdScO3 332 substrate peak. The map clearly shows the film is coherently strained to the substrate.
82
We carefully studied the structural evolution dependence of film thickness in the method of
XRD. The thickness of the films is precisely controlled with the growth rate calculated from
RHEED intensity oscillations. The XRD pattern for 20 nm to 200 nm BCZT films is presented in
Figure 4.9. All the films have three major reflections corresponding to the substances indexed in
the Figure 4.9. The fixed angular positions of GSO and SRO indicate the constant out-of-plane
lattice parameters, whereas the lattice parameters of BCZT-50 shift to the higher 2-theta angle as
the thickness increases. This can be explained as the film relaxation. The further RSM
Figure 4.9 Short angular range XRD plot of BCZT thin film with thickness of 20 nm, 50 nm, 80nm,
100nm and 200 nm.
Figure 4.10 Reciprocal space map of (a) 50 nm (b) 100 nm and (c) 200 nm films. The black x marks indicate the
reflection position of the fully strained film and red x mark indicates the fully relaxed reciprocal lattice constant
position.
(c) (b) (a)
83
measurements also confirm the strain state of the BCZT thin film in Figure 4.10Figure 4.11. The
lattice parameter of the fully strained BCZT is calculated to be 3.969Å and 4.110Å for the x and z
axis, respectively. The lattice parameter in the x direction is consistent with the lattice parameter
of the GSO. From Figure 1.1Figure 4.10 (a) and (b), the films at 50 nm and 100 nm thickness are
coherently strained to the substrate while the 200 nm films are partially relaxed as the (103)
reflection shifts from the fully strained position indicated by the black x mark to the fully relaxed
position at the red x mark.
To investigate the atomic structure of BCZT/SRO heterostructures, STEM experiments were
performed on BCZT (109 nm)/SRO (15 nm) thin film. We did not observe any misfit dislocations
at the film/substrate interface in the cross-sectional high-angle annular dark-field (HAADF) STEM
images as shown in Figure 4.11Figure 4.10 (a). The atomic resolution HAADF image in STEM is
obtained by elastic scattering of the electron beam from different atomic columns (Ba, Ca, Zr, and
Ti), where the degree of elastic scattering is approximately proportional to the squared atomic
number (~Z
2
).
224
Therefore, it is easy to distinguish the elements by the brightness of the atomic
(a) (b)
(c)
Figure 4.11 (a) Cross-sectional low-magnification HAADF image of a BCZT/SrRuO3/GdScO3 sample. No obvious misfit
dislocations were observed in BCZT thin film. Atomic resolution HAADF images of (b) BCZT/SrRuO3 and (c)
SrRuO3/GdScO3 interfaces with overlaid atomic models. The brown, blue, green, grey, purple, and pink atomic symbols
correspond to (Ba, Ca), (Ti, Zr), Sr, Ru, Gd and, Sc elements, respectively.
84
columns. As a result, atomic columns corresponding to (Ba, Ca) appear brighter than the (Ti, Zr)
atomic columns. This is consistent with the theoretical structure of BCZT that is overlaid in Figure
4.11 (b) with negligible lattice parameter difference.
45,48
Sharp interfaces of between SRO/GSO
and BCZT/SRO were observed and confirmed in Figure 4.11 (b) and (c).
Strain analysis on the HAADF STEM imaging clearly reveals that the films of BCZT and
SRO were fully strained to GSO substrate as shown in the Figure 4.12. The red square box in the
Figure 4.12 is the area chosen as the lattice parameter reference where the strain is calculated with
respect to. The strain in the horizontal direction is negligible throughout the cross-section due to
the small mismatch between the film and substrate indicating a fully strained film. The strain map
in the lateral direction shows the difference in lattice parameter across the sample. The lattice
parameter is homogeneous in the film whereas the GSO substrate and the SRO bottom electrode
Figure 4.12 Strain analysis of the HAADF image of the BCZT/SRO/GSO sample. The
𝜀 𝑥𝑥
and 𝜀 𝑦𝑦
are the strain in the lateral and horizontal directions which refer to the lattice
parameters measured in the red square box in the HAADF image.
85
have smaller lattice parameter. This result is consistent with conclusion from RSM measurement
shown in Figure 4.10Figure 4.11 (b)
4.5 Ferroelectricity and Piezoelectricity Response
To demonstrate the ferroelectric properties in the epitaxial BCZT-50 thin films, ferroelectric
measurements are carried out in collaboration with Zheng Wang and Dr. Asif Khan at Georgia
Institute of Technology.
94
Figure 4.13 (a) shows the dielectric constant (𝜀 𝑟 ) vs. electric field (E)
characteristics of a 200 nm BCZT-50 capacitor with SRO and Au/Ti electrodes measured at 1 kHz
for both upward and downward sweeps. A slight shift in the 𝜀 𝑟 −𝐸 characteristics between upward
and downward sweeps is observed, and at their intersection, 𝜀 𝑟 =1400 is measured. The
corresponding phase angle of the impedance spectroscopy is shown in Figure 4.13 (b). This
demonstrates that the sample has low loss with the phase angle close to 90° over the range of
applied electric field. Figure 4.13 (c) depicts the measured polarization (P)-electric field (E)
characteristics at f=1 kHz of the same sample. Note in Figure 4.13 (c) that the hysteresis in the P-
E loop has a narrow opening; such slim hysteresis loops are characteristic of ferroelectric
Figure 4.13 (a) Dielectric constant and (b) impedance angle as a function of DC electric field at room temperature
(solid line and dash line indicate the scans with increasing and decreasing electric fields) and (c) ferroelectric
hysteresis loop of a typical BCZT-50 film. Dash line indicates the build-in electric field. The blue and red lines
correspond to sweeps starting with positive and negative applied electric fields.
86
relaxors.
225
Our measured remnant polarization (Pr) of 3.5 𝜇 C/cm
2
and coercive field (Ec) of 26
kV/cm are in the same range of BCZT-50 films as previously reported by Luo et al.
226

In addition, the P-E hysteresis loop are not symmetric with respect to the origin which is
presumably due to our use of different metallic layers with different work functions as top and
bottom electrodes (top Au/Ti, bottom: SRO). The resulting built-in electric field is calculated to
be -38 kV/cm. This built-in electric field has also been reported in many compositional
ferroelectric films, such as (Ba,Sr)TiO3, Pb(Zr,Ti)O3, and BCZT superlattices.
227–229
The origin of
the internal field are still not completely understood. Both intrinsic (polarization gradient, free
space charge, etc.) and extrinsic (asymmetric contact, strain at interface, oxygen vacancies, etc.)
230

factors could play a role in the offset of the polarization or the built-in electric field.
231,232

(a)
(b)
Figure 4.14 PFM responses of a BCZT film. (a) the phase and (b) amplitude plot as a function of electric
field. The box-in-box pattern is shown in terms of (c) phase and (d) amplitude. The corresponding film
thickness is 100 nm for this measurement.
(c)
(d)
87
To understand the microscopic polarization characteristics of BCZT-50, we PFM learn about
the spatially resolved switching characteristics. For these measurements, the applied electric field
is perpendicular to the surface of the sample. The amplitude of the PFM signal is sensitive to the
deformation of the surface and is mainly determined by the piezoelectric effect. The phase signal
is corresponding to the polarization direction of the film. As shown in Figure 4.14 (a), the phase
changes 180° during the forward and backward scan of the voltage, indicating a polarization
switching from up polarization to down polarization. The amplitude of the displacement shows a
high value of nearly 1.5 nm under the applied voltage of -6 V, indicating a large piezoelectric
coefficient for BCZT-50 films.
For the BCZT-50 film, we can apply positive and negative electric fields to switch the
domains between up and down orientations. While the height signal indicates a flat topography
shown in Figure 4.7 (c), the structure written into the film is clearly visible in the PFM amplitude
and phase image. The phase between two different domain states is 180° , as expected for domains
oriented in opposing directions. The diffuse boundary of the inner box pattern indicates the relaxor
ferroelectric behavior where the spontaneous polarization would not last long as the hard
ferroelectric, which is also observed in the ferroelectric measurements.
4.6 Summary
In summary, we have shown high-quality epitaxial growth of BCZT-50 thin films on
SRO/GSO substrates. The growth condition has been optimized based on crystallinity as deduced
by XRD studies. Sustained layer-by-layer growth mode was achieved as monitored by RHEED.
Atomic force microscopy studies reveal one-unit cell high steps with atomically flat terraces in as-
88
grown BCZT-50 film surfaces. STEM studies did not reveal evidence of misfit dislocations and
strain relaxation, confirming high quality interfaces between substrate/SRO and BCZT/SRO. A
relaxor ferroelectric behavior has been observed with relatively high dielectric constant. Electro-
mechanical measurements show a large piezoelectric response.

89
Chapter 5. Electro-optic thin film integration on silicon platform
5.1 Background
Network interconnects for communication at the inter- or intra-chip level up to long distances
continue to increase the complexity with a need for larger bandwidth over the years.
12
There are
clear limitations of copper wires as the on-chip interconnect in terms of loss, heat dissipation, and
fundamental speed. In the foreseeable future, the interconnect market will see a gradual transition
from electrical to optical connections, with longer and more complex links at all levels. The state-
of-the-art optical communication remains long distance, i.e., intercontinental optical fiber links or
interconnection between servers in data center. The target application areas for optics lies not only
in the intra/interchip data connection, but also in minimizing the losses in the current silicon
photonics platform, both of which require minimization of the optical devices and integration to
the silicon platform for seamless integration of photonics and electronics (complementary metal-
oxide-semiconductor (CMOS) platform).
Silicon photonics has been a great platform for integrated photonic circuits for decades.
However, centrosymmetric crystals such as silicon do not show appreciable Pockels effect.
Materials with sizeable Pockels coefficient have to be integrated on to silicon photonics platform
to combine the benefit of the effective and low loss modulation with stable and cost-effective
silicon photonics. Epitaxial growth of thin films on silicon substrate is considered a key technology
for developing thinner and smaller photonic devices, compatible with the current CMOS
fabrication platform. It is generally believed that the leakage current and optical scattering are
90
lower for single crystalline epitaxial films than those of polycrystalline films. These features are
crucial to the applications such as field effect transistors, electro-optical modulators, and micro-
electro-mechanical systems.
A large community has focused on combining silicon with new materials to enrich the variety
of properties available in the photonic platform for new device concepts. Here are some examples:
III/V materials for integrated laser,
233
Ge photodetectors
234
and SiGe modulators
235
. Surprisingly,
the class of electro-optic materials, which is critical for state-of-the-art telecommunication, is not
widely integrated to silicon photonic devices. One of the reasons is the small (~few pm/V) electro-
optic coefficients of IV or III/V compounds.
172
Alternative materials such as ABO3 class of oxides
including perovskites shown to possess strong linear and quadratic electro-optic effects both
experimentally and theoretically.
19,36,118,196,236–239
LiNbO3 , for instance, has been used for decades
to modulate light at high frequency.
35
BaTiO3 also shows an even stronger EO response and Abel
et al. demonstrated the integration of BaTiO3 to Silicon platform.
123,125,196

5.1.1 Epitaxial Growth of Strontium Titanate on Silicon
The epitaxial growth of oxide thin films on a silicon substrate has few intrinsic problems. The
major limitation is the formation of a stable amorphous silicon dioxide on the surface of silicon in
oxidizing atmosphere which is required to achieve stoichiometric oxide film growth. Thus, it was
widely believed that no epitaxial oxide thin film can be prepared on crystalline silicon without an
interfacial SiO2. Second, interdiffusion of silicon and the film elements at high temperature result
in reaction or secondary-phases formation. Third, the proper lattice matching with specific crystal
orientation is also essential for epitaxial growth. There is a need for intermediate buffer layers to
91
grow epitaxial perovskite thin films with robust electro-optic responses on silicon. Several
different seed or buffer layers such as MgO
240
, SrTiO3
119
, LaAlO3
241
, YSZ(yttria-stabilized
zirconia)
214
, Pt/Ti/SiO2
242
have been studied to enable the growth and promote the quality of
perovskites films.
Indeed, in order to deal with the differences in bonding, chemistry and coordination between
silicon and the complex perovskite oxides, McKee et al.
119
developed a procedure for the growth
of an epitaxial SrTiO3 layer directly on silicon. After removal of the SiO2 from the surface using
wet chemical approaches, the Si substrate is immediately transferred to the ultra-high vacuum
molecular beam epitaxy chamber. First, half-a-layer of Sr metal is deposited on the surface of Si
which forms an ordered alkaline earth metal-silicide structure SrSi2 at high temperatures to prevent
the oxidation of Si, then SrTiO3 is deposited in the form of an amorphous at low temperature under
oxygen atmosphere, which is recrystallized at an elevated temperature. The deposited SrTiO3 films
Figure 5.1 schematic of epitaxial growth of SrTiO3 on Si, summarized from Ref. 119.
92
have a close lattice matching to the Si substrate with 45° rotation of the unit cell in-plane. The
layer-by-layer thermodynamic stability, which is maintained at atomic level during this process,
allows a sequentially stable, heteroepitaxial growth transiting from the Si to high-quality
crystalline complex oxides.
In our work, a 10-20 unit cells thick SrTiO3 buffer layer is grown onto 5 x 5 mm Si (001)
wafers by MBE provided from Dr. Zhe Wang and Prof. Darrell Schlom at Cornell University.
5.2 Epitaxial Growth of Barium Calcium Titanium Zirconium Oxide on
Strontium Titanate/Silicon Substrate
The approach of depositing BCZT-50 films on Silicon was previously reported,
243–246
but
most of them explore in the polycrystalline film without epitaxial relation. The primary issue is
the presence of an amorphous silicon dioxide layers, which eliminates any in-plane epitaxial
relationship, when non-epitaxial buffer layers are used. In the best-case scenario, we might be able
to get out-of-plane textured films on silicon. The large mismatch of 4% between the BCZT-50
(a)
Figure 5.2 (a) RHEED patterns at various stages during the growth process of 200 nm BCZT-50 Film. (b) The intensity
of specular spot for BCZT-50 grown on SrRuO3/SrTiO3/Si. (c) the topography of as-grown BCZT film measured by
AFM. The RSM roughness is 0.4 nm.
(c)
(b)
93
(3.998 Å) and Si (3.839 Å) (~4%) is another impediment to growing epitaxial films with smooth
surfaces and minimal extended defects such as dislocations. We can overcome this issue by using
STO and SRO as intermediate buffers with lattice parameter of 3.905 Å and 3.925 Å (pseudo-
cubic), respectively, to accommodate such mismatch.
The epitaxial growth of BCZT-50 thin films was carried out with the same equipment setup
and the condition from last chapter. The STO/Si substrate was first sonicated in acetone and IPA
for 5 minutes in sequence and then heated to 750 ° C. The thin layer of SRO film was grown as the
bottom electrode and then a BCZT-50 film was deposited. The RHEED of SRO surface showed a
2D pattern and then once the BCZT-50 deposition started, the pattern became streaky and
eventually ended up with completely 3D indicating an island growth mechanism. This could be
confirmed by monitoring intensity of the specular spot. The oscillations in the intensity of the
specular spot were visible for the first seven layers with a gradual decrease in intensity and then
the oscillation disappeared completely. The fast decay of the intensity results from surface
roughening which is induced by the large lattice mismatch. After the growth of a 200 nm film, a
low surface roughness of 0.4 nm of the BCZT-50 layers is measured by AFM as shown in Figure
5.2 (c). This number is twice larger than that of films on GSO with lattice mismatch below 1%.
94
X-ray θ–2θ diffraction displays only 00l reflections for BCZT-50 film as shown in Figure 5.3
(a), suggesting the film has out-of-plane texture with respect to the substrate. The position of the
002 reflection reveals a BCZT-50 c-axis lattice parameter of 4.05Å, corresponding to the fully
relaxed value. Rocking curve scan in Figure 5.3 (b) shows the good crystalline quality with a
FWHM of 0.205º of the BCZT 002 reflection (red) which is comparable to that of the BaTiO3
films integrated on Si.
196
However, this value is much larger than that of BCZT-50 films in blue
curve reported in the last chapter primarily due to the large lattice mismatch.
Figure 5.3 (a) High resolution, wide angular-range XRD plot of a BCZT-50 film grown on SRO/STO/Si substrate.
The peaks are indexed correspondingly above. The inserted figure is the short angular-range XRD scan of the film
in 40-50 degrees of 2-theta. (b) the rocking curve scans of BCZT 002 on Si (red line) and on GSO (blue line) 2-
theta peak at 44.7º . The full width at half maximum is 0.205 º and 0.02º for BCZT films on Si and GSO respectively.
95
We performed PFM studies to characterization piezoelectric and ferroelectric properties. The
switching of the ferroelectric state is demonstrated by the phase signal as shown in the Figure 5.4
(b). The difference between two domain states is 180 ° as expected for the domain switching to the
opposite direction during the upward and downward voltage scan. A typical “butterfly” loop is
observed for the BCZT-50 film on silicon. The slope of the butterfly curve is nearly ~200 pm/V
which qualitatively indicates a large piezo-response for the BCZT film integrated on Si.
5.3 Alternative Methods of Transfer BCZT Films to Silicon Substrate
As demonstrated above, direct integration of BCZT film to silicon substrate has been
achieved by buffer layers of SRO and STO. Nevertheless, there are fundamental materials issues
that cannot be solved even in epitaxial thin film. The large lattice mismatch and the dissimilar
crystal structure limit the quality of the films as one can easily distinguish the difference in the
rocking curves between the BCZT-50 films grown on silicon and GSO. To solve this issue, an
alternative method to integrate BCZT-50 thin films on silicon was also attempted though epitaxial
transfer.
Figure 5.4 Piezoelectric response of the BCZT50 films on STO/Si substrate. The result of typical measurements
of (a) amplitude and (b) phase signal.
96
The desired film material(s) is epitaxially deposited on a lattice-matched substrate with a
sacrificial layer which can be selectively removed later. After removal, the film is released from
the lattice-matched substrate and then transferred to silicon substrate. This approach will minimize
the issue of lattice mismatch or dissimilar structure. In this work, the sacrificial layer is selected as
La0.7Sr0.3MnO3 (LSMO) for the following two reasons. One is that the lattice parameter of LSMO
is 3.85Å (pseudo-cubic) which is close to the BCZT lattice parameter. Second, the LSMO could
be selectively etched by diluted KI + HCl solutions.
For the epitaxial transfer, the overview of the procedure is shown in Figure 5.5. We started
with the growth of the oxide films. The growth starts with a single crystalline smooth GSO
substrates which show a 2D RHEED pattern. Then the LSMO layer was deposited firstly as the
sacrificial layer. The RHEED pattern of LMSO became slightly steaky due to the surface
roughening along the step edges. BCZT-50 film shows similar RHEED pattern as grown on
SRO/GSO substrates which became streaky at 100nm thickness. Mr. Huandong Chen supported
me for the following process. We spin coated thick layers of polydimethylsiloxane (PDMS) and
Figure 5.5 Schematic for epitaxial growth and epitaxial transfer of BCZT thin films to silicon substrate
97
polypropylene copolymer (PPC) to support the free-standing film obtained by etching. The etchant
used in this work is KI(400 mg) + HCl (10 mL)+ DI water (500 mL). The as-grown film was
immersed in the etchant solution for few hours to dissolve the LSMO layer completely. The BCZT
thin film, which is supported by the polymer stamp becomes a free-standing film and is then
transferred to a gold coated silicon wafer for the following measurements. Then the polymer stamp
is removed by annealing in a tube furnace at 300 °C for 3 hours in the oxygen flow.
The insolubility of Mn (IV) is the primary reason for the chemical stability of LSMO. The
etch rate for LSMO can be increased by reducing the Mn (IV) to soluble Mn (II). The Mn (IV)
could be slowly reduced by using the KI + HCl in DI-water as reported by Bakaul et al.
247
The
possible chemical reaction between these two materials is:
To study the structure changes in the transferred films, we carried out the XRD scans of as
grown and transferred BCZT thin films as shown in Figure 5.6. The 𝜃 - 2𝜃 scan of the transferred
film shown in Figure 5.6 (b) is nearly identical to the as-grown film and shows reflections only
from BCZT 00l family planes, indicating the transferred film remains single-crystalline and
textured. As we zoom into the BCZT 002 reflection, it is obvious that its angular position is shifted
from 43.8 ° to 44.83 °, revealing film relaxation with a change of out-of-plane lattice parameter
from 4.13 (fully strained) to 4.04 Å (fully relaxed).
10𝐿 𝑎 0.7
𝑆 𝑟 0.3
𝑀𝑛 𝑂 3
(𝑠 )+13𝐾𝐼 +47𝐻𝐶𝑙
=7𝐿𝑎𝐶 𝑙 3
(𝑎𝑞 )+3𝑆𝑟𝐶 𝑙 2
(𝑎𝑞 )+10𝑀𝑛𝐶 𝑙 2
(𝑎𝑞 )+13𝐾𝑂𝐻 +
13
2
⁄ 𝐼 2
+17𝐻 2
𝑂
98
The switching behavior of transferred ferroelectric films is characterized by PFM. As shown
in Figure 5.7 (a), the ferroelectric domains of the transferred BCZT films on silicon can be
reversibly poled by applying positive and negative voltages from the AFM tip. The poled domain
does not retain long time which lead to phase of the up and down domains becomes nearly identical
as shown in Figure 5.7 (b). The amplitude shows pronounced difference in the up and down
domains represented by the light and dark regions in Figure 5.7 (c).
(b)
Figure 5.6 XRD scan of BCZT film (a) before transfer and (b) after transfer. Each reflection is indexed with
corresponding material. The inserts on the right are the short-angle XRD scan for 42-49° around the most intense
002 reflection of BCZT.
(a)
99
Quantitative measurements of the piezoelectric responses were also carried out to
demonstrate the switching behavior of transferred films. Amplitude and phase signal at various
voltages were measured directly from epitaxial transferred thin film on an Au/Si substrate. The
PFM results as a function of electric field is presented in Figure 5.7 (d) and (e). The butterfly-type
amplitude loop and phase hysteresis have been observed. The effective d33 value is estimated to
be 200 pm/V from the linear portion of the amplitude vs. electric field plot. The phase signal shows
180 degrees difference from the positive and negative poling fields suggesting an up and down
domain switching. The coercive field is estimated from half of the separation of the forward and
backward scan of the amplitude at two minima which is significantly increased from 26 kV/cm to
nearly 100 kV/cm after transfer. The same phenomenon was also observed in the experiments of
Pb(Zr, Ti)O3 transfer.
247
This is presumably related to the strain relaxation before and after transfer
and further experiments are needed to understand and explain this phenomenon.
Figure 5.7 (a) The PFM set up for the BCZT film. The box-in-box pattern is shown in terms of (b)
phase and (c) amplitude. PFM responses of transferred BCZT films. (d) the amplitude, (e) phase as
a function of field. The corresponding film thickness is 100 nm for this measurement. The piezo-
response hysteresis loop shown in the phase indicates a relaxer ferroelectric of BCZT-50 films.
100
5.4 Summary
Epitaxial growth and epitaxial transfer of the BCZT-50 films on Si have been established in
this Chapter. The island growth of BCZT-50 on SRO/STO buffered Si substrate is observed by
RHEED. XRD displays only the reflection from 00l family of BCZT-50 confirming the only c-
axis orientation film being deposited on Si substrate. The results from PFM show a slimly
hysteresis loop in the phase signal and the piezoelectric constant is estimated to be 200 pm/V for
BCZT-50 on silicon.
An epitaxial transfer method is also demonstrated for the Si integration. LMSO is selected as
sacrificial layer for its small lattice mismatch and the potential for selective etching by diluted KI
+ HCl solution. A film relaxation is observed via XRD in the transferred film as compared to the
as-grown BCZT films. The ferroelectric switching behavior remains in the transferred film.
Future Experiments
Additional experiments are required to verify the EO coefficients predicted by the simulation
model in Chapter 3. Material growth and integration have paved the way for identify the individual
EO coefficients. A selection of important experiments is given below:
Electro-optic coefficients measurements. EO coefficients under static electric field could
be characterized by various of methods, such as spectroscopic ellipsometry, prism coupling and
active Mach-Zehnder interferometer measurements.
Frequency dependent measurements. By changing the frequency of the modulation fields
from ~0 Hz to few tens of GHz, the contribution from lattice, ion and electron could be
differentiated. As the first step, clamped and unclamped EO coefficient could be measured by
101
applying AC electric field at MHz range. The time constant for lattice motion is estimated in ~ms
corresponding to several kHz.
181
Second, the measurement of ion contribution of acoustic and
optic phonon could be carried out using RF/microwave co-planar wave guide geometry.
Temperature dependent measurements. From the simulation in Chapter 3, the temperature
dependence of the EO coefficients have a converging feature near the phase transition temperature.
However, experimental evidence was rarely reported even for the conventional EO materials. By
varying the sample temperature in a controlled manner, the effective EO coefficient should be
enhanced by the optic-thermal coupling.

102
Chapter 6. Modeling of Low-Power and High-Frequency Phase
Change Electronic Oscillators
6.1 Background
As we approach to the physical limits of silicon-based electronics, high performance
computing with low energy demand beyond von Neumann architectures is urgently required.
Artificial neural network is one of the promising approaches for the development of next
generation computing architectures, which are suited for not only conventional computing but also
emerging applications such as the Internet of Things and associative learning.
57,60,248
Oscillatory
neural network (ONN) emulates the neuronal behavior found in brains
249
, where an elementary
cell comprises an oscillator circuit and the cells are locally coupled by resistors or capacitors.
Hardware implementation of ONNs are based on current CMOS devices (such as, phase-locked
loop circuits
250
or Van der Pol oscillators
251
) and on emerging new devices, such as, spin-torque
nano-oscillators,
63
and phase change oscillators based on the metal-to-insulator transitions.
61,82,93,252

6.1.1 State-of-the-Art Phase Change Oscillator Devices
Phase change materials like vanadium dioxide (VO2), are being explored for implementing
non-Boolean computational paradigms. VO2 undergoes a first-order structural transition with an
electrical conductivity change up to 5 orders of magnitude at 68℃ in bulk single crystals. It has
also been reported that the application of an electric field causes the conductivity switching of VO2
103
from the insulating state to the metallic state.
89
The VO2 phase transition offers two features, which
make oscillators particularly appealing:
1. The presence of a hysteresis in the insulator-to-metal (IMT) and the metal-to-insulation
transition (MIT) temperatures allows various methods to create feedback loop for switching
between the two phases with different conductivity.
2. VO2 devices also shows a negative differential resistance (NDR) regime in the I-V
characteristics, which is one of the prerequisites for obtaining the current/voltage oscillations.
The prototypical VO2 oscillator was introduced by Taketa et. al.
253
involving a lateral VO2
channel with a series resistor. VO2 is heated by Joule heating from the insulating state of VO2 and
when the temperature of the channel reaches the transition temperature, a transition to metallic
state occurs. The voltage across the VO2 channel decreases due to the drop in resistivity and the
heating power becomes low. This results in cooling of the sample and return to insulating state.
However, the insulating state of the VO2 is so resistive that driving voltage is usually at the level
of 10 V. Recently, vertical contact geometry VO2 oscillator has achieved oscillator frequency up
to 9 MHz at 13 V.
254

The VO2 devices suffer from two limitations, (a) the heating and cooling power available and
the thermal conductance of the bulk and interfaces, and (b) the time constant set by the electrical
parasitic. Instead of the conventional geometry, when a metallic material is put on the top of VO2,
we can address both these issues. The Joule heating will be fully regulated by the metallic layer
under the applied constant current. Once some portion of VO2 becomes metallic, the current will
flow predominantly in the VO2 layer and the device will cool under lower Joule heating power.
104
The heater-on-channel design has been attempted by Wang et al,
255
where a metallic Pt layer is
used as the heater as proposed above. However, their devices fail to show the voltage drop for the
following reasons. As demonstrated in the paper, the resistance of Pt ~few kohm is at similar level
of VO2 insulating state. The heating power of the Pt and the HRS of VO2 is similar. Another factor
is the interface quality, as the thermal conductance of the Pt/VO2 interface is limiting the heating
flow though the VO2 effectively that requires switching of large volume of VO2.
To address the two issues above, a bilayer oxide structure was proposed by our group
82
and
was predicted to achieve up to 3 GHz frequency with a low power of 15 fJ/cycle by a quasi-1D
model. here, this structure is demonstrated using SRO as the conductive layer for VO2. The SRO
has been shown to share a good epitaxial relation with VO2
256
and is expected to possess a minimal
interfacial thermal resistance.
In this chapter, I provide a validation of this approach by a more elaborate model based on
Mr. Boyang Zhao’s early work.
82
A bare VO2 lateral channel and a heater-on-channel design
involving SRO/VO2 heterostructure are considered to achieve high electrical oscillation with low
power. The coupled thermal and electrical simulations are used with consideration of 2-D heat
flow to visualize the minimization of the effective VO2 transition area.
105
6.2 Theoretical Framework
6.2.1 The Resistivity Fitting of VO2
This temperature-resistivity relationship of VO2 is used as an input to the model. The
resistivity of VO2 estimating from experimental result of temperature dependent resistivity
measurements is shown in Figure 6.1. The resistivity ratio of the HRS and LRS of the VO2 varied
from 10
2
to 10
5
in the range from room temperature 300 to 400 K.
53,257,258
Typically, the resistive
ratio for VO2 in the thin film form is lower than that of bulk. Here a ratio of 10
3
is selected in this
calculation for the values of VO2 films as measured from our experiments.
53
The hysteresis of
about 10 K and transition temperatures around 340 – 360 K are usually observed in the temperature
dependent resistivity measurements.
53,257,258
Therefore, the transition temperature is set to be 345K
and 355K for MIT and IMT, respectively.
Figure 6.1 The resistivity-temperature relationship of VO2. Different transition temperature is used to differentiate the
heating and cooling cycle for first-order phase transition.
106
6.2.2 Device Structure
I consider two types of structure in this work. One is the conventional VO2 based lateral
structure which consists of a wide VO2 channel with metal contacts from top. And another
VO2/SRO epitaxial bilayer structure has similar dimensions as the VO2 device. Both devices are
placing on a semi-infinite substrate of SrTiO3 which thickness is greatly larger than the devices by
orders of magnitude. The schematics of each device are shown in Figure 6.2.
Unless specified, the device geometry for the simulation is constructed as follows. The
thickness of metal contacts is 100nm for both and the width between two electrical contacts is L=
1 μm. The thickness of VO2 and SRO is 30 nm and 5 nm. The dimension of the substrate is selected
to be 2 x 2 μm to keep the simulation size neither too large nor too small such that the simulation
can be carried out quickly without losing any features in the thermal relaxation. The interfacial
properties are also carefully considered in this work. The thickness of each interface is fixed at 1
nm (~ 2-unit cells). The material parameters used in the following calculation are listed in the
Table 5.

Figure 6.2 The illustration of device structure of (a) VO2 and (b) VO2/SrRuO3 oscillators.
(b)
(a)
107

Table 5 Electrical and thermal properties of the materials used in the simulation.
6.2.3 Conservation of Heat
The temperature variation of the device due to Joule heating is calculated by a parabolic
partial differential equation (equation (6.1)) that describes the relationship of temperature variation
in a given volume over time. From the device configuration in Figure 6.2, we could assume an
isotropic and homogeneous distribution of heat and electric current and fields in the x-y plane and
no variation in the direction perpendicular to the channel so that the heat flux in 3D could be
simplified to a 2-dimensional slice across the channel. Thus, equation (6.1) could simplify to
equation (6.2) of a 2D simulation that the temperature variation in the perpendicular direction from
the film to substrate and in the direction to the metal contacts as illustrated in Figure 6.3. Under
this assumption, the temperature for a given area at location (x,z) and time t is obtained as T(x,z,t).
The parameters describing the temperature variation are given as follow, the density of matter 𝜌 𝑚 ,
specific heat capacity Cm, thermal conductivity 𝜅 , electric field E, resistivity 𝜌 𝑟 , and ambient
temperature T0 which is chosen to be 300K for room temperature.
Property Value Property Value
Resistivity of VO 2 (300K) 10
-2
Ω m
Specific heat capacity of VO 2 690 J kg
-1
K
-1
Resistivity of VO 2 (400K) 10
-5
Ω m

Specific heat capacity of SrRuO 3 650 J kg
-1
K
-1

Resistivity of SrRuO 3 10
-5
Ω m Specific heat capacity of SrTiO 3 540 J kg
-1
K
-1

Temperature of IMT 335 K Thermal conductivity of VO 2 6 W m
-1
K
-1
Temperature of MIT 345 K Thermal conductivity of SrRuO 3 5 W m
-1
K
-1

Density of VO 2 4570 kg m
-3
Thermal conductivity of SrTiO 3 12 W m
-1
K
-1

Density of SrRuO 3 6490 kg m
-3

Interfacial thermal conductance
SrRuO 3/VO 2
2× 10
8
W m
-2
K
-1
Density of SrTiO 3 5110 kg m
-3

Interfacial thermal conductance
VO 2/SrTiO 3
1× 10
8
W m
-2
K
-1

108
To generate the temperature profile for these devices, device models with the geometry
described in Figure 6.2 were built in the MATLAB Toolbox. The whole geometries are discretized
into a mesh so that 2-D thermal transport properties could be simulated. The boundary conditions
and initial conditions were generated according to the regular experimental setup. The initial
temperature for the whole devices was set at 300 K for the room temperature. The lower boundary
of the substrate and the ambient temperature were fixed at 300 K, and zero heat flux through the
vacuum is considered in this thermal model. The transient condition with time steps down to 1 ps
was carried out in this simulation to capture the transition of the VO2 and the heat transport
properties. Figure 6.3 shows typical temperature profiles for bare VO2 and VO2 /SRO device near
the phase transition under constant current. The heat is concentrated on the VO2 and most of VO2
region under the gap between the contact have transformed to the LRS. However, with an
additional SRO layer acting as heat source from the top of VO2. The IMT phase transition only
𝜌 𝑚 𝐶 𝑚 𝜕 𝑇 𝜕 𝑡 =𝐾 (
𝜕 2
𝑇 𝜕 𝑥 2
+
𝜕 2
𝑇 𝜕 𝑦 2
+
𝜕 2
𝑇 𝜕 𝑧 2
)+
𝐸 2
𝜌 𝑟 −𝜅 (𝑇 −𝑇 0
) (6.1)
𝜌 𝑚 𝐶 𝑚 𝜕 𝑇 𝜕 𝑡 =𝐾 (
𝜕 2
𝑇 𝜕 𝑥 2
+
𝜕 2
𝑇 𝜕 𝑧 2
)+
𝐸 2
𝜌 𝑟 −𝜅 (𝑇 −𝑇 0
) (6.2)
Figure 6.3 Temperature profile of typical (a) VO2 and (b) VO2/SRO devices near transition temperature. The
thickness of VO2 layers presented here are 30 nm for both devices. The SrRuO3 (SRO) thickness is 25 nm for the
illustration purpose.
(b) (a)
109
happens in those areas at the middle surface of VO2, and thus minimizes the volume of VO2 that
undergoes the transition. More benefits from this approach will be discussed below. The
temperature discontinuity at the interfaces is determined by the interfacial thermal conductivity.
Later in this chapter, careful analysis on the interfacial thermal conductivity is preformed and
shows that the theoretical limitation of the oscillator frequencies is the interface quality.
Figure 6.4 shows typical simulation results of VO2 and VO2/SRO device. The input voltage
pulse raises at t=0 and falls at t=1μs with input values of 4.5 V for VO2 device and 1.3V for VO2
/SRO device. To investigate the temperature profile under the step voltage, a compliance of 10
-4
Ωm of LRS is used to accommodate the overshoot of the temperature after transition due to the
large resistance difference between the LRS and HRS. A clear two-step dynamic is observed in
both cases, corresponding to the HRS and LRS in the devices. When the voltage pulse is turned
off at t=1μs, the temperature gradually returns to room temperature due to the heat dissipation. The
(a)
(b)
(d)
T c
(f)
HRS LRS
(e)
(c)
T c
HRS LRS
Figure 6.4 Turn-on and turn-off transient at a step voltage input. The comparison of VO2 and VO2/SRO device of
(a) (b) input voltage, (c) (d) average temperature in between the metal electrodes, and (e) (f) total current across the
device, respectively.
110
VO2/SRO device could operate at a low voltage which nearly 66% lower than the driving voltage
of a pure VO2 device. Moreover, the total current scales the same way with the input voltage.
Therefore, the total power driving the device is greatly decreased by nearly 9 times by simply
adding a 5 nm SRO layer. The heating power of SRO is also slightly higher than that of VO2 HRS
regardless of a lower voltage supply, indicated from the short time to reach the transition
temperature. All of these advantages are results from the design of the structure that the
significantly lower the HRS of the devices by bypassing the current through SRO.
Quasi-static voltage scans (Figure 6.5) are carried out to imitate the dc measurement for
electric induced transition. Triangle wave function has been applied with a time step of 20 ms
shown in Figure 6.5(a) and (g). This time scale is more than sufficient to stabilize the thermal flux.
Figure 6.5 Voltage forward and backward scan of (a-f) VO2 and (g-l) VO2/SRO devices. (a) and (g) The applied step voltage to the
30 nm thick VO2 device and 5 nm SrRuO3 / 30nm VO2 bilayer device. The time step is 20ms which could be considered as steady-
state simulation condition. The time domain evolutions of (b) (h) the temperature at the VO2 layer top surface and (c) (i)
corresponding overall resistance of device. Distinctive two state of VO2 could be observed. (d) (j) characteristic I-V loop and (e)
(k) corresponding temperature and (f) (l) overall resistance as a function of applied voltage.
111
The temperatures at the center of the surface of VO2 for both devices are extracted for the Figure
6.5 (b), (e), (h), (k). The resistances in (c), (f), (i), (l) are the overall resistance of each device.
The simulated I-V characteristics in Figure 6.5 (d) and (j) show a similar pattern to the
experimental I-V.
61,259
The transitions are observed at different voltages for each device. The
forward sweep shows a IMT where temperature increases and the resistance drops at a transition
voltage, VIMT. The reverse sweep indicates a MIT process with a VMIT. The value of VIMT is larger
than VMIT because the higher voltage and temperature is required to induce the phase transition
than that to maintain the metallic phase. This is similar to what has been demonstrated in the
temperature-induced transition. The transition voltage is significantly reduced by adding an SRO
layer due to decreasing the overall resistance at low temperature. As we conclude from the on-off
voltage simulation, the heating power of SRO is much larger than that of VO2 insulating state. A
smaller voltage is required to trigger the transition of VO2, which decreases the driving voltage
below 1V for VO2 based oscillators.
In the next section, a circuit analysis by introducing a feedback loop will be studied for
investigation of VO2-based oscillators. The important results discussed above set the stage to
create an algorithm for the VO2-based oscillators with the heater-on-VO2 design.
112
6.3 Operating Mechanism
The schematic of the physical circuit for an oscillator is shown in Figure 6.6, which contains
a VO2-based device, a parallel capacitor. The circuit is governed by the conservation of charge:
where I0 is the current applied, C the parallel capacitor, V the voltage across the device. R is the
overall resistant of the device. Specifically, R is total resistance of RMIT and Rm in parallel, where
RMIT is for VO2 and Rm is for the SRO.
The simulation algorithm combined with the thermal equation (6.2) and electrical equation
(6.3) is presented in Figure 6.7. First, device structures are built for single layer VO2 and bilayer
VO2/SRO with different thicknesses and widths. To analysis the circuit system shown in Figure
𝐼 0
=𝐶 𝑑𝑉
𝑑𝑡
+
𝑉 𝑅 (6.3)
Figure 6.6 Circuit schematic for a VO2 -based oscillator. The I0 is applied current delivered by a current source.
The VO2 based device is paralleled with a capacitance. The voltage oscillation V could be detected by an
oscilloscope.
Figure 6.7 Simulation algorithm of thermoelectrical model of VO2 based oscillator.
113
6.6, the equations 6.2 and 6.3 are solved by finite element method. Discretized time step dt down
to ps is used for high-frequency oscillation simulation. At each iteration, a 2-D heat map is
generated to learn the heat flow mechanism of each device and used as the initial condition for the
next iteration. The final voltage and heat oscillations are extracted from each iteration and thus,
the frequency and the power per circle can be calculated in a self-consistent manner.
Understanding the mechanism of the electrical oscillation is of important to design high-
frequency and low power oscillator. Figure 6.8 (a) shows a typical voltage and temperature
oscillation of a bare VO2 device for 0.73 mA and 4 pF. The frequency for the oscillation is 20
MHz. The four regimes of operation are represented in the voltage and temperature oscillation by
four critical points: A, B, C, and D. Starting from point A, the charge firstly accumulates in the
capacitor which is uncharged at initial state. In parallel with the charging, minor current flowing
to the VO2 and heating effect is so small that it is not enough to heat the VO2 channel. Therefore,
(a)
(b)
Figure 6.8 Operation mechanism of the VO2 oscillator. (a) Time-evolution of temperature and voltage of the VO2 channel
for the highest achievable frequency of 20 MHz; the parallel capacitance used in this simulation is 4 pF and driving current
is 0.73 mA. The operating stage is denoted as A, B, C, and D. (b) Simulated I-V characteristic curve for an oscillation
period corresponding to (a). The four stages of operation of the oscillation are charging, heating, discharging, and cooling.
The A and C points are the lowest and highest voltage position corresponding to the onset of changing and discharging
stage. The B and D are the transition points of min. and max. temperature corresponding to the heating and cooling stage,
respectively.
114
the temperature decreases regardless of the raising voltage. As soon as the capacitor is charged to
some extent, the major current passes though the VO2 device and the heating stage onsets at point
B. The temperature raises as the resistance becomes smaller. Once the temperature goes beyond
the transition temperature, dramatic change in resistance triggers the discharge of the capacitor.
This also cause the temperature overshoot from point C to point D. The heating power becomes
smaller as VO2 transits to LRS, resulting in temperature decreasing from D to A. The heat cycle
could be monitored by the voltage-current characteristics of the VO2 device. In Figure 6.8 (b), we
show the I-V relation of a VO2 channel. The cycle starts from the current equal to the applied
current. The charging is the regime where the supplied current decreases as the increasing voltage.
The heating process follows with the charging where the current increases with the voltage. As the
voltage cross the transition voltage in the Figure 6.5, the phase transition and associated
discharging of capacitor begin. It is worth to mention that the current could go much higher than
the applied current due to the discharging and this process could happen fast as the capacitance
becomes smaller. In this simulation, the discharge only takes ~2 ns at 4 pF capacitor. Final, the
cooling happens at the metallic state of the VO2 as the resistance becomes 3 orders smaller. The
sustained voltage oscillations are achieved by moving counter-clockwise in the I-V curve and
continue in a cyclical manner.

115
Similar mechanism is also observed in VO2/SRO bilayer device. Distinctive four stages are
also demonstrated as A, B, C, and D in Figure 6.9 (a) and I-V cycle is also similar to what has
been established for VO2 device in the last two paragraphs. However, the bilayer device shows a
double of the oscillation frequency at nearly same condition as optimized for VO2 device. This is
because of, as it has been repeated several times, the low resistivity of the SRO which gives raise
to fast heating compared to insulating state of VO2. Moreover, the transition voltages confirm the
results of the voltage scan simulation. The amplitude of the oscillation has decreased from nearly
6 V to 1.3 V, resulting in a low-power device nearly 0.9 mW.
(a) (b)
Figure 6.9 Operation mechanism of the VO2/SRO oscillator. (a) Time-evolution of temperature and voltage for the
unoptimized device shows a frequency of 40 MHz; the simulation condition is used as the same as the previous VO2 device
simulation, I=0.9 mA and C=4 pF. The operating stage is denoted as A, B, C, and D. The four stages of operation of the
oscillation are charging, heating, discharging, and cooling. The A and C points are the lowest and highest voltage position
corresponding to the onset of changing and discharging stage. The B and D are the transition points of min. and max.
temperature corresponding to the heating and cooling stage, respectively. (b) Simulated I-V characteristic curve for an
oscillation period corresponding to (a).
116
6.4 Factors Influencing the Operation of the Oscillator
6.4.1 Interfacial Thermal Conductivity
Figure 6.10 shows a demonstration of heat flow in the simulation device to visualize the heat
transfer in detail. The heat is generated in SRO layer by Joule heating. The VO2 layer is heated
from above through the interface of the SRO and VO2. In the meantime, the surrounding VO2 and
the substrate act as heat reservoirs to cool the VO2. The rate of heating and cooling depends on the
thermal conductance of individual elements and interfacial thermal conductivity at the layer
interface. The interfacial thermal conductance is very sensitive to the interface conditions such as
roughness, interface bonding strength, interfacial mixing, and interfacial disorder.
260–265
The
thermal transport analysis on the effect of thermal conductivity has been performed. A typical
oscillation evolution with regards to the interfacial thermal conductivity has been investigated and
presented in Figure 6.10. There are three distinct regimes where the devices show sustained
oscillations, damping oscillations and no oscillation. The sustained oscillation regime is desired
for the purpose of neuromorphic computing and only accessible in the balance of heating and
cooling power. When the interfacial thermal conductivity become half, four damping oscillations
could be observed but eventually, the voltage stops oscillating as the thermal energy accumulates
in the VO2 layer. To the extreme conditions where the interfacial thermal conductance is set to be
Figure 6.10 A schematic to demonstrate the heat flow considered in the theoretical model.
117
one order lower, the temperature keep raising such that the VO2 goes to the metallic state and is
not able to switch back.
6.4.2 Current and Capacitance
The tunability of the oscillation frequency up to several orders of magnitudes is critical to the
use of these devices in ONN network. To demonstrate the tunability of the oscillator characteristics,
the effect of applied current with different level of parallel capacitance has been studied in this
work. Here, I first demonstrate the tunability of a typical VO2 devices in Figure 6.2. The applied
currents vary from 0.01mA to 0.8 mA with parallel capacitance from 10
-9
to 10
-12
F. Overall, the
frequency goes up with the applied current at a fixed capacitance until reach a critical point which
is nearly 0.75 mA in this case. Within the region below critical current, sustained voltage
oscillation could be achieved as long as the external current supply continues to provide to the
device. Beyond this point, the oscillation is not stable and shows a damp oscillation behavior where
the heating power is too much to stabilize the thermal oscillation. At a fixed current, the
capacitance has a qualitatively inverse proportional relation to the frequency. The critical
Figure 6.11 Oscillation evolution regarding the interfacial thermal conductivity (ITC). The ITCs used for the
simulation that shows sustain oscillation are 2x10
8
W/m
2
K and 1x10
8
W/m
2
K for SrRuO3/VO2 and VO2/SrTiO3
interface. The ITCs for the damping oscillation and no oscillation are half and one tenth of that for sustain oscillation.
118
capacitance for device geometry is 4 pF. Similar to current effect, beyond this value, the sustained
oscillation cannot be achieved. The highest frequency is estimated to be 20 MHz and the voltage
and temperature oscillation have been presented in Figure 6.8 (a). In this calculation, I only present
the frequency above MHz level. Low frequency down to kHz could be generated with low parallel
capacitances.
Figure 6.12 (b) shows a I-C map of a VO2/SRO bilayer device. The maximum frequency is
calculated to be 44 MHz at 1.1mA with a 4pF parallel capacitance. This value is more than double
of the maximum frequency of bare VO2 device. Besides the absolute value, the bilayer device also
shows a wider operation range from 0.7 mA to 2.2 mA at the capacitance level of few pF which
allows a wide range frequency tuning without changing the capacitance.
6.4.3 Effective Volume
One of the important points in this study to design the switching elements based on VO2
devices is the modeling of its physical properties and estimation of the frequency of the oscillator
depending on the size of channel length/area. The key parameters including the transition voltages
(a) (b)
Figure 6.12 The oscillation frequency dependence on applied current and parallel capacitance map of (a) VO2 and
(b) VO2/SRO device. Only the oscillation frequency above 1 MHz have been shown in the figure.
119
VMIT and VIMT and the corresponding currents IMIT and IMIT. The characteristic I-V of the devices
of VO2/SRO bilayer devices have been calculated and summarized in Figure 6.13 (a). Here,
transition voltages as a function of channel length from 0.1-1.5 µm are plotted. The channel width
of the devices in this simulation is equal to channel length. The thicknesses of SRO and VO2 are
5 nm and 30nm, respectively. Based on the observation of VIMT and VMIT in Figure 6.13(a), we
propose an empirical approximation for the transition voltage:
where L is the channel length in µ m.
The maximum frequencies for varying channel length have been investigated by optimizing
the current and capacitance which has been used the same in section 6.4.2. The detail conditions
used for each channel size are presented in Table 5. The maximum oscillation frequency increases
nearly 7 times from 1 µ m to 100 nm. With the size decrease to 100 nm, one can expect an increase
in frequency up to 260 MHz. As the effective transition area becomes smaller and smaller, the
𝑉 𝐼𝑀𝑇 =0.94𝐿 0.6
(6.4a)
𝑉 𝑀𝐼𝑇 =0.5𝐿 0.6
(6.4b)

L
VO 2
SRO
Substrate
M M
Figure 6.13(a) The transition voltage and (b) the optimized frequency as a function of channel length (L). The yellow
marked region refers to the voltage that could generate sustain oscillation. The insert is the schematic for the channel
length. M refers to the metal contacts. The thicknesses of SrRuO3 (SRO) and VO2 are 5 nm and 30nm, respectively.
(a) (b)
120
thermal energy required to trigger the phase transition also becomes less while the resistance of
each layer depends only on the thickness in this case which remain a constant in this calculation.
This could be also observed in the decay of transition voltages. Besides the thermal transport, the
minimal capacitance required for the sustained oscillation also scales with the channel size. This
is another reason why the optimal frequency goes up with the decreasing device size. On the other
hand, it seems contradictory to the earlier conclusion that the current required to achieving high
frequency decreases. It is account for the lower heat requirements. This feature allows to operate
the oscillator at low power ~0.13 pJ/cycle, which is 300 times lower than that of devices at 1 µ m
footprint.
Table 6 Simulation data of the maximum frequencies of VO2/SRO bilayer oscillators depending on the channel size. The current
I0 and capacitance Ca is corresponding to the values optimized for max. frequencies (fmax). The electrical time constant 𝜏 𝑒 is
estimated by the Equation 5.6
6.5 Discussion
Direct calculations of several periods of self-oscillation in the VO2-based oscillator have been
demonstrated in this chapter. However, optimization is extremely time consuming to calculate the
maximum frequency through this pathway for different geometry size. To overcome this issue, a
L (µ m) VMIT (V) VIMT (V) IMIT (mA) IIMT (mA) fmax (MHz) Ca (pF) I0 (mA)
0.1 0.104 0.208 1.04 0.104 262 0.6 0.24
0.2 0.18 0.348 1.8 0.174 200 0.8 0.4
0.3 0.252 0.456 2.52 0.228 148 1 0.48
0.4 0.28 0.54 2.8 0.27 110 1.3 0.54
0.5 0.32 0.62 3.2 0.31 88 1.7 0.6
0.6 0.38 0.72 3.8 0.36 77 2 0.8
0.7 0.42 0.78 4.2 0.39 67 2.4 0.9
0.8 0.44 0.82 4.4 0.41 55 2.8 0.95
0.9 0.48 0.88 4.8 0.44 50 3 1.00
1 0.504 0.924 5.04 0.462 47 4 1.10
1.5 0.644 1.176 6.44 0.688 23 7 1.50
121
phenomenological estimation of the maximum frequency using the switching time extracted from
the electrical and thermal transport Equations (6.5 and 6.6).
⚫ Electrical Time Constant 𝝉 𝒆 :
where the R and C are the resistance and capacitance respectively. The resistance used here is
estimated from the HRS of the device, which is the resistance of SRO layer. It is worth to mention
that the resistance of the SRO is independent on the footprint and only depends on the thickness
of the film. The capacitance of the circuit, for example, is taken as 1 nF of the optimized
capacitance for the maximum frequency at L=0.3µm. Then the 𝜏 𝑒 is calculated as 2 ns for the
VO2/SRO device where thickness of SRO is 5nm. The other 𝜏 𝑒 is summarized in Table 7.
Table 7 Estimation of electrical time constant 𝜏 𝑒 and thermal time constant 𝜏 𝑡 ℎ
for the VO2/SRO bilayer devices with various
channel length L. The estimated frequency 𝑓 𝑒𝑠
is calculated by inversion of the lowest time constant which is the 𝜏 𝑡 ℎ
𝑉𝑂
2
−𝑆𝑇𝑂 for this
case. The deviation from the optimized fmax is also listed.
⚫ Thermal Time Constant 𝝉 𝒕𝒉
:
𝜏 𝑒 =𝑅𝐶 (6.5)
L (µ m) 𝜏 𝑒 (ns)
𝜏 𝑡 ℎ
𝑆𝑅𝑂 −𝑉𝑂
2
(ns) 𝜏 𝑡 ℎ
𝑉𝑂
2
−𝑆𝑇𝑂 (ns)
𝑓 𝑒𝑠𝑡 (MHz) fmax (MHz) Deviation
0.1 1.2 1.85 2.98 335.95 262 28%
0.2 1.6 3.71 5.95 167.98 200 -16%
0.3 2 5.56 8.93 111.98 148 -24%
0.4 2.6 7.41 11.91 83.99 110 -24%
0.5 3.4 9.26 14.88 67.19 88 -24%
0.6 4 11.12 17.86 55.99 77 -27%
0.7 4.8 12.97 20.84 47.99 67 -28%
0.8 5.6 14.82 23.81 41.99 55 -24%
0.9 6 16.67 26.79 37.33 50 -25%
1 8 18.53 29.77 33.60 47 -29%
1.5 14 27.79 44.65 22.40 23 -3%
𝜏 𝑡 ℎ
=
𝜌 𝑐 𝑝 𝑉 𝐾 𝐴 𝑠 (6.6)
122
where the 𝜌 is the mass density, cp the specific heat, K the thermal conductance and As the surface
area. All these values come from the Table 5. For a VO2 layer with a thickness of 30nm and length
of 1μm, the thermal time constant for interfaces of SRO/VO2 𝜏 𝑡 ℎ
𝑆𝑅𝑂 −𝑉𝑂
2
and VO2/STO 𝜏 𝑡 ℎ
𝑉𝑂
2
−𝑆𝑇𝑂
are summarized in Table 7.
One can easily point out that the system is limited by the VO2/STO interfacial thermal contact
as it shows the lowest time constant. One could estimate the corresponding frequency by simply
taking the reciprocal of time constant and finds that the magnitude of the estimated frequencies fest
(= 1/𝜏 𝑡 ℎ
𝑉𝑂
2
−𝑆𝑇𝑂 ) agrees with the values optimized from current and capacitance analysis with the
max. deviation of 29%. For most of the channel length, the estimated frequency is underestimated
from the simulated value. Part of the reason comes from the dynamic of the heating and cooling
throughout the oscillation process. The heating power constantly changes with the temperature of
the VO2, especially in the vicinity of the transition temperature.
6.6 Summary
A thermo-electrical 2-D model has been established for VO2 based oscillator. I applied the
2D model to two device geometries, planar bare VO2 device and bilayer VO2/SRO heterostructure
devices. Voltage switching and characteristic I-V hysteresis can be emulated by pure thermal
model. The transition voltage and current are greatly subtracted by adding epitaxial thin SRO
conductive layer as the heating source at low temperature. The oscillation waveform of VO2 based
oscillators is investigated by implementing the thermal model to the electric circuit consisting of
a parallel capacitor to the VO2 based device. The voltage and temperature waveforms show a clear
cycle of the four stages, i.e. heating, cooling, changing and discharging. Up to 47 Mhz oscillation
123
frequency has been observed in 5nm SRO / 30 nm VO2 devices, which is 2 times larger than the
optimized frequency of the pure VO2 devices. The oscillation frequency can be widely tuned by
varying the applied current or substituting different capacitors, which is promising to achieve
oscillatory neural networks. Analysis on effective areas of the VO2 /SRO devices reveals that the
fundamental limitations of the oscillatory frequencies is the thermal boundary conductance for the
fact that the corresponding time constants are much slower than the electric time constants. The
optimized frequency of 260 MHz with 0.13 pJ/cycle power consumption has been predicted for a
100 x 100 nm area device. Further experiments are necessary to verify the model.
124
Chapter 7. Fabrication and Characterization of the Epitaxial
SrRuO3/ VO2 Heterostructure
7.1 Background
VO2 is widely studied for its sharp metal-to-insulator transition (MIT) over a very narrow
range of temperatures close to room temperature (~ 340 K).
83,84
At this transition temperature, VO2
undergoes a large change in resistivity, as high as five orders of magnitude, in high-quality single
crystals.
85
This transition is accompanied by a structural transition from monoclinic (M1) to
tetragonal rutile (R) structure. The role of this structural change, and the strong correlation on the
physical properties and MIT in VO2 remains an important topic of investigation. The sudden and
large resistivity change in VO2 near room temperature has attracted tremendous attention for
electronic and photonic applications such as logic devices,
266,267
oscillators,
268
filters,
269
thermal
Figure 7.1 V-O phase diagram showing VO2, V2O3 V2O5, Magné li
series, VnO2n+1, and the Wadsley series, VnO2n-1. (Taken from Ref
263)
125
regulation,
270
and smart windows
271
. The MIT can also be induced by other impulses such as
ultrafast lasers, where the transition can be achieved in sub-picosecond timescales,
272
making it an
attractive material for ultrafast optical switches and sensors.
Thin film growth of VO2 is of fundamental importance, as many device applications rely on
this platform and one can achieve meta-stable strain-induced phases in thin films.
257
Thin films of
VO2 have been synthesized using various vapor phase deposition techniques such as chemical
vapor deposition, reactive electron-beam evaporation, radio frequency sputtering and pulsed laser
deposition (PLD).
273–279
As the vanadium-oxygen phase diagram
280
consists of principle oxides
such as VO, V2O3, VO2, V2O5, Magné li phases with a general formula VnO2n-1 and composition
between VO2 and V2O3, and Wadsley phases with a general formula VnO2n+1 and composition
between VO2 and V2O5, precise control of the oxygen stoichiometry is critical to achieving the
desired phase. Hence, thin film growth of VO2 is often sensitive to growth conditions such as
oxygen partial pressure, which regulates the stoichiometry of the vanadium oxides. Pulsed laser
deposition (PLD) is a powerful technique for the fabrication of high-quality VO2 films as it allows
precise control of the stoichiometry by tuning the deposition parameters.
Another important limitation to the growth of high-quality VO2 films is the lack of single
crystal substrates with a good epitaxial match. To maintain favorable conditions for hetero-epitaxy,
VO2 thin films have been grown on rutile TiO2 substrates, which are isostructural to the high
temperature phase of rutile VO2.
281,282
The lattice parameters of rutile VO2 are slightly smaller than
rutile TiO2, and this leads to small tensile strain for different orientations of rutile TiO 2
substrates.
283
Epitaxial growth of VO2 thin films on substrates with 3m symmetry, such as ZnO
126
(0001) and Al2O3 (0001), has been investigated in the past. These substrates produce high-quality
VO2 thin films with three orders of magnitude change in resistance around the transition
temperature, but structural domains along the in-plane direction in such films are randomly
distributed and hard to control.
284,258
Cubic perovskite substrates with (111) orientation possess
3m symmetry and can provide the desired epitaxial surface for the growth of VO2 thin films. (111)-
oriented SrTiO3 (STO) has been successfully used as the substrate for VO2 films with excellent
electrical properties.
257
[LaAlO3]0.3[Sr2AlTaO6]0.7 (LSAT) is one of the widely used cubic
perovskite substrates with a lattice parameter of 3.868 Å. The lattice mismatch of VO2 and LSAT
is relatively small, -5.17% and 1.59% in a- and c-axis direction, respectively. Hence, LSAT can
Figure 7.2 Crystal structure illustrations of (a) monoclinic VO2 (010), (b) rutile TiO2 (010), (c) LSAT
(111) and (d) SrTiO3 (111).
127
be also a good candidate for epitaxial growth of high-quality VO2 thin films. This work has been
published in the Journal of Vacuum Science and Technology A.
53

7.2 Epitaxial Growth of Vanadium Dioxide on (111)-Oriented Perovskite
Substrates
7.2.1 Thin Film Growth
Commercially available single crystal (111)-oriented LSAT wafers were used as substrates
(purchased from MTI Corporation). The substrates were pretreated by annealing with a constant
flow of O2 at 1000C for 4 hours. We used a 248 nm KrF excimer laser with an energy density of
1.5 J/cm
2
for the growth. Prior to the deposition, the chamber was evacuated to a background
pressure of ~ 10
-7
Torr and then backfilled to an optimal oxygen partial pressure of 10 mTorr
before heating up the substrate to the growth temperature of 500 C as measured by a thermocouple
welded to the substrate heater. The VO2 film was deposited from a dense polycrystalline target of
V2O5. The target was sanded and fully pre-ablated to maintain a fresh surface for each growth.
After the deposition, the samples were cooled at a rate of 5-10 C/min to room temperature at an
oxygen partial pressure of 10 mTorr.
7.3 Characterization of Vanadium Dioxide Thin Films
Figure 7.3 shows the representative in-situ RHEED patterns for the VO2 thin film growth,
which indicate the epitaxial in-plane orientation relation between the film and substrate. The
substrate of LSAT and STO patterns along [101
̅
] and [12
̅
1] which are 90 degrees away from each
other and both perpendicular to [111] the out-of-plane direction of the substrate are shown in
Figure 7.3 (a) and (c) respectively and the (b) and (d) are the diffraction patterns for the sequence
128
growth of VO2 along the same direction. The difference of the substrates along same direction is
subtle and not show here. The surface of the substrates is atomically smooth and thus shows a 2D
feature diffraction pattern. As soon as the growth starts, the pattern becomes 3 dimensional and no
oscillation is observed throughout the process, indicating an island growth mode. At process
temperature of 500 C, the VO2 is in the high-temperature rutile structure. Therefore, the crystal
orientation discussed here are all refer to the rutile structure. The rutile VO2 has a six-fold and
four-fold symmetry along the two different orientations shown in Figure 7.3 (b) and (d). To
identify the crystal orientation, primary axis of [100]R, [010]R, and [001]R are considered. R in the
subscript refers to rutile VO2. Based on the crystal symmetry of the rutile structure, the (100)R and
(010)R planes are symmetrically equivalent and are perpendicular to each other, indicating that the
Figure 7.3 RHEED diffraction pattern for (a) LSAT, (b) rutile VO2 [100], (c) STO, and (d) rutile
VO2 [001] at 500 C. The primary diffraction spots for VO2 have been indexed according to the
rutile structure symmetry.
129
out-of-plane axis of VO2 films cannot be the [001]R as otherwise, the patterns in the two directions
should be identical. Moreover, the [001]R axis has a four-fold symmetry and is in agreement with
the symmetry in the Figure 7.3 (d). With this hypothesis, one may set the out-of-plane lattice axis
to be [010]R due to the equivalency. Then the leftover direction is the [100]R axis corresponding
to the Figure 7.3 (b). The result is also agree with the simulation result of TEM diffraction pattern
from the reference.
285
In this way, we could conclude that the epitaxial relation of the VO2 rutile
phase grown on (111)-type perovskite substrate is VO2(010)R || Perovskite(111) (out-of-plane) and
VO2[100]R||Perovskite[101
̅
] , VO2[100]R || Perovskite[12
̅
1] (in-plane). The orientation of the low
temperature monoclinic phase is then determined by the XRD and partly evident to the orientation
discussed here.
Figure 7.4 (a) shows a representative XRD pattern from the out-of-plane 2θ-θ scan of the as-
grown VO2 thin film on LSAT substrate at room temperature. The well-resolved sharp reflections
at 19.87 , 40.40 , 62.35 and 87.17 correspond to reflections from (111)-oriented LSAT substrate,
namely LSAT 111, 222, 333, and 444, respectively. Only the 0k0 family of reflections are visible
for the VO2 thin film over the range of 15 -95 in 2θ. This indicates that the VO2 thin film is highly
Figure 7.4 (a). High resolution 2θ-θ XRD pattern of VO2 thin film on LSAT substrate. (b). Off-axis φ scan of VO2
110 and LSAT 022.
130
oriented along the out-of-plane direction of the LSAT substrate. The diffraction 2𝜃 angle of VO2
0k0 is overlapping with the STO (111)-type diffraction position. Therefore, it is difficult to extract
the structure information for VO2/STO structure. The XRD figure for VO2/STO samples is not
shown here.
We used pole figure analysis to determine the in-plane film/substrate orientation relationships.
We performed off-axis φ scan for VO2 110 and LSAT 022 reflections. We observed six peaks
separated by 60° for the VO2 110 reflection, whereas the LSAT 022 reflection showed three peaks
separated by 120° (as shown in Figure 7.4 (b)). Three of the peaks of VO2 films were aligned with
the substrate LSAT’s peaks, whereas three other equally spaced peaks were found in between these
matching peaks. This implies a direct one-to-one relationship between the film and substrate with
a possible three types of in-plane domains for the VO2 substrate. Based on these results, we
conclude that VO2 films in the M1 phase were epitaxially grown on LSAT (111) substrates with
epitaxial relationships VO2(020)||LSAT(111) and VO2[001]||LSAT[112
̅
]. This result is consistent
with the RHEED transmission diffraction pattern and with previous reports on the growth of VO2
thin films on STO (111) substrate.
257

Figure 7.5 Thickness dependent (a). 2θ-θ XRD patterns and (b). X-ray reflectivity (XRR) of VO2 thin film on
LSAT substrate and (c) STO substrate. Simulation curves fitting to XRR data is shown as black line.
131
Past investigations have established a correlation between the electrical properties of VO2
and the structural domain sizes.
286
Hence, an understanding of the epitaxial relationship between
the substrate and the film and the nature of VO2 domains is crucial to achieve single crystal-like
properties in thin film VO2. In our case, we explored the structural evolution of the VO2 films as
a function of film thickness. The structural evolution, in terms of the texture, and surface roughness
are summarized in Figure 7.5 and Figure 7.6. The texture and crystallinity of these VO2 films as
characterized earlier using out-of-plane XRD is summarized in Figure 7.5 (a). The thickness of
each film is carefully characterized by X-ray Reflectivity. The data is fitted using the GenX
software. The result is shown in Figure 7.5 (b-c). It is worth noting that films below 17 nm were
hard to detect in out-of-plane XRD studies due to the small structure factor of VO2 and the tiny
volume of material that was probed. The presence of VO2 films at these thicknesses was further
confirmed by XRR. The thickness of the films as determined by the simulation of the measured
XRR patterns were 17 nm, 31 nm and 63 nm, respectively. The slow decay of the thickness
oscillations indicates that the surface of VO2 thin films is smooth. This was further confirmed by
Figure 7.6 AFM topography image of (a). annealed LSAT surface, (b). 17 nm, (c). 31 nm, (d). 63 nm as-
grown VO2 surface (e). annealed STO surface, and 60nm as-grown VO2 surface.
132
AFM. The representative topography image of an annealed LSAT and STO substrate is shown in
Figure 7.6 (a) and (e). We observed a relatively smooth surface with an RMS roughness of up to
~0.24 nm for the annealed LSAT (111) substrates. Please note that this value is larger than (001)
oriented substrates due to the polar nature of the material. In Figure 7.6 (b), one can clearly see a
relatively flat surface at 17 nm with an RMS roughness of ~1.1 nm. We observe the formation of
sub-micron size islands as we increase the thicknesses to 31 and 63 nm as shown in Figure 7.6 (c)
and (d) respectively. Meanwhile, the RMS roughness of the films increases to 3.3 nm and 5.1 nm
for 31 nm- and 63 nm-thick film, respectively. The roughness is significant lower for the films on
(
-
)
( )
VO
2
/LSAT HT
VO
2
/LSAT RT
LSAT HT
LSAT RT
Figure 7.7 Raman spectra of VO2 thin film on LSAT substrate and LSAT substrate measured at 350 K (HT) and room
temperature (RT) respectively. The 11 Raman active modes from room temperature VO2 are highlighted by grey triangles.

133
STO substrate for better lattice matching of STO and VO2. Since the surface smoothness is directly
related to the interface thermal conductivity, we decide to use the STO as the substrate for the
proposed bilayer oscillators.
Raman spectroscopy study on VO2 films on LSAT substrates and plain LSAT substrates at
298 K (RT) and 350 K (HT) is carried out to demonstrate the structural transition. The Raman
spectra of LAST substrates at 350 K were nearly identical to that at room temperature. However,
the VO2/LSAT showed distinct Raman spectra for below and above transition temperature as
shown in Figure 7.7, presumably for the metallic and semiconducting phases, which have different
structures. At room temperature, VO2 has a monolithic structure with space group 𝐶 5
2ℎ
=𝑃 2
1
/𝑐
(14). Theoretically, there are nine Ag and nine Bg Raman active modes for this symmetry. In the
Raman response of VO2/LSAT at room temperature, one can clearly distinguish 11 modes for VO2
M1 phase apart from the Raman modes attributed to LSAT substrates, corresponding to six Ag and
four Bg modes. Detailed information about the nature of the Raman modes and the corresponding
wave vectors are shown in Table 8. It is worth noting that we were unable to observe all the
possible modes, possibly due to thermal smearing, as our measurements were carried out at room
temperature, as compared to 85 K for the previous report.
287
The high temperature phase of VO2
crystallizes in the rutile structure with a space group of 𝐷 14
4ℎ
=𝑃 4
2
/𝑚𝑛𝑚 (136). In the high
temperature phase, four modes (A1g, B1g, B2g, Eg) are Raman active. We observed a large
background intensity enhancement in addition to the peaks from LSAT substrates in the Raman
spectrum of VO2/LSAT at 350 K. However, comparing to the background level in the Raman
spectrum of LSAT substrates at 350 K, we can conclude that this background enhancement did
134
not arise from any thermal effects. Notably, one important characteristic of the rutile TiO2 Raman
response is absence of strong, sharp peaks.
288
We believe that the broad enhancement in the
background signal is due to the R phase of the VO2 as observed in high-quality single crystals of
VO2.
289

Table 8 Comparison of the observed Raman modes and the nature of these modes with the reference report.
This work (300K) Peter Schilbe
287
(85K)
Raman
Frequency
(cm
-1
) Raman Mode
Raman
Frequency
(cm
-1
) Raman Mode
146 … 149 …
195 Ag 199 Ag
224 Ag 225 Ag

259 Bg
263 Bg 265 Bg
310 Ag 313 Ag
340 Bg 339 Bg
391 Ag 392 Ag

395 Bg

444 Bg

453 Bg

489 Bg
500 Ag 503 Ag

595 Ag
613 Ag 618 Ag
662 Bg 670 Bg
827 Bg 830 Bg
Temperature dependent resistivity measurements on 30, 50, and 100 nm VO2 films on LSAT
and 100 nm VO2 on STO substrate were performed. Figure 7.8 (a) shows the four-probe resistivity
of the VO2/LSAT film from room temperature to 400 K for both the heating and cooling cycles.
We saw large, up to four orders of magnitude changes in the resistivity, as VO2 transformed from
M1 to R phase. The resistivity ratio between the two phases, which can be defined as R
298K
/R
400K
,
135
were ~8 10
2
, 8 10
3
, and 10
4
for 30, 50, and 100 nm films respectively. These are amongst the
highest resistivity ratio values observed for VO2 grown on surfaces with 3m symmetry.
257,258
The
four probe resistivity of VO2 film on STO is also measured. High, near four order of magnitude,
resistivity change has been obtained from 100 nm VO2 film. Compared to the one on LSAT, this
ratio is slightly smaller. However, take the surface smoothness into account, it is still better to
choose STO as the substrate of the bilayer oscillator.
The temperature dependent resistivities of a bare 30 nm VO2 and a 5 nm SRO/ 30 nm VO2
on STO are shown in Figure 7.8 (c). The metal-insulator transition is still visible in the bilayer
sample and the resistance of the SRO layer lies in between the insulating state and metallic state
VO2 resistance. The resistivity of insulating state is significantly reduced by one order of
magnitude due to the SRO metallic layer. This potentially lower consumption of the entire device
by the same fold.
Figure 7.8 Temperature-resistivity characteristics for VO2 thin films. (a) Temperature dependent four probe resistivity of
30, 50, and 100 nm VO2 films on LSAT (111). (b) Comparison of four probe resistivity of 100 nm VO2 on LSAT and STO
substrate. (c) Four probe resistivity of 30 nm VO2 and 5 nm SRO / 30 nm VO2 bilayer on STO substrate.
136
7.4 Oscillator Characteristics of the Vanadium Dioxide/Strontium Ruthanate
Bilayer Devices
7.4.1 Geometry of the Devices
Devices were fabricated on 5nm SRO and 30nm VO2 bilayer planar samples and bare 30nm
VO2 on STO films grown by PLD. The growth parameters used is the same as previous sections.
The planar devices are patterned by optical lithography, followed by metal deposition and lift-off
processes. Au-Ti metal contacts with the overall thicknesses of 50 nm were deposited by electron
beam evaporation. To study the effect of thermal coupling, electrically isolated planar
microstructures with different geometries were fabricated. The width and gap of the electrodes
varied from 1𝜇 m to 10 𝜇 m as shown in Figure 7.9
Electrical properties of devices are measured with the circuit schematically drawn in Figure
6.6. Voltage is supplied as a triangle wave by an analog function generator for I-V characteristic
measurements. The oscillations are triggered by a constant current from a current source. The
voltage oscillation is monitored by an oscilloscope. All the experiments are performed in the
vacuum at room temperature.
Figure 7.9 Device structure illustration and photos. (a) the 3D device structure for a 30 nm VO2 and 5 nm SRO
on SrTiO3. Top view photos of (b) head-to-head geometry and (c) overlap geometry of the Au/Ti electrodes.
(a) (b)
(c)
137
7.4.2 I-V and Oscillator Characteristics
Representative results for forward and backward voltage sweeps of a VO2 sample and an
SRO/VO2 sample is shown in Figure 7.10. Both of the devices have an effective area of 4 × 4 𝜇𝑚
with the head-to-head geometry as shown in Figure 7.9 (b). Similar I-V hysteresis of VO2 phase
transition have been observed for both devices as predicted by the simulation. Abrupt resistance
switching from HRS to LRS is observed at a voltage of 13 V during forward sweep, whereas the
LRS is maintained until 3.7 V during the reverse sweep. However, the value becomes nearly 3
times smaller of the IMT for SRO/VO2 devices due to the effective heating as proposed in the
Figure 7.10 I-V characteristic scan of (a) VO2 and (b) SRO/VO2 device. A current compliance of 7 mA has been applied to
prevent failure of the SRO/VO2 device.
(a) (b)
Figure 7.11 Typical oscillation waveforms for (a) VO2 and (b) SRO/VO2 devices operating at 0.3 mA with a parallel capacitor
of 200 nF.
(a) (b)
138
simulation. The corresponding oscillation waveforms with constant I0 applied are shown in Figure
7.11. Obviously, one can see that the maximum and minimum voltage of the waveforms are within
the transition region between the IMT and MIT voltages for both the devices. The maximum
voltage of VO2 device reaches nearly 12 V whereas the SRO/VO2 could operate below 4 V. When
we look more closely at a single oscillation cycle, the SRO/VO2 shows a more pronounced
asymmetric behavior, consisting of an abrupt drop and a gradual rise. According to the analysis of
the thermal heating mechanism of SRO/VO2 device, the frequency is limited by the heating cycle,
where the current applied to generate heat is not sufficiently fast as compared to the cooling. This
is consistent with our observation that the heating cycle, section between B and C in Figure 6.9,
takes most of the time during a single cycle. This indicates that the frequency could be even
optimized by tuning the applied voltage. Regardless of any optimization, the time for the entire
cycle of SRO/VO2 has already become much faster than that of pure VO2. Given the advantage of
lower operation voltages and faster frequency of the bilayer devices, I will stress on the SRO/VO2
bilayer device for the rest of the discussion.
Figure 7.12 (a) Characteristic current vs. voltage loop of a head-to-head device with 1 μm x 1 μm dimension, obtained sourcing a
current and measuring the voltage for the blue line and sourcing voltage and measuring current for the yellow line. (b) oscillation
waveform obtains at 1.0 mA applied current and 560 pF parallel capacitor.
(b)
(a)
139
Figure 7.12 (a) shows the I-V characteristics from different source. The phase transition can
be electrical triggered either by sourcing a current or voltage across the device. Noticeably, as
shown in the temperature dependent measurements, abrupt change in resistance is also observed
with different external stimulus. The transition voltages and currents are similar for both
measurement setup (current or voltage driven), which is approximately 1.3 V for the IMT and 0.6
V for IMT and 0.2 mA for the current. Corresponding oscillation waveform is also measured at an
applied current of 1 mA with a parallel capacitor of 560 pF. The frequency of the oscillation
waveform is calculated to be 1.5 MHz for the 1x1 μm sample, which is comparable to the highest
oscillation frequencies among the VO2 based oscillator.
93,252,255,290

7.4.3 Applied Current and Tuning of Capacitance
A systematic study on the tunability of the devices has been carried out by varying applied
current and the capacitance used in the circuit. The results of the oscillation frequency
measurements are summarized in Figure 7.13 (a). The frequency of an oscillator is inversely
proportional to the parallel capacitance. The lowest capacitance that maintains the sustainable
oscillations for a 1 μm x 1 μm VO2/SRO device is 560 pF. No oscillation could be measured using
a capacitor with smaller capacitance. As shown by the model in the previous chapter, the cooling
power from the discharging of the capacitor is too low for the LRS to reverse to HRS. The effect
of the applied current is studied at fixed capacitance at 1.08 nF. The frequency of the oscillator
increases with the applied current in a linear manner. The sustained oscillation waveforms are
observed up to 1.5 mA. The tunability of the oscillator at constant capacitance is 80%, calculated
from frequencies ranging from 0.2 MHz to 1.05 MHz. With different levels of the capacitance, the
140
tunability could be even higher across 3 orders of magnitude. The optimized frequency of 1.5 MHz
is measured at the lowest parallel capacitance under largest applied current and the waveform is
shown in Figure 7.12 (b)
7.4.4 Footprint Effect
Oscillators with different footprints are also investigated and summarized in Table 9. The
same relation between device length and frequency is observed both in the simulation and
experiment. The optimized frequency increases exponentially with the decrease of the device size.
More precisely, shrinking to quarter of the size gives raise to one order of magnitude acceleration
in oscillating frequency. However, the maximum frequency from the experiment is far below the
simulation value. I would attribute the deviation to the overestimation of the thermal boundary
conductance. One possible explanation is that the finite roughness of the VO2 and SRO interface
may induce non-ideal thermal transfer conditions and lower the interfacial conductance.

Figure 7.13 (a) The effect of the oscillation frequency on parallel capacitance for a 1 μm x 1 μm VO2/SRO device. The variation of
frequencies under constant parallel capacitance is due to measurements carried out at different applied current. (b) The dependence
of the electrical oscillation frequency on applied current which is measured with a capacitance of 1.08 nF.
141
Table 9 Optimized electrical oscillation frequency summary of various footprints.
7.5 Summary
In conclusion, we have presented high-quality epitaxial growth of VO2 thin films on LSAT
and STO (111) substrates. The epitaxial relationship between the VO2 thin film and the LSAT
substrate was obtained by pole figure analysis. The pole figure patterns displayed the quasi-
hexagonal azimuthal symmetry for VO2, which resulted presumably from the three types of VO2
domains on the surface with 3m symmetry. Raman spectroscopy demonstrated the concomitant
structural phase transition of VO2 thin film with the MIT. The VO2 film revealed a MIT at 348 K
with a large resistance ratio (~3 10
4
).
Planar device has been fabricated on the epitaxial bilayer VO2/SRO with the thickness of
30 nm and 5 nm, respectively. The I-V characteristic has been studied by sourcing current or
voltage. Compared to the bare VO2 device, transition voltage and current are significantly reduced
due to the lower resistance state provided by the thin SRO layer. Moreover, the oscillation
frequency measured at the same conditions is also faster than that of pure VO2 oscillators. This
can confirm the frequency enhancement predicted by simulation in the last chapter. After
optimization of the parallel capacitor and applied current, a maximum frequency of 1.5 MHz is
measured with an effective device footprint of 1 μm x 1 μm, which is comparable to the measured
frequency for pure VO2 devices.
Sample thickness SRO/VO2 5 nm/30 nm
Device size 1 μm x 1 μm 4 μm x 4 μm 10 μm x 10 μm
Optimized frequency (MHz) 1.5 0.11 0.01
142
One would anticipate a higher electrical oscillation frequency in devices with smaller device
footprint. This is consistent with both experiments and theoretical models, where the oscillation
frequency scales exponentially with the miniaturization of the device size. Therefore, I could
envision oscillators with up to 100 MHz in oscillation frequency in the proposed bilayer devices
for neuromorphic applications. To achieve this, further thermal measurements such as time-
domain thermoreflectance would be urgently needed to understand the thermal transport properties
of the device and provide precise correction to the assumption of the theoretical model.
Synchronization of multiple oscillators is also important to reach the goal of next
generation of neural computing. Understanding the coupling dynamics of oscillators could be
essential to make ONN and that can be examined by linking the oscillators using electrical
coupling elements, specifically resistors or capacitors, to an array.

143
Chapter 8. Conclusion and Outlook
Living in the information age, we are surrounded by technologies that enables us to solve
problems on a daily basis and communicate though social media, which have revolutionized the
way we learn, build, communicate and understand our world. Without any doubt, semiconductor
materials in general constitute the basis for the high-performance computation and communication.
In the current era of information age, the conventional transistor size is approaching the physical
limit and emerging electronic and photonic devices are becoming more complex and
multifunctional, which demands greater progress in materials science to finding materials with
desirable properties; creative ways to synthesis pure and high-quality crystals; develop integration
strategies to augment and improve current devices that transmit, receive, process, and store data.
Phase change materials as associated with abrupt changes in physical properties offer unique
opportunities to extend beyond the current CMOS technology. In particular, I focus on ferroelectric
materials offering abrupt and reversible polarization switching in the present of electric field,
which could result in large EO response for low loss, highly efficient optic modulation applications;
VO2, its abrupt change in resistivity under external stimulus such as temperature, voltage, current
and optical illumination, offers distinctive two states to generate electrical oscillations in
oscillatory neural networks.
First part of this work is centered on EO effects. Theorical model for ferroelectrics has been
established to find large EO materials. The model takes the energy landscape inputs from first-
principles calculations in consideration of the phonon, electron-phonon interaction, electron
144
energies. The EO tensors are calculated from the coupling between the polarization, electric field,
and dielectric function (refractive index). The results of the tetragonal BaTiO3 are in good
agreement with the experiment results from literature. Temperature and strain dependence of the
EO are theoretical investigated with the model and find that the magnitude of the EO coefficients
becomes surprisingly high at the paraelectric to ferroelectric and ferroelectric (orthorhombic) to
ferroelectric (tetragonal) transition. To further explore the possibility of building materials with
large EO, characteristic factors of ferroelectric materials, i.e., spontaneous polarization and energy
well depth, are carefully studied in the framework of perovskite ferroelectrics. I could conclude
that materials with low spontaneous polarization and shallow well depth are likely to have larger
EO response. BCZT-50 is found to nicely fits our expectations and large EO values are predicted.
To verify the prediction from theoretical calculations, we then synthesis the materials with
PLD, a versatile technique allows growth of materials in high purity and quality in the form of
single crystalline films and with the control of growth at atomic level. Single crystalline thin films
of BCZT-50 have been successfully grown on GSO substrate with atomically smooth surface,
which can be envisioned as a fundamental platform for the future EO measurements. Excellent
ferroelectric and piezoelectric properties have also been established in the BCZT-50 thin films.
Integration on Si is always demanding to take advantage of the mature materials processing
and fabrication techniques and advancing electronics and photonics that has already existed on
silicon platform. Therefore, I focused on two ways, directly integration: epitaxial growth of BCZT-
50 on Silicon in the assistant of a buffer layer of SrTiO3; indirect transfer: epitaxial transfer BCZT-
50 thin films from oxides substrate to Silicon wafer by a sacrificial layer of LMSO. Both methods
145
successfully integrated the BCZT-50 films epitaxially on Si and the polarization switching is
confirmed by the piezoelectric measurements.
EO measurements have far been established on the parent material BaTiO3. BCZT-50 in
principle, could adapt all the methods including the fabrication and process methods that is
applicable to BaTiO3 to build specific device for EO measurements since 85% of the chemical
composition in BCZT-50 is BaTiO3. Given the high-quality epitaxial thin film on complex oxides
and on silicon, clean EO measurements could be performed for BCZT-50 to:
⚫ Measure the EO coefficient – confirm the prediction from the model.
⚫ Understand the loss mechanism – scattering, insertion loss, leakage loss etc.
High frequency modulations such as RF modulation should also be tested for BCZT-50
materials to be compatible with the high computing speed in CMOS. Therefore, a complete
package of electronics to EO modulator to photonics could be realized in the foreseeable future.
The next steps for this research envision the expansion of the EO modulator to enable the full
spectrum from intercontinental optical communications which has been achieved, to nm size
optical links on chip in an energy efficient manner.
Second part of my work focused on the MIT materials, specifically VO2. Theoretical model
based on thermal and electrical transport has been established. A comparison of planar VO2 device
and VO2 / SRO bilayer device is carried out in terms of transition voltages and oscillation
frequencies. The bilayer device has absolute advantages in both criteria and shows a potential to
reach ~ 100 MHz frequency of electrical oscillations. Realization of this prediction greatly relies
on the high interfacial thermal conductance of the epitaxial films. Experiments are also performed
146
to verify the simulation. Epitaxial thin films of VO2 with abrupt interfaces and surfaces have been
grown on 3m surfaces. Large and abrupt resistivity transition has been observed for the epitaxial
thin film on oxide substrates with various thicknesses. Raman analysis confirmed the structural
transition of the VO2 thin films.
Oscillation behavior has been observed in the VO2/SRO bilayer devices. With optimized
conditions, a maximum frequency of 1.5 MHz have been measured. However, this value is smaller
than predicted by the theoretical model. Systematical thermal analyses at different level, i.e., layers
and interfaces, are necessary to understand the deviation between the experiment and simulation.
Further minimization of the footprint of the bilayer device would be anticipated to high frequency
oscillation with low power consumption since both the electric and thermal resistance decrease
with the device size.
Further long term, synchronization of the oscillation arrays starting from 2 oscillators to a
complex n-by-n arrays should be investigated. The availability of synchronization and capabilities
of phase matching are essential to the ONN applications. The scaling of the network to comprise
a high number of oscillators poses a challenge in the realization of a large coupling matrix, which
would represent the bottleneck in the area of associative learning. Ultimately, the physical
realization of a complete ONN system is needed to assess the overall performances of the
architecture and to compare it with state-of-the-art specialized neural network.

147
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166
Appendix A
The EO tensors, 𝑟 13
,𝑟 33
, and 𝑟 42
, are defined in Equation (7). Here we provide detail
derivations to them. From Equations (6.b-c), we have E2 and E3 as
For the left hand side of the Equation (7), we have:
Then substituting the Equations (A1) and Equations (A2) to Equation (7), we obtain:
𝐸 2
=
𝜕𝑓
𝜕 𝑃 2
=2𝑎 1
∗
𝑃 2
+4𝑎 11
∗
𝑃 2
3
+2𝑎 12
∗
𝑃 1
2
𝑃 2
+2𝑎 13
∗
𝑃 2
𝑃 3
2
+6𝑎 111
𝑃 2
5
+𝑎 112
(2𝑃 2
(𝑃 3
4
+𝑃 1
4
)+4𝑃 2
3
(𝑃 1
2
+𝑃 3
2
))+2𝑎 123
𝑃 1
2
𝑃 2
𝑃 3
2

(A1.a)
𝐸 3
=
𝜕𝑓
𝜕 𝑃 3
=2𝑎 3
∗
𝑃 3
+4𝑎 33
∗
𝑃 3
3
+2𝑎 13
∗
𝑃 3
(𝑃 1
2
+𝑃 2
2
)+6𝑎 111
𝑃 3
5
+𝑎 112
(2𝑃 3
(𝑃 1
4
+𝑃 2
4
)+4𝑃 3
3
(𝑃 1
2
+𝑃 2
2
))+2𝑎 123
𝑃 1
2
𝑃 2
2
𝑃 3

(A1.b)
1
𝑛 1
2
=𝜀 0
𝜕 2
𝑓 𝜕 𝑃 1
2
=𝜀 0
(2𝑎 1
∗
+12𝑎 11
∗
𝑃 1
2
+2𝑎 12
∗
𝑃 2
2
+2𝑎 13
∗
𝑃 3
2
+30𝑎 111
𝑃 1
4
+𝑎 112
(12𝑃 1
2
(𝑃 2
2
+𝑃 3
2
)+2(𝑃 2
4
+𝑃 3
4
))+2𝑎 123
𝑃 2
2
𝑃 3
2
)
(A2.a)
1
𝑛 3
2
=𝜀 0
𝜕 2
𝑓 𝜕 𝑃 3
2
=𝜀 0
(2𝑎 3
∗
+12𝑎 33
∗
𝑃 3
2
+2𝑎 13
∗
(𝑃 1
2
+𝑃 2
2
)+30𝑎 111
𝑃 3
4
+𝑎 112
(12𝑃 3
2
(𝑃 1
2
+𝑃 2
2
)+2(𝑃 1
4
+𝑃 2
4
))+2𝑎 123
𝑃 1
2
𝑃 2
2
)
(A2.b)
1
𝑛 4
2
=𝜀 0
𝜕 2
𝑓 𝜕 𝑃 2
𝜕 𝑃 3
=𝜀 0
(4𝑎 13
∗
𝑃 2
𝑃 3
+𝑎 112
(8𝑃 2
3
𝑃 3
+8𝑃 2
𝑃 3
3
)+4𝑎 123
𝑃 1
2
𝑃 2
𝑃 3
) (A2.c)
𝑟 13
=
𝜕 (
1
𝑛 1
2
)
𝜕 𝐸 3
=
𝜀 0
(4𝑎 12
∗
𝑃 3
+8𝑎 112
𝑃 3
3
)
2𝑎 1
∗
+12𝑎 11
∗
𝑃 3
2
+30𝑎 111
𝑃 3
4

(A3.a)
𝑟 33
=
𝜕 (
1
𝑛 1
2
)
𝜕 𝐸 3
=
𝜀 0
(24𝑎 11
∗
𝑃 3
+120𝑎 111
𝑃 3
3
)
2𝑎 1
∗
+12𝑎 11
∗
𝑃 3
2
+30𝑎 111
𝑃 3
4

(A3.b)
𝑟 42
=
𝜕 (
1
𝑛 4
2
)
𝜕 𝐸 2
=𝜀 0
(
8𝑎 123
𝑃 3
4𝑎 12
∗
+4𝑎 123
𝑃 3
2
+
4𝑎 13
∗
𝑃 3
+8𝑎 112
𝑃 3
3
2𝑎 1
∗
+2𝑎 13
∗
𝑃 3
2
+2𝑎 112
𝑃 3
4
+
4𝑎 13
∗
+24𝑎 112
𝑃 3
2
4𝑎 13
∗
𝑃 3
+8𝑎 112
𝑃 3
3
)
(A3.c)
167
We use the same procedure to derive the Equations (9.a-c) except the fact that the P1 and P2
are the non-zero terms in the orthorhombic phase.
For the tetragonal BaTiO3, up to six-order parameters are in Chapter 3. However, for the most
accurate estimation from first principles and experimental result, the 8
th
order Landau parameters
are considered. Therefore, I summarized the general EO tensor derivations for perovskite oxides
in the lattice symmetry of rhombohedral (BiFeO3), orthorhombic (KNbO3), and tetragonal
(BaTiO3, PbTiO3 and BCZT-50).
For the rhombohedral structure, all three polarizations are non-zero. Therefore, we have the
full expansion of the electro-optic coefficient. The electric field could be shown as:
The dielectric stiffnesses are:
𝐸 1
=2𝑎 1
𝑃 1
+4𝑎 11
𝑃 1
3
+2𝑎 12
(𝑃 2
2
+𝑃 3
2
)𝑃 1
+6𝑎 111
𝑃 1
5
+𝑎 112
(2𝑃 1
(𝑃 2
4
+𝑃 3
4
)+4𝑃 1
3
(𝑃 2
2
+𝑃 3
2
))+2𝑎 123
𝑃 1
𝑃 2
2
𝑃 3
2
+8𝑎 1111
𝑃 1
7
+𝑎 1112
(2𝑃 1
(𝑃 2
6
+𝑃 3
6
)+6𝑃 1
5
(𝑃 2
2
+𝑃 3
2
))+𝑎 1122
(4𝑃 1
3
(𝑃 2
4
+𝑃 3
4
))
+𝑎 1123
(2𝑃 1
(𝑃 2
4
𝑃 3
2
+𝑃 2
2
𝑃 3
4
)+4𝑃 1
3
𝑃 2
2
𝑃 3
2
))
(A4.a)
𝐸 2
=2𝑎 1
𝑃 2
+4𝑎 11
𝑃 2
3
+2𝑎 12
(𝑃 1
2
+𝑃 3
2
)𝑃 2
+6𝑎 111
𝑃 2
5
+𝑎 112
(2𝑃 2
(𝑃 1
4
+𝑃 3
4
)+4𝑃 2
3
(𝑃 1
2
+𝑃 3
2
))+2𝑎 123
𝑃 1
2
𝑃 2
𝑃 3
2
+8𝑎 1111
𝑃 2
7
+𝑎 1112
(2𝑃 2
(𝑃 1
6
+𝑃 3
6
)+6𝑃 2
5
(𝑃 1
2
+𝑃 3
2
))+𝑎 1122
(4𝑃 2
3
(𝑃 1
4
+𝑃 3
4
))
+𝑎 1123
(2𝑃 2
(𝑃 1
4
𝑃 3
2
+𝑃 1
2
𝑃 3
4
)+4𝑃 1
2
𝑃 2
3
𝑃 3
2
))
(A4.b)
𝐸 3
=2𝑎 1
𝑃 3
+4𝑎 11
𝑃 3
3
+2𝑎 12
(𝑃 1
2
+𝑃 2
2
)𝑃 3
+6𝑎 111
𝑃 3
5
+𝑎 112
(2𝑃 3
(𝑃 1
4
+𝑃 2
4
)+4𝑃 3
3
(𝑃 1
2
+𝑃 2
2
))+2𝑎 123
𝑃 1
2
𝑃 2
2
𝑃 3
+8𝑎 1111
𝑃 3
7
+𝑎 1112
(2𝑃 3
(𝑃 1
6
+𝑃 2
6
)+6𝑃 3
5
(𝑃 1
2
+𝑃 2
2
))+𝑎 1122
(4𝑃 3
3
(𝑃 1
4
+𝑃 2
4
))
+𝑎 1123
(2𝑃 3
(𝑃 1
4
𝑃 2
2
+𝑃 1
2
𝑃 2
4
)+4𝑃 1
2
𝑃 2
2
𝑃 3
3
))
(A4.c)
168
The third order electro-optic tensor of interest could be derived by the following equation:
We have
𝑋 11
=2𝑎 1
+12𝑎 11
𝑃 1
2
+2𝑎 12
(𝑃 2
2
+𝑃 3
2
)+30𝑎 111
𝑃 1
4
+𝑎 112
(2(𝑃 2
4
+𝑃 3
4
)+12𝑃 1
2
(𝑃 2
2
+𝑃 3
2
))+2𝑎 123
𝑃 2
2
𝑃 3
2
+56𝑎 1111
𝑃 1
6
+𝑎 1112
(2(𝑃 2
6
+𝑃 3
6
)+30𝑃 1
4
(𝑃 2
2
+𝑃 3
2
))+𝑎 1122
(12𝑃 1
2
(𝑃 2
4
+𝑃 3
4
))
+𝑎 1123
(2(𝑃 2
4
𝑃 3
2
+𝑃 2
2
𝑃 3
4
)+12𝑃 1
2
𝑃 2
2
𝑃 3
2
)
(A5.a)
𝑋 22
=2𝑎 1
+12𝑎 11
𝑃 2
2
+2𝑎 12
(𝑃 1
2
+𝑃 3
2
)+30𝑎 111
𝑃 2
4
+𝑎 112
(2(𝑃 1
4
+𝑃 3
4
)+12𝑃 2
2
(𝑃 1
2
+𝑃 3
2
))+2𝑎 123
𝑃 1
2
𝑃 3
2
+56𝑎 1111
𝑃 2
6
+𝑎 1112
(2(𝑃 1
6
+𝑃 3
6
)+30𝑃 2
4
(𝑃 1
2
+𝑃 3
2
))+𝑎 1122
(12𝑃 2
2
(𝑃 1
4
+𝑃 3
4
))
+𝑎 1123
(2(𝑃 1
4
𝑃 3
2
+𝑃 1
2
𝑃 3
4
)+12𝑃 1
2
𝑃 2
2
𝑃 3
2
)
(A5.b)
𝑋 33
=2𝑎 1
+12𝑎 11
𝑃 3
2
+2𝑎 12
(𝑃 1
2
+𝑃 2
2
)+30𝑎 111
𝑃 3
4
+𝑎 112
(2(𝑃 1
4
+𝑃 2
4
)+12𝑃 3
2
(𝑃 1
2
+𝑃 2
2
))+2𝑎 123
𝑃 1
2
𝑃 2
2
+56𝑎 1111
𝑃 3
6
+𝑎 1112
(2(𝑃 1
6
+𝑃 2
6
)+30𝑃 3
4
(𝑃 1
2
+𝑃 2
2
))+𝑎 1122
(12𝑃 3
2
(𝑃 1
4
+𝑃 2
4
))
+𝑎 1123
(2(𝑃 1
4
𝑃 2
2
+𝑃 1
2
𝑃 2
4
)+12𝑃 1
2
𝑃 2
2
𝑃 3
2
)
(A5.c)
𝑋 12
=4𝑎 12
𝑃 1
𝑃 2
+𝑎 112
(8𝑃 1
𝑃 2
3
+8𝑃 1
3
𝑃 2
)+4𝑎 123
𝑃 1
𝑃 2
𝑃 3
2
+𝑎 1112
(12𝑃 1
𝑃 2
5
+6𝑃 1
5
𝑃 2
)+𝑎 1122
(16𝑃 1
3
𝑃 2
3
)+𝑎 1123
(8𝑃 1
𝑃 2
3
𝑃 3
2
+4𝑃 1
𝑃 2
𝑃 3
4
+8𝑃 1
3
𝑃 2
𝑃 3
2
)
(A5.d)
𝑋 13
=4𝑎 12
𝑃 1
𝑃 3
+𝑎 112
(8𝑃 1
𝑃 3
3
+8𝑃 1
3
𝑃 3
)+4𝑎 123
𝑃 1
𝑃 2
2
𝑃 3
+𝑎 1112
(12𝑃 1
𝑃 3
5
+6𝑃 1
5
𝑃 3
)+𝑎 1122
(16𝑃 1
3
𝑃 3
3
)+𝑎 1123
(8𝑃 1
𝑃 2
2
𝑃 3
3
+4𝑃 1
𝑃 2
4
𝑃 3
+8𝑃 1
3
𝑃 2
2
𝑃 3
)
(A5.e)
𝑋 23
=4𝑎 12
𝑃 2
𝑃 3
+𝑎 112
(8𝑃 2
𝑃 3
3
+8𝑃 2
3
𝑃 3
)+4𝑎 123
𝑃 1
2
𝑃 2
𝑃 3
+𝑎 1112
(12𝑃 2
𝑃 3
5
+6𝑃 2
5
𝑃 3
)+𝑎 1122
(16𝑃 2
3
𝑃 3
3
)+𝑎 1123
(8𝑃 1
2
𝑃 2
3
𝑃 3
+4𝑃 1
4
𝑃 2
𝑃 3
+8𝑃 1
2
𝑃 2
𝑃 3
3
)
(A5.h)
𝑟 𝑖𝑗𝑘 =𝜀 0
𝑑 𝜒 𝑖𝑗
𝑑 𝐸 𝑘 =𝜀 0
∑
𝜕 𝑋 𝑖𝑗
𝜕 𝑃 𝑙 𝜕 𝑃 𝑙 𝜕 𝐸 𝑘 𝑙
(A6)
𝑟 33
=𝜀 0
(
𝜕 𝑋 33
𝜕 𝑃 1
𝑋 13
+
𝜕 𝑋 33
𝜕 𝑃 2
𝑋 23
+
𝜕 𝑋 33
𝜕 𝑃 3
𝑋 33
)
(A7,a)
169
where the
𝑟 13
=𝜀 0
(
𝜕 𝑋 11
𝜕 𝑃 1
𝑋 13
+
𝜕 𝑋 11
𝜕 𝑃 2
𝑋 23
+
𝜕 𝑋 11
𝜕 𝑃 3
𝑋 33
)
(A7,b)
𝑟 42
=𝜀 0
(
𝜕 𝑋 23
𝜕 𝑃 1
𝑋 12
+
𝜕 𝑋 23
𝜕 𝑃 2
𝑋 22
+
𝜕 𝑋 23
𝜕 𝑃 3
𝑋 23
)
(A7,c)
𝜕 𝑋 33
𝜕 𝑃 1
=4𝑎 12
𝑃 1
+𝑎 112
(8𝑃 1
3
+24𝑃 3
2
𝑃 1
)+4𝑎 123
𝑃 1
𝑃 2
2
+𝑎 1112
(12𝑃 1
5
+60𝑃 3
4
𝑃 1
)
+𝑎 1122
(48𝑃 3
2
𝑃 1
3
)+𝑎 1123
(2(4𝑃 1
3
𝑃 2
2
+2𝑃 1
𝑃 2
4
)+24𝑃 1
𝑃 2
2
𝑃 3
2
)
(A7,d)
𝜕 𝑋 33
𝜕 𝑃 2
=4𝑎 12
𝑃 2
+𝑎 112
(8𝑃 2
3
+24𝑃 3
2
𝑃 2
)+4𝑎 123
𝑃 2
𝑃 1
2
+𝑎 1112
(12𝑃 2
5
+60𝑃 3
4
𝑃 2
)
+𝑎 1122
(48𝑃 3
2
𝑃 2
3
)+𝑎 1123
(2(4𝑃 2
3
𝑃 1
2
+2𝑃 2
𝑃 1
4
)+24𝑃 1
2
𝑃 2
𝑃 3
2
)
(A7,e)
𝜕 𝑋 33
𝜕 𝑃 3
=24𝑎 11
𝑃 3
+120𝑎 111
𝑃 3
3
+336𝑎 1111
𝑃 3
5
+120𝑎 1112
𝑃 3
3
(𝑃 1
2
+𝑃 2
2
)
+𝑎 1122
(24𝑃 3
(𝑃 1
4
+𝑃 2
4
))+24𝑎 1123
𝑃 1
2
𝑃 2
2
𝑃 3

(A7,f)
𝜕 𝑋 11
𝜕 𝑃 1
=24𝑎 11
𝑃 1
+120𝑎 111
𝑃 1
3
+𝑎 112
(24𝑃 1
(𝑃 2
2
+𝑃 3
2
))+336𝑎 1111
𝑃 1
5
+120𝑎 1112
𝑃 1
3
(𝑃 3
2
+𝑃 2
2
)+𝑎 1122
(24𝑃 1
(𝑃 3
4
+𝑃 2
4
))+24𝑎 1123
𝑃 1
𝑃 2
2
𝑃 3
2

(A7,g)
𝜕 𝑋 11
𝜕 𝑃 2
=4𝑎 12
𝑃 2
+𝑎 112
(8𝑃 2
3
+24𝑃 1
2
𝑃 2
)+4𝑎 123
𝑃 2
𝑃 3
2
+𝑎 1112
(12𝑃 2
5
+60𝑃 1
4
𝑃 2
)
+𝑎 1122
(48𝑃 1
2
𝑃 2
3
)+𝑎 1123
(2(4𝑃 2
3
𝑃 3
2
+2𝑃 2
𝑃 3
4
)+24𝑃 1
2
𝑃 2
𝑃 3
2
)
(A7,h)
𝜕 𝑋 11
𝜕 𝑃 3
=4𝑎 12
𝑃 3
+𝑎 112
(8𝑃 3
3
+24𝑃 1
2
𝑃 3
)+4𝑎 123
𝑃 2
2
𝑃 3
+𝑎 1112
(12𝑃 3
5
+60𝑃 1
4
𝑃 3
)
+𝑎 1122
(48𝑃 1
2
𝑃 3
3
)+𝑎 1123
(2(4𝑃 3
3
𝑃 2
2
+2𝑃 3
𝑃 2
4
)+24𝑃 1
2
𝑃 2
2
𝑃 3
)
(A7,i)
𝜕 𝑋 23
𝜕 𝑃 1
=8𝑎 123
𝑃 1
𝑃 2
𝑃 3
+𝑎 1123
(16𝑃 1
𝑃 2
3
𝑃 3
+16𝑃 1
3
𝑃 2
𝑃 3
+16𝑃 1
𝑃 2
𝑃 3
3
) (A7,j)
170
For the orthorhombic structure, the non-zero polarization terms are P1 and P3. Analogy to the
derivation of rhombohedral structure, the electrooptic tensor could be derived from Equation (A7
a-c) expect all the terms contain P3 vanishes. Therefore, the remaining items in Equation (A7 a-c)
for orthorhombic structure is summarized here.
For the denominators:
For the nominators:
𝜕 𝑋 23
𝜕 𝑃 2
=4𝑎 12
𝑃 3
+𝑎 112
(8𝑃 3
3
+24𝑃 2
2
𝑃 3
)+4𝑎 123
𝑃 1
2
𝑃 3
+𝑎 1112
(12𝑃 3
5
+30𝑃 2
4
𝑃 3
)
+𝑎 1122
(48𝑃 2
2
𝑃 3
3
)+𝑎 1123
(24𝑃 1
2
𝑃 2
2
𝑃 3
+4𝑃 1
4
𝑃 3
+8𝑃 1
2
𝑃 3
3
)
(A7,k)
𝜕 𝑋 23
𝜕 𝑃 3
=4𝑎 12
𝑃 2
+𝑎 112
(8𝑃 2
3
+24𝑃 3
2
𝑃 2
)+4𝑎 123
𝑃 1
2
𝑃 2
+𝑎 1112
(12𝑃 2
5
+60𝑃 3
4
𝑃 2
)
+𝑎 1122
(48𝑃 3
2
𝑃 2
3
)+𝑎 1123
(24𝑃 1
2
𝑃 2
𝑃 3
2
+4𝑃 1
4
𝑃 2
+8𝑃 1
2
𝑃 2
3
)
(A7,l)
𝑋 11
=2𝑎 1
+12𝑎 11
𝑃 1
2
+2𝑎 12
𝑃 3
2
+30𝑎 111
𝑃 1
4
+𝑎 112
(2𝑃 3
4
+12𝑃 1
2
𝑃 3
2
)+56𝑎 1111
𝑃 1
6
+𝑎 1112
(2𝑃 3
6
+30𝑃 1
4
𝑃 3
2
)+𝑎 1122
(12𝑃 1
2
𝑃 3
4
)
(A8.a)
𝑋 22
=2𝑎 1
+2𝑎 12
(𝑃 1
2
+𝑃 3
2
)+𝑎 112
(2(𝑃 1
4
+𝑃 3
4
))+2𝑎 123
𝑃 1
2
𝑃 3
2
+𝑎 1112
(2(𝑃 1
6
+𝑃 3
6
))+𝑎 1123
(2(𝑃 1
4
𝑃 3
2
+𝑃 1
2
𝑃 3
4
))
(A8.b)
𝑋 33
=2𝑎 1
+12𝑎 11
𝑃 3
2
+2𝑎 12
(𝑃 1
2
)+30𝑎 111
𝑃 3
4
+𝑎 112
(2𝑃 1
4
+12𝑃 3
2
𝑃 1
2
)
+56𝑎 1111
𝑃 3
6
+𝑎 1112
(2𝑃 1
6
+30𝑃 3
4
𝑃 1
2
)+𝑎 1122
(12𝑃 3
2
𝑃 1
4
)
(A8.c)
𝑋 12
=4𝑎 12
𝑃 1
𝑃 2
+𝑎 112
(8𝑃 1
3
𝑃 2
)+4𝑎 123
𝑃 1
𝑃 2
𝑃 3
2
+𝑎 1112
(12𝑃 1
𝑃 2
5
)+𝑎 1123
(4𝑃 1
𝑃 2
𝑃 3
4
+8𝑃 1
3
𝑃 2
𝑃 3
2
)
(A8.d)
𝑋 13
=4𝑎 12
𝑃 1
𝑃 3
+𝑎 112
(8𝑃 1
𝑃 3
3
+8𝑃 1
3
𝑃 3
)+𝑎 1112
(12𝑃 1
𝑃 3
5
+6𝑃 1
5
𝑃 3
)
+𝑎 1122
(16𝑃 1
3
𝑃 3
3
)
(A8.e)
𝑋 23
=4𝑎 12
𝑃 2
𝑃 3
+𝑎 112
(8𝑃 2
𝑃 3
3
)+4𝑎 123
𝑃 1
2
𝑃 2
𝑃 3
+𝑎 1112
(12𝑃 2
𝑃 3
5
)+𝑎 1123
(4𝑃 1
4
𝑃 2
𝑃 3
+8𝑃 1
2
𝑃 2
𝑃 3
3
)
(A8.h)
171
It has to be noted that there are chances of making errors when simply remove all the terms
contain P2, for example the X12, X13
𝜕 𝑋 33
𝜕 𝑃 2
,
𝜕 𝑋 11
𝜕 𝑃 2

𝜕 𝑋 23
𝜕 𝑃 1
,and
𝜕 𝑋 23
𝜕 𝑃 3
since they are essentially zero. If one
looks closely to the Equations (A7, a-c), those “zero” terms coincidently sit on the nominators and
denominators which the differential of them may not be zero. Thus, I solved the Equation (A7 a-
c) by cancelling out the P2 in the nominators and denominators and removing all the higher order
terms that P2 still exists in.
𝜕 𝑋 33
𝜕 𝑃 1
=4𝑎 12
𝑃 1
+𝑎 112
(8𝑃 1
3
+24𝑃 3
2
𝑃 1
)+𝑎 1112
(12𝑃 1
5
+60𝑃 3
4
𝑃 1
)+𝑎 1122
(48𝑃 3
2
𝑃 1
3
) (A9,a)
𝜕 𝑋 33
𝜕 𝑃 2
=4𝑎 12
𝑃 2
+𝑎 112
(24𝑃 3
2
𝑃 2
)+4𝑎 123
𝑃 2
𝑃 1
2
+𝑎 1112
(60𝑃 3
4
𝑃 2
)+𝑎 1123
(4𝑃 2
𝑃 1
4
+24𝑃 1
2
𝑃 2
𝑃 3
2
)
(A9,b)
𝜕 𝑋 33
𝜕 𝑃 3
=24𝑎 11
𝑃 3
+120𝑎 111
𝑃 3
3
+336𝑎 1111
𝑃 3
5
+120𝑎 1112
𝑃 3
3
𝑃 1
2
+𝑎 1122
(24𝑃 3
𝑃 1
4
) (A9,c)
𝜕 𝑋 11
𝜕 𝑃 1
=24𝑎 11
𝑃 1
+120𝑎 111
𝑃 1
3
+336𝑎 1111
𝑃 1
5
+120𝑎 1112
𝑃 1
3
𝑃 3
2
+𝑎 1122
(24𝑃 1
𝑃 3
4
) (A9,d)
𝜕 𝑋 11
𝜕 𝑃 2
=4𝑎 12
𝑃 2
+𝑎 112
(24𝑃 1
2
𝑃 2
)+4𝑎 123
𝑃 2
𝑃 3
2
+𝑎 1112
(60𝑃 1
4
𝑃 2
)+𝑎 1123
(4𝑃 2
𝑃 3
4
+24𝑃 1
2
𝑃 2
𝑃 3
2
)
(A9,e)
𝜕 𝑋 11
𝜕 𝑃 3
=4𝑎 12
𝑃 3
+𝑎 112
(8𝑃 3
3
+24𝑃 1
2
𝑃 3
)+𝑎 1112
(12𝑃 3
5
+60𝑃 1
4
𝑃 3
)+𝑎 1122
(48𝑃 1
2
𝑃 3
3
) (A9,f)
𝜕 𝑋 23
𝜕 𝑃 1
=8𝑎 123
𝑃 1
𝑃 2
𝑃 3
+𝑎 1123
(16𝑃 1
3
𝑃 2
𝑃 3
+16𝑃 1
𝑃 2
𝑃 3
3
) (A9,g)
𝜕 𝑋 23
𝜕 𝑃 2
=4𝑎 12
𝑃 3
+𝑎 112
8𝑃 3
3
+4𝑎 123
𝑃 1
2
𝑃 3
+12𝑎 1112
𝑃 3
5
+𝑎 1123
(4𝑃 1
4
𝑃 3
+8𝑃 1
2
𝑃 3
3
) (A9,h)
𝜕 𝑋 23
𝜕 𝑃 3
=4𝑎 12
𝑃 2
+𝑎 112
(24𝑃 3
2
𝑃 2
)+4𝑎 123
𝑃 1
2
𝑃 2
+𝑎 1112
(60𝑃 3
4
𝑃 2
)+𝑎 1123
(24𝑃 1
2
𝑃 2
𝑃 3
2
+4𝑃 1
4
𝑃 2
)
(A9,i)
172
The equations for the tetragonal phase are simplest among the three phases since there is only
one variable P3 and other polarizations are zero. Therefore, I present below the full equations, by
simply adding the eight-order terms:

𝑟 33
=
𝜀 0
(24𝑎 11
∗
𝑃 3
+120𝑎 111
𝑃 3
3
+336𝑎 1111
𝑃 3
5
)
2𝑎 1
∗
+12𝑎 11
∗
𝑃 3
2
+30𝑎 111
𝑃 3
4
+56𝑎 1111
𝑃 3
6

(A10.a)
𝑟 13
=
𝜀 0
(4𝑎 12
∗
𝑃 3
+8𝑎 112
𝑃 3
3
+12𝑎 1112
P
3
5
)
2𝑎 1
∗
+12𝑎 11
∗
𝑃 3
2
+30𝑎 111
𝑃 3
4
+56𝑎 1111
𝑃 3
6
(A10.b)
𝑟 42
=𝜀 0
(
8𝑎 123
𝑃 3
+16𝑎 1123
𝑃 3
3
4𝑎 12
∗
+4𝑎 123
𝑃 3
2
+4𝑎 1123
𝑃 3
4
+
4𝑎 13
∗
𝑃 3
+8𝑎 112
𝑃 3
3
+12𝑎 1112
P
3
5
2𝑎 1
∗
+2𝑎 13
∗
𝑃 3
2
+2𝑎 112
𝑃 3
4
+2𝑎 1112
𝑃 3
6
+
4𝑎 13
∗
+24𝑎 112
𝑃 3
2
+60𝑎 1112
𝑃 4
4𝑎 13
∗
𝑃 3
+8𝑎 112
𝑃 3
3
+12𝑎 1112
P
3
5
)
(A10.c)
Table 10 Landau coefficients summary of ABO3 materials
Landau-
Devonshire
Coefficient
BaTiO 3 PbTiO 3 BCZT LiNbO 3 LiTaO 3 KNbO 3 BiFeO 3
This work
Bell and
Cross
168

Chen
291

Wang et
al.
169

Chen
291

Bandyop-
adhyay et
al.
193

This work Chen
291
This work Chen
291

Liang et
al.
292

Marton et
al.
293

𝑎 1
(Nm
2
/C
2
) -6.07× 10
8
-2.71× 10
7
-3.63× 10
7
-3.29× 10
7
-1.72× 10
8
-4.57× 10
7
-1.20× 10
9
-1.01× 10
9
-1.54× 10
9
-6.28× 10
8
-3.29× 10
7
-3.36× 10
9
𝑎 11
(Nm
6
/C
4
) 4.32× 10
9
-6.38× 10
8
-2.10× 10
8
-6.30× 10
8
-9.73× 10
8
-5.83× 10
9
9.03× 10
8
9.27× 10
8
2.21× 10
9
9.02× 10
8
-6.46× 10
8
2.65× 10
9
𝑎 12
(Nm
6
/C
4
) 6.29× 10
9
3.23× 10
8
7.97× 10
8
-2.30× 10
8
7.50× 10
8
1.83× 10
9

- - - -
9.66× 10
8
1.64× 10
9

𝑎 111
(Nm
10
/C
6
) 1.29× 10
10
7.89× 10
9
1.29× 10
9
4.30× 10
9
2.60× 10
8
2.26× 10
11

- - - -
2.81× 10
8
-5.96× 10
8

𝑎 112
(Nm
10
/C
6
) -1.44× 10
10
4.47× 10
9
-1.95× 10
9
-2.20× 10
9
6.10× 10
8
3.00× 10
10
- - - -
-1.99× 10
9
8.78× 10
7
𝑎 123
(Nm
10
/C
6
) -1.67× 10
10
4.91× 10
9
-2.50× 10
9
5.51× 10
10
-3.70× 10
9
1.45× 10
11
- - - -
6.03× 10
9
-1.19× 10
9

𝑎 1111
(Nm
14
/C
8
)
- -
3.86× 10
10
4.48× 10
10
- - - - - -
1.74× 10
10
9.04× 10
7
𝑎 1112
(Nm
14
/C
8
)
- -
2.53× 10
10
2.53× 10
11
- - - - - -
5.99× 10
9
-5.71× 10
7
𝑎 1122
(Nm
14
/C
8
)
- -
1.64× 10
10
2.80× 10
11
- - - - - -
2.50× 10
10
7.73× 10
7
𝑎 1123
(Nm
14
/C
8
)
- -
1.37× 10
10
9.53× 10
10
- - - - - -
-1.17× 10
10
1.24× 10
8

173

Abstract (if available)

Abstract Our modern information age and its exponential growth in the use of computing and communication is prompted by the continuous increase in the number of transistors packed in a unit area. As transistor feature size approaching the physical limits, it is obvious that room for future miniaturization has run out. Further, it is unclear whether the current computing and communication methods are the most efficient in solving emerging needs such as associative learning. Particularly, there is a need to develop novel hardware capabilities that can be more effective in solving such problems. As materials underpin the development of most hardware technologies, it is necessary to discover and develop novel materials to solve such problems. In this thesis, I address two important materials problems that are critical for next generation computing and communication technologies. First, I address the modeling of electro-optic materials with large coefficients and their integration to Silicon photonics platform to achieve high-speed communication, and the other is the development of alternative computing architectures such as neuromorphic computing to minimize energy consumption without sacrificing computing speed.
Ferroelectric oxides often possess not only large dielectric constants but also electro-optic responses leveraging the abrupt polarization switching arising from the broken symmetry. A theoretical pathway for finding ferroelectric oxide materials with large electro-optic (EO) response has been investigated using the model of Landau-Devonshire phenomenological theory with input from first-principles density functional theory. The model is first applied to a paradigmatic oxide, BaTiO3, and find that the predicted electro-optic constants agree well with the experimental results. The agreement of the temperature dependence of the electro-optic coefficients with the results from other models also demonstrates the efficacy of the model. Besides, the frequency- and strain-dependence of the EO response are also established. The model is then applied to six well-known ferroelectric ABO3-type materials and find that the spontaneous polarization of ferroelectric materials and well depth in the free energy profile are the keys to designing a material with giant electro-optic responses. Based on the matrix of spontaneous polarization and the well depth, a material, 0.5 Ba(Zr0.2Ti0.8)O3 – 0.5 (Ba0.7Ca0.3)TiO3 (BCZT-50), with smaller Ps and well depth comes into view, and we predict electro-optic coefficients as high as 1880 pm/V for r42 and 399 pm/V for r33 for experimental validation.
High-quality BCZT-50 thin films with atomically flat surface have been epitaxially grown on single crystalline GdScO3 substrate by pulsed laser deposition. Growth conditions have been carefully studied with the effect on the crystalline quality and surface condition. With the optimized growth condition, sustained layer-by-layer growth of up to 100 unit cells has been observed. Atomic force microscopy investigations show atomically smooth step terrace morphonology. Transmission electron microscopy results reveal good epitaxial relation between the film and the substrate without any line defects. High dielectric constant (~1400) and slim hysteresis loops in polarization-electric field characteristics were observed in BCZT-50 films, which are characteristic of relaxor-type ferroelectric materials.
Integration to the silicon platform is a critical requirement for the utilization of the EO materials. Direct deposition and indirect transfer methods are explored in this work. Epitaxial growth of BCZT-50 films on silicon substrate is performed using thin SrTiO3 as a buffer layer. The growth results show a similar quality to that of GdScO3 with better lattice matching with BCZT-50. The preferred orientation of the film is along the c-axis of BCZT-50. The piezoelectric response is measured to confirm the relaxor-type ferroelectric behavior. Free-standing BCZT-50 films that could be transferred to Si substrate were attempted as an alternative process with a sacrificial thin layer of (La,Sr)MnO3. The switching behavior of the transferred film was observed in the piezoelectric force microscopy measurements.
Another aspect of the thesis focuses on VO2, which possesses a reversible metal-to-insulator transition. This makes it an excellent candidate to realize electrical oscillators for next generation electronic applications such as hardware implementation of oscillatory neural networks. Theoretical models based on thermal and electrical transport have been established to understand the mechanism of VO2-based oscillators operating under the application of constant current. Here, a bilayer structure of VO2 and SrRuO3 that could potentially have high maximum frequency with lower power consumption is proposed. The simulation results show high tunability and predict a high-frequency oscillator could be built with a 100 nm size device. Experiments were carried out to validate our simulation results. Epitaxial growth of VO¬2¬ and VO2/SRO bilayer devices have been grown on epitaxial oxide substrates. I carefully investigated the structural and surface quality of the VO2 film and achieved low surface roughness with over 3 orders of magnitude change in resistance during the transition. The oscillation frequency for a pure VO2 and bilayer SRO/VO2¬¬ have been measured under the same conditions, the bilayer device shows a faster voltage waveform and low operating power, which is indicated by the amplitude of the voltage. A maximum of 1.5 MHz frequency has been achieved for a bilayer device and further investigation on thermal management, and a smaller footprint to achieving sub-GHz frequency with low power is ongoing.

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Asset Metadata

Creator Liu, Yang (author)

Core Title Phase change heterostructures for electronic and photonic applications

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Materials Science

Degree Conferral Date 2022-08

Publication Date 07/26/2022

Defense Date 06/01/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag electro-optic modulation,ferroelectric,metal-to-insulator transition,OAI-PMH Harvest,perovskite oxide,phase change,pulsed laser deposition,thin film

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ravichandran, Jayakanth (committee chair), Armani, Andrea (committee member), Branicio, Paulo (committee member), Nakano, Aiichiro (committee member), Wang, Han (committee member)

Creator Email 15801404060@163.com,liu570@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111375216

Unique identifier UC111375216

Legacy Identifier etd-LiuYang-10987

Document Type Dissertation

Format application/pdf (imt)

Rights Liu, Yang

Type texts

Source 20220728-usctheses-batch-962 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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