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The Pennsylvania State University

The Graduate School

Department of Materials Science and Engineering

NANOSCALE PROBING AND PHOTONIC APPLICATIONS OF

FERROELECTRIC DOMAIN WALLS

A Thesis in

Materials Science and Engineering

by

Lili Tian

2006 Lili Tian

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

December 2006

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The thesis of Lili Tian was reviewed and approved* by the following:

Venkatraman Gopalan Associate Professor of Materials Science and Engineering Thesis Advisor Chair of Committee

Eric Cross Evan Pugh Professor of Electrical Engineering

Qiming Zhang Professor of Electrical Engineering and Materials Science and Engineering

Zhiwen Liu Assistant Professor of Electrical Engineering

James Runt Professor of Polymer Science Associate Head for Graduate Studies in Materials Science & Engineering

*Signatures are on file in the Graduate School

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ABSTRACT

Ferroelectrics are a versatile solid-state platform for a new generation of micro-

and nanophotonic applications. Conventional integrated optics has often treated the

phenomenon of ferroelectric domains and domain walls more as a nuisance rather than an

asset. Ironically, domain walls can be immensely valuable in realizing a wide variety of

new functionalities such as laser scanning, dynamic focusing, frequency conversion,

beam shaping, waveguiding, high-speed modulation, and photonic crystal structures. All

of these functions can be realized by shaping ferroelectric domain walls into arbitrary

shapes on micro to nanoscale dimensions. Domain walls, however, have a mind of their

own when it comes to shaping them.

This thesis will focus on the fundamental domain switching characteristics under

the uniform electrical fields, and local electromechanical response across the single

ferroelectric domain wall in ferroelectric crystals lithium niobate, lithium tantalate and

strontium barium niobate. The local electromechanical response across the single was

modeled using finite element method to better understand the fundamentals of

piezoelectric force microscopy in order to quantitatively interpret the measured material

properties. The influence of stoichiometry on domain dynamics on macroscale and on

local electromechanical properties on nanoscale was studied. The challenges in shaping

ferroelectric domain are discussed and the examples of optical devices such as optical

switch and optical beam deflector based on ferroelectric domain walls are presented.

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TABLE OF CONTENTS

Chapter 1 Introduction and Outline of the Thesis.....................................................1

1.1 Overview of ferroelectric materials..............................................................1 1.2 Structure of ferroelectric materials...............................................................2 1.3 Lithium niobate, lithium tantalate and strontium barium niobate crystals .....7 1.4 Fatigue in ferroelectrics ..............................................................................12 1.5 Ferroelectric domain wall and its applications .............................................13 1.6 Thesis objectives .........................................................................................17 1.7 Thesis organization.....................................................................................18 References ........................................................................................................19

Chapter 2 Domain Reversal in Ferroelectric Materials.............................................23

2.1 Domain reversal in lithium tantalate ............................................................23 2.1.1 Domain reversal with liquid electrode...............................................25 2.1.1.1 Transient current......................................................................25

2.1.1.2 Hysteresis loop and Coercive fields.........................................29 2.1.1.3 Switching time........................................................................33

2.1.2 Domain reversal with other electrodes ..............................................34 2.1.3 Domain structure in lithium tantalate ................................................39 2.1.4 Backswitching ..................................................................................42

2.2 Domain reversal in strontium barium niobate crystal ...................................44 2.2.1 Real-time observation of domain wall motion under EOIM ..............45 2.2.2 Coercive fields and hysteresis loop ...................................................47 2.2.3 Switching time..................................................................................52 2.2.4 Wall mobility....................................................................................54 2.2.5 Backswitching ..................................................................................57 2.2.6 Discussion ........................................................................................58

2.2.6.1 Switching current and switching time......................................59 2.2.6.2 Internal Field and backswitching.............................................61 2.2.6.3 Electrodes and ferroelectric aging ...........................................61

2.2.7 Conclusions ......................................................................................63 References ........................................................................................................65

Chapter 3 Piezoresponse across Single Domain Wall ..............................................70

3.1 Introduction.................................................................................................70 3.2 Overview of Piezoelectric Force Microscopy (PFM) ...................................72 3.3 Overview of Finite element modeling - the numerical method .....................81

3.3.1 Field distribution in PFM system .......................................................83 3.3.2 Surface deformation modeled using FEM ..........................................93

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3.3.3 Validation of FE modeling.................................................................97 3.4 PFM imaging across the domain wall ..........................................................98

3.4.1 Background signal and frequency dependence of PFM imaging.........99 3.4.2 Vertical Piezoresponse Force Microscopy..........................................110

3.4.2.1 Dependence of the vertical PFM response on tip parameters ....113 3.4.2.2 The dependence of the crystal stoichiometry in PFM ..............116 3.4.2.3 Spatial resolution of PFM imaging...........................................120 3.4.2.4 Vertical PFM response on SBN:61...........................................128

3.4.3 Lateral imaging of PFM across the domain wall ................................132 3.5 Conclusion ..................................................................................................137 References ........................................................................................................139

Chapter 4 Ferroelectric Domain Patterned Devices..................................................144

4.1 Introduction.................................................................................................144 4.2 Electro-optic Devices Fabricated in Ferroelectrics .......................................145

4.2.1 Theory...............................................................................................145 4.2.2 Optical Devices .................................................................................149

4.2.2.1 Phase-array electro-optic steering of large aperture laser beams using ferroelectrics ............................................................150

4.2.2.2 Eletro-optic optical switch .......................................................157 4.2.2.3 Anomalous electro-optic effect in Sr0.6Ba0.4Nb2O6 single

crystals and its application in two-dimensional laser scanning ......160 4.3 Optical Frequency Converter.......................................................................168 4.4 Conclusion ..................................................................................................172 References ........................................................................................................173

Chapter 5 Conclusions and future work...................................................................175

5.1 Conclusions on electromechanical response across the single domain wall ..175 5.2 Conclusions on the domain reversal in stoichiometric lithium tantalate

and SBN:61................................................................................................178 5.3 Domain wall shaping and applications.........................................................179 5.4 Outstanding issues.......................................................................................179 References ........................................................................................................180

Appendix A Electric Fields Distribution under the AFM Tip...................................181

A.1 Point charge above a semi-infinite dielectric plane......................................181 A.2 Point charge distribution to keep equal potential on a sphere.......................183 A.3 The tip sphere above a semi-infinite dielectric plane...................................185 References ........................................................................................................188

Appendix B ANSYS Batch File for Piezoelectric Response Simulation...................189

Appendix C Background Signal in PFM Measurement............................................193

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Appendix D Dielectric Properties of Lithium Niobate, Lithium Tantalate and Strontium Barium Niobate.................................................................................196

D.1 Lithium Niobate (LiNbO3)..........................................................................196 D.2 Lithium Tantalate (LiTaO3) ........................................................................196 D.3 Strontium Barium Niobate (Sr0.61Ba0.39Nb2O6 or SBN:61) ..........................197

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LIST OF FIGURES

Figure 1-1: Classification of piezoelectric, pyroelectric and ferroelectric properties in 32 point groups. ............................................................................2

Figure 1-2: Schematic structure of typical ABO3 ferroelectrics with BO6 octahedral frame (a) tetragonal BaTiO3 crystal with perovskite structure; (b) SrxBa1-xNb2O6 crystal with tungsten bronze structure; (c) ferroelectric LiTaO3 crystal with lithium niobate structure. (plotted using Software CaRine Crystallography 3.1. Lattice parameter in: (a) comes from Ref. [4]; (b) comes from Ref. [6]; (c) comes from Ref. [7, 8])..........................................................4

Figure 1-3: The unit cell of the lithium niobate (LiNbO3) structure (a) with up domain; (b) with down domain (by software CaRine Crystallography 3.1 with lattice parameters from Ref. [8, 7])....................................................................6

Figure 1-4: The spontaneous polarization in strontium barium nibate crystal. (a) Sr/Ba atom in 4-fold A1 site and Nb atom in octahedron, their positions are below the oxygen mean plane; (b) Sr/Ba atom in 5-fold A2 site and Nb atom in octahedron, their positions are below the oxygen mean plane. Crystal structure see details in Ref. [6] ..........................................................................7

Figure 1-5: The schematic phase diagram of Ta2O5-Li2O near the congruent composition (adapt from V. Gopalan at. el13, originally from S. Miyazawa and H. Iwasaki 16)..............................................................................................8

Figure 1-6: Transmission spectrum of lithium tantalate (LT) with different compositions and stoichiometric lithium niobate (LN). The thicknesses of samples are 0.31mm, 1.00mm, 0.83mm and 1.00mm for congruent lithium tantalate, near-stoichiometric lithium tantalate, stoichiometric lithium tantalate and stoichiometric lithium niobate. (a) the transmission spectra from near UV to mid-infrared; (b) spectra towards near UV band edge in (a). Fresnel reflection loss is not excluded. ..............................................................11

Figure 1-7: The schematic scanner based on ferroelectric domain patterning. (a) quasi-phase-matching structure; (b) electro-optic scanner; (c) dynamic focusing cylindrical lens; (d) photonic structure patterned by SPM technique, from Tarabe et. al. in NIMS, Japan....................................................................14

Figure 2-1: Transient currents observed during domain reversal in lithium tantalate crystals with liquid electrode at room temperature. (a) stoichiometric lithium tantalate prepared by VTE treatment; (b) near-stoichiometric tantalate grown by DCCZ method; (c) congruent lithium tantalate grown by CZ method. .......................................................................................................27

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Figure 2-2: The hysteresis loops at room temperature of stoichiometric, near-stoichiometric and congruent lithium tantalate...................................................30

Figure 2-3: Hysteresis loops of lithium tantalate crystals. (a) Hysteresis loops for 1st experimental cycle and 22nd experimental cycle of stoichiometric LiTaO3 single crystals (SLT-VTE). Cycling frequency was ~4 minutes/cycle. (b) Coercive fields and spontaneous polarization measured in 22 successive experimental cycles. Coercive fields Ec,f (~1.39±0.01kV/cm) and coercive field Ec,r (~1.23±0.01kV/cm) do not change with cycling. .................................31

Figure 2-4: Composition dependence of forward (Ec.f) and reverse (Ec.r) coercive fields, and the Curie temperature (Tc) in lithium tantalate single crystals. ..........33

Figure 2-5: The switching time (ts) f, r as a function of field E±Eint, where negative sign is for forward poling and the positive sign for reverse poling. The measured internal field Eint=0.08kV/cm......................................................34

Figure 2-6: The spontaneous polarization vs. cycles of domain reversal in stoichiometric lithium tantalate with (a) metal tantalum (Ta) electrode;(b) ITO (In2O3:Sn) electrode...................................................................................36

Figure 2-7: The spontaneous polarization vs. the domain reversal cycles with 10% LiCl solution at room temperature after removed the graphite electrodes, with which strong ferroelectric fatigue was also observed. ................................38

Figure 2-8: Domain image of lithium tantalate. (a) optical image of congruent lithium tantalate; (b) Optical image of near-stoichiometric lithium tantalate with 10kV/mm field on; (c) The phase piezoresponse force microscopy (PFM) image of the domains in stoichiometric lithium tantalate (SLT)..............41

Figure 2-9: Schematic of defect dipoles in lithium tantalate. (a) unit cell of perfect crystal with up domain; (b) up domain with up defect dipole formed by defect complex; (c) down domain with up defect dipole formed by original defect complex after the first domain reversal; (d) down domain with down defect dipole after the defect complex relaxation......................................43

Figure 2-10: Domain structure of SBN:61 crystals (a) with field 225V/mm; (b) 5s after frame (a); (c) after the reversal is complete; (d) Piezoelectric Force Microscopy image of domain (the product of amplitude and the cosine of phase)................................................................................................................47

Figure 2-11: The transient current observed during domain reversal of SBN:61 on applying a linearly ramped field at 1V/mm/s with water electrodes (solid line with square) or metal electrode (solid line with circle).......................................48

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Figure 2-12: The hysteresis loop for SBN:61 crystals measured by applying linearly ramped field at speed 1V/mm/s. (a) Poled with liquid (tap water) electrodes. The solid line and dot line loops are measured for successive polarization reversal cycle 1 and cycle 4. No obvious fatigue observed. (b) Poled with silver paste. Strong ferroelectric aging is observed. (c) The Ps (forward and reverse) measured for 1. tap water electrode, and 2. silver paste electrode. ..........................................................................................................50

Figure 2-13: The relationship between coercive fields and field ramping speeds for SBN:61 crystals. ..........................................................................................52

Figure 2-14: The switching time and switched charge in SBN:61 domain reversal under various applied fields with liquid electrode. The switching time is the time needed such that 95% of area has been reversed. The switched charges remain almost same at different field. ................................................................53

Figure 2-15: Domain sideways wall growth in SBN:61 crystals. (a) The distances traveled along x-axis and y-axis vs. time after nucleation of an independent domain under field E=3.15kV/cm; the slope of curve gives the sideways wall velocities along both x-axis and y-axis directions, which are the same and equal to 12.10±0.30µm/sec. (b) The distance traveled along serrated direction (<110> direction) vs. time for a merged domain wall velocity under field E=3.15kV/cm; The slope gives the sideways wall velocity, vs~17.10±0.77µm/sec. (c) Distances traveled (along either x-axis or y-axis) vs. time after nucleation of an independent domain under different fields; (d) Domain wall velocities of an independent domain under different fields............56

Figure 2-16: “Backswitching” tracking in c-cut SBN:61 crystal and no backswitch was observed. (a) A 1.25ms pulse of 4.0kV/cm field is applied antiparallel with spontaneous polarization on a single domain crystal to find out the RC response time of the circuit. RC constant of the circuit is ~0.06ms. (c) A 1.25ms pulse of 4.0kV/cm field is applied parallel with spontaneous polarization on the same area of same sample used in (b). Partial domain reversal is induced. (c) The switching current after taking away RC response current from the (b). It suggests no backswitching in SBN:61 under 1.25ms pulse of 4.0kV/cm field. ....................................................................................58

Figure 3-1: The detection system in an Atomtic Force Microscope (AFM)...............74

Figure 3-2: Schematic piezoresponse across the single 180° domain wall in lithium niobate, lithium tantalate and strontium barium niobate crystal. (a) the surface displacement (solid line) due to the electric field across the domain wall displayed in (e). The dot line is original surface plane; (b) the piezoresponse, both X and Y signal, across the domain wall. X is the product of amplitude (R) and the sine of the phase, θ, and Y is the product of

x

amplitude and cosine of the phase; (c) the piezoresponse, both X signal and Y signal, on both +c and –c surface plotted in vector XY plane. (d) the amplitude and phase of the piezoresponse across the domain wall; (e) schematic domain structure and electrical field..................................................78

Figure 3-3: An SEM image of an example of the typical metal coated AFM tip. (CSC37/Ti-Pt AFM probe from MikroMasch)...................................................84

Figure 3-4: Simplified sphere model of an AFM tip over an anisotropic material in PFM system. .................................................................................................87

Figure 3-5: The relationship between field inside the specimen and the distance, d, between the tip and top surface of the specimen and tip radius for a dielectric with dielectric constants εr=85.2 and εz=28.7. The applied voltage on the tip is 5V. (a) The total charge stored in the capacitor system of tip and the dielectric sample, which is equal to the total charge induced on the surface of the dielectric, whereas the sign of induced charge on the sample surface is opposite to the charge on the surface of the tip; (b) the maximum potential inside the dielectrics vs. the distance d; (c) the maximum electric component Ez vs. the distance d for different size tip; (d) the maximum electric component Er vs. the distance d for different tip size. (e) the maximum fields for a 50nm spherical tip, which is in contact (d=0nm); (e) the maximum fields fro a 50nm spherical tip, which is not in contact and d=0.01nm..........................................................................................................88

Figure 3-6: The field distribution inside the dielectric (εr=85.2 and εz=28.7), which is in contact (d=0nm) with a sphere tip with radius of 50nm. The voltage applied on the tip is 5V. (a) potential in z=0 plane; (b) potential in depth plane. (c) Er in depth plane; (d) Ez in depth plane. The maximum electric fields are 7.53×108 V/m and 4.35×109 V/m for Er and Ez, respectively...........................................................................................................................90

Figure 3-7: The dependence of the width of the potential and electrical field (Ez) along both in-plane and in depth direction on the spherical tip size. (a) full width (the distance between two points at which the potential or electric field reaches only 10% of its maximum value) of the potential and electrical field inside lithium niobate under a spherical tip with 5V on; (b) the full width half maximum (FWHM) of the potential and electrical field inside lithium niobate under a spherical tip with 5V on. .......................................................................91

Figure 3-8: Schematic of the simplified disc model. ................................................92

Figure 3-9: The potential distribution inside z-cut lithium niobate under a flat 50nm radius AFM tip with 5V applied voltage on. (a) The potential distribution on the z=0nm plane; (b) The potential distribution in depth plane; (c) Er distribution in depth plane; (d) Ez distribution in depth plane. ..................93

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Figure 3-10: The deformation on z=0nm plane of lithium niobate under a 50nm radius AFM tip with 5V applied voltage on. (a)-(c) for sphere tip; (d)-(f) for disc tip. .............................................................................................................94

Figure 3-11: The piezoelectric vertical and lateral response across the domain wall (located at 0) in lithium niobate for a tip with radius of 50nm, which is in contact (d=0nm) with lithium niobate. The driving voltage on the tip is 5V. The spontaneous polarization in the left region points up, which means +z surface, whereas the spontaneous polarization in the right region points down and the surface under the tip is –z surface. (a) displacement with a sphere tip; (b) displacement with a disc tip; (c) vertical PFM signal with a sphere tip; (d) vertical PFM signal with a disc tip; (e) slope of the deformed surface, which is proportional to 0°-lateral PFM signal with a sphere tip; (f) slope of the deformed surface with a disc tip. .......................................................................96

Figure 3-12: The piezoelectric response of the single domain in lithium niobate. (a)-(c) under the uniform electric field. The applied voltage is 5V; (d)-(f) under a 50nm sphere tip which is in contact at (0, 0, 0). The applied voltage on the tip is 5V..................................................................................................98

Figure 3-13: Typical frequency response of PFM. The sample here is congruent lithium niobate. .................................................................................................101

Figure 3-14: (a) The schematic diagram showing the measured PFM signal on both +c and –c surface of the ferroelectric material away from the resonance frequency of the probe. The measured signal includes the pure piezoelectric response signal, which is denoted as “electromechanical” signal, and a background signal, which is due to electrostatic response and non-local nonlinear response acting on the cantilever; (b) The schematic diagram showing to restore the pure piezoelectric response from the measured PFM signal. ...............................................................................................................104

Figure 3-15: Typical frequency dependence of PFM signal on +c surface of lithium niobate. (a) amplitude ( R); (b) phase. ...................................................106

Figure 3-16: The piezoresponse across the signal 180° wall in lithium niobate single crystal. (a) x and y signal at selective frequencies plotted in a complex XY plane. Solid line was the fitting, whereas the scattered dots are experiment data; (b) The maximum amplitude of the electromechanical contribution to the PFM signal at different frequencies; (c) amplitude (d) phase of the measured piezoresponse across the domain wall in lithium niobate at selective frequencies as in (a). ...........................................................108

Figure 3-17: (a) The frequency response of the PFM system on lithium niobate, which was plotted in Figure 3-15 (a); (b) The amplitude of the PFM response

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across the domain wall in lithium niobate, which was plotted in Figure 3-16 (b). ....................................................................................................................109

Figure 3-18: The piezoresponse across the single 180° domain wall in lithium niobate at the single frequency (~42.45kHz) with different phase setting in the lock-in amplifier. (a) x and y signal in the complex XY plane. The solid line was the fitting, whereas the scattered dots are experimental data; (b) the amplitude of the electromechanical contribution to PFM signal.........................110

Figure 3-19: PFM image across the single domain wall in lithium niobate. x signal (a) and y signal; (b) of the measured piezoresponse across the domain wall; (c) x and y signal of the measured piezoresponse; (d) amplitude and phase of the measured piezoresponse across the domain wall; (e) x and y signal of the piezoresponse across the wall after the “background” subtraction; (f) amplitude and phase of the piezoresponse across the wall after the “background” subtraction. The fitting used function: y=A1tanh(x/t1)+A2tanh(x/t2), where A1, t1, A2, and t2 are fitting constants. ........112

Figure 3-20: The piezoresponse across the single domain wall in periodic poled congruent lithium niobate with different applied voltage at 42.2kHz. (a) The amplitude of piezoresponse vs. the peak applied voltage on the tip. The slope is ~9.9±0.5pm/V (b) Normalized amplitude of the piezoresponse across the domain wall with different peak applied voltage on the tip. The domain wall interaction width does not change......................................................................113

Figure 3-21: FEM result along with the PFM measurement of the amplitude of the vertical piezoresponse across the domain wall in lithium niobate.......................114

Figure 3-22: Amplitude of piezoresponse across the single wall in PFM vs. the distance d between the tip and the surface of lithium niobate sample. (a) Amplitude of piezoresponse and the maximum potential inside lithium niobate sample vs. the distance between the tip and surface of lithium niobate; (b) The effective piezoelectric coefficient d′eff and deff vs. the distance between the tip and sample surface. d′eff is the piezoelectric coefficient determined by the ratio of the amplitude of the piezoresponse over the applied voltage on the tip; deff is determined by the ratio of the amplitude of piezoresponse over the potential in the surface of the lithium niobate sample. In this case, the tip is a 50nm-radius sphere tip. The applied voltage on the tip is 5V. Potentials on the sample surface are plotted in (a). ..................115

Figure 3-23: (a) Comparison of the the piezoresponse in lithium tantalate between the FEM modeling and measurement. The tip radius size is ~50nm. Congruent periodically poled lithium niobate was used as the reference. In FEM, the ratio between the vertical piezoresponse across the single wall in congruent lithium tantalate and congruent lithium niobate is ~0.73±0.07,

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whereas in the experiment, it was determined to be ~0.67±0.02. (b) Normalized piezoresponse in both lithium niobate and congruent lithium tantalate and stoichiometric lithium tantalate grown using VTE method. ...........118

Figure 3-24: Comparison of piezoresponse in stoichiometric lithium niobate with and periodically poled congruent lithium niobate (CLN). The ratio between bulk SLN and CLN is ~1.0. However, the domain interaction width in SLN is wider than that in CLN......................................................................................119

Figure 3-25: (a) FESEM image of the tip after PFM scan. (b) The full domain interaction width of congruent lithium niobate vs. the tip radius size. The very end of the tip was flat, like in (a). ..............................................................122

Figure 3-26: (a) FESEM image of the sphere like tip after the PFM imaging.. (b) The domain wall interaction width of congruent lithium niobate vs. the tip radius. The tips were sphere like in (a). The radius was determined as the radius of a/2 in inset when assuming indentation depth h is ~1nm. ....................123

Figure 3-27: FEM result of the domain interaction width and displacement vs. the distance d between the tip and surface in congruent lithium niobate under a 50nm sphere tip with 5V on...............................................................................124

Figure 3-28: FEM simulation of vertical piezoresponse across a tilted domain wall. (a) Side view of the geometry of the domain wall. The wall is tilt with an angle of θ. The origin is located at point O; (b) etched y surface of PPLN, in which maximum tilt angle of domain wall is ~2.6 degree in the region marked by blue rectangle; (b) The piezoresponse across the domain wall. The lower potion of the graph is enlarged in the inset, in which it shows that the point with minimum response moves ~2.5nm away from the origin O; (c) Comparison between the responses on both side of the wall, asymmetry can be seen. The region left to the wall in (a) has longer tail compared to the region right to the wall. The tilt angle θ is ~5 degree, and the tip is 50nm disc tip with applied voltage of 5V in FEM simulation. ............................................126

Figure 3-29: FEM result of domain width in PFM along with the PFM measurement result. (a) full width half maximum (FWHM) of the domain wall interaction width. Solid lines for measurement data are the fittings; (b) full width (FW) of domain wall interaction width. The solid lines are the fittings. All the fittings are linear except for the sphere tip which is 2nm away from the surface. ...............................................................................................128

Figure 3-30: The PFM amplitude image of domain structure in SBN:61. The applied voltage on the tip was 5Vrms at 42.35kHz. (a), (e) are the topography; (b), (f) are amplitude; (c), (g) are the phase. (e)-(g) are scanned in the area inside the square marked in (b). (a)-(c) are the images on the same area, and (e)-(g) are the images on the same area...............................................130

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Figure 3-31: Vertical piezoresponse across the single domain wall (y wall) in strontium barium niobate 60 under a 50nm radius disc tip with 5V applied voltage on (a) displacement in SBN:61 modeled by using FEM; (b) amplitude predicted using FEM.........................................................................131

Figure 3-32: Comparison of the amplitude of the piezoresponse in strontium barium niobate (SBN:61) and congruent lithium niobate (CLN). Use CLN as reference and its piezoresponse is 1.0. The ratio between SBN:61 and CLN is ~1.7...................................................................................................................132

Figure 3-33: 0° lateral PFM measurement across the single domain wall in congruent lithium niobate (CLN) and congruent lithium tantalate (CLT). (a) and (d) topography; (b) and (e) 0° lateral PFM measurement; (c) and (f) line profile of 0° lateral PFM measurement. (a)-(c) are for CLN, and (d)-(f) are for CLT.............................................................................................................134

Figure 3-34: FEM result of the slope of the surface deformation across a domain wall in congruent lithium niobate induced by a 50nm sphere tip. (a) the slope of the surface across the domain wall as d=0nm; (b) the amplitude of the slope vs. the distance, d, between tip and sample surface. ..................................135

Figure 3-35: FEM result of the amplitude (slope) of the surface deformation normal to the domain wall vs. the tip size and tip geometry. (a) the disc tip without the cone, disc tip with cone and sphere tip with cone; (b) disc tip with cone and disc tip without cone. Solid line are the fitting using 2nd exponential decay function y=y0+A1exp(-x/t1)+A2exp(-x/t2). (c) FEM results of the slope of surface for both congruent lithium niobate (CLN) and congruent lithium tantalate (CLT) for disk shape tip in contact. Rslope(CLT/CLN) is the ratio between slopes of FEM surfaces in CLT and CLN, which is ~0.70±0.05 and independent of the tip size. ................................................................................136

Figure 3-36: (a) 0° lateral amplitude signal along with FEM simulation result. The ratio between congruent lithium tantalate (CLT) and congruent lithium niobate (CLN) in experiment is ~0.68±0.01; whereas it is ~0.70±0.05 in FEM (b). (b) Comparison of slope of FEM surface in CLN and CLT. The tip radius is ~55nm, which was determined by FESEM image. .........................................137

Figure 4-1: Beam deflector (or scanner). (a) rectangular scanner; (b) horn shape scanner..............................................................................................................149

Figure 4-2: BPM simulation of 5-stage 13-beamlet scanner showing full deflection at 5 kV/mm. The polarization direction of the crystal is perpendicular to the page, with the area enclosed by the triangles opposite in spontaneous polarization (Ps) than the rest of the device. The peak deflection is 10.13° in one direction. The inset is the photolithographic mask fabricated for this device that shows two adjacent scanner channels...................................151

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Figure 4-3: (a) Far field images taken of the complex beam pattern introduced by the microlens array as imaged at the focal point of a lens. (b) Shows the far field beam image with the addition of the device. Both images (a) and (b) are attenuated equally and are 5.4 x 7.5 mm. Shown in (c) is beamlet steering for applied voltages. The horizontal panel size is 8.25 mm x 1.87 mm in (c). Only 10-12 beamlets are clearly seen in the panels above, and beamlets near the ends are difficult to see, due to the introduction of neutral density filters in order to avoid saturation of center beamlets in the camera. Upon saturation, all 13 beamlets are seen as shown in the bottom panel of (c). ...........153

Figure 4-4: (a) deflection angle versus applied voltage across only stage 1 of the beamlet device. (b) deflection angle versus the number of steering stages activated in the beamlet device. .........................................................................154

Figure 4-5: BPM simulation of 3X3 optical switc. The polarization direction of the crystal is perpendicular to the page, with the area enclosed by the triangles opposite in spontaneous polarization (Ps) than the rest of the device....158

Figure 4-6: (a) deflection angle versus applied voltage across the horn shape scanner in the input port. (b) the output beam from the input port of the optical switch with different applied voltage. There is no applied voltage on the output port. ..................................................................................................159

Figure 4-7: The output beam taken by CCD camera with the applied voltage on both stages in the optical switch. The stage 1 denotes the input port and stage 2 denotes the output port. ..................................................................................160

Figure 4-8: (a) Vertical scanning angle in the z-direction vs. electric field at 1Hz frequency. Inset is shown the experimental geometry; and (c) Scanning angle vs. distance to top surface (+c) at which the incident beam traverses through. A negative field swing of –0.95 kV/cm was present in all measurements (not shown). .............................................................................................................163

Figure 4-11: (a) the period of lithium niobate QPM structure versus the pump laser wavelength at room temperature (~24.5°C); (b) the period of lithium niobate QPM structure versus the temperature for second harmonic generation (SHG) at 1.064µm............................................................................170

Figure 4-12: Periodically poled congruent lithium niobate. (a) +z surface after hydrofluric acid (HF) etching; (b) the y surface of PPLN after HF acid etching. .............................................................................................................171

Figure 4-13: Periodically poled stoichiometric lithium niobate using PFM system. The applied voltage was ~60um and scan rate was ~5µm/s. (a) amplitude; (b) phase of PFM image..........................................................................................172

xvi

Figure C-1: The electrostatic (denoted as backgroundd ) and eletromechanical

contribution (denoted as d ) in PFM measurement. On –c surface, the

electromechanical contribution is d , whereas on +c surface it is d . PR is the amplitude of the measured PFM signal. .......................................................195

Figure D-1: Dielectric constant and conductivity of congruent lithium niobate (CLN) and stoichiometric lithium niobate (SLN) at room temperature...............196

Figure D-2: Dielectric constant and conductivity of congruent lithium tantalate (CLT) and stoichiometric lithium tantalate grown using vapor transport equilibrium treatment (SLN_VTE) at room temperature....................................197

Figure D-3: Dielectric constant and conductivity of strontium barium niobate 61 (Sr0.61Ba0.39Nb2O6 or SBN:61) at room temperature...........................................197

xvii

LIST OF TABLES

Table 1-1: The lattice parameters and Curie temperature of lithium niobate and lithium tantalate. ...............................................................................................10

Table 2-1: A comparison of congruent (CLT), near-stoichiometric (NSLT-CZ) and stoichiometric (SLT-VTE) crystals. Measurements not referenced below are from this study.............................................................................................44

Table 3-1: The piezoelectric strain coefficients of lithium niobate, lithium tantalate and strontium barium niobate ..............................................................76

Table 3-2: Elastic, piezoelectric and dielectric constants of lithium niobate, lithium tantalate and strontium barium niobate. .................................................83

Table 3-3: Amplitude of vertical PFM response in lithium tantalate. The reference was congruent periodically poled lithium niobate (PPLN) and applied voltage is 5Vrms @42.35kHz. .......................................................................................117

Table 3-4: Amplitude of vertical PFM response in lithium niobate. The reference was periodically poled congruent lithium niobate (PPLN). ................................119

Table 3-5: The relationship between the domain wall interaction width and tip radius R. ............................................................................................................125

Table 3-6: The ratio (Rlateral(CLT/CLN)) of amplitude of 0° lateral PFM signal between congruent lithium niobate and congruent lithium tantalate versus the tip size...............................................................................................................134

Table 4-1: Specification of Beamlet Scanner ...........................................................152

xviii

ACKNOWLEDGEMENTS

First, I would like to give special thank to my advisor, Dr. Venkatraman Gopalan,

for his patience, guidance, encouragement and support throughout these years at

Pennsylvania State University. To me, he’s been a mentor in all aspects of my life. In

addition, I would like to thank all the committee members, Dr. Robert Newnham, Dr.

Eric Cross, Dr. Qiming Zhang and Dr. Zhiwen Liu, for their time, evaluations and

comments on this thesis work. I would also like to thank the wonderful staff members,

especially Bill Drawl, Guy Lavallee, John McIntosh and Michael Rogosky, at MRL

Building, MRI building as well as the Materials Science and Engineering Department

who made it possible to complete this thesis work.

I give thanks to all the group members, namely David Scrymgeour, Alok Sharan,

Fui Fang, Dong-jin Won, Sava Denev, Aravind Vasudevarao, Eftihia Vlahos, Amit

Kumar, Mariola Ramirez, Mahesh Krishnamurthy, for valuable discussion and for

sharing a passion for research.

I would like to give my sincere thanks to my friends, especially Pan Xinhong, Li

Dongsheng, Jihong, and Cheng Jiangong, for their support and for always being there for

me.

I would like to thank my parents and my siblings for their unconditional love and

Dr. Crystal Cooper who inspired me to have the courage pursue and finish my Ph.D

studies.

Because of all these people, I’ve been enjoying the research and the beautiful

valley every single day during my studies at Pennsylvania State University, even though

xix

there were difficult moments. These years in State College would for sure leave me with

the most beautiful memories in my life. I wish my best to all these people.

1

Chapter 1

Introduction and Outline of the Thesis

1.1 Overview of ferroelectric materials

Ferroelectrics, as defined by Lines and Glass,1 are substances in which a

spontaneous polarization exists in a certain range of temperature and isotropic pressure in

the absence of an external electric field. This spontaneous polarization in a ferroelectric

has at least two or more orientational states that can be switched from one state to the

other by an external electric field (coercive field, Ec) smaller than the breakdown field Eb

or in some cases by a mechanical stress.2 Each region in which the spontaneous

polarization orients in the same direction in a ferroelectric is called a domain. The plane

that separates two domain regions is called the domain wall. The relationship between the

spontaneous polarization and the external field is typically described by its hysteresis

loop P(E). However, as pointed out by J. F. Scott,2 the hysteresis loop is a necessary but

not sufficient condition to ensure ferroelectricity. For instance the permanent dipole in an

electret can be switched with large external field;3 however, these poled states are not in

their thermal equilibrium. Ferroelectrics are in thermal equilibrium in each polarization

state,1 for instance, +P or –P. The ferroelectricity can only exist in certain materials,

which possess non-centrosymmetric crystal structures and are pyroelectric and

piezoelectric crystals. To quote, “Pyroelectricity is symmetry property of crystals; but

ferroelectricity is a practical engineering property, since some pyroelectrics will break

2

down electrically (short) before the coercive field is reached”.2 Therefore, even though all

the ferroelectrics are pyroelectric and piezoelectric, the converse is not necessarily true.

Ferroelectricity can only be experimentally determined for each crystal. Figure 1-1

illustrates the classification of piezoelectric, pyroelectric, and ferroelectric properties

based upon the symmetry of their crystal structures.

1.2 Structure of ferroelectric materials

Ferroelectricity was discovered first in Rochelle salt (NaKC4H4O6.4H2O) in

1920s, in potassium dihydrogen phosphate (KH2PO4, KDP) in 1930s and barium titanate

in 1950s.4,5 After that, many ferroelectrics such as lead titanate (PbTiO3), lead zirconate

titanate (PZT), ammonium salts (NH4H2PO4, ADP), strontium barium niobate (SrxBa1-

Figure 1-1: Classification of piezoelectric, pyroelectric and ferroelectric properties in 32 point groups.

3

xNb2O6), as well as lithium niobate (LiNbO3) and lithium tantalate (LiTaO3) etc. were

synthesized. Among these, ABO3 oxides form an important group of ferroelectrics. The

structures of these ferroelectric oxides share some common characteristics, namely that

BO6 octahedron building block constructs the main frame. These ferroelectrics are mainly

divided into three groups: simple or distorted perovskite, tungsten bronze and related

structure, and the lithium niobate (LiNbO3) structure (Figure 1-2). The difference among

the structures of these three groups lies in the way the oxygen octahedra connect to each

other and in the resulting interstitial sites. The BO6 octahedron in both perovskite and

tungsten bronze structure share corners whereas they share the faces (along c axis) or

edges (in ab plane) in lithium niobate structure.

The term perovskites comes from the mineral perovskite calcium titanate

(CaTiO3, which is a distorted perovskite structure). The perfect perovskite structure is

constructed with a general formula ABO3, where A is a monovalent or divalent metal and

B is a tetra- or pentavalent one. It is cubic, with the A atoms at the cube corners, B atoms

at the body centers, and the oxygen atoms at the face centers. In this structure, a set of

BO6 octahedron are arranged in a simple cubic pattern and linked together by shared

oxygen atoms, with the A atoms occupying the interstitial sites in between octahedron

cubes (Figure 1-2(a)). The cubes in the perovskite structure forms a network of vertices

sharing octahedra. The typical perovskite ferroelectrics are barium titanate (BaTiO3),

potassium niobate (KNbO3), lead titanate (PbTiO3) and lead zirconate titanate (Pb[ZrxTi1-

x]O3, or PZT).

4

Lithium niobate structure also possesses ABO6 lattice with oxygen octahedron

(Figure 1-2 (c)). 9,8,10,11,7 It is comprised of a set of distorted oxygen octahedron joined by

their faces along a trigonal polar c-axis. In the ferroelectric phase, Nb/Ta atoms and Li

atoms can be either above or below the shared oxygen planes. During the ferroelectric

Figure 1-2: Schematic structure of typical ABO3 ferroelectrics with BO6 octahedral frame (a) tetragonal BaTiO3 crystal with perovskite structure; (b) SrxBa1-xNb2O6 crystal with tungsten bronze structure; (c) ferroelectric LiTaO3 crystal with lithium niobate structure. (plotted using Software CaRine Crystallography 3.1. Lattice parameter in: (a) comes from Ref. [4]; (b) comes from Ref. [6]; (c) comes from Ref. [7, 8]).

5

phase transition, Nb/Ta atoms displace from their original location, for instance, below

the oxygen mean plane, to the position above the oxygen plane inside the octahedron;

whereas Li atoms move across the closed packed oxygen plane up to adjacent empty

octahedron. Hence, these displacements of Nb/Ta atoms and Li atoms along the trigonal

axis with respect to the oxygen framework leads to permanent electrical dipole (or say

spontaneous polarization) along +c axis inside crystal. When looking along the polar c

axis in lithium niobate and lithium tantalate, the sequence of cation-filling of the

octahedral is: empty, Li, Nb(Ta), empty, Li, Nb(Ta), empty,…etc., where the polarization

points, e.g., from left to right in this sequence. The cation positions at room temperature

have been precisely determined within the oxygen surroundings by X-ray and neutron

diffraction experiments. The relatively large offset of cations (0.0258nm for Nb and

0.069nm for Li in LiNbO3, 0.0201nm for Ta and 0.0601nm for Li in LiTaO3 8) from their

paraelectric phase positions suggests a large room-temperature spontaneous polarization,

which is indeed observed (~50µC/cm2 in LiTaO3 and ~70µC/cm2 in LiNbO3). In lithium

niobate structure, there are two possible positions with same energy for Li and Nb at

room temperature, which result in two possible permanent dipole moment directions

(pointing to +c-axis or –c-axis) (Figure 1-3). The domain with spontaneous polarization

direction pointing in the +c-axis is called up domain (Figure 1-3 (a)); the domain with

spontaneous polarization direction pointing in the –c-axis is called down domain

(Figure 1-3 (b)); and they are separated by a domain wall, in which the spontaneous

polarization gradually changes from +Ps to –Ps. Such a domain wall is called a 180° wall.

The energy for both up domain and down domain stays the same. In its ferroelectric

6

phase, lithium niobate structure belongs to R3c space group; and in the paraelectric

phase, it belongs to the R3c space group.

Tungsten bronze structure also has a framework of BO6 octahedron in an ABO6

lattice. The tetragonal unit cell consists of 10 BO6 octahedra linked by their corners in

such a manner as to form three different types of tunnels running right through the

structure parallel to the c-axis (Figure 1-2 (b)).6, 12 The O-Nb-O octahedral axes in the

octahedra are not precisely parallel to the c axis. They are tilted through about 8° from

the polar axis (c axis). 6 In strontium barium niobate (SrxBa1-xNb2O6, or SBN:100x), the A

(Sr, Ba) atoms take 5 interstitial sites out of 6 available sites (2A1+4A2) among the

octahedron. A1 site has four-fold symmetry while A2 is pentagonal (Figure 1-2 (b)). The

Figure 1-3: The unit cell of the lithium niobate (LiNbO3) structure (a) with up domain; (b) with down domain (by software CaRine Crystallography 3.1 with lattice parameters from Ref. [8, 7]).

7

interstitial sites (C) are empty. The small displacements of Sr/Ba and Nb atoms on c axis

from their oxygen planes at room temperature create the permanent dipole inside the

crystal and make them ferroelectric at room temperature (Figure 1-4). Therefore, SBN

also has two possible spontaneous polarization directions: up and down domain. SBN

crystal at room temperature also has 180° domain structure. In its ferroelectric phase,

barium strontium niobate has 4mm point group, P4bm space group; and 4/mmm point

group in the paraelectric phase, which is centrosymmetric.

1.3 Lithium niobate, lithium tantalate and strontium barium niobate crystals

Quickly after the discovery of ferroelectricity in crystals, people realized that

ferroelectrics can be used in many applications such as pyroelectric temperature sensors,

actuators, transducers, optical wavelength converters, ferroelectric memory etc.. Due to

(a) (b)

Figure 1-4: The spontaneous polarization in strontium barium nibate crystal. (a) Sr/Ba atom in 4-fold A1 site and Nb atom in octahedron, their positions are below the oxygen mean plane; (b) Sr/Ba atom in 5-fold A2 site and Nb atom in octahedron, their positions are below the oxygen mean plane. Crystal structure see details in Ref. [6]

8

their excellent optical and piezoelectric properties, lithium niobate, lithium tantalate and

strontium barium niobate have drawn lots of attention and are widely used in many

optoelectronic applications. For instance, optical frequency converters, surface acoustic

wave device, and optical modulators.13 Lithium niobate is even treated as the “optical

silicon” material. Its growth, structure, properties and defects has been extensively

studied. Detailed reviews can be found in a book by Prokhorov and Kuz’minov,14 and

review articles by A. Rauber15 and Gopalan 13 et. al. Lithium niobate, lithium tantalate

and strontium barium niobate crystals have wide range of crystal compositions; and their

properties rely on their compositions.

Lithium niobate and lithium tantalate share the same structure (lithium niobate

structure), which was discussed in the Section 1.2. They belong to point group 3m at

room temperature and 3m above their Curie temperatures. They only experience a single

Figure 1-5: The schematic phase diagram of Ta2O5-Li2O near the congruent composition (adapt from V. Gopalan at. el13, originally from S. Miyazawa and H. Iwasaki 16).

9

structural phase transition that corresponds to the Curie temperature (Tc), which is second

order (or close to second order) phase transition.1 Although commonly referred to as

“LiNbO3” and “LiTaO3”, lithium niobate and lithium tantalate have a wide solid solution

range varying from stoichiometric composition at which C=Li/(Li+B)=0.5 (B=Nb or Ta)

to the B-rich side where C ~0.47, in which the congruent ones with very good crystal

qualities can be commercially obtained. Figure 1-5 shows the phase diagrams of Ta2O5-

Li2O near the congruent composition. The Curie temperature, lattice parameters and

density of lithium niobate and lithium tantalate all change with a change in their

compositions.17

Compared with the congruent melting composition of lithium niobate and lithium

tantalate (CLN and CLT), which can be commercially grown by the conventional

Czochralski (CZ) method, 18 it is very difficult to grow the crystals with stoichiometric

compositions through conventional CZ method from lithium-rich or tantalum-rich melt

because they go through a phase separation during the growth process. In late 1990s, it

was reported by Kitamura et. al. 19 and Furukawa et. al. 20 that lithium niobate with non-

congruent compositions were successfully synthesized using the double crucible

Czochralski method (DCCZ). The coercive fields of these non-congruent lithium niobate

and lithium tantalate crystals grown by DCCZ methods are around ~1kV/mm, which is

much lower than the coercive fields (~22kV/mm) of congruent compositions. An

alternative way to achieve non-congruent lithium niobate and lithium tantalate is by

performing vapor transport equilibration (VTE) treatment21 on as-grown congruently

melting lithium niobate and lithium tantalate single crystals.22 In the latter, Li is in-

diffused into the crystal by thermal processing. An atmosphere rich in lithium is created

10

around the lithium–deficient wafers, allowing Li in-diffusion throughout the thickness of

the wafer. The diffusion process self-terminates when thermodynamic equilibrium is

reached, i.e. when all lithium vacancies in the material are filled and the crystal becomes

stoichiometric. Constant excess of lithium in the atmosphere surrounding the wafers

during the process ensures diffusion till equilibrium is reached and an excellent

compositional homogeneity in the material. The coercive fields of these crystal

compositions are only ~1kV/cm, which is around 100 times lower than those of

congruent compositions. Gopalan13 et. al. showed that the coercive fields, Ec decreases

linearly as C approaches 0.5, and it was recently confirmed by Tian23 et. al..

Many aspects of crystal properties in lithium niobate and lithium tantalate are

influenced by their non-stochiometry.13 For instance, as the crystal goes towards

stoichiometric composition (C→0.5), the absorption band edge moves towards shorter

wavelengths in lithium niobate and lithium tantalate. Figure 1-6 shows the transmission

spectrum of lithium tantalate at different compositions and stoichiometric lithium

niobate. The data of lattice parameters and Curie temperatures in Ref. [19,20] (Table 1-1)

Table 1-1: The lattice parameters and Curie temperature of lithium niobate and lithium tantalate.

Lithium Niobate

(LiNbO3)19

LithiumTantalate

(LiTaO3)20

Tc (°C) A0 (Å) C0 (Å) Tc (°C) A0 (Å) C0 (Å)

Congruent 1138 5.1505 13.8561 601±1 5.1543 13.7808

Stoichiometric* 1198 5.1474 13.8561 685±1 5.1512 13.7736

*Note: The stoichiometric in this table is actually considered as near-stoichiometric in this thesis.

11

suggests that the lattice parameters become smaller, and Curie temperatures increase as

lithium niobate and lithium tantalate moves closer to stoichiometry. The ultraviolet (UV)

and the infrared (IR) absorption band edges of lithium tantalate and lithium tantalate

move towards shorter UV and longer mid-infrared wavelengths respectively, as they

approach perfect stoichiometry. The transparency range in lithium tantalate is slightly

larger than in lithium niobate, which would also make it somewhat superior when making

periodically poled structures near the band edges.

Strontium barium niobate also varies over a wide range in its composition. It was

found that SBN crystal shows ferroelectric phase at room temperature in the composition

region Sr0.32Ba0.68Nb2O6 to Sr0.82Ba0.18Nb2O6.24 It was showed that many properties of

SBN crystals depend on the ratio of [Sr]/[Ba] such as the occupancy of the channels in

A1 site and A2 site, refractive indices and phase transition temperature from ferroelectric

(a) (b)

Figure 1-6: Transmission spectrum of lithium tantalate (LT) with different compositions and stoichiometric lithium niobate (LN). The thicknesses of samples are 0.31mm, 1.00mm, 0.83mm and 1.00mm for congruent lithium tantalate, near-stoichiometric lithium tantalate, stoichiometric lithium tantalate and stoichiometric lithium niobate. (a) the transmission spectra from near UV to mid-infrared; (b) spectra towards near UV band edge in (a). Fresnel reflection loss is not excluded.

12

phase to its paraelectric phase, and photorefractive property and etc.. Strontium barium

niobate is a typical relaxor ferroelectric. Its congruent melting composition is

Sr0.61Ba0.39Nb2O6.

1.4 Fatigue in ferroelectrics

Fatigue in ferroelectrics has been an issue and has been studied widely.25-27,2,28 A

large amount of experimental results have been reported, particularly in ferroelectric

systems such as PZT films and theories for the fatigue mechanisms have been proposed

(reviews can be found in Ref. [25-27,2,28]). However, the exact nature of ferroelectric

fatigue is still not fully understood.

Ferroelectric fatigue denotes a reduction of the switchable polarization or a

reduction of the piezoelectric coefficient with repeated polarization cycling with an

external electric field.27 This phenomenon is generally believed to be the result of charge

injection and the accumulation of space charge that pins domain switching.26,27,29,30,31

Even without well-understood mechanisms of polarization fatigue, one concludes that

careful electrode choices may reduce or even suppress the ferroelectric fatigue based on

the large amount of experimental data available in literature so far. For example, the

oxide ionic conduction such as RuO2, SrRuO3 IrO2 and others were used in place of metal

(mainly Pt) electrodes on PZT film.2,27 For congruent lithium niobate and lithium

tantalate, the electrodes such as asymmetric ITO/CrAu can help domain reversal and

suppression of the material breakdown.32

13

1.5 Ferroelectric domain wall and its applications

The applications based on ferroelectric domain walls are very wide, ranging from

piezoelectric, pyroelectric, nonvolatile memory, to nonlinear optical applications. For

instance, ferroelectric crystals are popularly used in optoelectronic applications such as

surface acoustic wave devices, 33,34 frequency converters,35, 36 and holography.37,38 A

typical example is the Mach-Zender interferometric switch used in telecommunications.

A majority of devices today, though, are based on the single domain state instead of

domain walls.

Recently, domain microengineering of LiNbO3 and LiTaO3 crystals has been

applied to realize a new class of efficient linear and nonlinear optical devices.39, 40, 41, 42, 43,

44 The ferroelectric domains and domain walls are shaped into diverse shapes and sizes to

create optical elements such as gratings, lenses, prisms etc. Examples include quasi-phase

matched frequency converters, 35,45 electro-optic scanners, dynamic focusing lenses, 39

total internal reflection mirrors, etc. Figure 1-7 shows the schematic drawing of grating,

scanner, and dynamic focusing cylindrical lens patterned by external electric field, as

well as photonic structure patterned by scanning force microscopy (SPM) techniques.

Ferroelectrics are non-centrosymmetric crystals, which therefore possess third

rank polar tensor properties such as linear electro-optics and nonlinear frequency

conversion. Electro-optic effect refers to the change in the refractive index in a material

when an external electric field is applied. For lithium tantalate and lithium niobate, an

electric field E3 along the polarization direction +c (also referred to by subscript 3),

changes the extraordinary index n33=ne by an amount ∆ne = −(1/2)n3r33E3. The index

14

decreases by this amount when the electric field is parallel to the polarization direction,

and increases when it is antiparallel to the polarization direction. Therefore, when a

uniform electric field is applied across a domain wall (Figure 1-7), an index change of

2∆ne is created across the wall, which is linearly electric field tunable. These devices are

based on domain patterning for beam shaping, dynamic focusing, beam deflection,

wavelength selection and frequency conversion etc. All of these applications can be

integrated on a single ferroelectric platform.

(a) (b)

(c) (d)

Figure 1-7: The schematic scanner based on ferroelectric domain patterning. (a) quasi-phase-matching structure; (b) electro-optic scanner; (c) dynamic focusing cylindrical lens; (d) photonic structure patterned by SPM technique, from Tarabe et. al. in NIMS, Japan.

15

Among many optoelectronic applications, 42 33 34 46 47 38,48 by using ferroelectric

crystals, one important application is for coherent light source generation by making

periodically poled structure using domain microengineering technique (Figure 1-7 (a)). 47

48Today, semiconductor lasers are cheap and highly efficient light sources; however, it is

still a challenge to make semiconductor lasers at shorter wavelength around blue-green

range, high power intensity and long lifetime for practical use.49,50,51,52 II-VI zinc

selenide (ZnSe) compound50 lasers brought the first success to the field of semiconductor

blue-green laser diodes. In-doped GaN53 lasers have already demonstrated high reliability

at wavelengths as short as 370 nm and are considered to be a very promising future

technology. However, these lasers have problems with relatively short life-time at the

required power levels, and also are at the green end of the visible range (460 to 520 nm).

At the opposite end, scientists can fabricate long-wavelength diodes to emit infrared

radiation anywhere from 2000 to 12,000 nm (2 to 12 µm) in quantum cascade lasers. 54

An alternative way for semiconductor lasers to generate coherent light source at

short wavelength, e.g. green light, or at long wavelength with high power is to utilize the

nonlinear optical crystals such as KTP, BBO, lithium niobate and so on. For certain

nonlinear optical crystals at certain frequencies, there are critical phase matching angles

required to satisfy momentum conservation condition for optical frequency conversion. 55

However, for some nonlinear optical crystals (for instance, lithium niobate and lithium

tantalate), there are no critical phase matching angles to achieve momentum conservation

condition for optical frequency conversion due to their relative small birefringence and

dispersion. To take advantage their large nonlinear optical coefficients, quasi-phase

matching 56 scheme was adopted to achieve phase matching (momentum conservation

16

condition), in which the phase mismatch between the fundamental waves and generated

waves is compensated by a periodic inversion of the sign of the relevant nonlinear optical

coefficient in a noncentrosymmetric nonlinear optical crystal. Ferroelectrics are a perfect

candidate to make quasi-phase matching structure, which is also called periodically poled

structure. Typical applications for a periodic poled structure are second harmonic

generation (SHG, review seen in Ref.35) and optical parametric oscillation (OPO). In

SHG, the energy is transferred from the fundamental light waves to the second harmonic

waves with frequency 2ω through two-photon absorption process. It is also called

frequency doubling. SHG is a special case of sum frequency generation (SFG). OPO is a

device based on the inverse process of SFG. In OPO, the pump light photon with higher

frequency ω1 is split into two photons with lower frequencies ω2 and ω3.

In the applications mentioned above, the creation and shaping of the ferroelectric

domain walls in controlled shape and size is the key. In realizing these applications, the

understanding of the underlying physics and the local structure as well as the domain

dynamics is essential. The intrinsic domain wall width is defined as the distance across

which the spontaneous polarization changes from –Ps to +Ps in an antiparallel

ferroelectric material. Across an idealized antiparallel ferroelectric domain wall, the

materials properties change abruptly, though stay same magnitude. In such case, it can be

predicted that the ferroelectric domains can never be switched at room temperature based

on Ginzburg–Landau–Devonshire free energy. For instance, the coercive field of LiNbO3

could be ~5420kV/cm.57 It was proposed that the much lower coercive fields in

ferroelectrics in reality may be due to the broadening of the intrinsic domain wall width.57

The recent perturbation analysis on Landau-Ginzburg model showed that the upper and

17

lower bounds of domain wall width were within the stability zone. The lower bound

agreed well with the first principles predictions, and the upper bound was found to

correspond well with experimental measurements in lithium niobate and lithium tantalate

ferroelectrics.58-60 Though there were only limited experiments on studying the intrinsic

wall width in a 180° domain wall. The high resolution TEM showed that the intrinsic

domain wall width in lithium tantalate was ~0.28nm, which was in a good agreement

with that predicted by first principle calculation. 61 However, there are also some

unexpected phenomena at a much longer scale reported across a 180° domain wall. For

instance, the X-ray synchrotron revealed long-range strain (which is in order of tens of

microns) across the domain wall in lithium niobate.62 It was also observed that there were

two different refractive index changes across single domain wall in lithium niobate in two

different length scales: 1) the refractive index change related to broad strain distribution

is order of tens of microns; 2) the localized narrow refractive index kink was observed in

order of 1~2 microns. 63 These phenomena suggest that the materials properties related to

the local structure of the antiparallel domain wall may have spatial resolution at a scale of

from tens of micron to sub nanometer.

1.6 Thesis objectives

The objective of this thesis work is to understand the domain wall phenomena and

the properties across single domain wall from microscale to nanoscale levers. Much work

has been done to try to link the macroscopic properties of ferroelectrics such as lithium

niobate and lithium tantalate as well as strontium barium niobate to their microscopic

18

structure and atomic defect structure. Many challenges remain in better controlling the

domain shaping. In this thesis, electric field poling techniques at room temperature with

in-situ monitoring have been employed to create the domain shapes of arbitrary

orientation or in a patterned domain shape on the macroscale level. On the nanoscale

level, the electromechanical responses across the single domain wall in lithium niobate,

lithium tantalate with different compositions as well as strontium barium niobate have

been studied by using by using piezoresponse force microscopy (PFM) technique. These

responses have been analyzed to link the material properties and domain wall properties.

1.7 Thesis organization

The thesis consists of 5 chapters. Chapter 2 focuses on macroscale domain

dynamics study under external electrical fields. The issues of domain reversal will be

discussed. The electromechanical response across the single domain wall in lithium

niobate, lithium tantalate as well as strontium barium niobate will be presented in Chapter

3. In this chapter, the quantitative interpretation of the material properties and domain

wall properties will be discussed. Chapter 4 presents examples of optical devices based

on domain shaping techniques. Finally Chapter 5 gives the summary, conclusions as well

as the future work related to this research.

19

References

1. Lines, M. E. & Glass, A. M. Principles and applications of ferroelectrics and related materials. (1977).

2. Scott, J. F. Ferroelectric memories (Springer-Verlag Berlin Heidelberg, 2000). 3. Electrets. Second enlarged edition (ed. Sessler, G. M.) (Springer-Verlag, 1987). 4. Megaw, H. D. Ferroelectricity in crystals (Methuen, London, 1962). 5. Smolenskii, G. A. et al. Ferroelectrics and Related Materials (Ferroelectricity

and Related Phenomena) (Taylor & Francis; 1 edition (January 1, 1984), 1984). 6. Jamieson, P. B., Abrahams, S. C. & Bernstein, J. L. Ferroelectric tungsten bronze-

type crystal structures. I. Barium strontium niobate Ba0.27 Sr0.75Nb2O5.78. Journal of Chemical Physics 48, 5048-5057 (1968).

7. Abrahams, S. C., Reddy, J. M. & Bernstein, J. L. Ferroelectric lithium niobate. III. Single crystal X-ray diffraction study at 24°C. Journal of the Physics and Chemistry of Solids 27, 997-1012 (1966).

8. Abrahams, S. C., Bernstein, J. L., Hamilton, W. C. & Sequeira, A. Ferroelectric lithium tantalate -- 1, 2. Journal of Physics and Chemistry of Solids 28, 1685-1698 (1967).

9. Abrahams, S. C. & Bernstein, J. L. Ferroelectric lithium tantalate. 1. Single crystal X-ray diffraction study at 24° C. Journal of the Physics and Chemistry of Solids 28, 1685-1692.

10. Abrahams, S. C., Hamilton, W. C. & Reddy, J. M. Ferroelectric lithium niobate. IV. Single crystal neutron diffraction study at 24°C. Journal of the Physics and Chemistry of Solids 27, 1013-1018 (1966).

11. Abrahams, S. C., Levinstein, H. J. & Reddy, J. M. Ferroelectric Lithium Niobate. V. Polycrystal X-ray diffraction study between 24° and 1200°C. Journal of the Physics and Chemistry of Solids 27, 1019-1026 (1966).

12. Francombe, M. H. The relation between structure and ferroelectricity in lead barium and barium strontium niobates. Acta Crystallographica 13, 131-140 (1960).

13. Gopalan, V., Sanford, N. A., Aust, J. A., Kitamura, K. & Furukawa, Y. Handbook of Advanced Electronic and Photonic Materials and Devices, Vol. 4 Ferroelectrics and Dielectrics, edited by H. S. Nalwa. Academic, New York, 2000, 59 (2000).

14. Prokhorov, A. M. A. M. Physics and chemistry of crystalline lithium niobate ( Bristol ; New York : Hilger, c1990., 1990).

15. Rauber, A. Chemistry and Physics of Lithium Niobate, Chapter 7 in Current topics in materials science, vol.1 (ed. Kaldis, E.) (North-Holland, 1978).

16. Miyazawa, S. & Iwasaki, H. Congruent melting composition of lithium metatantalate. Journal of Crystal Growth 10, 276-8 (1971).

17. Barns, R. L. & Carruthers, J. R. Lithium tantalate single crystal stoichiometry. Journal of Applied Crystallography 3, 395-9 (1970).

20

18. Fukuda, T., Matsumura, S., Hirano, H. & Ito, T. Growth of LiTaO3 single crystal for SAW device applications. Journal of Crystal Growth 46, 179-84 (1979).

19. Kitamura, K., Yamamoto, J. K., Iyi, N., Kimura, S. & Hayashi, T. Stoichiometric LiNbO3 single crystal growth by double crucible Czochralski method using automatic powder supply system. Journal of Crystal Growth 116, 327-32 (1992).

20. Furukawa, Y., Kitamura, K., Suzuki, E. & Niwa, K. Stoichiometric LiTaO3 single crystal growth by double crucible Czochralski method using automatic powder supply system. Journal of Crystal Growth 197, 889-95 (1999).

21. Bordui, P. F., Norwood, R. G., Jundt, D. H. & Fejer, M. M. Preparation and characterization of off-congruent lithium niobate crystals. Journal of Applied Physics 71, 875 (1992).

22. Baumer, C. et al. Composition dependence of the ultraviolet absorption edge in lithium tantalate. Journal of Applied Physics 93, 3102-4 (2003).

23. Tian, L., Gopalan, V. & Galambos, L. Domain reversal in stoichiometric LiTaO3 prepared by vapor transport equilibration. Applied Physics Letters 85, 4445-7 (2004).

24. Ulex, M., Pankrath, R. & Betzler, K. Growth of strontium barium niobate: the liquidus-solidus phase diagram. Journal of Crystal Growth 271, 128-33 (2004).

25. Scott, J. F. & Paz de Araujo, C. A. Ferroelectric memories. Science 246, 1400-5 (1989).

26. Fraser, D. B. & MALDONADO, J. R. Improved Aging and Switching of Lead Zirconate-Lead Titanate Ceramics with Indium Electrodes. 41, 2172-6 (1970).

27. Lupascu, D. C. Fatigue in Ferroelectric Ceramics and Related Issues (Springer-Verlag Berlin Heidelberg, 2004., 2004).

28. Tagantsev, A. K., Stolichnov, I., Colla, E. L. & Setter, N. Polarization fatigue in ferroelectric films: Basic experimental findings, phenomenological scenarios, and microscopic features. Journal of Applied Physics 90, 1387-402 (2001).

29. Merz, W. J. & Anderson, J. R. Ferroelectric storage devices. Bell Laboratories Record 33, 335-342.

30. Anderson, J. R., Brady, G. W., Merz, W. J. & Remeika, J. P. Effects of ambient atmosphere on the stability of barium titanate. Journal of Applied Physics 26, 1387-1388 (1955).

31. Scott, J. F. Ferroelectric memories today. 9th European Meeting on Ferroelectricity, Jul 12-Jul 16 1999Ferroelectrics 236, 247-258 (2000).

32. Scrymgeour, D. Local Structure and Shaping of Ferroelectric domain Walls for Photonic Applications. Ph.D thesis, Pennsylvania State University (2004).

33. Bei, L., Dennis, G. I., Miller, H. M., Spaine, T. W. & Carnahan, J. W. Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis techniques. Progress in Quantum Electronics 28, 67-87 (2004).

34. Brown, P. T., Mailis, S., Zergioti, I. & Eason, R. W. Microstructuring of lithium niobate single crystals using pulsed UV laser modification of etching characteristics. Optical Materials 20, 125-134 (2002).

21

35. Fejer, M. M., Magel, G. A., Jundt, D. H. & Byer, R. L. Quasi-phase-matched second harmonic generation: tuning and tolerances. IEEE Journal of Quantum Electronics 28, 2631-2654 (1992).

36. Yu, N. E., Kurimura, S. & Kitamura, K. Higher-order quasi-phase matched second harmonic generation in periodically poled MgO-doped stoichiometric LiTaO3. Journal of the Korean Physical Society 47, 636-9 (2005).

37. Dittrich, P. et al. Deep-ultraviolet interband photorefraction in lithium tantalate. Journal of the Optical Society of America B (Optical Physics) 21, 632-9 (2004).

38. Dittrich, P. et al. Sub-millisecond interband photorefraction in magnesium doped lithium tantalate. Optics Communications 234, 131-6 (2004).

39. Chiu, Y. et al. Integrated optical device with second-harmonic generator, electrooptic lens, and electrooptic scanner in LiTaO3. Journal of Lightwave Technology 17, 462-5 (1999).

40. Chiu, Y., Stancil, D. D. & Schlesinger, T. E. Large electro-optic modulation effect observed in ion-exchanged KTiOPO4 waveguides. Journal of Applied Physics 80, 3662-3667 (1996).

41. Chiu, Y., Zou, J., Stancil, D. D. & Schlesinger, T. E. Shape-optimized electrooptic beam scanners: Analysis, design, and simulation. Journal of Lightwave Technology 17, 108-113 (1999).

42. Scrymgeour, D. A. et al. Large-angle electro-optic laser scanner on LiTaO3 fabricated by in situ monitoring of ferroelectric-domain micropatterning. Applied Optics 40, 6236-6241 (2001).

43. Scrymgeour, D. A. et al. Hybrid electrooptic and piezoelectric laser beam steering in two dimensions. Journal of Lightwave Technology 23, 2772-2777 (2005).

44. Scrymgeour, D. A., Tian, L., Gopalan, V., Chauvin, D. & Schepler, K. L. Phased-array electro-optic steering of large aperture laser beams using ferroelectrics. Applied Physics Letters 86, 211113 (2005).

45. Maruyama, M., Nakajima, H., Kurimura, S., Yu, N. E. & Kitamura, K. 70-mm-long periodically poled Mg-doped stoichiometric LiNbO3 devices for nanosecond optical parametric generation. Applied Physics Letters 89, 011101 (2006).

46. Kurosawa, M. K. in Ultrasonics International 1999 Joint with 1999 World Congress on Ultrasonics, 29 June-1 July 1999 Ultrasonics 15-19 (Elsevier, Lyngby, Denmark, 2000).

47. Ashihara, S. et al. Nonlinear refraction of femtosecond pulses due to quadratic and cubic nonlinearities in periodically poled lithium tantalate. Optics Communications 222, 421-7 (2003).

48. Katz, M. et al. Vapor-transport equilibrated near-stoichiometric lithium tantalate for frequency-conversion applications. Optics Letters 29, 1775-7 (2004).

49. Nakamura, S. et al. Room-temperature continuous-wave operation of InGaN multi-quantum-well structure laser diodes with a lifetime of 27 hours. Applied Physics Letters 70, 1417 (1997).

50. Haase, M. A., Qiu, J., DePuydt, J. M. & Cheng, H. Blue-green laser diodes. Applied Physics Letters 59, 1272-4 (9).

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51. Nurmikko, A. & Gunshor, R. L. Blue and green semiconductor lasers: a status report. Semiconductor Science and Technology 12, 1337-47 (1997).

52. Steigerwald, D. et al. III-V nitride semiconductors for high-performance blue and green light-emitting devices. JOM 49, 18-23 (1997).

53. Risk, W. P., Gosnell, T. R. & Nurmikko, A. V. Compact Blue-Green Lasers (Cambridge University Press, 2004).

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58. Bandyopadhyay, A. K., Ray, P. C. & Gopalan, V. An approach to the klein-gordon equation for a dynamic study in ferroelectric materials. Journal of Physics: Condensed Matter 18, 4093 (2006).

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60. Bandyopadhyay, A. K., Ray, P. C. & Gopalan, V. Perturbation Model Validation for Domain Wall Width in different Ferroelectrics. In submission.

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62. Jach, T., Kim, S., Gopalan, V., Durbin, S. & Bright, D. Long-range strains and the effects of applied field at 180° ferroelectric domain walls in lithium niobate. Physical Review B (Condensed Matter and Materials Physics) 69, 64113-1 (2004).

63. Kim, S. Optical, electrical and elastical properties of ferroelectric domain walls in LiNbO3 and LiTaO3, Ph.D thesis, Pennsylvania State University (2003).

23

Chapter 2

Domain Reversal in Ferroelectric Materials

Lithium niobate, lithium tantalate and strontium barium niobate crystals are

widely used in optoelectronic devices mentioned in Chapter 1. In last few years, the

stoichiometic lithium tantalate has been successfully synthesized by using both vapor

transport equilibrium method (VTE) and double crucible Czochralski method (DCCZ). In

this chapter, the systematic studies of domain reversal in stoichiometric lithium tantalate

and strontium barium niobate crystals are presented. The comparison of domain reversal

characteristics among the congruent, near-stoichiometric and stoichiometric compositions

are also discussed. The issues in domain reversal in stoichiometric lithium tantalate and

strontium barium niobate are addressed.

This chapter is organized as follows: Section 2.1 gives the domain reversal

characteristics of stoichiometric lithium tantalate synthesized by VTE method; Section

2.2 presents domain reversal dynamics of strontium barium niobate crystal.

2.1 Domain reversal in lithium tantalate

From the phase diagram shown in Figure 1-5, it can be seen that stoichiometric

lithium niobate and stoichiometric lithium tantalate crystals coexist with a Li-rich melt.

To obtain lithium niobate and lithium tantalate crystal with stoichiometric composition,

the crystals must be grown from a Li-rich melt of the appropriate composition or done

24

with post-processing on the as-grown congruent lithium niobate and lithium tantalate

crystals. Recently, the stoichiometric lithium niobate (SLN) and lithium tantalate crystal

(SLT) with very low coercive field (~4kV/mm for SLN; ~1.7kV/mm for SLT) have been

successfully grown using double crucible Czochralski method (DCCZ).1 In this method,

the crucible used for stoichiometric lithium niobate or lithium tantalate growth consists of

two crucibles (inner crucible and outer crucible) which are connected through the holes in

the wall of the inner crucible. The stoichiometric lithium niobate or lithium tantalate is

grown by the Czochralski method from the Li-rich melt in the inner crucible. At the same

time, the stoichiometric melt in the outer crucible flows into the inner crucible through

the holes in the wall of the inner crucible; and the stoichiometric lithium niobate or

lithium tantalate powder is continuously supplied to the outer crucible by an automatic

power supply system in exact proportion to the weight of the crystal grown from the melt

in the inner crucible.2 Another method to obtain stoichiometric lithium niobate and

lithium tantalate crystal is to do postgrowth annealing procedure (vapor transport

equilibrium treatment) on the as-grown congruent lithium niobate and lithium tantalate

crystals. 3,4 In this method, the y- or z-cut as-grown crystalline congruent lithium niobate

or lithium tantalate thin plate (0.3mm to 2mm thick) is sitting on a platinum graticule just

above the Li-rich two phase lithium niobate or lithium tantalate powder surface. The

whole system is sealed in the crucible at high temperature to allow equilibration via

vapor-phase transport of Li indiffused from the powder to the crystal. The whole process

self-terminates when the crystal composition reaches the phase boundary of the single

phase region, which is very close to stoichiometric composition. Naturally VTE process

does not need precise control of powder composition or temperature to achieve

25

reproducible results. So far, stoichiometric lithium niobate or lithium tantalate

synthesized by using VTE treatment has very low coercive fields (~3kV/mm for SLN;5

<0.15kV/mm for SLT).

The samples in this study are z-cut VTE-grown stoichiometric lithium tantalate

(SLT-VTE) crystals with a thickness of 0.83mm. The samples are optically polished on

both z surfaces. This starting state of the crystal will be referred to as “virgin state”. The

first domain reversal from the “virgin crystal” will be referred as forward poling

(subscript f) and the second reversal as reverse poling (subscript r). The coercive field in

this paper is defined in the conventional way as the field at which 50% domain area is

reversed.

2.1.1 Domain reversal with liquid electrode

The electrode choice is very important in domain reversal for many ferroelectrics.

The electrodes like water based salt solution of nitrates (for instance, MgNO3) or

chlorides (e.g., LiCl) were typically used to study the domain reversal in lithium niobate

and lithium tantalate. In the following experiments, liquid electrodes (tap water and l0%

lithium chloride solution) were used as electrodes during the domain poling.

2.1.1.1 Transient current

Merz 6,7 first proposed a systematic study of the polarization reversal dependence

on time and applied electric field. The transient current can reflect many aspects of the

26

domain reversal characteristics such as switching time, wall velocities and etc. One of the

major differences in the kinetics of domain wall motion in congruent lithium tantalate

and near-stoichiometric as well as stoichiometric lithium tantalate is the nature of the

wall velocity, which is reflected by their transient current observed during domain

reversal.

The transient current of stoichiometric lithium tantalate with liquid electrodes (tap

water or 10% lithium chlorides solution) occur as “spikes”, which vary from sub-

milliseconds to hundred milliseconds (Figure 2-1 (a)). This spiky nature of the transient

current has been observed in near-stoichiometric lithium tantalate (Figure 2-1 (b)) and

congruent lithium niobate. 8 However, the transient current of congruent lithium tantalate

is a very continuous, smooth curve (Figure 2-1 (c)). The domain wall velocity for an

independently growing domain in congruent lithium tantalate was reported to be constant

for a given field, which corresponds to the smooth continuous poling transient current;

the wall velocities under different fields are exponentially proportional to the inverse of

the external fields. 9,10 The jerky type of transient currents in near-stoichiometric lithium

tantalate and stoichiometric lithium tantalate suggests a varying domain wall motion

under a constant field, which is similar to the nature of the domain wall motions in

lithium niobate crystals with different compositions.

27

Figure 2-1: Transient currents observed during domain reversal in lithium tantalate crystals with liquid electrode at room temperature. (a) stoichiometric lithium tantalate prepared by VTE treatment; (b) near-stoichiometric tantalate grown by DCCZ method; (c) congruent lithium tantalate grown by CZ method.

28

The transient current of domain reversal is strongly related to the microscopic

crystal defects. The different characteristics of the transient currents of near

stoichiometric lithium tantalate grown by CZ method (henceforth denoted as NSLT-CZ)

and SLT-VTE from that in congruent lithium tantalate (denoted as CLT) are believed

coming from different density of pinning sites in both congruent lithium tantalate and

stoichiometric lithium tantalate. 11-13 However, the nature of the pinning defects in

LiTaO3 is yet unknown. It was thought to be physical defects such as screw dislocations

or localized variations of point defects such as oxygen vacancy, inclusion of Nb2O5 (or

Ta2O5) clusters, or nonstoichiometry of the crystals. 14, 15 The density of the screw

locations vary depending on the quality of crystal growth. Another proposal of pinning

center source is related to the nonstoichiometry of the crystals such as lithium niobate and

lithium tantalate. In both congruent lithium niobate and lithium tantalate, lithium

deficiency is denoted by Li/(Li+Nb)≈ Li/(Li+Ta)~0.485. However, the transient current

in congruent lithium niobate also shows spiky type characteristics. 8 It is possible that the

lithium deficiency in congruent lithium tantalate is even lower, Li/(Li+Ta)~0.477. It was

proposed that the actual lithium deficiency in congruent lithium tantalate may be even

lower (~0.477). This proposal may be confirmed by the “spiky” characteristics of

transient current in near-stoichiometric lithium tantalate and stoichiometric lithium

tantalate now. As the density of pinning center decreases, the wall moves fast until it hits

the next pinning site. This effect is due to a reduction of the local field at the wall by a

residual depolarization field produced by bound charges in the newly switched area

behind the moving domain wall and compensated partially by fast external screen.16,17

The wall stops after some shift indicates that the defects locally increase the threshold

29

field playing the role of pinning centers. The pinning strength and the distances between

pinning centers define the power law distribution function of pulse width and

amplitude.17 In recent high voltage AFM domain reversal study with congruent lithium

niobate and stoichiometric lithium niobate, it was found that domain reversal saturated

with the field under the AFM tip, whereas there was no saturation found in stoichiometric

lithium niobate; and the pinning centers in congruent lithium niobate were imaged

directly next to domain wall curvature by AFM.18 It suggests that the densities in lithium

niobate decreases as the crystal go to its stoichiometry. In congruent lithium tantalate, the

high density of pinning sites causes many pinning events so that the spikes merge

together to form one continuous curve.

2.1.1.2 Hysteresis loop and Coercive fields

Due to characteristics of the spike-type transient currents in stoichiometric lithium

tantalate (<ms), the hysteresis loop was obtained by the integration of the transient poling

current, ( )

dt

APdi s2

= (Ps is the polarization and A is the area of domain reversal), with a

capacitor, which is in series with the sample and power supply. 10 A HP34401A

multimeter with 10GΩ input impedance was used to measure the voltage across the

capacitor to prevent leakage of the capacitor. The applied DC field across the crystal

thickness was linearly ramped up at 2V/s. The measured spontaneous polarization is

Ps=55.2±0.5µC/cm2. The coercive fields of SLT-VTE in this study are determined as Ec,f

~1.39±0.01kV/cm for forward poling and Ec,r ~1.23±0.01kV/cm for reverse poling,

30

respectively. Figure 2-2 shows the comparison among the hysteresis loops of congruent

lithium tantalate, near-stoichiometric lithium tantalate and stoichiometric lithium

tantalate. The coercive fields of SLT-VTE in this study are a factor of ~ 12 smaller than

the NSLT-CZ samples and a factor of ~ 130 smaller than CLT samples (Table 2-1 ).

The SLT-VTE crystal was successively switched 44 times. The time interval

between two successive domain reversals was about 2 minutes. Figure 2-3 (a) shows the

hysteresis loops of polarization versus electric field for the 1st hysteresis loop cycle and

the 22nd hysteresis loop cycle; and Figure 2-3 (b) shows the coercive fields as well as the

spontaneous polarization for both forward poling and reverse poling obtained in these 22

experimental cycles. These results show that the coercive fields at 2V/s ramp rate

(Ec,f~1.39±0.01kV/cm, Ec,r~1.23±0.01kV/cm) do not change significantly between

cycles. This is in strong contrast to CLT and NSLT-CZ lithium tantalate crystals

reported before in Ref. [19], where the coercive field changes with repeated cycling.

Figure 2-2: The hysteresis loops at room temperature of stoichiometric, near-stoichiometric and congruent lithium tantalate.

31

Similarly, the internal field, Eint=(Ec,f-Ec,r)/2~0.08kV/cm was observed for SLT-VTE,

which is only about 6.1% of its coercive field. In contrast, the internal field is about 25%

of its coercive field in CLT 20 and 13% in NSLT-CZ.19

(a)

(b)

Figure 2-3: Hysteresis loops of lithium tantalate crystals. (a) Hysteresis loops for 1st experimental cycle and 22nd experimental cycle of stoichiometric LiTaO3 single crystals (SLT-VTE). Cycling frequency was ~4 minutes/cycle. (b) Coercive fields and spontaneous polarization measured in 22 successive experimental cycles. Coercive fields Ec,f (~1.39±0.01kV/cm) and coercive field Ec,r (~1.23±0.01kV/cm) do not change with cycling.

32

No difference was observed in hysteresis loops by using tap water electrodes or

10% LiCl water solutions. The same experiment also was conducted with DI water. It

showed that the domain cannot be reversed. This is due to no charge compensation at the

surface of the ferroelectric SLT-VTE sample.

The internal field was observed in both congruent lithium tantalate 20,21 and near-

stoichiometric lithium tantalate. 19 It was pointed out in Ref. [20,21] that the internal field

in lithium tantalate comes from the nonstoichiometry defects in lithium tantalate. “The

origin of internal fields may lie in complexes of lithium and oxygen vacancies or

tantalum antisites and tantalum vacancies”.20 It was predicted that as the crystal reaches

towards stoichiometry, the internal field decreases. Once the crystal is stoichiometric, the

internal field vanishes. This was confirmed by the internal fields in near-stoichiometric

lithium tantalate and now by stoichiometric lithium tantalate. However, in SLT-VTE,

there is still small amount of internal field (~0.08kV/cm) existing, which indicates that

the crystal is still not stoichiometric yet and there is still very little Li+ deficiency.

The coercive fields and the Curie temperatures of lithium tantalate were also

proposed to be in linear relationship with their stoichiometry, C. 4,22 Coercive fields and

curie temperatures of lithium tantalate with different compositions are plotted in

Figure 2-4, which shows a linear dependence of the coercive field on the crystal

composition and the Curie temperature (Detailed data seen in Table 2-1). The fitting

curve for relationship between Curie temperature, coercive fields and composition in

lithium tantalate are:

33

The values are pretty close to the prediction in Ref. 8.

2.1.1.3 Switching time

The domain switching time was measured by applying step voltages across the

sample. The HP 33210A function generator and Trek 20/20C amplifier was used as

power supply. The transient current pulse resulting from the domain reversal process was

measured by Tektronics TDS 340A oscilloscope. The rise-time of the applied field across

the sample was ~50µsec. The current sensitivity was ~20nA. Figure 2-5 shows the

32.48C-1274.7 )( Tc +=°C Eq. 2.1

13.935C-697.02 (kV/mm) Ef = Eq. 2.2

8.158C-408.3 (kV/mm) Er = Eq. 2.3

cf 0.2153T-150.71 (kV/mm) E = Eq. 2.4

cr 0.1262T-88.56 (kV/mm) E = Eq. 2.5

Figure 2-4: Composition dependence of forward (Ec.f) and reverse (Ec.r) coercive fields, and the Curie temperature (Tc) in lithium tantalate single crystals.

34

electric field E versus switching time for both forward poling and reverse poling.

Switching time is defined as the total time required for switching 95% of the total

electrode area here. The switching time for ferroelectric domain reversal can be described

as:

where E-Eint is for forward poling, and E+Eint is for reverse poling. For SLT-VTE

crystals in this study, the switching time for both forward poling and reverse poling have

the same activation energy ( cmkVfr /22.084.10 ±== δδ ).

2.1.2 Domain reversal with other electrodes

The liquid electrodes cannot be used in a practical device operation. The

operation of devices with electrical signal cannot avoid solid electrodes such as metallic,

)exp()()(int

,,0, EE

tt frfrfrs

m

δ= Eq. 2.6

Figure 2-5: The switching time (ts) f, r as a function of field E±Eint, where negative sign is for forward poling and the positive sign for reverse poling. The measured internal field Eint=0.08kV/cm.

35

ionic oxides or even superconductors. However, there has been limited research on

domain reversal in stoichiometric lithium tantalate with different electrodes so far.

Scrymgeour 23 discovered that the choice of electrodes was critical for congruent lithium

niobate and congruent lithium tantalate. With metal electrodes such as CrAu on both

sides, the lithium niobate always breaks down soon after the onset of the poling process.

Congruent lithium tantalate’s case was little better, but it still frequently broke down.

However, with ITO (In2O3:Sn) electrodes on both sides, the congruent lithium tantalate

never breaks down during the process whereas the congruent lithium niobate infrequently

breaks down. Besides this, no ferroelectric fatigue on congruent lithium tantalate was

reported. It is worth pointing out that the domain patterned electro-optic devices of

lithium tantalate with metal electrodes worked well with the operating fields lower than

its coercive fields. No degradation in device performance was observed. In the following

section, the samples cut from the same wafer were used. As described in the previous

section, no ferroelectric degradation was found with liquid electrodes. Therefore, the

samples used in the following section were either poled with liquid electrodes or “virgin”

crystals.

Metal electrodes are most often used electrodes in devices. They can be sputtered

uniformly on a big surface at room temperature with high quality such as high

conductivity and high adhesion on most optically polished crystals. Metal electrodes are

the practical choice, easy to handle and have very good conductivities. Therefore, the

stoichiometric lithium tantalate samples were also poled with metal electrodes (such as

Au, Ta, Pt) on both sides.

36

As described in the previous section, the hysteresis loop does not change with the

cycles of poling with liquid electrodes for stoichiometric lithium tantalate. The sample

was poled into a single domain with liquid electrodes at room temperature. Metal

electrode (Au, Ta, and Pt) were sputtered onto both +z surface and –z surface at room

temperature. By using the same poling circuit mentioned in previous section, the

hysteresis loops of SLT-VTE were obtained (Figure 2-6 (a)). Strong fatigue was

observed for all these metals.

The ITO electrodes were also chosen based on previous work on congruent lithium

tantalate. At room temperature, the ITO electrodes are mainly electronic conductors;

however, the density of charge carriers is much lower than metals (~10-20cm-3 in ITO and

~10-28cm-3 in metals). The ITO electrodes were sputtered at an elevated temperature

(~100°C). However, strong fatigue was still observed. The fatigue rate is somewhat

slower than with metal electrodes (Figure 2-6 (b)).

Figure 2-6: The spontaneous polarization vs. cycles of domain reversal in stoichiometric lithium tantalate with (a) metal tantalum (Ta) electrode;(b) ITO (In2O3:Sn) electrode.

37

Stoichiometric lithium tantalate experiences strong ferroelectric fatigue with

metal electrodes (Au, Ta, and Pt), ITO, and water-based graphite electrode. The question

which arises here is what causes the fatigue and if this fatigue can be healed? To

understand the mechanism of fatigue, we need to explore its relation to the chemical

composition, defects structure and surface chemistry in stoichiometric lithium tantalate.

To distinguish if this fatigue is only a surface effect or a bulk effect would be the first

step, and also, we believe, could lead us to clues about the origin of fatigue.

The sample examined by the PFM was poled with liquid electrode again. The poling

condition remains the same as those in first time poled with liquid electrode. Figure 2-7

shows an example of the normalized spontaneous polarization versus the domain reversal

cycle after strong fatigue observed with water-based graphite electrode on both sides of

the crystal. The spontaneous polarization in the first domain reversal is consistent with

that in last domain reversal with solid electrode. There is no more ferroelectric fatigue

observed. Instead, the ferroelectric fatigue caused by solid electrodes used in this study

was slightly recovered (0.01 % of Ps recovery per cycle). However this slow recovery

stops after ~200 cycles and could never fully restore the strongly fatigued sample.

The surfaces of strongly fatigued sample with thickness 0.83mm were mechanically

polished away by ~4µm on each side with 6µm diamond slurry. Then this sample was

poled with 5% LiCl water solution again. The ferroelectric fatigue cannot be removed. To

further ensure this, the surfaces of the sample were mechanically polished away by

~100µm on each side to a thickness of ~0.6mm. The domain reversal experiment was

conducted with 10% LiCl water solution and tap water again. The experimental results

38

showed that the strongly fatigued areas still cannot be reversed. Same mechanical

polishing procedure was conducted on a non-fatigue sample, which was only poled with

liquid electrodes. The domain reversal after the polishing shows no fatigue happened.

This suggests that mechanical polishing itself does not cause any ferroelectric fatigue on

SLT-VTE. Hence, the result of the fatigued sample after mechanical polishing suggests

that the fatigue caused by the electronic conductor electrode were bulk effects instead of

only the surface layers of the stoichiometric lithium tantalate. The sample was also

slowly heated up (~2°C/min) to 400°C and held at this temperature for 5 hours in an O2

atmosphere (reduce Nb4+, if any present), then slowly cooled down. After annealing, the

domain reversal was attempted with liquid electrodes at room temperature. The fatigued

sample still does not recover.

It is not new that the ferroelectric fatigue is related to the electrode contacts used.

24-26 So far, the fatigue mechanisms proposed in ferroelectrics mainly include: 1) a

Figure 2-7: The spontaneous polarization vs. the domain reversal cycles with 10% LiCl solution at room temperature after removed the graphite electrodes, with which strong ferroelectric fatigue was also observed.

39

surface layer formation; 2) domain wall pinning by point defects; 3) clamping of

polarization reversal by volume defects; and 4) suppression of nucleation of oppositely

oriented domains at the surface. The removal of surface up to ~100µm on each side (both

+c and –c) of the fatigued sample suggests that the fatigue in stoichiometric lithium

tantalate is not just a surface effect; rather it is a volume effect. The electrodes (Au, Ta,

Pt, and ITO) used which causes ferroelectric fatigue share the following in common: they

are all electronic conductors by nature at room temperature. The conduction in both

congruent lithium niobate and lithium tantalate were reported to be dominated by

polarons,27,28 which are formed by point defect NbLi•••• that are deep electron traps.

Another source for its conduction is the impurities. If the electrons in electrode contacts

were captured and formed a charged layer on the surface, then electrical double layer29

can be formed near the contact surface region. If the concentration of charge is very low,

the Debye length could be very long. However, this needs a well understood point defect

picture in stoichiometric lithium tantalate, which is not the case. This will be an important

issue to solve to clearly understand the mechanism of ferroelectric fatigue.

2.1.3 Domain structure in lithium tantalate

The domain structure of LiTaO3 changes with its composition. The domain in

congruent LiTaO3 (CLT) can be seen under an optical microscope without any applied

voltage (Figure 2-8(a)).9 The domain shape is triangular with walls perpendicular to the

y-axes. The visibility of a domain wall in CLT under EOIM without any applied voltage

suggests the presence of optical birefringence at the domain wall, which indicates the

40

presence of local strains and electric fields.8 Due to the elasto-optic effect, the local strain

creates the optical birefringence even without external applied field.8 In NSLT-CZ

crystals, the extremely low birefringence only gives a very faint contrast at the domain

walls (Figure 2-8(b)).19 Unlike the triangular domain shape in CLT, the domain shape in

NSLT and SLT-VTE is hexagonal and the domain wall in NSLT can only be seen with

external applied field (~10kV/cm). The coercive field for NSLT-CZ is ~15kV/cm, thus

we can apply ~10kV/cm external field across c-surfaces to generate a ∆n~5×10-5, which

is sufficient for weak optical imaging. However, the domain walls cannot be seen in SLT-

VTE even with an external applied field. The field required for domain wall motion in

SLT-VTE is very low (~0.8kV/cm). Even with applied fields, the birefringence due to

electro-optic effect is extremely small (∆n~10-6 to 10-7) to induce sufficient optical

contrast. The domain shape in SLT-VTE is hexagonal (Figure 2-8 (c)) with wall parallel

to the crystallographic y-axis as revealed by piezoelectric response force microscopy and

HF etching in stoichiometric lithium tantalate. The optical imaging of domain walls and

the domain shapes in CLT, NSLT-CZ and SLT-VTE crystals suggested that there is a

clear correlation between the optical birefringence, and lithium stoichiometry in the

crystals.8

It is worth pointing out that the shape of the domain structure is very important in

making domain patterned optical devices. For instance, for a periodically poled structure

for optical frequency converter, we would like the domain wall to be straight since there

is birefringence around the domain wall. The phase front of the fundamental beam cannot

be in the same incidence plane when it encounters a non-straight domain wall, and the

41

phase matching condition will be destroyed. For instance, the triangular domain shape in

congruent lithium tantalate leads a jagged wall on micron scale in a periodic poled

structure. The efficiency of such devices would be low.30 Hence, most periodically poled

structures used today are mainly on lithium niobate due to its hexagonal domain shape.

However, the photorefractive effect of lithium tantalate is less than lithium niobate. It

was reported that the near-stoichiometric lithium tantalate has higher optical damage

threshold than even MgO doped lithium niobate. The prediction that the optical damage

threshold is related to the inverse of the number of the point defects in both lithium

niobate and lithium tantalate suggests that the stoichiometric lithium tantalate would have

even higher optical damage threshold. Now the hexagonal domain shape of

stoichiometric lithium tantalate and low coercive fields along with its high optical

damage threshold (even exactly threshold is unknown at this stage) would make it more

favorable in making thick crystal based periodic poled optical devices.

v (a) (b) (c)

Figure 2-8: Domain image of lithium tantalate. (a) optical image of congruent lithium tantalate; (b) Optical image of near-stoichiometric lithium tantalate with 10kV/mm field on; (c) The phase piezoresponse force microscopy (PFM) image of the domains in stoichiometric lithium tantalate (SLT).

42

2.1.4 Backswitching

The domain backswitching discussed in Ref.[19] was also studied in the SLT-VTE

crystals. The shortest pulse width of the applied field was about 1ms. The result showed

that there is only a switching current and no backswitching current for both forward and

reverse domain reversals. This means that the stabilization time, if any, for newly created

domains for SLT-VTE samples is tstab<1ms. This is in strong contrast to CLT crystals,

where the observed stabilization time was as high as 1.7s for forward poling and ~0.1-

0.3s for reverse poling.

These dramatic differences in domain reversal properties among CLT, NSLT-CZ,

and LT-VTE can be understood in terms of the non-stoichiometric defect model proposed

in Ref. [19], where the authors propose the structure of a defect complex as comprising of

a niobium/tantalum antisite surrounded by three Li+ vacancies in the nearest

neighborhood, plus one independent Li+ vacancy along the polar z-direction. This defect

complex is assumed to comprise of a dipole moment, which has two contributions: (a) the

contribution to the electrical dipole arising only from the TaLi antisite defect, and (b) the

contribution to the electrical dipole arising from the relative arrangement of the lithium

vacancies VLi around a tantalum antisite defect TaLi. With electrical field applied at room

temperature, only the dipole moment contributed by component (a) reverses its direction

whereas the defect dipole moment contributed by component (b) does not change its

direction at room temperature. This results in frustrated defects that manifest as internal

fields. During domain reversal at room temperature, it takes finite time for component (a)

to realign that manifests itself as the stabilization time. If the applied field is turned off

43

before this time, the new domain state switches back (backswitching). Thus this model

can explain stabilization time, backswitching, and internal fields. It is also pointed out

that the magnitude of the defect field and the coercive field are proportional to the density

of these defect dipoles. In SLT-VTE crystals, the TaLi and VLi are in very small amounts,

and thus the coercive fields, internal field and stabilization times are proportionately

smaller. We also note that the recently reported 31, 32 thickness dependence of the

switching times in CLT suggests that the relaxation time for these defects complexes is

substantially lower than 1ms when the defect is within ~250-500nm of the crystal

surface, thus resulting in smaller stabilization times, as well as lower asymmetry between

forward and reverse defect fields, 19 ED for crystals of <500nm thickness.

Figure 2-9: Schematic of defect dipoles in lithium tantalate. (a) unit cell of perfect crystal with up domain; (b) up domain with up defect dipole formed by defect complex; (c) down domain with up defect dipole formed by original defect complex after the first domain reversal; (d) down domain with down defect dipole after the defect complex relaxation.

44

2.2 Domain reversal in strontium barium niobate crystal

The ferroelectric materials with 180° domains have been widely used in photonic

applications, such as electro-optic switches, scanners, dynamic focusing lenses, and

frequency converters, by patterning the domains into various shapes such as gratings,

lenses, and prisms. 35-39 In these applications, controlled manipulation of domain

structures, from a few microns to hundreds of microns, is important for making electro-

optic and nonlinear optical devices. Although domain studies on LiNbO3 and LiTaO3

Table 2-1: A comparison of congruent (CLT), near-stoichiometric (NSLT-CZ) and stoichiometric (SLT-VTE) crystals. Measurements not referenced below are from this study.

Congruent (CLT) Near-stoichiometric (NSLT-CZ)

Stoichiometric (SLT-VTE)

Growth Technique Czochralski (CZ) method

Double-crucible Czochralski (CZ)method

VTE treatment on CZ grown CLT

Composition, C* 0.485 a 0.498 b ~0.5

Curie Temperature (°C) 601±2 b 685±1 b 701±2.5

Coercive fields (kV/cm), 296K (ramp rate 15V/s)

211.55±2.81(forward) c 125.99±1.65 (reverse) c

17 (forward) b 15 (reverse) b

1.61±0.06 (forward) 1.48±0.06 (reverse)

Coercive fields (kV/cm), 296K (ramp rate 2V/s)

- - 1.39±0.01 (forward) 1.23±0.01 (reverse)

Internal fields (kV/cm) 44.28±2.08 c 1.0b 0.08

UV Absorption edge (nm) 275 c 260 d 256

Activation field (kV/cm) 51.4±5.9 (forward) a

36.93±5.0 (reverse) a 26.48±2.1(forward) a

33.4±2.1(reverse) a 10.84±0.22 (forward) 10.84±0.22 (reverse)

Stabilization time ~1.7 s (forward) a

~0.1-0.3s (reverse) a ~700ms (forward) a ~100ms (reverse) a

<1ms (both forward and reverse) if present at all

Ps (µC/cm2) 60±3 c 55±3 b 55.2±0.5 *C=[Li]/([Li]+[Ta]) a See Ref. 19 b See Ref. 33 c See Ref. 21 d See Ref. 34

45

crystals have been widely conducted, 9,10,19,40,41 far fewer studies exist on domain

switching in strontium barium niobate (SrxBa1-xNb2O6 or SBN:x) crystals, which are of

interest due to their large electro-optic and piezoelectric coefficients. 42-48 Both optical

domain reversal49,50 and electrical domain reversal51 in SBN:x have been demonstrated.

However, the precise nature of domains inside the SBN:x crystals remains ill-understood

because of the complexity of interaction between the defect structure and the space

charge fields induced by light illumination and lack of systematic studies on SBN:x

domain wall dynamics.

In this work, we have studied domain reversal Sr0.61Ba0.39Nb2O6 (SBN:61)

crystals with liquid (tap water) electrodes at room temperature. The domain nucleation

and domain growth are observed in-situ in transmission mode using electro-optic imaging

microscopy (EOIM). 9 Significant differences in domain reversal between using metal

electrode versus water electrodes are observed, as reported here.

This section is organized as follows: Sections 2.2.1-2.2.5 present experimental

data on domain structure imaging, polarization hysteresis loops, switching time, domain

wall mobilities, and domain backswitching; Section 2.2.6 presents the discussion,

followed by conclusions in Section 2.2.7.

2.2.1 Real-time observation of domain wall motion under EOIM

Many groups have studied the domain structure of SBN crystals using different

methods. In 1970s, the microstructure of SBN crystals was examined using etching and

decoration methods.52 These two methods not only require a long time for sample

46

preparation but also cause destructive damage to sample surfaces. In late 1980s, H.

Arndt53 et al reported observing domain-like structure via polarized microscope using the

method developed by Merz.6,54 In this case, the sample was cut in an oblique angle such

that the field direction was at an angle of 45° with the c-axis of the crystal. In the last two

years, several groups have tried to use scanning probe microscopy (SPM) to characterize

domain structure of SBN crystals. 55,56 However, these processes cannot provide real

time features of domain structure in SBN crystals. Here, we use electro-optic image

contrast across antiparallel domain walls for in-situ domain observations in SBN:61,

similar to those reported for lithium niobate and lithium tantalate crystals. 9,41

SBN crystals possess tetragonal tungsten bronze type structure. The point group

of its ferroelectric phase is 4mm at room temperature. There are three independent

electro-optic coefficients: r13, r33 and r51. Under a uniform applied field E3 along the c-

axis of crystal and with the light propagating along the c-axis of the crystal, the refractive

index in one domain (with polarization, Ps, antiparallel to the applied field, E3) increases

by 3133

21 Ernn o=∆ , while it decreases by the same amount in the other domain (with

polarization, Ps, parallel to the applied field, E3). This provides an index contrast across

the domain wall. This method can be used to image the domain structure in a z-cut SBN

crystal.

In our experiments, the z-cut SBN:61 crystals were purchased from OXIDE

Corporation in Japan. The crystals are optical-grade polished (surface roughness ~ 1µm),

with a thickness of 1.00 mm. A step electric field was applied to the sample through

water electrodes across the sample c-surfaces. At the same time, the sample domain

47

reversal process was monitored with EOIM. The video image was recorded with a

camera and loaded into a computer through an image card. No image contrast was

observed without any applied electric field. Under a field, the domain reversal process

was observed as shown in Figure 2-10 (a)-(c). The shape of SBN:61 domain looks like a

square, which possesses 4-fold symmetry. The domain walls are along both

crystallographic x [100] and y [010] directions, as confirmed by Laue X-ray diffraction.

Further imaging of one of these domains was performed using piezoresponse force

microscopy 57 at room temperature, as shown in Figure 2-10 (d). The 4-fold symmetry of

the domain shape is clearly visible.

2.2.2 Coercive fields and hysteresis loop

We called the starting state of as-purchased crystals as “virgin” crystals, which

were in multi-domain states. The virgin crystals were poled into a single domain at room

Figure 2-10: Domain structure of SBN:61 crystals (a) with field 225V/mm; (b) 5s after frame (a); (c) after the reversal is complete; (d) Piezoelectric Force Microscopy image of domain (the product of amplitude and the cosine of phase).

48

temperature with water electrodes. We refer to this domain poling process as the first

poling process. Starting from this single domain state, the next domain reversal is

referred to as forward poling (subscript f) and the second reversal back to its original

state as reverse poling (subscript r).

In this experiment, the crystal sample is connected to a high voltage power supply

(IRCO) though a series resistor. The voltage across the resistor is measured for extracting

the transient poling current and was simultaneously measured during the poling

experiment. Figure 2-11 shows the typical transient current over time during domain

reversal of SBN:61 crystals.

The ramp voltages at various rates were applied across the sample. The time delay

between two consecutive forward and reverse poling sequences was about 2 minutes. The

domain reversals in the samples were performed in-situ, and the nucleation and growth of

domains were monitored under EOIM, which was already described in Section II. The in-

Figure 2-11: The transient current observed during domain reversal of SBN:61 on applying a linearly ramped field at 1V/mm/s with water electrodes (solid line with square) or metal electrode (solid line with circle).

49

situ monitoring of the domain reversal was used to confirm the progress and completion

of domain reversal in a given area. The EOIM was used to determine the starting

coercive field, Es, which is defined as the field at which the domain nucleation starts. Due

to the resolution of EOIM image, only when the nuclei reach around 1µm, it could be

seen. Therefore, in this study, the starting coercive field, Es, corresponds to the field at

which domain nuclei are ~ 1µm. The real starting coercive fields may be even lower for

even smaller nuclei size. The coercive field of SBN:61 crystals is defined as the electric

field at which the net sample polarization is zero (Figure 2-12), which corresponds to

equal area fractions of up and down domains in the poling area. The spontaneous

polarization was determined by integrating transient currents over time.

The starting poling field, Es, for SBN:61 crystals is ~2.0kV/cm for both forward

and reverse poling processes and independent of field ramping rates. At a given field

ramping rate, the coercive fields for both forward poling and reverse poling are about the

same. The coercive field, Ec, at a ramping rate of 1V/mm/s is ~2.39±0.04kV/cm. The

spontaneous polarization for SBN:61 crystal was Ps=27.71± 0.4µC/cm2. No obvious

degradation of coercive fields was observed in repeated poling cycles for a given field

ramping rate Figure 2-12 (a) and (b)). This is quite different from the previous results, 58-

60 in which the pure or doped SBN:61 crystal were poled with metal electrodes at room

temperature and strong ferroelectric fatigue (18%~28% of polarization remained) has

been observed.

50

(a)

(b)

(c)

Figure 2-12: The hysteresis loop for SBN:61 crystals measured by applying linearly ramped field at speed 1V/mm/s. (a) Poled with liquid (tap water) electrodes. The solid line and dot line loops are measured for successive polarization reversal cycle 1 and cycle 4. No obvious fatigue observed. (b) Poled with silver paste. Strong ferroelectric aging is observed. (c) The Ps (forward and reverse) measured for 1. tap water electrode, and 2. silver paste electrode.

51

The same sample used above was painted with conductive epoxy silver paste

(Chemtronics) on both +c and –c surfaces, then heated up to ~200°C and held for 40

minutes. After slowly cooling down, the sample was poled with the same circuit

configuration as before. The hysteresis loop was plotted by integrating the poling current

(Figure 2-12 (c)). Strong ferroelectric fatigue was observed. After two complete cycles,

only 50% polarization remains. This strong ferroelectric aging tendency is consistent with

the previous reports, 58-60 even though the fatigue rates and final remaining polarization

may not be the same. It also shows that after 4 runs, the spontaneous polarization almost

remains the same, which is only ~44% of the original polarization.

In these experiments, we note two important observations. In the first poling

process, the domain nucleation starts under a very low applied field, (Es~0.90 kV/cm)

which is much lower than starting poling fields (Es~2.0kV/cm) in the subsequent forward

and reverse domain reversal processes. The reason for this is presently not clear. The

second aspect is that the starting coercive fields, Es, are independent of the ramping rates,

but the coercive fields, Ec, are not. We have investigated the relationship between

ramping rates and coercive fields by choosing a set of ramping rates. At each ramping

rate, the forward poling and reverse poling were performed twice. The applied voltage

was linearly ramped from 0V to 600V. The poling process was performed at the same

area in the same sample. The time interval between two successive poling processes was

about 2min. Figure 2-13 (a) shows the forward coercive field and reverse coercive field

at different ramping rates. Both forward and reverse coercive field increase with

increasing ramping speed. From the transient current data, we also found that the peak

52

fields at which the transient current reaches its maximum also increase with increasing

ramping speed (Figure 2-13 (b)). This dependence of coercive fields and peak fields on

field ramp rate is understandable, since a faster ramp rate provides less dwell time at any

given field in comparison to the switching time at that field. Hence, this results in a

longer switching time for the 50% domain reversed state. Since the field and time are

linearly related in the ramp process, the coercive field also appears to be proportionately

higher for the higher ramp rates. This also explains the diversity of the coercive fields of

SBN:61 crystals reported in literatures before. However, the starting coercive fields are

determined by the activation energy for nucleation for the SBN:61 crystal under study,

therefore it should be independent of ramp rate.

2.2.3 Switching time

To study switching time of domain reversal in SBN:61 crystals, step voltages of

various amplitudes were applied and the transient current responses were measured.

(a) (b)

Figure 2-13: The relationship between coercive fields and field ramping speeds for SBN:61 crystals.

53

Figure 5(a) shows the typical transient current response. The power supply used in this

experiment consisted of an HP 31220A function generator and a Trek 20/20C high

voltage amplifier. The step voltage waveform was generated by the function generator.

The frequency of function generator was set to be 10mHz. The function generator was

working in burst and external trigger mode. Both field and current data were collected by

A/D box simultaneously in low field regime and oscilloscope in high field regime. The

current sensitivity was about 0.02µA.

In this experiment, the electrode area was fixed for various applied fields. The

integrated charge under the transient current peak equals 2PsA, where Ps is spontaneous

polarization of SBN:61 and A is electrode area. The switching time ts is the time needed

for 95% area of electrode area of domain reversal. The error in switching time is

Figure 2-14: The switching time and switched charge in SBN:61 domain reversal under various applied fields with liquid electrode. The switching time is the time needed such that 95% of area has been reversed. The switched charges remain almost same at different field.

54

determined by the time interval between the data points. Since there is a slight fluctuation

(<±5V) in the high power supply, the fields plotted in Fig. 5(b) were mean values of

applied fields. The error bar in the field direction is the standard deviation error of

applied field. As can be seen in Fig. 5(b), the switching times for both the forward and

reverse domain reversal are equal under a same applied field. The ln(ts, r, f) is in linear

relationship with 1/E. The slope of the linear relationship changes from low-field regime

to high-field regime. The switching time ts can be written as a function of electric field E

as follows:

whereδ is called activation field, which is the slope of the linear fits in Fig. 5(b).

The activation fields δ are 14.82±0.16kV/cm in high field regime (>3.75kV/cm) and

22.71±0.10kV/cm in low field regime (<3.75kV/cm).

2.2.4 Wall mobility

The sideways wall velocity of 180° domains in the z-plane of SBN:61 was

measured by applying step voltages. The videos were taken by Sony CCD-IRIS camera at

the speed of 30 frames/s and then digitized by software into frames. As was mentioned in

Section II, the edges of approximately square-shaped domains of SBN:61 crystals are

along crystallographic x-axis and y-axis, respectively. From these digitized video data,

the average distance traveled by each of the walls from the origin in a direction normal to

the wall (along crystallographic x-axis and y-axis direction) for an independently growing

)exp(0 Etts

δ= Eq. 2.7

55

domain after its nucleation was measured. Figure 6(a) shows the distances traveled (along

x-axis and y-axis) versus the time after the nucleation of an independently growing

domain under an external electric field E=3.15kV/cm, in which the slope (12.10±0.30

µm/sec) of the curve is the domain sideways wall velocity. This result showed that the

domain sideways wall velocities along both crystallographic x-axis and y-axis are the

same for an independently growing domain under an external field. As the domains grow

bigger, these domains start merging with neighboring domains. Due to their square

domain shapes they form serrated domain front along the diagonal direction <110>,

which move with a higher wall velocity. Figure 6(b) shows an example of the average

distance traveled by such serrated wall moving along diagonal direction from the merged

point versus the time under an external field E=3.15kV/cm. The slope of curve in Fig.

6(b) gives this merged domain sideways wall velocity (17.10±0.77 µm/sec), which is

~1.4 times faster that the wall velocity of an independently growing domain under the

same external field.

Similar measurements of sideways domain wall movements of an independently

growing domain under different fields were performed on a same sample. The distances

traveled by the wall along crystallographic x-axis from the origin where the domain was

nucleated was plotted for an independently growing domain under different fields in Fig.

6(c). The slopes of different curve in Fig. 6(c) give the domain sideways wall velocities

under different fields, which are plotted in Fig. 6(d). As it can be seen, the domain

sideways wall velocity is in exponential relationship with 1/E, which can be described as:

)exp(0 Evvs

α= Eq. 2.8

56

where vs is the sideways wall velocity, α is activation field for an independently

growing domain-wall velocity. The measured values in this experiment are ln(v0,

µm/sec)=8.83±0.29 and α=19.89±0.79kV/cm.

(a) (b)

(c) (d)

Figure 2-15: Domain sideways wall growth in SBN:61 crystals. (a) The distances traveled along x-axis and y-axis vs. time after nucleation of an independent domain under field E=3.15kV/cm; the slope of curve gives the sideways wall velocities along both x-axis and y-axis directions, which are the same and equal to 12.10±0.30µm/sec. (b) The distance traveled along serrated direction (<110> direction) vs. time for a merged domain wall velocity under field E=3.15kV/cm; The slope gives the sideways wall velocity, vs~17.10±0.77µm/sec. (c) Distances traveled (along either x-axis or y-axis) vs. time after nucleation of an independent domain under different fields; (d) Domain wall velocities of an independent domain under different fields.

57

2.2.5 Backswitching

In both non-stoichiometric lithium niobate and lithium tantalate single crystals, it

has been found that a domain created by the applied external field needs certain minimum

amount of time for which the electric field that created it should remain and stabilize it. 19

Otherwise, the reversed domain would switch back to its original state. Such a

phenomenon is referred to as backswitching.

We applied pulse voltage with different period widths across the thickness of

SBN:61 crystals. The video was taken by high-speed camera (Kodak Ektapro) that is

capable of 2000 frames per second in real time. The transient current and applied pulse

field data were recorded by Tretronix TDS 340A oscilloscope, whose sampling rate is

500MS/s. Figure 7(b) shows typical transient current and applied pulse field. The first

peak in transient current (at the beginning of the voltage pulse) is due to RC time constant

of circuit, whereas the second peak (at the end of the voltage pulse) may be due to the

effects of both the RC constant of circuit as well as backswitching. To separate these two

effects, we first poled the sample into a single domain, then applied a pulse voltage with

the same magnitude and pulse width, but with the non-poling polarity. Thus we are able

to measure the time constant of the RC circuit (Fig. 7(a)). By comparing transient

currents between poling and non-poling voltage pulses, we find that the there is no

evidence for domain backswitching in SBN:61 crystals down to a pulse width of 1.25 ms.

This means the stabilization time for SBN:61 domain reversal is less than 1.25ms, if any

at all.

58

2.2.6 Discussion

(a) (b)

(c)

Figure 2-16: “Backswitching” tracking in c-cut SBN:61 crystal and no backswitch was observed. (a) A 1.25ms pulse of 4.0kV/cm field is applied antiparallel with spontaneous polarization on a single domain crystal to find out the RC response time of the circuit. RCconstant of the circuit is ~0.06ms. (c) A 1.25ms pulse of 4.0kV/cm field is applied parallel with spontaneous polarization on the same area of same sample used in (b). Partial domain reversal is induced. (c) The switching current after taking away RCresponse current from the (b). It suggests no backswitching in SBN:61 under 1.25ms pulse of 4.0kV/cm field.

59

2.2.6.1 Switching current and switching time

Switching current is the most common characteristic to study reversal of

spontaneous polarization in a ferroelectric material, from which information such as

switching time, the nucleus-domain interaction, and the dependence of the switching time

ts on applied field can be extracted. 61

In Fatuzzo’s work, 61 the switching current is described as follows:

Where *R is probability per unit time that the domain nucleates around an

existing domain wall. R is the probability per unit time that the new domain nucleates

somewhere else. Therefore, the parameter k can be used to indicate “nucleus-domain

interaction”.

In Fig.5(c), we plot theoretical transient current calculated by the above equation

and an experimental transient current of SBN:61. In this case, k , ~5.96, suggests that the

probability of nucleation near the domain region is about 3 times larger than probability

of nucleation away from the domain wall, indicating that the domain sideways growth

was more important than nucleation in this case. The agreement between the theory and

experiment is reasonable, but the theory misses some details near the current peak. The

discrepancy arises because the theory assumes that the probability of nucleation is

constant everywhere and independent of time.

RtR

Rk

kkekkk

kkekRkPi ss

=

=

−−−−+++−−×

+−+++−=

−−−−−

−−−−

τ

τττ

τ

τ

τ

*

212112

2112

2

)]1(2

1)1()(

2

1)(1[2exp

]2

1)1()(1[4

Eq. 2.9

60

In this experiment, switching times measured shows different activation energies

for low field regime (<3.75kV/cm) and high field regime (>3.75kV/cm). However, the

domain sideways velocities had the same activation energy in these field regimes. The

activation energies of switching time are δ=14.82±0.16kV/cm in high field regime and

δ =22.71±0.10kV/cm in low field regime as well as α = 19.89±0.79 kV/cm for sideways

wall velocities. The velocity of growth of domains along the polarization direction was

not measured. However, in this experiment, all the domain reversals were performed in-

situ. The completion of domain reversals was determined by two criteria: (1) completion

of domain image contrast recorded by video camera; (2) the transient current goes to

zero. In this experiment, we found that the completion of domain image contrast and the

transient current going to zero happens at almost same time, so that we can conclude that

(1) the domain growth velocity along polarization direction is larger than its sideways

wall velocity; (2) the switching time of domain reversals are limited by the sideways

growth of domains in the z-plane of the crystal. Thus far, we have treated that the domain

reversal process as consisting of two steps: (1) nucleation with at rate of N nuclei/cm2 sec

and activation energy β; (2) sideways growth of the new nucleated domains with wall

velocity vs and activation energy α. In Ref. [61], it also claimed that

)/)3/3/2exp[( Ets βα +∝ . Therefore, we can estimate that in the low field regime, the

activation energy, β, for nucleation is ~28kV/cm and in the high field regime, it is

~5kV/cm.

61

2.2.6.2 Internal Field and backswitching

Built-in internal fields have been reported in ferroelectric crystals such as PZT,

LiNbO3 and LiTaO3. The studies have shown that internal fields are related to the defect

complexes inside these crystals.

In SBN:61 crystals, no such built-in internal field was observed. The starting

nucleation fields and coercive fields for both forward poling and reverse poling were

found to be the same with liquid electrodes.

2.2.6.3 Electrodes and ferroelectric aging

In the work done by previous researchers, the strong ferroelectric aging in both

pure SBN and doped SBN have been observed [58-60,62] when crystals were poled with

different metal electrodes such as silver, silver paste, gold and etc. Most researchers

believed that the strong aging effect in SBN domain reversal was due to the intrinsic

defects because of its unfilled tungsten bronze structure. Due to 6 available sites for only

total five Sr+Ba atoms in each unit cell of SBN, there is always an unfilled site in each

unit cell. These unfilled sites are randomly distributed in each unit cell, which creates

local lattice distortion. On the other hand, the difference between ion radius of Sr2+

(1.12Å) and ion radius of Ba2+ (1.34 Å) also creates the local site symmetry distortion.

These intrinsic defects inside of SBN structure leads to “quenched random fields”, which

stabilize the domain walls after first switching of the polarization. Most researchers

believed that the ferroelectric aging in SBN domain reversals were evidence of these

random fields.

62

Such aging phenomenon has also been observed in our experiments when poling

was done with metal electrodes (silver). However, since the poling was done on same

sample under same conditions such as electric field, temperature and electrical circuit for

poling, the different behaviors between water electrode (Fig.3(a)) and metal electrode

(Fig.3(b) suggests that the domain aging is strongly related to interface effects between

electrode and insulator, besides the intrinsic defects. The effect of the electrodes on

ferroelectric fatigue is not new. In PZT, traditional Pt/PZT/Pt 63 capacitors are prone to

fatigue. The use of conductive oxide electrodes, 64 of hybrid oxide/Pt electrodes, 65,66 as

well as of one metallic and one oxide electrode 67,68 have been reported to substantially

increase the fatigue endurance compared to the metallic electrodes Pt/PZT/Pt. 63 The

possible scenarios of the fatigue are: (1) reduction of the effective electrode area; (2) the

reduction of the effective field in the ferroelectrics; and (3) A frustrated domain

configuration may make it difficult to switch. In our case, the first scenario is excluded

by direct observation before and after poling measurements. In the poling process with

metal electrodes with field ramp rate is around 2V/s, we found that the conductivity

(~0.91*10-7 Ω-1m-1 ~ 2.3 *10-9 Ω-1m-1) of the SBN is much larger than that (~1.14*10-10

Ω-1m-1) with water electrode. Small polarons involving Nb4+ and O- have been identified

by electron-spin-resonance (ESR) studies in LiNbO3.69 It is likely that such species can

exist in SBN since both materials share a similar local structure based on distorted

octahedral oxygen ions coordinated to niobium. In previous work done by Neurgaonkar,

the existence of Nb4+ in SBN was found to be correlated to the increase in conductivity of

the SBN crystals. Since the charge carriers in metallic conductor are electrons, if the

electrons can be injected 25,67,68,70 into the near surface region in SBN, then these

63

electrons can perhaps reduce the niobium ion from Nb5+ to the Nb4+, thereby increasing

the conductivity in SBN with metallic electrodes. In addition, the space charge field also

can be generated near the electrodes contact surface region. Due to the higher

conductivity of SBN crystal and the space charge field screening near the surface, a

reduction of the effective field inside the ferroelectric can occur, leading to ferroelectric

fatigue.

2.2.7 Conclusions

In this work, we have chosen SBN:61 crystals as candidate material for the study

of domain reversal kinetics in SBN:x crystal system. The poling experiment was

performed at room temperature with liquid electrodes. By using EOIM, for the first time

to our knowledge, we have observed whole domain reversal process in real time, which

has been one of difficulties faced by researchers in making devices based on domain

structure in SBN:x crystals. The reproducible hysteresis loops of SBN:61 crystals poled

with water electrodes at room temperature indicate that there is no obvious degradation of

coercive fields of SBN:61 domain reversal during successive domain reversals. This

phenomenon may help to further elucidate the mechanism of domain control in SBN:61

crystals. We also observed square-like domain shape of SBN:61 under EOIM during

domain reversal, which was confirmed by its PFM scanning image. This result is helpful

for making domain-patterned frequency conversion devices when domain wall direction

can be parallel to an edge of a square domain. The different domain reversal behaviors

between with liquid electrodes and metal electrodes indicate that the interface between

64

conductor and SBN:61 plays an important role in ferroelectric aging. Further studies of

the role of contact junction between metal and insulator (SBN:x crystals) in domain

reversals are needed. These studies will lead us to a better understanding of the kinetics

of the domain reversal in these crystals and nature of this type of interesting materials.

65

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33. Kitamura, K., Furukawa, Y., Niwa, K., Gopalan, V. & Mitchell, T. E. Crystal growth and low coercive field 180° domain switching characteristics of stoichiometric LiTaO3. Applied Physics Letters 73, 3073 (1998).

34. Furukawa, Y., Kitamura, K., Suzuki, E. & Niwa, K. Stoichiometric LiTaO3 single crystal growth by double crucible Czochralski method using automatic powder supply system. Journal of Crystal Growth 197, 889-95 (1999).

35. Scrymgeour, D. A., Gopalan, V. & Gahagan, K. T. in Conference on Lasers and Electro-Optics, CLEO, May 17-19 2004 85-86 (Optical Society of America, Washington, DC 20036-1023, United States, Washington, DC, United States, 2004).

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37. Chiu, Y. et al. Integrated optical device with second-harmonic generator, electrooptic lens, and electrooptic scanner in LiTaO3. Journal of Lightwave Technology 17, 462-465 (1999).

38. Takahashi, H., Onoe, A., Ono, T., Cho, Y. & Esashi, M. High-density ferroelectric recording using diamond probe by scanning nonlinear dielectric microscopy. Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers 45, 1530-1533 (2006).

39. Marx, J. M., Eknoyan, O., Taylor, H. F. & Neurgaonkar, R. R. GHz-bandwidth optical intensity modulation in self-poled waveguides in strontium barium niobate (SBN). IEEE Photonics Technology Letters 8, 1024-1025 (1996).

40. Gopalan, V. et al. Ferroelectric domain kinetics in congruent LiTaO3. The 11th International Symposium on Integrated Ferroelectrics (ISIF99), Mar 7-Mar 10 1999, Integrated Ferroelectrics 27, 137-146 (1999).

41. Gopalan, V., Jia, Q. X. & Mitchell, T. E. In situ video observation of 180° domain kinetics in congruent LiNbO3 crystals. Applied Physics Letters 75, 2482-2484 (1999).

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43. Neurgaonkar, R. R., Cory, W. K., Oliver, J. R., Eknoyan, O. & Taylor, H. F. Ferroelectric tungsten bronze crystals for guided-wave optical applications. Journal of Optics 24, 155-69 (1995).

44. Neurgaonkar, R. R., Hall, W. F., Oliver, J. R., Ho, W. W. & Cory, W. K. Tungsten bronze Sr1-xBaxNb2O6: a case history of versatility. Ferroelectrics 87, 167-79 (1988).

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45. Neurgaonkar, R. R., Kalisher, M. H., Lim, T. C., Staples, E. J. & Keester, K. L. Czochralski single crystal growth of Sr0.61Ba0.39Nb2O6 for surface acoustic wave applications. Materials Research Bulletin 15, 1235-40 (1980).

46. Neurgaonkar, R. R., Oliver, J. R. & Cross, L. E. in Proceedings of the Fifth European Meeting on Ferroelectricity, 26-30 Sept. 1983 Ferroelectrics 1035-40 (Benalmadena, Malaga, Spain, 1984).

47. Shorrocks, N. M., Whatmore, R. W. & Ainger, F. W. in 1982 Ultrasonics Symposium Proceedings, 27-29 Oct. 1982 359-62 (IEEE, San Diego, CA, USA, 1982).

48. Neurgaonkar, R. R. & Cross, L. E. Piezoelectric tungsten bronze crystals for SAW device applications. Materials Research Bulletin 21, 893-9 (1986).

49. Kewitsch, A. S. et al. in Proceedings of 1994 IEEE International Symposium on Applications of Ferroelectrics, 7-10 Aug. 1994 719-24 BN - 0 7803 1847 1 (IEEE, University Park, PA, USA, 1994).

50. Kewitsch, A. S. et al. Optically induced quasi-phase matching in strontium barium niobate. Applied Physics Letters 66, 1865-1867 (1995).

51. Horowitz, M., Bekker, A. & Fischer, B. Broadband second-harmonic generation in SrxBa1-xNb2O6 by spread spectrum phase matching with controllable domain gratings. Applied Physics Letters 62, 2619-21 (1993).

52. Prokhorov, A. Ferroelectric Crystals for Laser Radiation Control (Adam Hilger Series on Optics and Optoelectronics). (1990).

53. Arndt, H., Van Dung, T. & Schmidt, G. Domain-like structures in strontium barium niobate. Ferroelectrics 97, 247-54 (1989).

54. Merz, W. J. Double hysteresis loop of BaTiO3 at the Curie point. Physical Review 91, 513-517 (1953).

55. Terabe, K. et al. Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope. Applied Physics Letters 81, 2044-6 (2002).

56. Lehnen, P., Kleemann, W., Woike, T. & Pankrath, R. Ferroelectric nanodomains in the uniaxial relaxor system Sr_0.61-xBa_0.39Nb_2O_6:Ce_x^3+. Physical Review B 64, 224109 (2001).

57. Kalinin, S. V. & Bonnell, D. A. Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces. Physical Review B (Condensed Matter and Materials Physics) 65, 125408-1 (2002).

58. Gladkii, V. V., Kirikov, V. A., Volk, T. R. & Ivleva, L. I. The kinetic characteristics of polarization of relaxor ferroelectrics. Journal of Experimental and Theoretical Physics 93, 596-603 (2001).

59. Granzow, T. et al. Influence of pinning effects on the ferroelectric hysteresis in cerium-doped Sr_0.61Ba_0.39Nb_2O_6. Physical Review B 63, 174101 (2001).

69

60. Granzow, T. et al. Evidence of random electric fields in the relaxor-ferroelectric Sr0.61Ba0.39Nb2O6. Europhysics Letters 57, 597-603 (2002).

61. Fatuzzo, E. Theoretical consideration on the switching transient in ferroelectrics. Physical Review 127, 1999-2005 (15).

62. Granzow, T. et al. Local electric-field-driven repoling reflected in the ferroelectric polarization of Ce-doped Sr0.61Ba0.39Nb2O6. Applied Physics Letters 80, 470-2 (2002).

63. Tagantsev, A. K. in 8th European Meeting on Ferroelectricity, 4-8 July 1995 Ferroelectrics 79-88 (Gordon & Breach, Nijmegen, Netherlands, 1996).

64. Bernstein, S. D., Wong, T. Y., Kisler, Y. & Tustison, R. W. Fatigue of ferroelectric PbZrxTiyO3 capacitors with Ru and RuOx electrodes. Journal of Materials Research 8, 12-13 (1993).

65. Al-Shareef, H. N., Kingon, A. I., Chen, X., Bellur, K. R. & Auciello, O. Contribution of electrodes and microstructures to the electrical properties of Pb(Zr0.53Ti0.47)O3 thin film capacitors. Journal of Materials Research 9, 2968-75 (1994).

66. Al-Shareef, H. N., Bellur, K. R., Auciello, O. & Kingon, A. I. in Fifth International Symposium on Integrated Ferroelectrics, 19-21 April 1993 Integrated Ferroelectrics 185-96 (Colorado Springs, CO, USA, 1994).

67. Nakamura, T., Nakao, Y., Kamisawa, A. & Takasu, H. Preparation of Pb(Zr,Ti)O3 thin films on Ir and IrO2 electrodes. Japanese Journal of Applied Physics, Part 1: Regular Papers & Short Notes & Review Papers 33, 5207-5210 (1994).

68. Stolichnov, I., Tagantsev, A., Setter, N., Cross, J. S. & Tsukada, M. Top-interface-controlled switching and fatigue endurance of (Pb,La)(Zr,Ti)O3 ferroelectric capacitors. Applied Physics Letters 74, 3552-4 (1999).

69. Schirmer, O. F., Thiemann, O. & Wohlecke, M. Defects in LiNbO3--I. experimental aspects. Journal of Physics and Chemistry of Solids 52, 185-200 (1991).

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70

Chapter 3

Piezoresponse across Single Domain Wall

3.1 Introduction

Ferroelectric materials possess a spontaneous electrical polarization even in the

absence of an external electric field. This polarization is however, by accepted definition,

switchable with an external electric field. 1 The variation of static material properties

across a domain wall in a ferroelectric is a fundamental problem of interest. Ferroelectric

domain wall is a region where the spontaneous polarization transitions from one direction

to another. It implies that the wall is a region of spontaneous polarization gradient, which

in turn may lead to a change of static properties such as strain and dielectric response

within the domain wall region. The 180° domain wall thickness in a ferroelectric is

typically a few lattice units wide, as determined both from first principles theory 2 and

transmission electron microscopy experiments. 3,4. Hence, property changes across the

walls, if any expected, will be on the same length scale. However, a number of recent

studies across antiparallel (180°) domain walls in ferroelectrics lithium niobate and

lithium tantalate have shown local strain,5 optical index contrast, 6 and changes in

electromechanical response 7 across antiparallel domain walls over length scales of ~50

µm or more. Besides the unexpected width of these effects, the very fact that

centrosymmetric properties such as refractive index change across a wall (that separates

two domains related by inversion symmetry) is rather unexpected and surprising. In

71

recent years, these effects have been shown to be extrinsic in origin, arising from non-

stoichiometric defects within the crystal that form defect complexes that are in different

energy states across a wall. 8 These in turn, result in order of magnitude changes in

coercive field, internal fields, and other bulk properties of the ferroelectric.8-10

How do we study such extrinsic effects across domain walls? Many techniques

such as etching, 11-13 surface decoration, 14-16 transmission electron microscope (TEM), 3,4

optical microscopy,17,18 x-ray synchrotron19,20 and so on have been extensively performed

to study these properties across the domain wall region. Among these techniques, etching,

surface decoration and optical microscope cannot provide high spatial resolution. TEM

does give high spatial resolution; however, the preparation of sample is rather very

challenging and can result in artifacts of its own.

In last decade, a wide range of scanning probe microscopy (SPM) techniques

have become popular for measuring electrical, electronic, magnetic, optical, mechanical,

electromechanical, thermal and topographic properties at the nanoscale.21-24 These

techniques undoubtedly brought the studies of ferroelectric domain walls to the fore. 25 In

particular, piezoelectric force microscopy (PFM) has been used extensively to study

ferroelectric domains. Recent work by Scrymgeour and Gopalan 7 indicates observed

changes in PFM response across a wall in lithium niobate, as well as wide regions of

contrast across the wall (order of 100nm). Observations such as these bring about their

own challenges; such as how to quantitatively interpret the experimental data and what

information we can get from these SPM measurements. What is the resolution of the

PFM technique and how is it related to the intrinsic width of the ferroelectric wall? Can

72

we obtain the intrinsic domain wall width in the ferroelectric materials from the PFM

measurement?

In this chapter, we are going to present both detailed experimental and theoretical

investigation of piezoelectric response across the single 180° ferroelectric domain wall.

The work will focus on 180° domain walls in three well-known ferroelectrics, namely,

lithium niobate, lithium tantalate and strontium barium niobate (Sr0.61Ba0.39Nb2O6:

SBN:61) single crystals. The bulk properties of these materials have been well studied.26-

30 Although they are all uniaxial crystals, their point group symmetry is different (4mm

for SBN:61 and 3m for both lithium niobate and tantalate). Further the values of their

dielectric and piezoelectric tensor coefficients are very different. The impact of these on

the piezoresponse force microscopy response is systematically explored in this chapter

through experiments and numerical simulation.

3.2 Overview of Piezoelectric Force Microscopy (PFM)

The first SPM technique was scanning tunneling microscope (STM) invented in

1982 by Binnig, Rohrer and Gerber.31 In 1983, the silicon (111)-(7X7) reconstruction

was imaged in real space for the first time,32,33 and a new field (SPM or scanning probe

microscopy) was born. The next year, an extension technique of STM, namely, the

atomic force microscopy (AFM) was born. In contact mode AFM, the tip is kept in

contact with the sample surface under a constant force. If the sample surface has

topographic variations, the feedback loop in AFM will try to accommodate this variation

to maintain the constant force (constant deflection in quadrant photodetector), thus the

73

AFM tip follows the variation of the sample surface and scans. In the AFM system, the

detection system consists of a collimated laser beam and a sensitive quadrant

photodetector (Figure 3-1). The laser beam is focused on the cantilever of the AFM

probe and then is reflected back to the quadrant photodetector whose photocurrents are

fed into a differential amplifier. A minute deflection of the cantilever of the AFM probe

would cause one section of photodetector to collect more light than the others, and the

output of the differential amplifier, which is proportional to the deflection of the lever, is

used to image the forces across a sample. AFM responds to all electrons, including core

electrons, while STM is sensitive to the most loosely bonded electrons with energy at the

Fermi level. Theoretically, AFM should be able to achieve even greater spatial resolution

than STM. Today, due to better-fabricated small tip radius and the more sensitive photo-

detection scheme of the AFM, experiments showed that AFM image reveal finer

structural details than simultaneously recorded STM images. The spatial resolution of

AFM can be of the order of ~10pm, which incredibly is at least an order of magnitude

smaller than an atom!33,34,35 Initially, AFM was developed as a tool that is sensitive to

strong short-range repulsive forces. It was almost immediately realized that AFM can be

extended to map forces of different types, for instance, magnetic force, electrostatic force

or chemical interactions.36 Piezoelectric force microscopy (PFM) is one type of scanning

probe technique in which a modulated oscillating voltage is applied to the sample through

the tip in a contact AFM configuration, and the first harmonic oscillation of the cantilever

is detected by a lock-in technique. This technique has been widely performed to study

domain dynamics in ferroelectrics. Polarization direction mapping, polarization switching,

ferroelectric fatigue, phase transitions, etc. have all been demonstrated. 7,22,37-41

74

Though PFM has been widely used to study the materials, the origin and the

contrast formation mechanism of the PFM is still in debate.42-48 As indicated by its name,

piezoresponse force microscopy, one presumes that the origin of the domain contrast by

this method arises from piezoelectric deformation due to the converse piezoelectric

effect.41 When an external electric field is applied onto a piezoelectric material, it induces

a strain in the material. Thus the surface of the piezoelectric material distorts. In a contact

AFM system, the tip is expected to follow this deformation of the surface. The vertical

PFM (bending mode) detects the displacement of sample surface perpendicular to the

sample surface. The lateral PFM signal originates from in-plane deformation of the

surface. Thus PFM is believed to be able to detect both in-plane polarization and out-of-

plane polarization in ferroelectrics. The displacement detection sensitivity of ~pm arises

because of the applied AC oscillating voltage on the tip to which one can lock-in this

displacement using a lock-in amplifier.

Figure 3-1: The detection system in an Atomtic Force Microscope (AFM).

75

Lithium niobate, lithium tantalate, and strontium barium niobate are ferroelectric

materials with 180° domain wall structure. When there is external applied field, the

induced strain due to converse piezoelectric effect in tensor form can be written as:

Where ijε are the strain tensor components, kijd are components of the

piezoelectric constant or piezoelectric modulus, and kE are the components of the

external applied electrical field. The independent nonzero components in piezoelectric

constant are determined by the crystal structure symmetry.

For lithium niobate and lithium tantalate, (point group 3m), the piezoelectric

constant for lithium niobate has 4 independent nonzero coefficients. The converse

piezoelectric effect can be written in a matrix form as:

For strontium barium niobate, (point group 4mm), there are only 3 independent

nonzero piezoelectric coefficient. The converse piezoelectric effect can be written in

matrix form as:

kkijij Ed=ε Eq. 3.1

−

−

=

3

2

1

22

15

15

33

3122

3122

6

5

4

3

2

1

002

00

00

00

0

0

E

E

E

d

d

d

d

dd

dd

εεεεεε

Eq. 3.2

=

3

2

1

15

15

33

31

31

6

5

4

3

2

1

000

00

00

00

00

00

E

E

E

d

d

d

d

d

εεεεεε

Eq. 3.3

76

The values of these coefficients for the relevant materials are given in Table 3-1 .

Now let us use antiparallel ferroelectric domains as an example to illustrate the

principle of PFM. Figure 3-2 illustrates the piezoresponse across the single 180° domain

wall when the PFM probe scans across the lithium niobate domain wall region from +c

surface to –c surface. The applied oscillating voltage on the tip has the following form:

Table 3-1: The piezoelectric strain coefficients of lithium niobate, lithium tantalate and strontium barium niobate

Material Piezoelectric Coefficient Value (⋅10-12C/N)

d15 69.2

d22 20.8

d31 -0.85

Lithium Niobate (LiNbO3)

d33 6.0

d15 26.4

d22 7.5

d31 -3.0

Lithium Tantalate (LiTaO3)

d33 5.7

d15 31

d31 -30

Strontium Barium Niobate

(SBN:60: Sr0.60Ba0.4Nb2O6)

d33 130

( )vacdctip tVVV φω ++= cos Eq. 3.4

77

The induced deformation (displacement) of the surface of lithium niobate can be

written as:

The bold lettering u, for example, indicates that it is a vector with three

displacement components (ux, uy, uz). 0u is the static displacement due to dc applied

voltage Vdc across the sample; Vac is the peak voltage of the ac voltage applied on the tip

and d is the piezoelectric constant. To first order, the deformation of the surface has the

same frequency as the driving voltage. For +c surface of a domain in lithium niobate, the

application of a positive bias tip (electric field E pointing into the crystal and antiparallel

to the ferroelectric polarization Ps), results in a contraction of the sample surface through

the d33 coefficient; thus it is π out-of-phase with the driving voltage. However, for the –c

surface of a domain in lithium niobate, the application of a positive bias tip results in a

expansion of the surface through the d33 coefficient; thus it is in-phase with the driving

voltage (Figure 3-2(a)). The amplitude of piezoelectric response on both +c and –c should

be equal and the phase changes 180° for a purely electromechanical response from two

180° domains related by inversion symmetry (Figure 3-2 (c), (d)). Differences, if any,

may arise from defects, nonstoichiometry, and other extrinsic effects that may not follow

the domain symmetry.

( ) )cos(cos0 φωφω +∗+∗=++= tVdVdt acdcAuu Eq. 3.5

78

Besides the piezoelectric deformation mechanism, the contrast mechanism of

PFM can also have contributions due to the electrostatic interactions between the charged

tip and the electric fields arising from surface polarization charges.44,48 The presence of

electrostatic forces was supported by the observed signals on the non-piezoelectric

surface such as silicon dioxide.48 Similarly, an undesired cantilever buckling induced by

the capacitive force interaction was found in PZT film.48 The temperature dependence of

Figure 3-2: Schematic piezoresponse across the single 180° domain wall in lithium niobate, lithium tantalate and strontium barium niobate crystal. (a) the surface displacement (solid line) due to the electric field across the domain wall displayed in (e). The dot line is original surface plane; (b) the piezoresponse, both X and Y signal, across the domain wall. X is the product of amplitude (R) and the sine of the phase, θ, and Y is the product of amplitude and cosine of the phase; (c) the piezoresponse, both X signal and Y signal, on both +c and –c surface plotted in vector XY plane. (d) the amplitude and phase of the piezoresponse across the domain wall; (e) schematic domain structure and electrical field.

79

the domain contrast on a triglycine sulfate (TGS) ferroelectric sample was found to be

contradictory to the expected trend of the piezoelectric coefficient, and instead, similar to

that of the spontaneous polarization. 44 The large lateral force in lateral PFM signal on

periodic poled lithium niobate (PPLN) sample was also measured. Therefore, the

electrostatic force interaction between the metallic coated AFM probe and sample was

considered to be a significant factor to the domain contrast in PFM. Hence some authors

[for instance,48] have referred to PFM as “dynamic contact mode electrostatic force

microscopy (DC-EFM)”. The first harmonic tip vibration due to the electrostatic

interaction between the sample surface and the PFM probe in PFM (or DC-EFM) can be

illustrated by the formalism developed by Hong 48 as:

where uω is the tip vibration signal at the frequency ω, which is the frequency of

applied voltage on the tip. Γ is (½) (∂C/∂z), and C is the electric capacitance between the

tip-cantilever system and sample, klever is the spring constant of the cantilever of the probe,

Vc is the contact potential difference between the tip and sample surface right under the

tip apex; Vdc is the DC bias voltage applied on the sample; Vacsinωt is the ac voltage

applied to the tip.

In general, the electrostatic force acting in PFM imaging can be separated into

two regimes:49

<>

=Φ

−Γ=

Φ=−Γ=

cdc

cdc

dcclever

acdcclever

VVif

VVif

VVVk

A

tAtVVVk

u

,180

,0

)(2

sincossin)(

1

ω

ω

ωωω ωω

Eq. 3.6

80

1). the local electrostatic force acting on the tip.

2). the non-local electrostatic force acting cantilever

where elΓ and nlΓ are the capacitance gradients between the tip-surface and

cantilever-surface system, respectively.

Therefore, by considering both electrostatic contributions and converse

piezoelectric contribution in PFM, the final PFM measured signal includes three main

contributions: 1) pure electromechanical contribution; 2) local electrostatic contribution

acting on the tip; and 3) non-local electrostatic contribution acting on the cantilever. The

displacement experienced on the probe tip in PFM can be written as:

elac uuuu ++= 0

where 0u and acu are described in Eq. 3.5. elu is the displacement due to both

local electrostatic force exerted on tip and non-local electrostatic force exerted on

cantilever. Both of them are described in Eq. 3.7 and Eq. 3.8, respectively. All these three

contributions are functions of operating frequency. The electromechanical contribution is

related to the pure mechanical properties of the sample. Electrostatic contribution is

determined by tip-surface capacitance, tip-surface contact stiffness as well as the

mechanical properties of the AFM probe. To fully explore the PFM techniques for

ferroelectric domain imaging and quantitatively measure the properties across the

ferroelectic domain wall in nanoscale, the electromechanical contribution in a PFM

tVVk

tVVVVFtAu dcclever

eldcloctipaclocelel ωωωω sin)(sin)(sin, −

Γ=−−== Eq. 3.7

tVVk

tVVVVFtAu dcclever

nldcavtipacnlnlnl ωωωω sin)(sin)(sin, −

Γ=−−== Eq. 3.8

81

measured signal is of interest to us, and it can be modeled and numerically calculated

using finite element modeling (FEM).

3.3 Overview of Finite element modeling - the numerical method

To find out the surface deformation induced by the PFM probe due to pure

converse piezoelectric effect, it needs to solve the coupling Eq. 3.9:

Where E and D are electric field and electrical displacement; c and e are elastic

stiffness constant and piezoelectric stress constant, respectively; χ and σ are strain and

stress. In this thesis, Eq. 3.9 was solved in a decoupled way as employed in Ref. [7]. First

the electric field distribution inside the ferroelectric sample was calculated; then the

deformation of the sample was calculated under the field calculated in the first step. This

method was justified for the rigid dielectric system.50-52 To calculate the 3-dimensional

deformation of the sample, finite element method was used.

Finite Element modeling (FEM) was first developed in 1943 by R. Courant, who

utilized the Ritz method of numerical analysis and minimization of variational calculus to

obtain approximate solutions to vibration systems.53 FEM consists of a computer model

of a material or design that is stressed and analyzed for specific results. There are

generally two types of analysis that are used: 2-D modeling and 3-D modeling. In the

model, FEM uses a complex system of points called nodes which makes a grid called a

mesh, which is then programmed to contain the material and structural properties which

EeD

eEcT

E

εχχσ

+=−=

Eq. 3.9

82

define how the structure will react to certain loading conditions. Nodes are assigned with

a certain density throughout the material depending on the anticipated load levels of a

particular area. Regions which receive abrupt changing loads usually have a higher node

density than those which experience constant or no load. For instance, in the FEM

simulation in this study, the mesh area right under the AFM tip is very dense because of

the field dies away very fast (~100nm), whereas the mesh area far away from the tip is

very coarse. The mesh acts like a spider web in which each node connects to adjacent

node and constructs a continuous solid, which satisfy all the boundary conditions.

The piezoelectric response across the domain wall in lithium niobate, lithium

tantalate and strontium niobate under an electric field applied through AFM tip was

modeled and calculated using the commercial software ANSYS, which utilizes FEM to

solve many types of problems. The parameters used for ANSYS simulations are elastic

stiffness, piezoelectric stress constants and dielectric constant, which are listed in

Table 3-2. The relationship between the piezoelectric stress constants and piezoelectric

strain constants (Table 3-1) is:

For the 3D piezoelectric model in ANSYS, the tetrahedral coupled-field solid

element with 20 nodes was used. Each node has 4 degrees of freedom: displacement

vector (Ux, Uy, Uz) and voltage (V). The boundary conditions are that the bottom surface

is clamped and electrically grounded (Ux=Uy=Uz=0 and V=0), and the top surface right

under the AFM tip is free to vibrate along with the potential induced by the electrically

Eqpiqip cde = Eq. 3.10

83

charged AFM probe tip. Thus, the piezoelectric response across the domain wall under an

AFM tip can be extracted. The mesh right under the tip was fine enough to accommodate

the sharp change of the potential distribution.

To solve the surface deformation in FEM simulation, the essential part is to find

out the potential distribution and electrical field distribution inside the dielectric

specimen induced by the charged AFM tip.

3.3.1 Field distribution in PFM system

In PFM system, the field (electrical potential and electrical field) distribution in

dielectric specimen is essential for quantitative analysis of PFM signal due to converse

piezoelectric effect. As mentioned in previous section 3.2, the PFM system contains a

metallic-coated AFM probe with an oscillating voltage. Through this conductive AFM tip

Table 3-2: Elastic, piezoelectric and dielectric constants of lithium niobate, lithium tantalate and strontium barium niobate.

LiNbO3 LiTaO3 Sr0.60Ba0.4Nb2O6

Elastic stiffness

1011Nm-2

c11E=2.030

c12E=0.573

c13E=0.752

c14E=0.085

c33E=2.424

c44E=0.595

c66E=0.728

c11E=2.298

c12E=0.440

c13E=0.812

c14E=-0.104

c33E=2.798

c44E=0.968

c66E=0.929

c11E=2.47

c12E=0.991

c13E=0.756

c33E=1.32

c44E=0.646

c66E=0.694

Piezoelectric stress constants Cm-2

e15=3.76 e22=2.43 e31=0.23 e33=1.33

e15=2.72 e22=1.67 e31=-0.38 e33=1.09

e15=5.19 e31=-1.89 e33=9.81

Dielectric constants ε11T=85.2

ε33T=28.7

ε11T=53.6

ε33T=43.4

ε11T=470

ε33T=880

84

and bottom electrode, the fields are applied across the piezoelectric sample. Normally the

tip of AFM probe is made of heavily doped silicon with height around ~10 to 20µm long.

Then the metals are coated on the surface of the silicon tip surface. The radius of the

metal-coated tip varies from 15nm to 100nm (Figure 3-3 ).

We now explore two different models for the tip-sample surface interaction: (a)

the sphere-plane model, and the disc-plane model, where the sphere or the disc refers the

tip shape and the plane refers to the sample surface. In both models, there are three

electromagnetic boundary conditions to satisfy:

1) equal potential on the surface of the AFM tip and this potential should be equal to

the electrical potential applied on the tip;

2) the tangential component of electric field E is continuous across the interface

between the dielectric medium (in this thesis, it is air) and the dielectric

specimen;

3) the normal component of electric displacement D is continuous across the

interface between the dielectric medium and dielectric specimen in PFM.

Figure 3-3: An SEM image of an example of the typical metal coated AFM tip. (CSC37/Ti-Pt AFM probe from MikroMasch)

85

Sphere-plane model: For simplicity, normally in PFM system, the probe and

sample can be treated as a sphere-conductor surface sitting on a semi-infinite perfect

dielectric surface (Figure 3-4).

To satisfy these above three boundary conditions and by using image charge

method54 and after considering the anisotropy of the dielectric material, 55 the electrical

potential distribution inside the uniaxial anisotropic dielectric in both Cartesian and

cylindrical coordinate system can be written as (derivation seen in Appendix 1):

where

∑=

−++++

+=>

02

2220

1

)()1(4

2)0,,(

i

i

i

rdRz

yx

Q

kzyxV

γ

πε

∑=

−+++

+=>

02

220

1

)()1(4

2)0,(

i

i

i

rdRz

r

Q

kzrV

γ

πε

Eq. 3.11

r

z

zr

ii

iii

ii

ii

i

r

RVQ

k

k

kb

Qk

kQ

rdR

RzdRr

QrdR

RbQ

rdR

RQ

εεη

πεεε

=

==

=+−=

+=′′

−+=−+=

−+=′

−+−=

++

++

+

0

4

1

11

2

)(2)(

)(2)(2

0

00

11

2

11

1

Eq. 3.12

86

where V is applied voltage on the metal-coated AFM tip; d is the distance between

the tip and top surface of the dielectric; R is the AFM tip radius; εr and εz are in-plane

(normal to z –axis) relative dielectric constant and relative dielectric constant along z-

axis direction. For a uniaxial crystal, εr equals to εx or εy.

From the Eq. 3.11, the electric field distribution in the dielectric in both Cartesian

and cylindrical coordinate system can be written as:

where Ex, Ey and Ez are the components of E field along x, y and z direction,

respectively, in a Cartesian coordinate system. Er and Ez are in-plane and out-of-plane

components of E field along r and z direction in a cylindrical coordinate system. For the

∑=

−+++++

=0 2

32

2220

)(

.

)1(4

2),,(

i

i

ix

rdRz

yx

Qx

kzyxE

γ

πε

∑=

−+++++

=0 2

32

2220

)(

.

)1(4

2),,(

i

i

iy

rdRz

yx

Qy

kzyxE

γ

πε

∑=

−++++

−++

+=

0 23

2

2220

)(

)(1

)1(4

2),,(

i

i

ii

z

rdRz

yx

QrdRz

kzyxE

γ

γγπε

Eq. 3.13

∑=

−++++

=0 2

32

220

)(

.

)1(4

2),(

i

i

ir

rdRz

r

Qr

kzrE

γ

πε

∑=

−+++

−++

+=

0 23

2

220

)(

)(1

)1(4

2),(

i

i

ii

z

rdRz

r

QrdRz

kzrE

γ

γγπε

Eq. 3.14

87

uniaxial dielectrics, the in-plane properties are isotropic. Ex and Ey are two components of

Er along x and y directions, respectively.

The Eq. 3.11 shows that the potential distribution inside the dielectric specimen in

a PFM system really depends on the distance (d) between the AFM tip and top surface of

the dielectric. For instance, for specimen with relative dielectric constants εr=85.2 and

εz=28.7 under the AFM tip with 5V applied. Figure 3-5 shows a number of quantities:

the total charge stored on the tip, the maximum electric potential and electrical fields

inside the specimen. These quantities are plotted as a function of two quantities: different

tip radius size (R) and different distances (d) between the tip and the top surface of

specimen. As can be seen, the total charge stored in a PFM system is related to the tip

size, but relatively independent of the distance between the tip and the top surface of the

specimen. However, the maximum potential field and electrical fields inside the

specimen are functions of both the tip size and the distance between the tip apex and the

top surface of the specimen.

Figure 3-4: Simplified sphere model of an AFM tip over an anisotropic material in PFM system.

88

(a) (b)

(c) (d)

(e) (f)

Figure 3-5: The relationship between field inside the specimen and the distance, d, between the tip and top surface of the specimen and tip radius for a dielectric with dielectric constants εr=85.2 and εz=28.7. The applied voltage on the tip is 5V. (a) The total charge stored in the capacitor system of tip and the dielectric sample, which is equal to the total charge induced on the surface of the dielectric, whereas the sign of induced charge on the sample surface is opposite to the charge on the surface of the tip; (b) the maximum potential inside the dielectrics vs. the distance d; (c) the maximum electric component Ez vs. the distance d for different size tip; (d) the maximum electric component Er vs. the distance d for different tip size. (e) the maximum fields for a 50nm spherical tip, which is in contact (d=0nm); (e) the maximum fields fro a 50nm spherical tip, which is not in contact and d=0.01nm.

89

The special case is that when the tip is in contact with the specimen (d=0nm). In

this case, the maximum electrical potential inside the specimen is the same as the

electrical potential applied to the tip, thus the potential becomes independent of the tip

radius (Figure 3-5 (e)). However, the maximum electrical fields decrease as the tip size

increases. In the AFM contact mode, there is ambiguity in the term “contact”. So far,

there is no clear experimental proof that “contact” means that the distance d between the

tip and surface of specimen is 0nm. Normally it is assumed that the distance d between

the tip and surface of the specimen is less than 1nm. Figure 3-5 (b)-(d) show that the

maximum electrical potential and electrical fields inside the dielectric specimen drop

down dramatically as the charged AFM tip moves away from the dielectric surface from

the “in contact” state. This drop is faster with depth z for smaller tip sizes. However,

when the distance d, between the tip and sample surface, is fixed, the maximum potential

inside the dielectric sample increases and maximum electrical fields decrease as the AFM

tip radius increases (Figure 3-5 (f)).

The field distributions inside the dielectric (εr=85.2 and εz=28.7) under a

spherical tip with radius of 50nm in contact (d=0nm) are plotted in Figure 3-6, in which

the tip is located at (0, 0, 0). As can be seen, the maximum potential and maximum

electric fields inside the dielectric are located at the very point that is right under the tip

apex with coordinates (0, 0, 0).

90

In the sphere model discussed above, there are several assumptions of ideality.

The geometry of the tip is ideally simplified as a hollow sphere, which is in contact with

dielectric sample at only one single point. Therefore, the field inside the sample right

under the tip is tightly localized. The electrical potential field distribution inside the

dielectric sample decreases rapidly both in lateral direction (in plane) and in depth

direction (Figure 3-7 ).

(a) (b)

(c) (d)

Figure 3-6: The field distribution inside the dielectric (εr=85.2 and εz=28.7), which is in contact (d=0nm) with a sphere tip with radius of 50nm. The voltage applied on the tip is 5V. (a) potential in z=0 plane; (b) potential in depth plane. (c) Er in depth plane; (d) Ez in depth plane. The maximum electric fields are 7.53×108 V/m and 4.35×109 V/m for Er and Ez, respectively.

91

Therefore, the resultant electrical fields inside the dielectric sample are extremely

high (Er= 7.53×108 V/m and Ez =4.35×109 V/m for a dielectric, with εr=85.2 and εz=28.7,

under a tip with a radius of 50nm and 5V on). These field values are much higher than

the coercive fields of lithium niobate. However, no domain switching in a ferroelectric

that is in contact with the AFM tip with such a low applied voltage has ever been

reported. The reason for not observing domain reversal with such low voltages may be

that the volume of the sample over which the field is above the coercive field (~20nm in

radius) may be smaller than the critical volume for a stable nucleation of a domain under

the tip, which was theoretically predicted to be around ~20nm according to Ref. [52,56.

The second assumption in the sphere-plane model is that there is no extra charge other

than the induced charge on the dielectric surface. However, for lithium niobate, lithium

tantalate and other ferroelectric materials, there is always an argument about under

(a) (b)

Figure 3-7: The dependence of the width of the potential and electrical field (Ez) along both in-plane and in depth direction on the spherical tip size. (a) full width (the distance between two points at which the potential or electric field reaches only 10% of its maximum value) of the potential and electrical field inside lithium niobate under a spherical tip with 5V on; (b) the full width half maximum (FWHM) of the potential and electrical field inside lithium niobate under a spherical tip with 5V on.

92

compensated or over compensated ferroelectric surfaces, [57,58] which may modify the

field distribution and lower the effective fields under the tip.

Disc-plane model: In reality, the AFM coated tip can be blunted soon. Normally,

after a few lines of scan, the very end of the AFM tip can be blunted into a flat plane

(Figure 3-25 (a)). In this case, the tip is in contact with the ferroelectric surface over a

finite area. Also, in the case that the tip indents into the ferroelectric surface,47 the tip is

also in contact with the ferroelectric over a finite area. In both these cases, the tip can be

simplified as a metal disc with a radius R (Figure 3-8 ), which is in contact with the

sample. In this model, the potential distribution inside the specimen can only be solved

numerically by taking care of the three boundary conditions mentioned earlier in this

section. For a 50nm radius flat tip with applied 5V voltage on, the potential field

distribution for lithium niobate is plotted in Figure 3-9.

The conical part the AFM tip contribution in a spherical tip can be modeled using

the line charge model developed by Hao et. al..59 The conical part of AFM tip

contribution in a disc tip was modeled using ANSYS. The conical part in this thesis was

simplified as a 20µm-long metallic coated silicon with a full cone angle of 30°.

Figure 3-8: Schematic of the simplified disc model.

93

3.3.2 Surface deformation modeled using FEM

By applying the potential (Eq. 3.11 and Eq. 3.12 for spherical tip or numerically

solved for disc tip using ANSYS) as the boundary condition for the piezoelectric

coupling simulation using ANSYS, the deformation of the ferroelectric resulting from the

AFM tip can be simulated. Figure 3-10 shows the surface deformation of lithium niobate

under a 50nm-radius spherical tip and a 50nm-radius disc tip with 5V applied. The

(a) (b)

(c) (d)

Figure 3-9: The potential distribution inside z-cut lithium niobate under a flat 50nm radius AFM tip with 5V applied voltage on. (a) The potential distribution on the z=0nm plane; (b) The potential distribution in depth plane; (c) Er distribution in depth plane; (d) Ez distribution in depth plane.

94

domain wall is a y-wall (mirror plane in lithium niobate structure) located at x=0. The

AFM tip is located at (0, 0, 0), right on the domain wall. As we move the tip location

across the domain wall, the piezoelectric response across the domain wall can be obtained.

One can study this response as a function of the distance between the tip and the

specimen surface, as well as the tip radius.

Figure 3-11 (a) and (b) show the examples of the piezoelectric response across the

single 180° domain wall in lithium niobate for a 50nm radius spherical tip and a 50nm-

radius disc tip with 5V applied, respectively. The distance between the tip and the

specimen surface is 0nm (no gap). The surface in left region (x<0) under the tip is +z

surface and the surface in right region (x>0) under the tip is –z surface. The domain wall

is located at x=0. As can be seen, for both the sphere and disc-type of tip, the

displacement Uz changes from being negative on +z surface (left region) to being positive

(a) (b) (c)

(d) (e) (f)

Figure 3-10: The deformation on z=0nm plane of lithium niobate under a 50nm radius AFM tip with 5V applied voltage on. (a)-(c) for sphere tip; (d)-(f) for disc tip.

95

on –z surface (right region), which means that +z surface contracts and –z surface

expands under the 5V applied. Hence, the +z surface is out-of-phase (180°) to the driving

voltage in PFM and –z surface is in-phase (0°) to the driving voltage in PFM system. The

amplitude of Uz reaches minimum while the tip is sitting right on top of the domain wall.

The amplitude of the displacement Ux and Uy are symmetrical across the domain wall,

however, the sign of Uy changes across the domain wall. It is worthy pointed out that

even though the tip shapes are different for sphere and disc tips, the shapes of the induced

surface deformation in the ferroelectric, and thus, the displacements Ux, Uy and Uz, are

similar. The amplitudes of the Uz are the same for both sphere tip and disc tip.

Due to the surface deformation, in vertical PFM, the tip follows the out-of-plane

surface deformation component (displacement Uz). Therefore, the amplitude of

displacement Uz across the domain wall gives the vertical PFM signal (Figure 3-11 (c)

and (d)). The 3D displacements (Ux, Uy and Uz) also cause the tip not only experience the

out-of-plane displacement, but also the in-plane displacement, which gives the lateral

PFM signal. While the tip scans, the AFM tip experiences the slope of the surface normal

to tip beam. The deformed surface oscillates at the same frequency as that of the driving

voltage applied on the tip. By processing the FEM, the slope of the deformation surface

normal to tip beam arm can be obtained, which is proportional to the 0°-lateral PFM

signal (Figure 3-11 (e) and (f)). The slope of the deformed surface depends on both tip

geometry and size.

96

(a) (b)

(c) (d)

(e) (f)

Figure 3-11: The piezoelectric vertical and lateral response across the domain wall (located at 0) in lithium niobate for a tip with radius of 50nm, which is in contact (d=0nm) with lithium niobate. The driving voltage on the tip is 5V. The spontaneous polarization in the left region points up, which means +z surface, whereas the spontaneous polarization in the right region points down and the surface under the tip is –z surface. (a) displacement with a sphere tip; (b) displacement with a disc tip; (c) vertical PFM signal with a sphere tip; (d) vertical PFM signal with a disc tip; (e) slope of the deformed surface, which is proportional to 0°-lateral PFM signal with a sphere tip; (f) slope of the deformed surface with a disc tip.

97

3.3.3 Validation of FE modeling

To check the FEM modeling results, the following simulations were performed

and referenced to bulk LiNbO3 properties.

(1) Single crystal, z-cut, single domain of lithium niobate (no domain walls) under

a static uniform electric field across the z-axis: The displacement Uz~30.2±2.5pm under a

voltage of V=5volts; this corresponds to a deff ~Uz/V=6.0±0.5pm/V, which agrees well

with the bulk d33=6 pm/V given in Table 3-1, as expected.

(2) Piezoelectric response of a single domain lithium niobate in contact with a

spherical tip simulated with different meshings, e.g. from coarse (~1000nodes/µm3) to

very fine (~6000nodes/µm3), was performed. The meshing was adjusted until the result

converged and became independent of the fineness of the meshing system (Figure 3-12).

It was found that the displacement values at the point right under the tip contact point

converged to 53.5±5pm for a tip with 5V, no matter what the geometry of the tip was.

This corresponds to a deff ~10.7±1.0pm/V, which is higher than d33. The difference from

case (1) is likely due to sharp displacement right under the tip to accommodate the sharp

change of the electric fields right under the tip.

(3) Then a domain wall was added into the system, and displacement measured

far away, for instance, 500nm for a tip with radius of 50nm, from the domain wall. The

simulated displacement Uz was found to be the same (53.5±5pm) which is physically

reasonable since the tip “sees” only single domain when the tip is far away from the

domain wall.

98

3.4 PFM imaging across the domain wall

PFM imaging consists of three main contributions as discussed in section 3.2. The

electromechanical contribution contains the mechanical properties of the materials.

However, both electrotatic and electromechanical contributions in a measured PFM

signal are function of the measured frequency. To extract the electromechanical response

from the measured PFM signal and then extract the material properties necessitates a

careful interpretation of the PFM signal

(a) (b) (c)

(d) (e) (f)

Figure 3-12: The piezoelectric response of the single domain in lithium niobate. (a)-(c) under the uniform electric field. The applied voltage is 5V; (d)-(f) under a 50nm sphere tip which is in contact at (0, 0, 0). The applied voltage on the tip is 5V.

99

3.4.1 Background signal and frequency dependence of PFM imaging

The complex PFM signal can be measured either as amplitude (R) and phase (θ)

or as x signal and y signal from a lock-in amplifier. The relationship between the output

set (x and y) and the output set (amplitude R and phase θ) is as follows:

In practice, the sampling rate to measure the output x and y from the lock-in

amplifier is faster than to measure the output of R and θ. On the other hand, during the

measurement of phase, θ, one observes sudden jumps, for instance, from 180° to -180°,

which are equivalent. However, during this jump, the intermediate phase values will also

sometimes be measured, which are an artifact. Thus, in the experiments to be discussed in

this chapter, all the raw measured values are x and y signals, unless otherwise stated. The

amplitude R and the phase θ of the measured PFM signal are derived from the output set

of x and y signals based on the relationships described in Eq. 3.15.

PFM signal is dependent on the frequency of the voltage applied to the tip.

Labardi et al.60 first reported such frequency dependence of the vertical PFM signal for

TGS single crystals. Normally there are lots of resonance peaks in the PFM signal as

shown in Figure 3-13 . It was found that even in non-piezoelectric materials such as silica

glass, [61] similar behavior of resonance peaks in PFM signal exists, though the origins of

these resonance peaks are, by far, not yet fully understood. However, the experimental

)cos(

sin

cos

22

22

yx

xa

yxR

Ry

Rx

+=

+=

∗=∗=

θ

θθ

Eq. 3.15

100

evidences showed that the resonance in PFM signal could be utilized to get optimal

imaging conditions for the system with weak electromechanical coupling; or for the

ferroelectric materials in the vicinity of a phase transition at small probing biases.62 As

mentioned in Section 3.2, the experimental amplitude of PFM contains the electrostatic

forces acting on the tip, three components of electromechanical displacement vector and

the non-local nonlinear response due to capacitive cantilever-surface interactions. All

these components interact with each other and result in the movement of the cantilever,

which is detected as the vertical (bending) and lateral (torsion) PFM signals in the AFM

system using a lock-in technique. It is found that all these components are dependent on

the operating frequencies. In a recent paper,63 the frequency dependent dynamic behavior

in PFM was analyzed using both modeling and experiments. An empirical approach to

restore the pure PFM signal without knowing the exact nature of the resonance in PFM

signal was also proposed in Ref. [61]. In this study, the frequency response of both non-

piezoelectric material SiO2 glass and piezoelectric material periodically poled lithium

niobate in PFM was examined. The result showed that based on the frequency dependent

behavior of PFM on both silica glass and ferroelectric material PPLN, the PFM signals

can be treated as the summation of the pure electromechanical response and a

“background” signal, which might originate from electrostatic force or non-local

nonlinear response. Even though, the approaches in these two papers [63, 61] were

different, the conclusions about the electrostatic contribution and the electromechanical

contribution in a measured PFM signal are similar. To fully utilize PFM as a quantitative

tool for local material characterization, recovering the pure electromechanical response

from the measured PFM signal is necessary. Due to the resonance peaks in PFM signal, it

101

was suggested [60] that for quantitative measurements, the frequency of the measurement

should be where there are no resonance peaks. We will look at the validity of this

assumption more carefully in this section.

The pure PFM signal across a single 180° ferroelectric domain wall has equal

amplitudes on both +c and –c surfaces of a ferroelectric material. The phase shift of the

PFM displacement of +c surface with respect to the driving voltage should be 180°,

whereas for –c surface, this phase shift should be zero (Figure 3-2). The contribution of

electrostatic forces acting on the tip, as well as the non-local nonlinear electrostatic forces

acting on the cantilever can be treated as “background” signals, which share the same

frequency as the electromechanical contribution in PFM and are then picked up by the

lock-in technique. In this way, the measured PFM signal can be thought to comprise of

two parts: 1) pure electromechanical response, d due to converse piezoelectric effect on

the ferroelectric material, and 2) background signal, backgroundd which is the sum of

responses due to electrostatic force acting on the tip and the nonlinear electrostatic force

Figure 3-13: Typical frequency response of PFM. The sample here is congruent lithium niobate.

102

acting on the cantilever. The electromechanical response of the material normally does

not share the same phase as the background signal. However, at a specific operating

frequency, these two signals can be treated as two vectors in the complex XY plane

(Figure 3-14(a)). Therefore, the amplitude of electromechanical (primary) and

electrostatic (background) components per unit applied voltage in the measured PFM

signal on both +c and –c domains can simply be written as:63

Where )( avcelecbackground VVFd −= , and elecF is the electrostatic contribution term, elF or

nlF (see details in section 3.2). acVu /+ ( acVu /− ) is the amplitude of displacement of +c

(-c) surface per unit applied voltage through the tip. In this case, we simply assume that

the electrostatic contributions (including both local and non-local components) for both

+c and –c domains are the same without exact information of the charges distribution on

both +c and –c domains. The phase delay between the pure electromechanical response

component and the electrostatic contributions to the PFM signal is ϕ. The phase delay

between the electromechanical response and the lock-in amplifier is ψ, which might

come from the external LC electronic circuit. Therefore, the maximum amplitude in each

of the domains and the phase shift θ between the +c and –c domains in a measured PFM

signal are derived as (see Appendix C for the derivation):

backgroundac

backgroundac

ddPRVu

ddPRVu

+==

+−==

−−

++

/

/ Eq. 3.16

103

Therefore, the existence of the electrostatic contribution in a measured PFM signal leads

to non-180° phase shift between the signals of +c and –c domains. In addition, the

measured amplitudes on both +c and –c domain are not equal either. However, the

relative phase shift between +c and –c domains is independent of the external electric

circuit. Thus, the deviation of the phase shift between +c and –c domains from 180°

provides a measure of the electrostatic contributions in a PFM measurement, and also

gives the basic criterion for quantitative PFM. By using this criterion, the pure

electromechanical response can be restored from the measured PFM signal.

Mathematically, the coordinate system for electromechanical response can be rotated and

translated into a new complex coordinate system (X′Y′) with respect to the coordinate

system (XY) in which the PFM signal is measured (Figure 3-14). In the new coordinate

system, the measured signals on both +c and –c domain surfaces from the lock-in.

amplifier should result in x (Rcosθ) component of these signals to be nonzero and equal

to each other, whereas y components (Rsinθ) should be zero.

22

22

22

sin2tan

cos2

cos2

dd

dd

ddddPR

ddddPR

background

background

backgroundbackground


−=

++=

−+=

−

+

ϕθ

ϕ

ϕ

Eq. 3.17

104

In the case where the electrostatic contribution is dominant, ( ddbackground >> ),

then the contrast of the PFM image will be smeared out:

In the case where the electromechanical contribution is dominant ( backgrounddd >> ),

the phase shift between +c and –c domain will be close to 180°; and the amplitude on +c

and –c domain are almost equal.

(a) (b)

Figure 3-14: (a) The schematic diagram showing the measured PFM signal on both +cand –c surface of the ferroelectric material away from the resonance frequency of the probe. The measured signal includes the pure piezoelectric response signal, which is denoted as “electromechanical” signal, and a background signal, which is due to electrostatic response and non-local nonlinear response acting on the cantilever; (b) The schematic diagram showing to restore the pure piezoelectric response from the measured PFM signal.

0

)cos1(

)cos1(

→

≈+=≈

≈−≈

−

+

θϕ

ϕ



dddPR

dddPR

Eq. 3.18

o180

)cos1(

)cos1(

→

≈+=≈

≈−≈

−

+

θ

ϕϕ

dddPR

dddPR

background

background

Eq. 3.19

105

If the phase delay ϕ between pure electromechanical response and the

electrostatic component is zero, then the phase shift between +c and –c domains will

remain 180°. However, the amplitude of PFM signal on both +c and –c domains are now

different. They can be written as:

To find out the electromechanical contribution and the frequency dependence of

the PFM in lithium niobate, the frequency spectrum of PFM was performed on a PPLN

sample. A modified PFM from the commercial AFM (ExplorerTM, ThermoMicroscopes)

along with the lock-in amplifier (Stanford Research Systems, Model SR830, 1mHz to

102kHz) were utilized. The conductive AFM probe used was Pt-Ti coated tip (NSC35

from MikroMasch) with ~40nm radius. The spring constant of the used cantilever is

~14N/m. The first typical resonant frequency of the cantilever is ~315 kHz. The tip was

tightly glued with silver paste on a piece of silica glass on the magnetic base on the AFM

head, which enables the AC voltage and DC bias to be applied on the tip. To get the

frequency response of the cantilever in contact with the PPLN sample, the external

trigger source, a function generator (HP 33210A), for the lock-in amplifier was used. The

AC output from the lock-in amplifier with amplitude of 5Vrms was applied onto the tip.

The sweep frequency from the function generator was from 1kHz to 100kHz in 100

seconds. The oscilloscope (Tetronix 340A) was used to collect the output (x signal and y

signal) from the lock-in amplifier with time constant set as ~3ms. The vertical response

of the AFM system was calibrated by using three standard gratings and a piezoelectric

o180→

+=

−=

−

+

θbackground

background

ddPR

ddPR

Eq. 3.20

106

ceramic PZT actuator. The typical frequency response of the cantilever in this PFM

system was plotted in Figure 3-15. There are a few resonances found in this region, in

which the frequency is much lower than the first harmonic frequency of the tip (~315kHz)

suggested by the manufacturer based on the geometry size of the tip.

(a)

(b)

Figure 3-15: Typical frequency dependence of PFM signal on +c surface of lithium niobate. (a) amplitude ( R); (b) phase.

107

The piezoresponse across a single domain wall in lithium niobate was performed

at several discrete frequencies on the same PPLN sample with the same tip used as in the

above PFM frequency spectrum experiment. The sensitivity of the lock-in amplifier was

500µV and the phase of the lock-in amplifier was fixed as 165.20° for each frequency.

The time constant of the lock-in was 10ms when the frequency was below 6kHz, 3ms

when the frequency was below 20kHz, and 1ms when the frequency was above 20kHz.

Both x and y signals across a single domain wall in lithium niobate were plotted in the

complex XY plane (Figure 3-16 (a)). It can be seen that the amplitude of the measured

PFM signal (1/2 of the length of the complex PFM signal vector in the XY plane)

changes with frequency. The amplitude and phase were restored by subtracting the

background signal (described in Eq. 3.17) and are plotted in Figure 3-16 (b). Figure 3-16

(c) and (d) plot the amplitude and phase of the measured PFM signal at 5 select

frequencies.

Comparing Figures 3-15(a) and 3-16(b) and then replotting them in Figure 3-17, it

can be seen that the amplitude of the PFM signal across the domain wall shows peaks

(solid red circles in Figure 3-17 (b)) at the resonance frequencies in the PFM frequency

spectrum (Figure 3-17 (a)) in a congruent lithium niobate sample. It implies that the

piezoresponse of PFM signal on a ferroelectric material gets enhanced at the resonance,

which is consistent with reported results. 60 The flat region in frequency response of PFM

at higher frequencies (Figure 3-15 (a)) suggests that for quantitative PFM measurement,

the driving frequency should be away from the resonant frequencies.

108

(a)

(b)

(c) (d)

Figure 3-16: The piezoresponse across the signal 180° wall in lithium niobate single crystal. (a) x and y signal at selective frequencies plotted in a complex XY plane. Solid line was the fitting, whereas the scattered dots are experiment data; (b) The maximum amplitude of the electromechanical contribution to the PFM signal at different frequencies; (c) amplitude (d) phase of the measured piezoresponse across the domain wall in lithium niobate at selective frequencies as in (a).

1kHz

6kHz

30kHz

55kHz

100kHz

109

The piezoresponse across a single domain wall in lithium niobate was also

measured at a single frequency. By changing the phase of the lock-in amplifier, the x and

y signals from the lock-in amplifier of the piezoresponse across the domain wall rotates in

the complex XY plane (Figure 3-18 (a)). However, the amplitude of the

electromechanical response does not change with the phase setting in the lock-in

amplifier. Also the relative phase shift between +c and –c domain does not change with

the phase setting in the lock-in amplifier (Figure 3-18 (b)). This suggests that the relative

phase and amplitude of the electromechanical response of the PFM signal on +c and –c

domain does not change with the external electrical circuit.

(a) (b)

Figure 3-17: (a) The frequency response of the PFM system on lithium niobate, which was plotted in Figure 3-15 (a); (b) The amplitude of the PFM response across the domain wall in lithium niobate, which was plotted in Figure 3-16 (b).

110

In the experiment discussed in following sections, the frequency used for the

driving voltage applied on the metal-coated AFM tip was between 35kHz to 50kHz,

which is the range where no resonance was found in PFM system. The electromechanical

contribution will be extracted from the measured PFM signal based on method mentioned

earlier in this section (Eq. 3.17 and Figure 3-14).

3.4.2 Vertical Piezoresponse Force Microscopy

Piezoresponse force microscopy (PFM) has been widely used to image the

ferroelectric domain structure and measure the piezoelectric properties in nanoscale level.

The vertical PFM gives the out-of-plane deformation of the sample specimen. The

amplitude of the vertical PFM image across a single 180° domain wall in ferroelectric

crystals such as c-cut lithium niobate, lithium tantalate and strontium barium niobate

(a) (b)

Figure 3-18: The piezoresponse across the single 180° domain wall in lithium niobate at the single frequency (~42.45kHz) with different phase setting in the lock-in amplifier. (a) x and y signal in the complex XY plane. The solid line was the fitting, whereas the scattered dots are experimental data; (b) the amplitude of the electromechanical contribution to PFM signal

111

reaches the minimum right at the location of the domain wall and reaches its maximum

value far away from the domain wall (Figure 3-2). The wall width found in PFM image is

actually the electromechanical interaction width, which is different from the intrinsic

domain wall width over which the polarization reverses. The domain wall width over

which the polarization reverses was measured to have an upper bound of ~10 lattice

parameter wide using high-resolution TEM images and was predicted to be ~3 to 5 lattice

parameters by the first principle theory calculation.3,4,64,65 However, the domain

interaction width in PFM image is far wider than the real domain wall width. In this

thesis, most often the interaction domain wall width is simply called the domain wall

width.

The samples used for this study are: periodically poled congruent lithium niobate

(including high temperature anneal after domain reversal), fresh poled lithium niobate at

room temperature (with no post-heat treatments), lithium tantalate and the strontium

barium niobate crystals. Figure 3-19 shows the PFM image across a domain wall in

lithium niobate. The applied voltage on the tip was 5Vrms with a frequency of 42.35kHz.

The electromechanical response across the single domain wall was extracted by the

method discussed in Section 3.4.1. The domain interaction full width is defined as the

width where the amplitude reaches 90% of its maximum. The full width half maximum is

defined as the width where the amplitude reaches 50% of its maximum. From the

amplitude of the vertical response of PFM after the “background” subtraction (Figure 3-

19 (f)), the asymmetry of the piezoresponse across the single domain wall is negligible in

this case. The fitting of amplitude of the experimental data fits the function

112

y=A1tanh(x/t1)+A2tanh(x/t2), where A1, t1, A2, and t2 are fitting constants. This function

was also used to fit the FEM simulation result (Figure 3-11 (c) and (e)).

(a) (b)

(c) (d)

(e) (f)

Figure 3-19: PFM image across the single domain wall in lithium niobate. x signal (a) and y signal; (b) of the measured piezoresponse across the domain wall; (c) x and y signal of the measured piezoresponse; (d) amplitude and phase of the measured piezoresponse across the domain wall; (e) x and y signal of the piezoresponse across the wall after the “background” subtraction; (f) amplitude and phase of the piezoresponse across the wall after the “background” subtraction. The fitting used function: y=A1tanh(x/t1)+A2tanh(x/t2), where A1, t1, A2, and t2 are fitting constants.

113

The piezoresponse on the same area in the periodically poled congruent lithium

niobate was checked with different applied voltages at same frequency (Figure 3-20). As

can be seen, the domain interaction width and the amplitude in units of the effective

piezoelectric coefficient (pm/V), which is the slope of the Figure 3-20 (a), do not change

with the applied voltage on the tip.

3.4.2.1 Dependence of the vertical PFM response on tip parameters

Measurements on periodic poled congruent lithium niobate were taken with

different tip sizes. After the measurement was done, the tips were imaged with Field

Emission Scanning Electron Microscope (FESEM) to determine the tip size. The

amplitudes of the measurement are plotted in Figure 3-21. The amplitudes of the PFM

(a) (b)

Figure 3-20: The piezoresponse across the single domain wall in periodic poled congruent lithium niobate with different applied voltage at 42.2kHz. (a) The amplitude of piezoresponse vs. the peak applied voltage on the tip. The slope is ~9.9±0.5pm/V (b) Normalized amplitude of the piezoresponse across the domain wall with different peak applied voltage on the tip. The domain wall interaction width does not change.

114

vertical response on congruent lithium niobate are independent of the tip size. From the

amplitude of vertical PFM response, the material property d33 was determined as

10.5±1pm/V.

To understand the amplitude of the vertical PFM response, we first discuss the

spherical tip model to find out the piezoelectric response across a single domain wall in

lithium niobate by changing the distance between the tip and the surface of the sample for

a fixed tip size. For a 50nm radius spherical tip, as it moves closer to the surface till it is

in contact, the maximum potential inside the sample increases. When the tip is in contact

with the surface, then the potential inside the sample reaches its maximum value, which

is the same as the applied voltage on the tip. Therefore, the piezoelectric response of the

sample also reaches its maximum when the tip is in contact with the surface (Figure 3-22

(a)).

Figure 3-21: FEM result along with the PFM measurement of the amplitude of the vertical piezoresponse across the domain wall in lithium niobate.

115

As can be seen in Figure 3-22, as the tip moves away from the surface from the

“in contact” state, the amplitude of the piezoresponse drops quickly. If the distance d

between tip and sample surface is greater than 0.5nm, the amplitude of piezoresponse

drops down slowly. Typically, d′eff is calculated by measuring the ratio of the amplitude

of the piezoresponse to the applied voltage on the tip. This method, however, makes it

appear as if the measured material property depends on the distance between the tip and

surface. However, when the tip is away from the surface, the potential distribution inside

the sample also changes. If we however calculate the actual deff coefficient using the ratio

between the amplitude of piezoresponse and the real potential on the sample surface

(a) (b)

Figure 3-22: Amplitude of piezoresponse across the single wall in PFM vs. the distance dbetween the tip and the surface of lithium niobate sample. (a) Amplitude of piezoresponse and the maximum potential inside lithium niobate sample vs. the distance between the tip and surface of lithium niobate; (b) The effective piezoelectric coefficient d′eff and deff vs. the distance between the tip and sample surface. d′eff is the piezoelectric coefficient determined by the ratio of the amplitude of the piezoresponse over the applied voltage on the tip; deff is determined by the ratio of the amplitude of piezoresponse over the potential in the surface of the lithium niobate sample. In this case, the tip is a 50nm-radius sphere tip. The applied voltage on the tip is 5V. Potentials on the sample surface are plotted in (a).

116

(obtained form modeling), we see that the piezoelectric coefficient deff does not depend

on the distance between the tip and sample surface, as expected.

The amplitude of the vertical piezoresponse for different tip sizes and geometry in

contact mode (d=0nm) were modeled using FEM (Figure 3-21). Along with the

experiment results, it can be seen that when the tip is in contact with the sample, the

amplitude of the vertical piezoresponse is independent of the AFM tip shape in both FE

simulation and experiment. This means that there is no need to calibrate the shape of the

tip while doing a quantitative piezoelectric measurement in PFM. Also, the excellent

match between the experiment and FE simulation in PFM suggests that periodically poled

congruent lithium niobate is a very good sample to be used as the reference when using

PFM to quantitatively measure the piezoelectric properties of a new sample. In the

following sections, congruent periodically poled lithium niobate was used as the

reference for quantitative measurement.

3.4.2.2 The dependence of the crystal stoichiometry in PFM

To quantitatively compare the piezoresponse across a domain wall in the lithium

tantalate and lithium niobate, the measurements performed in periodically poled

congruent lithium niobate, congruent lithium tantalate and stoichiometric lithium

tantalate grown using VTE method (See details in Chapter 2). Measurements were taken

in fresh poled congruent lithium tantalate and stoichiometric lithium tantalate (domains

created by tap water) to determine both the domain wall interaction width and the

amplitude response; then the same tip was used to image the piezoresponse across a

117

single wall in periodically poled congruent lithium niobate. To avoid the PFM domain

interaction width dependence on the tip shape and tip size broadening due to the

scanning, such experiments were always performed with the same tip by measuring CLT,

PPLN, and SLT_VTE in different sequences, e.g. CLT, SLT_VTE, PPLN, SLT_VTE,

CLT. The results are listed in Table 3-3.

The ratios between the maximum experimental piezoresponse in fresh poled CLT

and SLT_VTE to that in periodically poled CLN were determined to be ~0.67±0.02 and

~0.66±0.03, respectively. This says that the maximum piezoresponse is LT is about

2/3rds that of LN, and that the stoichiometric dependence is not significant in LT. We

next verify these with simulations.

The piezoresponse across the single domain wall in congruent lithium tantalate

was modeled using FEM using a disc-type tip model. For simplicity, the congruent

periodically poled lithium niobate was used as the reference (Figure 3-23(a)). The ratio

between the congruent lithium tantalate and congruent lithium niobate in FEM was found

to be ~0.73±0.07, which is in excellent agreement with the measurement result

(~0.67±0.02).

Table 3-3: Amplitude of vertical PFM response in lithium tantalate. The reference was congruent periodically poled lithium niobate (PPLN) and applied voltage is 5Vrms @42.35kHz.

Measurement CLT

(RCLT/RPPLN) SLT_VTE

(RSLT/RPPLN) Measurement Sequence

1 0.66±0.01 0.67±0.01 PPLN, CLT, SLT_VTE, CLT 2 0.65±0.02 0.66±0.01 PPLN, CLT, SLT_VTE, CLT, PPLN 3 0.67±0.01 0.66±0.01 SLT_VTE, CLT, PPLN 4 0.67±0.01 0.61±0.02 SLT_VTE, CLT, PPLN 5 0.70±0.01 0.68±0.01 CLT, PPLN, SLT_VTE

118

Since in the experiments, the tips used for CLT, SLT_VTE and PPLN in each set

of scan were the same, and the order in which they were performed as permuted, the

domain wall interaction widths in these three materials can be compared without

considering the tip geometry and exact tip size. After normalizing the piezoresponse, it

can be found that SLT_VTE has the smallest domain interaction wall width in PFM

among CLT, SLT_VTE and PPLN (or CLN). The domain wall interaction widths in both

CLT and PPLN (or CLN) are similar (Figure 3-23 (b)) for the same tip, which is in

excellent agreement with that predicted in FEM. For example, the FWHM domain

interaction widths in FEM for both CLT and CLN are 20.3±1nm and 20.1±0.72nm for a

10nm disc tip, respectively.

(a) (b)

Figure 3-23: (a) Comparison of the the piezoresponse in lithium tantalate between the FEM modeling and measurement. The tip radius size is ~50nm. Congruent periodically poled lithium niobate was used as the reference. In FEM, the ratio between the vertical piezoresponse across the single wall in congruent lithium tantalate and congruent lithium niobate is ~0.73±0.07, whereas in the experiment, it was determined to be ~0.67±0.02. (b) Normalized piezoresponse in both lithium niobate and congruent lithium tantalate and stoichiometric lithium tantalate grown using VTE method.

119

The PFM was also performed on the fresh-poled (with tap water) stoichiometric

lithium niobate (denoted as SLN#1) with coercive fields around 6kV/mm, and a

periodically poled CLN sample. In each case, the same tip was used to perform PFM scan

on both SLN sample and a periodic CLN sample. Table 3-4 lists the experimental results.

The results show that the amplitude of the piezoresponse in SLN is similar

(~1.02±0.08) to that of CLN. The domain wall width (FWHM ~130±5nm) in

stoichiometric lithium niobate (SLN) is larger than that (FWHM ~50±3nm) in

periodically poled congruent lithium niobate (Figure 3-24).

Table 3-4: Amplitude of vertical PFM response in lithium niobate. The reference was periodically poled congruent lithium niobate (PPLN).

Measurement SLN#1 ( RSLN#1/R PPLN)

1 1.12±0.01 2 1.10±0.01 3 0.96±0.01 4 0.97±0.01 5 0.98±0.01

Figure 3-24: Comparison of piezoresponse in stoichiometric lithium niobate with and periodically poled congruent lithium niobate (CLN). The ratio between bulk SLN and CLN is ~1.0. However, the domain interaction width in SLN is wider than that in CLN.

120

These results suggest that the piezoelectric coefficients do not significantly

depend on the crystal stoichiometry in both lithium niobate and lithium tantalate. The

wider domain interaction width in stoichiometric lithium niobate as compared to

congruent lithium niobate, is in contrast to the narrower domain interaction width in

stoichiometric lithium tantalate as compared to congruent lithium tantalite. The reasons

for this are presently unclear, though this might be elated to differences in the physical

properties (dielectric, elastic, piezoelectric) of these two materials. It can also be related

to the fact that while CLN, SLN, SLT_VTE have domain walls in the y-z plane, the

domain walls in CLT are along the x-z plane. The wall orientation therefore changes with

stoichiometry in LT, but not LN

3.4.2.3 Spatial resolution of PFM imaging

Ferroelectrics have been widely studied as ferroelectric nonvolatile memory data

storage materials. Moreover, the intrinsic domain wall was predicted to be extremely

narrow (2~10 unit cell). This means domain size of the order of nanometers can be

created. Ultrahigh density (~ 10Tb/in2) domain pattern has been fabricated and

demonstrated.66 In this application, several SPM techniques have been employed to

pattern and image the ferroelectric domain walls. Among them, PFM has become one of

the primary tools for imaging and writing ferroelectric domain structures. In these

applications, not only the quantitative understanding of the nature of the signal, but also

the spatial resolution of the measurement should be established. Moreover, the

understanding of the spatial resolution of PFM imaging might enable us to

121

unambiguously understand the domain wall structure at the nanoscale level, and then

correlate this domain wall structure to the macroscopic properties of the material, such as,

domain reversal dynamics.

In this section, the spatial resolution is determined by the domain wall interaction

width, which was mentioned earlier. The interaction domain wall width in PFM is

defined as either full domain wall width or full width at half maximum (FWHM), which

means distance between two points across the domain wall, at which the amplitude of the

piezoresponse reaches 90% or 50% of its maximum amplitude, respectively. Several tips

with different manufactured tip radii have been used in this experiment. Each tip was

used to scan 5 to 10 lines of scan. Then the tip was imaged by the FESEM to determine

its tip shape and tip size. Most often, the very end of the tip ends up flat (Figure 3-25 (a)).

Some of the tips still remain sphere-like after the scan (Figure 3-26 (a)). Based on their

shape, the tips were separated into two primary groups:

1). Disc-like tip. In this case, the very end of the tip is flat (Figure 3-25 (a)). The

radius was determined as the radius of the very end of the disc size. In this case, the

radius of the tip can be unambiguously determined.

122

2). Sphere-like tip. In this case, the very end of the tip is not flat (Figure 3-26 (a)).

In reality, it is also not a perfect sphere, and as discussed below, suggests that it has a

contact area instead of a point contact. Under a strong indentation, this area would be the

surface area of the convex surface of the sphere-like tip, which we denote as A. In our

experimental conditions, which corresponds to weak indentation, assuming a depth (h) of

1nm of the tip indentation into the surface, the length of the tip (a=2R) is treated as the

diameter of the tip (See inset in Figure 3-26 (b)). This corresponds to a penetration of ~ 1

unit cell into the material. The disk area with radius of (R=a/2) was used as the contact

area.

(a) (b)

Figure 3-25: (a) FESEM image of the tip after PFM scan. (b) The full domain interaction width of congruent lithium niobate vs. the tip radius size. The very end of the tip was flat, like in (a).

123

The resolution of PFM in this thesis was defined as the full domain interaction

width at 90% of the maximum of amplitude (denoted as full domain width, or FW) or full

domain interaction width at half maximum of amplitude (denoted as full domain width

half maximum or FWHM). In this case, the resolution is quite different from the

conventional concept in optics, which is defined as the minimum distance two points

must be separated to be able to distinguish two Gaussian beam spots. In this thesis, the

full domain width is rather the distance that the tip “sees” in the transition region between

two single domain regions; and within the full interaction domain width, the tip will

experience the influence of the domain wall on the measured piezoresponse. Therefore,

the resolution here is the piezoelectric interaction width of the domain wall.

The domain interaction width depends on both material properties and the contact

situation, which means that the distance between the tip and the surface. Figure 3-27

shows an example of the FEM result of the interaction domain width in congruent lithium

(a) (b)

Figure 3-26: (a) FESEM image of the sphere like tip after the PFM imaging.. (b) The domain wall interaction width of congruent lithium niobate vs. the tip radius. The tips were sphere like in (a). The radius was determined as the radius of a/2 in inset when assuming indentation depth h is ~1nm.

124

niobate under a 50nm sphere tip with 5V applied voltage on. As the tip moves away from

the surface, the interaction domain width increases whereas the displacement drops

down. After the distance is larger than 1nm, the interaction width does not change

significantly. However, Figure 3-21 shows that the amplitude of the vertical PFM (or

displacement of surface) does not change with the tip size. It means that in our

experiments, the tip is in contact (d=0nm) with the sample surface in PFM measurement.

FEM modeling was used to understand the dependence of the domain interaction

width on the tip size, and tip geometry as shown in Figure 3-29. The interaction domain

widths were found to be linearly dependent on the tip size when the tip is in contact no

matter what its shape is when it is in contact with the sample surface. In FEM, the sphere

tip gives very narrow (~10nm) full domain interaction width. Due to the saturation of the

domain wall interaction width as the distance is larger than 2nm for sphere model, a 2nm

gap was chosen to study the dependence of the domain interaction width on the tip size

e

Figure 3-27: FEM result of the domain interaction width and displacement vs. the distance d between the tip and surface in congruent lithium niobate under a 50nm sphere tip with 5V on.

125

even though a 2nm gap is an exaggeration. With a gap, d, between the tip and surface, the

domain wall interaction widths (both FW and FWHM) are not linearly proportional to the

tip size, but rather change nonlinearly and almost saturate as the tip size becomes greater

than ~50nm. Even with a 2nm gap, for a spherical tip, the FWHM of the domain

interaction width for a 50nm tip is still very small (~16.56±1.89nm). However, for a disc

shaped tip, the domain interaction width increases rapidly with the tip size. The

contribution of the conical part of the tip also leads to the broadening of the domain wall

interaction width, but its contribution is very small (<2%). This suggests that the contact

area is the key to determining the spatial resolution in PFM. For example, for a spherical

tip, the FWHM of domain interaction width is ~0.03 times the tip size whereas the

FWHM of domain interaction width is ~0.73 times of the tip size for the disc tip. Table 3-

5 lists the relationship between the domain interaction width and the tip size.

Therefore, whether the tip gets blunted or indentation is involved, the domain wall

interaction width would increase dramatically. The experimental interaction wall width

for the disc type tip appears to agree most closely with the predictions of the disc tip

Table 3-5: The relationship between the domain wall interaction width and tip radius R.

d (nm)

Type FW (nm) FWHM (nm) Note

0 sphere 0.328 (±0.015)*R 0.033(±0.001)*R FEM 0 sphere

+cone 0.2(±0.07)+0.46(±0.03)*R 0.02(±0.08)+0.036(±0.001)*R FEM

0 disc 3.16(±0.2)*R 0.72(±0.023)*R FEM 0 disc

+cone 23.3(±6.5)+3.9(±0.15)*R 2.0 (±0.2)+0.73(±0.01)*R FEM

2 sphere 337(±9)-326.9(±2.97)exp(-R/195(±10))

-18.3-12.8*(-R/19) +32exp(R/509)

FEM

disc 79(±10)+3.95(±0.1)*R 7.2(±3.14)+0.94(±0.09)*R expt.

126

model. This suggests that in PFM, the tip is in contact with sample surface and the

domain interaction width is linearly proportional to the contact area between the tip and

sample surface.

In FEM modeling, the intrinsic domain wall width was idealized as 0nm so that

the material properties change abruptly across the domain wall without considering any

(a) (b)

(c) (d)

Figure 3-28: FEM simulation of vertical piezoresponse across a tilted domain wall. (a) Side view of the geometry of the domain wall. The wall is tilt with an angle of θ. The origin is located at point O; (b) etched y surface of PPLN, in which maximum tilt angle of domain wall is ~2.6 degree in the region marked by blue rectangle; (b) The piezoresponse across the domain wall. The lower potion of the graph is enlarged in the inset, in which it shows that the point with minimum response moves ~2.5nm away from the origin O; (c) Comparison between the responses on both side of the wall, asymmetry can be seen. The region left to the wall in (a) has longer tail compared to the region right to the wall. The tilt angle θ is ~5 degree, and the tip is 50nm disc tip with applied voltage of 5V in FEM simulation.

127

gradual change. No matter what the tip shape is, when the tip size goes to zero, the

domain interaction width in FEM modeling also goes to zero. However, the extrapolation

of the experimental domain wall width in the limit that tip size tends to zero gives the full

domain interaction width of ~75±10nm, and full width half maximum ~7.2±3.14nm.

The domain interaction widths (FW~75±10nm and FWHM~7.2±3.14nm) of the

extrapolations are still significantly larger than the normally accepted intrinsic domain

wall width of the ferroelectrics (order of 1~2nm). The broadening may also arise from

electrostatic contributions to the PFM, if the surfaces are not completely charge

compensated.67 However according to the research done in Ref. [68], it was shown that

the surface potential difference in lithium niobate is no more than 2mV in an ambient air

environment, which would not give significant broadening. Another possibility is that the

domain wall is tilted instead of being straight (Figure 3-28 (a)). The FEM simulation

showed that the point with minimum response moves ~2.5nm away from the original

domain wall location on the top surface (Figure 3-28 (b)); besides the response across the

domain wall shows a little asymmetry, for a 5-degree tilted wall. The movement of the

location of domain wall also leads to the broadening of the domain interaction width. For

instance, for 50nm disc tip, the full domain width (FW) for 5-degree tilted wall is

~210±12nm and full width half maximum is ~52±2nm, whereas for the straight wall, the

full domain width is ~ 178±9nm and full width half maximum is ~40±1.44nm. Besides

the tilted wall, if the material properties change across the domain wall, similar

phenomena such as asymmetry and offset of the domain wall location would also occur.

A provocative possibility is that the broad domain interaction width in the measurement

may reflect property variations across a domain wall on this length scale. Indeed many

128

properties in congruent composition of lithium niobate have been shown to vary over

long length scales across a domain wall.5 A high temperature anneal (200-300C) typically

narrows these effects considerably from 10’s of microns down to nanometer scales; but

residual effects are still observed at the walls even after annealing.7 One possibility is

that these residual changes across a domain wall in dielectric, elastic, piezoelectric and

perhaps even ferroelectric polarization remain on ~79nm length scales.

3.4.2.4 Vertical PFM response on SBN:61

In both lithium niobate and lithium tantalate systems, PFM has been shown in this

study to be a tool for quantitative measurement on the nanoscale for the piezoelectric

properties of the materials. However, the experimental piezoelectric amplitude in

strontium barium niobate was significantly different from the FEM prediction. The

(a) (b)

Figure 3-29: FEM result of domain width in PFM along with the PFM measurement result. (a) full width half maximum (FWHM) of the domain wall interaction width. Solid lines for measurement data are the fittings; (b) full width (FW) of domain wall interaction width. The solid lines are the fittings. All the fittings are linear except for the sphere tip which is 2nm away from the surface.

129

sample was poled into single domain state with tap water electrodes at room temperature,

which was discussed in detail in Chapter 2. The d33 coefficient of the crystal was

measured to be ~110±5pm/V by the d33 meter. Then the sample was poled into

multidomain state with tap water electrodes again for PFM imaging.

Strontium barium niobate (SrxBa1-xNbO6, or SBN:100x) is a typical ferroelectric

relaxor. In this experiment, SBN:61 was used while congruent lithium niobate was used

as the reference. The domain wall shape in SBN:61 shows the four-fold symmetry, which

was discussed in Chapter 2.2.1. Due to low Curie temperature (~70°C), the domain wall

of SBN:61 is not straight. The vertical piezoresponse across the single domain wall in

SBN:61 was measured. The frequency of the driving voltage was ~42.35kHz and the

amplitude of the driving voltage was 5Vrms. Since SBN:61 is not a very good insulator

(see details in Appendix D), the applied voltage on the tip was simultaneously monitored

by using a high impedance multimeter to make sure there is no leakage current and that

the applied voltage applied to the SBN:61 sample surface is the same external voltage

applied to the tip.

The domain structure in SBN:61 was imaged first by PFM over a large area

(45x45µm). Then a single domain wall was imaged over a small area with same tip

(Figure 3-30). It can be seen that on the smaller scale, the domain in SBN:61 still has a

multidomain structure on the nanometer scale.

130

To quantitatively measure the piezoresponse across the domain wall, the domain

wall was scanned after the domain wall was located with a fresh new tip. Then the same

tip was used to scan the reference periodically poled congruent lithium niobate. The

amplitude of the piezoresponse in SBN:61 is only ~1.7 times higher than that in

congruent lithium niobate (Figure 3-32). For the bulk piezoelectric measurement, the d33

coefficient of SBN:61 is around 8.7~10 times higher than d33 coefficient of congruent

lithium niobate.

(a) (b) (c)

(e) (f) (g)

Figure 3-30: The PFM amplitude image of domain structure in SBN:61. The applied voltage on the tip was 5Vrms at 42.35kHz. (a), (e) are the topography; (b), (f) are amplitude; (c), (g) are the phase. (e)-(g) are scanned in the area inside the square marked in (b). (a)-(c) are the images on the same area, and (e)-(g) are the images on the same area.

131

The amplitude of vertical piezoresponse of SBN:61 was predicted to be ~7.9

times higher than that of congruent lithium niobate using FEM simulations. In the PFM

measurement, it was found only to be only ~1.7. The lower piezoresponse in PFM

measurements were also reported in other materials such as RTP.69 Figure 3-30 shows

that there are many nanodomains in SBN:61 even in areas that appear to be a single

domain state. This may explain a reduction in the piezoelectric amplitude even in

regions that appear distant from a domain wall.

(a) (b)

Figure 3-31: Vertical piezoresponse across the single domain wall (y wall) in strontium barium niobate 60 under a 50nm radius disc tip with 5V applied voltage on (a) displacement in SBN:61 modeled by using FEM; (b) amplitude predicted using FEM.

132

3.4.3 Lateral imaging of PFM across the domain wall

The tip displacement (a twist) normal to the cantilever axis and normal to the

surface of the sample in PFM gives the lateral PFM signal. In Ref. [7], two types of lateral

signals were described:

1) 0°°°° lateral scan. In this case, the cantilever arm is parallel to the domain wall. In

lithium niobate, the wall is parallel to the y axis, and hence the 0° lateral scan

means that the cantilever arm is parallel to crystallographic y-axis. This lateral

signal reveals the distortions across the domain wall in the crystallographic x-z

plane. In congruent lithium tantalate, the domain wall is parallel to x-axis.

Therefore, 0° lateral scan in congruent lithium tantalate means the cantilever

Figure 3-32: Comparison of the amplitude of the piezoresponse in strontium barium niobate (SBN:61) and congruent lithium niobate (CLN). Use CLN as reference and its piezoresponse is 1.0. The ratio between SBN:61 and CLN is ~1.7.

133

arm is parallel to its crystallographic x-axis and reveals the distortions across

the domain wall in the crystallographic y-z plane.

2) 90°°°° lateral scan. In this case, the cantilever arm is normal to the domain wall. In

lithium niobate case, 90° lateral scan means the cantilever arm is parallel to

crystallographic y-axis. This lateral signal reveals the distortions across the

domain wall in the crystallographic y-z plane.

In this chapter, only 0° lateral signal will be discussed. In this case, congruent

lithium niobate and congruent lithium tantalate crystals have been chosen for this study.

In congruent lithium niobate, the domain shape is hexagonal with domain wall parallel to

crystallographic y-axis. Even though congruent lithium tantalate shares the same

crystallographic structure with lithium niobate, its domain shape is triangular, with

domain wall parallel to crystallographic x-axis.

Same Pt-Ti coated tip with radius ~40nm was used to scan both congruent lithium

tantalate and lithium niobate. The applied voltage on the tip was 5Vrms with frequency

of 42.54kHz. Figure 3-33 shows lateral scan results on both congruent lithium tantalate

and lithium niobate. To compare the signals on lithium niobate and lithium tantalate,

same tip, same applied voltage on the tip, same frequency, and same time constant as

well as same sensitivity of the lock-in amplifier has been employed. As can be seen, the

lateral signal reaches its maximum right at the domain wall and almost zero when it is far

away from the domain wall region in both congruent lithium niobate and congruent

lithium tantalate. After normalizing the lateral signals on both congruent lithium tantalate

and congruent lithium niobate, the ratio (Rlateral(CLT/CLN)) between lateral response of

congruent lithium niobate and that of congruent lithium tantalate is around ~0.68±0.01.

134

The similar experiments were conducted using tips with different tip sizes. The results are

listed in Table 3-6.

The lateral PFM comes from the deformation slope of the sample surface. In

vertical PFM, it was found that the amplitude does not depend on the tip size and tip

geometry in both PFM measurement and FEM modeling. Though, it was found in FEM

(a) (b) (c)

(d) (e) (f)

Figure 3-33: 0° lateral PFM measurement across the single domain wall in congruent lithium niobate (CLN) and congruent lithium tantalate (CLT). (a) and (d) topography; (b) and (e) 0° lateral PFM measurement; (c) and (f) line profile of 0° lateral PFM measurement. (a)-(c) are for CLN, and (d)-(f) are for CLT.

Table 3-6: The ratio (Rlateral(CLT/CLN)) of amplitude of 0° lateral PFM signal between congruent lithium niobate and congruent lithium tantalate versus the tip size.

Tip Radius, R (nm) Rlateral(CLT/CLN)) Tip type 55±3 0.68±0.01 disc

79.7±4 0.65±0.01 disc 120±8 0.67±0.01 disc

135

modeling that the slope of the surface does depend on the tip size and tip geometry as

well as the contact condition. Figure 3-34 shows the surface deformation induced by a

50nm sphere tip as the tip moves away from the surface. It can be seen that as distance

between the tip and the sample surface gets bigger than 0.2nm, the slope of the

deformation drops down dramatically.

For the contact case (d=0nm), Figure 3-35 (a) and (b) show the relationship

between the amplitude (slope) of the deformation in congruent lithium niobate under

different tip radii and geometry. It shows that if the contact area is larger, for instance a

disc type tip, the amplitude is much lower as compared to the sphere tip with the same

radius size. However, the cone of the tip does not change the amplitude significantly. The

main contribution depends on the tip-sample contact area. As the tip radius exceeds

50nm, the slope of the surface deformation quickly decreases and become insensitive to

both sphere tip and disc tip. However, the ratio (Rslope(CLT/CLN)) between the surface

slope in congruent lithium niobate and the slope in congruent lithium tantalate is

(a) (b)

Figure 3-34: FEM result of the slope of the surface deformation across a domain wall in congruent lithium niobate induced by a 50nm sphere tip. (a) the slope of the surface across the domain wall as d=0nm; (b) the amplitude of the slope vs. the distance, d,between tip and sample surface.

136

independent of the tip size and tip geometry (Figure 3-35 (c)), and to be ~0.70±0.05,

which is in excellent agreement with the measured result (~0.67±0.02) (Figure 3-36 and

Table 3-6).

(a) (b)

(c)

Figure 3-35: FEM result of the amplitude (slope) of the surface deformation normal to the domain wall vs. the tip size and tip geometry. (a) the disc tip without the cone, disc tip with cone and sphere tip with cone; (b) disc tip with cone and disc tip without cone. Solid line are the fitting using 2nd exponential decay function y=y0+A1exp(-x/t1)+A2exp(-x/t2). (c) FEM results of the slope of surface for both congruent lithium niobate (CLN) and congruent lithium tantalate (CLT) for disk shape tip in contact. Rslope(CLT/CLN) is the ratio between slopes of FEM surfaces in CLT and CLN, which is ~0.70±0.05 and independent of the tip size.

137

Figure 3-36 also shows the comparison between the domain interaction width in

FEM simulation and the experimental measurement. It can be seen that the full domain

wall width (FW ~95±5nm) and full width half maximum (FWHM ~16nm±4) in FEM is

~10 times smaller than the experimental measurement (FW~800±10nm and FWHM

~204±5nm). This suggests additional broadening mechanisms in the lateral direction in

the crystal, as compared to the vertical direction.

3.5 Conclusion

The electromechanical responses across the single domain wall in lithium niobate,

lithium tantalate as well as strontium barium niobate have been measured by PFM

technique and modeled using FEM. The amplitude of the vertical response was found to

be independent of the tip size and tip geometry in the contact mode (d=0). The amplitude

(a) (b)

Figure 3-36: (a) 0° lateral amplitude signal along with FEM simulation result. The ratio between congruent lithium tantalate (CLT) and congruent lithium niobate (CLN) in experiment is ~0.68±0.01; whereas it is ~0.70±0.05 in FEM (b). (b) Comparison of slope of FEM surface in CLN and CLT. The tip radius is ~55nm, which was determined by FESEM image.

138

ratio of the vertical piezoresponse across the domain wall in congruent lithium tantalate

to that in congruent lithium niobate was found to be ~0.67±0.02, which is in agreement

with ~0.73±0.07 predicted using FEM; whereas the amplitude ratio of the lateral signal in

congruent lithium niobate and congruent lithium tantalate is 0.67±0.02 in measurement

and 0.70±0.05 in FEM. The amplitudes of the vertical piezoresponse do not change with

the crystal stoichiometry in both lithium niobate and lithium tantalate, whereas the

domain interaction width does change with the crystal stoichiometry. The wall interaction

width in stoichiometric lithium tantalate is narrower than that in congruent lithium

tantalate, whereas the wall interaction width in stoichiometric lithium niobate is wider

than that in congruent lithium niobate; which might be correlated to the intrinsic domain

wall width. The domain width in PFM depends linearly on the tip size. The lateral

amplitude was predicted that the lateral amplitude depends on the tip size. The

extrapolations of the domain wall width versus the tip size give that the full domain wall

width (FW) ~75±10nm and full width half maximum (FWHM) ~7.2±3.14nm.

Nanodomains were found in the strontium barium niobate, which might contribute to the

lower measured piezoresponse than that predicted using FEM.

139

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61. Jungk, T., Hoffmann, A. & Soergel, E. Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy. Applied Physics Letters 89, 163507 (2006).

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Chapter 4

Ferroelectric Domain Patterned Devices

4.1 Introduction

The field of optics has enabled many technologies that we would have never

imagined a few decades ago. From an optical fiber, which is as thin as a strand of hair, to

a laser system, the optics carries us into a world with terabit information transfer per

second and large scale high resolution real-time displays.1-3 To generate new laser

sources over a wide wavelength range from near UV to infrared, and to steer the laser

beam from one point precisely to another point at GHz speed with high efficiency and

low cost are still very challenging today.4-6 Similar to semiconductor chips manufactured

today, there is a definite drive for moving from bulk optics and benches to miniaturized

solid state optical components and their planar integration on a wafer. Thus, there is a

need for a versatile material platform, or a solid state optical bench, much like what

silicon is to the electronics industry today.

Ferroelectric materials possess built-in dipole moment, so-called spontaneous

polarization, and can be switched from its original direction (domain state) to a new

direction upon application of an external field. This enables them to be a candidate for an

optical platform for integration of optical components such as cylindrical lens, prisms and

gratings,7-11 which are the fundamental components for optoelectronic applications such

as beam deflection, beam wavelength conversion and selection. These components can be

145

fabricated though microdomain engineering techniques. In this chapter, examples of

ferroelectric domain microengineered optical devices such as an optical switch, an optical

beam deflector, and an optical frequency converter will be presented. The chapter

consists of 3 sections: Section 4.1 is the introduction; section 4.2 presents the electro-

optic devices, such as phase-array beamlets, optical switching and optical scanning

devices, fabricated in ferroelectrics; Section 4.3 presents optical frequency conversion

devices followed by the conclusion in Section 4.4.

4.2 Electro-optic Devices Fabricated in Ferroelectrics

Electro-optic prism scanners or deflectors based on domain inverted ferroelectric

crystals have been shown to control the angular position of a laser beam in one-

dimension with high precision and speed.8,9,11-13 These devices have several advantages

over mechanical gimbals and other systems including compact device size, high

operating speeds (intrinsic response speeds of >10 GHz)14, and non-inertial deflection.

4.2.1 Theory

The electro-optic effect describes the propagation of optical waves in crystals in

the presence of an externally applied electric field. The wave propagation can be

described by the impermeability tensor ηij. This tensor depends on the distortion of the

lattice, resulting in a charge distribution inside the crystal. The application of an electric

field results in the redistribution of the charges, causing a change in the impermeability

146

tensor, or equivalently, a change in the dimension of the orientation of the index

ellipsoid. This is known as the electro-optic effect.

With external electric field, the impermeability tensor becomes

where rijk and Sijkl are the linear (Pockel’s) and quadratic (Kerr) electro-optic

coefficients respectively.

In applications of electro-optic materials, where the applied electric field is small

compared to the intra-atomic electric field, the quadratic term in Eq. 4.1 is very small as

compared with the linear term. For non-centrosymmetric crystals, the quadratic term can

be neglected. However, for centrosymmetric crystals, the linear effect vanishes due to the

inversion symmetry and the quadratic effect is prominent.

Lithium niobate (LN), lithium tantalate (LT), and strontium barium niobate (SBN)

crystals are noncentrosymmetric. Lithium niobate and lithium tantalate belong to 3m

point group; and SBN belongs to 4mm point group. Their electro-optic coefficients are:

Kr

+++= lkijklkijkijij EEsErE )0()( ηη Eq. 4.1

−

−

=

002

00

00

00

0

0

)3(

22

51

51

33

1322

1322

r

r

r

r

rr

rr

mr

=

000

00

00

00

00

00

)4(

51

51

33

13

13

r

r

r

r

r

mmr

Eq. 4.2

147

The change of the impermeability therefore is

The refractive index change therefore can be found as:

The most basic device for deflecting light is by use of an optical prism. In paraxial

approximation, in which the deflection angles are very small, one can use a series of

prisms in sequence, each prism successively deflecting the light beam further and further

from the optic axis.

The simplest scanner design has a rectangular geometry (Figure 4-1 (a)). This

design consists of N identical prisms placed in sequence, each with base L and height W,

such that the total length of the rectangular scanners is l=NL and the width is W. The total

deflection angle, θint, at the output for a light beam incident along the axis, L, of the

rectangular scanner is given by 15

∆=

−

++−

=

−

−

=∆2

122

151

251

333

313222

313222

3

2

1

22

51

51

33

1322

1322

1

200

00

00

00

0

0

)3(n

Er

Er

Er

Er

ErEr

ErEr

E

E

E

r

r

r

r

rr

rr

mη

∆=

=

=∆2

151

251

333

313

313

3

2

1

51

51

33

13

13

1

0000

00

00

00

00

00

)4(n

Er

Er

Er

Er

Er

E

E

E

r

r

r

r

r

mmη

Eq. 4.3

∆−=∆2

3 1

2

1

nnn Eq. 4.4

148

The deflection angle can be enhanced using horn shape scanner design in which

the beam width is decreased such that the input aperture of the scanner is as small as

beam diameter, but the scanner size gradually increases so that it just accommodates the

trajectory of the beam (Figure 4-1 (b)). The beam trajectory can be determined as the

function of propagation distance z as 9

where the scanner width W(z) for a Gaussian beam is given as

Where ow and oλ are the Gaussian beam waist and the wavelength; n is the

refractive index of the medium.

In lithium niobate, lithium tantalate or SBN, normally the applied field is along c-

axis of the crystal and the extraordinary light would be used in electro-optic devices.

Therefore, the refractive index change in Eq. 4.4 can be rewritten as:

And therefore, due to the refractive index changes on both up and down domains,

the deflection angle in a rectangular scanner is:

W

l

n

n

W

NL

n

n ∆=

∆=intθ Eq. 4.5

)(

12

2

zWn

n

dz

xd ∆= Eq. 4.6

2

1

2

2)(1)(

2

)(

−++=

o

ooo nw

zzwzx

zW

πλ

Eq. 4.7

3333

3333 2

1Ernnne ±=∆=∆ Eq. 4.8

W

lErn

W

LN

n

n

W

l

n

n

e

e333

333int

2 ±=∆=∆=θ Eq. 4.9

149

4.2.2 Optical Devices

The optical devices to deflect the beam can be used in many applications such as

laser printing, laser display, optical switches and so on. The electro-optic beam deflector

can be operated at very high speed (~GHz) compared to electro-mechanical deflectors,

acoustic-optical deflectors and liquid crystals. In this section, a few examples such as the

large aperture laser beam steering, optical switch and 2D beam scanner will be presented.

(a)

(b)

Figure 4-1: Beam deflector (or scanner). (a) rectangular scanner; (b) horn shape scanner.

150

4.2.2.1 Phase-array electro-optic steering of large aperture laser beams using ferroelectrics

Electro-optic beam scanners or deflectors fabricated by microdomain engineered

ferroelectrics have an inherent advantage of speed, since the EO effect is extremely fast

(>40GHz). These devices, however, have strict requirements on the beam size – both in

the vertical (thickness) direction and in the plane of the device. The crystal thickness

limits the aperture – thicker crystals increase the aperture but also increase the driving

voltages. In the plane of the device, the deflection angle is inversely related to the width

of the domain prisms (see Eq. 4.9 for rectangular scanners).10 This leads to a tradeoff

between aperture size and deflection angles and limits the device apertures to 50-500 µm

for achieving angles of 1-5 degrees. While such small beam sizes are acceptable for

applications requiring smaller spot sizes and medium laser powers (such as optical

communications, optical data storage and analog-to-digital conversion) deflecting larger

or higher power laser beams is a challenge for this technology.

The proposed device concept for steering wide aperture beams in the device

plane is to split the beam into many smaller beamlets which are then scanned separately

by an array of individual prism scanners as shown in Figure 4-2. Each individual beamlet

is deflected separately, and all deflected beamlets are recombined to form a single large

beam in the far-field. The path lengths of all of the beamlets through the device are

designed to be exactly equal, resulting in equal relative phase shifts upon deflection. Any

small differences in phase can be compensated by using an electro-optic phase shifter for

each beamlet. This approach is similar to phased array scanning where the beam is

separated and delayed in the individual channels so that the resultant beam has a shifted

151

phase front.16 Each individual scanner channel can be composed of any of the different

scanner designs discussed in the literature10,12,17, the only requirement being that each

beamlet channel must avoid overlapping any other channel.

A 5-stage cascaded rectangular domain micropatterned scanner device with 13

beamlet channels was designed and fabricated to deflect a 1.064-µm infrared laser beam

by a total of 10º. The input beam was divided into 13 separate beamlets by a microlens

array with 0.5-mm spacing of cylindrical lenses of ~50 mm focal length.

Shown in Figure 4-2 is a beam propagation method (BPM) simulation18,19 of the

designed device with 5 kV/mm applied to each scanner element with the index of

refraction, ne = 2.1403, and r33 = 29.14 pm/V for light at 1.064 µm taken from tabulated

data.20 Specification of each of the individual scanner stages is given in Table 4-1.

Notice the width of each scanner decreases slightly to accommodate the width of the

focused beam in each scanner channel. Each channel is composed of equilateral triangles

with height and width equal to the width of the channel, D.

Figure 4-2: BPM simulation of 5-stage 13-beamlet scanner showing full deflection at 5 kV/mm. The polarization direction of the crystal is perpendicular to the page, with the area enclosed by the triangles opposite in spontaneous polarization (Ps) than the rest of the device. The peak deflection is 10.13° in one direction. The inset is the photolithographic mask fabricated for this device that shows two adjacent scanner channels.

152

The beamlets were focused into a single EO device and were steered using an

applied voltage. This cascaded scanner required a synchronized bias supply for

continuous steering operation of the laser beam, i.e. each successive scanner stage must

be ramped from 0 V bias to peak bias only after the previous stage is at full bias. A 5-

stage compact programmable voltage driver was designed and fabricated in a previous

study and detailed in the literature, but was unavailable for this study.21 However, the

device was tested with the following configurations: voltage applied to stage 1 only,

stages 1+2, stages 1+2+3, stages 1+2+3+4, and stages 1+2+3+4+5. . The maximum

deflection for each stage and for the total device were measured and compared with the

theory.

Table 4-1: Specification of Beamlet Scanner

Stage 1 2 3 4 5 Total Width, D (mm) 0.444 0.410 0.383 0.362 0.348 8.31

Stage Length, Ls(mm) 11.16 10.21 9.45 8.85 8.41 50 Field (kV/mm) 5 5 5 5 5 5

Internal deflection (º) 0.96 0.95 0.94 0.93 0.92 4.70 External deflection (º) 2.06 2.04 2.02 2.00 1.98 10.10

153

Without any applied voltage, the beamlet formation process by the beamlet lens

array was first analyzed as a function of distance from the output end of the beam

steering device. It was found that the microlens array which divided the beam into

beamlets introduced a complex phase front structure to the beam but distinct beamlet

formation was observed after a distance of ~ 275 mm from the output of the device. Far

field images of the beam were taken by imaging the focal point of a lens (f = 7.5 cm)

placed at a distance of ~30 cm from the microlens array. The 13 beamlets emerging from

the beamlet microlens array (Figure 4-2 (c)) merge into 5 beamlets in the far-field

Figure 4-3: (a) Far field images taken of the complex beam pattern introduced by the microlens array as imaged at the focal point of a lens. (b) Shows the far field beam image with the addition of the device. Both images (a) and (b) are attenuated equally and are 5.4 x 7.5 mm. Shown in (c) is beamlet steering for applied voltages. The horizontal panel size is 8.25 mm x 1.87 mm in (c). Only 10-12 beamlets are clearly seen in the panels above, and beamlets near the ends are difficult to see, due to the introduction of neutral density filters in order to avoid saturation of center beamlets in the camera. Upon saturation, all 13 beamlets are seen as shown in the bottom panel of (c).

154

without a device (Fig. 2(a)) or with a device (Fig. 2(b)). This arises mainly due to the

introduction of phase distortions by the beamlet microlens array itself (without the

device), as was observed experimentally and confirmed by Beam Propagation Method

simulations. Introduction of active electro-optic phase control for each beamlet can be

implemented to compensate these phase effects and obtain a single beam in the far-field.

The scanning of the beam for various bias fields is shown in Figure 4-2 (c) taken with a

Cohu Model ER-5001 camera in a plane at a fixed distance from the exit face of the

device.

The steering was tested in a continuous manner for the first stage and is shown in

Figure 4-4 (a). The measured deflection angle versus voltage for Stage 1 agrees well

with theory. Figure 4-4 (b) shows a plot of the deflection angle as a function of the

number of activated stages running at full bias voltage. The peak deflection was 10.3º at

5.39 kV/mm. The experiments were performed at 5.39 kV/mm, which gives a slight

increase of 4.7% in the observed deflection angle over the value when operated at

5kV/mm. This increase in deflection for fields above the designed value of 5 kV/mm is

Figure 4-4: (a) deflection angle versus applied voltage across only stage 1 of the beamlet device. (b) deflection angle versus the number of steering stages activated in the beamlet device.

155

due to the fact that the scanner channel widths were designed and fabricated to be 60%

larger than the focused beam waist as calculated from simple Gaussian optics using the

specified focal length of the cylindrical lens array. This allows for the application of

slightly higher fields than the design specified field. However, this deflection angle is

~4% smaller then the expected calculated value for a field of 5.39 kV/mm. We believe

this is due to the higher operating field of 5.39 kV/mm deflecting the beamlets out of the

steering portion of the device. Beyond an estimated field of 5.27 kV/mm, no additional

deflection can be obtained, and that is the deflection we observe experimentally.

The input and output faces of the beam steering device were not antireflection

coated for 1.064 µm wavelength and this resulted in 13.2% loss at each face. With these

reflection losses taken into account, the total insertion losses at zero bias were measured

to be less than 5%. Ferroelectric domains in LiTaO3 are known to scatter some light,

and crystal annealing at 300-400ºC may help reduce this loss.22 The power loss while

scanning was approximately 15% for the full 10.3° of scanning at 5.39 kV/mm. The

output face of the crystal was polished inadvertently at an angle of 1.82º relative to the

fabricated channels, which resulted in an overall incident angle (to surface normal of the

output face) inside the crystal of 6.58º at maximum deflection. Using Fresnel reflection

equations for transverse electric (TE) polarization, we estimate that the difference in

reflectance R between zero deflection and maximum deflection will be ~0.84%, which

does not explain the observed power loss on steering. We observed experimentally that

the increased loss arose because some fraction of light (~15% power) did not steer fully,

and formed a background streak. This is not expected from the device design, if the

initial beamlets are fully contained within the channels. One probable reason for the loss

156

is that the phase front and intensity profile of the light beam within 100-150 mm of the

beamlet array (near field) are quite complex, (see Figure 4-2 (a)) and some fraction of

light may not be properly traversing through the steering channels.

The convergence of the individual beamlets to form a coherent beam of larger

diameter in the far field for arrays of polished prism deflectors and phased optical

antennas has been shown previously.23,24 The exact pattern in the far field is shown to be

a function of the beamlet number, spacing, and channel width. The phases of the

beamlets converging to an angle θ (in the far field) from two adjacent channels separated

by D are normally shifted by the amount kDθ where k is the wave number. This gives rise

to an interference pattern and a modulation of the intensity. However, the component

waves can be brought back into phase by integrating small phase shifting electro-optic

patches prior to each steering channel. These pads were not included in the current

design, but future work will incorporate these.

In summary, a beamlet approach with 10.3º of beam steering of 1.064 µm laser

light was demonstrated. A large 5.5-mm incident beam was split into ~13 beamlets, 0.5

mm apart and all were steered synchronously at 5.39 kV/mm. There is no limit to the

number of beamlets, and hence no limits on the incident beam size in the crystal plane in

using this design approach. Demonstration of this beamlet scanner is a critical step

towards realizing large-aperture, large-angle beam steering. Further device design

improvement can potentially increase these steering angles to 30-40º. Stacking several

such scanners devices in the thickness direction will allow large aperture beams in the

thickness direction as well.

157

4.2.2.2 Eletro-optic optical switch

Concept of the optical switch based on patterned ferroelectric domains in

congruent lithium tantalate wafer and proof-of-principle results will be presented in this

section. The improvement of the switch design for better device performance such as

reducing operating voltage and increasing resolvable optical channels will be discussed.

Today, the commercially used optical switch is mainly Mach-Zehnder

interferometer fabricated in a single domain lithium niobate platform. The length of

Mach-Zehnder interferometer optical switch normally is ~10cm, whereas the length of

the optical switch based on domain patterned lithium tantalate can be reduced to few

centimeters long.

The horn shape scanner gives a large deflection angle as compared to rectangular

scanners with the same input aperture size and same applied electric field. Eq. 4.6 gives

the trajectory of the beam propagating through the horn shape scanner. The proposed

optical device concept for optical switch is to use two sets of the identical horn shaped

scanners which are fabricated on the same ferroelectric chip. Figure 4-5 is an example of

a 3X3 optical switch, in which there are identical sets of input and output horn shape

scanners. The input set of scanners is composed of 3 individual input ports and the output

set of scanners have 3 individual output ports. The input ports connect to the optical

fibers or other laser sources. The normal incident beams are then deflected by the first set

of horn shape scanners, then collected by the second set of the horn shape scanners and

deflected back to normal output from the end of the output ports. These scanners can be

158

individually operated such that the beam can be arbitrarily deflected from either one input

port to any one of the output ports.

Figure 4-5 shows the BPM simulation of a 3X3 optical switch designed for

1.55µm light with applied field of 14.9kV/mm in lithium tantalate wafer. In this switch,

the input aperture in the input port scanner is ~264µm in diameter and the output aperture

is ~793.2µm in diameter. The length of each scanner is ~10.0mm. The distance between

the ends of the input port and input aperture of the output port is ~28.5mm. The length of

the whole device is ~48.5mm. In this switch design, for simplicity, we fabricated one set

of electrode for all three inputs, and one set of electrodes for all the output ports,

respectively. The input ports were not operated individually at this stage. The sample

thickness was ~ 295µm.

The input port of the switch was tested in a continuous manner for different

applied fields with infrared light of wavelength 1.55µm (Figure 4-6). The measured

Figure 4-5: BPM simulation of 3X3 optical switc. The polarization direction of the crystal is perpendicular to the page, with the area enclosed by the triangles opposite in spontaneous polarization (Ps) than the rest of the device.

159

scanning angles show a linear relationship with the applied voltage, which is in good

agreement with that predicted using BPM simulation.

The optical switch was tested in a static manner. Two separate power supplies

were used to apply the voltages to input ports and output ports individually. The output

beam was monitored with a CCD camera (Cohu 4812). The beam was incident into the

center input port. With an applied voltage of 2.08kV/mm (or 1.99kV/mm) on both the

input ports and the output ports, the beam was successfully coupled into the output

(Figure 4-7). The voltages applied were a little lower than those (~2.15kV/mm) predicted

using BPM. This can be seen from the beam spot location and beam shape. When the

second stage (output port) was activated, the beam will be guided back towards to its

original location when there is applied field.

In this design, the number of the switches is limited by the input aperture of the

scanner and beam size as well as the applied field. The input aperture should be big

(a) (b)

Figure 4-6: (a) deflection angle versus applied voltage across the horn shape scanner in the input port. (b) the output beam from the input port of the optical switch with different applied voltage. There is no applied voltage on the output port.

160

enough to accommodate the beam size after the beam divergence. In order to operate the

optical switch individually, the applied voltage needs to be lowered such that the field

between two separate input ports or two separate output ports does not exceed the

breakdown of the gap. In order to do this, the input aperture of the scanner and the gap

between the input port and output port can be optimized to achieve better resolvable

beam spots and lower operating electric fields.

4.2.2.3 Anomalous electro-optic effect in Sr0.6Ba0.4Nb2O6 single crystals and its application in two-dimensional laser scanning

In this section, the observation of an anomalous electro-optic effect along the

ferroelectric polarization direction in SBN:60 is presented. Then using this effect, by

employing SBN:60 for vertical scanning in tandem with a conventional LiTaO3 scanner

for horizontal scanning, a 2-dimensional laser scanning system is demonstrated.

Figure 4-7: The output beam taken by CCD camera with the applied voltage on both stages in the optical switch. The stage 1 denotes the input port and stage 2 denotes the output port.

161

SBN:60 has a tetragonal unit cell with lattice parameters a=b=1.243nm, and

c=0.394nm. SBN:60 single crystal samples of c-cut orientation, (polarization direction, c

approximately along the thickness of the slice), and optical grade were commercially

obtained from Rockwell Scientific Company. These were first uniformly domain inverted

(or poled) along the c ([001]) direction using water electrodes at room temperature, or Au

or Ta electrodes at 22±1°C to create a single domain state. The spontaneous polarization,

Ps ~19±1µC/cm2, and the coercive field, Ec ~1.9 kV/cm, for domain reversal were

determined using transient current measurements during poling. 25 The measurement

setup was calibrated using LiNbO3 crystals. The literature values for SBN:60 crystals are

Ps~ 23-28 µC/cm2 and Ec~2.2-2.5 kV/cm. The discrepancy may be due to small

differences in compositions, or the manner in which Ps is determined using background

subtraction and charge integration of transient currents during poling. (We have

subtracted a total background charge of ~4µC/cm2 by subtracting the observed transient

current after the poling is complete). Piezoelectric constant d33 was measured to be ~150

pC/N, which compares well with reported values of 140pC/N-180pC/N. 26,27

We now describe the observed anomalous electro-optic effect. Below, the lab

coordinates defined as (x,y,z), (inset of 1(a)) are approximately parallel to the

crystallographic coordinates (a,b,c), respectively. Collimated laser beam from a 632.8nm

wavelength He-Ne laser, with a linear polarization (along the c axis of the crystal), is

focused by a plano-convex lens of 200mm focal length placed in front of the SBN:60

wafer with a focal point at the center of the crystal along the light propagation direction,

y. The crystal dimensions were 1.05 mm thick along electric field direction, z, and 15.0

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mm long in the light propagation direction, y. The intensity of the light at the focus is

~1.9 mW/cm2 with a beam waist of ~80µm. Care was taken not to clip the laser beam at

the input or output apertures of the crystal. A series of square wave voltages with a fixed

negative swing of ~-0.95kV/cm (opposite to the polarization direction but less than

coercive field) and variable positive swing at1Hz frequency were applied on the crystal.

Laser scanning was observed along the vertical direction (z-axis in the inset of

Figure 4-8 (a)) with applied field. The scan angle was calculated as total scan angle.

This effect suggests the presence of an index gradient in the thickness direction, which is

unexpected purely from a linear electro-optic effect that is expected to create a uniform

index change ∆ne=r33E3 throughout the crystal thickness, where subscript 3 denotes the c-

axis of the crystal, r33 is the electro-optic coefficient and E3 the applied field. This

observed effect is therefore called anomalous, in this paper. Figure 4-8 shows the vertical

scanning with the beam passing through the crystal with different distances (h) from the

top surface (+c) of the wafer. The scanning angles are the vertical scanning angles from

positive voltages (parallel to the polarization direction) to 0 voltage. The scanning angles

change as the incident beam moves from near the top surface (electrical ground) to the

bottom surface (positive voltage), decreasing as the incident beam approaches the center

of thickness of the crystal. In general, vertical scanning angles were observed to strongly

depend on the domain reversal history of the sample. While the systematic trend in this

dependence is yet to be established, in this study, the maximum scanning angle for light

polarized along c-axis varied between 0.1° - 0.4° for a triangular waveform oscillating

between –0.95kV/cm to +5kV/cm field applied to the crystal at 1Hz frequency. The

163

maximum scanning angle for ordinary polarized light (perpendicular to c-axis) was

~0.07° for a 8.25kV/cm field.

This vertical scanning was also tested at frequencies up to 2kHz, the upper limit

determined by the current limit of our power supply (2mA), as well as device packaging.

The set-up is shown in Figure 4-9 (inset). A slit was placed in front of a silicon

photodetector, and the laser beam scanned across the slit with a triangular waveform

voltage. During one complete cycle of applied voltage, the laser beam scans across the

photodetector twice, and gives rise to two intensity peaks in one voltage cycle, as shown

in Figure 4-9 for 2kHz. The frequency of the modulated light is within 1.0% of the

frequency of the applied electric field. The scanning angle decreases by ~3.5% from

100Hz to 2kHz. Under DC fields, temporary drifting of the laser beam is observed (even

when the field is constant) followed by the beam coming to rest at a maximum deflection

angle proportional to the field value. This drifting is detectable up to 100Hz, resulting in

Figure 4-8: (a) Vertical scanning angle in the z-direction vs. electric field at 1Hz frequency. Inset is shown the experimental geometry; and (c) Scanning angle vs. distance to top surface (+c) at which the incident beam traverses through. A negative field swing of –0.95 kV/cm was present in all measurements (not shown).

164

the variance of the scan angle with field, seen in Figure 4-8. This drifting is not

detectable in our study (Figure 4-9) above 100Hz.

The origin of this vertical scanning is presently not clear. We now discuss the

following possibilities for the origin of this unusual phenomenon: (1) the orientational

miscut of the crystal, (2) the piezoelectric bending of SBN:60 crystal, and (3) space

charge effects.

Using X-ray rocking curve experiments, the largest offset of the crystallographic

c-axis of SBN:60 from the thickness direction z of the crystal was 2.8±0.1o. Such a

miscut results in general, in the presence of all electric field components Ea, Eb, and Ec

along the three crystallographic directions of SBN:60. With external electric field on, the

electro-optic coefficient r15 would rotate the principle axes and change all the three the

principle indices of index ellipsoid to be unequal. Thus the crystal strictly becomes

biaxial and the incident beam splits into two extraordinary polarized light beams. Since

Figure 4-9: The detection of vertical scanning of laser light using inset geometry at an applied field frequency of 2kHz. For each complete scan cycle, two maxima in detector intensity is expected, as observed above, indicating that vertical scanning can operate at 2kHz.

165

the offcut is small and the incident polarization is almost parallel to the c-axis, one of

these extraordinary beams dominates. While this beam travels through the crystal, its

Poynting vector deviates from a straight-line path within the c-b plane. This deflection of

the energy propagation direction inside of the crystal is a function of the external field,

and hence vertical scanning can occur at the same frequency as the external electric field.

If an additional positive curvature of the output edge of the crystal (measured radius of

curvature was R=40cm) due to edge polishing is considered as well, the vertical scanning

angle would be about 4.2x10-4 deg for an applied field of 5kV/cm. This value is several

orders of magnitude smaller than the magnitude of the observed anomalous vertical

scanning in our experiment (0.1 - 0.4°). Further, orientational effects are fixed for a given

sample, however we observe large changes in scan angle with in-situ domain reversals.

Hence the role of the off-cut in the crystals and the curvature of the output face during the

polishing can be ignored as the primary reasons for the observed vertical deflection.

SBN:60 also has large piezoelectric coefficients, elastic compliance constants and

relative dielectric constants.[23] With the applied electric field along the c-axis of the

crystal, the thickness and length of the electric field will expand or shrink under no clamp

conditions. In the frequency range of ~100 kHz, only longitudinal modes and radial

modes exist. However, with asymmetric clamp conditions, such as for instance, the top

electrode surface of the crystal being free, and the bottom electrode surface of the crystal

totally clamped, a bending mode will arise.

Experimental dielectric measurements indicate a first resonance peak around

28.87 kHz, which was confirmed to be a bending mode by using a detailed Atila software

based simulation of our packaged device. Due to the bending mode, the incident plane of

166

the crystal will bend with the same frequency as the electric field. If the bending of the

crystal occurs along the light propagation direction (y) such that the two surfaces

concentrically bend with a radius of curvature, the input and output edges are no longer

parallel, but tilt towards each other by an angle 2δ, then under paraxial approximation,

the deflection angle, θ of light beam traveling through in the y-direction can be simply

estimated as θ=2δ(n-1), where n is the refractive index of the crystal. SBN:60 crystal is a

negative uniaxial crystal (no>ne, ne=2.27, no=2.33). Based on this equation, theoretically,

ordinary (o) light would scan more than extraordinary (e) light with the same external

electric field due to this piezoelectric effect. However, we observe that only extraordinary

(e) light shows any noticeable vertical scanning (0.02° to 0.08°/kV) whereas ordinary (o)

light shows very small vertical scanning (angles of 0.008 degrees/kV) in a 1.05mm thick

crystal. This conflicts with the proposed piezoelectric bending mode argument. With

900V on the sample, the expected scanning angle is ~1.78x10-5 degrees, which is still

several orders lower than the experimentally observed scanning angles of ~0.3-0.8° at

these fields.

This unusual vertical scanning therefore suggests that there is an inhomogeneous

internal electric field along the applied electric field direction inside the material. Due to

its photorefractive property, space charges can be created inside SBN:60 single crystals,

giving rise to an inhomogeneous electric field inside the crystal along the applied electric

field direction. This would give rise to index gradients along the thickness direction

through the electro-optic effect. Further studies to test this hypothesis are underway.

167

Combining the horizontal scanning from a LiTaO3 crystal and the vertical

scanning from SBN:60, 2-dimensional scanning was demonstrated. Figure 3 shows this

type of two-dimensional scanning. The lithium tantalate scanner used here is described in

detail in Ref. [1]. Briefly, it consists of a series of ferroelectric domain prisms that

successively deflect light under an external electric field through the electro-optic effect.

The output laser beam from He-Ne laser was expanded into collimated beam by using a

combination of 50mm and 100mm focal length planar convex lenses, and then focused by

a 200mm planar convex lens into a 40µm diameter beam at the waist. The thickness of

lithium tantalate scanner crystal was 294µm, and the input aperture of the LiTaO3

scanner was 150µm. The dimensions of SBN:60 crystal used was

15mmx14.5mmx1.03mm. By applying step voltages of +850V or –50V on a 1.03 mm

thick SBN:60 crystal, and voltages of -1kV, -0.5kV, 0kV, 0.5kV and 1kV on a 294µm

thick LiTaO3 crystal based scanner, 10 distinct beam spots were obtained (Figure 4-10 ).

The total vertical scanning angle is 0.79±0.07°. The total horizontal angle is 3.68°±0.14°.

CCD Camera

+/- +/- SBN:60

Laser

LiTaO3

Figure 4-10: Two-dimensional scanning by using a combination of SBN:60 (vertical) and LiTaO3 (horizontal) crystals.

168

In summary, an anomalous vertical scanning was observed along polarization

direction in ferroelectric strontium barium niobate 60 (SBN:60) crystal, which was

successfully tested up to 2kHz frequency, Such vertical scanning angles varied from

sample to sample, as well as domain reversal history. The origin of such unusual

phenomenon is not fully understood yet, but believed to arise from inhomogeneous index

gradients near the crystal surfaces, possibly arising from space charge fields. A 2-

dimensional scanner system was also successfully demonstrated by combining a lithium

tantalate based horizontal scanner and a SBN:60 based vertical scanner.

4.3 Optical Frequency Converter

Second harmonic generation (SHG) and optical parametric oscillation (OPO) are

nonlinear optical methods to generate new monochromic wavelength. Due to lack of the

laser materials to cover the wavelength region for light sources, SHG is an alternative

way to get new light source, especially green light source for display today. In SHG

method, the energy is transferred back forth from the fundamental wave to its second

harmonic wave through the nonlinear optical process, which corresponds to a two-photon

absorption process.28 The OPO is a method to convert one optical frequency to two

discrete optical frequencies (ω3→ω1+ω2) or to convert from two optical frequencies to

single optical frequency (ω1+ω2→ω3). This process needs the nonlinear optical materials

to be noncentrosymmetric. Most nonlinear materials do not have the critical phase

matching angle due to small dielectric dispersion to satisfy the momentum conservation

condition.

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Lithium niobate has high nonlinear optical coefficient, d33 (~86 KDPd36 ), however it

does not have critical phase matching angle at 1.06µm for SHG. In SHG, the energy

flows from the fundamental wave to its second harmonic wave during the first coherence

length, Lc, then the energy will would flow back from the second harmonic wave to its

fundamental wave within distance Lc to 2Lc. However, if the polar axis changes its

direction every other Lc, then the nonlinear dielectric coefficient changes its sign,

therefore, the energy would keep flowing from the fundamental wave to its second

harmonic wave. In this case, 2 Lc would be the period of the periodic nonlinear optical

structure. Ferroelectric crystal lithium niobate has two possible spontaneous polarization

directions which can be switched by an external electrical field. When the domain

structure in lithium niobate is poled into periodical poled structure with period of 2Lc,

then lithium niobate can be used for second harmonic generation. This technique to

generate SHG is called quasi-phase matching (QPM). The period of the structure (Λ=2Lc)

for 1st order QPM satisfy the following condition:

Where λ, andn ,)(ω )2( ωn are the fundamental wavelength, refractive index of the

fundamental wave, and refractive index of the second harmonic wave.

To achieve the SHG from 1.06µm at room temperature, the period (Λ ) of lithium

niobate QPM structure (or called periodically poled lithium niobate, PPLN) is plotted in

Figure 4-11. As can be seen the period of PPLN is ~ 6.8µm at room temperature for

1.064µm. In order to get such periodically poled structure, the +z surface of the congruent

)()2(2 ωω

λnn

Lc −==Λ Eq. 4.10

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lithium niobate was sputtered with uniform Cr electrode, then the electrode was etched

away into the pattern after photolithography. To minimize the surface conduction, the +z

surface of the lithium niobate was sputtered with a thin layer of photoresist (Shipley

1817) and then hard baked at 160°C for 3~4 hours. The poling was done at room

temperature with in-situ monitoring. Figure 4-12 shows the periodically poled structure.

The device was successfully tested at Corning inc. in Dr. V. Bhagavatula’s lab.

(a) (b)

Figure 4-11: (a) the period of lithium niobate QPM structure versus the pump laser wavelength at room temperature (~24.5°C); (b) the period of lithium niobate QPM structure versus the temperature for second harmonic generation (SHG) at 1.064µm.

171

Besides the periodical poling on congruent lithium niobate for SHG, the

stoichiometric lithium niobate with (Ec~6kV/mm) and stoichiometric lithium tantalate

(Ec~1kV/cm) make the poling with a charged AFM tip possible. For the sample of

stoichiometric lithium niobate (SLN) with structure of –z-face-SLN/+z face

SLN/ITO(In2O3:SnO2)/CLN, in which the thicknesses of ITO and CLN are 75nm and

0.5mm, respectively. In PFM, an applied voltage ~60V was applied to the ITO electrode

(bottom of SLN) of the sample and ground to the Pt/Ti coated tip. The scan rate was

~5µm/s and the resolution of the scan was ~10. The poled area was then imaged by PFM

(Figure 4-13 ). By adjusting the scan rate and applied voltage as well as the scan

resolution, different poling period and aspect ratio can be achieved.

(a) (b)

Figure 4-12: Periodically poled congruent lithium niobate. (a) +z surface after hydrofluric acid (HF) etching; (b) the y surface of PPLN after HF acid etching.

172

4.4 Conclusion

In this chapter, a variety of optical devices based on microdomain engineering in

ferroelectric crystals were demonstrated in lithium niobate and lithium tantalate. They

can be used for optical beam scanning, wavelength conversion and optical

communications. Improvement of the performance of these devices needs to be achieved,

such as reducing the operating voltages, improving the poling reproducibility and

reliability. The flexibility of domain reversal using PFM system was also demonstrated.

The stoichiometric lithium niobate and stoichiometric lithium tantalate make this method

applicable.

(a) (b)

Figure 4-13: Periodically poled stoichiometric lithium niobate using PFM system. The applied voltage was ~60um and scan rate was ~5µm/s. (a) amplitude; (b) phase of PFM image.

173

References

1. Steinmeyer, G. A review of ultrafast optics and optoelectronics. Journal of Optics A: Pure and Applied Optics 5, 1-15 (2003).

2. Limpert, J., Roser, F., Schreiber, T. & Tunnermann, A. in 2005 IEEE LEOS Annual Meeting, 22-28 Oct. 2005 643-4 BN - 0 7803 9217 5 (IEEE, Sydney, NSW, Australia, 2005).

3. Ogawa, Y. Trend of ultrafast optical device and laser technologies. Review of Laser Engineering 27, 246-50 (1999).

4. Lin, J. T. in Southcon/88 Conference Record, 8-10 March 1988 178-83 (Electron. Conventions Manage, Orlando, FL, USA, 1988).

5. Poprawe, R. & Schulz, W. Development and application of new high-power laser beam sources. RIKEN Review, 3-10 (2003).

6. Waidelich, R. M. & Waidelich, W. R. in Laser Florence 2000: A Window on the Laser Medicine World, 18-22 Oct. 2000

Proceedings of the SPIE - The International Society for Optical Engineering 1-6 (SPIE-Int. Soc. Opt. Eng, Florence, Italy, 2001).

7. Revelli, J. F. in 1979 IEEE International Symposium on Applications of Ferroelectrics, 13-15 June 1979

Ferroelectrics 93-6 (Minneapolis, MN, USA, 1980). 8. Zhai, J. et al. in Optical Scanning: Design and Application, 21-22 July 1999 Proceedings of the SPIE - The International Society for Optical Engineering 194-

201 (SPIE-Int. Soc. Opt. Eng, Denver, CO, USA, 1999). 9. Fang, J. C. et al. Shape-optimized electrooptic beam scanners: experiment. IEEE

Photonics Technology Letters 11, 66-8 (1999). 10. Chiu, Y., Zou, J., Stancil, D. D. & Schlesinger, T. E. Shape-optimized

electrooptic beam scanners: analysis, design, and simulation. Journal of Lightwave Technology 17, 108-14 (1999).

11. Chen, Q., Chiu, Y., Lambeth, D. N., Schlesinger, T. E. & Stancil, D. D. Guided-wave electro-optic beam deflector using domain reversal in LiTaO3. Journal of Lightwave Technology 12, 1401-4 (1994).

12. Scrymgeour, D. A. et al. Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics. Applied Physics Letters 81, 3140-2 (2002).

13. Yamada, M., Saitoh, M. & Ooki, H. Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals. Applied Physics Letters 69, 3659-61 (1996).

14. Noda, J., Uchida, N. & Saku, T. Electro-optic diffraction modulator using out-diffused waveguiding layer in LiNbO3. Applied Physics Letters 25, 131-3 (1974).

15. Lotspeich, J. F. Electrooptic light-beam deflection. IEEE Spectrum 5, 45-52 (1968).

16. Meyer, R. A. Optical beam steering using a multichannel lithium tantalate crystal. Applied Optics 11, 613-16 (1972).

17. Lotspeich, J. F. Electrooptic light-beam deflection. IEEE Spectrum, 45-53 (1968).

174

18. Feit, M. D. & Fleck, J. A. J. Light propagation in graded-index optical fibers. 17, 3990-3998 (1978).

19. Fleck, J. A. J., Morris, J. R. & Feit, M. D. Time-dependent propagation of high-energy laser beams through the atmosphere. 99-115 (1977).

20. Yamada, T. Landolt-Bornstein. Group III Condensed Matter LiNbO3 Family Oxides. Landolt-Bornstein. Numerical Data and functional relationships in science and technology, 149-163 (1981).

21. Muhammad, F. et al. Multichannel 1.1-kV arbitrary waveform generator for beam steering using ferroelectric device. IEEE Photonics Technology Letters 14, 1605-1607 (2002).

22. Yamada, M., Saitoh, M. & Ooki, H. Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals. Applied Physics Letters 69, 3659-3661 (1996).

23. Ninomiya, Y. Electro-optic prism array light deflector. Electronics and Communications in Japan 56, 108-14 (1973).

24. Revelli, J. F. High-resolution electrooptic surface prism waveguide deflector: an analysis. Applied Optics 19, 389-97 (1980).

25. Gopalan, V. & Mitchell, T. E. Wall velocities, switching times, and the stabilization mechanism of 180° domains in congruent LiTaO3 crystals. Journal of Applied Physics 83, 941 (1998).

26. Neurgaonkar, R. R., Oliver, J. R., Cory, W. K., Cross, L. E. & Viehland, D. Piezoelectricity in tungsten bronze crystals. Ferroelectrics 160, 265-76 (1994).

27. Neurgaonkar, R. R. & Cross, L. E. Piezoelectric tungsten bronze crystals for SAW device applications. Materials Research Bulletin 21, 893-9 (1986).

175

Chapter 5

Conclusions and future work

This thesis is centered on understanding the ferroelectric domain wall structure

and its relationship with the microscopic domain properties in ferroelectric crystals

lithium niobate, lithium tantalate and strontium barium niobate. To achieve this, the

ferroelectric domain wall was studied through the electromechanical response across a

single ferroelectric domain wall on nanoscale level using piezoresponse force microscopy

(PFM), and the domain reversal with external electric field on macroscopic level. Novel

applications based on domain wall shaping were demonstrated.

5.1 Conclusions on electromechanical response across the single domain wall

1. The electromechanical responses in congruent lithium niobate (tantalate) and

stoichiometric lithium niobate (tantalate) show similar amplitude, which suggests

that the piezoelectric properties of the crystals do not change significantly with the

crystal stoichiometry in lithium niobate and lithium tantalate.

2. The amplitude of the vertical electromechanical response in a single domain

region of lithium niobate or lithium tantalate was found to be independent of the

tip size and tip geometry, both experimentally, and by Finite element Modeling

(FEM) for the in-contact case in PFM. This suggests that the tip is in contact

(d=0) with the sample surface during Piezoelectric Force Microscopy (PFM)

176

imaging. This resolves the prevalent uncertainty of the actual nature of contact in

this microscopy technique, where typically a gap is assumed.

3. The amplitude ratio of the vertical piezoresponse (primarily d33) in congruent

lithium tantalate to that in congruent lithium niobate was found to be ~0.67±0.02,

which is in agreement with ~0.73±0.07 predicted using FEM.

4. The resolution of the vertical response in periodically poled congruent lithium

niobate shows a linear dependence on the tip size in both PFM measurements

which agrees well with FEM results for the case in which the tip is in contact

with the sample and has a finite contact area. The extrapolations of the domain

wall width versus the tip size to the limit of zero tip radius results in a full

domain wall width (FW) ~75±10nm and full width half maximum (FWHM)

~7.2±3.14nm. Whereas, the HRTEM studies showed that the domain wall width

in lithium tantalate is virtually zero with upper limit of ~0.28nm,1 and 4~6nm for

BaTiO3.2

5. The FEM modeling of a 5-degree tilt wall in lithium niobate suggested that in

the PFM image, the minimum in the amplitude indicating domain wall location

moves by ~2.5µm from its original wall location. The tilted wall also generates

an asymmetry of the vertical response across the wall in lithium niobate.

Modeling also predicts that the domain width broadens in the case with tilted

wall as compared to the case with the straight wall. This broadening is 26% for

FWHM for a 5 degree tilt and a 50nm tip contact radius. Actual tilts in the

domain walls studied were no more than ~2.6 degrees. Assuming that the

177

broadening of the FWHM scales linearly with the tilt angle the broadening in

the experiments cannot exceed 14%.

6. The overall conclusion from domain wall width studies is that there might be

some broadening of domain wall properties on the 4-10nm length scale, as

compared to an ideal wall.

7. In FEM results, it was found that the amplitude of the slope of the crystal

surface across a wall (under a field at the tip) does depend on the tip size and

tip geometry. However, the ratio of the amplitudes between the slope of FEM

surfaces in lithium tantalate and lithium niobate does not depend on the tip size

and ratio is 0.70±0.05, which agrees well with the lateral PFM measurements

of a ratio of 0.67±0.02 for different tip sizes.

8. The amplitudes of the vertical piezoresponse do not change with the crystal

stoichiometry in both lithium niobate and lithium tantalate, whereas the domain

interaction width does change with the crystal stoichiometry. The wall

interaction width in stoichiometric lithium tantalate is narrower than that in

congruent lithium tantalate, whereas the wall interaction width in

stoichiometric lithium niobate is wider than that in congruent lithium niobate;

which might be correlated to different extrinsic effects on domain wall widths.

One possible reason may be that domain wall orientation changes from x-wall

in congruent lithium tantalate to y-wall in stoichiometric lithium tantalate;

whereas, the wall orientation remains y-wall for all stoichiometries in lithium

niobate.

178

9. The vertical amplitude of the vertical response in SBN:61 is ~1.7 times higher

than that in congruent lithium niobate, which is much lower than the value

(~7.9) predicted using FEM. Nanodomains found in the strontium barium

niobate might be the reason for the lower measured piezoresponse.

5.2 Conclusions on the domain reversal in stoichiometric lithium tantalate and SBN:61

1. Domain wall reversal in stoichiometric lithium tantalate synthesized using vapor

transport equilibrium (SLT-VTE) method shows the coercive fields are only

~1kV/cm (Ec,f ~1.39±0.01kV/cm and Ec,r ~1.23±0.01kV/cm), which are ~100

times lower than those in congruent lithium tantalate. The domain shape in SLT-

VTE becomes hexagonal, which make the crystal to be a good candidate for QPM

structure devices. The characteristics of the transient current in SLT-VTE suggest

that the defects reduce as the crystal goes to stoichiometric. The reduction of the

internal field in SLT-VTE is one proof the defect dipole model.

2. The domain reversal in SBN:61 was performed at room temperature with in-situ

monitoring. The domain wall shape in SBN:61 shows 4-fold symmetry. The

coercive fields of SBN:61 were determined to be ~2.39±0.04kV/cm and the

spontaneous polarization (Ps)to be ~ 27.71± 0.4µC/cm2.

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5.3 Domain wall shaping and applications

The optical devices such as beamlet scanner with larger aperture, 3X3 optical

switch as well as the QPM structures for SHG based on ferroelectric domain

microengineering technique were presented and discussed. In the beamlet scanner, a

device concept for scanning large (>1 cm) laser beams using a domain microengineered

ferroelectrics was presented. A total of 10.3° at 5.39 kV/mm was achieved with 5 stage

cascaded rectangular scanners in a single lithium tantalate wafer. A 3X3 optical switch

was also proposed, and preliminary results were presented. The scanning angles are in

excellent agreement with those predicted by using BPM method. A novel 2D scanning

scheme combining lithium tantalate and SBN:60 was demonstrated, even though the

origin of the scanning in SBN:60 crystal is still not fully understood. The QPM structure

with period of 6.9µm was successfully fabricated in a 300µm thick congruent lithium

niobate wafer. The stoichiometric lithium niobate and lithium tantalate also make the

QPM fabrication with PFM tip possible.

5.4 Outstanding issues

PFM is a very effective technique to study the ferroelectric domain wall on the

nanoscale and to correlate the electromechanical response across the single domain wall

to the intrinsic domain wall structure. The experimental and modeling studies in this

work on PFM response in lithium niobate and lithium tantalate bring it closer to link the

response and the domain wall structure. However, all the studies so far were conducted in

a static manner. A dynamical study of the wall structure, for instance, the possible wall

180

movement under an external dc electric field would lead to a better understanding of the

intrinsic domain wall structure, as well as the wall structure dependence of the crystal on

stoichiometry in lithium niobate and lithium tantalate.

In this thesis, the FEM modeling has been shown to be a very efficient way to

understand the piezoresponse across the domain wall in ferroelectrics. So far the

modeling has been limited only considered the case in which the material properties

change abruptly across the wall, instead of a more gradual change. A more detailed

modeling which incorporates the gradual change of the material properties would lead us

to a better understanding of the intrinsic domain wall structure and therefore link the

microscopic and the macroscopic material properties.

The lateral signal shows ~10 times higher domain wall width than predicted in

FEM, which suggests different broadening mechanism on the surface of the crystal than

in the depth direction. More detailed studies, such as how to calibrate quantitatively, the

lateral signal, as well as its mechanism would lead to a better understanding of the PFM

technique.

References

1. Bursill, L. A. & Lin, P. J. Electron microscopic studies of ferroelectric crystals. Ferroelectrics 70, 191-203 (1986).

2. Floquet, N. et al. Ferroelectric domain walls in BaTiO3: fingerprints in XRPD diagrams and quantitative HRTEM image analysis. Journal De Physique, III 7, 1105-1128 (1997).

181

Appendix A

Electric Fields Distribution under the AFM Tip

Scanning probe microscopy (SPM) techniques have been widely employed to

characterize the material properties, eg, electrical, mechanical, and dielectric and so on,

with spatial resolution up to sub-nanometer. The application of the field on the probe tip

in SPM techniques is very common. The potential and electrical field distributions inside

the specimen are of significant importance in the interpretation of the experimental

results.

In SPM, normally a probe tip is sitting on top of the specimen sample, either in

contact or non-contact. For simplicity, the AFM tip can be simplified as a sphere. The

potential and electrical field distributions inside the dielectric can be solved based on an

ideal electrostatic sphere-plane model using image charge method.

A.1 Point charge above a semi-infinite dielectric plane

Figure A-1 shows the case in which a point charge Q is located a perpendicular

distance s above a semi-infinite linear isotropic dielectric medium where the surface of

the dielectric lies in the xy plane with z=0.

182

The field potential in the region z<0 (outside the dielectric) can be obtained by

superposing the unscreened potential from the point charge Q with the potential produced

by the bound charge induced in the dielectric, or otherwise the corresponding image

charge Q′, which is located at z=s′ inside the dielectric.1 The potential in the region z>0

(inside the dielectric) is equal to that produced by a different image charge Q″ which is

located at z=s″. Thus the potentials in both z>0 and z<0 region can be written as:

At z=0, the continuity of both potential and normal component of dielectric

displacement gives:

Figure A-1: A point charge sitting with distance s away from an isotropic dielectric medium with relative dielectric constant εr.

( ) ( )

′−++

′+

+++=<

2222220

1 4

1)0,,(

szyx

Q

szyx

QzyxV

πε Eq. A.1

( )

′′−++

′′=<

2220

2 4

1)0,,(

szyx

QzyxV

rεπε Eq. A.2

183

By solving Eq. A.3 and Eq. A.4, it gives:

Therefore, The potential in vacuum produced by the point charge above a semi-

infinite dielectric can be thought as the superposition of the potential produced by the

unscreened point charge Q itself located at z=-s and the potential produced by the image

charge Q′ located at z=s′=s. The potential inside the dielectric is equal to the potential

produced by the charge Q″ located at z=s″=-s.

A.2 Point charge distribution to keep equal potential on a sphere

Consider the case (Figure A-2) in which there is a point charge q which is r

distance away from the center (point O) of the sphere with radius of R. To keep the equal

potential, which is zero, at the sphere surface, another point charge q1 must be located at

(0, 0, r1). The potential at an arbitrary point (x, y, z) on the sphere surface can be written

as:

)0,,()0,,( 21 === zyxVzyxV Eq. A.3

)0,,()0,,( 2010 =∂∂==

∂∂

zyxVz

zyxVz rεεε Eq. A.4

ss

ss

−=′′=′

Eq. A.5

QQr

r

1

1

+−−=′

εε

Eq. A.6

QQr

r

1

2

+=′′

εε

Eq. A.7

184

To satisfy the zero potential at the sphere surface, there exist:

Figure A-2: A point charge inside an equal potential sphere.

( ) ( )

( )

−++

−+=

−++

−+=

−++

−+=

θθπε

θθπε

θθθθπε

cos21cos214

1

cos2cos24

1

cos)sin(cos)sin(4

1

1

2

1

1

1

220

12

12

1

2220

21

2

1

220

rR

rR

rq

Rr

Rr

Rq

RrrR

q

rRrR

q

rRR

q

RrR

qV

Eq. A.8

qr

Rq

r

Rr

−=

=

1

2

1

Eq. A.9

185

A.3 The tip sphere above a semi-infinite dielectric plane

Consider the case that a sphere with radius R and voltage V is above a semi-

infinite dielectric, it is very reasonable to assume that there is point charge Q0 located at

the center of the sphere, thus this point charge is:

Then the sphere tip can be treated as point charge Q0 located at the center of the

sphere. From Section A.1, we know that there should be an image charge Q′ of Q0

located inside the dielectric to satisfy the boundary condition on z=0 plane. The

coordinate of Q′ is (0, 0, z0), and z0=R+d. The existence of the image charge Q′ will

destroy the equal potential condition on sphere surface. To keep this condition, then a

point charge Q1 should be placed at (0, 0, z1). The values of Q1 and z1 are deduced in

Section A.2. In the case shown in Figure A-3, there exist:

Where ro is the distance between the location of Q0 and the center of the sphere, r1

is the distance between the location of Q1 and the center of sphere.

To keep the boundary condition at z=0 and equal potential at the probe tip sphere,

it is necessary to repeat doing the above process, which is keeping adding the point

charge inside the sphere and its image charge inside the dielectric. The resultant image

charges and their location (distance away from the center of sphere) are:

0

4

0

00

==

r

RVQ πε Eq. A.10

0

2

11

000

1

)(2)(

)(2)(2

rdR

RzdRr

QrdR

RbQ

rdR

RQ

−+=−+=

−+=′

−+−=

Eq. A.11

186

For an anisotropic medium, according to Ref. [2], the above equations can be

rewritten as:

0

4

1

1

1

2

)(2)(

)(2)(2

0

00

11

2

11

1

==

+−

=

+=′′

−+=−+=

−+=′

−+−=

++

++

+

r

RVQ

b

QQ

rdR

RzdRr

QrdR

RbQ

rdR

RQ

r

r

ir

ri

iii

ii

ii

i

πεεε

εε

Eq. A.12

Figure A-3: A charged sphere is above a semi-infinite dielectric

187

Therefore the potential inside the dielectric specimen is:

Hence the fields are:

r

z

zr

ii

iii

ii

ii

i

r

RVQ

k

k

kb

Qk

kQ

rdR

RzdRr

QrdR

RbQ

rdR

RQ

εεη

πεεε

=

==

=+−=

+=′′

−+=−+=

−+=′

−+−=

++

++

+

0

4

1

11

2

)(2)(

)(2)(2

0

00

11

2

11

1

Eq. A.13

∑=

−++++

+=>0

2

2220

1

)(

1

2

4

1)0,,(

i

i

i

rdRz

yx

Qk

k

kzyxV

γ

πε Eq. A.14

∑=

−++++

+=>

02

2220

1

)()1(4

2)0,,(

i

i

i

rdRz

yx

Q

kzyxV

γ

πε

Eq. A.15

188

References

1. Zahn, M. Electromagnetic Field Theory: a problem solving approach. (1987). 2. Mele, E. J. Screening of a point charge by an anisotropic medium: Anamorphoses

in the method of images. American Journal of Physics 69, 557-62 (2001).

∑=

−+++++

=>0 2

32

2220

)()1(4

2)0,,(

i

i

ix

rdRz

yx

xQ

kzyxE

γ

πε

Eq. A.16

∑=

−+++++

=>0 2

32

2220

)()1(4

2)0,,(

i

i

iy

rdRz

yx

yQ

kzyxE

γ

πε

Eq. A.17

∑=

−++++

−++

+=>

0 23

2

2220

)(

)(1

)1(4

2)0,,(

i

i

ii

z

rdRz

yx

QrdRz

kzyxE

γ

γγπε

Eq. A.18

189

Appendix B

ANSYS Batch File for Piezoelectric Response Simulation

/begin

/clear, nostart

/file, PFM, db

!the tip location regarding to domain wall

x_tip=0

!the sample thickness in nm

thickness=4000

!the size of the sample in nm

zbot=4000

!radius of the tip in nm

R_tip=50

!distance in nm between the tip and top surface of the sample

d=0

/Title, AFM tip away from domain wall around %x_tip% nm; R=%R_tip%nm;

d=%d%nm;

!define the materals properties

/prep7

ET, 1, solid98, 3

MAT, 1,

190

!import the materials library

MPREAD, CLN, SI_MPL, , Lib

vclear, all

vdele, all, , , 1

BLOCK,-zbot,0,-zbot,zbot,-thickness,0

BLOCK,0, zbot,-zbot,zbot,-thickness,0

vglue, all

cylind, 700, 350, 0, 400, 0, 360

vgen, 1, 2, , , x_tip, 0, 0, , , 1

vglue, all

vdele, 2, , , 1

cylind, 100, 0, 0, 400, 0, 360

vgen, 1, 1, , , x_tip, 0, 0, , , 1

vglue, all

vdele, 1, , , 1

Local, 11, 0, -200, 0, 0, 0, 0, 0,

Local, 12, 0, 200, 0, 0, 0, 180, 0

csys, 0

vsel,s, volu, , 2

vatt, 1, 0, 0, 11

vsel, s, volu, , 3

vatt, 1, 0, 0, 12

vsel, s, volu, , all

191

hptcreate, area, 2, 0, coord, x_tip, 0, 0

!define boundary conditions

DA, 1, Ux, 0

DA, 1, Uy, 0

Da, 1, Uz, 0

DA, 1, Volt, %BotV%

DA, 13, Ux, 0

DA, 13, Uy, 0

DA, 13, Uz, 0

DA, 13, Volt, %BotV%

DA, 2, Volt, %TopV%

DA, 7, volt, %TopV%

DA, 11, Volt, %TopV%

DA, 14, volt, %TopV%

DA, 19, Volt, %TopV%

smrtsize, , 0.10, 1, 1, 7, 15, 1.4, 0, 1, 4, 0

smrt, 1

mshape, 1, 3D

mshkey, 0

vmesh, all

erefine, all, , , 1, 0

/SOLU

SOLVE

192

/POST1

finish

save, , , , all

exit

193

Appendix C

Background Signal in PFM Measurement

Both electrostatic and electromechanical contribution in PFM can be treated as

the vectors backgroundd and dd , respectively, in a complex plane. d represents the

piezoresponse in -c domain, and d− represents the piezoresponse in +c domain

(Figure C-1). The piezoresponsePR on both +c and –c domain of the measured PFM

signal are:

Therefore the amplitudes of the piezoresponse on both +c and –c domain are:

The phase delay between the piezoresponse on –c domain and +c will not remain

180° because of the electrostatic (backgrounddr

) contribution, instead the phase delay would

be θ, which is the angle between the piezoresponse on –c domain and +c (Figure C-1).

backgroundddPRrr

+−=+

backgroundddPRrr

+=− Eq. C.1

( )ϕ

ϕϕ

cos*2

sin)cos(

22

22



dddd

dddPR

−+=

++−=+

( )ϕ

ϕϕ

cos*2

sin)cos(

22

22



dddd

dddPR

++=

++=−

Eq. C.2

194

For the case in which the electrostatic contribution is dominant ( ddbackground >> ),

the amplitude of the piezoresponse in Eq. C.1 can be rewritten as:

For the case in which the electromechanical contribution is dominant ( backgrounddd >> ), the amplitude of the piezoresponse in Eq. C.1 can be rewritten as:

Eq. C.7

21 θθθ +=

ϕϕ

θsin

costan 1

background

background

d

dd +=

ϕϕ

θsin

costan 2

background

background

d

dd −=

2221

sin2)tan(tan

dd

dd

background

background

−=+=

ϕθθθ

Eq. C.3

background

background


background



d

dd

d

dd

d

dddd

ddddPR

≈

−≈

−≈

−+=

−+=+

ϕ

ϕ

ϕ

ϕ

cos

cos21

)cos*2

(1

cos*2

2

2

22

Eq. C.4

background

background



d

dd

d

dd

ddddPR

≈

+≈

+≈

++=−

ϕ

ϕ

ϕ

cos

cos21

cos*222

Eq. C.5

0

0sin2

tan22

→

≈−

=

θ

ϕθ

dd

dd

background

background

Eq. C.6

195

dd

dddd

ddddPR



≈

−+=

−+=+

)cos*2

(1

cos*2

2

2

22

ϕ

ϕ

d

d

dddd

ddddPR



≈

++=

++=−

)cos*2

(1

cos*2

2

2

22

ϕ

ϕ

01

1

90

1cos

sin

→

=≈+

=−

θ

ϕθ

d

d

PR

dd background

01

2

90

1cos

sin

→

=≈−

=+

θ

ϕθ

d

d

PR

dd background

021 180→+= θθθ

Eq. C.7

Figure C-1: The electrostatic (denoted as backgroundd ) and eletromechanical contribution

(denoted as d ) in PFM measurement. On –c surface, the electromechanical contribution

is d , whereas on +c surface it is d . PR is the amplitude of the measured PFM signal.

196

Appendix D

Dielectric Properties of Lithium Niobate, Lithium Tantalate and Strontium Barium Niobate

D.1 Lithium Niobate (LiNbO3)

D.2 Lithium Tantalate (LiTaO3)

Figure D-1: Dielectric constant and conductivity of congruent lithium niobate (CLN) and stoichiometric lithium niobate (SLN) at room temperature.

197

D.3 Strontium Barium Niobate (Sr0.61Ba0.39Nb2O6 or SBN:61)

Figure D-2: Dielectric constant and conductivity of congruent lithium tantalate (CLT) and stoichiometric lithium tantalate grown using vapor transport equilibrium treatment (SLN_VTE) at room temperature.

Figure D-3: Dielectric constant and conductivity of strontium barium niobate 61 (Sr0.61Ba0.39Nb2O6 or SBN:61) at room temperature.

198

VITA

Lili Tian

Education Aug. 2001-Present

Pennsylvania State University, University Park, PA Ph.D Candidate in Materials Science and Engineering

Oct. 1998-Dec.2000

American University, Washington, DC MS in Physics

Experience Aug. 2001-Present

Research Assistant, Pennsylvania State University, University Park, PA

June 2004-Aug. 2004

Corning Incorporated, Corning, NY Summer Intern, Optical Physics & Network Technologies Division

July 2000-Aug. 2001

Database Programmer, WCL, American University, Washington, DC

Patent Jiyang Wang, Henfu Pan, Jinqian Pan, Yaogang Liu, Lili Tian,

Zhongshu Shao, Minhu Jiang, Growth technique of AxGa1-xAl3(BO3)4 (A=rare-earth elements) Single crystals, Chinese patent ZL 96 1 9014. Venkatraman Gopalan, David A. Scrymgeour, Lili Tian, Kenneth L. Schepler, “Phased Array Electro-optic Beam Steering”, PSU Invention Disclosure Number 2004-2991.

Language Chinese, English Activities SPIE Student Chapter at Penn. State University: Secretary 2004-2005

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