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The Pennsylvania State University
The Graduate School
Intercollege Graduate Program In Materials
DYNAMIC LINEAR ELECTRO-OPTIC FREQUENCY DEPENDENCE IN
PMN-32%PT AND PZN-8%PT FOR RF MICROWAVE PHOTONICS
A Thesis in
Materials
by
© 2005 Shikik T. Johnson
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2005
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UMI Number: 3187519
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The thesis of Shikik T. Johnson was reviewed and approved* by the following:
Karl M. Reichard
Assistant Professor of Acoustics
Research Associate
Co-Thesis Advisor
Co-Chair of Committee
Ruyan Guo
Professor of Electrical Engineering
Co-Thesis Advisor
Co-Chair of Committee_________
James K. Breakall
Professor of Electrical Engineering
Venkatraman Gopalan
Associate Professor of Materials Science and Engineering
Coming Fellow___________________________________
William B. White
Professor Emeritus of Geochemistry
Albert Segall
Associate Professor o f Engineering Science and Mechanics
Co-Chair Intercollege Graduate Program in Materials
*Signatures are on file in the Graduate School
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ABSTRACT
The electrooptic effect (at X— 633nm) in both PMN-32%PT and PZN-8 %PT
relaxor ferroelectric single crystals was investigated as a function of small signal
modulation frequencies. Piezo-resonance measurements were also conducted to examine
piezooptic coupling in these materials for selected resonance modes to observe the
influence of piezoelectric activity on the electro-optic behavior.
The electrooptic rc
coefficient in PMN-32PT and PZN-8 %PT crystals were found to have strong frequency
dependence at frequencies below 100s Hz apparently due to space charge effects.
Anomalous electrooptic properties near piezoelectric resonance frequencies are reported
to be attributed to a synchronization of the low frequency piezoelectric resonance and
high frequency transverse lattice vibrations near 4th-order harmonics.
Also reported is enhanced electrooptic properties near piezoelectric resonant
frequencies that may be attributed to synchronization of the low frequency fundamental
modes and up to their 5th order harmonics accompanied by nonlinear extrinsic activity in
the form of lateral domain region motion. A constructive interaction with overlapping
high order piezoelectric and electrooptic resonances can be engineered, using PMN32%PT rhombohedral and PZN-8 %PT crystals as an example, so that a small signal
(.25V/mm) amplified electro-optic detector in the RF frequency region may be envisaged
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TABLE OF CONTENTS
LIST OF FIGURES.........................................................................................................
vi
LIST OF TABLES..................................................................
xiii
ACKNOWLEDGEMENTS.............................................................................................
xiv
Chapter 1 INTRODUCTION........................................................................................
1
Chapter 2 BACKGROUND THEORY.........................................................................
7
2.1 Piezoelectricity..................................................................................................
2.2 Electric Field Effects in Ferroelectrics............................................................
7
14
2.2.1 Relaxor Ferroelectrics.................................................................................
2.2.2 Electrooptic Effect in Ferroelectrics..........................................................
19
20
Chapter 3 EXPERIMENTAL DESCRIPTIONS...........................................................
30
Materials Considerations and Selections.........................................................
Polarization vs. Coercive Field (Hysteresis)...................................................
Piezoresonance Method....................................................................................
Electrooptic vs. Frequency Measurements......................................................
AC Biasing........................................................................................................
DC Biasing........................................................................................................
30
32
34
34
41
43
Chapter 4 RESULTS AND DISSCUSSION................................................................
47
3.1
3.2
3.3
2.4
3.5
3.6
4.1 EO Effect in Low Frequency (<100,000 Hz or below piezoelectric
fundamental resonant modes)...........................................................................
4.2 Effective EO Coefficient at Higher Frequencies near Piezoelectric
Resonances........................................................................................................
4.3 AC Biasing to Assist Resonance Enhanced EO Effect in PMN-32%PT
4.4 AC Biasing to Assist Resonance Enhanced EO Effect in PZN-8 % P T
4.5 Interpretation o f AC Biasing Results...............................................................
4.6 DC Biasing.........................................................................................................
4.7 A ging..................................................................................................................
4.8 RF Optical Transduction...................................................................................
58
74
87
95
106
108
112
Chapter 5 CONCLUSIONS............................................................................................
115
4.3 Fuure W ork........................
47
117
iv
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Chapter 5 BIBLIOGRAPHY
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LIST OF FIGURES
Figure.
Caption
Page
Figure 1-1: Microchip laser structure showing complex composite crystal
where electrooptic section modulates the light source generated by
the NdYAG laser. This illustration comes by courtesy of reference [5]............ 3
Figuren 1-2: Dynamic EO measurement illustrating solid-state light modulation
apparatus used in this thesis............................................................................4
Figure 1-3: Illustration o f RF modulation of coherent light source. In this
depiction the x-axis shows RF modulating frequency and the y-axis
indicates the modulated optical output converted into voltage. This
data was collected by the author from our PZN-8 %PT crystals.................. 6
Figure 2-1: The direct effect, a), and b) the converse effect; c) expansion, and
d) contraction. The solid lines indicate theoriginal shape............................ 10
Figure 2-2: Illustration of two distinctive modes which have different resonance
values and are coupled by poison’s ratio.......................................................13
Figure 2-3: Depiction of BaTi0 3 unit cell undergoing FE phase transition from
para-electric cubic phase to FE tetragonal phase at Tc' 125°C. A
note surface charge develops on the Z-faces of the unit cell when
Ti4+ shifts during the FE phase transition, (not drawn to scale).................. 16
Figure 2-4: Hysteresis loop showing poling effects on FE. Where Pr refers to
remnant polarization, and Psa, refers to saturation. Ec is the coercive
field................................................................................................................... 17
Figure 2-5: Polarization versus electric field for ideal antiferroelectrics.........................18
Figure 2-6; Dispersion of the permittivity, s, and the electro-optic coefficient,
r 63 for NH 4 H2 PO4 , KH2P 0 4, and N 4 (CH2)6. e: 1)KH 2 P 0 4 ;2)
NH 4 PO4 ; 3) N 4 (CH2)6. r63: 4) KH2P 0 4; 5) NILPCV This figure
implicates the various polarization mechanisms ability to follow a
driving frequency into to optical regime where only the electronic
polarization mechanisms remain. (After Yu V. Pisarevski, et al, see
r e f [17])...........................................................................................................25
vi
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Figure 2-7:
Variation of er’ and s” as a function of frequency. Space charge and
dipolar polarization are relaxation processes and strongly
temperature dependant; ionic and atomic polarizations are
resonance processes and temperature independent. Over specific
frequency ranges the loss is maximum as shown by peaks in e (co)”.
Courtesy o f reference [30].............................................................................27
Figure 3-1: Illustration of our crystals showing poling direction relative to
crystallographic axes and directions. Note that the laser source will
traverse the direction parallel to <0 1 0 > perpendicular to the c-axis
or <001>...........................................................................................................31
Figure 3-2: Hysteresis loops showing polarization as a function of E-field
indicating domain structure as energy is required to reorient them
when bringing the ferroelectric to polarization saturation........................... 33
Figure 3-3: Transmittance of a crossed-polarized electrooptic modulator as a
function of applied voltage. The modulator is biased to the point T=
%I2, which results in a 50% intensity transmission. A small applied
sinusoidal voltage modulates the transmitted intensity about the
bias point......................................................................................................... 35
Figure 3-4: Schematic illustration of dynamic electrooptic frequency
measurement apparatus used to measure the rc coefficient for
PMN-32%PT and PZN-8 %PT samples........................................................36
Figure 3-5: Actual experimental Semamont set-up used to collect EO frequency
plots. This figure only illustrates the optical path o f the set-up for
clarity................................................................................................................37
Figure 3-6: Schematic showing AC-bias configuration and DC supply to
augment effective EO coefficient rc for PMN-32%PT ad PZN8 %PT samples................................................................................................. 43
Figure 3-7: T-Blocking circuit used to isolate AC and DC sources while
conducting EO measurement.........................................................................44
Figure 3-8: Transfer Function - displays voltage output across the crystal in dB
with respect to the input voltage.................................................................... 45
Figure 3.9: Voltage curve signifying the voltage correction when calculation rc..........46
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Figure 4-1:
Apparent EO coefficient rc of PMN-32PT crystal as a function of
frequency of dynamic modulating field, obtained using Senarmont
dynamic measurement method. The solid curve is the fitted result.
Inset illustrates details of improved resolution obtained for higher
frequency by polynomial fitting.....................................................................49
Figure 4-2:
Comparison of measured apparent rc coefficient with the two terms
(space charge effect - term l, and domain reorientation effect - term
2 ) used in the fitting (top), and (bottom) figure showing polynomial
fitting for improved fitting results at higher frequency region.................... 54
Figure 4-3:
Admittance plot for PMN-32%PT showing feature-less spectra at
low frequencies below piezoresonance with only spurious
inflections possibly due solely to the circuit of the measurement
apparatus.......................................................................................................... 55
Figure 4-4:
Low Frequency EO and rc coefficient for PZN-8 %PT, showing
monotonic decrease, in rc, as a function of increasing frequency.
Note rC value is quite large (> 2500 pm/V) at 10KHz...............................56
Figure 4-5:
Admittance plot (top) and corresponding EO spectrum for PMN32%PT crystal showing clear piezo-optical contributions which
enhances the EO rc coefficient.......................................................................57
Figure 4-6:
Admittance plot (top) and corresponding EO spectrum for PMN32%PT crystal showing clear piezo-optical contributions which
enhances the EO rc coefficient.......................................................................00
Figure 4-7:
Thickness mode and corresponding EO frequency response
showing enhancement.....................................................................................61
Figure 4-8:
Showing d3 i (fr ~ 203kHz) mode and a mixed d32 (fr ~ 245kHz)
modes, depicting EO and piezoelectric correspondence in
PMN32%PT crystals. Also shown is a an illustration of the
crystallographic directions and sample dimensions..................................... 63
Figure 4-9:
Admittance plot (top) and corresponding EO spectrum for PZN8 %PT crystal showing clear piezo-optical contributions which
enhances the EO rc coefficient...................................................................... 65
Figure 4-10: A blow up of Figure 4-9 showing direct correspondence between
EO rc coefficient and piezoelectric resonance.............................................. 6 6
viii
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Figure 4-11: Comparison of measured and ATILA generated plot for PMN32%PT showing reasonable agreement considering discrepancy in
numerical values..............................................................................................69
Figure4-12: Comparison of measured and ATILA generated plot for PZN8 %PT showing reasonable agreement considering discrepancy in
numerical values..............................................................................................70
Figure 4-13: Admittance plots illustrating piezoelectric d33 , d3 i modes at relative
high frequencies. Note the small amplitudes of inflections as the
crystal strains cannot follow the high frequency electric field................. 71
Figure 4-14: Admittance plots illustrating piezoelectric d33 , d3 i modes at relative
high frequencies. Note the small amplitudes of inflections as the
crystal strains cannot follow the high frequency electric field ................. 72
Figure 4-15: PMN-32%PT high frequency EO measurement showing complex
spectra above piezoelectric frequency range where intrinsic elastic
motions are clamped out.................................................................................73
Figure 4-16: PZN-8 %PT high frequency EO measurement showing complex
spectra above piezoelectric frequency range where intrinsic elastic
motions are clamped out................................................................................. 74
Figure 4-17: Biasing the crystal around its thickness mode fr= 178kHz yields
broadening EO behavior at higher frequencies near 5th-order
harmonics........................................................................................................ 76
Figure 4-18: Illustration of relative EO enhancement when biasing the PMN32%PT crystal on its pseudo-thickness mode d33 .........................................77
Figure 4-19: Pseudo transverse lateral extension mode occurring at ~203kHz.
With accompanying EO enhancement spectra............................................. 78
Figure 4-20: Illustration of a closer look at ac-biased enhanced region showing a
roughly 10 dB difference between biased and unbiased EO
behavior............................................................................................................79
Figure 4-21: Illustration of longitudinal pseudo-transverse mode, showing
largest EO effect of the 3 natural modes....................................................... 80
Figure 4-22: Blow up of EO enhanced region with ac biasing the crystal on the
d32 pseudo-transverse mode. Roughly a 40 dB difference between
biased and unbiased regions is produced.......................................................81
ix
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Figure 4-23: Biased and unbiased comparison showing suppression of light
output across all corresponding piezo-resonance peaks. Shown
here on a Log plot to clarify the scale of output difference......................... 83
Figure 4-24: Comparison of biased (203 kHz, d3 i mode) and unbiased condition
on a linear scale in PMN-32%PT showing suppression of
corresponding thickness mode, d33 , but slight enhancement of light
output associated with d3 i (l=4mm) extension mode. The lateral
extension mode, d32 , seems to be broadened................................................. 84
Figure 4-25: Comparison of the biased 4mm lateral extension mode and
unbiased crystal showing a general suppression of EO effects
associated with thickness and 4mm lateral extension mode, but a
slight increase in the biasing d32 (l=2mm) extension mode......................... 85
Figure 4-26: PZN-8 %PT high frequency EO measurement showing complex
spectra above piezoelectric frequency range where intrinsic elastic
motions are clamped out................................................................................. 8 6
Figure 4-27: AC biasing PZN-8 %PT on its longitudinal thickness mode or
pseudo-tetragonal thickness vibrations. Showing dramatic effects
to the light output near its higher harmonics .............................................. 8 8
Figure 4-28: AC biasing PZN-8 %PT on its transverse longitudinal lateral
extension mode. Showing dramatic effects to the light output.................. 89
Figure 4-29: Thickness mode vibration of PZN-8 %PT showing markedly
difference between biased and unbiased condition...................................... 91
Figure 4-30: Illustration showing biasing effects of transverse lateral mode or d32
showing marked difference between biased and unbiased
conditions.........................................................................................................92
Figure 4-31: Thickness mode ac bias showing general suppressing of all modes
as compared to unbiased condition................................................................93
Figure 4-32: Close inspection low-end EO effect near fundamentals for PZN8 %PT illustrating noticeable enhancement in light output for
extension mode, (d32 .) near 129 kHz Also, note the nearly equal
light output near crystallographically equivalent (l=4mm) lateral
extension mode occurring around 225 kHz.................................................. 94
x
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Figure 4-33: Thickness mode (~119 kHz) biasing effects on PZN-8 %PT
showing anomalous effects after 150 MHz. It shows the unbiased
EO light output appears to be larger than the biased effect. This is
contrary to results shown in the lower frequencies...................................... 95
Figure 4-34: Proposed illustration of domain structure in PMN-PT and PZN-PT
crystals used in our investigation.................................................................. 97
Figure 4-35: Illustration of domain wall motion when crystal is biased under
longitudinal thickness wave conditions. Those walls situated more
favorable to the condensation direction will move in synch with the
wave..................................................................................................................98
Figure 4-36: Illustration of domain wall motion when crystal is biased under
transverse longitudinal lateral wave conditions. Those walls
situated more favorable to the condensation direction will move in
synch with the wave........................................................................................ 103
Figure 4-37: Illustration of longitudinal thickness mode vibration for PZN-8 %PT
located at 118 kHz.Motions advance from top down left to right............... 104
Figure 4-38: Illustration of longitudinal thickness mode vibration for PZN-8 %PT
located at 118 kHz, continued from previous Figure 4-37...........................104
Figure 4-39: Illustration o f longitudinal transverse lateral mode vibration for
PZN-8 %PT located at 225 kHz, Motions advance from top to down
left to right........................................................................................................105
Figure 4-40: Illustration of longitudinal transverse lateral mode vibration for
PZN-8 %PT located at 225 kHz, continued from previous Figure 439. Motions advance from top to down left to right.................................... 106
Figure 4-41: Direct current (DC) bias, of PZN-8 %PT showing some subtle linear
effects of increased polarization. After the first 10 volts the
crystal’s polarization seemed to saturate, and doubling the voltage
generated a new peak near 225 kHz...............................................................107
Figure 4-42: A closer inspection of increasing the voltage. A nearly linear
response was achieved with the application of DC voltage. After
the first 1 0 volts however the crystal’s microstructure seems to
change and we see the emergence of a peak around 225 kHz that
was not there with 1 0 volts............................................................................. 108
Figure 4-43: Comparison of virgin poled to aged sample after high frequency
dynamic measurement.....................................................................................109
xi
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Figure 4-44: Comparison of piezo-resonances after sustained ac biasing at
fundamental 1 resonance m odes....................................................................I l l
Figure 4-45: Comparison of piezo-resonances after ac biasing at fundamental
resonance modes. This sample was subjected to sustained EO
measurements, but to a lesser degrees than that for PMN-32%PT.
Hence there appears to be no change in the admittance spectra.................. 112
Figure 4-46: Power budget schematic for our proposed solid-state single crystal
technology implying at least -2 0 dB of light output is lost in the
systems by the time the light output reaches the photodetector...................113
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LIST OF TABLES
Table 2-1:
Dielectric and Piezoelectric Properties of Pb(B 1,B2 )0 3 -PT Crystals
(Bl=Zn2+, Mg2+, B2=Nb5+), values for 1 k H z ............................................. 20
Table 2-2:
Linear Electrooptic materials measured at room temperature and in
the visible visible wavelength range............................................................. 24
Table 3-1:
Samples dimensinons and symmetry evaluated in this thesis.......................32
x iii
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ACKNOWLEDGEMENTS
I would like to thank all family members, extended family members and friends
for their support throughout this work. Also I would like to thank all committee members
who were instrumental in designing the experimental apparatus and for their sound
technical advice. I would like to acknowledge very insightful discussions with Dr.
Robert Newnham "Bob" for without his assistance and stem consistent tone throughout
my college career my development in electroceramics would not have come to this stage
this rapidly.
I would like to acknowledge the Applied Research laboratory Exploratory
Foundational Research Program, for providing the financial support for this thesis. Also
I would like to acknowledge the National Science Foundation grant: number DMR0333191, for partial financial support of day to day operating costs. I feel it due to
acknowledge the Alfred B. Sloan Foundation scholarship for their demonstrated
commitment to advancing underrepresented members of our global society in the
engineering, science, and medical fields. Last buy not least I must pay homage to our
heavenly father for without his blessing none of this is possible and to my ancestors who
tread the treacherous waterways long before I came into existence; doing so without
reprieve or wherewithal of who might follow their navigation.
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Chapter 1
INTRODUCTION
As the demand for high-speed data systems becomes common so too does the
need for reliable broadband communications networks. One way to accomplish
broadband networks is to use light as the sub-carrier of information. To bring waveforms
such as a wireless signal for mobile phones, analog television signals, or multimedia
services, directly onto a sub-carrier of light one would increase the bandwidth limits of
copper wires and coax transmission lines enormously. In principle using light as the
carrier of information at its full potential, efficiently, is to operate communications
systems at bandwidths between 0.1 to 10 percent of the carrier’s frequency. Since light
frequencies are on the order of 1014 Hz, theoretically efficient modulation rates could
exceed 1000 GHz [1]. O f course this is an ideal situation and is currently unattainable.
Microwave communications systems operating at maximum bandwidths are on the order
of 10 GHz. Another factor in light communications is modulation depths which
determine the usefulness of the light signal, where typically depths of 10 dB are required.
Optical fibers can also give rise to low bit error rates, easy installation and
maintenance, all of which amounts to costs savings on the bottom line [2]. Fiber optic
communications systems can increase the capacity of wireless systems if one can impress
the radio signal onto the light signal and vice versa. This technique is often termed radio
over fiber (RoF). The commercial benefits of increasing data rate capacity in wireless
1
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communications are numerous. In military applications, radio over fiber technology can
be used onboard ships replacing numerous heavy copper cables with fibers, delivering a
lighter, more rapidly installed low maintenance means to link computers and various
other communication devices [3].
Many researchers are developing schemes to make Rof feasible. Currently, there
are several different hybrid fiber-optic wireless schemes, where a central communication
station serves as command and control for base stations linked to individual terminals by
way of millimeter (mm) wave radio fiber links [3]. These and similar approaches rely
heavily on sophisticated digital signal processing (DSP) methods to bring radio waves
onto fibers. They often require elaborate electronic components to generate an optical
sub-carrier which is externally modulated at radio frequencies. Often these schemes are
complex and expensive. Other methods use heterodynes to mix weak optical signals with
strong local oscillators. When the carrier wave modulated with the information is mixed
with the oscillator wave, a photodiode detects the composite signal and produces an
electrical signal identical to the modulating information (data) signal. This electrical
signal is then converted back to an optical signal for broadband applications [4]. These
systems are limited by the shot noise of the local oscillator and will require a means to
increase the signal to noise ratio while maintaining acceptable operating temperatures.
Another hybrid fiber-optic/wireless communication scheme involves using
electro-optically tunable single mode microchip lasers constructed monotonically in a
single composite crystal, Figure 1-1. The modulation is impressed onto the subcarrier
laser signal by applying a digital voltage signal to the electro-optic section of the
composite, thus impressing the radio information onto a millimeter wave sub-carrier.
2
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This technique utilizes minimum shift keying (MSK) standards which are well known to
generate efficient signaling scheme. However, this scheme employs several different
components in order to generate the sub-carrier that the light signal must traverse on its
path down the fiber. At the interfaces between different components, scattering and
absorption issues will have to be overcome before this technique becomes a viable
system [5].
V,(t)' 1
a
Si23ii3£5i6iK?jjj
NcfcYVa Gain
section
MgOLiNbO, Tuning
section
Figure 1-1: Microchip laser structure showing complex composite crystal where
electrooptic section modulates the light source generated by the NdYAG laser. This
illustration comes by courtesy o f reference [5],
Our approach to impress radio information onto an optical sub-carrier is
predicated on direct modulation solid state technology. In other words, the radio signal
3
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will be directly coupled to an optical light wave signal in continuous mode by applying a
time varying voltage signal, V(t)=Vo sin(cot), to a relaxor ferroelectric single crystal
while at the same time passing coherent light through the crystal, see Figure 1-2 . The
principal objective of our approach is to employ high-strain relaxor ferroelectrics to serve
as modulators in a radio-frequency (RF) optical transduction process. In particular, we
are focusing our attention on the piezoelectric and electrooptic characteristics of
Pb(Mg2 /3Nbi/3) 03-PbTi03,(PMN-PT) and Pb(Zn2/3Nbi/3)0 3 -PbTi0 3 ,(PZN-PT) single
crystals, whose high performance characteristics show potential in RF/Optical
applications.
0=133
xl
dioda
P.
polarizer
BC
I* '
Itns
analyzer
wtplale
Laser A-d33nm
SernaaioKt apparatus EO measurements
Figure 1-2: Dynamic EO measurement illustrating solid-state light modulation apparatus
used in this thesis.
By bringing the RF signal directly into the crystal and hence onto the light signal
one can simplify the RF optical transduction mechanisms, eliminating the need for bulky
4
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electronics or sophisticated digital signal processing schemes. As alluded to previously,
because o f the gain in bandwidth a single optical fiber can replace numerous copper wires
currently in use, delivering a high capacity data streams necessary for multimedia
products. A network of fibers means a tremendous reduction in weight which will
translate to a reduction in fuel cost.
In this thesis it will be demonstrated that one can feasibly impress a RF
modulating voltage directly onto a coherent light source over a wide frequency range
utilizing the effective electro-optic (EO) properties of the above mentioned relaxor
ferroelectrics, namely, 0.68Pb (Mgi/3Nb2/3)O3-0.32PbTiO3, (PMN-32%PT) and,
0 .9 2 Pb(Zni/3Nb 2/3 ) 0 3 -0 .0 8 PbTi0 3
, (PZN-8 %PT). In doing this, we observed a
broadening enhancement to the EO behavior at relatively higher frequencies under
constant-stress ac-biasing conditions that are believed to be based on piezo-optical
contributions to the effective EO coefficient, see Figure 1-3.
The magnitude o f the Pockels or linear EO effect in most electro-optic crystals at
moderate frequencies (<10 MHz) and field strengths alters the refractive index of the
crystal which in turns governs the optical output of the crystal. However, in the
microwave frequencies this effect is too small to be useable; however, if one can
optimize this effect in a crystal it may be possible to use EO materials in the GHz
frequency ranges. Accordingly, not only are we exploring the EO properties of our
selected crystals as they vary with frequency, we also aim to identify ways to improve the
practicality o f these materials to find application in the RF to microwave-photonic
technologies.
5
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Ac biasing around 225kHz PZN-8%PT
140
1 20
•
100
•
- Unbiased
- 2 1 6 kHz
- 2 1 8 kHz
221 kHz
2 2 5 kHz
2 2 8 kHz
wr.-
Frequency [kHz]
Figure 1-3: Illustration of RF modulation of coherent light source. In this depiction the
x-axis shows RF modulating frequency and the y-axis indicates the modulated optical
output converted into voltage. This data was collected by the author from our
PZN-8 %PT crystals.
6
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Chapter 2
BACKGROUND THEORY
In the following sections, the electrooptic (EO) effect in typical ferroelectrics (FE)
crystals, accompanied by updated information on their EO frequency dependence
behavior is reviewed. Similarly, relatively new families of now commercially available
relaxor FE are briefly discussed. Accordingly, as the subject of this thesis is concerned
with mechanical enhancements to electrooptic characteristics over a wide frequency
range, piezoelectric concepts will begin the discussion. These introductory sections will
provide the background leading the reader to the objective of this work.
2.1 Piezoelectricity
All dielectric materials undergo a change in shape when under the application of
an electric field. The degree o f the shape change depends on the physical properties of
the material and the electric field strength [4, 9, 7]. Some materials develop an electric
polarization when stressed, whether tensile or compressive, and these materials are called
piezoelectric. One can readily observe the magnitude of the polarization set-up in the
piezoelectric if electrodes are applied to the material on the appropriate faces. To a first
approximation, the polarization that develops due to piezoelectricity is directly
proportional to the stress imposed onto the material. This action of stress induced
7
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polarization is termed the direct effect [9], In contrast, the converse effect describes the
change in dimensions or strain when piezoelectrics are under an applied field. The
following equations illustrate the direct and converse effect respectively:
p i = d ijkkX j kk
2.1
and,
x.t = d UE
jk
jk t
i
2.2
Where P, represents the induced polarization in Coulombs/meters2, (C/m2), dtj k the
piezoelectric coefficient in Coulombs/Newton (C/N), A ^is applied stress in
Newtons/meter2 (N/m2), Xjk is strain, change in length/unit length, (Al/1), and E j represents
electric field in Volts /meter (V/m). Subscripts that designate that they are tensors and
give their rank. Tensors are, for all intended purposes, vectors that completely describe
the magnitude and direction of physical quantities [8 ,10]. The rank of a tensor, denoted
by the number of subscripts, implicates the number and rank o f tensors that the quantity
in question connects. For example, the piezoelectric tensor listed in Eq. 2.1, dp, relates 2
vectors; one of l st-rank, Pi, and another vector of 2nd-rank X tj. This makes d p a 3rd-rank
tensor with 3 subscripts, as listed in Eq.2.1. Each subscript can represent up to 3 values
of direction and magnitude describing completely the full set o f coefficients of the
physical quantity. However, the symmetry of the material will impose restrictions on the
number o f coefficients that are observed. Accordingly, one would have to design
8
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experiments, meaning geometry and orientation of the material and apparatus, adhering
to these restrictions that are based on crystal symmetry systems.
O f the 32 possible crystal symmetries, also referred to as point groups, a solid
material can assume,
21
o f them do not posses a center of symmetry, the absence of
which is essential for the existence of piezoelectricity, although point group 43m is the
one exception [6 , 8 ]. For instance, the separation of negative and positive ions in
piezoelectric crystals establishes electric dipole moments that when stressed give rise to
an asymmetric displacement of the ions. In centrosymmetric crystal systems, this stress
would result in a symmetric displacement of ions producing no net dipole moment.
As alluded to previously in description of the direct effect, applying stress to
piezoelectrics changes the distance between the charges making up dipole moments
inducing a net polarisation in the crystal manifesting itself as surface charges at the
electrodes. For example let’s say we have a piezoelectric in the shape of a parallelepiped
with electrodes covering entirely its larger sides, as shown in Figure 2-1. Under
compressive stress (Figure 2-1 a), a current is observed in the circuit. Likewise, if the
stress is reversed (Figure 2-1 b); the current flows in the opposite direction. Conversely,
applying a voltage across the electrodes will induce strains in the material along a
direction determined by the crystal’s piezoelectric coefficients; and partly on the
voltage’s polarity and magnitude (Figure 2-1 c and d).
9
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Figure 2-1: The direct effect, a), and b) the converse effect; c) expansion, and d)
contraction. The solid lines indicate the original shape.
Fundamentally, electric dipoles can be described by:
p = QSx
2.3
where p is the dipole moment, Q is the charge of the ions separated by a distance S x . In
poled piezoelectrics, the dipoles can be thought of as stacked on end, (e.g., negative end
to positive end) according to the poling field. At the top and bottom surfaces of the
crystal, the ends of the dipoles make up the bound charge distribution that defines the
surface charge also termed the electric flux density D. In piezoelectrics the total flux
density can be described as:
10
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SD = dSX + sS E
2.4
Sc = sS K + dSE
2.5
and conversely as
where D is the electric flux density, X is the applied stress, e is the permittivity of the
material, d is the piezoelectric constant, and E is the applied field. The symbol 8
implicates the nonlinear characteristics of piezoelectricity in ferroelectrics, e.g., the
physical quantities can be regarded as functions of the independent variables; d(X, E),
e(X, E), and s(E) [6 ].
The magnitude o f the piezoelectric coefficients and thus the magnitude of the
strains and surface charge density are directly influenced by the poling history of the
crystal. In fact, it is often impossible to measure certain piezoelectric coefficients
without first poling the crystal because their values are too small [8 ]. (Even after poling,
19
typical values of piezoelectric coefficients are in the 10' C/N range [10]. Many
ferroelectric crystals cool to a multi-domain state with domains situated in juxtaposed
positions offsetting each other. Basic poling processes involve a direct current electric
field across a sample in order to stretch the separation between opposite charge ions that
make-up the dipoles. In addition to increasing the distance between oppositely charged
ions, this action will align dipoles to the orientation of the applied E-field. As a result
11
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the polarization in the piezoelectric is increased, resulting in a larger surface charge
density, along with larger piezoelectric coefficients.
Piezoelectric coefficients and related constants can be obtained by applying a
sinusoidal voltage across a poled sample of regular geometry across the crystals, natural
resonance frequencies [9]. Piezoresonance occurs when the frequency of the driving
voltage matches the frequency of the elastic standing waves set up in the crystals. In a
longitudinal or bar shaped piezoelectric resonator, the resonance and anti-resonance
frequencies (fr, fa) can be estimated by the following equations, respectively:
2.6
and
/ = 2-L ^ p—s D
2.7
*
where p is the density, sE is the compliance in constant E-field, sDis the open circuit
compliance, and L is the dimension of the sample along the mode vibration direction.
These equations pertain to parallelepiped geometries and are readily obtained from the
admittance plots which will be described in later sections. From these equations one can
identify fundamental resonance modes of the sample in question. For example, S3 3
longitudinal thickness mode, will have a different resonance frequency than s u lateral
mode sees Figure 2-2. At resonance, electrical energy is converted to mechanical energy
and vice versa.
12
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X3
*3
Thickness mode s33
Lateral mode s^
Figure 2-2: Illustration of two distinctive modes which have different resonance values
and are coupled by poison’s ratio.
The efficiency o f this energy conversion is characterized by the coupling constant (k)
which is related to the resonant frequencies by the following equations:
£2_ stored electrical energy
stored mechanical energy
and
As an illustration, Eq. 2.10 details the calculation of the piezoelectric coefficient
d333 , which in short notation can be written as d.3 3 . We chose d33 because it is the
piezoelectric coefficient that is of primary concern for our measurements based on our
samples' symmetry and orientation. Also the following equation shows the use of
13
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parameters calculated using piezo-resonance admittance data to derive piezoelectric
constants. It should be noted that the d33 piezoelectric coefficient can also be readily
obtained using a d33 meter.
2.10
2.2 Electric Field Effects in Ferroelectric Crystals
Ferroelectrics are materials possessing permanent spontaneous polarization whose
polarity can be changed by applying a sufficiently large field [7,9,9] Virtually all
ferroelectrics have a transition or Curie temperature (Tc), above which the spontaneous
polarization disappears. Above Tc, negative and positive ions acquire enough thermal
energy for random motion that destroys the ordered arrangement of dipoles. Hence,
without an ordered geometry o f separated positive and negative ions the ferroelectric
material becomes paraelectric, [9 , 8 ]. All ferroelectrics display piezoelectricity and like
piezoelectrics do not possess a center of symmetry. One of the most widely studied
ferroelectrics is Barium Titanate (BaTiOs) BaTi0 3 has a curie temperature, Tc, ~ 125°C
above which it is paraelectric and assumes the cubic perovskite crystal structure. Below
125°C it takes on a ferroelectric tetragonal phase and the polarization axis falls along the
<001> crystallographic c-axes direction. Thus electrodes on the sample with
parallelepiped shape will develop surface charge on the c-faces of the crystal, see
Figure 2-3. The onset of spontaneous polarization (Ps), or the alignment of dipoles
14
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generates strains in the crystal generating domains that situate themselves to alleviate the
electric and elastic energies that developed during the transition [7,9]. Domains are small
regions in the crystal consisting of dipoles with the same orientation and strong
interactions between them [6 ,12]. This multidomain state can be reduced to a few
domains by applying a sufficiently large E-field, where domains that are favorably
aligned to the orientation of the applied field will grow at the expense of other
neighboring domains. This continues with ever increasing applied field until least
favorable domains are aligned. This process is called poling and there is a limit to which
randomly distributed dipoles can be aligned. The corresponding polarization saturation
(Psat) is measured by the flux density D or surface charge density (see Figure 1-2 ). Upon
removing the field a remnant polarization (Pr) exists in the material due to the inability of
the domains to return to their original orientation without additional energy. Applying the
E-field in the opposite sense will cause the ions comprising the domains to shift and tilt
as they align accordingly to the field (switching). The field where the polarization (Ps)
goes to zero is called the coercive field (Ec). Likewise increasing the field further
induces saturation in the opposite, or for example, negative sense. Again applying a
positive E-field will re-orient the dipoles tracing a hysteresis loop whose area is
proportional to the energy expended during the process [7,13]. (See Figure 1-2).
15
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Ps = 0, T >Tc
P s^O || [001], C/m2,
T < Tc'125°C
Figure 2-3: Depiction of BaTiC>3 unit cell undergoing FE phase transition from para-electric
cubic phase to FE tetragonal phase at Tc' 125°C. A surface charge develops on the Z-faces
of the unit cell when Ti + shifts during the FE transition, (not drawn to scale).
Other phase transitions occur in BaTi0 3 as the temperature decreases from the Tc,
namely, tetragonal to orthorhombic crystal symmetry at ~0°C, and then to rhombohedral
symmetry at ~90°C. These mechanical distortions are accompanied by anisotropic
dielectric characteristics with high permittivity (s) values near the transitions [7, 9].
Single crystal BaTi0 3 relative permittivity (er also denoted at K at low frequencies) value
can be > 10,000 near 125°C. Thermodynamically, ferroelectrics are easier to pole near Tc
having smaller Ec values. Thus, it is common practice in poling to achieve large Ps and K
values by applying the field above Tc and maintaining it below the Tc. Because of
16
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values by applying the field above Tc and maintaining it below the Tc. Because of
ferroelectrics’ high K values their use in capacitors revolutionized the electronics
industry and they have found wide applications as transducers.
p
sa
Figure 2-4: Hysteresis loop showing poling effects on FE. Where Pr refers to remnant
polarization, and Psa, refers to saturation. Ec is the coercive field.
Antiferroelectrics show anomalies in dielectric constant and structural phase
transitions with temperature in a way similar to ferroelectrics. However, because of the
existence of antiparallel domains no net macroscopic polarization can persist [7,13].
Transmission electron microscopy (TEM) studies conducted by Randall et al. indicate
superlattice crystal structure consisting of adjacent antiparallel domains within unit cells
17
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[15]. These materials exhibit double hysteresis loops in their polarization verses E-field
characteristics at comparable field strengths. Applying high field levels, above a
threshold (Ef), can induce ferroelectricity in antiferroelectrics; however, upon removing
the field, the polarization vanishes and the material returns to its non-polar state at a field
strength designated by Ea on Figure [1-3], [7,13].
T
Figure 2-5: Polarization versus electric field for ideal antiferroelectrics.
18
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2.2.1 Relaxor Ferroelectrics
The types of ferroelectrics that are the focus of this work are called “relaxor”
ferroelectrics, discovered in 1950 by Soviet scientists,
Single crystal relaxors have
gained renewed interest for high performance piezoelectric, ferroelectric and electrooptic
(which will be described in the following section ) features [18],[19],[21]. Their name
stems from their pronounced changes in permittivity maxima with frequency near their
transition temperatures quite typical of relaxation in dielectrics [20]. Relaxors of the
perovskite-type structure come in many different compositions, based on isovalent and
aliovalent substitutions of both the A and B sites in the perovskite structure. The samples
studied in this thesis have a general formula consisting of Pb (Bi, B2 ) O3 where
(Bi=Mg2+, Zn2+, Ni2+, Sc3+), (B2 =Nb5+, Ta5+, W5+). In particular, we are investigating
single crystals based on the solid solutions of Pb(Mgi/3 Nb2/3 ) 0 3 -PbTi0 3 (PMN-PT) and
Pb(Zni/3Nb2/3 )0 3 -PbTiC>3 , (PZN-PT) systems. Solid solutions of PbTiC>3 (PT) in PMN,
and PZN relaxors yield a morphotropic phase boundary (MPB) at -33 mol%PT in PMN
and -10 mol% PT in PZN systems [4, 10, 20, 21].
At the MPB, a pseudo-cubic
rhombohedral PNM or PZN and tetragonal PT crystal merge. Bringing together these two
systems provides for
6
domain states of the tetragonal phase together with
8
states from
the rhombohedral phase for a total of 14 different possible polarization orientations. This
MPB condition optimizes poling conditions making it easier to align dipoles, yielding
large ionic displacements, large strains, high permittivity values, large electrooptic
coefficients and high coupling factor values. Consequently, the hysteresis loops of these
solid solutions exhibit relatively thin areas corresponding to small coercive fields and
19
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rapid domain switching. Below, Table 2-1 lists some of the relevant piezoelectric
constants of the above mentioned relaxors.
Table 2-1:
j
Dielectric and Piezoelectric Properties o f Pb ( B l, B 2 ) 0 3-PT Crystals
(Bl=Zn2+, Mg2+, B2=:Nb5+) values for 1 kHz
Crystal
^
f'max (°C
PZN
-140
Cut
111
001
PZN
8 %PT
-165
PZN
9.5%PT
-176
PMN30%PT
PMN35%PT
--150
--160
111
001
111
001
001
001
Dielectric Constant
(loss)
Coupling factor
d33
(*10‘12m /V)
900 (0.012)
3000(0.008)
(^33 )
0.337
0.852
3150(0.012)
4200 (0.007)
0.395
0.938
82
2070
4300 (0.004)
1400 (0.007)
0.644
0.894
405 (600**)
880(1600**)
2800 (0 .0 1 2 )
3100 (0.014)
0.808
0.923
730
1240
83
1100
Dielectric and Piezoelectric Properties o f Pb ( B l, B 2 ) 0 3-PT Crystals (B l= Z n 2+, Mg2+, B2=N b5+)
Courtesy of: S. E. Park, T. R. Shrout, “Characteristics of Relaxor-Based Piezoelectric
Single Crystals for Ultrasonic Transducers, ” IEEE Trans. On UFFC, Vol. 44 No. 5 Sept.
1997. (**) indicate values determined by Berlincourt d33 meter
2.2.2 Electrooptic Effect in Ferroelectrics
When dielectrics are under the influence of an electric field, their atoms’ electronclouds move away from their nuclei giving rise to a subtle change in shape. This action is
called electrostriction [6 ]. In this instance, the degree of distortion is governed by the
atoms’ polarizability and the field strength. With respect to optical fields, the
polarizability of the electron clouds is characterized by the material’s refractive index,
20
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(riij),
and the refractive index dependence on the electric field can be described by the
following:
na
IJ = n n
o + aE + bE2
2.11
where n 0 is the refractive index without applied field, and a, b are constants, [7], [9]. The
refractive index is not only a function of applied field but also of stress on the crystal.
The change in the refractive index caused by stress is called the photo-elastic effect.
Without delving into the theories of light propagation in materials, we will adhere to the
common notation designated by (B) the impermeability to describe the change in the
refractive index (An). Accordingly the change in refractive index imposed by E-field and
stress has the form:
AS = r \ E t + R xmEkEl + 7tEmXti
2.13
where ABy is the impermeability tensor, rXp represents the linear electrooptic coefficients
Y
p
at constant stress, R pi denotes the quadratic or Kerr effect at constant stress, and % pi
components represent the photoelastic effect at constant E-field [9], [20]. The subscripts
i, j, k, 1, indicate that the parameters are tensors and the number of subscripts determine
their rank. The subscripts take the values 1 ,2 ,3 , in sum, similar to Einstein’s notation.
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The photoelastic effect can also be described in terms of strains. Thus, equation (12) may
be described by:
A Bt = r x„Et + F m E 'E , + p liuxu
2.14
where the p-^ term denotes the piezo-optical coefficients and Xki represent the strains.
When applying an E-field at low frequency, and if the crystal is free to actuate with the
field, it is considered “free or unclamped,” and at constant stress. In contrast, at high
frequencies, the crystal’s elastic-motion can no longer follow the frequency and in this
situation is considered to be constant strain or “clamped” conditions. Under unclamped
conditions, the change in the refractive index is due to both the piezo-motion termed the
secondary effect and to the electrooptic behavior called the primary effect. The cut-off
frequency where the piezo-motion (secondary effect) no longer significantly contributes
to the change in refractive index is often not always well defined but typically falls well
beyond the fundamental piezoresonance modes in the 100s of kHz. O f course the
sample’s size and dimensions govern the frequency where the piezoresonance
fundamental modes occur and thus where the crystal is considered clamped or
unclamped. To this end, one can tailor the dimensions of a piezoelectric resonator to
shift resonance frequencies to higher and lower values. However for the samples used in
this thesis work, fundamental modes lie in the 100s of kHz.
22
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We can quantify the changes in the refractive index using the electrooptic
coefficient which describes both the low and high frequency contributions by the
following equations:
An = - — r*Et
2.15
and,
r ijk
~
r ijk + P i j k l d ,kl
2.16
where rx yk designates the electrooptic coefficient at constant stress, (unclamped), rx y k
denotes constant strain, (clamped conditions), and pyki, represents the piezo-optical
coefficients combined with the piezoelectric coefficient contribute to the ‘secondary
effect.’ As a demonstration of Eq. 2.16, below is an illustration o f KH 2PO 4 (KDP), and
NH 4 H2 PO4 (ADP) electrooptic coefficient r 63 as a function of frequency, Figure 2-6. We
see at the lower frequency region the contributions of both terms in Eq. 2.16, or rx, then
above ~104 Hz the crystal can no longer deform at the driving field and the piezo-optical
terms drop out leaving only the primary effect represented by the term r*.
The authors responsible for the plot in Figure 2-6, did not explicitly describe the
experimental set-up and way by which they calculated the values. From inspection it
appears the authors left out subtle details of data, especially in the piezo-optical regions
(~100s kElz), while showing the overall effects over the wide frequency range. The
accompanying permittivity plots in the figure show the dispersion of KDP, ADP and
hexamethylenetetramine. Here the authors suggest that there are no abrupt variations in
23
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the electro-optic coefficient, ui, of NH4H2PO4, down to the ~ 300kHz. Also, the authors
mentioned at that time it was very difficult to obtain such data for NH4H2PO4 due to
immense light scattering strains in the sample. Table 2-2 below list the values of some
important electro-optic materials.
Table 2-2: Linear Electrooptic materials measured at room temperature and in the visible
wavelength range.
EO materials
n
LiNb0 3
2 .2
30.9
re f [9]
8.59
BaTi0 3
2 .0
97
re f [24]
191
KH2 PO4
3.0
10.3
ref
Sro.6Bao.39Nb306
2 .6
-224
r e f [33]
PLZT 8/35/65
2 .6
500
ref
[9]
710
PMN32%PT
2.5
250
r e f [16]
1560
PZN 8 %PT
2.5
450
re f [2 1 ]
2000
r"ijk
(pm/V) @10KHz
[9]
D 33
(pC/N)
21
(d36)
-24.6(d3i)
Values obtained from various sources see bibliography for cross reference list
24
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to
>> 18
8
CJ
cu
in
PP JO
fO
Frequency cycles
Figure 2-6: Dispersion of the permittivity, s, and the electro-optic coefficient, r63i for
NH 4 H2 PO4 , KH2 PO4 , and N 4 (CH2)6. s : 1) KH2 P 0 4; 2 ) NH 4 PO4 ; 3) N 4 (CH2 ) 6 . r63: 4)
KH 2 PO4 ; 5) NH 4 PO4 . This figure implicates the various polarization mechanisms ability
to follow a driving frequency into to optical regime where only the electronic polarization
mechanisms remain. (After Yu V. Pisarevski, et al, see ref. [17]).
By is a 2nd rank tensor and geometrically represents a quadratic surface of an
ellipsoid called the optical indicatrix (Eq. 2-14). The optical indicatrix describes the
refractive index value(s) experienced by the E-vector of a light wave passing through a
crystal. Anisotropic crystals display double refraction or birefringence, meaning there are
two waves present in the crystal, namely, the ordinary and the extraordinary waves along
any arbitrary direction except that of the optic axis. Isotropic optical materials’ indicatrix,
mathematically characterized by quadratic surfaces, are spherical, thus having only one
refractive index, no, and one ordinary wave, [8 ,9]. As such, the change in the refractive
index described by AB is more accurately a change of shape of the optical indicatrix.
25
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In our experiments we are primarily concerned with the material coefficients
describing the changes to the refractive index along the crystallographic c-, and a-axis
due to an E-field applied along the X3 or c-axis. Therefore using Voigt condensed matrix
notation to designate the tensors, r, p, d, and n, the material parameters describing the
phenomena, 333=33, and 113=13. More will be said about how and what coefficients are
relevant later in the experimental section.
As referenced earlier, poled relaxor ferroelectrics are noted for their high
permittivity near the MPB which gives rise to large strains and large electrooptic
coefficients. These features are desirable in communication devices because they provide
for adequate modulation depth of light intensity. The following equation illustrates the
electrooptic’s directly proportional relationship to permittivity illustrating this point:
2.17
The quadratic effect is much smaller than the linear effect at comparable field
strengths and for that reason is often ignored.
The permittivity variation with frequency follows a curve shown in Figure 2-7.
On the curve e’ represents the relative permittivity (or K 33 as above) and e” represent the
imaginary permittivity implication dielectric loss. The peaks depict where the different
mechanisms contributing to the permittivity tail-off as the frequency increases. Ionic and
atomic mechanisms show resonance behavior; however, the space charge and dipolar
regions show relaxation and time-dependant responses to frequency [7,12]. As shown on
26
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Figure 2-7 , the atomic mechanism is the primary contributor to the index of refraction
since it is the only mechanism rapid enough to follow fields into the visible range. In
ferroelectrics, all four of these mechanisms can play a significant role in their properties;
however, for the purposes of our study, we are primarily interested in dipolar, ionic and
atomic mechanisms because they have the largest impact on the piezoelectric and
electrooptic properties at microwave and higher frequencies.
SPACE
CHARGE
ff RE L A X ATtON
>
ION J U M P
-■' ' RELAXATION
£
"
1
-
lONtC
Electronic
resonance
s"r
dielectric
loss spectra
10
Figure 2-7: Variation o f sr’ and s” as a function of frequency. Space charge and dipolar
polarization are relaxation processes and strongly temperature dependant; ionic and atomic
polarizations are resonance processes and temperature independent. Over specific frequency
ranges the loss is maximum as shown by peaks in s (to)”. Courtesy o f reference [30]
27
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In ferroelectrics, electrooptic coefficients are generally regarded not to vary
greatly with frequencies above -500 Hz to several GHz [6]. Yu Lu et. al, reported PZN12%PT single crystals’ electrooptic coefficients remained constant between 200Hz40kHz, with average values o f ~173±4 pm/V for r33 and 44±lpm/V for rn [21], [22].
They chose this frequency window to avoid piezoresonance effects which begin in
hundreds of kHz. Their experiments were conducted in a stress free apparatus employing
both the Mach-Zehnder interferometer and Senarmont compensator techniques. A.
Johnson and J. Weingart, examined electrooptic properties of BaTiC>3 as a function of
frequency and temperature, reporting rc ( s r33 - r13) to be independent o f frequency over
a window spanning from O-lOOkHz [24]. In their report, they showed rc to increase
markedly as the samples approached the Curie temperature. This observation
demonstrates the linear relationship, described in equation (17) between the electrooptic
coefficient and the permittivity below the Curie point and at moderate fields of <
7.5kV/cm.
Electrooptic measurements conducted at frequencies away from resonance have
linear relationships with applied field below Tc. However near resonance and the
transition temperature, optical properties of ferroelectrics behave nonlinearly, [8,9,25,
26]. To this end, whether piezo-mechanical displacements that are otherwise too slow
may couple with other more rapid mechanisms and to what extent if any they can
contribute to nonlinear effects have not yet been studied. For example, piezoresonance,
which consists of crystal lattice displacements are usually long ago clamped out at
frequencies approaching the 10s of MHz. However at resonance, macroscopic ionic
displacements may couple to ionic polarization mechanisms and influence the
28
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electrooptic coefficient at gigahertz frequencies. More will be said about this later. Such
topics are significant in search of effective EO materials suitable for RF and microwave
applications, and to advance the scientific understanding of electro-mechanical optical
properties in piezoelectric materials over a broad frequency range.
29
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Chapter 3
EXPERIMENTAL DESCRIPTIONS
3.1 Materials Considerations and Selections
All PMN-32%PT and PZN-8 %PT single crystal samples examined were obtained
primarily from TRS Ceramics Technologies and cut from flux-grown batches into
parallelepipeds. Although the samples came with their crystallographic orientation
labeled, we verified their orientation using the Multiwire Laboratories Ltd back reflection
Laue x-ray machine. All samples used were polished to optical finishes on their opposite
crystallographic b-faces {0 1 0 }, taking special care not to remove any material
unnecessary to achieve an optical finish. If any additional polishing was necessary, it
was done in accordance with the polishing done by TRS. Next, and also done by TRS,
samples were electroded by applying thin layer of Ag paint (<0.01 mm) on their
crystallographic c-faces {001}. This is done in order to maximize d33 and r33 values
through poling. The parallelepipeds were cut in dimensions to allow the optical path to
traverse the thinnest part of the samples and to amplify d33 (or thickness mode) the
fundamental resonance mode of vibration. In particular the laser light source traveled
along the b-axis <0 1 0 > (which is equivalent to the a-axis by virtue of the crystallographic
symmetry o f the sample) that is perpendicular to the polar c-direction.
30
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c-axis
4mm
2mm / /
y /
temporary
tg electrode
<001 >
< 100>
<010>
4mm
a-axis
PMN_32%PT on left and
PZN-8 %PT on right
/
as cut
surface
b-axis
Figure 3-1: Illustration of our crystals showing poling direction relative to
crystallographic axes and directions. Note that the laser source will traverse the direction
parallel to < 0 1 0 > perpendicular to the c-axis or <0 0 1 >.
Polling was done using a high voltage DC source manufactured by Trek. PZN8 %PT
samples were taken to 5-10°C above their Curie temperature (~140°C), while
PMN-32%PT samples were also poled at ~ 140°C. PMN-PT crystals have been reported
to be successfully poled at room temperature by Shrout et al, [28]. As mentioned earlier,
samples poled above their Curie temperature, are done so by maintaining the electric field
at ~5-10kV/cm while the samples cool below their ferroelectric transition temperature.
When poling, there is always the risk of sample cracking due in part to large strains
generated by crystal lattice and density mismatch as the sample cools. Also conductive
particles in the oil bath forming currents along the surfaces of the samples may introduce
cracks which will propagate under the coercive E-field. Therefore special precautions
and techniques were taken to prevent cracking samples during poling. For example,
31
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administering the voltage in pulses and using silicone oil baths relatively free of
conducting particles. In our crystals, poling increased the optical transparency. This is
generally the case for ferroelectrics as poling simplifies the domain structure. Below
Table 3-1 lists our samples' dimensions and measured d33 values.
Table 3-1: Samples dimensions and symmetry evaluated for this thesis
Crystal
Symmetry after poling Dimensions
___________________________________(W, t, L) (mm)
PZN-8 %PT
pseudo-Tetragonal
4,4,2
PMN-32%PT pseudo-Tetragonal
4,4,2
d33
(10 12m/V)
-2000
-1540
3.2 Polarization vs. Coercive Field (Hysteresis)
Polarization versus E-filed measurements were taken to verify ferroelectric
characteristics in our material and to determine the extent of domain populations in our
samples. See Figure 3-2.
32
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PM N -32% PT
0 .3 -
-600
-400
■200
400
600
KV/m
-
0.1
-
-
0.2
-
- 0 . 3 -I
PZN-8%PT
0.3 -
-600
-200
200
00
600
KV/m
-
0.1
-
-0.3 -I
Figure 3-2: Hysteresis loops showing polarization as a function of E-field indicating
domain structure as energy is required to reorient them when bringing the ferroelectric to
polarization saturation.
33
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3.3 Piezoresonance Method
Piezoresonance in ferroelectrics, with mm dimensions, occurs in the acoustic and
RF regions; therefore in order to observe fundamental modes and their harmonics, we had
to take measurements over the entire range. Samples do not require any additional
preparation after poling. Low frequency piezoresonance measurements for thickness and
transverse longitudinal modes were conducted using the HP Impedance/Gain-phase
analyzer 41941A which operates from 0 to 40MHz. Higher frequency electrical
impedance measurements were taken using the HP 4291ARF Impedance material
analyzer which operates 1 MHz to 1.8 GHz. The data obtained from these measurements
was used to locate where elastic resonances are occurring so we can compare them to
electrooptic measurements at similar frequencies.
3.4 Electrooptic vs. Frequency Measurements
The Senarmont compensator technique was employed to measure dynamic
electrooptic frequency variation in the linear region on the transmittance curves of our
crystals. This linear region occurs at the 50% point on the transmittance curve. To
achieve maximum modulation depth it is essential to operate in the linear region to avoid
distortion effects that would occur if operating near the non-linear parts of the curve [2 ]
(see Figure 3-3 ). The optical arrangement shown in Figure 3-4 and Figure 3-5,
determines the relative phase retardation and is particularly useful when the axes of the
elliptically polarized light incident on the A/4-plate remains fixed. The A/4-plate is
adjusted so its fast or transmission axis is parallel to the polarizer which is set at a 45°
34
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elevation angle to the c-axis of the crystal. In this configuration, the E-vector of the laser
light vibrates through the crystal with equal components along the c- and a-axes
establishing orthogonal extraordinary and ordinary waves [24]. The A/4-plate converts the
elliptically polarized light exiting the crystal into plane-polarized light at an angle
determined by the retardation due to the natural birefringence of the crystal and the
applied field. Following Figures 3-3, 3-4 and 3-5, Eq. 3-1 describes the retardation:
Io /I,
0.5
T Output light intensity
Voltage
Modulating voltage
Vm sin ojmt
Figure 3-3: Transmittance of a crossed-polarized electrooptic modulator as a function of
applied voltage. The modulator is biased to the point T= nl2, which results in a 50%
intensity transmission. A small applied sinusoidal voltage modulates the transmitted
intensity about the bias point.
35
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Lock-m
u S JL iiL
X
polarizer
Laser A-633nm
Serxnutent apparahis for determining IB VS. fts^
Figure 3-4: Schematic illustration of dynamic electrooptic frequency measurement
apparatus used to measure the rc coefficient for PMN-32%PT and PZN-8%PT samples.
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Laser
sam ple
polarizer
Hens
A nalyzer -
plate
Figure 3-5: Actual experimental Semamont set-up used to collect EO frequency plots.
This figure only illustrates the optical path of the set-up for clarity.
r _
2n{8L)
A
nVapp
V.
3.1
where V app is the applied modulation voltage, V* is the voltage needed to induce a phase
difference o f 7t, and 8 L is the optical length in the crystal that the light wave undergoes as
it is traversing the crystal, defined by:
37
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where 10 is the original length of the crystal along which light travels while E=0, An is the
natural birefringence o f the crystal, Vout is the modulated output voltage impressed on the
transmitted light intensity, Vp.p is the peak to peak transmission curve voltage, and the
term A1 refers to the change in length along the optical path induced by the piezo effect
and can be defined as:
31
1
3.3
where t is the thickness across which voltage is applied, 10, and Al. are the same as
mentioned above.
A He-Ne laser (X= 632.8nm) was used as a monochromatic light source. Using a
laser light source eliminates chromatic dispersion. Without the A74- plate or crystal in the
optical path, parallel polarizers give rise to
100%
transmission (non-retarded) at the photo
detector and crossed polarizers correspond to 0% transmittance (see Figure 3-4).
Introducing the crystal into the optical path retards the light with its own natural
birefringence then the A/4-plate adds additional retardation and simultaneously optically
biases the transmission to the 50% linear region. The peak to peak intensity collected at
the photo-detector is converted directly into voltage by way of the photo-detector which
is measured using a HP ac/dc multimeter. The modulation occurs about the linear region
o f the transmittance curve The modulation voltage has the form:
38
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Vmsin cot
3.4
where Vm is the amplitude of the modulation voltage, and to is the modulation frequency.
The phase retardation associated with the modulation voltage is:
Ymsin cot
3.5
where r m is the retardation associated with Vm. With the A/4-plate in place the retardation
can be written as:
T = — + T sin cot.
2
3.6
The transmittance is the ratio of the light intensity exiting the crystal to the light
that enters the crystal, where the phase between the ordinary and extraordinary waves is
zero. This can be described in mathematical terms by:
= sin
n
r „ sin cot
4
2
— + —!
—
3.7
where I0 and Iin are the output and input intensities. This equation can be simplified using
half-angle trigonometric identities to:
39
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7 ^ * l [ 1+ r msinH
3.8
* in
for rm« i .
According to this experimental configuration, we are measuring the electrooptic
rc coefficient which is an algebraic combination of two tensor components, namely, ro
and r3 3 , that is:
(n Y
where n 0 and rie are the ordinary and extraordinary refractive indices, respectively. For
<0 0 1 > poled perovskite-type ferroelectrics, the resulting pseudo-tetragonal point group
symmetry is 4mm; consequently, the remaining non-zero independent electrooptic
coefficients are: rn, r33 , and
If the E-field is only applied along the c-axis represented
by E 3 , as in our experiments, then only r^ and r33 are considered. For similar reasons
based on symmetry and the applied field direction of E 3 , d33 and d3 i are the only piezo
electric coefficients we have to consider which account for the change in length along the
optical path as these two coefficients are coupled by Poisson’s ratio. Eq. 3.3, and Eq. 3.9
illustrate this point.
In terms of modulation and output voltages, rc can be expressed as:
40
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Y
c
2X ( A ( V
\
( V *V /
<■' \
O /
\
p -p
°ut
app
3.10
where Vout refers to the rms value of small signal output voltage, Vapp, the rms
modulation voltage, and Vp.p corresponds to 100% transmission light intensity converted
to voltage.
The Stanford Research Systems SRS 830, and the SRS 844 DSP lock-in
amplifiers were used to generate the low and high frequency modulation voltages, and to
measure the output voltages phased-locked with the modulating source. The Vp-p is
taken directly from the trans-impedance amplifier connected to the photo-detector, with a
digital multi-meter. Thus applying a small signal over a range of frequencies, one can
obtain the electrooptic coefficient as a function of frequency.
3.5 AC Biasing
To accentuate the resonance enhanced piezo-optical contributions to the
electrooptic coefficient, isolated fundamental piezo-resonant modes were applied to the
crystal in parallel with the sweeping modulation signal. It is desirable to observe the
effects of individual resonance modes on the EO coefficient frequency dependence, and
thus applying the ac-bias in this fashion facilitates this observation. The modulation
signal was conducted over a spectrum ranging from 25kHz to 200MHz. The
piezoresonance modes were identified using the HP network analyzers mentioned in
section 2. As will be shown in following sections, most of the piezoresonance activity
41
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occurs in the 100s of kHz with l nd order harmonics occurring before 1MHz. With this in
mind, we expect to see enhancements to the electrooptic properties in corresponding
frequency regions due to piezo-optical coupling and perhaps 1st and 2nd order harmonics
to the fundamental modes.
Accordingly, we employed a separate function generator, namely, the variable
WAVETEK 4MHz sweep function generator model 189. Figure 3- illustrates this
scheme with the WAVETEK shown in bold red line type on the upper right of the
diagram. Under ac-biasing conditions the crystal is considered to be in a constant strain
state.
DC supply
• ..
a
Function g en erato r
AC-bias
Lock-In Amplifier
O sc
0 = 135“
135" ,L
i
■sample
Lens
Amp PD
Analvzer
A/4-plate
r
polarizer
Laser: A-632.8nm
Figure 3-6:
Schematic showing AC-bias configuration and DC supply to augment
effective EO coefficient rc for PMN-32%PT ad PZN-8%PT samples.
42
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The isolated ac-biased signals were administered at variable frequencies on either
side of the apparent fundamental piezoresonance frequency in question. For example,
lets say the 1st fundamental occurred at 178kHz, accordingly approximately 2 volts were
applied to the crystal in parallel with the lockin using the function generator at isolated
frequencies of 173 kHz, 175kHz 178kHz 181Khz, 184kHz and 188kHz. Care was taken
not to apply ac-biasing signals too far below or above the fundamental mode in question
in an attempt not to convolute the different fundamental modes and their piezo-optical
contribution to the effective electrooptic coefficient. Furthermore, ac-biasing was
conducted to be certain we were observing the effects of the specific fundamental mode
in question.
3.6 DC Biasing
DC biasing was also conducted to observe effects of polarization to the
electrooptic rc coefficient. To do this we employed the TREK high voltage supply model
6100. A T-blocking circuit was used to intercept the signals protecting the lock-in from
the DC supply spikes and the DC source from the driving effects of the lock-in. The
configuration is illustrated in Figure 3-. Figure 3- illustrates the T-block circuit showing
its elements and their values. In this measurement we expect to reinforce the polarization
o f the poled crystals and by doing so suppress the movement o f domain walls in the
dynamic EO measurements. This may have the effect of increasing the electrooptic
coefficient by allowing more light to pass through the crystal as the domain structure is
43
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made more simple when favorable domains consume less favorable ones propagating
across the structure.
0.01pF
5012
"VVVAC(Pu)
lockin
crystal
1pF
100mH
100pH
fuse
6
0.01 |jF
Figure 3-7 T-Blocking circuit used to isolate AC and DC sources while conducting EO
measurement
The frequency response of the T-blocking circuit is shown in Figure 3-. This
illustration indicates that there is negligible loss of voltage between the sources and the
crystal over our entire frequency range from 25 kHz to 200 MHz.
44
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80.00
40.00
20.00
-
20.00
-40.00 -
-60.00
-80.00
10
100
1k
10k
100k
1M
10M
100M
1G
Frequency (Hz)
Figure 3-8: Transfer Function - displays voltage output across the crystal in dB with
respect to the input voltage.___________________________________________________
Finally in the calculation of the rc coefficient a voltage correction was applied to
the modulation voltage because the voltage delivered to the crystal by the lockin varies
with frequency. Figure 3-9 shows the voltage profile of which values are pulled from
and incorporated into the calculation using Microsoft excel spreadsheets software.
45
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Voltage Profile for SR S844 lockin
1.4
1.2 -
1.0 CD
O)
B
o
> 0.8 -
0.6 -
0.4
1--------------- 1--------------- 1--------------- 1--------------- T
0.0
5.0e+7
1.0e+8
1.5e+8
2.0e+8
2.5e+8
Frequency [Hz]
—
•
Profile fitted to accomodate entire frequency spectrum
Real profile data
Figure 3-9: Voltage curve signifying the voltage correction used in calculating rc
The apparent large oscillation occurring near 70 MHz is due to a low to high
frequency switching mechanism.
46
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Chapter 4
RESULTS AND DISCUSSIONS
In this chapter the author describes the electrooptic (EO) frequency dependence in
PMN-32%PT and PZN-8%PT, highlighting the anomalies observed in specific
measurements. The beginning section involves the measured low frequency (<50 kHz)
EO rc coefficients; gradually increasing to higher frequencies in the following sections.
In pursuant to this end, illustrations are provided that demonstrate piezoelectric
contributions to the EO property. Accordingly, results obtained from small ac-biasing
field (~ 0.5V/mm) are described; where evidence of extrinsic effects is noted. The
following section deals with aging effects as a result our samples subjected to extensive
EO and piezoelectric experiments Finally, I refer briefly, to possible applications of this
technology in RF microwave photonic devices..
4.1 EO Effect in Low Frequency (<100,000 Hz or below piezoelectric fundamental
resonant modes)
Strong frequency dependence was observed for 6 8 %Pb(Mgi/3Nb 2/3)0 3 32%PbTi03 (PMN-32PT) crystals as shown in Figure 4-1. Anomalously high values of
rc coefficient (> ~40,000pm/V) were calculated at near DC small signal driving
conditions. The apparent rc value decreased rapidly with increasing frequency of the
small signal driving electric field. High values of electrooptic coefficient rc was obtained
47
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for frequencies between -100 Hz to 1 KHz (for example, -500 pm/V at 400Hz) which is
comparable with the results reported for PMN-32%PT using a similar but different
measurement technique [16]. Note the rc coefficient decreases to roughly 28 pm/V at 10
kHz, which is comparable to that of LiNbC>3 , an EO material with a much higher phase
transition temperature.
Frequency dependence studies of the electrooptic coefficient of PMN-32PT and
PZN-8%PT crystals have not been reported to date. One possible reason for the scarcity
of other reports on EO measurements as a function of frequency may be due to
piezoelectric resonances, present in all ferroelectrics crystals, that can askew the accuracy
of the results at frequencies near and beyond fundamental modes [10].
The mechanism o f the seemingly strong frequency dependence of the EO
48
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-mr
4-
£
E
<o
?
Fitted
c
d)
o
Ea>
o
O
u
■_
01
10
100
1000
10000
100000
Log scale [Hz]
Figure 4-1: Apparent EO coefficient rc of PMN-32PT crystal as a function of frequency
of dynamic modulating field, obtained using Senarmont dynamic measurement method.
The solid curve is the fitted result. Inset illustrates details of improved resolution
obtained for higher frequency by polynomial fitting.
coefficient rc may be attributed to several possible time dependent charge distributions
that induce dynamic changes to the effective refractive index, that directly augment the
observed high EO value. At relatively low frequencies, the modulating electric field can
motivate space charges (such as oxygen vacancies, due to the presence of Ti3+, which is
known to exist in flux grown PMN-PT crystals) that contribute significantly to the EO
coefficient frequency dependence through a reverse process of photorefraction; that is,
space charge transported and trapped under incident light become mobile and begin to
drift under driving electric field destabilizing the photorefractive local field. Space
charge effects are slow processes with millisecond time scales and are clamped out at
frequencies above ~105 Hz. Also contributing down to the low frequencies, are dipolar
49
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polarization which in PMN-32%PT comprise of Ti4+-0 , Nb5+-0 and Mg2+-0 shifted in an
distorted oxygen octahedral lattice; and in PZN-8%PT, Zn2+-0 , Pb2+-0 , Nb5+-0 , and
Ti4+-0 in distorted oxygen octahedral lattice. The reorientation of the dipoles in response
to the driving electric field can be considered a relaxation process with dispersion time
constant of the form:
CO
where V0 is the energy barrier associated with dipole reorientation, to is the
corresponding frequency, k is Boltzman constant and T is the absolute temperature in
Kelvin. The energy barrier is decreased to V0-qE, where E is the modulating electric
field. Dipolar reorientation process persists up to 100s of MHz. Also contributing to EO
behavior into the GHz range are dipole displacements at the tail end o f ionic resonance as
one approaches the infrared region. Finally the ferroelectric domain wall motion can also
contribute to the apparent EO effect which can follow typically into the MHz depending
on the size(s) of the domains and the nature of their walls.
The modulating electric field applied to generate the dynamic linear EO effect
shown in Figure 4-1, was small (~0.5V/mm), peak-to-peak; therefore at these levels of
field, domain reorientation may contribute in a form of localized polar regions coalescing
into micro or nano-domains which are thermodynamically unstable. Nevertheless,
domain wall motions , although small, may be significant at such low frequencies and
modulating voltage values especially in relaxor ferroelectrics such as PMN-32%PT and
PZN8%PT crystals with compositions near a morphotropic phase boundary. At the
50
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boundary, two different domain orientations are possible: One for a pseudorhombohedral crystal system, and the other for a pseudo-tetragonal crystal system. I use
the prefix ‘pseudo’ because the poling direction actually determines which crystal
symmetry the resulting crystal will assume. This property facilitates the poling of these
crystals but also makes domains unavoidable. Careful poling along thermodynamically
favorable directions must be undertaken to minimize unwanted domains [20,30]. For
our crystals, poling along the [001] (tetragonal) direction not only forces the pseudotetragonal symmetry, but also stabilizes the symmetric [111] domains oriented along the
poling field. This description pertains to the elementary contributions to our anomalously
high EO characteristics are of course accompanied by piezo-optical mechanisms under
constant stress conditions, which clamp out typically after several MHz. It should also be
noted that the piezoelectric and/or piezooptical coefficients can be positive or negative;
therefore piezo-optical terms may add or subtract from the electrooptic effect, see
Eq. 2.16. In our measurements it appears to be adding to the EO effect at piezoresonance
frequencies as will be seen in following figures.
It is found that the contribution from the time dependent processes proposed
above to the measured effective EO coefficient, rc, can be fitted by a combination of one
space charge independent term and two exponentially decaying functions as follows:
/;, = r" + Ate
(./ +./q)
(,/ +./o)
B‘ +A2e Bl = r" + term \ + term 2
51
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where r°c refers to the space-charge independent EO coefficient corresponding to dipolar
reorientation and piezooptic contributions modeled as a constant and valid only in a
narrow frequency range well below piezoelectric resonance. Ai and A 2 are the
amplitudes of the first and second exponential terms, respectively. As one can see from
Figure 4-1, the overall curve-fitting results are quite satisfactory when the fitted
parameters rc° = 201 pm/V at frequency fo= 1615 H z , with Ai = 2.12xl068, Bi = 9.27,
A 2 - 7.86 and B2 = 78.1. (Eq. 4.2 , serves as a low frequency approximation based on the
curve fitting and our space charge theory proposed above.) The first term has a much
smaller decaying constant (Bi) or diminishes rapidly with increasing frequency while the
decaying constant o f the second term (B2) is nearly nine times as large suggesting it is
persistent over a broader frequency range. Therefore the two terms may be assigned to
the space charge effect (term 1) and domain reorientation effect (term 2). A comparison
to examine the individual’s contribution is shown in Figure 4-2 (top). It is highly
possible that term 1 contribution is related to crystal quality and may be suppressed by
reducing defects through an annealing process.
Although the two-term exponential fitting gives excellent account for the low
frequency region (<200 Hz); a polynomial fitting provides much improved resolution for
the experimental result in a higher frequency region (see bottom of Figure 4-2).
It is significant to point out in Figure 4-2 what appears to be a monotonic trend in
the EO spectra. The admittance spectra for this crystal in the corresponding frequency
range also displays a monotonic trend, Figure 4-3. We see immediately the resemblance
of the two spectra. From the approximately linear increase in the admittance or
susceptance curve dielectric permittivity have constant values in this frequency range, but
52
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may have different conductivities at frequencies between 1000 Hz to 3000 Hz. In the
next section the results will clearly demonstrate the direct links between electrooptic
characteristics and piezoelectricity and the change In refractive index or rc.
Similarly, low frequency EO results for PZN-8%PT are displayed in Figure 4-4.
Also shown in Figure 4-4 is the measured rc value for PZN-8%PT which is considerably
larger than PMN-32%PT reaching roughly 3000pm/V at 10 kHz. PZN-8%PT is widely
known to be naturally more transparent than PMN-32%PT and so its EO properties are
larger. Notwithstanding PzN-8%PT relatively large EO values, the space charge
mechanisms responsible for augmented rc values at low frequencies are similar to those
described above for PMN-32%PT and generally true for all dielectrics. Following
Figure 4-4 is the corresponding admittance plot for PZN-8%PT illustrating similar
monotonic behavior as shown in PMN-32%PT, see Figure 4-5.
53
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♦
4.E-08
rc measured
rc calculated
c
2
'M 3.E-08
^4<-iD
O
V
- - - rc contribution from term2
— rc contribution from term l
2.E-08
o
w
.Us 1.E-08
O
53
W
1.E-10
10
100
1000
10000
100000
Log scale [Hz]
3000
0
2500
rc measured
Fitted -polynomial
Fitted - 2 term exponantial
2000
£
E
1500
CM
o
1000
o
500
-500
100
1000
10000
Log scale [Hz]
Figure 4-2: Comparison of measured apparent rc coefficient with the two terms (space
charge effect - term l, and domain reorientation effect - term 2) used in the fitting (top),
and (bottom) figure showing polynomial fitting for improved fitting results at higher
frequency region.___________________________________________________________
54
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Low Frequency Admittance spectra for PMN32%PT
0.025 -
0.020 -
<o
0 .0 1 5 -
©
o
c
0. 0 1 0 -
2
Q.
a>
(0
0 .0 0 5 -
3
(0
0.000 -
0
10
20
30
40
50
Frequency [kHz]
Figure 4-3: Admittance plot for PMN-32%PT showing feature-less spectra at low
frequencies below piezoresonance with only spurious inflections possibly due solely
to the circuit of the measurement apparatus.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
EO m e a s u r e m e n t for P Z N -8 % P T
10
T
D a ta : D a ta 4 _ B
M odel: y = y0 + A,*
C h iA2 = 0 .0 0 0 0 4
yO
0 .0 1 1 4 1
A1
0 .6 7 6 6 2
xO
2 1 1 6 .8
t1
2 3 1 2 .8
A2
0 .3 5 9 7
t2
1 9 2 9 2 .0 7
0.8 -
- 8
± 0 .0 0 1 3 7
±0
± 1 1 .4 9 8 5
±0
±0
±0
3 0 .6
- 4
UJ
0.4
i ------------- ■------------- r
5000
10000
15000
20000
25000
30000
35000
Frequency [Hz]
6
o — rc m easured fo r PZN-8PT
5
— (Polynomial fitting)
o
3
o
5t
a> 2
-o„
1
5
10
20
25
Frequency [kHz]
15
30
35
Figure 4-4: Low Frequency EO and rc coefficient for PZN-8%PT, showing monotonic
decrease, in rc, as a function of increasing frequency. Note rC value is quite large (>
2500 pm/V) at 10 KHz.
56
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Low Frequency Admittance plot for PZN-8%PT
25-
20o
o
a
©
o
(0
3
(0
15-
10-
0
10
20
30
40
50
Frequency [kHz]
Figure 4-5: Low frequency admittance plot for PZN-8%PT, showing monotonic
increase in susceptance as a function of increasing frequency, with spurious
inflections from measurement circuit.
As a final observation to results presented in this section, it was shown that both
PMN-32%PT and PZN-8%PT exhibited large EO values below 1 kHz; however desirable
this may seem, one should be cautioned about using EO characteristics of ferroelectric
materials in high frequency applications. Notwithstanding exceptionally high EO
coefficients at low frequencies, the material performance at high frequency may be
limited to electronic and ionic displacement polarization contributions. Such
57
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contributions are typically small in the range of 10s of pm/V and so insufficient for
microwave photonic applications.
4.2 Effective EO Coefficient at Higher Frequencies near Piezoelectric Resonances
Following our initial report on frequency dependence of the electrooptic
properties found in ferroelectric tungsten bronze crystals, [23] a comprehensive study of
EO frequency dependence was conducted of PMN-32%PT and PZN-8%PT crystals to
further understand the frequency relationships to EO characteristics pursuant to possible
microwave to optic energy conversion for communication applications. We found that
exceptionally high electrooptic coefficients are obtained in PMN-32%PT and PZN-8%PT
crystals at specific frequencies corresponding to piezoelectric resonances. Figure 4-6
illustrates the admittance spectrum obtained using resonance anti-resonance
measurements, (top), for PMN-32%PT featuring its piezoelectric fundamental modes;
along with the corresponding EO Vout spectrum obtained using our dynamic Semamont
apparatus, (bottom), which is directly proportional to rc as described by Eq. 3.10. These
modes are longitudinal-extension and transverse-extension in nature. Figure 4-6
demonstrates the elasto-optical components of the EO coefficient particularly near
piezoelectric fundamental modes where the strains have large amplitudes. Further
inspection of the admittance plot Figure 4-6, shows up to 3rd -order harmonics that are
not readily apparent in the EO measurement. We can see from Eq. 2.16, that is, r* = r* +
Z p d , the piezoelectric and elasto-optical effects contribute to the EO coefficient most
significantly near piezoresonance frequencies where the crystal strains can follow and are
in sync with the modulating electric field. In this frequency region, the crystal is said to
58
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be free or under constant stress (stress =0) conditions. The elasto-optic contribution is
accounted for by the 'Lpd term in Eq. 2.16, where p represents the 4th rank piezo-optical
or elasto-optical coefficient and d, represents the 3rd rank piezoelectric coefficient. As
suggested by their product, the two terms are not independent in their influence to the EO
effect [14]. Figure 4-7 shows a close-up of Figure 4-6 comparing the EO coefficient,
which is directly proportional to Vout, (see Eq. 3-10) obtained near the fundamental
resonance and anti-resonance frequencies (bar-longitudinal thickness vibration or sE33 , d33
mode) that is , fr=175kHz and fa=178.5kHz. The magnitude of Vout is large near fr=173
and fa=178.5 kHz, as the free crystal is allowed to strain at resonance. These large strains
are translated directly to changes in refractive index which is directly proportional to the
square-root of the permittivity and the EO coefficient.
It should be noted here, that although the 3 modes appear distinguishable from
each other they are not entirely independent. By virtue of the crystals’ geometry and
similarity in dimensions, meaning the thickness ( || to E-field d33 mode) and lateral
59
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Admittance plot for PMN32%PT(measured)
0.20
— 2 5 K H z to 9 0 0 K H z
Q
0.10
>
®
0 .0 5
© 000
o
«
-0 .0 5
Q.
d> -0.10
O
(0
3
<0 -0 .1 5
-0.20
0
200
400
600
800
100 0
Frequency [kHz]
EO m easurem ents for PMN-32%PT
300 -
250 -
200>
o
o
150 -
100 50:
200
400
600
800
1000
Frequency [kHz]
Figure 4-6: Admittance plot (top) and corresponding EO spectrum for PMN-32%PT
crystal showing clear piezo-optical contributions which enhances the EO rc coefficient.
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
PMN-32%PT Adm_Vout in PMN-32%PT EO compare
60
A dm itance
-O- EO V
0.5o->G
o
x
©
o
£
■
S
0.0-0.5-
Q.
O
O
W -to­
co
O'1
-1.5
167
170
173
177
180
183
187
190
193
197
200
Frequency [kHz]
Figure 4-7: Thickness mode and corresponding EO frequency response showing
enhancement.
( || to light propagation d32 mode) both about 4mm in length, and their relatively
equivalent compliance values in these directions, all 3 modes are intricately mixed.
Because of the crystals’ geometry, and cubic perovskite parent structure, we can think of
these crystals poled along [0 0 1 ] as having a pseudo-tetragonal, symmetry with d33 , d3 i,
d32 , elastic vibrational modes under E 3 ^
0
conditions.
Accordingly, the enhancement of electrooptic properties corresponding to
piezoelectric resonance is also demonstrated in adjacent resonances, fr=203, for [100]
bar-transverse resonance or d3 i mode, and fr”=245 kHz for the equivalent d32 mode [010]
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
occurring at a higher frequency because the sample is smaller in the length dimension
than in its wide, but these two dimensions are crystallographically equivalent.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
A dm itance
—o — EO V ,
25
0.5-
G
o
20
0.0-
0)
o
| -05O.
®
o
§ -1.0<0
10O
UJ
-1.5
193 200 207 213 220 227 233 240 247 253 260 267
Frequency [kHz]
c-axis <ooi>
A
temporary
Ag electrode
2mm
a-axis
width
<ioo>
►
b-axis <01o>
Figure 4-8: Showing d3 i (fr ~ 203kHz) mode and a mixed d32 (fr ~ 245kHz) modes,
depicting EO and piezoelectric correspondence in PMN32%PT crystals. Also shown
is a an illustration of the crystallographic directions and sample dimensions
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Continuing in pursuant to PMN-32%PT discussions, the admittance and EO
spectra for PZN-8%PT show linear correspondence at piezoelectric resonances (barlongitudinal vibration along the [001] direction or d33 mode), Figure 4-9. Also shown in
the figure are the lateral modes, d3 i, occurring at higher frequencies roughly 225 kHz.
PZN-8%PT is naturally slightly more transparent than PMN-32%PT, and thus the Vout
and rc parameters are larger. A closer look at Figure 4-9 reveals resonance and anti­
resonance frequencies for the bar longitudinal d33 mode: fr = 117.070kHz fa =
120.070kHz, respectively. Also shown are the coupled bar transverse longitudinal d3 i
and d32 modes occurring at ~ 129 kHz and ~225 kHz, along with their associated EO
spectra. (See Figure 4-10)
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A dm ittannce Plot for PZN-8%PT (m easured)
0.8-
©
o
c -0.2-
(0
4-4
g- -0-4-
O
w -0.6(0
-0.8-
-1.0200
400
600
800
1000
Frequency [kHz]
EO measurement for PZN-8%PT
140
120 100 S?
80 -
> ’
60 -
o
1X1
40 -
200
200
400
600
800
1000
Frequency [kHz]
Figure 4-9: Admittance plot (top) and corresponding EO spectrum for PZN-8%PT crystal
showing clear piezo-optical contributions which enhances the EO rc coefficient
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
140
—o—EO V
„
out
120-
aA dm ittance
1.0
100-
+•*
3
O
>~
O
LU
60-
40 _
-0.5
op
20-
-1.0
Po
-1.5
100
150
200
250
Frequency [kHz]
Figure 4-10: A blow up of Figure 4-9 showing direct correspondence between EO rc
coefficient and piezoelectric resonance.
The above description for the piezoresonance enhancement to the electrooptic
value in the PMN-32%PT and PZN-8%PT relaxor ferroelectric crystals is plausible at the
frequency range where the crystals can deform under the influence of a driving electric
field (constant stress). Such amplification can be explained qualitatively using the
theoretical model of transverse acoustic phonons, piezoelectric lattice waves that when
coherent in scale with crystal dimensions, vibrate in sync with dipole stretching and
therefore enhance the EO coefficient at the given frequency. Notwithstanding the pliable
high-strain nature of these relaxor ferroelectrics, in large part due to their multitude of
dipole orientations, beyond a certain cut-off frequency the crystal strains will no longer
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
contribute to the EO effect in appreciable amounts. For millimeter size crystals this
cutoff frequency falls certainly around 10 MHz. Sample size, shape, and mechanical
loading of the sample mount can heavily influence the location of its piezoelectric
resonance frequencies; but these are controllable quantities and their influences are
predictable. On the other hand, because PMN-32%PT and PZN-8%PT crystals possess
multiple polarization direction possibilities, they have a strong tendency to generate a
multifarious population of domains, which may vary in dimensions depending on but not
limited to sample preparation techniques and sample handling, that is, mechanical
polishing and cutting o f the crystal. Furthermore, because these crystals’ composition lie
in a morphotropic phase region comprising two distinct crystal classes, namely,
rhombohedral and tetragonal, their domain population can have orientations favoring any
one or combination of the 2 distinct crystal classes even after poling. The symmetry of
the poling will be reflected in its overall crystal symmetry and the domain orientation.
Accordingly, while admittance plots allow one to locate the piezoelectric
resonance modes and therefore the piezo-optical contributions to the measured EO
values; the admittance measurements by themselves may not immediately reveal the
physical nature of all individual vibrations or inflections. However, by modeling the
crystals using a finite element analysis (FEA) software application, namely ATILA,
which simulates piezo-actuators; we can pinpoint the location of specific fundamental
modes and identify which peaks and inflections are caused by mechanical vibrations
(intrinsic) and which are not (extrinsic). Figure 4-11 and Figure 4-12 depict a
comparison of ATILA generated admittance plots with actual measured data for our
samples. O f course, ATILA plots do not incorporate or account for domains or defects.
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
It assumes the crystal is perfect. Thus, when making our comparisons we can distinguish
between spurious inflections caused by coupling of natural harmonics, and inflections
which may be attributed to meso-structure or domain regions. Moreover, by changing
the dimensions of one side of our simulated parallelepiped shaped crystals while holding
all others constant, and tracking peaks shifts, we can ascribe specific resonance peaks to
their corresponding natural modes. These comparisons between ATILA generated plots
and those measured suggest reasonable agreement between simulated and actual crystals
facilitating inferences about the illusive extrinsic properties of the samples. (More will
be said about this later.) Unfortunately, ATILA like other FEA applications can require
enormous computational capacity especially as one increases the bandwidth and thus can
easily exceed the capability of our computers.
The discrepancy between measured and
simulated resonance frequency values can be attributed to the differences in mechanical
parameters such as compliance, piezoelectric, permittivity, capacitance, and loss values,
furnished by the vendor, and the published data used for the ATILA simulation. More
accurately, the difference in resonance frequencies is governed primarily by the
compliance coefficients, and the amplitude of the susceptance is controlled mainly by the
loss, capacitance, and permittivity values. The values furnished by the crystal vendor are
specific to their samples and the samples’ history; which undoubtedly will vary from
vendor to vendor. Therefore the mechanical constants values published have a high
likelihood of being different from our vendors. Furthermore, ATILA simulations
required two additional coefficients, namely sE44 and sE66, that were not furnished by the
vendor. All things considered, the simulated plots and the real plots show good
agreement. See Figure 4-11 and Figure 4-12.
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(Measured after EO &ATILA) Admittance (PMM32PT)
o
0. 20 -
0.20
0.15-
0.15
0. 10 -
0.10
0.05-
0.05
0.00 -
0.00
C -0.05-
-
0.05
-
0.10
-0.15-
-
0.15
0 . 20 -
-
0.20
-
0.25
100KHz to 1 5IVHz measured
ATILA generated___________
-
-0.25
0
250
500
750
1000
1250
1500
Frequency [kHz]
Measured Impedance PMN-32%PT
1
"
i I '
'1----1
300
11 1 I I " ----1---- h I I » " 'I----1----T
1000
- Measureed Impedance after extensive EO mes.
- ATILA gernerated Impedance
i—i 500
C5
CO
-
o
T”
X
M
100
g
CD
O
c
2
O -500
<
0
CD
-100
-1000
-200
-|------- 1-1------- .-1------- 1-1--------1-1--------i-1--------1-1--0
250
500
750
1000
1250
1500
Frequency [kHz]
Figure 4-11: Comparison of measured and ATILA generated plot for PMN-32%PT
showing reasonable agreement considering discrepancy in numerical values.
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C o p a ris o n of M e a s u re d A d m itta n ce a n d ATILA g e n e ra te d plot
2.5-
2.5
2 .0 -
2.0
• — ATILA g en e ra te d
- M easured A dm ittance
'a
©
T“
«XI
ao> 0.5c
(0
a. 00'
a>
W -0-5-
0.5
0.0
-0.5
3
CO
-1.0
-1.0-
0
100
200
300
400
500
600
-1.5
700
Frequency [kHz]
C om parison of ATILA g e n e rte d Im p ead an ce & M eaured plots
280-
-I 540
■— ATILA ge n erate d
• — M easured im p ed an ce PZN-8%T
210140wcT
b
180
70-
X
do>
c -70re
4->
O
re -mo 2
-210
-180
-360
-540
-
-720
-280-
0
200
-900
400
600
800
1000
Frequency [kHz]
Figure 4-12: Comparison of measured and ATILA generated plot for PZN-8%PT
showing reasonable agreement considering discrepancy in numerical values.
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4-13 and Figure 4-14 depict monotonic admittance plots at frequencies ~5
MHz and beyond. These plots can tell us several things: one, we should not expect to see
large intrinsic piezooptical contributions in EO measurements analogous to what we
observed near fundamental modes; and two, the crystals are responding electrically as the
admittance continues to rise with frequency. The small wiggles or inflections shown on
the plots indicate mixing or overlapping of higher order harmonics (>5th -order) whereby
their magnitudes may be on the order of the noise levels of the measurement equipment.
This behavior was shown for both PMN-32%PT and PZN-8%PT crystals.
Atritterce plate PhM32%PT
aE
8
Sca.
8
a
a
E
ao)
c
(0
E
8c
Q.
8i/i
a.
3
3
CO
3
CO
3
9
Frequency [MHz]
12
15
CO
14.0
17.5
21.0
245
Frequency [M-b]
28.0
31.5
320
3®
360
393
Frec|jency[M-k]
Figure 4-13: Admittance plots illustrating piezoelectric d33 , d3 i modes at relative high
frequencies. Note the small amplitudes of inflections as the crystal strains cannot
follow the high frequency electric field.
71
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
admittance PZN-8%PT
A*rtttancePZN^tf=T
A d m itta n c e f o r P Z N -8 % P T
2.4
2.2
a
a
vo
cIB
a0)
uac>
E
s
3
2.0-
m 1.8
a.
ao>
* 1.61.4
2
4
6
8
10
Frequency [MHz]
Figure 4-14: Admittance plots illustrating piezoelectric d33 , d3 i modes at relative high
frequencies. Note the small amplitudes of inflections as the crystal strains cannot follow
the high frequency electric field
To this end, take a look at Figure 4-15 and Figure 4-16. It is apparent from these
figures that there is appreciable enhancement to the EO effect above frequencies where
piezoelectric and elasto-optic contributions are by all conventional wisdom not
significant [8,10]. These “EO resonances” may therefore be explained by extrinsic
contributions, namely domain motions, and or dipole tilting which are widely reported as
polarization effects in ferroelectrics. Not to be misleading, but it is interesting that the
EO enhancements appears to have 3 distinct resonance peaks, namely, 52.5, 60.3, and 72
MHz, which coincide with the 300th -order harmonics of piezoresonance modes 175 kHz,
203 kHz, and 248 kHz, respectively. The author is not suggesting in normal instances,
even the most sensitive instruments can detect and measure mechanical vibrations of
300th -order harmonics. These corresponding, peaks are noted as an interesting curiosity
or an unusual ferroelectric material.
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
PMN32%PT EO m e a s u re m e n t High F requ en cy
1800
16001400 -
— B
12005>
1000-
5
800 -
>°
O
HI
600 400 -
200 -
-25
0
25
50
75
100
125
150
175
200
225
F requency [MHz]
Figure 4-15: PMN-32%PT high frequency EO measurement showing complex spectra
above piezoelectric frequency range where intrinsic elastic motions are clamped out.
Similarly, PZN-8%PT exhibits a complex EO spectrum in the 10s to 100s of MHz
region. While the interpretation of Figure 4-15 is speculative we can rule out system
error by the contrast of both plots, and again a curious set of peaks can be linked to the
300th-order of fundamentals for this crystal, that is: 118 kHz to 35MHz, (bar longitudinal
thickness mode d33 ) 129 kHz or 39 MHz, (transverse longitudinal lateral extension d3 i)
and 225 kHz to 68 MHz (transverse longitudinal lateral extension d32 ). See Figure 4-16
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
EO m e a s u r e m e n t for PZN-8%PT
3500 3000 2500 2000
>
O
LU
-
1500 -
1000
-
5 00 -
-25
0
25
50
75
100
125
150
175
200
225
F re q u en cy [M H z]
Figure 4-16: PZN-8%PT high frequency EO measurement showing complex spectra
above piezoelectric frequency range where intrinsic elastic motions are clamped out.
4.3 AC Biasing to Assist Resonance Enhanced EO Effect in PMN-32%PT
At this point in the thesis, we are now in a position discuss piezoresonance effects
on the rc EO phenomena at frequencies beyond normal piezoresonance. By
demonstrating enhanced effective EO coefficient, rc , near piezo-resonance modes we are
interested in extending this enhancement of the EO effect at higher frequencies to
eventually employ electrooptic materials in microwave applications. A term ‘microwave
transduction,’ was introduced in the early stages of this investigation. Accordingly we
narrowed our search from a host of candidate materials to high-strain lead-based
perovskite relaxor ferroelectrics analytically evaluating their electrooptic behavior as it
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
varies with frequency hoping to discover novel ways of impressing wireless radio
signatures on to an optical sub-carrier taking advantage of greater bandwidth and data
flow capacity. To this end, I now direct your attention to Figure 4-17 where it is apparent
that by biasing the PMN-32%PT crystals with a small ac signal around its pseudo­
thickness mode frequency, namely fr ~ 178 kHz the crystal’s EO Vout characteristics
increase in a broadening sense at higher frequencies near the 2nd and 3rd-order harmonics
of the fundamental modes. Approximately 2 volts (0.5V/mm) of biasing signal was
applied to all crystals and we can see a fairly obvious effect on the output, Vout- A closer
look at the enhanced broadening EO region is shown in Figure 4-18 depicting a ~ 20 dB
voltage output difference between biased and unbiased voltages. This broadening region
occurs near the spurious inflections shown on the top diagram of Figure 4-11 and has
implications of coupled harmonics along with extrinsic or domain motion activity. This
region implicates domain activity because the measured plots have a higher density of
inflections than the plots generated by ATILA. The coupled harmonics fall within the
higher order overtones up until the 4th -order and for our crystals' geometry harmonics
are certain to be entangled due to their geometric low aspect ratio.
Similarly biasing the crystal around its longitudinal transverse mode pertaining to
the 2mm dimension (b-axes) or d32 mode, exhibited broadening effects on the EO
behavior, (see Figure 4-19.) Figure 4-20 depicts a closer look at the broadening region
on a dB scale. Figure 4-21 reveals biasing the crystal on the crystallographically
equivalent longitudinal transverse mode d3 i along the 4mm dimension (a-axes).
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AC B ias EO m eas. PMN32PT
J _______i_______I_______i______ I_______i______ L.
350
350
300-
300
U nbiased
178KHz
180KHz
182KHz
184KHz
186KHz
189KHz
250-
200>
150
til
100
o
250
200
150
100
50
50
o-l
200
600
400
800
1000
Frequency [kHz]
1.0-
1.0
a 05■
O
0.5
r>
X
ao>
c
0.0-
0.0
-1.0-
-1.0
f | f
Pseudo-Thickneaa mode
d33
CD
Q_
SB
13
(0
CO
160
180
200
220
240
260
280
Frequency [kHz]
Figure 4-17: Biasing the crystal around its thickness mode fr- 178kHz yields broadening
EO behavior at higher frequencies near 5th-order harmonics
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AC Bias EO m eas. PMN32PT
i
350-
i___ i___ i
.
i
300-
300
U nbiased
178KHz
180KHz
182KHz
184KHz
186KHz
189KHZ
250-
200>
o
111
350
150-
100-
250
200
150
100
50-
50
200
400
600
800
1000
Frequency [kHz]
AC Bias EO m e a s. PM N-32%PT
U nbiased
178KHZ
180KHZ
182KHz
184KHz
186KHz
1E-4-
>
-70
-80
100 O
1E-5
o
IU
1E-6
400
600
800
1000
Frequency [kHz]
Figure 4-18: Illustration of relative EO enhancement when biasing the PMN-32%PT
crystal on its pseudo-thickness mode d33 .
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AC Bias EO meas. PMN32PT
J _______ ._______ 1_______ ._______ I_______ i_______ L
150
125-
Unbiased
—
203kHz
206kHz
■ - 209kHz
210kHz
100 -
>
3
O
o
UJ
0
100
200
300
400
500
600
700
800
900
1000
F re q u e n c y [kHz]
Pseudo-Transverse lateral
modes
Frequency [kHz]
Figure 4-19: Pseudo transverse lateral extension mode occurring at ~203kHz.
accompanying EO enhancement spectra.
With
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AC Bias EO m eas. PMN32PT
i
I
i
I
i
L.
150
150 -
125
5
100-
15
>
125
Unbiased
203kHz
206kHz
209kHz
210kHz
o
o
HI
7 5 -|
100
75
50-
50
25-
25
0200
400
600
800
1000
Frequency [kHz]
AC Bias EO m eas. PMN32PT
Unbiased
- • - 2 0 3 kHz
206 kHz
- * - 2 0 8 kHz
210 kHz
1E-4
-80
Q
-100 C
T
3
E 1E-5
O
>
3
-110
o
LU
1E-6
-120
-130
300
450
600
750
900
Frequency [kHz]
Figure 4-20: Illustration of a closer look at ac-biased enhanced region showing a roughly
10 dB difference between biased and unbiased EO behavior.
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
EO measurement AC Bias PMN32PT (25KHzto 900KHz)
100-
- Unbiased
-245KHz
- 248KHz
-2 5 1 KHz
-253KHz
- 260KHz
8 0 --
^
>
60-
O
4 0-
o
in
20-
200
400
600
800
1000
Frequency [kHz]
Pseudo-Transverse lateral
modes
0.0000
160000
180000
200000
220000
240000
260000
280000
Figure 4-21: Illustration of longitudinal pseudo-transverse mode, showing largest EO
effect of the 3 natural modes.
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
EO measurement AC Bias PMN32%PT (25KHz to 900KHz)
100--
— - — Unbiased
245KHz
248KHz
251 KHz
253KHz
2 6 0 KHz
80-
1000
Frequency [kHz]
1E-4
-80
-90
- ® —d B s c a le
-100
1E-5
m
-110 T3
-120
UJ 1E-6-
-130
400
600
800
1000
Frequency [kHz]
Figure 4-22: Blow up of EO enhanced region with ac biasing the crystal on the d32
pseudo-transverse mode. Roughly a 40 dB difference between biased and unbiased
regions is produced.
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
At this point, note that the Vout or the light output is roughly twice as intense for
the 2mm extension mode, Figure 4-22, compared to the previous other two, namely the
thickness and 4mm extension mode; Figure 4-18 and Figure 4-20, respectively. Closer
inspections of the resonance frequency regions show suppression of EO intensity under
ac biasing conditions. In my view, this enhancement accompanied by suppression is
consistent with conservation of energy arguments. We will look at each biasing
condition starting with the thickness mode at -178 kHz. (See Figure 4-23) In this figure,
it appears that biasing with the longitudinal thickness mode suppresses light output in all
3 corresponding fundamental modes with d32 lateral extension mode (occurring near
-240 kHz) suppressed the least. Figure 4-24 illustrates biasing under d3 1=lateral 4mm
extension mode (203 kHz). It shows a suppression of EO effect associated with the
thickness mode, but a slight EO enhancement in the biasing mode. The 2mm lateral
mode appears to be unaffected. Figure 4-25 depicts the last of the 3 main fundamental
modes the 2 mm lateral extension mode which generates the largest light output of the
three. The other lateral extension mode showed Vout enhancement at the low-end, but its
effect was less pronounced, Figure 4-24. These 2 modes are equivalent. They only differ
in frequency because of the samples dimensions. Again the longitudinal thickness mode
ac biasing condition appears only to suppress the Vout signal across all fundamentals.
The broadening effect observed in our EO measurements is consistent with
observations from other reports on PMN-32%PT and PZN-8 %PT type relaxors, on
topics ranging from Raman studies to electromechanical coupling. Such broadening
effects are due to disordering among Mg2+, Nb5+ , Zn2+, and Ti4+ atoms occupying the B|
and B2 lattice
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AC Bias EO meas. PMN32PT
i
. ..
i
.
i
— ■— Unbiased
178KHz
180KHz
• 182KHz
• 184KHz
186KHZ
189KHZ
1000
Frequency [kHz]
Unbiased
■ 178 kHz
180 kHz
182 kHz
189 kHz
1E-4
1E-5
1E-6
180
200
220
240
260
Frequency [kHz]
Figure 4-23: Biased and unbiased comparison showing suppression of light output across
all corresponding piezo-resonance peaks. Shown here on a Log plot to clarify the scale
of output difference.
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AC B ias EO m ea s. PM N32PT
160
140Unbiased
203 kHz
■ 206 kHz
- 209 kHz
210 kHz
100'
*-*
80"
>
o
60
3O
LU
40
-20
0
200
400
600
800
1000
Frequency [kHz]
160
140 =
Unbiased
203 kHz
206 kHz
209 kHz
210 kHz
120100-
>
o
3o
hi
6040-
20
-20
180
200
220
240
260
Frequency [kHz]
Figure 4-24: Comparison of biased (203 kHz, d3 i mode) and unbiased condition on a
linear scale in PMN-32%PT showing suppression of corresponding thickness mode, d33 ,
but slight enhancement o f light output associated with d3 i (l=4mm) extension mode. The
lateral extension mode, d32 , seems to be broadened.
84
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
EO m e a su re m e n t AC B ias PM N32% PT (25KHz to 900KHz)
0.10
- -
>
0.06--
>
0.04--
0.02
Unbiased
245KHZ
248KHz
251 KHz
253KHz
- 260KHZ
- -
0.00-200
400
600
1000
Frequency [kHz]
Unbiased
235 kHz
248 kHz
251 kHz
253 kHz
260 kHz
Frequency [Hz]
Figure 4-25: Comparison of the biased 4mm lateral extension mode and unbiased crystal
showing a general suppression of EO effects associated with thickness and 4mm lateral
extension mode, but a slight increase in the biasing d^ 2 (l=2mm) extension mode.
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
sites in the perovskite crystal structure. Also note the region just before the first
fundamental mode is attributed to noise in the circuit.
At higher frequencies the ac biasing didn’t seem to have an appreciable effect on
the EO coefficient as shown in Figure 4-26. Although the EO spectra is complex at these
frequencies, it is of no surprise why they do not show appreciable effects due to biasing
at fundamental modes; because the effects of biasing the crystal near fundamentals are
effectively clamped-out. The first few harmonics, have measurable effects, but occur
well below 10 MHz. Under normal conditions the vibration amplitude of harmonics that
do fall in the 10s to 100s of MHz region are too small as the crystal’s strains are unable to
follow at these frequencies.
RF F re q u e n c y EO d e p e n d a n c e (P M N 32% P T ))
1400
1200
1400
-
179K H z V out (V)3M to 200M
3M to 200M u n b ia s e d
1000
1000
800 ?
L1J
600 400 -
200 0Frequency [MHz]
Figure 4-26: Higher frequency EO effect showing complex spectra, which may be
attributed to microstructural effects and instrument artifacts.
86
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4.4 AC Biasing to Assist Resonance Enhanced EO Effect in PZN-8%PT
Similarly, PZN-8%PT exhibited broadening effects with ac biasing. Although
PZN-8%PT appeared to be more susceptible to “ageing” as the experiments were
conducted, see Figure 4-27, and Figure 4-28. In Figure 4-28 ac biasing at 225 kHz seem
to have the most dramatic effect, while the others appear to yield the same general
broadening enhancement near higher order harmonics. The 225 kHz fundamental belong
to the lateral extension mode or d32 type vibration and appears to have a more
pronounced effect than the thickness node. Perhaps the effects of biasing the crystal
several times prior to driving at 225 kHz allowed for aggregate or lodged domain regions
to separate to a more stable state. Hence the appearance of one anomalous peak near 600
kHz. Figure 4-29 and Figure 4-30 are close up views of enhanced effects near the
harmonics regions, on a dB scale.
87
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AC biasing around 118KHz PZN-8%PT
140-
— • — Unbiased
- -1 1 4 K H z
116KHz
118KHz
119KHz
121 KHz
120
100
^
80 H
I
60
>
O
LU
4Q J
^
20m M*
0200
400
600
800
1000
Frequency [kHz]
Adm iittace poit m e a su re d PZN- 8% PT
0.4
Pseudo-Thickness mode
0 .3 '
0.2
0.1
0.0
-0.1
-0.2 .
-0 .3 '
-0.4
0
200
400
600
800
1000
Frequency [kHz]
Figure 4-27: AC biasing PZN-8%PT on its longitudinal thickness mode or pseudotetragonal thickness vibrations. Showing dramatic effects to the light output near its
higher harmonics
88
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Ac biasing around 225kHz PZN-8%PT
140-
■— U nb iased
— 2 1 6 kHz
— 2 1 8 kHz
- 2 2 1 kHz
- 2 2 5 kHz
- 2 2 8 kHz
1201008 0 -|
1
>
O
60-
4o_|
UJ
200-
.rJ
i
200
400
'
r
*i
600
800
>
r
1000
F req u en cy [kHz]
Admiittace polt measured PZN-8%PT
0.4
0.3-
Pseudo-Transverse lateral
mode
0.2-
coupled
0.1o.o-
a
-0.1 .
£ -0.2-0.3-0.4
200
1000
Frequency [kHz]
Figure 4-28: Ac biasing PZN-8%PT on its transverse longitudinal lateral extension mode.
Showing dramatic effects to the light output.
89
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Now let’s look at Figure 4-32 , we can see from this close up view what was not
so obvious on the admittance plots located in Figure 4-27 etc. It shows a noticeable
enhancement near -129 kHz while the other corresponding modes are nearly unaffected.
This confirmed its association with the d3 i (l=4mm) transverse lateral extension mode and
helped to ascribe the other d32 (l=2mm) lateral extension mode to the frequency near 225
kHz. Because 129 kHz lies so close to the 118 kHz longitudinal thickness mode and the
thickness mode admittance peak is so large, they were not easily distinguishable in the
admittance plots. However, in the EO or light experiments, biasing the crystal on its
4mm lateral extension mode (~ 129 kHz) revealed the enhancing effects of its
crystallographically equivalent mode, but half in dimension (2mm) near 225kHz.
Because the frequencies are not separated exactly by a factor of 2, one might think these
modes are not equivalent. However they are related. Besides identifying these modes
using ATILA, their non-integral separation can be explained by the coupling of natural
vibrations in a piezoelectric crystal with dimensions 4 x 4 x 2 (mm). It is well
documented that to observe pure mode resonances in solids the crystals should be cut
with a minimum 5:1 aspect ratio. The crystals used for this investigation have aspect
ratios of 2:1 and 1:1 in the cross section dimension. Therefore, their fundamental modes
will not be pure motions and their harmonics will be intricately mixed.
90
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AC biasing around 118K H z P ZN -8% PT
1 40 -
U n b ia se d
— 114K H z
- -1 1 6 K H z
1 18K Hz
- — 119K H z
1121 KHz
120 -
100 -I
80 2
S
o
60 -
o
m
40 -
>
20 -
0 20 0
400
—i—
600
—i—
800
1000
F r e q u e n c y [kHz]
1E-4
*6#
1E-5
-100
110
>
o
C
D
T3
LU
1E-6
-
-1 2 0
130
600
F r e q u e n c y k[Hz]
Figure 4-29: Thickness mode vibration of PZN-8%PT showing markedly difference
between biased and unbiased condition.
91
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A c b iasin g aro u n d 225 k H z P Z N -8% P T
140
1 00
-
--------U n b ia s e d
--------2 1 6 kH z
— — 2 1 8 kH z
— — 221 kH z
--------2 2 5 kH z
--------2 2 8 kH z
-
*
"
_
a 60
■s*fs
600
800
Frequency [kHz]
Ac biasing around 225kHz PZN-8%PT
1E-4
1E-5
>
o
HI
1E-6
600
800
Frequency [kHz]
Figure 4-30: Illustration showing biasing effects of transverse lateral mode or di2
showing marked difference between biased and unbiased conditions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AC biasing around 118KHz PZN-8%PT
140 •
120
-
100
-
U n b iase d
— — 114K Hz
— — 116K Hz
118KHZ
— — 1 1 9KHz
1121 KHz
80 60 -
>
^J
U
40
40 20
•
—
200
400
600
I----------- '------------- 1-------
800
1000
Frequency [kHz]
AC biasing around 118KHz PZN-8%PT
U nbiased
114KHz
116KHz
118KHz
119KHz
1121 KHz
120100
>
-
o 60
2 40
180
200
Frequency [kHz]
Figure 4-31: Thickness mode ac bias showing general suppressing of all modes as
compared to unbiased condition.
93
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Ac biasing around 225kH z PZN-8% PT
160 -
U n b ia sed
2 1 6 kHz
218 kHz
221 kHz
225 kHz
228 kHz
140 120
-
100
-
80 -
>
O
in
60 40
20
-
0
200
400
600
800
1000
Frequency [kHz]
Ac biasing around 225kHz PZN-8%PT
— U n b iased
216 kHz
— 218 kHz
221 kH z
225 kHz
228 kHz
f
100
140
160
180
200
220
Frequency [kHz]
Figure 4-32: Close inspection low-end EO effect near fundamentals for PZN-8%PT
illustrating noticeable enhancement in light output for extension mode, (d 32 .) near 129
kHz Also, note the nearly equal light output near crystallographically equivalent (l=4mm)
lateral extension mode occurring around 225 kHz
94
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AC Bissing at 119kHz PZN-8%PT
«
1
«
1
•
1
•------
4000 3500
119 kH z
U n b ia se d
3000 2500
3
>
2000
-
o
Q 1500 ■
IU
1000
-
500
0
-
0
50
100
150
20 0
Frequency [MHz]
Figure 4-33: Thickness mode (-119 kHz) biasing effects on PZN-8%PT showing
anomalous effects after 150 MHz. It shows the unbiased EO light output appears to be
larger than the biased effect. This is contrary to results shown in the lower frequencies.
4.5 Interpretation of AC Biasing Results
Many investigators have studied PMN-PT and PZN-PT families of relaxor
ferroelectrics and throughout their reports there is a consensus of their multifaceted
domain structure, high strain, large piezoelectric coefficients, and large electrooptic
coefficients, [6,8,19, 20, 22]. There also seems to be a consensus on the direct links
between domain structure and their observed high piezoelectric related properties.
However, in many reports, there are no clear descriptions on how exactly their domains
are affecting the measured electrooptic properties on the basis of structure property
95
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relationships. In this thesis, I offer my assessment of how domains influence our
measured EO values.
Let us turn our attention to Figure 4-34. In this illustration, which by the way is
only a cartoon schematic of one possible domain structure for purposes of this discussion,
we find domain walls situated in a sense consistent to the poling orientation. This
drawing was constructed based on knowledge of the growth morphology of our samples,
knowledge of their poling orientation, and reported geometries of domain structures for
these and related lead-based perovskite solid solutions with morphotropic phase boundary
compositions. In these relaxor ferroelectrics, the poling orientation determines not only
the resulting crystal symmetry by aligning dipoles, but in the same way develops the
domain orientations which are comprised of aligned dipoles. The overall domain
geometry will tend to align according to the symmetry of the poling field as described by
the curie principle [9] Now turn your attention to Figure 4-35, showing how the crystal
behaves under longitudinal thickness vibrations setting domain walls into motion
according to their orientation. In this Figure we can imagine how the longitudinal
thickness wave occurring at ~ 178 kHz, for PMN-32%PT, set the domain walls into
motion with those aligned favoring the condensation of the wave able to move back and
forth with the wave as it passes through the crystal. Those walls oriented more parallel
along the poling direction will move, just not as gracefully as those favoring the
mechanical compressions of the longitudinal wave. When light is introduced into the
crystal under small signal ac-biasing condition, it will be scattered by the complex
motions of the domain wall structure. Depending on how complex the domain structure
throughout the
96
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Domain walls
Domains
2mm
Figure 4-34: Proposed illustration of domain structure in PMN-PT and PZN-PT crystals
used in our investigation.
volume of the crystal is in the light path, will determine the magnitude of scattering that
will take place.
Inspection o f Figure 4-17, Figure 4-18 and Figure 4-23 show the light output
when biasing the crystal under thickness mode conditions. In the higher-order harmonics
region, there is enhancement. In the low-end near the fundamentals, there is general
suppression under biasing conditions. The low-end frequency region suppression o f light
output occurs in large part due to light scattering by the complex domain wall motion in
our PMN-32%PT crystals under thickness mode bias. In the harmonics regions the
enhanced light output is due to the intricate coupling of the transverse lateral modes.
97
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crystal. The illustration depicts the domain walls as one dimensional, however, they were
drawn this way for simplicity. The walls are more likely not to be one dimensional.
It appears that a pure d32 (1 = 2mm) lateral extension mode will have the largest
amount of light exiting the crystal because it is lies directly in the light path and the
domain would be able to open and close collectively in a bending motion in this
direction. If we view Figure 4-24 we see a slight increase of light output associated with
the d3 i (1 = 4mm), mixed lateral extension mode occurring at ~ 203 kHz, while the
associated d32 (1= 2mm) lateral mode seems to be more complex , slightly increased in a
broadening sense around the resonant frequency. The broadening shape of the light
output may be indicative of the complex mixed vibrational modes associated with the
lateral extensions. Li, Cao, and Cross, reported large d3 i piezoelectric values due to
extrinsic effects investigating piezoelectric moduli in sofit-PLZT crystals under small
signal conditions [26]. In their report, the authors made use of a phenomenological
treatment that modified the piezoelectric modulus describing the nonlinear extrinsic
effects of the 90° domain walls. Soft-PLZT is also a lead-based relaxor ferroelectric with
solid solution composition lying in a morphotropic phase boundary region.
In Figure 4-25, we see the how biasing he crystal in the (1 = 2mm) lateral
extension mode also exhibits a slight increase in output on its associated resonance
occurring at ~ 248 kHz with suppression in the thickness mode and the other
(1 = 4mm) lateral mode. Under this biasing condition, it appears the 4mm lateral mode is
crowded by the motions of the (1 = 2mm) mode and thus its associated light output is
suppressed. It is difficult to say exactly how these modes are behaving because they are
mixed. Comparing the dB plots of Figure 4-18, Figure 4-20, Figure 4-22, which
99
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Now turn our attention to Figure 4-36. In this figure we see how biasing the crystal under
the transverse longitudinal modes, d3 i, d32 , the domain walls open and close in such a
Domain m il motion
longitudinal wave
d„mode
Domains
Figure 4-35: Illustration of domain wall motion when crystal is biased under longitudinal
thickness wave conditions. Those walls situated more favorable to the condensation
direction will move in synch with the wave.
way that is favorable for a larger transmission of light reaching the photodetector. This
action occurs like a ‘pumping lens’ changing its shape under the driving ac-biasing field,
where the polar regions throughout the volume of the crystal captures light entering the
98
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thickness mode illustrated in Figure 4-18, exhibits appreciable EO enhancement near the
harmonic regions is due to its harmonics mixing with those of the transverse lateral
modes. In other words, the coupled harmonics are a collection of vibrations, namely,
transverse lateral and longitudinal modes, set into motion by the force of the ac-biasing
electric field. When piezoelectric crystals are struck with an ac field, vibrations of all
types will be excited; those which are natural to the crystal and their harmonics, and those
which are non-natural. The natural fundamental modes will vibrate with the largest
amplitude. Those which are not natural modes will move to a lesser extent and will damp
out rapidly. The enhancements to the light transmission near the harmonics in Figure 4-
18, are primarily attributed to the transverse lateral motions that are coupled to the
pseudo-thickness mode which are large in amplitude. Again these motions are mixed.
The domain structure o f PMN-32%PT is widely reported as being more complex
than that for PZN-8%PT, however, we observed consistent effect to the effective EO rc
coefficient over a comparable frequency spectrum. The relative light output for our PZN8%PT crystals appears larger than that for the PMN-32%PT under similar biasing
conditions comparing both thickness and lateral modes see Figure 4-29 and Figure 4-30.
Viewing the low-end sections of the EO measurements for PZN-8%PT in
Figure 4-31, where the longitudinal thickness mode is exciting the crystal, we see a
general suppression of all modes in much the same way as was seen for PMN-32%PT
shown n Figure 4-23. In Figure 4-32, we see the effects of biasing the crystal on its 2mm
transverse longitudinal lateral mode d3 i, whereby a slight increase of light associated with
its crystallographically equivalent d32 4mm lateral extension mode occurs. Again the
close relationship between these equivalent modes, namely d3 i and d32 , testifies to the
100
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complex mixing of modes for crystals with these dimensions. At the time I would have
biased the crystal around its apparent -129 kHz mode but the admittance plots did not
reveal this mode clearly from the others. At any rate, all the results obtained thus far
would indicate that by biasing the crystal around 129 kHz would not introduce any new
additional information pertaining to the EO frequency decadence for our samples.
In view of the empirical evidence supporting my explanation provided above for
the EO frequency dependence, a question could arise regarding the difference in
magnitude o f the electro-optic coefficients along the different directions and how they
may influence the respective values. For instance, the ri 3 electro-optic coefficient
pertains to the (1 =2 mm) and (1 = 4mm) lateral extension modes and the r33 coefficient
corresponds to the longitudinal thickness mode Therefore according to our results one
might think that the r^ coefficient is naturally larger than r 33 . On the contrary, PMN32%PT and PZN-8 %PT poled along the [001] crystal axes are both widely reported to
have r33 as its largest electrooptic coefficient [11,19]. In fact, these crystals are poled
along the c-axis to ensure r33 is larger than its other nonzero EO coefficients. This
corroborates the explanation of apparent light output due to extrinsic effects which are
often more pronounced than their intrinsic counterparts. Evidence of domains is verified
by the hysteresis loops depicted in Chapter 3, Figure 3-2 in the experimental section.
The EO behavior in the high frequency region under ac-biasing conditions is not
clear, just as the EO behavior in this region without biasing. (See Figure 4-26 for PMN32%PT and Figure 4-33 for PZN-8 %PT.) PMN-32%PT showed no significant changes
under thickness mode biasing conditions, while PZN-8 %PT showed no changes up until
-150 MHz where it appears to suppress the light output. In some respects, this is
101
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contrary to the biasing effects at lower frequencies where the crystal strains can follow
the driving voltage. But as shown in Figure 4-31, longitudinal thickness mode vibrations
tend to suppress light output. This leads the author to believe the EO behavior in both
crystals at the high frequency end may be attributed to a complex mixture of
microstructural motions triggered by overlapping micro-domain structures Also because
150 MHz approaches the frequency limit o f the instrumentation, some, but not all, of the
peaks near 150 MHz and above could be associated with circuit resonances or artifacts.
102
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Domain wall motion
Domains
Transverse longitudinal lateral wave
d32modes
Figure 4-36: Illustration of domain wall motion when crystal is biased under transverse
longitudinal lateral wave conditions. Those walls situated more favorable to the
condensation direction will move in synch with the wave.
To illustrate the complexity of the piezo-motions associated with the resonance
modes of these crystals described above, Figure 4-37 and Figure 4-38 depict a series of
snapshots generated by ATILA for these crystals undergoing the longitudinal thickness
vibrations for PZN-8%PT. Figure 4-37 shows the 118 kHz vibrational mode and is
continued on Figure 4-39. Again note ATILA does not take into account extrinsic
activity or defects in the crystals and so these snapshots do not entirely represent the real
world.
103
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Figure 4-37: Illustration of longitudinal thickness mode vibration for PZN-8%PT located
at 118 kHz. Motions advance from top down left to right.
r
L
\
j
Figure 4-38: Illustration of longitudinal thickness mode vibration for PZN-8%PT located
at 118 kHz, continued from previous Figure 4-37.
104
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Accordingly, below are a series of illustrations generated by ATILA for the
transverse lateral modes for PZN-8%PT. In particular the vibration corresponds to the
225 kHz mode shown on Figure 4-28. This motion appears more complex so more
snapshots are needed to capture its detail. Note the change in dimensions along the
(1= 2mm, 4mm) lateral directions.
Figure 4-39: Illustration of longitudinal transverse lateral mode vibration for PZN-8%PT
located at 225 kHz, Motions advance from top to down left to right.
105
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Figure 4-40: Illustration of longitudinal transverse lateral mode vibration for PZN-8%PT
located at 225 kHz, continued from previous Figure 4-39. Motions advance from top to
down left to right..
4.6 DC Biasing
In our attempts to increase light output, we applied various levels of DC voltage
to the crystal while sweeping across its piezo-resonance modes, in order to increase the
polarization and therefore optical throughput, See Figure 4-41. Accordingly, applying 10
volts (0.4V/mm field) appeared to increase the light output roughly by a factor of 10.
Applying 20 volts (5V/mm) had no further increasing effects, generally; however, at 20
volts there was an emerging peak at 225 kHz or the 2mm traverse lateral mode (d3 i),
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
which may be a result of the crystal’s domain structural changes after the application of
the first 10 volts, see Figure 4-42. This peak appears consistently in the other EO
measurements illustrated in previous figures. Overall, the application of a DC bias does
not appear to change the frequency response, significantly, across the entire range, but it
did expose the instability of these crystals. Microstructure metastability was and remains
to be a consequence o f solid solution lead-based relaxor ferroelectrics whose composition
lie within a morphotropic phase boundary.
DC Biasing PZN-8%PT
700600-
Unbiased
10 Volts
20 Volts
50 0 ^
400 H
i^i
|
300 H
>
o
200100-
200
400
600
800
1000
Frequency [kHz]
Figure 4-41: Direct current (DC) bias, of PZN-8%PT showing some subtle linear effects
of increased polarization. After the first 10 volts the crystal’s polarization seemed to
saturate, and doubling the voltage generated a new peak near 225 kHz.
107
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DC Biasing PZN-8%PT
700
600-
—o— Unbiased
— — 10 Volts
20 Volts
500-
S£« 4 0 0 -
>
2
IO 3 0 0 -
200
-
100
0100
125
150
175
200
225
250
275
F re q u en c y [kHz]
Figure 4-42: A closer inspection of increasing the voltage. A nearly linear response was
achieved with the application of DC voltage. After the first 10 volts however the
crystal’s microstructure seems to change and we see the emergence of a peak around 225
kHz that was not there with 10 volts.
4.7 Aging
The poling condition of the single crystals did not seem to be significantly
affected by repeated measurement in various modulating electric field conditions.
However, it is noted that the crystals became more transparent compared to the originally
poled states after the DC biasing. This translates directly to a slight increase in Vp.p
values used to calculate rc. The piezo-resonance curve obtained after extensive
measurement was less spurious near the main resonant frequencies as shown clearly in
Figure 4-43.
108
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---------- ■---------- >---------- <---------- r
n
8.0
jT
-
6.0-
1
Original Poled Sample
After High Freq EO Measurement
(0
(0
4.0-1
©
2.0 -
4->
«
©
0)
a
c
(0
Q.
a>
o
(0
o.o--
2 .0 -
-4 .0 -
-6.0 H
3
(0
- 8 .0 -I
200000
225000
250000
F re q u e n c y [Hz]
Figure 4-43: Comparison of virgin poled to aged sample after high frequency dynamic
measurement.
As the modulation electric field applied across the c-axis of the crystals is low in
magnitude (~2V/4mm or 0.5 V/mm), and parallel to the poling E-field direction, no fieldinduced depolarization is expected. The effect may be attributed to the local heating due
to the sustained ac driving. Local heating by ac field may have similar effects as ‘aging;’
a process advanced by migrating charges to domain boundaries that become trapped.
Point-defects such as oxygen vacancies and Ti3+ ions are known to exist in flux grown
crystals. Some strong evidence of this process is that over time the ferroelectric crystals
show hardening behavior exhibited by a smoothing out of spurious inflections in piezo­
resonance peaks. Another indicator is a decrease in piezoelectric coefficients as the
109
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
domain wall mobility is hindered or stuck on the defects resulting in a decrease of their
displacement. In our crystals, the measured d33 coefficient for PMN-32%PT decreased
from -1560 pC/N to -1326 pC/N. PZN-8%PT d33 value did not appear to decrease
significantly, but PZN-8%PT underwent fewer extensive ac-biasing measurements.
Applying a relatively large DC bias field can dislodge domain walls as they “hop” across
the crystal. This effect would give rise to a domain but not necessarily to larger
coefficient.
Sustained ac biasing, even at small signal levels, around piezoelectric resonant
modes while simultaneously sweeping across a broad range o f frequencies, appears to
have a more dramatic effect than simply sweeping the crystal across a wide frequency
range. Figure 4-44 shows a comparison of PMN-32%PT piezo-resonances before and
after extensive ac-biasing measurements. Again this signifies accelerated aging. Also at
resonance, the energy generated by an ac signal in a capacitor is directly proportional to
tan8, that is, w = coV2C tan
where w represents watts (joules/second) C, capacitance
(farads) and tan8, represents loss (e"/e') [31].
Therefore a sustained ac-biasing signal at
resonance where the tan8 term or loss term is also at resonance, (analogous to the term in
Figure 2-7), the crystal will generate an appreciable amount of energy in a relatively short
period of time as a response to the modulating field. This will exasperate local heating
and can lead to accelerated aging. PZN-8%PT was not subjected to EO measurements or
ac-biasing measurements to the same degree as that for PMN-32%PT. After observing
the damaging effects o f these measurements care was taken to preserve the quality of the
samples. Hence the admittance spectra for PZN-8%PT appears to be unchanged,
Figure 4-45. Furthermore the clarity of the PZN-8%PT piezoresonance plots along with
110
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the EO spectra indicate a relatively less complex domain structure in PZN-8%PT than for
PMN-32%PT. Therefore, PZN-8%PT EO behavior may be easier to
(m easured after EO) Admittance
1.0 -
■— 165KHz to 265KHz after extensive EO w/ Ac Bias
• — Before extensive EO and AC Bias
0.5
0 .5 -
->?G
<
o
X
O 00o
c
JS
a
0) _Q 5 _
<0 Ub
3
(0
-
1. 0
0.0
-0.5
-
-
160
180
200
220
240
260
1.0
280
Frequency [kHz]
Figure 4-44: Comparison of piezo-resonances after sustained ac biasing at fundamental 1
resonance modes
111
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After Measurements PZN-8$PT
0 .8
-
0 .6 -
After EO M eassurem ents
Before EO m easurem ents
0 .4 -
G
O
0 .2
-
2L o.o©
o
c
JS
Q.
0)
O
(0
3
W
-
0 .2
-
-0.4- 0 .6 -
-0 .8 - 1.0 -
0
200
400
600
800
1000
Frequency [kHz]
Figure 4-45: Comparison of piezo-resonances after ac biasing at fundamental resonance
modes. This sample was subjected to sustained EO measurements, but to a lesser degrees
than that for PMN-32%PT. Hence there appears to be no change in the admittance
spectra.
interpret when applying a voltage parallel to its poled orientation than its PMN-32%PT
counterpart, all other sample preparation methods being equal.
4.8 RF Optical Transduction
As mentioned in the introduction chapter of this thesis. One of the driving forces
behind this work was to develop solid-state single component technology to carry or
impress an RF signal onto an optical fiber. The benefits for this transduction would be
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enormous in weight and cost savings. To achieve this end, there are ‘power-budget’
requirements that need to be addressed in terms of how much light output must pass
through the optical system and to what depth must the signal be modulated. Figure 4shows the losses in a hypothetical RF to optical transfer system supported with solid-state
single crystal technology.
Power Budget
light in
OdB
splitter -6dB
light out
connector
-19.3dB
sp |jce
PD
-3dB
SNR
Figure 4-46: Power budget schematic for our proposed solid-state single crystal
technology implying at least -20 dB of light output is lost in the systems by the time the
light output reaches the photodetector.
This implies that the light signal would undergo roughly 20 dB of losses by the time it
reaches the photodetector. Thus is our observations we see how to increase the EO value
beyond 20 dB with ac-biasing. More accurately we can increase the modulation depth
between the biased and unbiased EO response exploiting its piezo-optical resonance
characteristics. These losses can be overcome in a number of ways. One in particular
would be to increase the optical carrier signal’s intensity.
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Accordingly, for optical systems, 10 dB of modulation depth is sufficient to
resolve information from the carrier at the receiver.
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Chapter 5
CONCLUSIONS
In this thesis electrooptic, EO, and piezoresonance measurements were conducted
to understand how one could exploit piezoelectric enhanced electrooptic coefficients,
namely rc, in PMN-32%PT and PZN-8%PT crystals, for microwave photonic
applications. In doing so, we independently applied, weak ac-biasing signals at
piezoresonance frequencies and observed EO enhancements near 4th order harmonics of
piezoelectric resonance modes. While biasing the crystals we observed light suppression
in the d33 longitudinal thickness mode attributed to light scattering from complex motions
throughout the volume of the crystals.
Also, we observed a general reduction in admittance behavior due primarily to
aging advanced by extensive measurements. Below are more detailed descriptions o f the
results and conclusions o f this thesis.
The abnormal increase of EO rc coefficient is a direct result of the increase of
field dependent transparency (dl/dE) for the given crystal. While the modulating field
amplitude remains constant, the modulating field induced intensity (or the light output),
has increased proportional to the slope of the impedance (dY/dE). Sample’s dimensional
change and domain wall motions can cause additional scattering or noise; which
nevertheless do not convolute the measurement results as the lock-in analyzer effectively
removes all but the synchronized signal with the modulating field frequency. While it is
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perhaps not surprising that piezoelectric resonance amplifies the electrooptic property
[11,10,14], no theoretical model has been developed to establish the details of the
micro-structural relations among the phenomena. A simple model that deals with the
gradient of displacement within a crystal at its resonance frequencies is predicated on
complex domain wall motions, and can be quantified by extending nonlinearities to the
electrooptic equation similar in scope to a phenomenological theory introduced by Arlt,
Dederiehs, and Herbeet [32], but applied to electrooptic behavior. This equation would
predict that the transverse lateral resonance (vibration direction perpendicular to light
propagation direction), elongation or shear modes, will amplify the electrooptic
properties as a result o f domain wall motions that are favorably oriented to the original
poling direction acting as a light valve or shape-changing lens, under small ac-signal
conditions. On the other hand, longitudinal thickness resonances, decreases the effective
EO coefficient near the ‘low-end’ around fundamental frequencies. The current results
demonstrate that all three permitted modes in the crystal enhance the EO coefficient in a
broadening sense at frequencies up to 5th -order harmonics. Some of our most
interesting results suggest that a resonantly enhanced electrooptic effect can be extended
to high frequency (100 MHz) where RF to microwave-photonic devices are in demand.
Figure 4-14 and Figure 4-16 show the amplification for electrooptic coefficient well
beyond 20 MHz though it is unclear how the crystal is responding.
DC biasing the crystal did generally improve the light throughput of the crystals,
but did not appear to significantly change the EO frequency behavior. While a relatively
large DC field may dislodge domain walls trapped by defects, it had little effect on
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enhancing the EO light output near 5th order harmonic which was observed for a small ac
biasing fields.
Electrooptic coefficients of ferroelectric PMN-32%PT crystals consist of both
intrinsic and secondary contributions arising from piezoelectric coupling.
At low
frequencies (<50 kHz) space charge effects may make up majorityt of the apparent EO
effect measured, which however decreases exponentially with increasing frequency. In
the absence of domain inversion (small signal condition) the linear EO contribution
comes primarily from ionic dipole reorientation following the modulating electric field,
which is however typically small in value, in frequencies exceeding 100s kHz. When the
wavelength of lattice vibration is in harmony with piezoelectric resonance frequencies, it
is found that the EO coefficient is greatly amplified. Such amplification can be explained
qualitatively using the theoretical model of transverse acoustic phonons. Piezoelectric
lattice waves, when comparable in scale with crystal dimensions, motion in sync with
dipole-stretching, and therefore enhance the EO coefficient at the frequency of the
piezoelectric motion. Lattice vibration EO amplification is the crux of engineering single
crystal resonators as detectors or modulators in selected frequencies for applications in
microwave photonics.
5.1 Future Work
Further studies specific to piezoelectric mode selection would allow for
quantitative analysis o f r33 , ro, and m shear modes, may shed some light on domain wall
contributions. More importantly, cutting samples with high aspect ratios will facilitate
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mode separation and simplify the crystal lattice vibrations especially in the high
frequency (>1 MHz) ranges. Cutting the sample thin in the direction of light propagation
ensures low absorption and may possibly help to control or minimize multifarious
domain orientation allowing for clarification of domain activity on EO effect. Also TEM
studies while under ac-biasing may allow one to view domains as they change shape
under a weak ac biasing field. Perhaps a less expensive way to ascertain domain activity
while under a biasing field would involve a polarizing light microscope where the view
can see the crystals' light transmission go in and out of extinction as the crystals change
shape under the driving signal. O f course, TEM would yield superior resolution.
The significance of these finding, although less clear, in the high frequency region
(> 3 MHz) lends itself to a simple but innovative approach to EO behavior specific to
PMN-32%PkT and PZN-8%PT and other crystals with similar solid solutions within a
morphotropic phase boundary. Furthermore, the results in this thesis provide the entrance
to a pathway for further material engineering techniques applied to relaxor high strain
ferroelectrics that can make feasible their application in microwave-photonic devices.
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VITA
Growing up in the ghetto of south Philadelphia, the harsh realities of everyday life
did not provide for a proper environment where a young mind can gain an appreciation
for academics. Without living tangible examples of professionals demonstrating what it
takes to become a self-sufficient productive citizen contributing to society, many of us
started without a compass. The types of life-long lessons that were being taught stem
from the laws of the jungle where the strong lead the weak. These lessons can temper
your will creating an indomitable spirit, that if goes untrained or unchecked can turn into
notions of resentment and distrust leading to a rejection of the mainstream and accepting
criminal activity as a means of survival. Most of my childhood peers are still living at
home in the old neighborhood, in the throes of organized or unorganized crime, or worse.
I grew up in a broken home, by the time mother was 25 she had 6 kids, divorced,
and without a college education. Mom worked for the city of Philadelphia as a librarian
for 29 years earning at the end of her career just over $28,000. She had to grow up fast
by passing her teenage years but insightful enough to instill in us a strong ethics for
education. My father wasn’t exactly a dead-beat, but heavy drinking and overtime shifts
around the clock limited his visibility even though he lived only 10 miles away.
Living with a librarian, overdue books crowded the empty spaces in our basement.
Although mostly fiction novels; they provided a playground for an inquisitive mind
where I developed an enormous appetite for knowledge for the unknown. At the age of
12, on a weekday evening I decided to see what books in the cellar that could possibly
help me embellish my homework assignments. I started with an elementary physics text,
a book on Egyptology, astrology and the huge early 20th century collapsing Webster
dictionary. I think the homework was for my Latin class. Accordingly, I began looking
up the names of mythological heroes and villains, which naturally lead me, deeper into
the chronology of their lives and their relationships to other subjects. This went on for
hours past the time when everyone in the house and on the block was asleep. Then in a
brief moment I deduced a connection between math, science and religion. It was
extraordinary and filled me with uncontrollable excitement. The rest is history.
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