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Strain and thickness effects on the microwave properties of barium strontium titanate thin films

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STRAIN AND THICKNESS EFFECTS ON THE MICROWAVE
PROPERTIES OF BST THIN FILMS
by
JEFFREY A. BELLOTTI
A Dissertation submitted to the
Graduate School - New Brunswick
Rutgers, The State University of New Jersey
in partial fulfillment o f the requirements
for the degree of
Doctor of Philosophy
Graduate Program in Ceramic and Materials Engineering
written under the direction of
Professor Ahmad Safari
id approved b y .
~
-
c i'
—
New Brunswick, New Jersey
May 2003
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UMI Number: 3092914
Copyright 2003 by
Bellotti, Jeffrey A.
All rights reserved.
®
UMI
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© 2003
Jeffrey A. Bellotti
ALL RIGHTS RESERVED
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ABSTRACT OF THE DISSERTATION
Strain and Thickness Effects on the Microwave Properties o f
BST Thin Films
by JEFFREY A. BELLOTTI
Dissertation Director:
Professor Ahmad Safari
Heteroepitaxial Bao^Sro^TiCb films were deposited on (100) LaAlCb and (100) MgO
substrates by pulsed laser deposition in the thickness range o f 22 nm to 1150 nm. The
state of strain in the films as a function of thickness and substrate type was correlated
with the microwave dielectric properties in the frequency range of 1 to 20 GHz. Films
deposited on LaAlCh showed a compressive in-plane strain, which increased to -0.25%
for the thinnest films, while films on MgO showed an increasing tensile in-plane strain
with decreasing thickness, which reached a maximum of +0.35%. The tunability of each
film series was distinctly different depending on both the direction and magnitude of the
in-plane strain. Tensile strains were shown to be preferable to compressive strains for
maintaining high tunability across a wide thickness range. A maximum tunability of
-65% was achieved for the thickest films in each series, while the thinnest films on MgO
showed substantially higher tuning (30%) as compared to those on LaA 1 0 3 (3%). A
region o f maximum tunability was defined by the strain states of the films with the
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highest tunability in each film series, which was found to be in the range o f 0 to +0.07%
in-plane tensile strain. In addition, a thickness dependence of the non-linear dielectric
response was observed in the field-induced in-plane charge of the films. The behavior
was related to the strain-effected tunability and shows that the non-linearity of the fieldinduced dielectric response is a direct indication of the degree of tunability. Finally, the
temperature-dependent permittivity and tunability of several films on MgO were studied
over the temperature range of 78 K to 328 K. Strain was shown to suppress the three
phase transitions normally present over this temperature range, resulting in a single
maximum in the permittivity, which was observed to shift towards higher temperatures
and broaden with increasing in-plane tensile strain. Hysteresis measurements at 78 K,
278 K, and 308 K also showed that these films have significant internal polarization,
which may be related to the broadening of the ferroelectric to paraelectric phase
transition.
iii
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ACKNOWLEDGEMENTS
First, I would like to thank God for giving me the strength and resolve to
complete this task. I owe much to my family as well for always being there for me and
helping me in many ways through these long years of work.
I am also very grateful for the guidance and help of Dr. E. Koray Akdogan, the
direct supervisor of this project. He was an excellent mentor and I learned a great deal
working with him through countless scientific discussions. I thank Professor Safari, my
thesis advisor, for providing me with the opportunity to work on this project as his
graduate student. Through his support and the financial support of the Glenn N. Howatt
Foundation I was able to establish a brand new PLD thin film laboratory at Rutgers for
my work, which will also be used by future students for many years to come. The Glenn
N. Howatt Foundation has been very gracious in their support o f the electroceramics
work at Rutgers University, and as the first recipient of the Howatt Fellowship at Rutgers,
I thank them for making it possible for me to perform this study.
This project would also not have been possible without the help of the U.S. Naval
Research Laboratory. The collaboration I formed with the NRL through Dr. Jeffrey Pond
was critical in being able to conduct the microwave measurements for this work. I thank
everyone that I worked with at the lab, which includes Dr. Jeffrey Pond, Dr. Steven
Kirchoefer, Dr. Wontae Chang, and Dr. Walter Kruppa. They generously accommodated
me, giving me access to their measurement equipment and taking time out of their busy
schedules to discuss my work. I especially owe many thanks to Dr. Wontae Chang who
trained and guided me every step of the way with the photolithographic processing and
microwave measurements of thin films. I learned a great deal from him regarding the
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testing and analysis o f ferroelectric microwave devices. I am proud to say that I will be
joining their group at the NRL to work on tunable ferroelectrics after my graduation from
Rutgers.
Furthermore, I thank Dr. Tom Emge of the Chemistry Department for all of the
time he spent training me on single crystal x-ray diffraction, which was one of the most
important measurements necessary for this work. I also thank Dr. Sabyasachi Guha of
the Physics Department for originally introducing me to the science of pulsed laser
deposition.
Finally, I thank all the other scientists that I have worked with at Rutgers,
including Dr. Andrei Kolkin, Dr. Alexander Semenov, and the late Dr. Harmut Schulte,
and I thank Mr. John Yaniero, our laboratory equipment manager, for his help in
facilitating the construction of the PLD laboratory.
There were so many things that needed to be done to even begin this work—it is
truly rewarding to have everything come together and finally reach an end. Looking back
on the past 414 years, I only now realize how far I have come in this journey. Looking
ahead, I now also realize where I want to go. I am fortunate to have worked with, and
learned from people that have a passion for science and discovery, and I wish them well
and continued success.
v
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TABLE OF CONTENTS
A bstract
........................................................................................................................................................ ii
A cknow ledgem ents
Table
of
Co n t e n t s
.............................................................................................................................. iv
................................................................................................................................. v i
L ist
of
T ables
L ist
of
F ig u r es ............................................................................................................................................ x i
1.
............................................................................
In t r o d u c t io n
and
x
B ackground
1.1.
Brief Overview o f Strain Effects in BST Thin Films
1
1.2.
Ferroelectricity
4
1.2.1. Crystallographic symmetry of ferroelectrics
4
1.2.2. Polarization mechanisms
6
1.2.3. Characteristics of ferroelectric materials
1.2.3.1. Material properties o f BaxSr(i_X)Ti0 3
10
14
1.3.
Thermodynamics of Film Growth
16
1.4.
Pulsed Laser Deposition
22
1.4.1. Processing parameters influencing film growth
23
1.5.
1.4.1.1. Substrate temperature
24
1.4.1.2. Oxygen pressure
25
1.4.L3. Laser fluence, repetition rate, spot size, and wavelength
26
1.4.1.4. Target to substrate distance
28
Microwave Thin Film Passive Components
29
Chapter S u m m a r y
33
vi
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34
References
2.
3.
L it e r a t u r e R e v ie w
2.1.
Strain Effects in BST Thin Films
38
2.2.
Tunable Microwave BST Thin Film Devices
70
Ch a p t e r S u m m a r y
80
R e fe r e n c e s
81
Sta tem en t
of t h e
Pr o blem
and
M ethod
of
A ttack
R e fe r e n c e s
4.
84
88
E x pe r im e n t a l P r o c e d u r e /M e t h o d s
4.1
4.2
4.3
Structural Characterization
89
4.1.1 X-ray diffraction
89
4.1.2 Field-emission scanning electron microscopy
96
4.1.3 Atomic force microscopy
97
4.1.4 Rutherford backscatter spectroscopy
99
4.1.5 Medium-energy ion spectroscopy
102
Pulsed Laser Deposition of BST Thin Films
105
4.2.1 PLD system design
107
4.2.2 Target preparation
111
4.2.3 Preparation o f substrate and pre-deposition conditions
114
Measurement o f X-Band Microwave Properties
117
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4.3.1
Interdigitated capacitor fabrication
117
4.3.2
Microwave Sii measurements
124
4.3.2.1
126
Room temperature microwave measurements
4.3.2.2 Cryogenic microwave measurements
128
Microwave data extraction
130
4.3.3.1
130
4.3.3
Parallel resistor-capacitor model
4.3.3.2 Conformal mapping method
5.
133
C h a pt e r S u m m a r y
13 8
R e fe r e n c e s
139
R esu lts
and
D is c u s s io n
5.1 Optimization o f PLD Processing Conditions for EpitaxialGrowth
140
5.1.1
Effect o f primary PLD parameters on film morphology
141
5.1.2
Film stoichiometry and thickness measurements
147
5.1.3
Surface roughness
150
5.1.4
Degree of epitaxy and film quality
152
5.2 Microwave Properties of Strained BST Thin Films
156
5.2.1
Effects o f film thickness on the BST unit cell
156
5.2.2
Capacitance and Q-Factor vs. film thickness
164
5.2.3
Strain and thickness effects
175
5.2.3.1 Tunability
175
5.2.3.2 Permittivity
192
5.2.3.3 Field-induced in-plane charge
199
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5.3
6
Temperature Dependence of the Microwave Properties
210
5.3.1
Dependence of the permittivity maximum on the in-plane strain
211
5.3.2
Residual polarization effects related to the phase transition
220
Ch a p t e r S u m m a r y
224
R e fe r e n c e s
228
. C o n c l u s io n s
233
7.
239
Fu t u r e W o r k
A p p e n d ix
241
C u r r ic u l m V it a
248
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LIST OF TABLES
Table 2.1 Microwave measurements of 500 nm BST (50/50) thin films.
...... 41
Table 2.2 Material parameters for BST, including Curie temperature (7c), Curie
constant (C), fitting parameters (ay), elastic coefficients (Sy), and
electrostictive coefficients (Q y ) ......................................................................... 59
Table 2.3 Possible phases o f strained BST films as predicted by theory....................... 60
Table 4.1 Scan settings used for lattice parameter measurements o f BST thin films. .. 94
Table 4.2 Deposition times for growth o f films............................................................. 105
x
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LIST OF FIGURES
Figure 1.1
Perovskite unit cell showing displacement of center Ti atom, which
is the mechanism for spontaneous polarization............................................... 5
Figure 1.2 Polarization and loss mechanisms versus frequency........................................ 9
Figure 1.3 Hysteresis curve for a ferroelectric material................................................... 11
Figure 1.4 General behavior of material properties near the transition temperature...
12
Figure 1.5 First order phase transition from ferroelectric to paraelectric state
13
Figure 1. 6 First order phase transition from ferroelectric to paraelectric state
13
Figure 1.7
Various atomic mechanisms occurring during film growth......................... 16
Figure 1. 8
Schematic of pulsed laser deposition system, showing ablation of
ceramic target...................................................................................................
Figure 1.9
2 2
Laser pulse ablating a BST target, showing plume expansion towards the
substrate............................................................................................................ 27
Figure 2.1 Capacitance per unit area (C/A) as effected by applied stress. Capacitor 1
has been loaded, then unloaded. Capacitor 2 was stressed until substrate
failure................................................................................................................ 44
Figure 2.2
Dieleetic constant as a function of temperature showing the suppression of
the bulk phase transition from ferroelectric to paraelectric......................... 45
Figure 2.3
Shift in the magnitude and position of the maximum permittivity toward
lower temperatures with decreasing film thickness...................................... 48
Figure 2.4
Appearance o f ferroelectricity, seen as increased remnant polarization,
with decreasing film thickness....................................................................... 51
Figure 2.5
Maximum in the dielectric constant shifts toward higher temperatures with
decreasing film thickness (or increasing in-plane strain)............................ 52
Figure 2.6
(a) Hystersis of in-plane permittivity with DC bias, (b) In-plane permittivity
vs. film thickness............................................................................................. 54
Figure 2.7
Effect o f compressive strain on the permittivity o f BST thin films
on LSAT........................................................................................................... 55
Figure 2.8
Permittivity vs. film thickness for BST (50/50) on MgO............................. 57
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Figure 2.9
Effect o f tensile strain on the permittivity of BST (50/50) on MgO
58
Figure 2.10 Theoretical phase diagram showing stable phases as a function of
temperature and strain. Dotted line is for BST (60/40) and solid line is for
BST (70/30)...................................................................................................... 60
Figure 2.11 Calculated misfit strain vs. film thickness for BST (60/40) at 25 °C on (a)
compressive substrates, (b) tensile substrates............................................... 63
Figure 2.12 Calculated dependence of (a) out-of-plane permittivity for BST (70/30),
(b) in-plane permittivity for BST (60/40), on misfit strain at 25° C
64
Figure 2.13 Calculated dependence of (a) out-of-plane permittivity for BST (70/30),
(b) in-plane permittivity for BST (60/40), on film thickness at 25° C
65
Figure 2.14 Tunability of (a) out-of-plane permittivity, (b) in-plane permittivity for BST
(50/50) at 298 K with application o f electric field, predicting a maximum at
a phase transition............................................................................................. 67
Figure 2.15 Tunability of out-of-plane permittivity for BST (50/50) at 298 K on (a)
compressive LaAlCb substrate, (bj tensile MgO substrate.......................... 68
Figure 2.16 Dual BST thin film varactors fabricated on high-resistivity silicon with Pt
electrodes.......................................................................................................... 70
Figure 2.17 Capacitance per unit area o f BST thin film varactors as a function of
DC bias............................................................................................................. 71
Figure 2.18 Meandering path BST thin film CPW phase shifter..................................... 72
Figure 2.19 Tunability o f CPW phase shifter with DC bias, (a) phase shift,
(b) insertion loss....................
72
Figure 2.20 Tunable bandpass CPW filter design using SrTi0 3 for low temperature
operation........................................................................................................... 73
Figure 2.21
Tuning of filter showing shift of bandpass frequency with DC bias
74
Figure 2.22
Design of tunable waveguide filter using BST thin film varactors
75
Figure 2.23
Tunability of BST varactor-based waveguide filter.................................... 76
Figure 2.24 Capacitance per unit length vs. DC bias for BST thin film transmission line
at 235 K ................................................................................................................ 77
Figure 2.25 Phase shifter based on BST thin film composite showing capable of ~180°
phase shift......................................................................................................... 78
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Figure 2.26 Phase-array antenna schematic using tunable BST phase shifters between
feed lines and patch antenna elements........................................................... 78
Figure 2.27 Performance o f BST phase shifter circuit, (a) phase shift, (b) insertion and
return loss as a function of DC bias from 1 to 10 GHz................................ 79
Figure 4.1
Diffracted x-ray beam as seen by scintillation detector and GADDS Hi-Star
wide area detector............................................................................................ 90
Figure 4.2
GADDS diffractometer with Hi-Star wide-area detector............................. 91
Figure 4.3
Fixed chi stage ( x ^ S 0) showing thin film sample mounting position
Figure 4.4
Nanoscope II atomic force microscope.......................................................... 98
Figure 4.5
Schematic o f RBS system..............................................
Figure 4.6
Ion scattering of incident He+ denoted Mi, with target atom M 2 .............. 101
Figure 4.7
Channeling of particles along a major crystallographic direction via
small-angle scattering................................................................................... 103
Figure 4.8
Channeling zone (blue) for center atom, defined by rmin and r0 ................ 104
Figure 4.9
Film thickness vs. deposition time showing linear deposition rate
92
100
106
Figure 4.10 Pulsed laser deposition system constructed by the author, (a) target carousel
view, (b) substrate heater assembly view.................................................... 109
Figure 4.11 Interdigitated capacitor array........................................................................ 118
Figure 4.12 NRL multilayer photolithographic lift-off process for patterning o f IDC
array................................................................................................................ 123
Figure 4.13 Microwave measurement equipment connections...................................... 125
Figure 4.14 Parallel resistor-capacitor circuit model...................................................... 130
Figure 4.15 Modeling o f IDC structure for calculation of three partial capacitances,
C„, C3, and CerKi.............................................................................................. 135
Figure 5.1
Film morphology o f SrTiCL vs. PLD deposition temperature (a) 750 °C,
(b) 600 °C, (c) 500 °C, and (d) 400 °C......................................................... 143
Figure 5.2
Effect o f target-to-substrate distance (a) 6.4 cm and (b) 8.3 cm on the
morphology o f SrTi0 3 thin films................................................................. 144
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Figure 5.3
BST (60/40) epitaxial films grown on (a) LaAlOj and (b) MgO showing
greatly reduced number and size of surface crystals.................................. 145
Figure 5.4
Two views o f the cross-section o f a BST (60/40) film on LaA1 0 3 showing
dense epitaxial film growth and high surface roughness for deposition at
350 mTorr O 2 ................................................................................................. 146
Figure 5.5
RBS spectra of BST (60/40) films on LaA1 0 3 for a thickness o f (a) 270 nm,
(b) 160 nm, (c) 110 nm, (d) 44 nm, and (e) 22 nm showing ideal
stoichiometry of Ba:Sr:Ti ratio o f 3:2:5 within 5 atomic%....................... 148
Figure 5.6
Cross-section FESEM images of BST (60/40) films on LaA 1 0 3 for a
thickness o f (a) 1150 nm, (b) 625 nm, (c) 400 nm, and (d) 22 nm showing
dense film layer with uniform thickness and low surface roughness
149
Figure 5.7
AFM scans o f BST (60/40) films on LaAlCb showing (a) 500 x 500 nm scan
for t—1150 nm, (b) 1000 x 1000 nm scan for t=270 nm, (c) 1000 x 1000 nm
scan for t=110 nm, and (d) 500 x 500 nm scan for t=22 nm
150-151
Figure 5.8
Omega-scan x-ray diffraction o f (a) BST/LaAlCh and (b) BST/MgO
showing ( 1 0 0 ) and (2 0 0 ) reflections of highly epitaxial film and single
crystal substrate............................
Figure 5.9
153
MEIS channeling spectrum for BST (60/40) on LaAlC>3 (black) and random
spectrum at 7° off normal (red) showing large decrease in the yield for the
channeling condition..................................................................................... 155
Figure 5.10 Effect o f film thickness on the (a) normal and in-plane lattice parameters,
and (b) normal and in-plane strain o f BST (60/40) thin films
onLaAlOs...................................................................................................... 157
Figure 5.11 Effect o f film thickness on the (a) normal and in-plane lattice parameters,
and (b) normal and in-plane strain of BST (60/40) thin films on M gO ... 161
Figure 5.12 Measurement o f the (a) gap size and (b) finger length of an interdigitated
capacitor with FESEM.................................................................................. 164
Figure 5.13 Capacitance and Q-factor from 1 to 20 GHz and C vs. V (two traces) for
BST on LaAlOs—(a) 1150 nm, (b) 825 nm, (c) 625 nm, (d) 400 nm, (e) 270
nm, (f) 160 nm, (g) 110 nm, (h) 44 nm, and (i) 22 nm. For capacitance/Qfactor vs. frequency plots the DC bias is incremented in steps of 5 V, where
red trace is 0 V and black trace is 40 V.............................................. 167-169
Figure 5.14 Capacitance and Q-factor from 1 to 20 GHz and C vs. V (two traces) for
BST on MgO— (a) 1150 nm, (b) 825 nm, (c) 625 nm, (d) 400 nm, (e) 270
xiv
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nm, (f) 160 nm, (g) 110 nm, (h) 44 nm, and (i) 22 nm. For capacitance/Qfactor vs. frequency plots the DC bias is incremented in steps o f 5 V, where
red trace is 0 V and black trace is 40 V.............................................. 172-174
Figure 5.15 Capacitance vs. DC bias voltage at 10 GHz (a) LaAlC>3 series, (b) MgO
series for the film thickness range of 2 2 to 1150 nm................................. 176
Figure 5.16 Tunability (at 10 GHz) and in-plane strain vs. film thickness for (a) LaA 1 0 3
series and (b) MgO series. Vertical dotted lines are critical film thickness
corresponding to major change in unit cell dimensions............................. 178
Figure 5.17 Tunability o f BST(60/40) films at 10 GHz as a function of misfit strain
as created by deposition on LaA 1 0 3 (red) and MgO (blue)....................... 181
Figure 5.18 Dielectric constant vs. film thickness for BST (60/40) on LaAK> 3 (red) and
MgO (blue) at 10 GHz. Dotted lines indicate predicted trend
193
Figure 5.19 In-plane charge vs. electric field (a) as a function of film thickness for the
BST/LaA 1 0 3 series, (b) zoomed view of thinnest films showing decreased
non-linearity................................................................................................... 2 0 0
Figure 5.20 In-plane charge vs. electric field (a) as a function of film thickness for the
BST/MgO series, (b) zoomed view of thinnest films showing decreased
non-linearity.............................................................................. .................... 2 0 1
Figure 5.21 Electric field distribution in films of varying thickness, showing change in
penetration depth (yellow shaded area) with decreasing dielectric constant of
the film............................................................................................................ 205
Figure 5.22 Meandering path between the fingers of an IDC used for the length in a
calculation of the in-plane polarization....................................................... 206
Figure 5.23 Attempted calculation of the in-plane polarization based on the film
thickness multiplied by the meandering path length for (a) BST/LaAlCb
and (b) BST/MgO.......................................................................................... 207
Figure 5.24 Dependence of (a) capacitance, (b) dielectric constant, and (c) Q-factor on
temperature over the range o f 78 K to 328 K for an 825 nm BST (60/40)
film on MgO................................................................................................... 212
Figure 5.25 Dependence of (a) capacitance, (b) dielectric constant, and (c) Q-factor on
temperature over the range o f 78 K to 328 K for a 270 nm BST (60/40)
film on MgO................................................................................................... 215
Figure 5.26 Dependence o f (a) capacitance and (b) Q-factor on temperature over the
range o f 78 K to 328 K for a 44 nm BST (60/40) film on MgO............. 215
xv
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Figure 5.27 Two cycles of the capacitance vs. DC bias for a 270 nm BST (60/40) film
on MgO at 78,278, and 308 K, showing varying amounts of hysteresis due
to residual polarization changes with temperature..................................... 2 2 1
Figure 5.28 Two cycles of the capacitance vs. DC bias for a 44 nm BST (60/40) film on
MgO at 78,278, and 308 K, showing varying amounts o f hysteresis due to
residual polarization changes with temperature.......................................... 2 2 1
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1
CHAPTER 1 - INTRODUCTION
This chapter begins with a brief introduction to the topic of this thesis, followed
by discussions o f the main subjects involved in this work. Sections on ferroelectricity,
thin film growth modes, pulsed laser deposition, and microwave passive components are
included.
They provide background knowledge for those not familiar with the
classification, fabrication, and applications of thin film ferroelectrics.
1. 1
B r i e f O v e r v ie w o f S t r a i n E f f e c t s in
BST T h in F ilm s
Non-linear high-permittivity dielectrics such as the solid-solution BaxSr(i.X)Ti0 3
(BST) have undergone extensive investigation since the mid-1990’s due to the electric
field-dependent properties of the material. With application of a DC bias in the range of
several MV/m the dielectric constant o f the material can be tuned over a wide range,
resulting in a large change in the permittivity, typically 3-4:11-6. Tunability is frequently
defined as,
( C0-C(E)^
xlOO
(1.1)
C,
where the zero-bias capacitance is C0, and C(E) is the capacitance under DC bias. As a
result o f the large tunability possible with this material system, there is a great deal of
interest in the application o f BST for tunable passive microwave components such as
varactors, phase shifters, filters, and resonators7"13. The challenge has always been to
obtain high dielectric tuning and low loss (or high Q-factor) together, especially in thin
film form.
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2
Bulk BST ceramics have Q-factors in the range of 50 to 500+, depending on the
proximity to the phase transition temperature14"16. It is estimated that bulk single crystal
BST has a Q>1000, similar to bulk single crystal SrTiCb17'20. However, moderate to high
losses (Q<50) have been reported in most studies of thin film BST thus far.
Unfortunately, this has limited their immediate use in thin film form to low-frequency
microelectronic applications where loss is not a critical operating parameter for the
performance o f the device (i.e., non-volatile memory).
It is well known that the properties of a thin film are largely dependent on the
processing conditions, microstructure, stoichiometry, impurities, state of stress, and even
thickness. Recently, much interest has been directed towards strain effects in BST thin
films, as the state of stress/strain in the film layer is of prime importance in the resulting
electrical response of the film.
Strain in a thin film is caused by two main factors; lattice mismatch between film
and substrate, and thermal expansion coefficient differences. In addition, it can cause
91 9 3
stress-induced phase transitions, and a shift and broadening of the Curie temperature ' .
Several studies have investigated the effects of strain on the microwave dielectric
properties of BST thin films 1,2,24"27. Chang et al.1 reported on the correlation o f strain and
tunability for as-deposited and annealed BST (50/50) films, where annealing treatments
were used to adjust the lattice parameter, which resulted in increased tunability when the
strain transitioned from a compressive to tensile state.
Hyun et al.24 measured the
microwave response of BST (50/50) films in compressive and tensile states using a
resonance probe positioned in the electrode gap of the test structure. It was shown that
higher tunability is present in regions where the direction of the elongated unit cell (in­
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plane for tensile strain and normal for compressive strain) coincides with the direction of
the applied electric field. Kim et al.25 studied tetragonally distorted BST (50/50) thin
films to determine the effect of the ratio of the in-plane to normal lattice parameter,
designated as D=a/c, on the microwave properties. It was determined that films with
D~1 showed the greatest permittivity and tunability versus films under compression
(D<1) and tensile strained films (D>1).
Furthermore, studies have shown that dislocations caused by misfit strain
relaxation greatly influence the dielectric properties. Canedy et a l}6, reported that the
strain fields associated with threading dislocations, present in numbers of
1 0 11
cm ' 2 in
their BST (60/40) films, may be a possible mechanism for the degradation of the
dielectric properties, as post-annealing removed some of the defects and improved
properties. Li
also reported that annealing BST films reduced the concentration of
dislocations and improved the properties, including the loss, and concluded that the
reduction of oxygen vacancies are secondary to removal of dislocations in achieving the
optimum dielectric response o f a film.
It is clear that the effects of strain on the electrical response of thin films are
profound.
Although several groups have investigated strain effects, much work still
needs to be done to study the effects over a much larger range to better understand how it
influences the microwave tunability, permittivity, and loss. It is hoped that this research
will provide some insight into the strain and thickness effects in BST thin films that
previously have not been explored.
Ultimately, we all wish to contribute to the
optimization o f BST for next generation ferroelectric tunable microwave devices.
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1.2
F e r r o e l e c t r ic it y
The material o f choice for this study, Bao.6 Sro.4 Ti0 3 , falls into a classification of
materials called ferroelectrics. Ferroelectricity is a phenomenon discovered in 1921, and
in the most basic sense can be described as a material’s ability to maintain a reversible,
spontaneous polarization in the absence of an electric field. It was first discovered in
Rochelle salt (KNaC^CVdHaO), and since then has been found in several other groups
of materials, including the perovskites29. BST is one of many perovskites, a solidsolution of BaTiC>3 and SrTiC>3 . Over the last ten years there has been much interest in
this system for its composition dependent properties, and applicability to a wide variety
of electronic applications, which will be discussed later in Section 2.2. In the following
sections, however, a brief overview of the basics of dielectric behavior is presented,
including topics that will help to define the characteristics of ferroelectrics.
1.2.1
C r y s t a l l q g r a p h ic S y m m e t r y
of
F e r r o e l e c t r ic s
All materials are classified into one of seven major crystal systems (cubic,
tetragonal, hexagonal, rhombohedral, orthorhombic, monoclinic, and triclinic). In each
of these systems there exists a certain number of point groups, depending on the number
of symmetry operations o f a particular crystal system. In total there are 32 point groups,
of which 11 are centrosymmetric and 21 are non-centrosymmetric30. Centrosymmetry is
defined as having mirror planes about the x, y, and z-axes, thus producing a center of
symmetry. The 11 point groups which have this symmetry have no permanent dipoles,
and hence cannot be polarized without a sustained electric field30. The remaining 21
point groups, except for point group 432, can all maintain a permanent polarization
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without the presence of an electric field. They are classified as piezoelectrics, and can be
polarized either with application of electric field or by stress. Further division of the 21
point groups separates a group of 10 which have spontaneous polarization.
These
materials do not require poling (application of an electric field) or stress to generate a
TO
permanent polarization . Materials in these 10 point groups are then classified into two
distinct groups called ferroelectrics and pyroelectrics. This last division distinguishes
materials that have a reversible spontaneous polarization, ferroelectrics, from those that
have a spontaneous polarization in only one direction, pyroelectrics.
One of the more common ferroelectric structures is the perovskite, which has the
formula ABO3 . The A represents the large cations of the structure which sit at the
comers of the unit cell.
The B represents the small cation which undergoes dipole
switching in the electric field, and is positioned along the center line of the cell. The
oxygen atoms then fill in the cell at the center of the faces. Figure 1.1 depicts the
perovskite unit cell. In the case of BST, the A cations are filled in the ratio of the Ba to
Sr concentration. The center titanium atom shown is black can be polarized in any of the
six orthogonal directions which are all equivalent. Additional, ionic polarization occurs
in the oxygen and A-cation sub-lattices which also shift when the center dipole switches.
*
i t
Figure 1.1: Perovskite unit cell showing displacement of center Ti atom,
which is the mechanism for spontaneous polarization.
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1.2.2
P o l a r iz a t io n M e c h a n is m s
In order for a material to be ferroelectric, there must be a form of dielectric
displacement of a charge species in the material.
This displacement, involving the
creation or reorientation of charges in a material with the application o f an electric field,
is defined as polarization. A material in the presence of an electric field can develop a
polarization of31,
P = s 0KE - e0E = s0E( K - 1)
(1.2)
which essentially is the effect of the electric field on the material minus the effect on
vacuum, where So is the permittivity of free space, K is the dielectric constant, and E is
the electric field. A measure of the ability of a material to be polarized can also be
defined in several ways from this expression. One measure is from the ratio of the
polarization in the material, P, to the effect on vacuum. This is defined as the dielectric
->i
susceptibility , %e.
Z ' = -P= = Kr - li
( 1.3)
s„E
Another is in terms of the number of elementary dipoles, N, where the term polarizability,
a, can be defined as31,
<2 = -
E
= ^ - = - ^
NE
( 1.4 )
N
essentially a ratio o f an individual dipole moment, p (C m), to the applied field, E.
Polarization, as described above, can develop in four different ways in a material,
each operating through a different frequency range. They will occurwhen positively
and/or negatively charged species shift in the structure, due to the presence of an electric
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field. In materials such as ferroelectrics, where the arrangement of atoms in the unit cell
is non-centrosymmetric, this results in a permanent dipole oriented in the direction of the
applied electric field.
The first type o f polarization mechanism is space charge, which responds to
electric fields in the frequency range of DC to 104 Hz32. It is essentially due to free
charge carriers which can move over large distances in a material in response to an
electric field. Typical examples are excess charge generated at material interfaces such
as grain boundaries, and interstitial defects in the crystal structure.
The next type, and perhaps the most important with respect to ferroelectrics, is
dipole or orientation polarization. This is due to the field alignment o f permanent dipoles
in non-centrosymmetric materials, and is dominant over the frequency range of
T9
-
10 4 10 9
It is primarily the reason for the high dielectric constant in many ferroelectrics, and
in BST the result of the alignment of the non-centered titanium dipoles. The induced
polarization can then be described quantitatively as ,
P=
p 2E
----3 kT
(1.5)
where the polarization, P, is proportional to the electrical field. The term 3kT (with
Boltzmann constant, k, and absolute temperature, T) shows that temperature has the effect
of randomizing dipoles, and hence decreasing the polarization, which at high enough
temperature will result in the transition from polar ferroelectric state to a non-polar
paraelectric state.
The last two types of polarization are ionic and electronic. Ionic polarization
occurs when cations and anions in an ionically bound solid shift from their equilibrium
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8
positions, inducing dipoles, which results in polarization that dominates in the frequency
range of 109 -10 13 Hz32. In BST, the shift of the anion oxygen lattice in the opposite
direction of the electric field, combined with the shift of the cation lattice (namely Ba and
Sr) in the same direction as the electric field give rise to a small amount o f ionic
polarization in the material. However, it is only a fraction of the overall polarization,
with most as a result o f the alignment o f the permanent dipole of the central Ti atom of
the unit cell.
Electronic polarization is the only mechanism remaining at very high frequencies
in the range o f 1013 -1016 Hz32. It is a process, in which the electrons of an atom displace
from their center position around the positively charged nucleus. The distortion of the
electron cloud causes a dipole opposite that of the applied electric field. Only at these
very high frequencies (near the visible region of the electromagnetic spectrum), when
electronic displacement is the only polarization mechanism, does the dielectric constant
39
obey the relation ,
K -n 2
(1.6)
where K is the dielectric constant and n is the index of refraction.
The transition from one polarization mechanism to another is the result o f a
dispersive process in which the frequency becomes too large for a mechanism to keep up
with the alternating field, as shown in Figure 1.2.
polarization through a loss mechanism.
The result is a decrease in the
The space charge and dipole polarization
mechanisms both decay through a relaxation processes near the upper edge o f their
frequency range. The ionic and electronic mechanisms decay as a result of a resonance
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9
process, with all of these loss processes essentially resulting in phonon generation in the
crystal.
f
RELAXATION
PHENOM ENA
RESONANCE <
ph en o m en a '
X-band
window
2
es
.a
I
o
04
3
~102
-1 0 s
~ 1 0 10
-1 0 “
~10«
Frequency (Hz)
Figure 1.2: Polarization and loss mechanisms versus frequency.
Therefore, the dominance of a particular loss phenomenon will greatly depend on
the frequency at which the dielectric is used. Since the polarization mechanisms are
dispersive, so are their contribution to the dielectric constant and loss of the material.
The permittivity can then be represented as real (s') and imaginary (s ") parts with
dependence on the frequency, 0), and relaxation time, T, of these processes, and the static,
Ss, and dynamic, Sac dielectric constants.
Additionally, a loss factor, tan S, can be
defined as the fraction o f energy dissipated, with a ratio of the imaginary part over the
real part of the dielectric constant. These relations are called the Debye equations, and
are as follows30:
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10
£ = £
00
+
(1.7)
1 + c o 2t 2
:,
={^-sJw T
(1.8)
(1.9)
1.2.3
C h a r a c t e r is t ic s
of
F e r r o e l e c t r ic M a t e r ia l s
Ferroelectrics exhibit certain properties which define them as a separate group of
materials. As mentioned previously, the most easily recognizable trait of a ferroelectric
is the reversible spontaneous polarization. This can be observed by cycling the applied
electric field between positive and negative.
The result is a hysteresis trace of the
polarization in the material, as shown in Figure 1.3. The trace begins from the origin
with initial application of the electric field, as all spontaneous dipoles are aligned in the
direction of the field. If after reaching a saturation polarization (indicated by the dotted
line trace to the y-axis) the field is removed, the polarization decays to a value called the
remnant polarization (where the trace intersects the y-axis). In addition, the coercive
field is that which is required to reduce the polarization to zero. Through the cycle of the
hysteresis curve, it can be seen that spontaneous polarization can be reversed by applying
a voltage higher than that required for the coercive field31.
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11
Polarization (p.C/cm2)
A
®coersh?e
E
(MV/m)
remanent
Figure 1.3: Hysteresis curve for a ferroelectric material.
Another important property of a ferroelectric material is that it exhibits a welldefined transition from a ferroelectric (polar) to a paraelectric (non-polar) state. The
temperature o f the transition is often referred to as the Curie temperature, To.
The
behavior of the dielectric constant above To can be described by the Curie-Weiss law30’31,
( 1. 10)
where K is the dielectric constant, C is the Curie constant, and T is the temperature.
Figure 1.4 shows the general trend of the dielectric constant at the phase transition
between the ferroelectric and paraelectric state.
The dielectric constant peaks at the
transition temperature and then decays as described by the Curie-Weiss law as the
temperature is further increased beyond To- Additionally, the tunability and loss tangent
of the material are very temperature dependent in the vicinity of the transition. The loss
tangent and the tunability are greatest around the transition temperature, and both
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decrease away from the transition31. These two properties are inversely proportional, and
thus there exists a tradeoff between tunability and loss.
This is an important consideration for the application o f the material.
For
example, microwave applications require a material in the paraelectric state with high
tunability and low loss. Therefore, the material composition must be carefully chosen so
that the transition temperature is below the application temperature, yet not too far as to
result in low tunability. Consequently, a compromise between high tunability and low
loss must be made to yield the best performance.
Ferroelectric
P S> 0
Paraelectric
P g= G
k
Low Tunability
>
Low Loss
Figure 1.4: General behavior of material properties near the transition temperature.
The transition temperature between the ferroelectric and paraelectric state does
'j'y
not always coincide with the Curie temperature . This is dependent on the order of the
phase transition. First order phase transitions are characterized by an abrupt drop in the
polarization to zero at the transition temperature (Figure 1.5) . This type of transition
involves a latent heat in which the ferroelectric phase and paraelectric phase exist in
equilibrium at the transition temperature. Most ferroelectrics are first order, and can have
transition temperatures which are 10 °C, or more, higher than their Curie temperature.
Bulk BaxSr(i.X)Ti0 3 (x>0) falls into this category along with BaTi0 3 and PbTiCb32.
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13
1st order transition
-JG
3T
i Paraelectric
s
P=0 V
Ferroelectric 1
P>0
!
Paraelectric
P=0
Ferroelectric
P>0
—►
Temp
Temp
Figure 1.5: First order phase transition from ferroelectric to paraelectric state.
Second order phase transitions are characterized by a smooth decay in the
polarization to zero, where the transition temperature and Curie temperature are
identical32. In this case, the transition occurs with no latent heat, thus the change from a
ferroelectric to paraelectric state is instantaneous (Figure 1.6).
2nd order transition
-3G
i i.
Paraelectric
P=0 y
Ferroelectricv
P>0
I
—►
Temp
Ferroelectric 1
P>0
!
Paraelectric
P=0
Tn=T,
Temp
Figure 1.6: First order phase transition from ferroelectric to paraelectric state.
Therefore, the properties listed above, are required for a material to be classified
as a ferroelectric. The following section discusses the properties of bulk BST (60/40).
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14
1.2.3.1
M a t e r i a l P r o p e r t i e s o f BaxSr(i.x)T i0 3
BST in the bulk form is a first order ferroelectric, but as will be discussed in
Chapter 2 and 5, the transition temperatures, and therefore the general electrical
properties, are affected dramatically by strain in the thin film form. Nevertheless, the
bulk material parameters including lattice constants, transition temperatures, and thermal
expansion coefficients are used as reference points for analysis of BST thin film data.
One of the greatest advantages of this material system is that the Curie
temperature can be shifted to lower temperatures with the substitution of isovalent Sr2+
into the crystal lattice. Pure BaTi03 has a Curie temperature of 120 °C (393 K), which
decreases when alloyed with SrTi0329. It drops linearly at a rate o f -3.4 °C/mol of Sr
until the composition approaches SrTi03 ’ . At pure SrTi03, however, the electrical
response changes drastically, as the material is a quantum paraelectric, meaning that it
has no Curie temperature and the permittivity increases exponentially as the temperature
drops toward 0 K.
The composition BST (60/40), the material of choice for this study, has a
ferroelectric to paraelectric transition temperature near 0 °C (273 K) in bulk form,
although the exact temperature of the transition varies as reported by different groups. It
has been reported to occur at 250 K by Jona et al.34 and Benguigui et al.35; at 257 K by S.
Ezhilvalavan et a l 33; at 275 K by the Landolt-Bomstein numerical database36; and
referenced as 278 K by Ban and Alpay37. In addition, to the ferroelectric to paraelectric
transition, there are two other transitions for BST (all compositions, x>0) between
ferroelectric phases with different crystal symmetries. Starting near 0 K, BST (60/40) is
a rhombohedral ferroelectric up to -150-165 K where it undergoes a phase transition to
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15
an orthorhombic cell34,35. It remains orthorhombic until -190-220 K where it transitions
to the tetragonal cell, and is ferroelectric until the primary transition to the non-polar
cubic cell of the paraelectric state34,35.
The lattice parameter o f the material will also decrease with the addition of Sr.
BaTiC>3 has a lattice parameter of 4.031
and to 3.947
A, which decreases to 3.965 A with 40 mol% Sr,
A with 50 mol% Sr, eventually reaching 3.905 A for pure SrTiOs38.
Furthermore, the thermal expansion coefficient of BST compositions39 around 40-50
mol% Sr is approximately 10.5 x 10*6 /°C, and the density varies with composition as
follows38: Pbst(60/40)-5.683 g/cc, Pbst(so/50>=5.627 g/cc, psrTi03=5.118 g/cc.
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16
1.3
T h e r m o d y n a m ic s o f F il m G r o w t h
There are three types o f primary growth mechanisms that have been observed in
thin films: 1. Volmer-Weber (three-dimensional island growth), 2. Frank-van der Merwe
(two-dimensional full monolayer growth), and 3. Stranski-Krastonov (two-dimensional
growth of full monolayer followed by nucleation and growth of three-dimensional
islands). The major factors that determine the particular mode of film growth are the
thermodynamics relating the surface energies of the film and substrate materials, and the
film-substrate interfacial energy40.
Volmer-Weber nucleation and growth is characterized by the formation of
clusters of atoms. These clusters form when atoms arrive at the substrate surface and
deposit on the bare substrate or on top of other clusters. The process of cluster formation
itself involves several mechanisms all acting continuously as shown in Figure 1.7. The
figure shows: (a) atoms that bond to the substrate, (b) atoms that re-evaporate from the
substrate, (c) cluster nucleation, (d) diffusion to a cluster, (e) atom deposition on a
cluster, (f) re-evaporation from a cluster, (g) dissociation from a cluster, and cluster
diffusion40.
b /
G a
.
Cluster
c
y
, o
/
•
u
.
--
<.
;
■:
%X y
v
t
')
^
■. '
Figure 1.7: Various atomic mechanisms occurring during film growth.
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17
The balance between the growth and dissolution processes is determined by the free
energy o f a cluster relative to the individual atoms comprising the cluster. For a cluster
that is large enough to be treated as a continuum solid, the free energy can be expressed
according to the following equation40,
AG = aj r2Tcv + (a2 r2
- a2 r2 Tsv) +
AGy
(1.11)
where r is the radius o f the cluster, the r ’s are the interface energies between clustervapor, substrate-cluster, and substrate-vapor, A G y is the change in volume free energy on
condensation of the cluster, and the a ’s are geometrical constants that depend on the
shape o f the cluster. If the derivative of the free energy change with respect to the cluster
of atoms is negative then cluster formation is favorable, but if the derivative is positive
then dissolution of the cluster will occur. The volume free energy, A G y, in the above
equation can be expressed as40,
AGv = (-k T /Q ) ln(P/Peq)
(1.12)
where k is Boltzmann’s constant, T is the absolute temperature, Q is the atomic volume
of the film atoms, P is the pressure of the arriving atoms, and Peq is the equilibrium vapor
pressure of the film atoms40. This equation is only valid for the condensation o f free
atoms in the vapor phase and does not take into account the other aforementioned
atomistic processes that occur during film growth.
Therefore, using these approximations it is clear that an increase in the vapor
pressure of atoms near the substrate surface such as the arrival of a flux of atoms from a
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18
material source will lead to a negative value of A G y. In order for cluster growth to occur,
the following inequality40 must be satisfied,
&i r cv + &2 Tsc > a2 Tsv
(1-13)
This states that if the sum of the cluster-vapor and substrate-cluster interfacial
energies are greater than the substrate-vapor interfacial energy then the system will reach
its lowest energy by maintaining as much of the substrate-vapor interface as possible
while the film is growing. Therefore, the only way for this to occur is through cluster
formation instead o f the atoms spreading over the entire surface.
Greene41 has calculated the critical size for the formation o f a cluster by setting
the derivative o f the free energy with respect to the cluster size equal to zero, yielding a
critical size of,
r* = -2(aj
rcv+ a2rsc-
a2 rsv) / (3 a3 AGV)
(1.14)
This can then be substituted into Equation 1.11 (the cluster free energy) to determine the
free-energy barrier to nucleation of a cluster40,
AG = 4 (a i r cv + a2 r sc- a 2 r sv) 3 / 2 7 (a 3 AGy)2
(1.15)
Horowitz and Sprague40 have also stated that the nucleation rate can be
approximated by the arrival rate of atoms at a critical size nucleus multiplied by the
concentration of critical nuclei. The arrival rate will be proportional to the deposition
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19
rate and the surface diffusivities of the various atomic species that follow the previously
mentioned Arrhenius equation 1.12.
Therefore, to change the growth mode of a film, either the interfacial energies of
the substrate and film materials must be modified through a surface reconstruction or
reaction with the ambient gas environment or the deposition conditions must be modified.
Increasing the deposition rate will in effect increase the vapor pressure of film material
near the surface of the substrate, as will decreasing the temperature of the substrate.
However, lowering the temperature o f the substrate will lead to decreased surface
diffusion and lower the nucleation rate because atoms will not be able to form a cluster o f
critical size as quickly as at higher temperatures. Although, the overall effect of lower
temperature deposition does not slow down the film growth, it will slow down the
formation of an equilibrium crystal structure. This implies that even though there are less
clusters forming, film growth is proceeding through the formation of a metastable phase
such as an amorphous layer.
The second growth mode for thin films is called Frank-van der Merwe. This is
characterized by two-dimensional monolayer growth, where a film grows layer by layer.
The relation of the interfacial energies for monolayer growth is40,
(rsv/rcv) - ( r cs/rCT)>i
(i.i6>
so that there is strong bonding between the substrate and the film material. Low film
surface energy and high substrate surface energy will also promote monolayer growth. It
should be noted that film growth in this manner also involves clusters, but the clusters are
only one monolayer thick. These clusters nucleate over the entire substrate and grow
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20
together to completely cover the surface and form a monolayer film before forming the
next layer.
Greene41 has stated that in this case there is no free energy barrier to nucleation
since the free energy change of two-dimensional island formation is always negative.
The general trends o f increasing the number density of islands with increasing deposition
rate and lower substrate temperature are the same as for three-dimensional island
formation. In addition, the degree to which true monolayer coverage occurs is related to
the density o f islands formed. Higher densities of two-dimensional islands will lead to
more complete coverage o f the substrate. Atoms that attach to the top of an island will
likely diffuse to the edges of the island and bond with the substrate if such sites are
available. Once all sites in the first monolayer are occupied, film growth will continue
with a layer-by-layer coverage of the film surface because it is still more energetically
favorable to form two-dimensional islands than three-dimensional islands. This is due to
the fact that the low film surface energy promotes the spreading of the atoms to maximize
the surface area o f the film as it grows, rather than forming clusters.
The third film growth mode is Stranski-Krastonov. This is characterized by the
formation of one or more monolayers, followed by island growth on top of the initial
layers. The change from monolayer growth to island formation may be due to one or
more reasons that are specific to a particular material system. Proposed causes o f this
behavior include stress buildup in successive monolayers due to lattice mismatching of
the film and substrate, and changes in the film surface energy with monolayer coverage
due to strong bonding effects with the substrate40.
Again the factors effecting the
nucleation and growth for the other growth modes are also valid in this case.
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21
Another important determinant of the film growth mode and the final
microstructure o f the film is the substrate surface structure. In the above discussion it
was assumed that the substrate was an atomically flat and homogeneous surface on which
atoms nucleated at random sites. However, real substrate surfaces have defects such as
steps, point defects, impurities, etc., all o f which provide low energy sites for atoms to
nucleate into clusters.
At lower film vapor pressures near the substrate surface this
process of heterogeneous nucleation can overcome the homogeneous nucleation rate.
Only at high deposition rates will the homogeneous nucleation rate dominant on a
substrate surface with many defects. Therefore, the preparation of the substrate surface is
very important in controlling the growth mode of the film. For this reason, pre-annealing
heat treatments are used to prepare the surface for film growth (discussed in Sec. 4.2.3).
With these thermodynamic effects in mind, the processing parameters o f a
particular film deposition method must be adjusted and refined to yield the desired film
growth. The following section discusses the method of pulsed laser deposition and the
various effects of the processing parameters on film deposition.
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22
1.4
P u l s e d L a s e r D e p o sit io n
Thin films can be fabricated by a wide variety of deposition techniques. There
are methods of physical vapor deposition, chemical vapor deposition, and chemicalsolution processing, all of which can be used to produce high quality epitaxial thin films.
Pulsed laser deposition (PLD), or pulsed laser ablation, is a physical vapor
deposition process. It was the method chosen to fabricate films for this study. The
process itself is simple in terms of the actual mechanics of depositing the thin film, but
there are many process parameters and mechanisms to be understood.
PLD is
characterized by the use o f a focused, pulsed excimer laser to ablate a ceramic target
inside a vacuum system in a controlled gas atmosphere, subsequently producing plasma,
or plume that reacts with the background gas and is deposited on a heated substrate
(Figure 1.8). Film production in this manner not only has the advantage of simplicity of
process, but also high deposition rates, good stoichiometric transfer of the target material,
the capability of depositing many different materials either separately or in multilayers,
and a relatively low cost compared with techniques such as MOCVD (metal-organic
chemical vapor deposition) and MBE (molecular beam epitaxy)40.
Kwima laser
K.I-
Faensbig
Lens
MSiifii
Substrate Heat
Assembly
Figure 1.8: Schematic of pulsed laser deposition system, showing ablation of ceramic target.
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23
The main disadvantage is that the area of uniformity of the deposited film, in
terms of thickness and composition, is typically on the order of 1 cm . In addition,
particulates generated by the ablation process (from incomplete vaporization of the target
surface) are often present in the film42,43. They can be greatly reduced by optimizing the
laser fluence for the target material, as well as using dense targets (> 90%). Uniformity
problems have been addressed with complicated ablation techniques such as laser beam
rastering, where the beam is scanned across the target to move the plume with respect to
the substrate, producing larger area uniform films. Alternatively, the substrate can also
be rotated at an off-axis condition as to effectively raster the plume over a large area
substrate surface; however this adds significantly to the cost of the system.
1.4.1
P r o c e s s in g P a r a m e t e r s In f l u e n c in g F il m G r o w t h
The most important parameters affecting the film growth include the temperature
of the substrate onto which the film is deposited, the background gas pressure, the
distance from the target to the substrate (z-distance), the laser fluence or energy density
on the target, the laser pulse repetition rate, and the laser spot size on the target.
Although not a processing parameter, the choice of substrate is also of great
importance on the type o f film growth that will dominate during deposition. The primary
factors when choosing a substrate material will be its crystal structure and lattice
parameter match to the film material.
The smaller the lattice mismatch, the more
favorable is epitaxial growth with minimal generation of misfit dislocations at the
interface. Generally, the single crystal substrate will be cut along an atomic plane which
yields a smoothly terminated surface; for most substrates, the natural cleavage planes are
the most desirable (i.e. for cubic crystals, the (100) family of planes).
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24
In addition, the surface energy of a particular substrate plane, as well as the
surface energy o f developing film clusters with respect to the gas environment and
substrate are important (as discussed in section 1.3), but can be manipulated by changing
the deposition environment.
Once a substrate and substrate orientation have been chosen, the critical
deposition parameters, as mentioned above, must be determined through experimentation
with a variety of combinations to yield ideal conditions for the desired film growth. The
following sections list the effects of the most important parameters.
1.4.1.1
Su bst r a te Tem perature
Beginning with the substrate temperature, it is clear that this parameter is one of
the most important variables, as it will have a number of effects on the evolving film
microstructure. Typical deposition temperatures used for the PLD process are in the
range o f 500 - 850 °C. Surface diffusivities of the various atomic species of the target
material will be directly related to the temperature and follow an Arrhenius behavior40,
D = « 2<V exP
( ____
- E a_\
RT
r
A> exp z A
v
(1.17)
RT
where the diffusion constant (D) is a function of the jump distance (a), jump frequency
( Kiiff), activation energy for diffusion (Ea), and temperature (7).
Increasing the
temperature o f the substrate will increase the diffusion rate o f the atoms that arrive on the
surface44,45. These atoms with higher energy can then more easily form a homogenous
layer, as well as nucleating clusters on sites that were previously energetically
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25
unfavorable due to diffusion barriers40.
However, at high temperatures less of the
impinging atoms will remain on the substrate surface due to the greater vibrational
amplitude of the surface atoms. This results in a lower thermal accommodation and thus
a thinner film for equivalent deposition time, but only for higher deposition temperatures
on the same substrate material. As was shown in this study, the deposition rate for BST
on LaA1 0 3 at 700 °C, and on MgO at 825 °C, produced films with very similar thickness
(discussed in Sec. 5.1.1).
1.4 .1 .2
O x y g e n P r essure
The background gas pressure is also another major consideration in growing
epitaxial films. Typically oxygen is used for the most commonly deposited materials by
PLD, ceramic oxides.
The pressure is usually in the range of 50 mTorr to several
hundred mTorr for these materials, and the greatest effects of the pressure are on the
stoichiometry o f the film, the deposition rate, and the shape of the plasma plume46'49.
The incorporation o f oxygen in the crystal lattice of the film will vary depending on the
pressure; too little oxygen during deposition will result in oxygen vacancies throughout
the lattice, which negatively affects the electrical properties.
Higher oxygen pressures will also increase the number of scattering events
between the plume constituents and the oxygen gas, resulting in a lower deposition rate47.
In addition, the size and shape of the plume, determined by the scattering with the
background gas, affects both the area of uniform compositional homogeneity of the
deposited film on the substrate surface46, and the distance at which the substrate must be
placed from the target (z-distance).
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26
1.4.1.3
L a s e r F l u e n c e , R epetitio n R a t e , S p o t S iz e , a n d W a v e l e n g t h
The laser energy density (or laser fluence) is the quantity of energy on the target
per unit area, per pulse of the laser. It is tied to the laser spot size on the target, in that a
smaller spot size at the same pulse energy will increase the energy density, and therefore
the ablation rate of the target material. Due to the fact that BST is a ternary in terms of
the number of metallic species in the material, the laser fluence must be set above the
ablation threshold for all three species. This will prevent preferential atomic ablation of
the target, which would result in a less than ideal stoichiometry. For example, a study on
the stoichiometric transfer of complex oxides, using a SrTiOs target, reported a strontium
deficiency in the surface o f the target when the laser energy density dropped below the
critical level for ablation o f strontium atoms50. In addition, preferential ablation may not
only affect the stoichiometry, but possibly the growth mode due to the differences in the
composition o f the growing film.
The laser frequency is another important factor in the structural quality of the
deposited film. At higher pulse frequencies, the deposition rate increases, which in turn
will affect the quality of the film. Films that are deposited too quickly are often of poorer
quality as a result o f too much material impinging the film’s growth front before surface
diffusion and atomic rearrangement can occur40. The resulting film would likely be
polycrystalline, or textured, rather than epitaxial, unless further heat treatments were
added to the processing.
The spot size o f the laser beam on the target is another parameter to consider.
The main effect of the beam shape is that it directly determines the shape of the plume of
ablated material.
When the plume reaches the substrate, its shape is important for
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27
uniform deposition o f the ablated material across the entire area of the substrate51,52.
Since nearly all excimer lasers have rectangular beam profiles, the plume is typically
wider on one expansion front than the other; the direction perpendicular to the line (1 mm
x 8 mm for this study) created by the focusing lens. Figure 1.9 shows the height of the
plume in the vertical direction, which is about one-half the width of the plume as viewed
from the top. Therefore, careful placement of the substrate in the center of the plume, is
required to yield the most uniform and stoichiometric films51.
Figure 1.9: Laser pulse ablating a BST target, showing plume expansion towards the substrate.
The laser wavelength chosen for ablation is not a particularly critical parameter,
but it does affect the ablation process . Typical laser wavelengths used for PLD are ArF
at 193nm, KrF at 248nm, XeCl at 308 nm, NdtYAG at 1064 nm, and CO 2 at 10.4 pm,
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28
with the most common being KrF.
The energy of longer wavelength lasers such as
Nd:YAG and CO 2 are absorbed over a greater volume of the target below the focus
spot53. As a result less material reaches the ablation threshold per pulse at the same
energy density, resulting in a greater fraction of slower moving fragments such as molten
droplets and particulates54. These undesirable components of course affect epitaxy in the
surrounding regions and produce films with many structural defects. Therefore, excimer
lasers are most commonly used due to the superior quality of films that can be produced
with a UV laser wavelength, where surface ablation dominates over volume ablation54.
1.4.1.4
Target
to
S u b s t r a t e D is t a n c e
The z-distance as previously mentioned is the target-to-substrate distance. This
parameter will have an impact on the resulting film microstructure because as the
substrate is moved further from the target, the energy of the atomic and ionic species in
the plasma decreases as the number of scattering events increases55. This effect on the
energy of the ablated species in turn affects their ability to diffuse and/or nucleate new
crystallites of various orientations. There is also a difference in the velocities of ablated
•
•
C 1)
,
atomic species due to their atomic mass difference . This produces a non-homogenous
plume that contains compositional gradients across its dimensions.
Therefore, the
chemical composition and structure of the film will depend on the z-distance used for
deposition.
It is then critical to set the substrate at a position in the center of the
expanding plume, where compositional uniformity will be the highest51.
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29
1.5
M ic r o w a v e T h in F il m P a s s iv e C o m p o n e n t s
Miniaturization of microwave circuits and devices is one of the key driving forces
for wireless component manufacturers. Rapid progress in production technology and
circuit design has resulted in more efficient and ever smaller wireless electronics that
have been incorporated into a variety of consumer products; the most notable being
cellular phones, laptop computers, and most recently handheld “pocket PCs”. With the
rapid increase in wireless communications, the market for mobile devices that allow
information transfer, both locally and globally, has grown significantly over the past 5-10
years. The progression toward higher frequency (GHz) wireless networks is driven by
the desire for greater bandwidth which will allow the transfer of greater amounts of data.
At the heart of the wireless communication devices are the materials of which the
circuit elements are comprised. Currently, both bulk ferrites and semiconductor-based
circuits are used to guide and filter microwaves, with limited use of bulk and thin film
ferroelectric materials.
Tunable ferroelectric thin films offer advantages that older
technologies cannot meet, but they are in still in the early stages of development. In
general, they can be used (in the paraelectric state) for a wide variety of applications
including phase shifters, coplanar waveguides, resonators, filters, and phased array
antennas.
The high tunability of this class of materials (Equation 1.1) is arguably the most
important property that makes them ideal for many types of microwave devices. It is due
to the high non-linearity of the permittivity with the application of a DC field
superimposed on the AC operating frequency.
This is a result of the strong field-
dependence o f the polarization, and hence the dielectric susceptibility and permittivity,
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30
on the higher-order terms of the applied field. Therefore, in the presence of a DC bias the
permittivity can be continually decreased as the applied voltage is increased, resulting in
a permittivity change o f up to 2-4 times1'6, depending on the material composition and
temperature (Section 1.2.3).
These materials are often referred to as frequency-agile
because o f the ability to tune the dielectric constant by applying a bias voltage.
To understand the advantage of using thin film ferroelectrics for microwave
integrated circuits, a comparison to existing technology is needed.
Currently the
competing technologies are semiconductor varactors and ferrites.
Semiconductor
varactors are typically used for low frequency, low-power applications, and suffer from
significant degradation at higher frequencies (> 1 GHz) due to series losses in the
patterned metallization used to create the device . Ferrite-based tunable devices are
capable of high-power applications and have low losses (<0.5%) in the microwave
regime57. However, they require expensive, bulky power-consuming tuning circuitry to
be able to generate the magnetic fields necessary to tune the device.
In contrast, thin film ferroelectric-based devices offer a highly tunable dielectric
response with a low controlling voltage; usually a DC bias less than 50 V. They also
have high dielectric strength (i.e. high breakdown fields) for use at high microwave
10
power levels . In addition, the high-speed response to the applied electric field (-0.01
ns), due to the nature of the tuning mechanism, a dipolar polarization mechanism, makes
them a very attractive replacement12. The only drawback is the moderate loss usually
observed in thin film ferroelectrics (Q<50), which is gradually being reduced with the
understanding o f processing effects on the electrical properties of films.
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31
The ultimate goal of the microelectronics manufacturers would be to integrate all
microwave circuit components onto a single wafer in thin film form. This would be a
great advantage in manufacturing, which would greatly reduce the cost and size of
wireless devices. Typically tunable microwave thin film passive components, such as
phase shifters, resonators and filters, are fabricated by depositing the ferroelectric layer
directly on a dielectric substrate, followed by metal top electrodes which define the
device7"13.
These devices are created by patterning two or more electrodes with a
precisely defined gap(s) or interdigitated structures with fingers separated by a gap of ~520 pm11. The microwave radiation can then propagate in the ferroelectric layer between
the electrodes, in the gap, in a variety of transmission modes (detailed explanations o f the
propagation of electromagnetic waves in devices can be found in standard microwave
theory texts58). Particular microwave device designs will be discussed in Section 2.2, but
an overview of the advantages of coplanar devices follows.
The coplanar configuration for tunable thin film devices has been shown to be
very adaptable to microwave circuitry59'61. The capacitance and impedance values of the
device can easily be modified by varying the thickness of the ferroelectric film to change
the relative amount o f microwave energy propagating in the film and the low-K substrate
(assuming no thickness effects). Furthermore, the larger gaps (-5-20 pm) in coplanar
structures make it easier to create lower capacitance devices for better impedance
matching versus parallel plate designs where the separation between the top and bottom
electrode is rarely more than 1 pm11.
In addition, one of the greatest advantages to using only a top coplanar electrode
is that the thin film may be deposited directly on a lattice-matched substrate. This allows
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32
excellent epitaxial growth of the film versus film growth on a textured metal bottom
electrode which usually results in a polycrystalline film. The effects on the performance
of the device are clearly seen in the form of higher tunability and permittivity for
epitaxial films. Lastly, the direct deposition of the film on a dielectric substrate also
allows for post-deposition annealing at high temperatures; a processing step not possible
with a metal bottom electrode. This helps to improve the crystallinity and eliminate some
growth defects, which may reduce the loss and increase permittivity and tunability.
Most o f the interest in tunable ferroelectric thin films has been directed towards
the material system BaxSr(i.X)Ti0 3 (x<0.7, the limit for the paraelectric phase at room
temperature), including the composition SrTiC>3 for cryogenic applications.
These
compositions have all o f the desired characteristics for tunable microwave applications,
as mentioned previously. They are continually being explored by researchers to better
understand and further optimize their properties. The next chapter will overview research
on a particularly important consideration for the performance of a thin film device; the
effect of strain (associated with epitaxial growth on a single crystal substrate) on the
electrical response o f a thin film.
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33
C h a p t e r Su m m a r y
This chapter has presented the basics of the subject areas involved in this work.
The classification o f ferroelectrics and their general dielectric behavior was discussed.
The thermodynamics of thin film growth and the fabrication method of pulsed laser
deposition were reviewed.
Finally, the use of thin films in microwave passive
components was discussed, which highlighted the reasons for the great interest in tunable
thin film materials, such as BST, for next-generation microwave integrated circuits.
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34
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38
CHAPTER 2 - LITERATURE REVIEW
This chapter highlights the important studies of strain effects in BST thin films
reported in the open literature. A section on experimental microwave devices created
using BST thin films is also included which shows the possible future microwave
applications o f this material. The results of this thesis (Chapter 5) will be discussed with
reference to many o f the works presented below to gain the best possible insight on the
phenomena associated with strain effects.
The following discussion is organized by
research group for the purpose of allowing others not familiar with this area of study to
easily seek out knowledge on this topic.
2.1
S t r a in E f f e c t s
in
BST T h in F il m s
Since the initial investigations of the microwave properties of high-K thin films in
the early to mid-1990’s, a great deal of attention has been given to the material system
BaxSr(i-X)Ti0 3 . This solid solution of barium titanate and strontium titanate yields bulk
materials that are paraelectric and cubic at and below room temperature for a mole
12
fraction of Ba (x) < 0.7 ’ . All other compositions are ferroelectric and tetragonal at room
temperature in bulk form, with transition temperatures above 298 K.
The entire
stoichiometry range has been explored with the most interest on a Ba:Sr ratio of 60/40
and 50/50 for microwave applications. While all compositions in this material system
exhibit both very high dielectric constants and highly electric field-dependent properties
close to their respective transition temperature, the 60/40 and 50/50 compositions yield
the highest permittivity and tunability at room temperature3, with the material still in the
paraelectric state; a requirement for microwave applications. This is due to the proximity
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39
to the transition temperature (as discussed in Section 1.2.3), which occurs at -257 K for
BST (60/40) and -223 K for BST (50/50)2’4’5.
Many studies have shown that the properties of thin films are largely dependent
on the processing conditions, microstructure, stoichiometry, impurities, state of stress,
and even thickness. Recently, much interest has been directed towards strain effects in
BST thin films, as the state of stress/strain in the film layer is of prime importance in the
resulting electrical response.
Several research groups are actively involved in investigating strain effects in an
attempt to separate the effects of strain, processing, and thickness effects in the material.
The following is an overview of such work, which will discuss the type and scope of the
studies as conducted on BST thin films. It is not intended to be an exhaustive account,
but rather a concise view o f the progress and accomplishments of researchers of this
material system. Below, the major research efforts from internationally known groups
are presented.
Naval Research Laboratory (Washington, D.C.)
Study #1 - Influence of strain on the microwave dielectric properties of (Ba.Sr)TiO? thin
films
Chang et al.6 grew epitaxial BST (50/50) thin films on (100) LaAK>3 and (100)
MgO substrates using pulsed laser deposition in order to study the effect of strain on the
microwave properties o f the material. All films were grown to approximately 500 nm,
and the capacitance and Q-factor were studied in the range of 1 to 20 GHz as a function
o f electric field (Emax=67 kV/cm) at room temperature using interdigitated capacitors.
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40
The films were deposited at 750 °C in an oxygen environment o f 350 mTorr. The
KrF laser was set at ftuence of 1.9 J/cm2 at a pulse rate of 5 Hz, with the target ~4cm
from the substrate. After deposition films were annealed in flowing O2 at 900-1250 °C
for 6 to 24 hours.
In order to measure the strain in the films from an equilibrium lattice parameter,
unstrained films were created for reference. They were fabricated by first depositing a 5
nm buffer layer o f BST (50/50) at room temperature, followed by the normal film
deposition, resulting in a polycrystalline film with £=3.961
A. The lattice parameters of
the strained (normal samples) were then measured with x-ray diffraction, both before and
after annealing, to determine the in-plane strain. The films grown on LaAlCb showed an
in-plane compressive strain of -0.20% before annealing, and 0.42% after annealing. The
films deposited on MgO showed the opposite behavior, with a tensile strain of 0.23%
before annealing, and -0.05% after annealing.
Microwave measurements were then made on annealed samples only for this
study (Table 2.1). The average microwave properties of films on LaAlCh and MgO were
compared and shown to be dependent on the strain state in the film. The microwave
response of the films indicate that compressive strains as generated in annealed samples
on MgO, limited the dielectric tuning and the maximum dielectric constant. For films on
LaA 1 0 3 , where tensile strains were generated after annealing, the average dielectric
constant and tunability were significantly higher. It was also found (from the maximum
data) that either high dielectric tuning or high Q-factor was obtainable, but not both at the
same time. Additionally, high dielectric constant samples on both substrates led to lower
Q-factors, as samples with lower dielectric constants showed much higher Q-factors.
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41
Table 2.1: Microwave measurements of 500 nm BST (50/50) thin films6.
Maximum data
Average
Substrate
£
% tuning
Q
MgO
LAO
1000
30
45
1500
50
25
MgO
2973
62
5-20
763
22
100-250
LAO
3328
75
4-44
1003
9
50-70
Study #2 - Microwave properties of tetragonally distorted (Ban sSrnj)TiCh thin films
In a collaboration with the Naval Research Laboratory, Kim et
of SFA Inc.
(Largo, Maryland), studied tetragonally distorted BST (50/50) thin films to determine the
effect o f the ratio o f the in-plane to normal lattice parameter, designated as D=a/c, on the
microwave properties. Films were deposited onto (001) MgO substrates using pulsed
laser deposition. The films were all the same thickness, 300 nm, and grown at 750 °C,
with oxygen pressures in the range of 3 to 1000 mTorr, using a KrF laser at 2 J/cm2. The
microwave properties were measured in the range of 1 to 20 GHz using the same
interdigitated capacitor structure as the previous study.
Films deposited at low oxygen pressures (<50 mTorr) were elongated in the
growth (normal) direction with D=0.996.
Although these films had in-plane tensile
strains over 1% they were compressed in-plane relative to the normal lattice parameter.
These films showed lower dielectric constants, -50-100, and a tunability o f -10%.
At around 50 mTorr, the unit cell was nearly cubic with H=1.0004, and an in­
plane strain o f -1% (of course the cell volume was still larger than that of bulk BST).
Films grown at this pressure showed the best properties, as the dielectric constant reached
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42
500 and a tunability o f 60% was measured with the application of an 80 kV/cm electric
field.
At oxygen pressures above 50 mTorr the film became tetragonally distorted in the
in-plane direction (the direction of the tetragonal distortion changed from normal to in­
plane). Films that were deposited at higher oxygen pressures showed a linear decrease
toward a dielectric constant of 150 and a tunability of 15% at 800 mTorr, where D=1.003.
The method o f creating strained films in this study was by varying the oxygen
pressure during deposition. This led to the incorporation of oxygen vacancies in varying
concentrations and along different crystallographic directions over the pressure range
studied, as stated by the author. However, the stoichiometry change likely affected the
microwave properties together with the changing ratio of the a and c lattice parameters.
Nevertheless, the effect o f strain on the dimensions of the unit cell was shown to be of
critical importance in the microwave response, and it was concluded that deviations from
the near cubic unit cell, D ^ l, led to a decrease in both the dielectric constant and
tunability.
Study #3 - Strain relieved Ban ^Sro fTiCh thin films for tunable microwave applications
Chang et al.9 studied strain relieved BST (60/40) thin films in a collaboration with
Paratek Microwave, Inc. (Columbia, MD). The focus of the study was to yield films with
significantly reduced dielectric loss at microwave frequencies. Films were deposited on
(100) MgO substrates by pulsed laser deposition using the same conditions as described
in Study #1. Three different types of films were fabricated to study the effect of strain
relief in the film layer. Films were grown 300 nm thick and were deposited without a
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43
buffer layer, or with a 20 nm or 60 nm thick BST buffer layer deposited at room
temperature.
Epitaxial (100) films were achieved for direct deposition on MgO. The in-plane
lattice parameter o f these films deposited without a buffer layer was measured at 3.969 A,
which was 0.2% larger than that of the normal lattice parameter, resulting in an in-plane
tetragonal distortion. Films deposited on the 20 nm buffer layer, were (100) textured but
not epitaxial. These films had a tetragonal distortion in the normal direction of 0.2%,
with an in-plane lattice parameter of 3.957
A. Finally, the films deposited on the 60 nm
buffer layer were cubic and polycrystalline (no preferential orientation) with a lattice
parameter of 3.966 A.
The strain relieved films on the 60 nm buffer layer were shown to exhibit
reasonably good tuning at 20% (with application o f DC bias of 200 kV/cm) and a high Qfactor o f >100. Strained films, where the in-plane lattice parameter was greater than the
normal lattice parameter (no buffer layer), showed high tuning (>50% at 250 kV/cm)
with low Q-factor (-20 at 0 V bias). Films with the opposite strain condition, or those
deposited on the 20 nm buffer layer where the normal lattice parameter was greater than
the in-plane lattice parameter, showed low tunability (-5% at 25 kV/cm) and high Qfactor (-150 at 0 V bias).
Therefore, the microstructure and strain state of the films directly influenced the
microwave tunability and Q-factor.
Films that were near an equilibrium lattice
parameter, or bulk lattice parameter of 3.965
A, with no distortion were shown to yield
good Q-factors with reasonable tuning.
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44
IBM Research Division, T. J. Watson Research Center (Yorktown Heights, NY)
The effect of stress on the dielectric properties of barium strontium titanate thin films
Shaw et a/.10 investigated the effect of stress on the capacitance of a
Bao.7 Sro.3 TiC>3 thin film capacitor.
The films were deposited with chemical vapor
deposition at 700 °C on both silicon and Pt-coated silicon substrates. The residual stress
in the film was determined by a radius of curvature method whereby the substrate was
etched away with HF, and the stress in the film was calculated from the Stoney
equation10,11. The residual stresses were found to be around 610 MPa ±100 MPa.
Next, BST thin film planar capacitors (-100 nm thick) were subjected to stress
and the change in the capacitance was measured. Figure 2.1 shows the effect of the
applied load on the capacitance of two samples. The first sample, Capacitor 1, showed a
reversible change in the capacitance upon loading and unloading. The second sample,
Capacitor 2, was loaded to substrate failure and showed a clear decrease in the
capacitance with increasing load.
The capacitance per unit area decreased from 35
fF/pm2 to 31 fF/pm2 with the application o f 450 MPa of stress (from a 120 N load).
35 4
Capacitor 2
UCapacitor I
0
SO 100 l i T 200’250'sop'850'400 4S0 500
Stress (Mpa)
Figure 2.1: Capacitance per unit area (C/A) as effected by applied stress10. Capacitor 1 has been loaded,
then unloaded. Capacitor 2 was stressed until substrate failure.
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45
A plot o f the total stress in the film, which is the residual stress plus the applied
stress, versus the reciprocal capacitance per unit area was then used to estimate the stressfree capacitance of the film. This resulted in a linear extrapolation of the experimental
•*)
data to the y-axis where stress-free capacitance per unit area was found to be 44 fF/pm .
This value is 23% larger than that of the strained film and thus shows the large effect of
residual stresses on the electrical properties.
Additionally the effect of strain on the dielectric constant and phase transition
temperature were observed from a measurement of the permittivity versus temperature.
The normal phase transition temperature of -300 K for bulk BST (70/30) was suppressed
due to stress, and instead one very broad maximum was observed for the 100 nm thin
film (Figure 2.2).
100000
BA,7SW
!° 3
100007
Ceramic
100
Thin Film
t=1Q0nm
0
100 200 300 400 500 600 700
Temperature (K)
Figure 2.2: Dielectic constant as a function of temperature showing the suppression of
the bulk phase transition from ferroelectric to paraelectric10.
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46
Department o f Physics and Center for Stronslv Correlated Materials Research, Seoul
National University (Seoul Korea)
Anisotropic tuning behavior in epitaxial Ban sSrn sTiCh thin films
Hyun et al.n measured the difference in the tunability of strained BST (50/50)
thin films on (001) LaAlCL and MgO. The films were grown by pulsed laser deposition
to a thickness o f 600 nm using a KrF laser. The deposition conditions were 750 °C, 300
■y
mTorr oxygen pressure, and a laser fluence of 2 J/cm . The tunability was measured at 1
MHz with an LCR meter by applying a bias between two strip electrodes (spaced 4 pm
apart) and measuring the capacitance change. In addition the tunability was measured
with another method called scanning microwave microscopy (SMM), in which a probe
was placed between the electrodes. In this way, the tunability is measured by changes in
the resonance frequency o f the probe tip from its unperturbed resonant frequency (1.471
GHz) when not in the prescence of an electric field.
The standard tunability measurement with the LCR meter showed a tunability of
32% for the film on LaA103 as compared to 24% for the film on MgO (with the
application of 100 kV/cm).
However, the measurement conducted with the SMM
showed near zero tunability for the film on LaA1 0 3 , while the field in the MgO sample
caused a 20 kHz shift in the resonance frequency of the probe with the application of 150
kY/cm. Through a finite element method, this change was estimated to correspond to a
change in the dielectric constant from 700 to 620, or a tunability of 11%.
This was correlated with the state of strain in the films, as measured with XRD,
by referencing the cell constants to the bulk cubic lattice parameter of 3.947
A for BST
(50/50). Films on LaAlCL showed on average, a normal lattice parameter of 3.980 A, and
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47
in-plane lattice constant of 3.946
3.958
A. The lattice constants o f the BST on MgO were
A in the normal, and 3.962 A in-plane. This resulted in a c/a ratio of 1.009 for
LaA 1 0 3 samples and 0.999 for MgO samples.
It was shown that the tunability was directly affected by the strain in the films.
Since the SMM (positioned in the middle of the electrode gap) detects only the
microwave field directly beneath the probe tip, it was concluded that films on LaA 1 0 3
show little tuning in this region due to the compressive strains in the in-plane direction.
Since the films on LaA 1 0 3 showed significant tuning using the LCR meter, it then
follows that the greatest tunability should arise from regions where the electric field
vectors have a z-component (normal direction). Thus, in this region the tuning results
from ionic shifts in the elongated normal direction.
Films on MgO should then have
greater tuning near the middle of the electrode gap where the field has only an xcomponent (in-plane), and the unit cell is elongated in-plane.
It was then concluded that this behavior is a result of changes in the soft phonon
mode due to strain, since the soft phonon mode directly arises from vibrations of Ti and
O ions in the oxygen octahedra in opposite directions13. Therefore, constraints on ionic
displacements in the structure from compressive strains resulted in lower tunability.
Department o f Materials Science and Engineering, North Carolina State University
(Raleigh. North Carolina)
Temperature and thickness dependent permittivity of (Ba,Sr)TiQ3 thin films
Parker et al . 14 studied the effects of film thickness on the maximum in the
permittivity of BST (70/30) thin films over the temperature range of 100 to 450 K. The
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48
films were grown by liquid-source metal-organic chemical vapor deposition on
Pt/SitV Si substrates, from 15 to 580 nm.
Planar capacitors were used to test the
electrical properties. The (100) textured films were deposited on a (111) textured Pt
layer, followed by a shadow mask patterning of sputtered circular top electrodes of Pt.
The measurement of the capacitance was made at a frequency of 4 kHz with an
impedance analyzer attached to a cold stage.
Figure 2.3 shows that as the film thickness decreased, the maximum dielectric
constant decreased. The temperature of the maximum dielectric constant also decreased
with film thickness and the peak in the permittivity became more diffuse. The dielectric
constant of the thickest film (580 nm) reached a maximum of 662 at a temperature of 269
K. This is well below room temperature (-300 K) where bulk BST (70/30) undergoes a
phase transition.
As the temperature decreased the maximum moved toward lower
temperatures until the maximum gradually disappeared as the peak became more diffuse.
100
0
66
-8.7 x 10-5
15 nm, r n p 109
100
200
300
400
500
Temperature (IQ
Figure 2.3: Shift in the magnitude and position of the maximum permittivity
toward lower temperatures with decreasing film thickness14.
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49
A model was used to quantify the diffuseness of the dielectric anomaly, which
may be related to the transition. An equation often used to describe the temperature
dependence of the permittivity in relaxor ferroelectrics was used to describe the
experimental data shown in Figure 2.314.
i
i
£
s max
- =
+ -
^
(2.1)
1emax 8
The maximum in the permittivity is represented as £^ax, and the temperature at
which it occurs is r raax. The coefficient
8
is called the diffuseness coefficient, where
large values indicate a more diffuse permittivity maximum. The
8
coefficients are also
shown in Figure 2.3, and range from 8.5 for the thickest film to 66 for the thinnest film.
A possible explanation of the increasing diffuseness of the maximum permittivity
with decreasing film thickness was proposed based on the Binder approach to finite-size
effects in ferroelectric systems14. The measured dielectric response is predicted to be that
of a three-layer structure which consists of a thickness-dependent bulk-like middle layer
between two exterior layers that remain ferroelectric but with significantly reduced
polarization. It was hypothesized that the exterior components of the total permittivity of
the film had a lowered permittivity and transition temperature.
Therefore, with
decreasing film thickness, this component lowers the effective permittivity o f the entire
stack, while the lower transition temperature results in the broadening of the permittivity
maximum.
However, the reason for the decreased polarization and lower transition
temperature of the thin exterior layers was not addressed.
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50
Department o f Pure and Applied Physics, Queen’s University (Belfast, England)
Thickness-induced stabilization of ferroelectricitv in SrRuO^/Ban ^Srn sTiOVAu thin film
capacitors
Sinnamon et a/ . 15 reported on the effects of a strain stabilized ferroelectric state in
BST (50/50) thin films deposited on a SrRuC>3 electrode. The films were fabricated with
pulsed laser deposition on (001) MgO substrates (using deposition parameters found
elsewhere16). The dielectric constant was measured using an LCR meter in a cryostat,
through the temperature range of 100 to 400 K. Polarization loops were also measured to
determine the existence o f a ferroelectric state.
X-ray diffraction measurements showed that both the SrRuOa electrode layer and
the film grew epitaxially from the (001) MgO substrate. The normal (growth direction)
lattice parameter was shown to increase systematically as the film thickness decreased.
The in-plane lattice constants were smaller than that of bulk BST (3.947
smaller lattice constant o f the SrRuOa layer (-3.93
A) due to the
A). This in-plane compressive strain
resulted in an out-of-plane tetragonal distortion, which was prominent in films with
thickness below -300 nm.
The electrical properties were measured with a parallel plate capacitor
configuration, using Au electrodes deposited on top o f the films.
Polarization loops
showed the existence of a remnant polarization even in the thickest films around 620 nm.
As the film thickness decreased, the remnant polarization increased showing the gradual
stabilization o f a ferroelectric phase (Figure 2.4).
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51
20
-15
-3 107-2 I07- l 107 0
1 107 2 JO7 3 10'
Electric Field / Van'1
Figure 2.4: Appearance of ferroelectricity, seen as increased remnant polarization,
with decreasing film thickness15.
Additionally, the effect of strain on the polarization was explored using a LandauGinzburg-Devonshire (LGD) expansion, the details of which can be found in the paper15.
The room temperature polarization data was fit to the expression,
A/0'
—— = E = C.P + C.P3 +C.P5 + ...
dP
’
3
5
(2.2)
which relates the free energy, G, and the polarization, P, through an expansion of the
polarization with fitting parameters, cj, c2 , and C3 which in themselves encompass many
terms that ultimately describe the order of the phase transition.
Through modeling, Sinnamon determined that the term cj was positive for a 620
nm film, but below -500 nm the parameter changes to a negative quantity implying a
thickness-induced ferroelectric phase transition. In addition, the cj term was shown to be
positive for all films, indicating a second-order paraelectric to ferroelectric phase
transition, rather than the typical first-order transition for bulk BST.
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The strain was shown to have a direct influence on the term ci, which can be
written as,
cl = a ( T - T a) - Q „ X l
(2.3)
where, a is an order parameter, Q,3 is an electrostrictive coefficient, X t is the mismatch
stress at the interface. Therefore, it was proposed that strain in the material couples
electrostrictively, resulting in polarization which ultimately leads to the stabilization of a
ferroelectric phase.
Finally, the dielectric constant (as measured at 10 kHz) was plotted as a
function of temperature in the range 100-400 K for films of varying thickness. The
maximum in the permittivity was shown to shift to higher temperatures as the film
thickness decreased and the compressive in-plane strain increased (Figure 2.5).
.00
150
2GG 250
300
350
400
Temperature / K
Figure 2.5: Maximum in the dielectric constant shifts toward higher temperatures with
decreasing film thickness (or increasing in-plane strain)15.
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53
Department o f Materials and Nuclear Engineering. University o f Maryland (College
Park. Maryland)
Study #1 - Dielectric properties in heteroepitaxial Ba^Srn dTiCh thin films: Effect of
internal stresses and dislocation-type defects
Canedy et al.xl investigated the effects of strain on the dielectric constant of
heteroepitaxial BST (60/40) thin films** deposited on 0.29(LaA103):0.35(Sr2TaA10g}
substrates, also referred to as LSAT. Films were grown with pulsed laser deposition
using a KrF laser and the following deposition conditions: 800 °C, 120 mTorr O2 , and
1.5-2 J/cm2 laser fluence. The films were then photolithographically patterned with 100
nm Au interdigitated electrodes consisting o f 50 fingers separated by a 15 pm gap.
X-ray diffraction scans showed only (00/) type reflections indicating epitaxial
growth on the substrate. The normal lattice parameters were directly measured, and the
in-plane strain was calculated from the relation,
X l = X X L =X X
a
l
X
u
(2.4)
Cn
where X 1, is the normal (out-of-plane) strain, a 1 and a 0 are the normal and bulk lattice
parameters, Cy are the elastic stiffness coefficients, and Xm is the in-plane strain.
Epitaxial growth on the substrate material, with a lattice parameter of 3.865 A,
resulted in an elongated normal lattice parameter and an in-plane compressive strain. The
magnitude of the in-plane strains were calculated at -0.25% for the thinnest film (8 nm),
decreasing to around -0.10% for the thickest film (325 nm).
The capacitance as a function of DC bias (up to ±40 V) was measured at 1 MHz
with a standard impedance analyzer. Permittivity data for the thicker films was then
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
extracted using a model for interdigitated electrodes created by Gevorgian, Linner, and
Kolberg18. For the thinnest films, a perturbation approach was used, where the properties
of a bare substrate were measured and subtracted from the capacitance measured for
17
samples with films .
The films showed significant hysteresis with the application of DC bias, (Figure
2.6a) with dielectric constants up to 1400 for the 325 nm film. The zero bias dielectric
constant (1 MHz) was also plotted as a function o f thickness at 300 K. Figure 2.6b shows
that the permittivity remained nearly constant down to a thickness of 100 nm, and then
drops quite rapidly to about half its maximum value (-600-700) for the 8 nm film.
Additionally, the tunability was reported to follow a similar trend, reaching a maximum
o f -50%.
i--------— Sms
j
Voltage (volts)
(a)
Thickness (run)
(b)
Figure 2.6: (a) Hystersis of in-plane permittivity with DC bias, (b) In-plane permittivity vs film thickness17.
Next, the dependence of the dielectric constant on internal stress was estimated
from LGD theory17, where an expression for the relative permittivity, £r, was written in
terms o f the electrostrictive coefficients, QtJ, the elastic constants, Q , the dielectric
stiffness, a, and the misfit strain, Xu-
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55
S,11
1
2 £ , [ a - C X u(Qn +Qn)\
(2.5)
Equation 2.5 is an expression for the relative permittivity at zero bias, or P=0,
where a ^ (T -T o )/2 eo C , with the Curie temperature and Curie constant represented by To
and C, respectively. In addition, the term C for a particular BST composition can be
calculated from,
—
2C 2
C = C n +Cu - — *
(2.6)
^11
where C// and C n for the composition are generated from the constants for both BaTiC>3
and SrTiC>3 using a weighted average19.
A theoretical plot o f the inverse permittivity versus the misfit strain was created
from Equation 2.5 to show the effect of the strain on the degradation of the dielectric
properties. Figure 2.7 shows the experimental data and the theoretical prediction of the
effect of strain. It was shown that the increasing compressive strain in thinner films
decreased the permittivity.
1.2
ibcoiy
2
]
0.8
Annealing
0.4
-0.30
-0.25
-0.20
-0.15
41.10
Misfit Strain, xM(%)
Figure 2.7: Effect of compressive strain on the permittivity of BST thin films on LSAT17.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
Finally, a 120 nm film was examined with transmission electron microscopy,
where it was discovered that a very large number of threading dislocations were present,
on the order of 2.2 x 10u cm'2. This was a density approximately 3-4 times greater than
that observed in typically semiconductors. Therefore, the samples were annealed for 15
hours at 975 °C in an attempt to remove some of the dislocations. Subsequently, the
permittivity was measured again, and found to approach those values as predicted by
theory (indicated in Figure 2.7 as the shift due to annealing). It was suggested that the
presence o f threading dislocations due to strain alters the dielectric stiffness of the
material, resulting in lower dielectric constants.
**Note: Although Canedy et al }
1
claims to have investigated the properties of
BST (60/40) thin films, it is more likely that his study was conducted on BST
(50/50). The x-ray diffraction data he presents for the ceramic target gives a
lattice constant o f 3.9505
3.965
A, whereas BST (60/40) has a bulk lattice constant of
A. In addition, the measured out-of-plane lattice constants of the films for
this study are all below 3.965
A, and therefore could not possibly generate an in­
plane compressive strain with the already present contraction in the out-of-plane
direction. Instead, the films are likely BST (50/50), in which case, the out-ofplane lattice constants for the films are greater than the bulk value of 3.9505
A,
allowing an in-plane compressive strain. Using BST (50/50) as the reference for
this study supports the general trends and conclusions, however there are small
errors due to the dependence of Equation 2.5 on the Curie temperature and elastic
constants. It apparently was a simple error by Canedy and co-workers.
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57
Study #2 - Dependence of dielectric properties on internal stresses in epitaxial
barium strontium titanate thin films
Li et al . 2 0 studied the effects of misfit strain on the dielectric constant of BST
(50/50) films deposited on (001) MgO substrates. The thickness o f the films was varied
from 14 to 500 nm to produce a systematically decreasing amount of in-plane strain.
Films were grown with pulsed laser deposition using the same deposition parameters as
described in the previous study by Canedy17.
The electrical properties were also
measured in the same manner as the previous study, using interdigitated electrodes and a
data extraction model by Gevorgian18, at 1 MHz with a DC bias up to ±40 V.
X-ray diffraction data collected on the films through the thickness range of the
study show that the out-of-plane (normal direction) lattice parameter decreases with
decreasing film thickness. This is due to the increasing in-plane tensile strains generated
in successively thinner films. The measurements show that above 100 nm, the normal
lattice parameter approaches the bulk value o f 3.9505 A for BST (50/50).
Measurements o f the dielectric constant of the films are shown in Figure 2.8. The
experimental fit to the data shows that the permittivity remains nearly constant with
thickness until ~100 nm. At that point, the in-plane tensile strain is shown to cause a
large increase in the permittivity to nearly 2300 for the thinnest film (14 nm).
0
100
260
300
400
503
Thickness (run}
Figure 2.8: Permittivity vs. film thickness for BST (50/50) on MgO20.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
58
The in-plane tensile strains were then calculated from Equation 2.4 and plotted
versus the theoretical inverse permittivity obtained from Equation 2.5, as in the previous
study. Figure 2.9 shows good agreement between the experimental data points and the
theoretical fit. It also shows that increasing amounts of tensile strain, as generated in
successively thinner films on MgO, increased the permittivity. This effect is opposite to
that of the compressive strain in BST deposited on LSAT.
0.7
.snear fit 1
0.6
o
0.4 i
xMMisfit Strain
<%)
Figure 2.9: Effect of tensile strain on the permittivity of BST (50/50) on MgO20.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
Department o f Metallurgy and Materials Engineering and Institute o f Materials Science,
University o f Connecticut (Storrs. Connecticut)
Study #1 - Phase diagrams and dielectric response of epitaxial barium strontium titanate
films: A theoretical analysis
Ban and Alpay21 have developed theoretical phase diagrams for epitaxial (001)
Bao.6 Sro.4 TiC>3 and BaojSrojTiOs films on cubic substrates of SrTiCb, LaAKTj, MgO, and
Si. The diagrams were created using a LGD phenomenological model, and show the
existence o f various polar phases as a function of misfit strain. An analysis of the misfit
strain as a function o f film thickness is presented along with a calculation of the dielectric
response o f both compositions on the different substrates as a function of film thickness.
The phase diagrams were constructed by considering the thermodynamic free
energy of the films, G , as a function of polarization, temperature, and misfit strain, which
includes the dependence on the substrate and film lattice constants.
originally derived by Pertsev
00 O'X Of\
material parameters ’ '
-y>y
The expression
can be found in the paper. It involves a number of critical
(Table 2.2), which are weighted averages of the parameters for
BaTiC>3 and SrTiC>3 for calculation of the coefficients of the free energy expansion.
Table 2.2: Material parameters for BST, including Curie temperature (7}), Curie constant (C),
fitting parameters (a,,), elastic coefficients (V,;), and electrostictive coefficients (Q,j)21Parameter
ty re )
C(105oC)
a 11 ( 1O'1 trrVC-F)
</i2(I0* n r
S u t 10
n r /N )
BST 70/30
BST (.0 40
34
1.20
2.52 2'+ 189 ( T i n °C)
7.21
V,,(10 ,2ra2/N)
5.92
— 1.92
STtflO 12n r /N )
0 , (i n i' ( 51
6.7
0.1
fiw fa A 'C 2)
0 ,w(m 4/ € 2)
5
1.22
2 .1 6 ? '/ 462 ' T in C .
7.98
5.12
1.65
5.S6
--0.034
0.1
0.034
0.029
0.029
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60
The free energy expression was then differentiated and set to zero to find the
minima for the six polarization states, or phases, as predicted by Pertsev2 2 (Table 2.3).
Table 2.3: Possible phases of strained BST films as predicted by theory21,22.
PototnMwii wnpwrass
fltstse
Paraelecnrir
rs*o
c ptiase
f,
o phase
P, #0, P ^ P ^ O
V—v
m phase
aa phase
/J, “ 0
r phase
Pjt-0
W
The resulting phase diagram for both BST compositions was created by plotting
boundary lines which delineate the regions where a particular phase (as listed in Table
2.3) is the most stable, with the lowest free energy. Figure 2.10 shows the resulting phase
diagram as it depends on temperature and misfit strain.
120
paraeiet
U
80
*
60
S3.
20-
m phase
o te s c '
-03
-0.2
-0.1
0.0
0.1
0.2
03
Misfit strain, umf%l
Figure 2.10: Theoretical phase diagram showing stable phases as a function of temperature and strain21
Dotted line is for BST (60/40) and solid line is for BST (70/30).
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61
It can be seen that the paraeleetric region exists only in the top quadrant of the
diagram, with all phases below that region have some internal polarization due to the
strain-induced stabilization o f a ferroelectric phase.
Therefore, as the misfit strain
increases, either tensile or compressive, the phase transition is shown to shift to
considerably higher temperatures. Another important conclusion from this analysis is
that all phase transitions for constrained BST films were found to be second order. This
was indicated by a positive sign (+) for the critical coefficients of the free energy
expression which determine the order of the transition. Normally, BST shows a firstorder transition from the ferroelectric to paraeleetric state as discussed in Sec. 1.2.
The phase diagram predicts existence of three ferroelectric phases. The aa phase
occurs as a result of tensile misfit strains from substrates with lattice parameters larger
than that of the film.
This phase allows for the existence of two equal polarization
directions in the plane of the film. Due to the expansion of the lattice in the in-plane
directions, and the corresponding contraction in the normal direction, the out-of-plane
polarization is suppressed.
The c phase exists where compressive misfit strains result from substrates with
lattice parameters smaller than that of the film. This phase allows for only a single
polarization in the normal direction, with no in-plane polarization. Therefore, the in­
plane contraction suppresses polarization in that direction, and dielectric response may
occur due to the polarization in the normal direction only.
The r phase is an unusual phase that is forbidden in single crystals and bulk
ceramics. It is monoclinic, in terms of crystallographic symmetry, with polarization in all
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62
three directions, having equal in-plane polarizations and a separate out-of-plane
polarization.
The next item considered was the effect of misfit dislocations and the substrate
lattice parameter. The formation of misfit dislocations at the growth temperature allow
the epitaxial strain to relax as films are grown thicker. As a result, the in-plane strain
changes with film thickness. A modified thermodynamic model o f misfit dislocations
was used to create misfit strain versus film thickness diagrams.
The effective misfit
strain, « °, at the deposition temperature, Tq, scales with film thickness, h, as27,28,
(2.7)
J
where p is the equilibrium linear misfit dislocation density at Tg- The equilibrium film
lattice parameter (bulk value) is represented by ao, and hp is the critical thickness below
which the formation o f misfit dislocations is not feasible.
To account for the fact that the misfit strain changes with film thickness, an
effective substrate lattice parameter, as was defined,
-
at {T)
a A T ) = ------ 7 ^ — 7
paXT) + l
(2.8)
where as(T) is the substrate lattice parameter as a function of temperature.
Figure 2.11a and 2.11b shows the misfit strain diagrams for BST (60/40) as
generated from the above equations. Films deposited on compressive substrates such as
LaAl( > 3 and SrTiCb show a very large in-plane compression which relaxes significantly
as film are grown thicker. The films deposited on MgO and Si, the tensile substrates,
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63
show a similar behavior as the tensile strains relax with increasing film thickness. In
addition, films on MgO substrates are predicted to transition from a tensile state to a
compressive state above a critical thickness due to thermal stresses upon cooling from the
deposition temperature. This is a result of the higher thermal expansion coefficient o f
MgO (13.5 x 10' 6 °C 1) relative to BST (10.5 x 10' 6 °C4)29.
0.0
-
^
2.5-
0.2
MgO
-Si
-0.4
a -0 .6
i.o-
1.0
0 .0 -
0
so
100
150
Film thickness [nmj
(a)
-0.5
0
50
100
150
200
Film thickness {nmj
(b)
Figure 2.11: Calculated misfit strain vs. film thickness for BST (60/40) at 25 °C on (a) compressive
substrates, (b) tensile substrates21.
The plots suggest that films may undergo a phase transition from one polar state
to another, or to a non-polar paraeleetric state, as the misfit strain decreases with
increasing film thickness. As a result of these phase changes, the dielectric response may
change drastically. Therefore, the next step of Ban and Alpay’s theoretical analysis was
to determine the effect of misfit strain on the permittivity.
The dielectric constants as a function of misfit strain were obtained from the
inverse of the second derivative, with respect to the polarization, of the original free
energy expression used to create the phase diagram in Figure 2.10.
The relative
permittivity both in-plane, Bn, and out-of-plane, £3 3 , could then be described in terms of
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64
the polarization and the coefficients for the free energy expression for all phases as
predicted by the phase diagram.
These predictions are shown for room temperature in Figure 2.12a and 2.12b.
The behavior of the dielectric constant versus misfit strain is plotted with an overlay of
the transition boundaries between stable phases. The most apparent characteristic is the
anomaly in the dielectric constant that occurs near the phase boundaries.
For BST
(60/40), in particular, the in-plane permittivity (si i) is plotted. It shows that as the misfit
strain decreases, the film may transition from either the c phase (for compressive
substrates) or the aa phase (for tensile substrates) into the paraeleetric state.
Most
importantly, at or near the transitions, the permittivity increases rapidly, resulting in
maximum dielectric response.
sooo
SOM­
'S 4000
= 4000
3000
2000
1000
-(M -0.3 -0.2 -0.1
0.0
0.1
0.2
Misfit strain, um [%]
(a)
*
0.3
0.4
0.0 flTl *ST~03^0.4
Misfit strain, u j % )
-fli.4 -0.3 -0.2 -0.1
(b)
Figure 2.12: Calculated dependence of (a) out-of-plane permittivity for BST (70/30),
(b) in-plane permittivity for BST (60/40), on misfit strain at 25° C21.
Finally, Ban and Alpay also created theoretical plots of the permittivity as a
function of thickness for both BST (70/30) and BST (60/40) on the four different
substrates. From the phase diagram (Figure 2.10) and the predicted relaxation of misfit
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65
strain with increasing film thickness (Figure 2.11a and 2.11b), it is seen that BST films
on the substrates SrTiCb, LaA1 0 3 , and Si all remain in one phase through the thickness
range studied.
However, it was predicted that BST on MgO will undergo a phase
transition at a critical thickness resulting in a large increase in the permittivity. Figure
2.13a and 2.13b show the anomaly that occurs at -40 nm. As the thickness of a BST film
on MgO increases, it switches from the aa phase to the paraeleetric state and finally to
the c phase as the strain transitions from tensile to neutral to compressive, respectively.
sm
SrTiO
- - SrTiO
MgO
MgO
R 4000n
LaAKJj
— LaAIO,
— -SI
-■SI
30OG-*
0
SO
100
ISO
200
Film thickness [nm]
(a)
250
300
0
50
100
150
200
250
Film thickness [nm]
(b)
Figure 2.13: Calculated dependence of (a) out-of-plane permittivity for BST (70/30),
(b) in-plane permittivity for BST (60/40), on film thickness at 25° C21.
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300
66
Study #2 - Optimization o f the tunabilitv of barium strontium titanate films via epitaxial
stresses
The tunability of epitaxial BST films has also been investigated theoretically by
Ban and Alpay3 0 using the same thermodynamic phenomenological model based on LGD
theory as discussed in the previous paper21. Tunability for this study was defined as30,
<D =
1
-----£3 3 ( ^ 3 = ° )
0
=
1
(2.9)
en{Ex =0)
where S3 3 (E3 ) indicates the out-of-plane permittivity under a DC bias of E3 , and sh(E i)
indicates the in-plane permittivity under a DC bias of Ei.
Theoretical plots of the tunability as a function of misfit strain were created using
Equation 2.9 and a modified partial derivative o f the free energy expression, G , with
respect to the polarization, P, (the full expansion can be found in the paper)30,
eAEt)
r
£
S'0
n
v
- v‘
dG
° a^p*2J
(2.10)
The tunability was calculated for BST (50/50) at room temperature as a function
o f misfit strain for a 67 kV/cm electric field in the out-of-plane direction (Figure 2.14a)
and a 40 kV/cm electric field in the in-plane direction (Figure 2.14b). It can be seen that
the tunability is expected to reach a maximum at a critical misfit strain corresponding to a
phase transition, and degrade as the strain increases in either direction.
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67
so-
40-
H I®.
44
0.4
Misfit Strain, uj%)
(a) *
0.2
(1.4
Mfe® Strain, « J% )
(b)
Figure 2.14: Tunability of (a) out-of-plane permittivity, (b) in-plane permittivity for BST (50/50) at 298 K
with application of electric field, predicting a maximum at a phase transition30.
The maximum in the tunability in the out-of-plane direction occurs at the
transition between the paraeleetric state and the c phase (-0 . 1 % misfit strain) where a
spontaneous polarization is created in the normal direction by compressive strain at the
film-substrate interface (as predicted by Pertsev 2 2 in Table 2.3). However, the tunability
in the in-plane direction reaches a maximum at the transition between the paraeleetric
state and the aa phase (+0.1% misfit strain). This is as a result o f the creation of two
equal in-plane polarization directions from the tensile strain at the film-substrate
interface.
As discussed previously, the misfit strain can be altered by the film thickness due
to the formation of misfit dislocations at the growth temperature. To understand the
effect of film thickness on the tunability, Ban and Alpay created plots to show the
interaction between the three factors (tunability, misfit strain, and film thickness). Figure
2.15a and 2.15b show the predicted behavior for BST (50/50) on LaA 1 0 3 and MgO
substrates.
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68
*'w'
ss8
£ *
m.
ss
§
100
m
m
290 m
Film tbtekmm {« « )
(a)
58
IM 150 200 25#
Film thktattss (*sta)
3M
(b)
Figure 2.15: Tunability of out-of-plane permittivity for BST (50/50) at 298 K on (a) compressive LaA103
substrate, (b) tensile MgO substrate30.
Ban and Alpay showed that high tunability can be achieved by adjusting the
misfit strain to obtain maximum dielectric response near a phase transition temperature.
Their theoretical analysis predicted a maximum tunability for a film thickness of 120 nm
on LaAlCb and 90 nm on MgO for BST (50/50) at room temperature.
The two theoretical studies discussed above present some interesting predictions
of the dielectric behavior o f BST thin films. However, the limitations of this model as,
stated by Ban and Alpay30, include the following:
1. The coefficients of the free energy expansion for BST compositions are the
averages of data collected on bulk samples of BaTiC>3 and SrTiC^.
2. The sixth-order polarization terms and their coupling with internal stresses are
neglected (a reasonable approximation in the vicinity of T o ) .
3. The formation of polydomain (polytwin) structures is not accounted for, as it
may be a mechanism for the relaxation of large internal stresses in the film.
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69
4. The misfit dislocation model is also a thermodynamic analysis, and therefore
the real critical thickness for dislocation formation may be different due to
kinetic factors.
5. The model may not be accurate for films less than -20 nm in thickness due to
the possibility o f surface effects and depolarization fields in thin ferroelectric
layers, as it was recently suggested that the LGD expansion coefficients may
be size-dependent31.
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70
2 .2
T u n a b l e M ic r o w a v e B S T T h in F il m D e v ic e s
The high tunability o f BST compositions, with the application of a DC bias field
in the range o f several MV/m, gives this material great potential for use in a wide variety
of microwave applications. Future microwave device designs are likely to incorporate
paraeleetric BST for a variety of tunable passive microwave components such as
varactors, phase shifters, filters, and resonators. The following is a brief look at the
possible uses o f BST thin films in microwave devices, as proposed by researchers.
York et al? 2 has fabricated BST (50/50) thin films (-100 nm thick) on Pt-coated
high-resistivity silicon in an effort to optimize the microwave tunability and loss of
integrated varactors for phase shifter circuits.
Devices have been fabricated using a
parallel-plate configuration to allow lower control voltages versus interdigitated
structures. Figure 2.16 shows a schematic o f the design, which consists of two tunable
varactors in series. Silicon nitride is used to insulate the tunable BST film from the top
electrode. The silicon nitride layer is etched in two separate areas to allow Pt deposition
on the film for the top electrical contacts of each device.
a—c
x-E
SI N
71
EST
Pt
Figure 2.16: Dual BST thin film varactors fabricated on high-resistivity silicon with Pt electrodes32.
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71
In order to create a vertical device such as the BST varactors, the deposition of
several interlayers between the substrate and bottom Pt electrode is needed.
Silicon
substrates are oxidized to form a SiC>2 layer. Next, a thin layer of TiC>2 is deposited, and
then finally the Pt bottom electrode, onto which the ferroelectric is grown.
These
interlayers help to eliminate adhesion problems, and reduce interdiffusion and leakage
currents, which are presently not fully understood. The result is a complex multilayer
stack that requires carefully controlled deposition conditions for each layer. This type of
BST varactor shows good performance (Figure 2.17), with a tunability of -55% under a
20 V DC bias.
3. 0 1 0 *®
\ q i O'0
-20
-15
-10
-5
0
5
10
B ia s Voltage [V]
15
20
Figure 2.17: Capacitance per unit area of BST thin film varactors as a function of DC bias32.
Wu et al . 33 created coplanar waveguide meandering-line phase shifters using BST
(60/40) thin films on substrates of LaAlCb and MgO. The coplanar waveguide (CPW)
was fabricated by direct deposition of the electrode on the film surface using a Ag/Au
lift-off metallization technique. The center line of the CPW was 100 pm with 25 pm
gaps on either side of the center strip, and a total length of 1.62 cm (Figure 2.18). The
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72
bulk of the electrode was a 1.5 pm silver layer, typical for coplanar devices (waveguides,
interdigitated capacitors, etc.) to reduce metallization losses.
B a„,S rn ,TiO, Thin Film
LuA!0 3 or MgO Substrate
Figure 2.18: Meandering path BST thin film CPW phase shifter33.
The device was measured by applying a DC bias voltage between the center line
and the ground planes. Scattering parameter data (from S21 transmission measurements)
was collected to determine the phase shift and insertion loss as a function of bias and
frequency for a 500 nm film deposited directly on a LaA1 0 3 substrate (Figure 2.19a and
2.19b). The significant insertion losses are attributed to the characteristic impedance
mismatch o f the device and network analyzer circuit; -22 Q for the CPW versus the
standard 50 Q for the test circuit.
10 GHz
1. . . 1. . .
60
80
100
4,
0
20
40
60
80
100
DC Bias (volt)
(a)
Figure 2.19: Tunability of CPW phase shifter with DC bias, (a) phase shift, (b) insertion loss33.
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73
Findikoglu et al?4 fabricated tunable adaptive 3-pole half-wave bandpass
coplanar waveguide filters.
The filters were created depositing SrTiC>3 on LaA1 0 3 ,
followed by top superconducting YBa2Cu3 0 7 _x electrodes. Although this device does not
implement a BST composition because it is designed for low temperature use, it takes
advantage of the high tunability of a non-linear dielectric. BST could very easily be
substituted in place o f SrTiC>3 , and be used with different top electrodes if the device is
operated at room temperature. The design of the filter is shown in Figure 2.20, which
shows the dimensions of the electrode gaps and the thickness of each layer.
—iLPF 1-Bias (*;
Bias (-) - j w j —
lO0-|«w-wi<te coxa-line
SO-jun-w&iegap
STlliXl!
Ea
Y B j j C u ^ O ^ SHpercoiKkictor
i n
SQOjim
» j |
S1T1O3 nonlinear dielectric
LaAtD^ sabstram
I cm
Figure 2,20: Tunable bandpass CPW filter design using SrTi03 for low temperature operation3'
This device allows for the electrical tuning of the filter to achieve symmetric and
optimized response versus typical mechanical tuning optimization (such as tuning screws
or other inserts that affect the signal). It also allows for broadband tuning of the passband
over a wide-ffequency range for low-pass and high-pass applications, all fabricated in an
area of 1 cm2.
The characteristics of the filter are shown in Figure 2.21. The relatively large
voltages (25-95 V) shown for the transmission peaks are those needed to tune the
electrical lengths o f the poles of the filters to shift the passband to different frequencies.
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74
The optimization of the filter profile is achieved by applying an order of magnitude lower
bias between the gaps to tune the coupling capacitances between electrodes and create
symmetric passbands.
-20
95 V'
co
a
% -20
Bias
1<D
OS
-40
'No'
-60
-30
2.1
76 K
2 .3
2.5
2.7
2 .9
Frequency [GHz]
Figure 2.21: Tuning of filter showing shift of bandpass frequency with DC bias34.
Keis et al.35 fabricated BST thin film varactors and then constructed two-pole
tunable waveguide filters composed of four BST varactor elements. The planar varactors
were 5 pm thick polycrystalline BST (60/40) films deposited on MgO substrates. Two
Ag electrodes (-0.5 mm x 0.5 mm) were deposited directly on top of the film separated
by a 50 pm gap for DC bias tuning.
The filter was a symmetrical fin-line design constructed in a rectangular
waveguide (Figure 2.22). Three copper foil plates (-0.2 mm thick) were placed at the
center o f the waveguide along the longitudinal axis. Two of the plates (one connected to
the wall of the input side of the waveguide, and the other to the output side of the
waveguide) were grounded to the metal waveguide and functioned as shorted end fin-line
resonators with dimensions of 6.5 mm in length by 0.35 mm in width. The center plate
was isolated from the other two by a mica substrate. The four BST varactors were then
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75
placed upside-down with one Ag electrode in contact with an outer copper plate, and the
other Ag electrode in contact with an inner copper plate. They were arranged with two
varactors on the input side of the filter and two on the output side.
foil copper plates
output
waveguide
flange
/
^8STO film
MgO substrate
Figure 2.22: Design of tunable waveguide filter using BST thin film varactors’5.
The performance of the filter was measured at a frequency of 20 GHz as a
function of DC bias by measuring the S21 scattering parameter, which was subsequently
converted to capacitance through equivalent circuit device modeling.
Due to the
relatively thick film layer a large DC bias, up to 400 V, was applied to achieve a
tunability o f -65%. The capacitance and loss o f this four element tunable filter is shown
in Figure 2.23.
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76
0.45
0.13
0.40
0.16
0.35
Q.30
tO
u.
O-i
o.io §
0.20
0.08
0.15
0.06
0.10
0.04
G.Q5
0.02
0.00
0
50
100
150 200
ub,v
250
300
350
400
Figure 2.23: Tunability of BST varactor-based waveguide filter35.
Booth et al.i6 created coplanar waveguide (CPW) transmission lines using BST
(30/70) thin films. The films were 400 nm in thickness and grown on LaA1 0 3 substrates
with dimensions o f 16 mm x 16 mm.
The CPW transmission lines had a center
conductor line-width of 53 pm and a gap spacing of 101 pm to the ground planes on
either side.
The Ag metallization was patterned using a photolithographic lift-off
technique, and deposited to a thickness of 1 pm with e-beam evaporation.
A CPW transmission line of length 10.52 mm was measured at 3 GHz, at a
temperature of 235 K as a function of DC bias. The capacitance per unit length of the
transmission line is plotted in Figure 2.24 for a DC bias up to 100 V. The device shows
only a 10% tunability because of the high Sr content of the BST (30/70) composition,
which shifts the transition temperature, and therefore the permittivity and tunability
maximum, to temperatures well below 235 K.
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77
3 .5
Ba0> 0.7Tib3 fl!m
235K
i
■ ........ f ......■■■
:
UL
Q.
Temp(K)
%
1
.......................
JO.----.... I&LJ2QQ..
r — _ 3tQQ__L
•
ei
*
X
0
=
&
© 3.-1
o
3
2.9
.
20
'B '
y / N
1C!
ioS
.— I-----i— _ n
j ■ i
J — »—L f c
20
40
60
8 0 100
Voltage (V)
Figure 2.24: Capacitance per unit length vs. DC bias for BST thin film transmission line at 235 K'36
Sengupta et al?1 has developed planar ferroelectric microwave phase shifters
based on BST composite thin films. The films are ~1.5 pm thick and are fabricated from
composite targets of BST (60/40) with 1 to 60 wt% MgO, which results in lower loss
than pure BST, but does sacrifice some tunability.
The phase shifter was designed with an 8 pm center strip with 3 pm gaps on
either side between the center conductor and the ground planes.
The 1 wt% MgO
composite device was tested and showed a 24° phase shift at 35 GHz.
In addition, collaborations between Sengupta of Paratek Microwave, Inc. and the
Army Research Laboratory have led to the development of other phase shifter designs
(Figure 2.25) and phased array antennas (Figure 2.26) using BST composites38. The
phase shifter design allows for -180° phase shift (at DC bias of 2 V/pm) with 6 dB
insertion loss in the frequency range of 2 to 10 GHz.
The phased array antenna is
designed for operation at 4.55 GHz and allows a beam sweep of 50° in a scan time of 7
'j
msec with a radiative power output o f 15 pW/cm at a distance of 1 m.
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78
DC Mocks
Xm’tVrA
Ferroelectric
material
matching
Figure 2.25: Phase shifter based oa BST thin film composite showing capable o f-180° phase shift38.
ferroelectric
Phase Shifters
Patch Antenna
DC Control Line
Corporate Feed
DC Block
Figure 2.26: Phase-array antenna schematic using tunable BST phase shifters between feed lines
and patch antenna elements38.
Recently, Acikel et al.
IQ
has developed a new X-band high-performance phase
shifter based on BST (50/50) thin films. The device was created by depositing a Pt/Au
bottom electrode on a sapphire substrate, followed by the BST film and then a top Pt/Au
electrode. The electrodes were deposited to a thickness >1 pm to reduce conductor losses.
The phase shifter circuit design consisted of a transmission line periodically loaded with
thin film BST varactors. Therefore, by applying the DC bias it was possible to tune the
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79
capacitance of the varactors and vary the phase velocity and characteristic impedance of
the transmission line.
The performance of the individual BST varactors used for the phase shifter were
measured using parallel plate capacitors fabricated with a zero-bias capacitance of ~2 pF.
The tunability of these capacitors was measured at 2.5:1 at a frequency of 10 GHz using
single-port Sn measurements.
The phase shifter circuit was tested using a two-port measurement with DC bias
voltages up to 17.5 V. The performance from 1 to 10 GHz is shown in Figure 2.27a and
2.27b. A phase shift up to 240° was achieved with insertion loss and return loss o f 3 dB
and 10 dB, respectively, at 10 GHz.
" " — 17.5V
210*
410®
610*
Frequency (Hz)
(a)
810*
110"
210*
410*
610s
810*
Frequency (Hz)
110'
(b)
Figure 2.27: Performance of BST phase shifter circuit, (a) phase shift, (b) insertion and
return loss as a function of DC bias from 1 to 10 GHz39.
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80
C h a p t e r Su m m a r y
In summary, research by many groups has shown that strain has a profound
impact on the dielectric response. Most research has shown that strained films have
significantly lower capacitance and permittivity. However, a clear understanding of the
causes of the degradation of the dielectric properties is not well established.
“Strain effects” is a relatively new area of exploration for high permittivity
materials, as researchers realize that next-generation miniaturized electronic devices must
contain thin film components with the same or better properties as that obtained from
bulk components. Many published studies discuss the effects on only a few films, and
are limited in scope.
In addition, direct comparison between studies conducted by
different groups in often problematic.
The differences that exist between thin films
produced in one laboratory as compared to another is often enough to drastically change
the dielectric response, as seen by the aforementioned investigations. Factors that weigh
heavily on device response are the thin film microstructure (which is a result of the
processing), as well as the electrode configuration and specifics of electrical test signal
(direction and magnitude of applied field, frequency, etc).
The recent theoretical works by Ban and Alpay21,30 have analyzed the dielectric
properties of BST thin films as a function of misfit strain and film thickness.
The
experimental findings o f this thesis, as discussed in Chapter 5, will be compared with
their theoretical predictions to offer insight on where theory and experiment should meet.
The variety of devices that can be fabricated using BST show that it has great potential.
It is hoped that the new results of this work will lead to a better understanding of the
strain effects in BST films for the production of optimized thin film microwave devices.
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81
Referenc es
[1]
B. Jaffe, W. R. Cooke, and H. Jaffe, Piezoelectric Ceramics. Academic Press Inc.,
London, UK, 1990, p. 94,101.
[2] S. Ezhilvalavan and T.-Y. Tseng, Mater. Chem. Phys., 6 5 , 227 (2000).
[3] L. Wu, Y.-C. Chen, L.-J. Chen, Y.-P. Chou, and Y.-T. Tsai, Jpn. J. Appl. Phys., 38,
5612(1999).
[4] F. Jona and G. Shirane, Ferroelectric Crystals, Dover Publications Inc., New York,
1993, p. 248.
[5] L. Benguigui, Phys. Stat. Sol. A, 4 6 , 337, (1978).
[6] W. Chang, C. M. Gilmore, W. J. Kim, J. M. Pond, S. W. Kirchoefer, S. B. Qadri, D.
B. Chrisey, and J. S. Horwitz, J. Appl. Phys., 8 7 , 3044 (2000).
[7]
W. J. Kim, W. Chang, S. B. Quadri, J. M. Pond, S. W. Kirchoefer, D. B. Chrisey,
and J. S. Horwitz, Appl. Phys. Lett., 76, 1185 (2000).
[8] W. J. Kim, H. D. Wu, W. Chang, S. B. Quadri, J. M. Pond, S. W. Kirchoefer, D. B.
Chrisey, and J. S. Horwitz, J. Appl. Phys., 88, 5448 (2000).
[9] W. Chang, S. W. Kirchoefer, J. M. Pond, J . S. Horowitz, and L. Sengupta, J. Appl.
Phys., 92, 1528 (2002).
[10] T. M. Shaw, Z. Suo, M. Huang, E. Liniger, R. B. Laibowitz, and J. D. Baniecki,
Appl. Phys. Lett., 7 5 , 2129 (1999).
[11] G. G. Stoney, Proc. R. Soc. London, Ser. A 82, 172 (1909).
[12] S. Hyun, J. H. Lee, S. S. Kim, K. Char, S. J. Park, J. Sok, and E. H. Lee, Appl.
Phys. Lett., 77,3084 (2000).
[13] T.
Schimizu, Solid State Comm., 102, 523 (1997).
[14] C.
B. Parker, J.-P. Maria, and A. I. Kingon, Appl. Phys. Lett., 81 , 340 (2002).
[15] L.
J. Sinnamon, R. M. Bowman, and J. M. Gregg, Appl. Phys.Lett., 81,889 (2002).
[16] L.
J. Sinnamon, R. M. Bowman, and J. M. Gregg, Appl. Phys.Lett., 78,1724
(2001).
[17] C. L. Canedy, H. Li., S. P. Alpay, L. Salamanca-Riba, A. L. Roytburd, and R.
Ramesh, Appl. Phys. Lett., 77, 1695 (2000).
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82
[18] S. S. Gevorgian, P. L. J. Linner, and E. L. Kolberg, IEEE Trans. Microwave Theory
Tech, 44, 896 (1996).
[19] Elastic constants for BST single crystal compositions are unavailable so they are
taken from weighted averages of the values for BaTi03 and SrTi03:
Cn(BaTi03)=2.75 x 10n N/m2, Ci2(BaTi03)=1.79 x 1011 N/m2,
Cn(SrTi03)=3.48 x 1011 N/m2, Ci2(SrTiO3)=1.00 x 1011 N/m2
Handbook of Chemistry and Physics, CRC Publishing, Boca Raton, FL, 1995.
[20] H. Li, A. L. Roytburd, S. P. Alpay, T. D. Tran, L. Salamanca-Riba, and R. Ramesh,
Appl. Phys. Lett., 7 8 , 2354 (2001).
[21] Z.-G. Ban and S. P. Alpay, J. Appl. Phys., 9 1 , 9288 (2002).
[22] N. A. Pertsev, A. G. Zembilgotov, and A. K. Tagantsev, Phys. Rev. Lett., 8 0 , 1988
(1998).
[23] Landolt-Bomstein. Numerical Data and Functional Relationships in Science and
Technology, Vol. 16, edited by K.-H. Hellwege and A. M. Hellwege, Springier,
Berlin, 1981.
[24] N. A. Pertsev, A. K. Tagantsev, andN. Setter, Phys. Rev. B, 61, R825 (2000).
[25] T. Yamada, J. Appl. Phys., 43, 328 (1972).
[26] A. D. Hilton and B. W. Ricketts, J. Phys. D, 2 9 , 1321 (1996).
[27] J. S. Speck and W. Pompe, J. Appl. Phys., 7 6 , 466 (1994).
[28] S. P. Alpay and A. L. Roytburd, J. Appl. Phys., 8 3 , 4714 (1998).
[29] W. Chang, J. S. Horwitz, A. C. Carter, J. M. Pond, S. W. Kirchoefer, C.M.
Gilmore, and D. B. Chrisey, Appl. Phys. Lett., 74,1033, (1999).
[30] Z.-G. Ban and S. P. Alpay, J. Appl. Phys., 93, 504 (2003).
[31] E. K Akdogan and A. Safari, Jpn. J. Appl. Phys., 41, 7170 (2002).
[32] R. York, A. Naga, E. Erker, T. Taylor, P. Periaswamy, J. Speck, S. Streiffer, and O.
Auciello, Proc. 12th IEEE Int. Symp. on Appl. Ferro., 1, 195, (2000).
[33] H.-D. Wu and F. S. Barnes, Integ. Ferro., 22, 291 (1998).
[34] A. T. Findikoglu, Q. X. Jia, X. D. Wu, G. J. Chen, T. Venkatesan, and D. W.
Reagor, Appl. Phys. Lett., 68, 1651 (1996).
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83
[35] V. N. Keis, A. B. Kozyrev, M. L. Khazov, J. Sok, and J. S. Lee, Electronic Lett.,
34, 1107 (1998).
[36] J. C. Booth, R. H. Ono, I. Takeuchi, and K.-S. Chang, Appl. Phys. Lett., 81, 718
(2002).
[37] S. Senguptaand S. M. Green, Appl. Surf. S et, 1 2 7 -1 2 9 , 486 (1998).
[38] Army Research Laboratory, Electronics and Power Sources Directorate,
Technology Briefs, http://www.arl.army.mil/
[39] B. Acikel, T. R. Taylor, P. J. Hansen, J. S. Speck, and R. A. York, IEEE MTTInt.
Symp. Digest, 3, 1467 (2002).
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84
CHAPTER 3 - STATEMENT OF THE PROBLEM AND
METHOD OF ATTACK
The general attractiveness of BaxSr(i.X)Ti0 3 thin films for microwave applications,
typically passive components, such as phase shifters, varactors, and filters, stems from its
many advantages over current technologies.
The material system exhibits a widely
tunable Curie temperature from cryogenic temperatures to well above room temperature1,
(depending on Sr content) which allows for the adjustment of the permittivity maximum
into the intended application temperature range. The non-linear dielectric properties are
also of great interest, as this material shows a highly field-dependent permittivity, which
is very useful for tunable microwave applications. It has been shown that capacitance
and dielectric constant of BST can be tuned up to 4;l 2'7. In addition, the fast polarization
switching allows for much faster tuning than semiconductor based phase shifters, and its
high breakdown field allows for greater power handling capabilities8.
All of these
features from a single material yield high potential for next-generation microwave thin
film devices. However, the moderate to high loss observed for BST thin films is its
limiting attribute.
Between the bulk and thin film form, there exist many differences in both the unit
cell structure and the electrical response of BST. These differences have been attributed
to a variety o f factors, as discussed in the previous section, but perhaps most importantly
the distortion of the lattice constants due to strain. It is precisely these strain effects
which are of great interest to understand in order to better control the properties of the
material.
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85
Strain is generally thought to have negative effects on the microwave properties
of BST thin films. The performance of ferroelectric thin film varactors, phase shifters,
and filters are known to be constrained by material limitations induced by the interfacial
stress generated between the grown epitaxial film layer and the single crystal substrate.
The resulting strain in the film has been shown to alter the dimensions of the unit cell,
which in turn, either directly or indirectly, affect the tunability, dielectric constant, and Q*
2 3 9-13
factor (the reciprocal o f the loss tangent) of the ferroelectric layer ’ ’ " .
Several groups are actively involved in investigating strain effects, and much
work still needs to be done to decouple the effects of strain, processing, and thickness
effects in the material. It is hoped that the feedback from such research will provide
microwave component manufacturers with the appropriate processing and fabrication
requirements of these materials, so that they will see more widespread and direct
application in next-generation microwave thin film passive components.
This research will investigate the effects of strain on the microwave properties of
Bao.6 Sro.4 Ti0 3 thin films.
Strain effects on the microwave tunability and dielectric
constant have not been studied over a wide range of film thickness from very thin layers
of 20 nm to thick films o f over 1 micron. The advantage of performing such a study is
the insight provided by the large changes in the strain, which occur over this thickness
range. In addition, by using different substrate materials, it is possible to perform this
study on both compressive and tensile strained films, which will provide additional
understanding o f how the strain state affects the electrical properties. Furthermore, the
fabrication of all films in a set (each covering the entire thickness range) will be carried
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86
out using the exact same processing conditions and procedures to allow direct
comparison between films o f the same thickness in different strain states.
Epitaxial film growth is the optimal deposition mode for controlling film strain.
Non-oriented polycrystalline films have lattice constants that are not as greatly dependent
on the substrate as epitaxial films because of the presence of grain boundaries which
allow the relaxation of the stress. Therefore, epitaxial thin films of BST will be deposited
with pulsed laser deposition over the thickness range of 20 to 1150 nm. The films will be
studied as a function of thickness and epitaxial strain, where the magnitude of the strain is
inversely proportional to the film thickness. Therefore, as the film thickness increases,
the strain in the film decreases and relaxes due to the formation of misfit dislocations14.
Bao.6 Sro.4 Ti0 3 thin films on both LaAlOs (referred to as compressive substrates, due to
the smaller lattice parameter of the substrate compared to that of the film) and MgO
(referred to as tensile substrates, due to the larger lattice parameter of the substrate
compared to that of the film) substrates were examined over this thickness range, and a
direct mapping between the strain and tunability will be created to better understand their
relationship.
Additionally, through a thorough discussion of the results of this project, the
following questions will be addressed and answered as completely as is possible based on
the findings of this study.
1. What is the effect of compressive and tensile strain states on the tunability and
permittivity at microwave frequencies?
2. How does this effect scale with film thickness, from very thin films of 20 nm to
thick films o f over 1 micron?
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87
3. What is the preferable strain state, in any, for microwave device fabrication from
BST films?
4. Is there also a thickness effect involved for very thin films which will limit the
tunability and dielectric constant?
5. How does strain affect the ferroelectric to paraelectric transition?
6. Do we observe the standard transitions for BaoftSro/riC^, from rhombohedral to
orthorhombic to tetragonal to cubic, (typically occurring at -150-165 K, -190220 K, and -250-278 K, respectively) over the studied temperature range of 78 K
to 320 K for thin films? If not, are the transitions suppressed due to strain?
7. How does the internal polarization change with temperature as the measurement
temperature approaches the ferroelectric to paraelectric transition?
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88
REFERENCES
[1]
B. Jaffe, W. R. Cooke, and H. JafFe, Piezoelectric Ceramics. Academic Press Inc.,
London, UK, 1990, p. 70-72, 91, 94,101.
[2]
W. Chang, C. M. Gilmore, W. J. Kim, J. M. Pond, S. W. Kirchoefer, S. B. Qadri, D.
B. Chrisey, and J. S. Horwitz, J. Appl. Phys., 87, 3044 (2000).
[3] W. J. Kim, H. D. Wu, W. Chang, S. B. Quadri, J. M. Pond,S. W. Kirchoefer, D. B.
Chrisey, and J. S. Horwitz, J. Appl. Phys., 88, 5448 (2000).
[4] P. Padmini, T. R. Taylor, M. J. Lefevre, A. S. Nagra, R. A. York, and J.S. Speck,
Appl. Phys. Lett., 75, 3186 (1999).
[5]
B. H. Park, Y. Gim, Y. Fan, Q. X. Jia, and P. Lu, Appl. Phys. Lett., 77,2587 (2000).
[6]
C. M. Carlson, T. V. Rivkin, P. A. Parilla, J. D. Perkins, D. S. Ginley, A. B.
Kozyrev, V. N. Oshadchy, and A. S. Pavlov, Appl. Phys. Lett., 76,1920 (2000).
[7]
W. Chang, S. W. Kirchoefer, J. M. Pond, J. S. Horowitz, and L. Sengupta, J. Appl.
Phys., 9 2 ,1528 (2002).
[8]
R. York, A. Naga, E. Erker, T. Taylor, P. Periaswamy, J. Speck, S. Streiffer, and O.
Auciello, Proc. 12th IEEE Int. Symp. on Appl. Ferro., 1, 195 (2000).
[9]
W. Chang, S. W. Kirchoefer, J. M. Pond, J. S. Horowitz, and L. Sengupta, J. Appl.
Phys., 9 2 ,1528 (2002).
[10] C. B. Parker, J.-P. Maria, and A. I. Kingon, Appl. Phys. Lett., 81, 340 (2002).
[11] L. J. Sinnamon, R. M. Bowman, and J. M. Gregg, Appl. Phys. Lett., 81, 889 (2002).
[12] C. L. Canedy, H. Li., S. P. Alpay, L. Salamanca-Riba, A. L. Roytburd, and R.
Ramesh, Appl. Phys. Lett., 77, 1695 (2000).
[13] H. Li, A. L. Roytburd, S. P. Alpay, T. D. Tran, L. Salamanca-Riba, and R. Ramesh,
Appl. Phys. Lett., 78,2354 (2001).
[14] Z.-G. Ban, and S. P. Alpay, J. Appl. Phys., 91, 9288 (2002).
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89
CHAPTER 4 - EXPERIMENTAL PROCEDURE/METHODS
This chapter describes the experimental techniques used to characterize the thin
films. It is divided into three sections: structural characterization for analysis of the thin
film microstructure; PLD conditions for optimum film growth, as well as PLD system
design and procedures; and microwave measurements, including data extraction models.
4.1
S t r u c t u r a l C h a r a c t e r iz a t io n
A variety o f structural characterization techniques were used to examine the
microstructure and the growth mode of the thin films at various processing conditions, in
order to find optimal processing conditions for epitaxial growth. Each of the following
sections describes the specifics of the characterizations techniques used in this study.
4.1.1
X - r a y D if f r a c t io n
X-ray diffraction measurements were used to determine the orientation, texture,
and the lattice parameters of the films in the normal and in-plane directions. The Bruker
AXS GADDS (General Area Detector Diffraction System) diffractometer was used for
collection o f this data.
This system differs from most conventional Bragg-Brentano
diffractometers, because o f the ability to collect diffraction data in 2D, rather than OD
point intensities in a step method using a scintillation detector. The greatest advantage to
this wide-area detector system is the ability to collect the desired data in a much shorter
time, as it collects a conic section of diffraction space in a single frame. Normally this
would require several separate scans with various rotations and sample re-positioning.
Figure 4.1 shows the portion of the diffraction cone that can be captured by a 2D detector
versus a single point on a slice through the diffraction cone by a typical scintillation
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90
detector. The section of the forward diffracted cone gives information on the texture of
the film, which can be defined as the spatial orientation of crystallites in the plane of the
film with respect to the normal.
Texturing appears as a distribution of diffracted
intensities along a conic section at a particular 20 value. Depending on the detector
distance from the sample, 50 to 70° of x-space (angle along the diffraction cone) can be
mapped, along with 52° in 20-space across the width of the detector face.
Forward Diffraction Cone
Scintillation Detector
GADDS Hi-Star
wide-area detector
Diffractometer Plane
X-ray beam
Detector Circle
Backward Diffraction Cone
Figure 4.1: Diffracted x-ray beam as seen by scintillation detector and GADDS Hi-Star wide area detector.
True epitaxial films show only point reflections for a particular Bragg condition1
satisfied by nA.=2dsin0. It is therefore, immediately apparent if a film is epitaxial from a
short scan with the GADDS diffractometer. In addition to a map of the reciprocal space,
showing the degree of orientation of the films, precision lattice parameter measurements
were made with ESDs (estimated standard deviation) in the range of 0.0005 to 0.001 A.
The geometry o f the GADDS diffractometer is shown in Figure 4.2.
The
position-adjustable wide-area detector sits along a track, which rotates around the center
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91
of the diffractometer. The range of the detector for this particular system was -27 degrees
to 89 degrees, a 20 range of 116 degrees. The x-ray source positioned directly opposite
the detector remains fixed. It is a 2kW maximum, rotating copper anode, with a graphite
monochromator, producing Cuk« radiation (A,=1.5418 A), focused to a point source with
a 0.5 mm circular collimator.
Hi-Star wide-area detector
z
^
Fixed Chi = 45° stage
X-ray source rC\
Alignment microscope
Figure 4.2: GADDS diffractometer with Hi-Star wide-area detector.
The 10 x 10 mm thin film samples were comer-mounted on a fixed chi (%= 45°)
stage. Figure 4.3 shows the configuration of the chi stage and the corresponding machine
directions x, y, z, as well as the sample rotation axis, co, with the arrow showing the
positive rotation direction.
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92
4
Thin film sample
z
jbBL'^v* •’sv
•***
i I
=%/
:^= d5®>-
<2>
Figure 4.3: Fixed chi stage (x=45°) showing thin film sample mounting position.
In order to ensure minimal sample displacement error, the surface of the thin film
sample was aligned on the center of the rotation axis of the chi stage, the z-axis. Samples
were installed on the stage, and aligned at ® = 0°, and to = 180°. The sample was rotated
back and forth between the two angles until the displacement error, or distance off of the
rotation axis, was reduced to near zero.
At this condition, the surface of the film
remained on the diffraction axis through the entire rotation from to = 0° to 180°.
In addition, to sample alignment issues, the detector position from the sample and
photon counting threshold as a function of position on the 2D detector face had to be
calibrated. The detector is capable of operating in two modes, 512 x 512 pixels, and a
higher resolution mode o f 1024 x 1024 pixels.
The choice o f operating mode is
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93
dependent on the desired measurement, but for most routine lattice parameter
measurements a setting o f 512 x 512 was acceptable. This is because the high intensity
point reflections from the single crystal substrate and epitaxial film were spaced far
enough apart to allow easy determination of the peak centroids. Scans were collected in
both resolution modes and showed no significant difference in the lattice parameters of
both film and substrate.
After choosing the appropriate resolution mode, the first step in detector
calibration was to establish threshold values for the photon detection across the entire
detector surface. This was accomplished by mounting a radioactive 55Fe source on the
chi stage in place of the sample. It emits a uniform spread of beta particles which were
recorded by the detector as photon events. After the “flood field” reached a saturation of
15,000,000 counts the flood calibration was complete.
The next step was to create a map of the position dependence of the ability of the
detector to count photon strikes. For this “spatial calibration” as brass plate with a grid of
drilled holes, spaced approximately 1 cm apart, was placed over the detector face (which
had a diameter o f 11.5 cm).
Again, the 35Fe source was used to simulate photons
impinging the detector. After recording 300,000 counts, sufficient intensity was recorded
at each grid point.
The GADDS calibration software then used this map to create a
position dependent correction function for the entire detector surface by interpolating
between the points o f the grid. This provided a uniform detector counting rate over the
entire area.
In order to accurately determine the distance from the sample to the detector,
calibration was made with a reference standard with known reflections. A capillary of
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94
crashed mica was mounted on the fixed chi stage and aligned. The capillary was set to
rotate in phi (the axis along the sample mount) and scan through 10° in omega about the
{» = -90° position (parallel with the x-ray beam) to provide a powder diffraction pattern
with concentric diffraction rings. The pattern was then matched with the standard dspacings from the JCPDS file for mica2. The center point and spacing of the concentric
diffraction rings was adjusted to match the image recorded by the detector.
In this
manner, the center point o f the detector, with respect to the x-ray beam, and the distance
from the sample were accurately determined.
In order to obtain accurate lattice parameter measurements with minimal ESDs
(estimated standard deviation), a scan was devised to collect as much data as possible
within the allowed range of the detector, using the aforementioned setup. Table 4.1 lists
the optimized scan consisting of seven parts, each overlapping the previous scan (except
for scan #7), through the detector’s range of -27 to 89 degrees.
Table 4.1: Scan settings used for lattice parameter measurements o f BST thin films.
Scan#
20
(o start
Phi
Chi
Scan axis
Step
# frames
Dwell (sec.)
1
30.0°
-85.0°
0°
45.0°
omega
0.25°
200
10.0
2
45.0°
-85.0°
0°
45.0°
omega
0.25°
240
10.0
3
52.0°
-85.0°
0°
45.0°
omega
0.25°
260
10.0
4
60.0°
-85.0°
0°
45.0°
omega
0.25°
280
10.0
5
75.0°
-85.0°
0°
45.0°
omega
0.25°
320
10.0
6
89.0°
-85.0°
0°
45.0°
omega
0.25°
360
10.0
7
-27.0°
-95.0°
180°
45.0°
omega
0.25°
200
10.0
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95
All scans were done with a 40 kV/40 mA beam, starting at +5° from grazing
incidence at a = -85° (or a = -95° for scan #7). For each position of the detector, a 20
width of 26° before and 26° after the setting was covered, essentially allowing coverage
from 4° to 115° in the positive direction and -1° to -43° in the negative direction.
After data collection, the frames were processed by setting threshold values for
the identification of diffraction spots. The software stepped through each frame picking
out the peak centroids for all reflections above the threshold setting. Following this
procedure, was the indexing of the list o f reflections. This process assigned indices to all
reflections and calculated a preliminary unit cell with all reflections, both film and
substrate included.
The next step in resolving the unit cell was to sort film reflections from substrate
reflections, based on omega error, x and y position errors, and h, k, and 1 (Miller indices)
errors. Once a suitable list was compiled, the film cells were then calculated with the
Bruker AXS lattice refinement program available in their GADDS software package. It
uses a least-squares method to fit all o f the identified reflections into a cell of specified
crystallographic constraints.
All lattice constants were refined with a non-linear triclinic constraint, which
essentially does not confine the lattice constants or unit cell angles to any particular
geometry. For all samples, the film cells were refined to achieve the lowest least squares
error, with no omega errors above 0.05°, x and y positional errors within a few pixels, and
h, k, and 1 errors below ±0.01.
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96
4.1.2
F ie l d -E m is s io n S c a n n in g E l e c t r o n M ic r o s c o p y
Film morphology and thickness were examined with a Leo-Zeiss Gemini 982
field-emission scanning electron microscope (FESEM). The main advantage to using this
type of SEM is that the films do not have to be coated with gold to prevent charging that
is normally associated with high accelerating voltages. Coating the films with even a thin
layer of gold must be avoided, as this will obscure the details of the film microstructure,
typically in the range o f 20 to 500 nm. The FESEM employs a (100) single crystal W tip
coated with ZrC>2 to reduce the work-function of the tip, thereby allowing electron
•5
extraction at much lower voltages than standard SEMs . The low work-function of the
Zr02-coated tip also translates to a very bright beam, with 10 times the number of
-i
electrons emitted versus conventional tips .
Two different modes of operation were used to examine the thin films, each
offering distinct advantages.
The first, and most common mode, is using the
backscattered electron detector. Samples were explored with beam voltages in the range
of 2 to 5 kV at a working distance of 7 to 12 mm. By biasing the detector to collect only
the backscattered electrons (electrons of highest energy), the topography of the film
surface could be imaged, providing good 3D relief, due to the larger depth of focus at
greater working distances.
The second way to image the films was using the secondary electron in-lens
detector. At lower working voltages, usually 1 to 2 kV, and at a much shorter working
distance of 3 to 5 mm, greater lateral resolution could be obtained for examining surface
structures. Using the in-lens detector, the film growth mode was examined, and the
dimensions of cluster sizes and surface crystals were measured.
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97
Preparing the samples for the FESEM involved fracturing the 10 x 10 mm
samples into two halves, followed by mounting on a piece of carbon tape on an aluminum
stud. The two pieces of the sample were mounted such that one piece would be used for
surface examination, while the other was mounted vertically for cross-section imaging.
In cross-section, both the film morphology in the growth direction and the film
thickness were examined. In this manner, the layer thickness of the film and of the
interdigitated electrode (patterned on top of the film) could be measured simultaneously.
Furthermore, the film thickness values measured with this method matched well with
those obtained using RBS.
4.1.3
A t o m ic F o r c e M ic r o s c o p y
A Nanoscope II atomic force microscope was used to measure the surface
roughness and topography of the films. It was used solely in a constant height, contact
mode (repulsive mode). In that configuration, the tip is scanned across the surface of the
sample, and the cantilever deflection signal is measured and used to create an image of
the surface. A schematic of the AFM is shown in Figure 4.4.
The scanning of the sample surface is accomplished by means of a piezoelectric
tube scanner. The tip is first brought within a few hundred microns o f the sample surface
by using the stepper motor and manual height adjustments. Then the final placement of
the tip on the surface is done with the voltage driven piezoelectric tube. The piezoelectric
also rasters the sample in the x and y-direction under the tip over the set scan area.
The deflection signal is measured by focusing a laser beam onto the top o f the
cantilever to which the tip is attached. The gold-coated surface of the silicon cantilever
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98
reflects the beam to a mirror just above the sample, and then into the photodetector. It
consists of two elements, where the difference signal between those elements is the
deflection signal, which is normalized by dividing it by the sum of the output o f the two
signals.
Mezodectric
_X
' "j*''
I.
HB
j
..
Sample
Figure 4.4: Nanoscope II atomic force microscope.
The tips used for scanning were Ultralevers from Thermomicroscopes, with a 10°
half-angle (angle between the center and edge of the cone shaped tip). There were four
separate cantilevers on each Ultralever, each with a 10° half-angle tip.
Two of the
cantilevers were short with higher force constants (1.6 and 2.1 N/m), and the other two
were longer, with smaller force constants (0.26 and 0.40 N/m). The cantilever with the
smallest force constant was used to be able to measure very small forces (deflections) on
the rather featureless films.
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99
To install a film in the AFM, it was mounted on a magnetic disc with double­
sided 3M Scotch tape. Once positioned in the microscope, the tip holder was installed.
The laser was then focused on the cantilever, and the total output signal of the two
element photodetector was maximized to between 5 and 6 volts, by adjusting the position
of the laser spot to reflect the maximum amount of light.
The difference signal, or
deflection signal, was set at a reference value of -4.0 volts.
After the laser and photodetector were set, the entire AFM was placed on a
vibration isolated platform to allow a sharp scan with little noise. The tip was then
automatically driven to the surface of the film. Once the tip contacted the surface, the x-y
scanner began to raster the sample over the set area.
Scans were performed over square areas with edges of 200 to 2000 nm, at a scan
rate of 2 Hz, or two lines per second of the 400 line scan. The scans were then analyzed
with the Nanoscope II software, which allowed statistical calculations o f the surface
roughness, as well as the generation of 3D surface maps.
4.1.4
R u t h e r f o r d B a c k s c a t t e r Spe c t r o s c o p y
Film stoichiometry and thickness were determined with Rutherford backscatter
spectroscopy (RBS).
^ i
RBS involves the impingement o f low-MeV He
ions upon a
sample, and the measurement of the number of ions backscattered as a function of
backscattering energy (a schematic of the experimental setup for RBS is shown in Figure
4.5). Typically 4He2+ ions are used, enabling the detection of Li and heavier atoms. The
sensitivity varies as Z and thus heavier atoms are more easily detected at lower
concentrations, and sample thickness up to several hundred nanometers can be profiled4.
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100
Focusing
Collimators
Mamets
|
|
Accelerator
4He2+ ions
Tfrin flliw
Nuclear particle
detector
Figure 4.5: Schematic ofRBS system.
In order to determine the mass, and hence the identity of the atoms in the thin film
sample, a relation between the incident energy and mass of the He ions, and the
backscattered energy resulting from collisions in the sample is derived by using
conservation of energy and momentum.
The energy transfer resulting from an ion
striking an atom in a crystal depends only on the masses and the angle of the scattering
event. Therefore, the mass o f the target ion can be measured based on the energy of the
incident ion as it scatters into a fixed angle. The scattering energy can be described by
the equation5,
E S= K * E.I
(4.1)
where K is the kinematic factor, depending on the scattering angle 0 (which is measured
from the incident direction to the scattering direction).
(4.2)
E
o
M2 +M]
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101
Figure 4.6 illustrates the scattering of an ion Mi from an impact with a target atom M 2 . It
can be shown that at 180° the ratio Ei/E0 has its lowest value, due to the fact that
maximum energy is transferred to the target atom for direct backscattering.
M-.
Figure 4.6: Ion scattering of incident He+denoted Mb with target atom M2.
The atomic concentration, N, or number o f target atoms per cm3, (with N = Ns/ t ,
where Ns is the atoms/cm and t is the film thickness) can then be determined, without the
need for standards, from a basic principles calculation of the probability of the incident
ion scattering. This probability is represented by the differential scattering cross-section5,
da/dQ, which is measured as the number of detected particles Qd, scattered through a
differential solid angle Q, about the detector angle 6, relative to the number of incident
He ions Q.
Q , = N sQ ^ d n
d
<Xl
(4.3)
The RBS system employed in this study used 1.72 MeV He2+ ions, with a detector
resolution of 15 keV, positioned at an angle of 165° with respect to the beam line, at a tilt
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102
o f 7°. The yield was plotted as a function of both energy and channel number. The
overall shape of the energy spectrum was a result of the additive intensities of the peaks
from each of the individual elements in the film. In order to determine stoichiometry and
thickness, the SRIM simulation program was used to create a pattern based on the known
elements in the sample. Various iterations were then run, changing the stoichiometry and
thickness, until the simulated pattern matched the collected data.
Typical simulation
accuracy was within 5% for films on LaA1 0 3 , due to the high background signal of the
La.
4.1.5
M e d iu m E n e r g y I o n S p e c t r o s c o p y
To study the quality o f the epitaxial film in the growth direction, channeling
experiments were performed using a medium energy ion spectroscopy system (MEIS).
This system is very much similar to RBS, except it uses a beam of protons, with energies
around 100 keV. The protons are accelerated and focused to a narrow beam, and the
energies of backscattered protons are measured with a nuclear particle detector, just as in
the RBS system.
However, since the beam is of much lower energy, it is ideal for
exploring the first few layers of the film surface, as it will not penetrate more than
-10 nm into the sample5.
In general, channeling refers to the path taken through the crystal lattice when the
incident particles undergo small-angle scattering and are confined in the open channels
along one of the major crystallographic axes of the lattice, while penetrating deep into the
sample (shown in Figure 4.7). The particles may travel far into the sample before a large-
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103
angle scattering event occurs. As a result the number of backscattered particles reaching
the detector drops significantly, by a factor of
10
- 1 0 0 , depending on the crystallinity5.
SHADOW
CONE
X
100 ,
Figure 4.7: Channeling of particles along a major crystallographic direction via small-angle scattering3.
If a particle approaches too closely to the atoms defining the wall of the channel
then a large-angle backscattering event will occur. For an angle of incidence parallel to
the atomic planes, y/= 0 °, a minimum value, rmin, can be defined so that if a proton comes
within this radius it cannot channel. Therefore, for a column of atoms in a crystal, there
is an area around each column equal to 7tdmin in which the incident particles cannot
channel. Particles that enter the crystal at a position r>rmi„ can channel. The region
outside of rmin up to the midpoint to a nearest neighbor atom is defined as nr0 ,
.2
1
W 0 = T77
~ Nd
(4-4)
with N equal to the atomic concentration o f atoms, and d is the atomic spacing along the
string5. The ratio of m^min / w 02 is known as the minimum yield, or Xmin (Figure 4.8).
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104
The quantity rmin is approximately
0 .1
A, with the minimum yield on the order o f 1 %,
with -99% channeling5.
®T '
icr2
Figure 4.8: Channeling zone (blue) for center atom, defined by r ^ and r0.
Channeling measurements were performed on an annealed BST film on LaAlC>3 .
The minimum yield, Xm^ for the case of normal incidence, was measured after
thoroughly cleaning the surface of any carbon contaminants. The spectrum was then
simulated with the same program (SRIM) used for the RBS spectra.
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105
4 .2
P u l s e d L a s e r D e p o sit io n of B S T T h in F ilm s
Pulsed laser deposition (PLD) was the method chosen to fabricate thin films of
BaoeSro^TiOs on (100) LaAlOa and (100) MgO substrates. A RrF excimer laser (X = 248
nm) was used to ablate a die-pressed powder target of the desired composition. It was
focused to a laser energy density of 2 J/cm2, at a pulse frequency of 2 Hz, with a laser
spot size of 1 mm x
8
mm. The laser was operated at a pulse energy of 230 mJ, to
compensate for the 70 mJ energy drop as the beam passed through the “beam cutter”,
focusing lens, and window on the deposition chamber. Films grown on LaA 1 0 3 were
deposited at 700°C, while on MgO they were grown at 825°C. All films were deposited
in an oxygen background gas pressure of
approximately 8.25 cm.
100
mTorr, and a target-to-substrate distance of
The deposition time varied depending on the desired film
thickness. Nine samples were created for each film series covering the thickness range of
20 nm to over 1 micron, as shown in Table 4.2. Figure 4.9 shows the deposition rate for
films grown with the aforementioned conditions, which was approximately
100
nm/hr.
Table 4.2: Deposition times for growth of films.
Film
Thickness
(nm)
22
44
Deposition
Time
15
min.
30
min.
110
1 .0
hr.
160
270
400
1.5
hrs.
3.0
hrs.
4.5
hrs.
625
825
1150
6 .0
8 .0
1 2 .0
hrs.
hrs.
hrs.
After deposition, the films were either annealed or cooled to room temperature
without a post-anneal (both procedures were done in-situ with the substrate still fixed to
the heater). Annealed films were first cooled from the deposition temperature to 500 °C,
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106
at the deposition pressure o f 100 mTorr o f oxygen. Once the temperature dropped to 500
°C, the chamber was filled with 1 Atm of oxygen, and the sample was allowed to soak for
a time equal to half of the deposition time (e.g. A 3.0 hour film would anneal for 1.5
hours). After annealing was complete, the sample was allowed to cool naturally to room
temperature.
This particular annealing schedule was chosen to allow a sufficient time for the
film to further crystallize through the coalescence of individual clusters6. It promoted the
removal of misfit dislocations , generating highly epitaxial films with strain states
dependent on the lattice mismatch with the substrate.
1200
^ 1000
S
|
i
JS
H
800
600
E 400
S3
200
0
2
4
6
8
10
12
Deposition Time (hrs.)
Figure 4.9: Film thickness vs. deposition time showing linear deposition rate.
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107
4.2.1
P L D S y s t e m D e s ig n
A pulsed laser deposition system, in the most basic sense, consists of a deposition
chamber, a vacuum system, and a laser. Since PLD is limited to research laboratories,
and not a commercial manufacturing process, there are few companies that supply the
components for constructing a system.
The 12 inch diameter deposition chamber, along with the substrate heater
assembly and target carousel, were purchased from Neocera in Beltsville, MD.
The
main advantage of their spherical vacuum chambers is that they provide a more uniform
temperature profile in the chamber so that the plume does not pass through any large
temperature gradients.
In addition, the large interior volume allows for maximum
positioning capabilities o f the substrate heater block and other deposition monitoring
equipment. The laser port of the chamber was sealed with a UV transparent fused silica
glass window. Two other Pyrex viewports, one on top of the chamber, and the other on
the side, were included to allow optimum viewing of the plume position relative to the
substrate heater block.
The substrate heater assembly was manufactured on an
8
inch flange for attaching
to the vacuum chamber. It consisted o f a 2 inch diameter Inconel alloy heater block with
coiled resistance heaters and a type K thermocouple imbedded in the block. The current
supply to the heater coils, as well as thermocouple output, was monitored by a
EuroTherm temperature controller (model 2408). The maximum operating temperature
for this system was 950 °C, with a temperature stability of ± 1 °C. The substrate heater
flange also had a separate mechanical feedthrough for a steel shutter to shield the
substrate surface during target cleaning prior to deposition.
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108
The target carousel was also built on an
installation of six different
1
8
inch flange, allowing space for the
inch diameter targets, with the capability of rotating the
carousel between targets without breaking the vacuum. The targets were rotated through
a separate mechanical feedthrough at a rate of 17 rpm. A target shield with a single
circular cut-out was also incorporated to prevent the plume from contaminating the
surface of the other targets during deposition.
The deposition environment was controlled through the means of an MKS gas
pressure control system.
Most PLD work is done in an oxygen environment in the
pressure range o f 10 to 500 mTorr, and appropriate size control valve was needed to
allow pressure control over this range. The MKS Type 248A control valve was chosen,
which allowed a controlled flow of ultra-high purity oxygen gas (99.99%) through the
range of 1 to 1000 mTorr. This was connected to an MKS Type 250E pressure/flow
controller, along with the MKS Baratron Type 626A absolute pressure transducer. The
signal from the pressure transducer was used to provide feedback for the opening and
closing of the solenoid control valve to maintain a constant pressure in the deposition
chamber. The MKS controller operated using a phase delay of 7 sec., and a gain o f 10%,
on a 0 to 10 V signal corresponding to the 1 to 1000 mTorr pressure range.
The control valve was place directly across from the vacuum pump port where
oxygen gas would be draw out of the chamber, so that it would first flow across the path
of the plume and substrate surface. The Baratron pressure transducer was placed on the
opposite side o f the chamber to ensure that the flowing oxygen environment was of the
desired pressure.
These components, as well as all of the other aforementioned
equipment are shown in Figure 4.10.
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(b)
Figure 4.10: Pulsed laser deposition system constructed by the author,
(a) target carousel view, (b) substrate heater assembly view
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110
The vacuum system consisted of two independent pumping systems. The primary
high-vacuum system was a Leybold TMP 151 turbopump backed by a Leybold D16B
mechanical roughing pump charged with Leybold HE-200 hydrocarbon oil.
turbopump was connected to the bottom
8
The
inch port on the deposition chamber, and
capable o f pumping the chamber down to approximately IQ' 6 Torr, sufficient for
evacuation o f airborne contaminants and water vapor.
In order to isolate the high vacuum system from the chamber, an
8
inch manually
operated gate valve was used to seal the bottom port of the chamber. The gate valve was
closed when the second mechanical pump, connected directly to the chamber, was in
operation during both the initial pumping from 1 Atm, and during the deposition process.
The secondary pumping system was a Leybold D16BCS mechanical pump,
designed for corrosive service. It was used to evacuate the chamber prior to switching
over to the high-vacuum system, as well as pumping pure oxygen during the deposition
process. To allow this, the pump was charged with fluorocarbon oil, either Fomblin or
Leybold HE-1200. A simple right-angle valve was used to isolate this pump from the
chamber, when the high-vacuum system was in operation.
To accurately monitor the pressure inside the chamber, several different types of
vacuum gauges were used, depending on the pressure range. A Kurt J. Lesker (KJL)
IG4400 ionization gauge controller was used to monitor the pressure below 1 mTorr, as
measured with a standard Bayard-Alpert ion gauge.
Pressures above 1 mTorr were
monitored with both a KJL-6000 thermocouple pressure gauge (connected to the
IG4400), and a Granville-Phillips Series 275 Convectron gauge with independent
controller.
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I ll
Finally, the laser used for ablation of the BST target was a Lambda Physik
Compex 205 (fluorine version). It was a KrF excimer laser operating at 248 nm, and
capable of a maximum output power of 30 Watts, with a maximum pulse energy o f 650
mJ, and a maximum repetition rate of 50 Hz. The laser beam profile directly from the
laser was a rectangle o f approximately 1 inch in height and Vi inch in width. It was
focused into the deposition chamber, through the UV transparent fused silica window,
with a single UV grade, plano-convex lens that had a focal length of 19 inches. A “beam
cutter” was also used to remove the non-uniformity of the edges of the laser beam. It was
fabricated from a plate of aluminum, cut to dimensions slightly smaller than the beam
profile directly out of the laser; it was positioned before the focusing lens.
4 .2 .2
T a r g e t P r e p a r a t io n
The quality o f the target material is very important in growing a high quality
films.
Any impurities in the target will obviously be present in the deposited film.
Commercially sold targets are often less than adequate in terms of phase purity,
homogeneity, and impurity level due to the starting materials and processing route by
which the bulk ceramic is fabricated. Therefore, targets that have been made “in-house”
with strict process control and high purity powders are best. Bulk single-crystal, opticalquality material is an alternative, however, there is not a great variety of dielectric
materials, for electronic applications, available in this form.
The Bao.6 Sro.4 Ti0 3 targets made for this study were fabricated from a
commercially available 99.9% pure nanopowder, made by Nanophase, Inc. (New
Mexico). The following processing steps were used in the fabrication o f the BST targets.
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112
Batch preparation
1. The BST powder was mixed in a 250 g batch with 15 g o f a 10 wt% polyvinyl
alcohol solution.
2. The batch was then set on the ball-mill for 2 days (without grinding media) to
further mix the PVA with the powder.
3. The coated powder was then ground by hand with a mortar and pestle.
4. The powder was sieved with a coarse 1 mm screen to remove large
agglomerates o f PVA.
5. Steps 3 and 4 were repeated for a second time.
6
. The powder was sieved through a 150 pm screen, and then ground with
mortar and pestle, and sieved. This was repeated three more times.
7. After the final sieving, the powder was dried in a steel pan at 80 °C to remove
adsorbed surface water.
8
. The powder was then ground with mortar and pestle and sieved through the
150 pm screen for the final time.
9. The batch was then divided into amounts of 15 g for die-pressing.
Die-Pressing
1. A 1.33 inch diameter, D2 tool-steel die was sprayed with silicone lubricant
and filled with 15 g of the prepared BST powder.
2. The powder was then compacted to 2,500 psi, and then allowed to springback
to release trapped air.
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113
3. The pellet was pressed to 10,000 psi, to a green density of approximately
55%, and then ejected from the die.
Binder Burnout
1. The PVA was then removed from the pellets by placing them in a furnace on a
piece o f porous zirconia.
2. The pellet was then heated to 220 °C at 2 °C/min, and allowed to soak for 3
hours.
3. The temperature was then increased to 450 °C at 2 °C/min, followed by
another soak for 3 hours.
4. The furnace was then shut down and allowed to cool naturally to room
temperature.
Sintering
1. To prevent the pellet from warping during sintering, pellet was sandwiched
between two alumina trays, with a thin layer o f loose Nanophase BST powder
on the top and bottom of the pellet to prevent any contamination from the
alumina tray surface.
2. The pellet was then heated to 1525 °C at 7 °C/min and allowed to soak for 3
hours.
3. The pellet was then slowly cooled to 1000 °C at the rate of 15 °C/min.
4. The furnace was then shut down and temperature was brought to room
temperature at the natural cooling rate of the furnace.
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114
The final sintered density of the targets was calculated by simply dividing the
mass by the volume (determined from measuring the dimensions of the pellet with a
caliper), and comparing it to the theoretical density of Bao.6 Sro.4 Ti0 3 (5.683 g/cc). Only
targets with densities above 90% were used for deposition, with most targets sintering to
90-92% of theoretical density.
4.2.3
P r e p a r a t io n
of
Su b st r a t e
and
P r e - d e p o s it io n C o n d it io n s
The cleaning of the substrate, the preparation of the chamber vacuum
environment (or the base pressure before deposition), and the pre-anneal heat treatment
of the substrate are necessary steps in obtaining high quality films.
After sample installation, the chamber is pumped down to a pressure of about 10' 6
Torr to promote the desorption of water vapor and other organic contaminates that enter
the chamber each time it is exposed to the atmosphere.
Under vacuum these
contaminates will desorb from all surfaces inside the chamber, and be swept into the
vacuum system. By keeping a record of the base pressure vacuum obtained in the set
time allowed for pumpdown, the cleanliness of the deposition chamber can be gauged.
Therefore, if the vacuum does not drop to a suitable pressure during the normal time
allowed for pumpdown, the chamber must be baked out at high temperature (900 °C).
A pre-annealing of a substrate is also done to prepare the surface for film
deposition. This involves heating the substrate in vacuum and in the presence oxygen to
remove most organic surface contaminants and to homogenize the substrate surface.
Through the removal o f most of the organic contaminants on the substrate surface, the
number of defects in the film is reduced.
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115
The standard operating procedures used to clean the substrate and prepare the
chamber vacuum for film deposition are described in a shortened procedural manner
below.
1. Place substrate in a beaker of acetone for a few minutes.
2. Rinse the substrate in acetone, then methanol, and place in a beaker of
methanol for a few minutes.
3. Rinse the substrate in methanol, then rinse with deionized water, and dry with
clean nitrogen.
4. Shake the silver paint (Leitsilber 200, available from Ted Pella Inc., Redding,
CA) vigorously and apply small drop on substrate heater block.
5. Carefully place the substrate on the drop of silver paint and allow it to flow to
edges, while gently pressing on each comer of the substrate with Teflon
tweezers.
6
. Dry the silver paint by heating to 150 °C.
7. Shut off the heater and allow the organics from the paint to continue burning
off. When the temperature drops to 120 °C, install the heater flange into the
chamber and restart the heating program for deposition.
8
. Begin pumping out the chamber with the mechanical pump #2.
9. At -50 mTorr bleed oxygen into the system to flush out contaminants and
wait for pressure to drop below 50 mTorr. Repeat this two more times dining
roughing pumpdown.
10. Begin pumping out the turbopump with mechanical pump #1.
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116
11. Wait for the heater to reach deposition temperature and the chamber vacuum
to drop below 2 0 mTorr.
11. Start the turbopump, and switch the vacuum from mechanical pump #2 to the
high vacuum system by closing the valve to mechanical pump
# 2
and opening
the gate valve to the turbopump.
12. Allow the system to pumpdown for 1 Vi hours at minimum. The pressure
should be below 5 x KT6 Torr before continuing.
13. Next the transition from high vacuum to the oxygen pre-anneal stage is made
by closing the gate valve to the turbopump, and immediately introducing
100
mTorr of oxygen.
14. The valve to mechanical pump #2 (which is charged with Fomblin, and can
pump pure oxygen without an explosion hazard) is then reopened to establish
a flowing oxygen environment.
15. The substrate will then be allowed to soak in the oxygen environment for 1
hour, during which time, the surface contaminants can react with oxygen and
bum off.
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117
4 .3
M e a s u r e m e n t o f X - B a n d M ic r o w a v e P r o p e r t ie s
In order to measure the microwave response of the BST films, a suitable
microwave electrode needed to be patterned on the surface o f the films.
Since
microwave testing requires that the dimensions of the electrodes be many times smaller
"7
(—1 0
3
-1 0
o
) than the wavelength of the test signal, a photolithographic metallization
technique was required to deposit devices with gap sizes around
10
pm.
A collaboration was formed with the U.S. Naval Research Laboratory (NRL) in
Washington, D.C. where both metallization and microwave testing could be
accomplished.
The following sections discuss the specifics of both the electrode
preparation and the microwave measurements as carried out at the NRL.
4.3.1
I n t e r d ig it a t e d C a p a c it o r F a b r ic a t io n
An interdigitated electrode was chosen as the most suitable way to measure the
microwave capacitance, tunability, dielectric constant, and loss. Models were already in
existence and in use at the NRL, where device testing using interdigitated capacitors
(IDCs) was a common practice. The IDC structures were arranged in 3 x 4 arrays, with
gap sizes of 6 , 8 , 10, and 12 pm along a row, and finger lengths of 40, 60, and 80 pm in
each column, as shown in Figure 4.11.
They were patterned on the films using the
NRL’s multilayer photolithographic lift-off process9, with the metallization deposited by
e-beam evaporation. The electrodes were a layered structure starting with a 20 nm Cr
adhesion layer (to promote good bonding between the film and electrode), followed by
1.5 pm o f Ag, and capped with 50 nm of Au to prevent oxidation of the surface of the
IDC.
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Figure 4.11: Interdigitated capacitor array.
It was necessary to make the electrode very thick for the purpose of reducing
resistance and inductance losses in the IDC itself.
The electrode should ideally be
several times the skin depth of the metal (8 ), which is the distance over which an
o
electromagnetic field will decay to 1/e of its initial strength . It is defined as,
where
oj
is the angular frequency (a)=2nf), fx0 is the permeability o f free space (4 7 t* 1 0 ‘ 7
H/m), and cr is the conductance (for Ag, cr = 0.617* 108 S/m). Therefore, the 1.5 pm IDC
electrode is 2.3 times the skin depth of Ag at 10 GHz, which is equal to 0.64 pm.
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119
The photolithographic patterning of the IDC was done in a cleanroom
environment according to the procedure outlined below. Figure 4.12 (at the end o f the
procedure) illustrates this process step by step.
Cleaning the film surface before first coating
1. Scrape the silver paint residue from the reverse side of the sample with a razor
blade, and blow away residue with dry N 2 .
2. Soak the sample in a beaker of trichloroethylene, acetone, isopropyl alcohol,
and deionized water. Between solutions, rinse in a stream of current solution,
then next solution. Place on bibulous paper and dry with N 2 . Put the sample
on hot plate at 110 °C for a few minutes to remove all water.
1st layer-PM M A
3. Place the sample on a spin coater, and start the sample spinning at 2500 rpm.
Blow N 2 over sample to remove dust while spinning. Place three drops of
polymethylmethacrylate (PMMA is 4.5 % solids in chlorobenzene) on center
of spinning sample and wait 15 seconds, then increase to 6000 rpm, and wait
10 seconds. Stop spinner and carefully use tweezers to push sample from the
holder (PMMA is sticky). If sample if dropped or mishandled, damaging the
PMMA coating, wash away PMMA with acetone, IPA, and DI water and stmt
again. (Note: For 5x5 mm samples, use 7,000 rpm for the second spin.)
4. Place the sample in oven at 200 °C for 1 hour to harden the PMMA.
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120
2nd layer - Copper
5. Deposit 2000 A with the e-beam evaporator (manufactured by CVC Products,
with a Telemark e-beam gun) at a rate of 15 A/sec.
3rd layer - 1818 Photoresist
6
. Place the sample on the spin coater and the start the sample spinning at 6000
rpm.
Place
three
drops
of
1818
Photoresist
(manufactured
by
Microlithography Chemical Corporation) on the center of the sample and wait
30 seconds. Stop the spinner and remove the sample without damaging the
1818 coating.
7. Place the sample in the oven at 90 °C for 15 minutes to harden the 1818
Photoresist.
IDC patterning o f 3rd layer - Near-UV exposure
8
. Inspect the IDC electrode mask for contamination.
Clean it using same
procedure as for sample. After the deionized water rinse, spray isopropyl
alcohol onto mask and blow dry with N 2 . Clean the glass side first, then the
chromium coated side (this side will be in contact with the 1818 Photoresist).
Align the sample so that the IDC electrodes will be parallel with the edges of
the sample. Expose the 1818 Photoresist layer to near-UV light (Hg vapor
bulb at -300-350 nm) for 3.5 seconds to weaken the 1818 in the area of the
IDC structure.
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121
Removal of 3rd layer (in IDC area only)
9. Develop 1818 Photoresist using a mix of Developer 351 and deionized water
in a 1:1 ratio (351 manufactured by Microlithography Chemical Corporation).
Dip into solution for 10 seconds and then rinse with solution for 2.5 seconds.
Immediately dip into beaker o f deionized water, then rinse with DI water and
dry with N 2 . Check under microscope with green incandescent filter (GIF) if
the 1818 has been removed in the electrode areas. These areas should look
clean with no residue. If 1818 remains then dip again for 1-2 seconds, rinse,
and check again.
10. Place the samples in the oven at 90 °C for 15 minutes to re-harden the 1818
Photoresist.
Etching IDC into 2nd layer
11. Etch the Cu layer with FeCl solution. (Note: This is the most critical step!)
Dip in the solution for 4-5 seconds and immediately rinse in deionized water
and dry with N 2 . Check under the microscope with the GIF filter if the Cu has
been etched from the electrode area. If some remains, dip for 0.5-1 second
and immediately rinse in deionized water, and check again.
Complete removal of 3rd layer
12. Expose the 1818 Photoresist layer to near-UV light (Hg vapor bulb at -300350 nm) for 30 seconds.
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122
13. Remove the 1818 Photoresist layer using the Developer 351 and deionized
water mix (1:1 ratio). Dip into the solution for 10 seconds and observe the
dark top layer dissolving. Rinse with DI water and dry with N 2 .
IDC patterning o f 1st layer - Deep-UV exposure
14. Expose the PMMA with Deep-UV light (Xe vapor bulb -254 nm) for 45 min.
to 1 hour to weaken the PMMA in the IDC area.
Removal of 1st layer (in IDC area only)
15. Develop the PMMA using methyl-isobutyl ketone (MiBK).
Dip into the
solution for 15 seconds and dry with N 2 . DO NOT rinse with deionized water.
The film surface is now exposed and ready fo r the IDC metallization.
Deposition of the IDC electrode
18. Install the sample into the e-beam evaporator and allow the chamber to
pumpdown overnight to obtain a vacuum of <1.0 x 10' 6 Torr. Deposit the
multilayer electrode. The first layer is
A/sec, then 1 .5 pm of Ag at
10
2 0 0
A of Cr, at a deposition rate o f 5
A/sec, and finally 500 A of Au at 5 A/sec.
Lift-off o f negative area of IDC array
19. Soak the sample in acetone overnight to dissolve the PMMA layer leaving
only the loose copper layer around all of the IDC structures.
20. Remove the samples from acetone and use a dry N 2 gun to blow away excess
metallization, leaving the IDC array.
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123
_J
Deposit 2000 A Cu layer
Spin on PMMA
i
1*1-4
|
L
Spin on 1818 Photoresist
|
Near-IT csposure to
pattern IDC array
Develop 1818 Photoresist
Etch Csi layer with
FeCI solution
tilt
Removal of 1818 Photoresist
Deep-UV exposure to
weaken PMMA
Removal of PMMA to
expose film surface
Soak in acetone to
dissolve PMMA
Lift off excess metallization
iitl
Deposition of IDC
Figure 4.12: NRL multilayer photolithographic lift-off process for patterning of IDC array.
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124
4 .3 .2
M ic r o w a v e S n M e a s u r e m e n t s
Microwave dielectric measurements were performed using a single-port Sn
measurement technique, in which scattering parameter and phase data are collected.
This data is later converted to device impedance and modeled accordingly to extract the
capacitance, dielectric constant, and loss. Data was taken with an HP 85IOC vector
network analyzer with an HP 8516A S-parameter test set in the range of 1 to 20 GHz, as
a function of DC bias from -40 to +40 V. A Keithley 230 programmable voltage source
was used to apply up to +/- 40 V DC bias for tunability measurements, and two HP
3478A multimeters were used to monitor and stabilize the DC bias.
The same
measurements were also performed as a function of temperature using a cryogenic
microwave prober.
The only difference between room temperature and cryogenic
measurements was the probing station. The basic equipment setup (excluding the probe
station) for both of these measurements is shown in Figure 4.13.
The following sections discuss the specifics of the room temperature and
cryogenic microwave measurements, as well as the extraction of the data by a parallel
resistor-capacitor model and conformal mapping techniques.
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125
H P 8510C N g f f o r k A B a l m r
Kettiiley 230 Voltage Source
Common Output
Q
Q
(Back)
Port IBias
(Back)
Com puter
GPm
100 Q
±0-05%
Type500-D
HP M7HA M ultim eter n l
HP 3478A M ultim eter #2
c j"
1 0 Hi
■©
(Frcait)
(Front)
La
Input
(Barit)
Figure 4.13: Microwave measurement equipment connections.
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I GHB \
2 layer
126
4 .3 .2 .1
R o o m T e m p e r a t u r e M ic r o w a v e M e a s u r e m e n t s
The properties o f the BST thin films were first measured at room temperature.
Device capacitance, dielectric constant, and loss were obtained from the scattering
parameter and phase data collected with the aforementioned experimental setup. In order
to ensure that the microwave measurements were accurate, several steps were taken to
eliminate noise and errors through the careful connection of microwave test components
up to the microwave probe tip, and the calibration of the HP 85IOC vector network
analyzer.
In order to measure the IDCs in a single-port Sn reflection mode, a signal and
ground connection was made with the two contact pads of the IDC.
Picoprobes from
GGB Industries, Inc. were used, with a signal-ground tip configuration and a pitch size
(gap size) of 200 pm, rated to 40 GHz (part# 40A-SG-200-LP).
The probes were
connected to x-y-z micropositioners from Line Tool which allowed precise x-y
movement of the tip over the IDC, and z-direction movement for placing the probe on the
IDC contact pads.
In addition, due to the micron-size features of the device, a
stereomicroscope with
120
x magnification was used to be able to accurately place the
microwave probe tip on the IDC structure.
All connections from the Picoprobe to the network analyzer were gold-plated
threaded coaxial couplings, with the appropriate adapters to convert from the small
diameter probe conduits to the large inputs of Port 1 on the network analyzer.
The
couplings were secured with a standard torque wrench with the appropriate force setting
for the specific microwave conduit. All conduits were then securely fastened to the work
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Ill
station area to prevent movement during testing, which would stress the connection
points and influence the transmission of the microwave test signal.
Once the probes had been set up, the calibration of the network analyzer was
necessary to account for the impedance o f the conduits leading to the device, and the
stray capacitance and inductance of the probe. This was accomplished using a GGB
Industries microwave calibration substrate (#CS-8 ). The alumina substrate was patterned
with gold OPEN, SHORT, and 50 Q LOAD devices. The calibration proceeded with a
measurement o f each of these devices, followed by the automatic calculation of
calibration coefficients, by the network analyzer, for each of the points in the frequency
range of the measurement. Standard sweeps from 1 to 20 GHz were done in STEP mode
with 400 data points and an averaging factor of 64.
The DC bias for tunability measurements was also applied in a step-wise manner,
in increments o f 5 volts, with a current of -100 and +100 mA. All measurements began
with a 4 cycles of the bias from -40 V to +40 V, to remove any trapped electrical charge
in the film layer. The bias sweep, as well as the actual microwave measurement, was
controlled with a visual-basic program run with Norton System Commander.
The
program controlled the operation the network analyzer and other auxiliary equipment
through GPIB connections, and collected the scattering parameter data.
As mentioned previously, the IDCs were arranged in 3 x 4 arrays, with varying
gap sizes and finger lengths. Whenever possible, the device with the smallest gap
and longest finger length (80 pm) was used to test the film properties.
(6
pm)
This is to
maximize the confinement o f the microwave field to the film layer with the smallest gap,
and minimize the contribution of the end gap of each finger by using the longest fingers.
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128
4 .3 .2 .2
C r y o g e n ic M ic r o w a v e M e a s u r e m e n t s
Microwave measurements were also made as a function of temperature in the
range o f 78 to 328 K. They were very much similar to the standard room temperature
measurements excepted for the probe station used to contact the devices. Due to the fact
that the devices were cooled below the freezing point of water, the entire probe station
was enclosed in a vacuum chamber to avoid the condensation of water vapor. Therefore,
in order to measure the IDC devices inside the vacuum vessel, microwave feedthroughs
with flexible bellows were necessary to be able to move the probe onto different devices
and between samples.
The microwave cryogenic system was manufactured by RMC-Cryosystems,
which included built-in micropositioners and microwave conduits. The probe was the
same model Picoprobe as used for room temperature. Samples were secured inside the
vacuum chamber with thermally conductive vacuum grease to effectively draw heat from
the samples, so that the temperature measured by the thermocouple mounted in the metal
sample holder was the actual sample temperature.
The samples were prepared by first pumping out the vacuum system until the
pressure was in the range of 10' 6 Torr, followed by cooling the samples down to 78 K
with liquid nitrogen. The temperature was increased in steps (either 5 K or 20 K) and
allowed to stabilize before each measurement.
Measuring devices over such a wide temperature range required calibration of the
network analyzer across the entire temperature range, in order to ensure that the
scattering parameter and phase data were accurate. Calibration was performed using the
same GGB Industries substrate (installed into the vacuum chamber with the samples) and
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129
procedure as described in the previous section. In addition, the capacitance of the OPEN
device, the inductance o f the SHORT device, and the impedance of the LOAD device
required adjustment, as these parameters changed with temperature and caused a drift in
the calibration of the network analyzer.
A drift in the open circuit calibration was seen when the probe was lifted from the
IDC. This was caused by an over estimation of stray capacitance, and subsequently
corrected by changing the first-order capacitance of the OPEN device to smaller values at
lower temperatures (within the range o f 1 to 10 fF). Similarly, the first-order inductance
of the SHORT device was adjusted in the range of 1 to 20 pH. The impedance was
corrected by directly measuring the impedance of the LOAD device through the Port 1
bias connection on the network analyzer.
The value, typically higher at lower
temperatures, due to the contraction of conduit connections (which create small gaps
around some of the pins in the connectors), was input as the new Z0 for the standard
internal impedance o f the network analyzer (normally 50 Q). These parameters were
checked at each temperature increment and on average required adjustment when the
temperature was increased by more than 80 K.
Samples were measured in increments of 20 K, with a standard calibration before
each new measurement (with the exception of one sample with 5 K increments). The
tunability was measured only at 0, 10, 20, 30, and 40 V for most temperature points. A
full two-cycle measurement from -4 0 to +40 V was performed at three points over the
temperature range (78, 278, and 308 K) to generate enough capacitance vs. voltage points
for a hysteresis plot. Additionally, devices with the smallest gap and longest fingers were
used whenever possible for the same reasons as mentioned previously.
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130
4 .3 .3
M ic r o w a v e D a t a E x t r a c t io n
After the scattering parameter and phase data had been collected, the next step
was to extract the capacitance, loss, and dielectric constant. This required the creation of
a circuit model to calculate device capacitance and device Q-factor.
The device
capacitance was then input into a conformal mapping program to calculate the
permittivity of the film layer.
4.3.3.1
P a r a l l e l R e s is t o r -C a p a c it o r M o d e l
The first step in the data extraction was to model the interdigitated capacitor with
a parallel resistor-capacitor structure (shown in Figure 4.14). Using this type of circuit,
the S u scattering parameter could be equated to the impedance of the circuit, Z2 , with the
loss modeled as a resistor9.
Figure 4.14: Parallel resistor-capacitor circuit model.
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131
The following calculation shows how the device capacitance and device Q-factor
are obtained from the scattering parameter, F, and phase angle,
The internal
impedance of the network analyzer is represented by Z\ - 50 Q.
Definition of the scattering parameter:
5n(dB) = 101og|r|:
(4.6)
Su(dB)
r =10 20
(4.7)
The complex scattering parameter, containing real and imaginary components:
r = |r|cos^ + /|r|sin^
(4.8)
The scattering parameter, r , in terms o f impedance:
s„= r
(4.9)
= z ? ~ z '
z2+z,
The circuit impedance, Z2 , written in terms of circuit impedance parameters:
Z 22 —Z Rr
KC + Z-im
z2 = _ L_
1
Zc
1
1
(4.10)
1
. _
=^>--- = -----h lOjC
(4.11)
1
ia>C + ±
R
ZR
Z>
*
' i + r N
Z
2
= Zj
U-r,
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(4.12)
132
Substituting equation 4.8 into equation 4.12:
1
1
(l - |r| cos <j> - i \ r \ sin (f) (l +|r| c o s (j) (l + r cos (f> + z'Jrjsin <f) (l + |r |c o s ^ -
r i- n
ll +r ;
z'jr| sin (f)
/|r |s in ^ )
(4.13)
Simply the equation to obtain:
1 _
Z2
1
( i - l r | 2) - 2 / |r ] s m ^
(4.14)
S O ^ + lr lc o s ^ )2 + (jr| sin (/)f
Separate the expression into the two components of the circuit impedance, Z^:
f
R ~ 50
coC =
1
\
,
1^12
i-rr
( i + | r | c o s (f))2 + (jr |s in ^ )2
(4.15)
- 2 /|r ls in ^
50 (l + fr lc o s ^ )2 + ^ r |s i n ^ ) 2
Substitute the scattering parameter values, F, obtained with the network analyzer at
frequency,^ and obtain the device capacitance and device Q-factor:
coC
(4.16)
^ 'd e v i c e
tane) =
1
1
coRC
Q
Q*** = °>R C
(4.17)
(4.18)
The device capacitance, or total capacitance (Ctoto/), is then divided into partial
capacitances o f three distinct regions of the IDC structure, as explained in the next
section.
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133
4.3.3.2
CONFORMAL MAPPING METHOD
Permittivity was extracted using partial capacitance techniques in a modified
conformal mapping method proposed by Gevorgian et a/.10’11. The IDC structure is
deconstructed into sections which have capacitance contributions to the overall device
capacitance, including the capacitance along the finger lengths of the IDC, at the end
gaps of the IDC, and of the outside fingers of the interdigitated structure. Then the
conformal mapping method basically allows for the separation of the microwave field
around the IDC into filling factors. These filling factors are used for the separation o f the
field in the three distinct regions of the device; the air above the sample, the film layer,
and the substrate. Using the partial capacitances of the IDC structure, with the field
calculations in the film layer, the permittivity of the film can then be calculated.
The primary assumption of this method is that the gap size, finger length, and
finger width of the IDC are much less than the wavelength of the microwave test signal.
Additionally, there must be no capacitance contribution from non-adjacent fingers.
The program used to calculate the partial capacitances of the IDC, and then the
permittivity o f the film layer, was written by Jeffrey Pond and Steven Kirchoefer at the
Naval Research Laboratory. It is based on two papers by Spartak Gevorgian, et al. 10,11
and is listed in Appendix A. The following is a brief walk-through o f the program
calculations. For full details o f the calculation see Appendix A and the two references as
listed above.
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134
The calculation begins by running the program and entering the dimensions of the
IDC test structure, namely the gap size, finger length, finger width, number of fingers,
and metallization thickness. Next, the dielectric constant and thickness of the substrate
layer are entered, and finally, the thickness of the film layer.
The total capacitance o f an IDC with finger number n>3 is the sum o f three partial
capacitances of the IDC structure. It is divided into the capacitance o f a three-finger IDC
(C 3 ), plus the contributions from the additional n fingers (C„), and the end gaps (Cencj).
The total capacitance is then represented by the following equation.
Cmd = CJ + C. + Cmi
(4.19)
The partial capacitance, Cn, is the sum of capacitances of the periodic
structures, or fingers. In other words, an IDC with three fingers is used
(n-3)
as the base
structure. It accounts for the outer finger contributions of total capacitance of the IDC, in
the partial capacitance term, C3 . These outer fingers are different from the inner fingers
in the IDC because the field on the outer side does not meet an adjacent finger, but rather
penetrates into free space. Therefore, IDCs with finger number, n, greater than 3, must
be summed as (n-3) separate contributions added to the middle section of the IDC
structure. The last term, Cend, accounts for the fringing fields at the end gaps (or end of
the fingers). This is where the field is least uniform due to the 90° comers at the end of
each finger. Figure 4.15 shows the parts of the IDC which contribute to each of the three
aforementioned partial capacitance terms.
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135
Add additional (n-3) structures
i c .
Top view
l
L
2g
2s
J Cj
a
air
— L .L n ..c i
g^d
substrate
1 lA fingers
'
1 V£ fingers
End gaps
3 fingers include capacitance of outer fingers o f IDC
Figure 4.15: Modeling of IDC structure for calculation of three partial capacitances, C„, C3, and Cend.
The partial capacitances, C„, C3, and Ce„d must be solved independently and sum
to Ctotai, which is known from the parallel resistor-capacitor model.
The capacitance contribution of the middle section of an IDC with n fingers, o f
length /, is
C = { n - 3 )£.£ K ( K ) I
0 *" K{k\)
(4 .2 0 )
where ko = s/(s+g) and k?o - ^(l-fa 2) are the moduli of the elliptic integrals K. The
dielectric constant o f the corresponding partial capacitance term can be written as,
* * =01*1+02*2+03*3
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(4 .2 1 )
136
The filling factors for each o f the three layers of the model are denoted by qt, with
the subscripts representing: l=air, 2-film , and 3=substrate. They are expressed as,
qx= 0.5
q2 =
/(*>w , g )
(4.22)
q3 = 0.5 - q2
with q2, the filling factor of the film layer, a function of film thickness t, finger width w,
and gap size, g. Therefore, by calculating the filling factor of the film layer, q2, the
expression for the effective dielectric constant can be solved for S2, the dielectric
constant of the film layer alone.
In general, qt can be written as,
(4.23)
q‘
where the moduli, k,, o f the elliptic integral K, is,
(4.24)
For a thin ferroelectric film, where s/h, » 1, the moduli can be simplified to
(
V
(4.25)
/
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137
The elliptic integrals are used to map the electric field lines of the microwave
signal onto the surface o f the IDC structure and film.
The integrals are solved by
numerical approximation and are often substituted with a natural logarithm function to
facilitate its solution. The log function is of the form,
K(k ) _
K( k)
71
(
Ln
q + (* ’)
1/2
(4.26)
\
»\ l / 2
V( ! - ( * ' )
1/2
(4 .2 7 )
Additionally, the filling factors (qi) for the partial capacitances, C? and Cend have
their own elliptic integrals with moduli, kt 3 , k2 1 3 , ka 3 ,
3,
and k , e n d ,
end,
k0 md,
end,
respectively. The basic expressions for the partial capacitance of these two terms are
listed below. For further details, regarding the filling factors and moduli see Appendix A
and the two references upon which these calculations are based10,11.
C3 - 4 s £
K(kf )
03
I
(4.28)
1
\
=
4 ms(2 +
K {K ,J
e$ en d
VW
I J ;
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(4 .2 9 )
138
C h a p t e r Su m m a r y
The experimental procedures and methods used for the fabrication and analysis of
BST thin films have been detailed. The equipment settings and scan parameters for each
structural characterization technique have been described. The optimum PLD conditions
for epitaxial growth o f BST (60/40) on (100) LaAlCb and MgO substrates are included,
as well as the design specifics of the PLD system, BST target preparation, and pre­
deposition procedures. The microwave measurements section discussed the equipment
setup and scan parameters necessary for collecting scattering parameter and phase data
with DC bias as a function of frequency at both room temperature and cryogenic
temperatures.
Lastly, the microwave data extraction models used to obtain device
capacitance, Q-factor, and permittivity were presented.
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139
R eferences
[1] D. K. Bowen and B. K. Tanner, High Resolution X-ray Diffractometry and
Topography, Taylor and Francis Ltd., New York, 1998, p. 2.
[2] JCPDS-Intemational Center for Diffraction Data, 1997.
Mica (muscovite), KAl2 (Si3 Al)Oio(OH, F)2 , Pattern #06-0263
[3] J. I. Goldstein, D. E. Newbury, P. Echlin, D. C. Joy, A. D. Romig, Jr., C. E. Lyman,
C. Fiori, and E. Lifshin, Scanning Electron Microscopy and X-rav Microanalvsis.
Plenum Press, New York, 1992.
[4] J. B. Wachtman, Characterization of Materials, Butterworth-Heinemann, 1992,
Chapter 26.
[5] L. C. Feldman and J. W. Mayer, Fundamentals of Surface and Thin Film Analysis.
North-Holland, 1986, Chapters 2,3, 5.
[6 ] W. D. Nix and B. M. Clemens, J Mater. Res., 14, 3467 (1999).
[7] H. Li, Ph.D. Thesis, University of Maryland, 2001.
[8 ] R. S. Elliott, An Introduction to Guided Waves and Microwave Circuits. Prentice
Hall, Englewood Cliffs, NJ, 1993, Chapter 7.
[9] S. W. Kirchoefer, J. M. Pond, A. C. Carter, W. Chang, K. K. Agarwal, J. S.
Horwitz, and D. B. Chrisey, Microwave Opt. Technol. Lett., 18,168 (1998).
[10] S. S. Gevorgian, P. L. J. Linner, and E. L. Kolberg, IEEE Trans. Microwave Theory
Tech., 44, 896 (1996).
[11] S. Gevorgian, E. Carlsson, S. Rudner, L.-D. Wemlund, X. Wang, and U.
Helmersson, IEE Proc. Microwaves, Antennas, and Propagation, 143, 397 (1996).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
140
CHAPTER 5 -- RESULTS AND DISCUSSION
This chapter is divided into three parts: a section discussing the optimization of
the PLD processing conditions to produce epitaxial BST thin films, and two sections that
present the strain and thickness effects on the microwave properties of the films at room
temperature and cryogenic temperatures. The room temperature microwave properties
section is divided such that the strain effects on the unit cell of BST films on both
LaAlt >3 and MgO is presented first, followed by the capacitance and Q-factor data, and
finally the strain effects on the tunability, permittivity, and field-induced charge. The
cryogenic microwave properties section explores the ferroelectric to paraelectric phase
transition o f films with different strain states and ties together with the conclusions from
the room temperature data to present the overall behavior of the BST/LaA 1 0 3 and
BST/MgO systems.
5.1
O p t im iz a t io n
of
P L D P r o c e s s in g C o n d it io n s
fo r
E p it a x ia l
G row th
The BST (60/40) thin films were analyzed with the characterization techniques
discussed in Section 4.1 to determine the effect of the processing conditions on the
crystalline quality and orientation, stoichiometry, surface roughness, and film thickness.
This first part of the overall study of strain and thickness effects on the microwave
dielectric properties involved the fabrication of highly epitaxial thin films which were
strained from lattice mismatch with the substrate material. In order to ensure that a range
of strain values could be attained by varying the thickness, the film lattice needed to be
highly dependent on the substrate lattice. In this manner, a range of compressive strain
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141
states could be generated in BST films on LaAlCb, and a range of tensile strains states in
BST films on MgO. Therefore, it was of great importance to be able to grow epitaxial
BST thin films on both substrates. The film morphology was then studied as a function
of the most important PLD deposition parameters, including substrate temperature,
oxygen pressure, target-to-substrate distance, and pre-annealing conditions for the
substrate.
The initial investigation of the film morphology (primarily with FESEM) at the
very beginning of this study was conducted using SrTiCL on LaAlOa, since it had not yet
been decided that BST (60/40) would be the material of choice for this study. Once the
basic effects of varying the temperature, target-to-substrate distance, etc. were established
using SrTi0 3 (chemically very similar to BST), the film growth optimization continued
with BST (60/40). The final optimization of the deposition parameters was accomplished
by closely examining BST (60/40) film growth on both LaA1 0 3 and MgO substrates with
the full range o f characterization methods.
5.1.1
E ffect
of
P r im a r y P L D P a r a m e t e r s
on
F il m M o r p h o l o g y
An investigation o f the surface morphology of the thin films versus deposition
temperature began with SrTiCb and was carried out with field-emission scanning electron
microscopy (FESEM). SrTi0 3 films were grown directly on (100) LaAlOs substrates at
temperatures o f 400, 500, 600, and 750 °C in 100 mTorr O2 at a laser fluence of 2 J/cm2.
Figure 5.1 shows the morphology of the films as affected by deposition temperature. The
films grown at higher temperatures, 600 and 750 °C (Figure 5.1b and 5.1a), showed a
similar structure o f a smooth epitaxial layer with triangular-shaped and square crystallites
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142
populating the surface. The difference in morphology between these two films was that
the surface crystals o f the 750°C film grew in a randomly oriented manner and with a less
well-defined structure than the triangular surface crystals of the 600°C film, which grew
at 90° and 180° with respect to each other, and at 45° with respect to the sides of the
squares. This is likely due to the added surface mobility of diffusing species at higher
temperatures, allowing more nucleation sites at various orientations. Nevertheless, (100)
epitaxial growth was achieved at both of the higher temperatures as confirmed with x-ray
diffraction.
As the temperature was decreased to 500 °C, the film growth occurred in a mosaic
structure of thin square layers (Figure 5.1c) rather than a pure epitaxial layer comprised
o f very small crystallites.
X-ray diffraction scans of these films showed a textured
growth around a (100) orientation.
Further reduction of the temperature to 400 °C
resulted in a completely amorphous layer (Figure 5.Id) as no SrTiC>3 peaks were
observed in the x-ray diffraction pattern.
The well-defined surface crystals that grew on these SrTiC>3 films were
determined to be of the same composition as the film layer, as no anomalous x-ray
diffraction reflections were observed in scans of films with these crystals. In addition,
these surface crystals were further studied by Semenov et al. 1 with atomic force
microscopy and determined to be of a (2 1 1 ) orientation, relative to the ( 1 0 0 ) growth of
the epitaxial layer. The growth of these crystals is believed to be due to nucleation at
impurities on the surface o f the substrate. As will be shown later, these crystals were
greatly reduced with the development of better pre-annealing and cleaning procedures for
the substrate surface.
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Figure 5.1: Film morphology of SrTi03 vs. PLD deposition temperature (a) 750 °C, (b) 600 °C,
(c) 500 °C, and (d) 400 °C.
The effect o f changing the target-to-substrate distance (z-distance) on the
morphology o f the film was next examined. SrTiOs thin films were fabricated at 600 °C,
100 mTorr O2 , and 2 J/cm2, at two different z-distance settings, 6.4 cm and 8.3 cm. The
change in the position of the substrate heater by
~ 2
cm led to a distinct change in the
morphology o f the surface crystals as seen in Figure 5.2a and 5.2b. The majority of the
surface crystals at 6.4 cm were triangular, whereas at 8.3 cm the surface crystals were
squares likely o f the same (100) orientation as the film. This was the only observed
effect with a change in the z-distance, as the epitaxial layer remained the same. It is
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144
explained by the fact that as the ablated atomic and molecular species from the target
travel through greater distances in the oxygen background gas, they lose more energy due
to increased scattering with the gas molecules2'4. This in turn prevents the nucleation of
higher energy growth planes such as the (211), the orientation of the triangles. Instead,
square crystals grew out o f the film with the same ( 1 0 0 ) orientation, which is a structure
closer to the desired smooth near-perfect epitaxial layer.
(a)
(b)
Figure 5.2: Effect of target-to-substrate distance (a) 6.4 cm and (b) 8.3 cm on the
morphology of SrTi03thin films.
Further optimization o f the deposition conditions continued with Bao.6 Sro.4 Ti0 3
thin films, the chosen material for this study. The next issue to be addressed was the
presence of surface crystals on the surface of the SrTi0 3 films, which were discovered to
also be present on the surface of BST films. Since the presence of such large surface
crystals would interfere with the patterning of a top electrode, better cleaning procedures
were established to reduce the number of defects in the film.
Previously, the substrate was allowed to soak at the deposition temperature for 30
minutes under a vacuum o f ~10 ' 5 Torr prior to film deposition. After trying several
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145
different procedures to prepare the substrate surface for film growth, a multi-step
cleaning procedure was established. All LaAlC^ and MgO substrates were prepared
using the standardized procedure described in Section 4.2.3. Using that procedure, a
substrate was first soaked in acetone and methanol, and finally rinsed in de-ionized water
and dried with nitrogen. The substrate was then inserted into the vacuum system and
allowed to soak at the deposition temperature for a minimum of 90 minutes, during which
time a vacuum of 5x1 O' 6 Torr was achieved.
substrate was pre-annealed in
100
After the high-vacuum bakeout, the
mTorr of flowing oxygen for
1
hour to aid in the
desorption and bum-off o f organic impurities before the deposition o f the film.
As a result, the impurities on the substrate surface were greatly reduced, which
was directly observed as a large reduction in the number and size of the surface crystals
on the films. The epitaxial BST (60/40) films fabricated on LaAlOa and MgO thereafter
had morphologies like those shown in Figure 5.3a and 5.3b. The epitaxial film appeared
as a smooth featureless layer sparsely populated with randomly oriented surface crystals
at the occasional impurity site.
(a)
(b)
Figure 5.3: BST (60/40) epitaxial films grown on (a) LaA103 and (b) MgO showing greatly
reduced number and size of surface crystals.
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146
Other deposition parameters such as the oxygen pressure and laser fluence
remained the same as used for the initial depositions of the experimental films. This is
due to the fact that 100 mTorr O2 and 2 J/cm 2 are common deposition parameters for
perovskite oxides such as BST and SrTiOa5' 10. Therefore, since highly epitaxial growth
was achieved using these conditions there was no need for extensive experimental trials
of different oxygen pressures and laser energy density settings. Figure 5.4 shows two
images of the cross-section of a film deposited at an oxygen pressure of 350 mTorr. Two
important features can be seen from this view of the film structure. The first is that the
film has a greater surface roughness (-20 nm) than that of films deposited at 100 mTorr
(-5-10 nm, AFM images o f 100 mTorr films are presented later). This is due to the
increased grain size of the film from the higher oxygen pressure, an effect common for
PLD films10,11. The second important feature is that the film layer is free of any largeangle grain boundaries often observed in polycrystalline or textured columnar growth,
and appears as a dense single layer.
Cross-section images of films deposited at 100
mTorr (presented in the following section) also show this dense structure.
Figure 5.4: Two views of the cross-section of a BST (60/40) film on LaA103 showing dense epitaxial film
growth and high surface roughness for deposition at 350 mTorr 0 2.
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147
5 . 1 .2
F il m S t o ic h io m e t r y a n d T h ic k n e s s M e a s u r e m e n t s
Rutherford
backscatter
spectroscopy
(RBS)
was used
to
measure the
stoichiometry and thickness o f the BST films in the thickness range of 22 to 270 nm. It
was especially important to measure these thinner films with RBS since any
stoichiometry variations would be most apparent in very thin films. Figure 5.5 shows the
RBS spectra of BST (60/40) films on LaAK>3 (700 °C, 100 mTorr O2 , 2 J/cm2, z=8.3 cm)
for a thickness of 22, 44, 110, 160, and 270 nm. A simulated spectrum was fit to each
raw data spectrum using a program called SRIM
19
(The Stopping and Range of Ions in
Matter). The simulation in each case showed an ideal stoichiometry, with a Ba:Sr:Ti
ratio o f 3:2:5.
The data fits were limited to an accuracy of 5 atomic% due to the
relatively high background caused by the La in the substrate. The Ba, Sr, and Ti peaks
can be seen above the background counts which increase as the film thickness decreases,
eventually masking the Ba peak at 22 nm.
This data shows that a laser fluence of 2 J/cm was ideal for stoichiometric
transfer o f the BST (60/40) target. Studies have shown that non-stoichiometry in the film
can result from preferential ablation if the laser fluence is below the ablation threshold of
1T
one or more o f the atomic species in the target . It is also important that the desired
stoichiometry be achieved as it has been shown that deviations from the ideal (Ba+Sr):Ti
ratio can affect the electrical properties14 from changes in the film morphology and
possibly shifts in the Curie temperature.
Thickness was also calculated from the data simulations from the basic ion
scattering principles, and confirmed with cross-section FESEM images of the films.
Figure 5.6 shows several o f the cross-section images of films over the thickness range of
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148
Counts
6000
5000
5000
4000
4000
3000
o 3000
2000
2000
IBM geometry
IBM geometry
D e te c to r-165‘
Tilt = 7°
I
Resolution^ 15 keV
1000
0
0.5
1000 ^ Detector = 165°
• T ilt= 7°
Resolution - 15 keV
1
0.5
0
2
1.5
1
1
Energy (MeV)
Energy (MeV)
(a)
(b)
6000
6000
5000
Tt Sr
i
*
Counts
4000
1.72 M eV He2+
1.72 M eV He*+
2000
2000
IBM geometry
Detector -1 6 5 °
Tflt=7*
;.............
Resolution =1 15 keV
1000
0
0.5
IBM geometry
Detector = 165°
'Tflt = 7®.I
.......
Resolution H 15 keV
1000
1
1.5
0
2
0.5
Energy (MeV)
1
1.5
Energy (MeV)
(d)
(C)
6000
5000
4000
!O
3000
L72
2000
D5te to rr;1 6 S ”.......
Titt = 7”
i
Resolution 15 keV
1000
0
0.5
1
1.5
2
Energy (MeV)
(«)
Figure 5.5: RBS spectra of BST (60/40) films on LaA103 for a thickness of (a) 270 nm, (b) 160 nm,
(c) 110 nm, (d) 44 nm, and (e) 22 nm showing ideal stoichiometry of Ba:Sr:Ti ratio of
3:2:5 within 5 atomic%.
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149
22 to 1150 nm. The thickness values measured with FESEM are in excellent agreement
with those obtained from the RBS data fits. These cross-section images again show only
fracture lines through the thickness of the film, and no evidence of large-angle grain
boundaries, attesting to the dense highly epitaxial growth of the films. In addition, the
images show excellent film thickness uniformity and low surface roughness compared to
the films shown in Figure 5.4. The next section will explore the growth mode of these
films and provide more details of the surface structure of the films.
(b)
(a)
lflitl§ ltl
135 f
t» 0 /4 0 .
frrt
Figure 5.6: Cross-section FESEM images of BST (60/40) films on LaA103 for a thickness of (a) 1150 nm,
(b) 625 nm, (c) 400 nm, and (d) 22 nm showing dense film layer with uniform thickness and
low surface roughness.
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150
5. 1. 3
Su r fa c e R o u g h n ess
Atomic force microscopy (AFM) was used to examine the surface topography of
the films in an effort to understand the film growth mode. Figure 5.7 shows both x-y
AFM scans and the corresponding 3D surface plots (generated from the 2D scans) of
several BST (60/40) films on LaA103 (again fabricated using the optimized deposition
parameters of 700 °C, 100 mTorr 0 2, 2 J/cm2, z=8.3 cm) as a function of film thickness.
The scans revealed that the surface roughness for these films was about 5-10 nm over an
area of 5 x 5 pm, which is typical of the PLD process15. The surface roughness increased
only slightly with increasing thickness, approaching
10
nm for the thickest films.
Crystallite cluster sizes were also measured and determined to be in the range of
25-50 nm, indicative o f a Volmer-Weber (island/cluster) growth mechanism.
The
thickest films also contained slightly larger clusters of 50-80 nm. This implies that the
growth of the films proceeds by island coalescence, followed by island growth in the
normal direction.
Therefore, heterogeneous nucleation occurs uniformly across the
surface o f the substrate, and due to the large number of clusters the individual island size
remains small
(< 1 0 0
nm).
Film thickness = 1150 nm
u
iu_
- < -----------
uu-
•_u_
4U_
5 0 0 uni
-------
(5.7a)
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151
Film thickness = 270 rim
U
L_U_
-"•€-------
4U_
LUw
LU-
1000 nm
■>
(5.7b)
dla-aroz
*.‘
Film thickness = 110 nm
DlsrWicei
U
i_U_
-<— —
4U -
LU-
LU.
1000 nm ——
>■
(5.7c)
Film thickness = 22 nm
I PC
?
V tftrufcilrA
1U_
LU-
^QQ
LU-
tV -^ fa ^ r-rs :
tm .n o r j
2 5 Z . ' .V-i
-4n% '.w ^>
l r n . n r .-j
E E 9." .V J
L>tfA
4 f n -f lr .fi
4U-
«— —
(5.7d)
Figure 5.7: AFM scans of BST (60/40) films on LaA103 showing (a) 500 x 500 nm scan for t=l 150 nm,
(b) 1000 x 1000 nm scan for t=270 nm, (c) 1000 x 1000 nm scan for t=l 10 nm, and
(d) 500 x 500 nm scan for t=22 nm.
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152
These findings are similar to a study by Cotell et al. 16 that investigated BST
(50/50) thin film growth on LaA 1 0 3 and MgO substrates. It was reported that BST films
on both substrates showed an island growth mechanism with the same amplitude of
surface perturbations, or surface roughness. The AFM data of the BST (60/40) films
grown for this study combined with the cross-section FESEM images indicate excellent
coalescence between islands, or clusters, leading to the observed high degree of epitaxy.
5.1.4
D egree
of
E p it a x y
and
F il m Q u a l it y
The orientation, degree of epitaxy, and lattice parameters of the films were
measured with omega-scan x-ray diffraction as described in Section 4.1.1. Initially when
first determining the optimum deposition parameters, single frame diffraction scans of the
film were collected to quickly determine the orientation and degree of epitaxy. This was
accomplished by rotating the sample on the omega axis while leaving the detector fixed
at the angle o f the BST (60/40) (200) reflection, 45.7°. In this manner, the detector was
positioned to collect both the ( 1 0 0 ) and (2 0 0 ) reflections for both the film and substrate
on the same frame. Figure 5.8a and 5.8b show the single frame scans of the reciprocal
space for highly epitaxial BST (60/40) films on LaA1 0 3 and MgO, respectively. Both the
reflections from the substrate and film appear as point reflections with FWHM of
approximately 0.40° +/-0.03. Since the FWHM of the film was approximately the same
as the single crystal substrate, and about the same as the angular divergence, or
instrumental broadening, o f the x-ray beam it was confirmed that a high degree of epitaxy
had been achieved. The FWHM values were also similar to reported values for BST thin
films on these substrates6,8,16,17.
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153
\ | ^t 5 1’Mi
(b)
Figure 5.8: Omega-scan x-ray diffraction of (a) BST/LaA103 and (b) BST/MgO showing (100) and (200)
reflections of highly epitaxial film and single crystal substrate.
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154
Through the course o f the structural characterization of BST (60/40) films, the
optimized PLD processing parameters were found to be 700 °C, 100 mTorr Cb, 2 J/cm ,
and z=8.3 cm. These conditions provided excellent epitaxial growth for BST (60/40) on
LaAlCL, however fine tuning of the deposition temperature for BST (60/40) on MgO was
required. After the fabrication of each set of samples, all films were always scanned with
x-ray diffraction to determine if epitaxy had been achieved. It was discovered that the
700 °C deposition temperature was not high enough to allow good crystallite coalescence
for films on MgO. Films grown at that temperature were high textured, but not epitaxial
as evidenced by a faint diffraction ring occurring at the ( 1 0 0 ) and (2 0 0 ) reflection angles.
Therefore, after a few experiments with the deposition temperature of films on MgO, it
was found that 825 °C produced the desired highly epitaxial growth. The optimized
deposition parameters for BST (60/40) thin films on MgO were then 825 °C, 100 mTorr
O2 , 2 J/cm2, and z=8.3 cm. Further details on all of the PLD deposition parameters have
been described previously in Section 4.2.
In addition, as a last check of the degree of epitaxy, channeling measurements
were performed using lower-energy protons in a medium-energy ion spectroscopy
system. The lower-energy particles (100 keV protons compared to 1.72 MeV He2+) were
only able to probe the top 10 nm of the film. Figure 5.9 shows the spectrum collected for
a BST (60/40) film on LaA 1 0 3 at the channeling condition (normal beam incidence on the
film surface) and at a random direction of 7° off normal. The %min was then calculated
from the ratio o f the channeling spectrum height to the random spectrum height. It was
discovered that the %m;n was -
1
%, again confirming the extremely high crystalline
quality o f the epitaxial films. Although the measurement was only o f the surface layer, it
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155
is expected that the crystalline structure and quality is the same through the thickness of
the film. For comparison, semiconductor thin films often have Xmin values around a few
percent18,19.
700
600
500
4 00
C h an n e lin g
R andom
ts
a>
£
3 00
Ba
200
100
.■]!ii i | |i"«y i | « | i " H i
■fip
72
74
76
78
80
82
84
86
88 90
92
,
V
94
96
E n e rg y (keV)
Figure 5.9: MEIS channeling spectrum for BST (60/40) on LaA103 (black) and random spectrum
at 7° off normal (red) showing large decrease in the yield for the channeling condition.
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156
5.2
M ic r o w a v e P r o p e r t ie s o f S t r a in e d
BST T h in F il m s
This section presents the microwave dielectric properties of strained BST thin
films deposited on LaAlOa and MgO substrates over the thickness range of 22 to 1150
nm. The effects of strain, developed by decreasing film thickness, on the unit cell are
discussed first. This is followed with the general microwave properties of these same
films, and then by the effects of strain and film thickness on the tunability, permittivity,
and field-induced charge.
5.2.1
E f f e c t o f F ilm T h ic k n e s s o n t h e BST U n i t C e l l
The orientation and strain in the thin films, on both LaA1 0 3 and MgO substrates,
were measured with x-ray diffraction to determine the effect of the lattice mismatch on
the unit cell dimensions o f the films. All films were grown on (100) oriented substrates,
resulting in epitaxial growth in the (100) direction. As such, the normal direction will be
referred to as the (100) and the in-plane direction will indicate the (010). It should be
noted that strain measurements of thin films using a conventional x-ray diffraction source
(i.e. copper, molybdenum, etc.) give an average strain for the entire film thickness due to
the penetration depth o f the radiation, which is on the order of several microns.
Figure 5.10a and 5.10b show the measured lattice parameters and strain of the
BST/LaA 1 0 3 series o f films, through the thickness range of 44 nm to 1150 nm. BST
(60/40) has a bulk lattice constant of 3.965 A, compared to 3.789 A for the pseudo-cubic
LaAlC>3 substrate, resulting in a lattice mismatch of about -4.4%. As discussed in Section
5.1, the films were highly epitaxial, and therefore the unit cell geometry o f the film is
highly dependent on the lattice of the substrate. A compressive substrate such as LaAlC>3
will therefore generate compressive stresses at the interface between the BST film and
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157
Error Bars = 3 ESD (99.74%)
0
200
400
600
800
1000
1200
Thickness (nm)
0 0
1 .0 0 0 0
0.7500 0.5000 cn 0.2500
J_ (normal)
0 .0 0 0 0
- On-plane)
Compressive
Tensile
-0.2500
0
200
400
600
800
1000
1200
Thickness (nm)
(b)
Figure 5.10: Effect of film thickness on the (a) normal and in-plane lattice parameters, and (b) normal
and in-plane strain of BST (60/40) thin films on LaA103.
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158
the substrate, which was observed by x-ray diffraction measurements. A tetragonal-like
distortion in the growth (or normal) direction was present in all films up to the limit of
the thickness range for this study (1150 nm), as the normal lattice parameter was always
larger than the in-plane lattice parameter. However, at a thickness of 400 nm there exists
a critical point (defined here as a point where the unit cell geometry changes
significantly) where the in-plane strain state changes from compressive (negative) to
tensile (positive).
For films less than 400 nm, a compressive in-plane strain was present, causing a
contraction of the unit cell in the in-plane direction.
The magnitude of the strain
increased with decreasing film thickness, resulting in a contraction of the in-plane lattice
parameter by up to 0.25%. For the thinnest film measured with x-ray diffraction (44 nm),
the corresponding induced strain in the normal direction approached nearly 1 %. Such
large values of strain translate to very high stresses in the films on the order of several
GPa, which will be shown in following sections to effect the electrical properties of the
films.
Above 400 nm, the unit cell of the film showed a slight expansion from the bulk
value in all directions, as the in-plane strain transitioned from compressive to tensile.
The normal strain decreased significantly with the relaxation of the in-plane strain, with
both the ( 1 0 0 ) and (0 1 0 ) lattice parameters approaching an equilibrium lattice parameter
o f 3.968 A for the thickest films. The relaxation of the in-plane strain can be attributed to
the formation o f increasing numbers of misfit dislocations as the films were grown
thicker, but it is unclear if expansion of the film unit cell to a value greater than the bulk
is attributed to the same reason. It should be noted that the critical thickness for the
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159
formation of misfit dislocations in BST (60/40) thin films grown on LaAlC>3 and MgO
substrates are 2.6 nm and 1.5 nm, respectively, as calculated by Ban and Alpay20.
Therefore, all films greater in thickness than those critical values will contain increasing
numbers of misfit dislocations as described by Equation 2.7.
It is interesting to note that the effect of the strain due to the lattice mismatch is
diluted as the films are grown thicker from the formation of misfit dislocations. It is
however likely that a compressive strain still exists near the interface between film and
substrate. Thus it is likely that a strain gradient exists through the thickness of the film,
but at present no technique is suitable to profile strain in sub-micron films.
The total measured in-plane strain, as discussed above, can be separated into
strain as a result of lattice mismatch and strain due to thermal expansion differences
between the film and substrate.
Since the film and substrate are cooled from the
annealing temperature o f 500 °C, a certain percentage of the total in-plane strain will be
due to the difference in the thermal expansion coefficients. The coefficients as obtained
from other researchers21, are
( X b s t( 6 0 /4 0 ) = 1 0 . 5 x
10' 6 K '1, and a i . aA i o 3= 10.0 x 10' 6 K '1. This
results in a slight tensile strain on the film as the sample is cooled to room temperature.
Assuming that the thermal expansion coefficients do not change much through the
temperatures experienced by the sample, the difference in the thermal expansion
coefficients of the two materials can be approximated at +0.5 x 10"6 K '1. A 475 °C drop
in temperature from the deposition condition to room temperature results in a net change
in the lattice parameter o f the BST film of +0.000234 A. This translates to a tensile strain
in the BST film o f about +0.006% strain caused by thermal contraction of the system.
However, this is not significant since the standard deviation of the lattice parameter
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160
measurement falls in the range of 0.0005 to 0.001
A. Therefore, for this system, BST on
LaAlC>3 , the effect can be ignored, as it is a negligible contribution to the total strain.
The strain in BST deposited on MgO, a tensile substrate, shows a much different
behavior due to the opposite in-plane strain state developed from the lattice mismatch.
The lattice constant of MgO is 4.2112
A, which results in a lattice mismatch of +5.8%
with BST (60/40). As a result, tensile in-plane strain develops in epitaxial BST films,
and although a corresponding decrease in the normal lattice parameter might be expected,
a much different behavior is observed. Unlike the BST films on LaA 1 0 3 , where the
normal lattice parameter elongates due to the contraction of the in-plane lattice parameter
(a converse effect), in this system an elongation of both the in-plane and normal
directions was observed leading to a large volume expansion of the unit cell.
Figure 5.11a and 5.11b show the measured lattice parameters and strain of films
over the thickness range of 44 to 1150 nm. A critical point also exists for the strain
behavior in this system at a film thickness of -140 nm. For films below a thickness of
about 140 nm, the in-plane [010] unit cell length is larger than the [100], or growth
direction. This results in an in-plane tetragonal-like distortion, where what is normally
denoted as the c-axis o f the cell (here denoted the [ 1 0 0 ] direction) is shorter than the
other two axes. Above this thickness, the in-plane tetragonal-like distortion flips to the
normal direction, and the [ 1 0 0 ] lattice parameter becomes larger than the in-plane [0 1 0 ].
It will be shown later that the critical point at -140 nm directly correlates with a change
in the microwave properties. As the film thickness increases beyond 140 nm, the normal
strain remains nearly constant at 0 .2 % and the in-plane strain continues to relax, changing
to a slightly compressive state at -825 nm.
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161
4.0000
|
E rro r Bars = 3 ESD (99.74%)
3.9900 -
&0
i
3.9800 “
s(100)
3.9700
0,^=3.9651
'(0 1 0 )
8 3.9600
3.9500
0
200
400
600
800
1000
1200
Thickness (nm)
(a)
1 .0 0 0 0
0.7500
0.5000
± (normal)
■§ 0.2500
m
0 .0 0 0 0
-0.2500
Tensile
Compressive
-0.5000
0
200
400
600
800
1000
1200
Thickness (nm)
(b)
Figure 5.11: Effect of film thickness on the (a) normal and in-plane lattice parameters, and (b) normal
and in-plane strain of BST (60/40) thin films on MgO.
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162
In this system (BST on MgO), the thermal contraction of the sample is of
importance due to the larger difference in the thermal expansion coefficients between
film and substrate.
The thermal expansion coefficient of MgO
is 13.8 x 10
/T
1
K" ,
(\ 1
resulting in a net change in the film lattice parameter of -3.3 x 10' K' . This results in a
compressive strain in the film on cooling from the 500°C annealing temperature. Using
the same assumptions as stated previously, an estimate of the thermal component of the
strain can be calculated.
The change in the BST lattice parameter due to thermal
contraction of the system over a temperature range of 475°C will be -0.00157 A,
corresponding to a compressive strain of -0.04%.
This contribution to the total measured strain will be significant for only the
thickest films where the strain is near zero. The measured strain values across the entire
thickness range should then contain 0.04% contribution from thermal expansion
coefficient mismatch. This assumes that the substrate has the same “pulling effect” on
the film at all thickness values, regardless of misfit dislocation density. An assumption
that seems correct based on the fit to the experimental data, as it shows that the in-plane
strain transitions to a compressive state beyond about 825 nm, likely due to compressive
stresses from the thermal expansion coefficient mismatch. Therefore, this contribution
does not affect the trend o f the total strain with film thickness and will not affect the
analysis o f the effect o f strain on the microwave properties.
Ban and Alpay’s theoretical prediction of the in-plane misfit strain versus film
thickness2 0 (Figure 2.11a and 2.11b) matches well with the experimentally measured
values presented here. The misfit strain is predicted to relax according to the same trend
as observed experimentally. There is one discrepancy between experiment and theory in
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163
the relaxation of strain in BST films on MgO. It is predicted theoretically that the strain
state should change to slightly compressive beyond a critical thickness of 52 nm due to
thermal expansion mismatch. However, the calculation was made for cool down from a
growth temperature o f 800 °C, -63% greater thermal contraction for a temperature
change o f 775 °C, without considering the effects of a post-annealing step.
It is likely that annealing the films at 500 °C before cooling to room temperature
(to promote better crystallization) has the effect of eliminating some of the misfit
dislocations formed during deposition at the growth temperature.
With fewer
dislocations through the film thickness, annealed films on MgO exhibit much more
dependence on the lattice parameter o f the substrate, and remained in a tensile strain state
over a larger thickness range.
It was predicted by Nix et al . 2 2 that the tensile strain in thin films may be
increased through crystallite coalescence. It was shown theoretically, that as crystallite
islands join together the surface free energy is reduced with the creation of grain
boundaries at the expense of the strain energy in the film. Annealing thin films will also
lead to increased crystallinity through this mechanism. In addition, it was experimentally
observed by Li22, with transmission electron microscopy, that the number of threading
dislocations in BST films was greatly reduced after annealing, leading to better dielectric
properties. It is then reasonable to assume that the annealing procedure led to increased
film strain through one or more mechanisms involving the reduction of defects in the film
layer, resulting in greater tensile strains than predicted.
Therefore, strain relaxation
through misfit dislocation formation at the growth temperature was essentially reversed
through a post-deposition annealing step.
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164
5.2.2
C a p a c it a n c e
and
Q -F a c t o r
v s.
F il m T h ic k n e s s
The capacitance, Q-factor, tunability, and permittivity of the films were derived
from the measured S h scattering parameter and phase data in the range of 1 to 20 GHz,
using the procedures described in Section 4.3. All measurements in Section 5.2 and 5.3
were made using interdigitated capacitors with a 5.5 pm gap and 80 pm finger length,
and are directly comparable due to the identical electrode geometry for each
measurement. The dimensions of the electrodes were measured with FESEM, as shown
in Figure 5.12, to confirm that the photolithographic metallization procedure yielded the
desired geometrical specifications. This electrode configuration has the smallest gap and
longest fingers o f all the interdigitated structures in the 3 x 4 array. It was chosen for
measurements because it maximizes the contribution from the area between the parallel
fingers and minimizes end gap contributions. In addition, the microwave field is more
confined in small gap structures, and therefore minimizes fringing field components.
r 'y
M
(»j
(b)
Figure 5.12: Measurement of the (a) gap size and (b) finger length of an interdigitated capacitor
with FESEM.
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165
Comparisons of the data for the LaA1 0 3 and MgO series were made at 10 GHz,
the midpoint o f the measurement range, since both film series showed weakly frequencydependent dielectric properties. Capacitance values were approximately the same for the
BST films on LaAlOa as compared to films of the same thickness on MgO substrates.
The 0 V bias capacitances of the 825 nm films were about 1.9 pF at 10 GHz for both
series. The thickest films grown for this study, 1150 nm, showed approximately the same
dielectric properties at lower frequencies near 1 GHz, but were affected by an electrical
size effect at higher frequencies.
The Sn impedance measurements, and hence the
derived capacitance data, o f the 1150 nm samples showed a resonance-type behavior,
which was broader for films on MgO as compared to LaA 1 0 3 . This electrical size effect
is due to the fact that the wavelength of the microwave radiation in the high dielectric
constant film (for thickest films only) approaches the gap size of the interdigitated
electrode (5.5 pm), within approximately order of magnitude. Because of the broad
resonance o f films on MgO, the 10 GHz tunability of the 1150 nm film is not reported for
the MgO series, but approximated to be the same as that of the 825 nm film.
The thinnest films, at 22 nm, exhibited 0 V bias capacitances around 0.15 pF.
Films in between the two extremes in thickness, exhibited successively smaller
capacitance with decreasing film thickness.
Figure 5.13a to 5.13i show the measured capacitance and Q-factor over the entire
frequency range as a function DC bias (0 V to +40 V) for all films in the LaA 1 0 3 series.
Also shown for each film thickness are the capacitance vs. voltage (C vs. V) curves at the
midpoint frequency of 10 GHz, for two voltage cycles denoted Trace 1 (-40 V to +40 V)
and Trace 2 (+40 V to -4 0 Y). All measurements were conducted at room temperature,
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166
where BST (60/40) is normally paraelectric. However, hysteresis is observed in many of
the C vs. V curves, indicating the presence of a residual internal polarization. This issue
will be thoroughly addressed in Section 5.4, where hysteresis measurements are
presented as a function of temperature.
The capacitance data (the top set of data on the double y-axis plots in Figure 5.13a
to 5.13i) is presented to show the representative microwave response for each film
thickness because it is of greater interest when designing microwave components than is
the dielectric constant (which is presented later). The capacitance data is also the true
“device capacitance” which means it is the response of the BST film as it would be
measured in an integrated microwave IDC application.
As mentioned previously in
Section 1.5, one o f the greatest advantages o f interdigitated structures with gap sizes >5
pm is the ability to attain device capacitances in the picofarad (pF) range while still
taking advantage of the large tunability of high permittivity materials such as BST. Other
conventional parallel-plate capacitor designs often yield capacitances which are in the
nanofarad (nF) range making it difficult to integrate into a microwave circuits because of
the inability to attain a reasonable impedance match with such a high capacitance
structure.
In general, the capacitance data has no major features other than the electrical size
effect which can be seen in the 1150 and 825 nm films. There are no other apparent
relaxation effects in this frequency range, which would appear as a similar anomaly. The
capacitance is shown to decrease with film thickness, as does the field-dependence of the
capacitance—or the tunability.
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167
3
1150 nm
2.5
298 K —1
60
50
2
'9
2.5
%
1.5
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Frequency (GHz)
(5.13a)
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—825 Hill
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168
298 K --
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F req u en cy (G H z )
(5 .1 3 1 )
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40
169
50
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298 K - 110 am
40
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8
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-30
-20
-10
0
10
40
B € B » a s (V )
(5.131)
Figure 5.13: Capacitance and Q-factor from 1 to 20 GHz and C vs. V (two traces) for BST on
LaAlG3—(a) 1150 nm, (b) 825 nm, (c) 625 nm, (d) 400 nm, (e) 270 nm, (f) 160 nm,
(g) 110 nm, (h) 44 nm, and (i) 22 nm. For capacitance/Q-factor vs. frequency plots the
DC bias is incremented in steps of 5 V, where red trace isO V and black trace is 40 V.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
170
The Q-factors, 1/tan 8, (the bottom set of data on the double y-axis plots in Figure
5.13a to 5.13i) ranged from 4 at 0 V bias to 20 at 40 V bias for the LaAlOa series. It is
expected that as the capacitance and tunability decrease with film thickness, the Q-factor
should increase since many studies have shown that the tunability and loss are inversely
proportional23’25. However, the Q-factors were observed to remain in the same range of
4-20 regardless of film thickness.
The Q-factor of BST thin films has been shown to be dependent on the
microstructure.
Lower loss is usually observed for films that are polycrystalline or
textured, but not epitaxial. It is believed that the high loss of these films is a result of the
highly epitaxial structure, since other groups have reported Q-factors in the range of 50 to
100+ using the same interdigitated electrodes23. It was recently suggested by Li26 that
large numbers of misfit dislocations, especially in thicker films, may contribute to high
loss. However, it is indeterminable exactly what phenomena cause high loss without
further study of the crystal structure at the atomic level.
Other proposed contributions to the high loss are signal loss in the metallization,
although this would appear as a series loss component, and it has been shown that these
IDC structures behave as parallel resistor-capacitor structures27. The Q-factor of the
devices may also be limited by the geometry of the interdigitated electrodes. Among the
many geometrical factors that may influence the loss, are the aforementioned electrical
size effect, which reduces the Q-factor to near zero (a short-circuit condition) as seen in
Figure 5.13a and 5.13b. In addition, the high field concentration around sharp points on
less-than-perfect straight edges along the length of the IDC fingers is also another
geometrical consideration.
This could lead to local shorted areas on the device.
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171
Nevertheless, IDCs have great potential for coplanar microwave devices, and if the high
loss has a geometrical loss component, it could be avoided by patterning IDCs with
optimum gap sizes, finger lengths and widths, etc. for the material of choice using
industry standard photolithographic techniques.
The capacitance and Q-factor data for the MgO series are shown in Figure 5.14a
to 5.14i for the exact same measurement conditions as the LaA 1 0 3 series. As mentioned
previously, the electrical size effect appears broader for the 1150 nm film, causing the
capacitance to drop significantly at higher frequencies. Overall the capacitance decreases
with film thickness in the same manner, however the field-dependence of the capacitance
is much greater for thinner films on MgO. The C vs. V curves are also shown for each
film thickness for the ±40 V DC bias cycling at 10 GHz. Hysteresis is again observed in
a normally paraelectric BST composition at room temperature. The behavior is similar to
the LaA1 0 3 series, as both sets of samples show significant internal residual polarization,
especially in the thinnest films, where the strain is highest.
The Q-factor of the MgO series of films is also quite low with approximately the
same values as the LaA 1 0 3 series. Average values were 4 at 0 V bias to 20 at 40 V bias,
and seem to be typical for highly epitaxial microstructure of these films (Note: some
films contain limited Q-factor data due to equipment malfunction). Again, it can only be
assumed that the dislocations present in thin films add to the total loss o f the material, but
it is likely that many other types of defects also have significant contributions. This has
been a problem for all researchers of this material system, and prevents immediate wide­
spread application o f the material in microwave thin film devices.
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O
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Capacitance (pF)
3*5*
173
1.2
1.2
70
Trace 1
1
0.8
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0.6
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Frequency(GHjs)
(5.14d)
0.8
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270
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Trace 2
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(5.14e)
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T race 2
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20
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8
0.1
-40
12
Frequency(GHz)
30
-20
10
0
10
DC Bias (V)
(5.14f)
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20
30
40
174
0.S
SO
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298 E —110 tom
1101
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Frequen<7 (GHz)
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-20
-10
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10
20
30
40
DC Bias (V)
(5.14i)
Figure 5.14: Capacitance and Q-factor from 1 to 20 GHz and C vs. V (two traces) for BST on
MgO—(a) 1150 nm, (b) 825 nm, (c) 625 nm, (d) 400 nm, (e) 270 nm, (f) 160 nm,
(g) 110 nm, (h) 44 nm, and (i) 22 nm. For capacitance/Q-factor vs. frequency plots the
DC bias is incremented in steps of 5 V, where red trace is 0 V and black trace is 40 V.
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175
5 .2 .3
S t r a in a n d T h ic k n e s s E f f e c t s
5 .2 .3 .1
T u n a b il it y
The most noticeable difference between the MgO series and LaAlCE series is that
the field-dependence of the capacitance is much greater for BST films on MgO. Even in
very thin films a large change in the capacitance is observed with the application of a DC
bias. The strong tunability observed in the thinnest films on MgO compared to the same
thickness on LaA. 1 0 3 is believed to be due to the strain effects on the unit cell dimensions
as discussed in Section 5.2.1. Figure 5.15a and 5.15b show the set o f C vs. V curves for
both the LaA1 0 3 and MgO series at 10 GHz. The thickest films show similar 0 V bias
capacitance, with a slightly higher maximum for the LaAK>3 series, approaching 2.5 pF.
As the thickness decreases below 400 nm, both the 0 V maximum capacitance and the
field-dependence o f the capacitance decrease rapidly for the LaA1 0 3 series o f films,
resulting in a large drop in the tunability. For example, at 400 nm the tunability is about
52%, but at 270 nm it has decreased to 40%. However, the MgO series of films show
quite a different response; the 0 V maximum capacitances were significantly higher with
decreasing film thickness, as was the tunability. The tunability of these films remained
above 50% for all but the thinnest samples (<100 nm).
Since the growth and processing procedures were exactly the same for both sets
of films, processing effects and microstructural differences can be ruled out, as all films
were highly epitaxial with the same growth modes as shown in Section 5.1. Therefore, to
better understand the relationship between the distortion of the unit cell dimensions due
to misfit strain and the resulting effect on the tunability, the correlation o f the in-plane
strain and the capacitive tunability was further analyzed.
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176
DC Bias (V)
(a)
DC Bias (V)
(b)
Figure 5.15: Capacitance vs. DC bias voltage at 10 GHz (a) LaA103 series, (b) MgO series
for the film thickness range of 22 to 1150 nm.
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177
Figure 5.16a and 5.16b are plots of the tunability of the LaAlCb and MgO series
o f films as a function of thickness and in-plane strain. A comparison with the in-plane
strain is used because the electric field lines between the fingers of the interdigitated
electrode pass through the film approximately perpendicular to the normal direction in
the gap. Therefore, the field-induced polarization direction is in the plane o f the film.
The tunability and in-plane strain are shown to follow the same trend with
thickness for the LaA1 0 3 series. As the magnitude of the in-plane strain changes, the
tunability is found to be directly proportional.
For these films on LaA 1 0 3 , the
compressive strain induced in the film was found to cause a large decrease in tunability,
especially in very thin films, where the in-plane strain was the highest. As shown, the
tunability drops down to about 3% for the 22 nm film, where the in-plane strain
approaches a maximum of -0.25%. At the other end of the thickness range, it is shown
that the tunability saturates at a value of about 65% around 800 nm.
This is where the
unit cell of the BST film approaches an equilibrium size of approximately 3.968 A and
the in-plane strain is slightly tensile.
The critical point for this set of BST films on LaAlC>3 was -400 nm as indicated
by the x-ray diffraction strain data in Figure 5.10b. That is the thickness were the strain
transitions from slightly tensile (>0 %) to compressive (<0 %) as the film thickness is
decreased. The unit cell below that critical thickness was tetragonally distorted in the
normal direction due to the compressive in-plane strain state. This is likely due to the
fact that the dislocation density in films <400 nm was not high enough to allow relaxation
o f the strained unit cell. As a result, the tunability drops off rapidly as the unit cell
becomes more constrained in the in-plane direction from increasing compressive strain.
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178
70
0.1
i........
60
£
50
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2
40
0.05
a
5 30
20
l.....
10
Tunability
In-Plajae Strain
-
0.2
0
200
0
400
600
800
1000
1200
Thickness (nm)
70
0.4
60
.m ,
50
40
0.2
XI
S3
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3
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op
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f Tunability
•> in-Flatfe Strain
20
0.1
t
10
0
0
200
400
600
800
1000
1200
Thickness (nm)
(b)
Figure 5.16: Tunability (at 10 GHz) and in-plane strain vs. film thickness for (a) LaA103 series and
(b) MgO series. Vertical dotted lines are critical film thickness corresponding to major
change in unit cell dimensions.
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179
The relation o f tunability and strain for BST films on a compressive substrate
such as LaA1 0 3 shows that a compressive state of strain in the film limits the maximum
achievable tunability, as the strain increases with decreasing film thickness. In-plane
strain relaxation which occurred at the critical thickness of 400 nm was followed by
increase in tunability toward a maximum value of 65%. The trend shows that once the
strain relaxed from misfit dislocation formation, the tunability increases only slightly and
saturates at 65% at a tensile strain of -0.05%. Although, the strain effect is not separated
from any possible thickness effects (similar to particle size effects in bulk materials), it
nevertheless shows that the tunability is greatly dependent on the strain.
The tunability and strain relationship was also studied for BST on MgO (Figure
5.16b). An immediately noticeable difference between the two film sets is that the large
in-plane tensile strain in the 22 nm BST film on MgO results in 30% tunability, compared
to the 3% seen in the 22 nm film on LaA1 0 3 . For the MgO series, tunability is observed
to be nearly constant with decreasing film thickness until a critical thickness is reached
where the tunability drops off sharply at around 140 nm. The tunability remains high
when the in-plane strain is relatively low (<0.1 %), but at the critical thickness of 140 nm,
the strain increases significantly and the tunability decreases rapidly from - 65% for the
thicker films to 30% for the 22 nm film. This critical thickness exactly corresponds to
the change in the unit cell dimensions, where the distortion of the unit cell switches from
the in-plane to the normal, as discussed previously (Figure 5.11a). Since the microwave
field lines for the IDC structure are oriented in the in-plane direction between the fingers,
it is clear that the relaxation of the in-plane strain causes the large increase in the
tunability.
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180
This is very similar to the effect observed in the LaA103 series except that the unit
cell relaxes from different strain states in each case. The thinnest films deposited on both
the LaA103 and MgO substrates have strain states that are opposite in direction, but
similar in magnitude. The maximum measured strain for the LaA103 series was about
-0.25% corresponding to a large compressive strain for the 44 nm film. The maximum
strain for the MgO series was about +0.35% for the same thickness resulting in a large
tensile strain. The difference between the maximum strains results from the larger lattice
mismatch for BST on MgO (+5.8%) versus BST on LaA103 (-4.4%).
This lattice mismatch difference is also the reason for the different trends
observed in the strain relaxation as the film thickness increases. Films on LaA103 are
able to relax gradually with the addition of misfit dislocations at the growth temperature
due to two main reasons: the smaller magnitude o f the in-plane strain (compared to films
on MgO) and the similar crystal structure o f the film and substrate (both are perovskites).
In comparison, films on MgO initially try to match the rocksalt structure of the MgO
substrate by growing in a highly strained state. Once enough misfit dislocations are
produced in the film (as film thickness increases) the film can no longer maintain
coherency with the substrate lattice. As a result, the film relaxes at a much smaller
thickness (-140 nm) than observed for films on LaA103.
The result of the strain
relaxation in both cases is an increase in the tunability. However, much thicker films are
needed to achieve maximum tunability on LaA103 versus MgO. The tunability plateaus
at 65% around 800 nm on LaA103 substrates, and at about 300 nm on MgO substrates.
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181
Since the two sets of films offer insight on both compressive and tensile strain
states (depending on substrate), it is useful to examine the tunability purely as a function
of the misfit strain. Figure 5.17 shows both sets of tunability data as measured across the
thickness range of this study.
It shows that there is an overlapping region o f high
tunability defined by the maximum tunability (endpoints) for each film series.
This
region corresponds to a misfit strain of 0 to +0.07%. It is an estimate based on the two
film series, and it should be noted that in order to obtain the ideal misfit strain for each
system, BST on LaA1 0 3 and BST on MgO, the other half of each curve must be explored.
In other words, tensile-strained LaA1 0 3 films and compressive-strained MgO films must
be grown, by modifying the processing conditions, to trace out the maximum of each data
set. Nevertheless, this plot clearly shows that tunability reaches a maximum when the
films are in a near strain-free state, or a weakly tensile state.
80
BST/MgO
o
60
«
50
!I
40 0s
•i
os
30
30
20
20
VQ
... ^*
H
0.3
-0.2
-0.1
0
0.1
0.2
In-Plane Strain (%)
H
0.3
0.4
Figure 5.17: Tunability of BST(60/40) films at 10 GHz as a function of misfit strain
as created by deposition on LaAlQ3 (red) and MgO (blue).
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182
These experimental findings are in good agreement with the recent theoretical
■JO
predictions by Ban and Alpay et al. , previously discussed in Chapter 2. They have
calculated the strain effects o f several BST compositions as a function of thickness using
■JQ
a phenomenological thermodynamic model originally developed by Landau .
As
indicated in Figure 2.14b o f Section 2.1, the in-plane tunability o f BST (50/50) was
calculated as a function of misfit strain and predicted to peak at a tensile strain of 0.1%.
Although the calculation was made for BST (50/50), the material parameters of that
composition used for the calculation (i.e. elastic coefficients, electrostrictive coefficients,
Curie constant, etc.) are not very different from those o f BST (60/40). As such it serves
as a suitable model for comparison, and the experimental data presented here is in good
agreement with thermodynamic theory. Both the experimental results of this work and
their theoretical work predict a maximum tunability when the film is under a slight tensile
strain.
In addition, Ban and Alpay28 have created theoretical plots of the tunability and
misfit strain versus film thickness. In this work it is shown that the relaxation o f strain
leads to increased tunability, and therefore films above a certain thickness show the best
properties. As mentioned previously, the tunability rose to a maximum value of 65% at
800 nm for BST on LaA1 0 3 and at 300 nm for BST on MgO, as shown in Figure 5.16a
and 5.16b. A direct comparison with this experimental data is not possible here, because
their calculation is for the out-of-plane tunability for BST (50/50).
However, it is
interesting to note that their theoretical calculations show that maximum tunability is
achieved at a particular thickness, predicted to be around 90 nm on LaA1 0 3 and at 120
nm MgO substrates (Figure 2.15a and 2.15b, Section 2.1). These predictions are based
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
on the theory that the maximum tunability occurs in the vicinity o f a phase transition
between a polar phase and the paraelectric state. The calculations also show that very
little misfit strain occurs above 100 run, which is contrary to what we observe. Overall,
the general trends o f these calculations are similar to our experimental data, if the
singularities which led to near 100% tunability at the transition points are removed. The
existence of these new ferroelectric phases, due to strain-induced phase transitions, need
to be experimentally verified. It seems possible that misfit strain-dependent spontaneous
polarization states both in-plane and in the normal direction may exist, but whether or not
these states are a result o f a transition between different space groups is in question. To
date no such unique phases have yet been identified by x-ray diffraction measurements.
Further investigation of strain-effected phase transitions through temperature dependent
hysteresis measurements is presented later in Section 5.3.
Overall the experimental data presented here shows that the tunability is greatly
affected by strain in general, regardless o f the sign (+/-), and depends on only the
magnitude of the strain. It is shown that films that have near zero strain, or slightly
tensile strain, have the highest tunability. The notion that strain-free BST films have
better properties has recently caught the attention of researchers30'34. However, growing
thin epitaxial films without strain has proven to be very difficult.
One method of
«
TO
producing strain-free films is deposition on a buffer layer , but that usually results in
textured or polycrystalline film growth. Another technique is through modification of the
oxygen pressure during deposition to introduce oxygen vacancies in preferential growth
T1
directions which are thought to counteract the strain . Neither has yet produced highly
epitaxial strain-free films with enhanced tunability.
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184
It was also concluded that for very thin films where large strains are usually
present, in-plane tensile strains are more favorable for high tunability over compressive
strains. This is also in agreement with the finding that the highest tunability of the
thickest films was obtained in films with a slight tensile strain. This behavior may be
attributable to several reasons related to the unit cell structure and lattice dynamics such
as the movement of polarizable species.
A physical model of tunability can be described as the limitation o f the dynamic
polarization (in an AC field) through the application of a superimposed DC bias field of
varying strength.
The reduced polarization, due to the limited maximum ionic
displacements in the lattice, results in lower capacitance and/or permittivity. Therefore, it
is possible that crystal lattices free of restrictions imposed by high levels of strain would
allow greater ionic displacement and polarization within the unit cell. This would then
allow the ions to better respond to the superimposed DC bias fields. It is then possible
that crystal lattices that are completely unstrained or slightly tensile strained, rather than
contracted, would have greater full-range ionic displacement in an electric field resulting
in higher tunability.
It then becomes a question of describing this behavior in terms of the known
lattice dynamics o f crystals and attributing a particular mechanism to the observed
decrease in tunability with increasing strain. Since the vibrational properties of the lattice
directly affect the permittivity and tunability, especially in the region of the phase
transition, it will be addressed first. Additionally, other less important effects, such as the
“dead layer” effect ’ , which are not believed to be strain-related, will be briefly
discussed later for completeness.
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185
One of the most important phenomena to consider is the contribution of polar
phonons to the dielectric permittivity, specifically the soft phonon mode. Several studies
have been conducted on the soft mode behavior of SrTi0 3 as it can be easily grown in
bulk single crystal form and also as an epitaxial thin film. It also can be grown in bulk
form free from compositional inhomogeneities, which are unavoidable in alloyed systems
such as BST. Therefore, the following discussion is focused on SrTiC>3 in an effort to
understand the soft-mode behavior in the absence of complications such as non-ideal
stoichiometry and incomplete alloying. Comparisons will then be drawn between the two
very similar materials in an effort to show how the soft mode behavior may be
responsible for the observed properties of BST films.
It is well known that the permittivity of SrTi0 3 is closely related to the soft
mode37. In fact, in a pure SrTiCb single crystal, the permittivity is solely related to polar
-20
phonons, in particular the lowest energy mode known as the soft mode . The soft mode
is basically the lowest frequency vibration of Ti4+ and O2' ions of oxygen octahedra in
opposite directions which lead to the maximum in the permittivity at or near the phase
transition temperature38,39. In perovskite titanate materials such as SrTiC>3 and BST the
frequency o f the lowest optical mode (soft mode) approaches zero at the Curie
temperature where the lattice undergoes a phase transition40"42.
As such, the static
dielectric constant, So (lower than optical frequencies, <THz), and dynamic dielectric
constant, s m, can be related to the optical phonon modes of the lattice through the
Lyddane-Sachs-T eller (LST) relation38,
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186
SQ= £<
.
n (O 1
TT J LO
•
(5.1)
2
J CO.
J TO
where N is the number of infrared-active optical modes, and
c o lo
and
Q)t o
are the
frequencies of the longitudinal and transverse optical phonon modes, respectively.
In a recent study be Sirenko et a l 4 3 the complex dielectric permittivity o f 2 pm
epitaxial SrTi0 3 films (on conductive SrRuCb-coated SrTi0 3 substrates) and a bulk
single crystal were measured using ellipsometry and infrared vibrational spectroscopy in
the range o f 30 to 700 cm’1 as a function of temperature from 5 to 300 K. It was found
that there are three infrared-active optical modes, and it was shown that only the
frequency of the soft mode (the lowest energy transverse optical phonon) is dependent on
the temperature43, or relative closeness to the phase transition. The soft mode frequency
decreased as the temperature was lowered and the FWHM of the peak was broader in the
SrTi0 3 films (40 cm'1) versus the bulk crystal (25 cm’1). In addition, the soft mode
frequency saturated at a fairly high frequency of 62 cm’1 for the films, whereas the bulk
soft mode frequency was measured at 13 cm’1. All other LO and TO phonon modes were
shown to be weakly dependent on temperature and did not show any frequency shift
between bulk and film. Therefore, according to the LST relation the dielectric constant
should depend primarily on the soft mode frequency, cdtoi• In separate measurements of
the static dielectric constant of the 2pm films and bulk sample, the temperature
dependence of So was measured and found to be the same as predicted by the LST
relation using the change in the soft mode frequency with temperature.
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187
The measured permittivity of the SrTiC>3 film was significantly lower than that of
the bulk crystal, which is as expected, since most materials in thin film form have
reduced dielectric properties. The lowering of the dielectric constant was consistent with
the reduced softening o f the soft mode frequency.
In other words, the soft mode
frequency did not decrease as rapidly or to the same extent as observed in the bulk
crystal.
This behavior, called soft mode hardening, is believed to be a result of
differences in the lattice of the thin film versus the bulk lattice.
Furthermore, a 280 nm film was also analyzed in the same maimer. It was found
to show similar soft mode hardening as the temperature decreased, but the static dielectric
constant deviated from that predicted by the LST relation due to interface “dead layer”
effects, which are more important is thinner films. Nevertheless, the soft mode frequency
was again affected in the same way by structural differences present in the film, but
absent in bulk crystals.
It was proposed that the mechanisms responsible for the soft mode hardening are
dependent on lattice structural defects typically present in films, possibly oxygen
vacancies and strain, the two most common issues associated with epitaxial growth of
perovskite oxides.
In an effort to further understand the causes of the soft mode
hardening, additional electric-field induced Raman scattering experiments were
conducted.
The second study conducted by Akimov et al.H focused on the dependence of the
soft mode frequency on electric field and temperature as they relate to the electric fieldinduced tuning of the static dielectric constant. Parallel-plate capacitors were constructed
using transparent indium-tin oxide (ITO) top electrodes, which did not effect the Raman
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188
measurement, on 1 pm epitaxial SrTiCh films.
A DC bias was applied via these
electrodes during the measurement up to a field of 25 kV/cm.
The zero-field soft mode was found to occur at around 40 cm'1 at a temperature of
5 K. However, under the applied DC field the soft mode split into two components, due
to the tetragonal distortion of the lattice, which correspond to the polarization
perpendicular and parallel to the applied field. It was found that the splitting of the soft
modes is twice as large as that observed for bulk SrTiCh, with the two peaks occurring at
40 and 63 cm'1 in the film, and at 13 and 20 cm'1 in the bulk. Therefore, hardening of the
soft mode frequencies were also observed under DC bias for the film. These effects
could be attributed to strain in the lattice, although strain should be minimal for
homoepitaxial growth of 1 pm thick films. It was then also proposed that this behavior
was a result of local polar regions associated with a quasistatic polarization around
ir
oxygen vacancies; a phenomenon shown to occur in perovskites .
The dependence of the soft mode frequency,
0J t o \,
can be written in terms o f the
polarization, P (either spontaneous or induced by an external field), by combining the
free-energy expansion of Devonshire with the LST relation, as shown by Fleury et al.46,
a > U T ,P ) = < , ( 7\ 0 ) + A-(3$>2 + 5 nP ')
where A,
(5.2)
and r\ are parameters of the Devonshire expansion of the dielectric
susceptibility. This suggests that at low temperatures, where SrTiCh is in a tetragonal
state with lower symmetry than the cubic phase (Tc~120 K) the influence o f the
polarization is strong because o f the hardening of the soft modes as compared to the bulk.
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189
The increase in the soft mode frequency was about 3 times greater in the films, a
difference of 30-40 cm '1 which was much stronger than the electric-field effect. At
higher temperatures (above 120 K), the difference was only 10 cm’1 and the effect of the
electric field is similar. Therefore, this showed that the hardening of the soft modes was
related to the concentration of local polar regions associated with the electric-field
induced alignment of electric dipoles associated with oxygen vacancies. Further proof of
the polar regions was supported by the Raman activity of other optical phonons induced
by the breaking of the central symmetry o f SrTiCL by the local polarization.
Akimov44 also showed that the LST relation is well-obeyed through independent
measurements of the low-frequency dielectric constant, So, as a function of temperature
and electric-field. Since the frequencies of the other Raman active phonons other than
the soft mode do not change much with electric field and temperature, the LST relation
can be simplified to,
£„(T,E) cc
1
where E is the electric field and T is the temperature.
(5.3)
Therefore, due to the nearly
identical behavior of the dielectric constant and soft mode frequency dependence on
temperature and applied field, the electric-field induced tunability can be directly related
to the hardening of the soft mode.
Few studies have been conducted on the soft mode behavior of BST. A recent
work by Goux et al.3S examined the soft mode effect on the dielectric constant of
epitaxial BST (60/40) thin films on SrTiC>3 substrates. Infrared reflection spectra were
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190
collected on two films of 240 nm and 486 nm thickness. To determine the relation o f the
dielectric constant to the reflectivity measurements over the range o f 30 to 1000 cm’1, the
spectra were fit to the LST relation with the Fresnel relation38,
(5.4)
which tied together the reflectivity, R, and the dielectric permittivity, s . The soft mode
frequency was shown to vary with film thickness between 80 and 100 cm’1 and cause an
increase in the dielectric constant. Another lower frequency peak was also observed
which caused a local increase in the dielectric constant, but did not vary with film
thickness.
Therefore, the behavior of the dielectric constant o f BST may be more
complex than in SrTiCL. Mueller et al. 4 1 has shown in BaTiCb that the soft mode is not
the only trigger o f the ferroelectric to paraelectric phase transition; it is also related to
polar critical fluctuations near Tc.
The two studies o f SrTiC>3 show that hardening of the soft mode frequency occurs
in thin films, and that the soft mode behavior can predict the dielectric response of the
film. The proposed mechanisms for the observed soft mode hardening were attributed to
several reasons all related to lattice defects common in thin films.
It would not be
unreasonable to then assume that strain in epitaxial BST films is a contributing factor to
the soft mode hardening. Furthermore, although the soft mode hardening may not in
itself fully explain the strain-effected properties, such as the decrease in tunability with
increasing in-plane strain, it seems likely that it is at least part of the reason for the
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reduced tunability in highly strained films. The contribution of the increased soft mode
hardening with higher strain levels could move the maximum permittivity and tunability
region further away from room temperature leading to a reduction in the tunability. In
addition, it may be partly due to the previously described limitation of the ionic
displacements in constrained unit cells. In fact, constrained ionic movement has also
AO
been shown to cause shifts in the soft mode frequency , which would again affect the
tunability both directly and indirectly.
Section 5.3 will explore the temperature dependence of the maximum permittivity
and tunability to the proximity to the strain-effected phase transition temperature. This
will further support the theory of reduced tunability due to soft mode hardening from
increasing strain levels.
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192
5 .2 .3 .2
P e r m it t iv it y
The permittivity of the films was determined using the conformal mapping and
partial capacitance techniques described in Section 4.3. Figure 5.18 shows the trend in
the dielectric constant with film thickness for both the LaAlC>3 and MgO series at 10 GHz
at room temperature.
The solid traces show the data extracted from the capacitance
measurements, which covers the thickness range of 270 to 1150 nm. Below that range
the dielectric constant calculation did not compute accurately, and therefore the predicted
trends are shown for each film series with dashed lines. The next film thickness in each
film series was 160 nm which was below the working range o f the program.
In
computations of the dielectric constant for films less than -200 nm the extraction
program produced inconsistent results that underestimated the dielectric constant and
eventually led to negative values for the LaA 1 0 3 film series below a thickness of about
100 nm. For that reason the dielectric constant data of the MgO film series for 160 nm
and below was also omitted. The reason for this error is believed to be due to the small
capacitance values, which made the calculation very dependent on the input parameters
such as the substrate dielectric constant.
The dielectric constant of the BST films on LaA 1 0 3 showed a gradual increase
with film thickness, and saturated at -1200 at around 825nm. The trend of the dielectric
constant was very similar to that of the tunability versus film thickness.
The higher
strains associated with the thinnest films may have shifted the transition temperatures
away from room temperature, and therefore the dielectric constant may also decrease as a
result of increasing strain. This trend was also observed by Canedy et al.
for BST
(50/50) on a compressive substrate of LSAT, as shown in Figure 2.6b of Section 2.1.
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193
2000
Ej. BST/LaAl03series :
e,. j- BST/LaAlOj series (predicted)
sr j- BST/MgO series
%. j- BST/MgO series (prejdiirted)
1500
&
s
U
*S 1000
s
500
0
200
400
600
800
Thickness (nun)
1000
1200
Figure 5.18: Dielectric constant vs. film thickness for BST (60/40) on LaA103 (red) and
MgO (blue) at 10 GHz. Dotted lines indicate predicted trend.
The BST films on MgO also showed a dielectric constant behavior similar to the
tunability versus film thickness. Films on MgO were shown to have a constant dielectric
constant of -1080 across the thickness range of 270 to 1150 nm. This corresponds very
well with the observed trend of the tunability. As was previously shown, the tunability
plateaus at -300 nm, which when combined with this data show that high tunability and
high dielectric constants occur concurrently (a conclusion also supported by the LaAlC>3
series data set). Also note that the strain for these films does not build to a significant
level until the thickness drops below 200 nm, and as such the strain has no perceivable
effect on the dielectric constant over this range.
However, below this thickness range an odd occurrence is predicted as indicated
by the dashed blue line. After many simulations of the dielectric constant tested with a
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194
range of substrate dielectric constant values, an even higher dielectric constant was
calculated for the 44 nm film.
This does not seem consistent with the measured
capacitance data, as that trend clearly shows a decrease with film thickness. In addition,
the tunability drops off sharply below -140 nm as mentioned in the previous section.
Despite this, the dielectric constant was calculated at nearly 1600 at a film thickness o f 44
nm. Strangely this trend in the dielectric constant of BST films on MgO has also been
experimentally observed by Li et al ? 4 using the Gevorgian dielectric constant extraction
method49, as shown in Figure 2.8 of Section 2.1. At this time it is difficult to say if this
trend is correct, as no physical mechanism has been experimentally identified as the
cause of this behavior.
It is then useful to compare this experimental data to Ban and Alpay’s20
theoretical predictions of the in-plane permittivity of BST (60/40) on compressive and
tensile substrates. There calculations are based on a modified free energy function that
relates the thermodynamic potential to the polarization, misfit strain, and temperature, as
discussed in Chapter 2. They predict that the in-plane permittivity rises sharply due to a
dielectric anomaly at -40 nm.
The anomaly is believed to be the result of a strain
induced phase transition from one polar phase to another, in this case the transition from
the aa phase (two in-plane polarizations states) to the r-phase (two in-plane polarization
states, and a third polarization direction in the normal). The trend they calculate from
their model shows that the dielectric constant increases to >5000 around 40 nm (Figure
2.13b, Section 2.1). Clearly both the dielectric constant of the 44 nm film from this work
and the thinnest films o f Li et al,34, as calculated from the Gevorgian model49, do not
approach such values. However, above a thickness of 200 nm the theoretical predictions
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195
of the permittivity match closely with the data presented here, as it saturates at around
1200. In addition, the theoretical permittivity of BST (60/40) films on LaAlC>3 is also
provided. Although the trend is similar to experiment, showing a gradual increase with
film thickness, the permittivity rises to values near 3000 for films of only 300 nm thick.
This is again much larger than what is experimental observed, likely due to the fact that
other extrinsic defects limit the maximum obtainable permittivity.
Dielectric constant measurements as a function of temperature will be presented
in Section 5.3 which will provide more insight to the observed behavior.
Those
measurements will show that the temperature of the permittivity maximum shifts with
strain away from room temperature, which is a likely contributor to the change in the
dielectric constant with film thickness.
Other commonly cited causes of the degradation of the properties of thin films
associated with decreasing film thickness include interface effects between film and
substrate and the “dead layer” effect, usually associated with film/electrode interfaces.
These phenomena are typically described in terms of a series capacitance contribution to
the dielectric properties o f parallel-plate capacitors. As such, they should not play a large
role in the strain-effected behavior of the microwave tunability and permittivity. This is
because the measured response of an IDC structure would be a parallel combination of
the signal passing through the “bulk” film layer and the defect layers. This would greatly
reduce the effect that such defect layers would have on the total measured signal.
Nevertheless, in very thin films the fraction of the field in the defect layers may be
significant, and therefore it is worth discussing further.
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196
Interface effects stem from the first few nanometers of the deposited film which
often are non-ideal in terms of composition and structure50’51.
Depending on the
similarity o f the two materials comprising the interface, interdiffusion may occur
resulting in intermediate compositions and phases.
This effect would be likely for
materials which are capable o f forming solid solutions such as an interface formed by a
BaTiC>3 film on SrTiC>3 substrate. No solid solutions are known to exist when BST and
LaA 1 0 3 or BST and MgO are mixed. They may be combined as a two-phase mixture
such as the BST-MgO composites for microwave applications discussed in Section 2.2;
however this does not imply favorable interdiffusion of the atomic species of each
material into the crystal lattice. In fact, in a study by Gao et al.
it is has been found
through cross-sectional transmission electron microscopy and selected-area electron
diffraction that the interface of BST (50/50) on LaA 1 0 3 is atomically sharp with no
precipitates or second phases. Only edge dislocations were observed along the interface
at intervals of 22 unit cells of BST to 23 unit cells of LaA 1 0 3 (estimated concentration of
0
9
2 x 10 c m '), which agrees well with the 4.3 % lattice mismatch. In addition, no large
angle grain boundaries were found across the entire cross-section, indicating near perfect
single crystal growth. It is then likely that a similar sharp interface exists between BST
films on MgO substrates. As discussed in Section 5.1, the cross-sectional field-emission
scanning electron microscopy images of the interfaces of the films produced for this
study, show no columnar structures or grain boundaries, also indicating near perfect
single crystal growth.
The “dead layer” effect has been studied by many researchers interested in the
development o f BST films for planar capacitor memory applications. It is commonly
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197
thought to occur at film/electrode and film/substrate interfaces where a “non-bulk-like”
layer of constant capacitance density exists in series with the “bulk” film layer. The
behavior is often described in terms an inverse capacitance density model of the form35,
A
(t - n ,
C
V
£ i£ 0
t
2ta
(5.5)
£ s£ 0 J
where C is the capacitance, A is the area, t is the film thickness, ts is the thickness of the
“non-bulk-like” surface layer, and Si, Ss, and So are the permittivity of the interior “bulk”
film layer, the surface layer, and free space, respectively. Using this model the inverse
capacitance density can be plotted versus the film thickness, and the non-zero intercept is
ei o
interpreted as the “non-bulk-like” layer ’ ' .
The model is not applicable to
interdigitated structures with constant gap size, where the capacitance has been observed
to decrease with film thickness.
It is derived from the standard equation for the
capacitance of planar structures with two electrodes (in a sandwich configuration, one on
the top and one on the bottom of the film) where the capacitance is inversely proportional
to the thickness, t.
C
A££q
=
(5.6)
This model also makes the assumption that the interior “bulk” layer of the film is
not affected as the thickness is decreased (i.e. no thickness effects), which as discussed
previously is not likely the case since the soft phonon mode frequency does shift with
strain caused by decreasing thickness. Furthermore, in a study by Zhou et al,53 on the
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198
“dead layer” he showed that the finite size of very thin films would lead to a suppression
of the soft mode near the interface in a way that would appear as a “dead layer”. This
behavior was attributed to interface effects on the dipole-dipole interactions involved in
ferroelectric ordering.
Therefore, to explain the behavior of the dielectric constant versus film thickness
is not trivial, as it is dependent on the distribution of the electric field in the thickness of
the film. This is because the electric field lines would pass through any such “dead
layer” in parallel with the regular film layer. Any significant contribution from “non­
bulk-like” layers would only exist in the thinnest films, but could not in itself explain the
decrease o f the dielectric constant of BST on LaA 1 0 3 . In addition, the dielectric constant
of BST on MgO shows no thickness dependence at all down to ~200 nm, the limit of the
calculation range.
Further investigation of thickness effects will be addressed in the following
section where experimental evidence of the thickness dependence of the non-linearity of
the field-induced charge of the film layer is presented, which is shown to be directly
related to the in-plane strain state.
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199
5 .2 .3 .3
F ie l d -I n d u c e d In -P l a n e C h a r g e
The capacitance vs. voltage data collected as a function of DC bias from -4 0 to
40 V was used for calculation of the in-plane field-induced charge in the films. The
calculation was performed by integrating the C-Y curves taken at 10 GHz. As will be
discussed later, only the calculation of the charge is presented, and not the polarization,
due to uncertainty of the area over which the charge distribution exists. The equation
which relates the in-plane charge, Q, to the measured capacitance, C, is,
Q = )c d V
0
(5.7)
where V is the voltage o f the applied bias (up to ±40 V). The electric field applied to
each film was the same due to the constant 5.5 pm gap of the interdigitated capacitors.
For a maximum voltage o f ±40 V, the corresponding maximum field was approximately
±7.3 MV/m, or ±73 kV/cm.
The in-plane field-induced charge was then plotted versus electric field for each
film thickness in the LaAlOg and MgO series to determine if any thickness effects were
present in these systems (Figure 5.19a and 5.20a). It was observed that both the nonlinearity and the magnitude of the in-plane field-induced charge decreased with film
thickness for both the compressive and tensile stress states. The thickest films show the
highest non-linearity in field-induced charge, with a field-dependence typical of a
ferroelectric material. This thickness effect behavior shows that regardless of the state of
strain (compressive or tensile), the non-linear dielectric response decreases with film
thickness.
However, subtle differences in the non-linearity of the in-plane charge
between compressive and tensile strained films can be seen for a thickness <160 nm.
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200
22 nm
44 nm
— 4B~ 110 nm
160 nm
270 nm
_ 0 _ 400 nm
o
625 nm
.
v s2 5 n m
1150 nm
—V —
B S m a A IO series
\
-6
-4
-2
0
2
I 11 'I
4
6
8
Electric Field (MV/m)
(a)
1.0e-5
~-®— 22 nm
- t — 44 nm
110 nm
O 160 nm
7.5e-6
^
5.0e-6
o
U
=L 2.5e-6
8 d o.o
5 -2.5e-6
U
-5.0e-6
-7.5e-6
BST/LaAlO, series
o
-1.0e-5
-8
-6
-4
-2
0
2
4
6
8
Electric Field (MV/m)
(b)
Figure 5.19: In-plane charge vs. electric field (a) as a function of film thickness for the
BST/LaA103 series, (b) zoomed view of thinnest films showing decreased
non-linearity.
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201
22 nm
44 nm
110 nm
160 nm
270 nm
—• — 400 nm
O
625 nm
V
825 nm
1150 nm
6e-5
5 e -5
G
4e-5
3e-5
2e-5
le-5
4>
0
P t
eg
-le-5.
-2e-5
-3e-5
-4e-5
-5e-5
-6e-5
BST/MgO s e r ie s
■ i" j
8
>
-6
'
'
|
-4
i' 'i
|
i.......>""'i
-2
)
0
' i
■ t
2
1
‘" 1 I
4
6
8
6
8
Electric Field (MV/m)
(a)
1.0e-5
—• — 22 nm
7.5e-6
^
5.0e-6
U
=L'
'w
2.5e-6
44 nm
•n - HO nm
O
160 nm
§0 0.0
u
2 -2.5e-6
U
- 5 .0 e - 6
- 7 .5 e - 6
D "
u.
cr
-1.0e-5
-8
-6
-4
-2
0
2
4
Electric Field (MV/m)
(b )
Figure 5.20: In-plane charge vs. electric field (a) as a function of film thickness for the
BST/MgO series, (b) zoomed view of thinnest films showing decreased
non-linearity.
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202
Figure 5.19b and 5.20b show a zoomed view of the in-plane charge behavior for
the thinnest films, 22 to 160 nm. The compressive strained films on LaA 1 0 3 exhibit a
much reduced non-linear response versus the tensile strained films on MgO. The non­
linear response can clearly be seen for the 44 nm film on MgO (and even slightly at 22
nm), while it is has virtually disappeared for the films below 110 nm on LaAlOa.
Another clear difference is that the 22 and 44 nm films on LaA1 0 3 actually have a higher
in-plane charge than films o f the same thickness on MgO. This is due to the slighter
higher measured capacitance for the two thinnest films on LaA1 0 3 as shown in Section
5.2.2.
This behavior can be directly related to the tunability vs. film thickness and strain
as shown previously. The polarization, when calculated from this in-plane charge, will
not result in any change of the non-linearity of this these curves as it will only require the
division by the area over which the charge is distributed, or in others words, the crosssectional thickness through which the electric field lines of the microwave signal pass.
P =Q =
A
fj.C
(5.8)
cm 2
Therefore, the in-plane charge divided by the area would only result in a change
o f the absolute difference between the slopes of the curves. This means that the curves
may shift along the polarization axis (or currently the in-plane charge axis) relative to one
another. The slopes may change, but not the change in the slope, or the second derivative
o f each curve. This is important for making sense of how the tunability and dielectric
constant relate to these in-plane charge curves.
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203
The polarization in any dielectric layer as defined by Equation 1.2 of Section
1.2.2 is,
P = £0£rE
(5.9)
where E is the applied electric field, and Sr and So are the relative permittivity and the
permittivity of free space, respectively.
Furthermore, the slope of a polarization vs.
electric field curve is then the related to the permittivity as,
dP
dE
=
(5-10)
0r
The slope of the in-plane charge vs. electic field curves as currently shown indicates that
the low-field (near zero bias) permittivity of the films is greater for the 22 and 44 nm
films on LaAlCE than for films of the same thickness on MgO, which was contrary to the
predicted behavior. However, it is expected that the slope, and hence, the permittivity
will change appropriately when the correct area is used to calculate the polarization.
Therefore, the trends of the permittivity as observed in Figure 5.18 should fall in
agreement with the P vs. E curves generated from the in-plane charge data.
The more important issue is how the tunability relates to the observed nonlinearity of the in-plane charge or polarization.
As mentioned previously, the non-
linearity o f the curves, whether represented as in-plane charge or polarization will not
change with division by a constant (the area). The change of the slope of the curves (the
non-linearity), or the second derivative of the curves is directly the tunability.
d 2P
—
dE
d£
-
—
...
Tunability
dE
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(5.11)
204
The tunability can then be directly related to the non-linearity of the in-plane
charge (or polarization) curves. It is then concluded that the clear non-linear response of
even the thinnest films on MgO is a direct indication of the high tunability observed for
these very thin films. The thinnest films on LaA 1 0 3 show almost no non-linearity, and
hence, have very little tunability. For example, the 30% tunability of the 22 nm film on
MgO, compared to the 3% tunability of the 22 nm film on LaA1 0 3 . This again proves
that the strain state in the films has direct influence on the dielectric response. Tensile
strain, as measured for films on MgO, then results in a better non-linear response with
applied field, which is the reason for the observed high tunability.
The calculation o f the true polarization of the films has been attempted, but due to
the complexity of the electric field distribution in interdigitated structures it is currently
not possible without electromagnetic field simulations and mathematical modeling. The
polarization is, o f course, dependent on the total area over which the charge is distributed,
as mentioned previously. In other words, the area through which the in-plane microwave
field passes must be known in order to calculate the polarization for each film thickness.
For films where the dielectric constant is the high (the thickest films in the LaAlC>3 series,
and all films in the MgO series), the field should be largely confined in the gap between
electrodes with little, if any, field actually reaching the substrate layer. However, for
films where the dielectric constant is relatively low, the field may penetrate into the
substrate. Thus, the distribution of the field in the thickness of the film is needed in order
to accurately calculate the in-plane polarization of the BST layer. Figure 5.21 shows the
nature of this problem for the changing electric field distribution in films of decreasing
thickness, as would be expected for the BST/LaA 1 0 3 series. Films on MgO may not
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205
show the same change due to the difference in the behavior of the dielectric constant with
decreasing film thickness. The reason for the penetration of the field into the substrate is
due to the fact that as the dielectric constant of the film becomes small, it may approach
values close to that o f the substrate (-23.5 for LaA103 and 9.8 for MgO at microwave
frequencies54). Therefore, the impedance mismatch between the layers may not be very
large, allowing some of the field to pass through the substrate. This effect would be more
likely to occur for very thin films on LaA103 substrates where the dielectric constant may
be similar to the substrate.
±
+
.................................................
...
....................................... ..... ........
.
!
T
Him
Substrate
f
t=625 nm ->High s r
H|-
+
t=1150 nm ->High s r
(’..... rv'.'" .................................... ...... .
+
^
t
Him
Substrate
*
*
1
t=160 nm -^M oderate s r
t=22 nm ->Low e*.
Figure 5.21: Electric field distribution in films of varying thickness, showing change in penetration
depth (yellow shaded area) with decreasing dielectric constant of the film.
Once the depth o f the field penetration is known it can be used to calculate the
cross-sectional area through which the field passes using a meandering path between the
fingers of the electrode. Figure 5.22 shows the trace of the path between the two contacts
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2 06
of the interdigitated structure. The length o f the path multiplied by the penetration depth
for each film thickness would then provide the area over which the in-plane charge is
distributed.
Meandering path
between fingers
+EE
±fc
Figure 5.22: Meandering path between the fingers of an IDC used for the length in a
calculation of the in-plane polarization.
An attempt at estimating the in-plane polarization was made by calculating the
area based on the meandering path length multiplied by the film thickness. This assumes
that the field is evenly distributed through the entire film thickness for each of the nine
different film thickness values. It also assumes that the dielectric constant change with
film thickness has no effect on the electric field distribution in the film.
Figure 5.23a and 5.23b show the result of this calculation for both film series.
The order o f magnitude polarization is correct based on reported values of the
polarization of BST thin films55. The trend observed in completely contrary to the
measured dielectric response. It shows that the polarization of the thinnest films in both
film series are the highest, with all other samples having a similar polarization. Clearly,
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207
by using larger areas for thickest films the polarization was reduced, and in the same
manner, using small areas for the thinnest films resulted in large polarization. However,
the fact that the thinnest films (22 and 44 nm) do not group with the other films implies
that the field distribution may be more complex in these films with possible field
penetration into the substrate.
22 nm
20
1150
u.
o -30
a*
B ST /L aA i03 series
-40
•8
6
4
2
0
2
4
6
8
Electric Field (MV/m)
=-•*0 * .-
0
22 nm
44 nm
110 nm
160 DID
270 nm
400 nm
625 nm
825 nm
1150 nm
.H -10
o -20
BST/M gQ series
-6
-4
-2
0
2
1i
4
‘"i
6
Electric Field (MV/m)
(b)
Figure 5.23: Attempted calculation of the in-plane polarization based on the film thickness multiplied
by the meandering path length for (a) BST/LaA103 and (b) BST/MgO.
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208
Overall, the thickness effect observed in the in-plane charge of these films is
likely similar to that which is commonly observed in thin films56'59 and in bulk ceramics
with small particle sizes60,61, which has been attributed to depolarization effects near the
surface, low-eapacitance “dead layers”, and even interface soft mode hardening, as
discussed previously. This effect has been shown to influence only the very thin films
(22 and 44 nm), where the non-linearity of the dielectric response begins to vanish.
Phenomenological theories that have been used to describe the behavior of thin
films in terms of a free energy thermodynamic potential often use bulk coefficients (as
listed in Table 2.3 of Section 2.1) to predict the properties of the film as affected by
polarization, temperature, and strain.
Theoretical predictions based on these models
show good agreement with the observed behavior of the films and are very useful for
analyzing experimentally observed properties. However, the prediction of new phases
for materials such as BST, as suggested by Pertsev el al .2 9 and used by Ban and Alpay20,28
for interpretation o f the dielectric response, is questionable.
The polarization states
predicted by their calculations seem reasonable (i.e. tensile strain induces two equal in­
plane polarization states, etc.) but the predicted phases, which have a variety of different
crystal symmetries, including orthorhombic and monoclinic, have never been observed
experimentally in x-ray diffraction studies.
Instead of attributing the dielectric properties to new phases, it may be possible to
relate the observed dielectric response to the thickness-dependent properties of the
material. The free energy equation of the form (in scalar notation),
A G(P,T,X)
= ~ a P 2 + \ p p t + \yP" - \ s X 2 - Q P ' x
2
4
6
2
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(5.12)
209
takes into account many o f the factors that effect the dielectric properties. The first three
terms include the order parameters a , P, and y, which determine the order of the phase
The last two terms represent the contribution of the stress, X, and
transition.
electrostrictive coupling of the strain, y. The other variables in the equation are: s, the
elastic constants); Q, the electrostrictive coefficient(s); P, the polarization; and T, the
temperature.
Studies o f the thickness-dependent electrostrictive coefficients, elastic
constants, and polarization would be very helpful in more accurately predicting thin film
behavior.
Such studies may also lead to new theories on the thickness-dependent
response of important thin film materials such as BaxSr(i_X)TiC>3 .
In addition, it has also been suggested that the phenomenological theory used to
describe the behavior o f thin films, which typically attributes the reduction of the
dielectric response to interface or surface depolarization effects, should be extended to
include soft-mode hardening43. By including fundamental lattice dynamical properties
such as the soft mode behavior even more realistic models may be created. Currently,
there are numerous proposed reasons for the observed behavior of thin films. Hopefully
both experimental and theoretical approaches will lead to better understanding o f this
complex behavior in the future.
The following section will present cryogenic temperature measurements of the
microwave properties o f the films. The temperature dependence of the maximum of the
dielectric response is investigated, as it is affected by strain. Both temperature and stain
dependent hysteresis measurements are also presented as a step toward the measurement
o f the strain/thickness dependent polarization.
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2 10
5 .3
T e m p e r a t u r e D e p e n d e n c e o f t h e M ic r o w a v e P r o p e r t ie s
In this section, the capacitance, permittivity, Q-factor, and hysteresis behavior of
the BST (60/40) films are presented as a function of temperature from 78 K to 328 K at
the mid-point frequency o f 10 GHz.
These measurements were performed using a
cryogenic microwave probing station as described in Section 4.3.2.2. Three BST films
on MgO, 44, 270, and 825 nm in thickness, were measured. The data presented herein
will show that strain shifts the temperature of the maximum dielectric response, which
may indicate a shift in the phase transition between the ferroelectric and paraelectric
phase.
In bulk BST (60/40) samples, the phase transition has been reported to occur in
the range o f 250 K to 278 K20’62"65.
To analyze the shift of the phase transition
temperature measured for the thin films studied in this work, a reference temperature of
257 K was chosen for the bulk transition temperature. This is as measured in a study by
fy
Ezhilvalavan et al. , where the addition of Sr
was determined to shift the transition
temperature by 3.4 °C/mol.
In general, the three phase transitions that normally occur in bulk BST (60/40),
rhombohedral to orthorhombic at 150-165 K63’64, orthorhombic to tetragonal at 190-220
K63’64, and tetragonal to cubic at 250-278 K, disappear in thin film form and become a
single broad peak. This broad peak observed for BST thin films has been shown to
broaden with decreasing film thickness32,35,55, but it is uncertain if the peak represents the
phase transition between ferroelectric and paraelectric state. To better understand the
significance of the peak as it relates to the phase transition, hysteresis measurements at
78,278, and 308 K are presented in the last part of this section.
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211
5.3.1
D e p e n d e n c e o f t h e P e r m i t t i v i t y M a x im u m o n t h e I n - P l a n e
S tra in
The three BST (60/40) films on MgO were measured as a function of temperature
and DC bias (±40 V) to examine the effect of the increasing in-plane tensile strain on the
permittivity maximum.
The three films were 44, 270, and 825 nm thick, with
corresponding in-plane strain states of +0.35%, +0.075%, and 0% as taken from Figure
5.11b. As mentioned previously, the dielectric constant calculation was not accurate
below -200 nm, therefore only the capacitance data is shown for the 44 nm film.
However, the trend of the capacitance with temperature is exactly the same as the trend of
the permittivity with temperature, allowing a comparison of the maximum in the
capacitance with the maximum in the permittivity of the other two samples.
Figure 5.24 shows the capacitance, dielectric constant, and Q-factor for the 825
nm film over the temperature range of 78 to 328 K. As expected the phase transitions
normally present over this range are absent, and instead a broad maximum is observed
centered at a temperature of 290 K. The capacitance and permittivity reach a maximum
of about 0.68 pF and 875, respectively, at 0 V bias. Even this sample, which has near
zero strain, shows a shift away from the normal maximum in the permittivity, which
occurs at the phase transition temperature at -257 K. It also seen that the durability is
dependent on temperature, and hence the relative closeness to the permittivity maximum.
At 78 K the durability is -37%, and at 290 K is reaches a maximum of -55%.
The Q-factor shows the inverse behavior of the permidivity and reaches a
minimum o f 8 at 0 V bias near the maximum permittivity. Away from the maximum at
290 K, the Q-factor increases only slightly to -12, but does show greater dependence on
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212
the applied bias at low temperature. The Q-factor increases by a factor of 2 at 290 K, but
a 150 K it increases by a factor of 3 with the application of a 40 V bias.
The overall behavior is typical of that which is observed near the phase transition
o f ferroelectric materials such as BST, as described previously in Figure 1.4 of Section
1.2.3. The permittivity reaches a maximum at the phase transition temperature, where the
tunability and loss are high (the Q-factor is low). At temperatures far from the transition,
the permittivity drops and the tunability and loss decrease (the Q-factor increases).
Therefore, it seems likely that the maximum in the permittivity is related to the phase
transition (hysteresis measurements supporting this will be presented later).
0.8
1000
BST on MgO —825 nm
BST on MgO - 825
0.7
800
600
0.4
400
0.3
0.2
200
-
0.1
50
100
150
250
200
300
50
350
100
150
200
250
300
350
Temperature (K)
Temperature (K)
(a)
(b)
50
30
6
10
so
100
150
200
250
300
Temperature (K)
(C)
Figure 5.24: Dependence of (a) capacitance, (b) dielectric constant, and (c) Q-factor on temperature
over the range of 78 K to 328 K for an 825 nm BST (60/40) film on MgO.
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213
It should be noted that there is a slight difference in the magnitude of the
capacitance, permittivity, and tunability presented in Section 5.2 for room temperature
and these measurements using the cryogenic probing station. It is likely the result of the
thermal history o f cooling the film to 78 K and then heating it back to room temperature.
If the film transitioned to a ferroelectric state at lower temperatures, the spontaneous
polarization may have affected the microwave response. Another reason may be the
equipment used for the cryogenic measurement. The probe tip was attached to a long
cantilever arm (~25 cm) which had several connection points that can develop micronsize gaps due to contraction at cryogenic temperatures. As a result, the impedance of the
line increases, and the derived capacitance and permittivity may then be lower than
normal. However, this will not affect trends or comparison between samples measured
with the cryogenic microwave system. In addition, the trends observed in the cryogenic
temperature measurements are certainly comparable with those trends observed in the
measurements taken solely at room temperature.
The 270 nm film, which contained a slight tensile strain of approximately
+0.075%, was measured next.
Figure 5.25 shows the behavior of the capacitance,
dielectric constant, and Q-factor with temperature. The most notable difference is that
the maximum has shifted to a slightly higher temperature, just outside the upper limit of
the measurement range.
The increase in the in-plane tensile strain has shifted the
maximum to about 340-350 K, and again there is no evidence of any of the other phase
transitions. The permittivity shows a small increase to just over 1000 at the projected
maximum compared to the 825 nm film, and is also slightly higher at lower temperatures.
The tunability has remained relatively unaffected, as it is still around 55% near the
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214
maximum, and decreases to -40% at 78 K.
The nearly identical tunability and
permittivity between the 825 nm and 270 nm films is in good agreement with the trend
observed at room temperature (Figure 5.16b). Therefore, an additional shift o f -+50 K in
the relative closeness to the phase transition does not seem to have affected these
properties much due to the broadening o f the transition.
The Q-factor also follows much the same behavior, with 0 V bias values of about
10, and 40 V bias values near 30. The slightly lower Q-factors of this sample are not
considered significant enough to conclude any difference in sample quality as the
calculation o f Q-factor is very susceptible to calibration errors. In fact, calibrations were
made at each temperature point (20 K increments) for this sample and the 44 nm film,
which is the reason for the greater scatter in the data.
Therefore, the Q-factor
measurements of the 825 nm film are likely less accurate, since only three calibrations
were made over the entire temperature range.
The thinnest of the films on MgO was the 44 nm film, which was under an in­
plane tensile strain of -+0.35%. Figure 5.26 shows the capacitance and Q-factor over the
same temperature range. As mentioned previously, it was not possible to calculate the
permittivity data; however, it has been shown that the capacitance maximum and
permittivity maximum occur at the same temperature (Figure 5.24a and 5.24b). The
capacitance maximum, and hence permittivity maximum, for this very thin film appears
to have shifted to slightly higher temperatures than the 270 nm film, around 350-375 K.
and become much broader, possibly as a result of an even more diffuse phase transition.
The dependence of the capacitance on the DC bias has also decreased and varies only
slightly with temperature; the tunability is -27% at 78 K and -32% at 308 K.
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215
1200
0.7
BST on M gO -2 7 0 !
BST on M gO -2 7 0
0.6
1000
I °-S
800
u
0.4
600
0.3
400
0.2
200
0.1
SO
100
150
250
200
50
300
100
Temperature (K)
ISO
200
250
Temperature (K)
(a)
300
350
(b)
so
BST on M g O - 270; nm
40 -
1 30
i
o
20
10
50
100
150
200
250
309
350
Temperature (K)
(e)
Figure 5.25: Dependence of (a) capacitance, (b) dielectric constant, and (c) Q-factor on temperature
over the range of 78 K to 328 K for a 270 nm BST (60/40) film on MgO.
0.25
;B S T o n r i g O - 4 4 n
st?
6?
o.
:
0.15
«
U
i
\1
'
'N
L ........-v
' \
......V...
0.1
:
0.05
50
100
150
200
Temperature (K)
(a)
300
50
100
150
200
250
300
Temperature (K)
(b)
Figure 5.26: Dependence of (a) capacitance and (b) Q-factor on temperature over the range
of 78 K to 328 K for a 44 nm BST (60/40) film on MgO.
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350
21 6
The Q-factor is approximately the same as that seen for the other films near room
temperature, ranging between -10 at 0 V bias to -2 0 at 40 V bias. It also increases with
decreasing temperature, but it is nearly twice that of the 270 nm film at the lower limit of
the temperature range. The reason for the increase is uncertain, but possibly due to lower
numbers of misfit dislocations, as they have been shown to increase loss in BST thin
films26.
Overall, it is clear that increasing in-plane tensile strain has the effect of shifting
the phase transition to higher temperatures. It was also observed that the phase transition
becomes broader with decreasing film thickness, which has also been observed by other
researchers35,55. Both o f these effects may contribute to the observed changes in the
permittivity and tunability with film thickness (Figure 5.16 and 5.18).
As discussed previously in Section 5.2.3.2 the permittivity varies quite differently
depending on the strain state. It was shown that an increase in the in-plane compressive
strain in BST films on LaA 1 0 3 (decreasing film thickness) caused a decrease in the
permittivity. However, because the in-plane tensile strain remained relatively constant
and low in magnitude for BST films on MgO down to a thickness of -200 nm, no
thickness effect was seen in the permittivity. From the temperature measurements of the
BST films on MgO, it is seen that the shift and broadening of the phase transition occur
in such a manner as to cause very little change in the permittivity at room temperature. It
is reasonable to believe that the shift and broadening of the phase transition will also
occur with compressive strains, such as those generated in the thinnest films on LaA1 0 3 ,
but it obviously does not occur in the same way for BST films on LaA1 0 3 . Instead, the
shift and broadening in the phase transition for films on LaA1 0 3 is observed as a gradual
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217
drop in permittivity with decreasing film thickness, beginning below a thickness of -800
nm. Therefore, the shift and broadening are likely affected differently by compressive
and tensile strain states. These two different effects are probably the result of a complex
interaction o f many factors including, the unit cell geometry, polarization states, and
lattice dynamics.
Tensile strain states may have the effect of increasing the width of the phase
transition, relative to compressive strain states. This would result in relatively constant
high permittivity and high tunability far from the phase transition.
This theory is
supported by the observed behavior of the films on MgO, where the permittivity and
tunability remained high and were less dependent on temperature, and hence relative
closeness to the phase transition. In fact, since the phase transition becomes very broad
for very thin films (Figure 5.26a), the region of highest permittivity (within a few degrees
of the transition temperature) may be extended over such a wide range as to appear as an
increase in the permittivity in very thin films; behavior that has been theoretically
predicted28 and observed experimentally34. Furthermore, the high tunability of very thin
films on MgO (-30%) is additional evidence that although the phase transition has
shifted to 350-375 K, the region of highest tunability may have been extended due to
broadening from the large tensile strain.
Fundamental properties of the crystal lattice that may be affected by strain include
the lattice vibrations (polar phonons) related to the phase transition.
As discussed
previously, the soft phonon mode frequency is dependent on the proximity to the phase
transition and is directly related to the increase in the permittivity at the phase transition
(Equation 5.1). The aforementioned studies of the soft mode behavior of SrTiOB43’44 and
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218
BST38, showed that it is dependent on the structure of the crystal lattice, and that soft
mode hardening occurs in thin films from defects (i.e. oxygen vacancies) and strain. It
was also suggested here that from those studies it could be inferred that soft mode
hardening may cause a shift in the phase transition temperature, leading to the reduced
tunability. This is consistent with the confirmation of reduced tunability corresponding
to the larger shifts o f the phase transition temperature with increasing strain. However, as
noted earlier, the tunability is also less temperature-dependent with increasing strain due
to broadening o f the phase transition. Therefore, it is possible that soft mode hardening
contributes to the shift, but it is uncertain if it has any contribution to the broadening of
the phase transition.
In addition, it has been suggested that the shift of the phase transition temperature
may be related to electrostrictive coupling between the strain and the polarization55,66.
This phenomena is known to occur in ferroelectric materials67, and is included in
thermodynamic phenomenological LGD models
'11 '7Ccc
’
of the form shown in Equation
5.12. For example, Sinnamon et al. 55 showed that the shift of the transition temperature
in BST (50/50) thin films may be due to a thickness-induced stabilization of the
ferroelectric phase. It was shown that the magnitude of the polarization of 100 nm films
was greater than that o f 175 nm and 625 nm films (Figure 2.4, Section 2.1), and that the
hysteresis o f the 100 nm film was larger than the thicker films. It was suggested that this
is due to electrostrictive coupling between the strain and the polarization as described by
Equation 2.3, where the first-order LGD coefficient, a , becomes negative below 500 nm
indicating a transition to a ferroelectric phase.
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219
However, it has clearly been shown in this work that even films with minimal
strain, such as the 825 nm film on MgO (Figure 5.24), show a +30 K shift in the phase
transition temperature from the bulk value of 257 K.
Therefore, strain-induced
electrostrictive effects may have some contribution to the shift, but as stated previously it
is believed to be the result of the complex interaction of the unit cell geometry,
polarization states, and lattice dynamics.
Hysteresis measurements as a function of temperature are presented next in an
effort to determine how the internal polarization of the films is affected by strain below
and above the Curie temperature.
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220
5.3.2
R e s id u a l
P o la riz a tio n
E ffe c ts
R e la te d
to
th e
P hase
T ra n s itio n
To understand the relation of the broad maximum in the dielectric response with
the phase transition, hysteresis measurements were taken at 78, 278 and 308 K. As
discussed previously, BST (60/40) is paraelectric at room temperature, and has a Curie
temperature around -257 K. Spontaneous polarization from the ferroelectric tetragonal
phase should then only be present below the Curie temperature. Above that temperature
no hysteresis should be observed due to the absence of stable spontaneous polarization
states in the cubic phase20,29. However, the room temperature hysteresis measurements of
the C-V curves presented in Section 5.2.2 (Figure 5.13 and Figure 5.14) for all films of
the LaAlCL and MgO series showed that there is some residual polarization which
increases in magnitude as the film thickness decreases, or the magnitude of the strain
increases. Therefore, hysteresis measurements of the C -V curves were also measured
below and above room temperature to determine how the residual polarization changes
with temperature.
Figure 5.27 and 5.28 are the hysteresis measurements for the 270 nm and 44 nm
BST (60/40) films on MgO. At the 78 K it is clear that large hysteresis exists due to
internal polarization, likely from spontaneous polarization in the ferroelectric phase. As
the temperature increased beyond the Curie temperature, the measurement of the C -V
curves still showed a significant hysteresis at 278 K, indicating that some type of residual
polarization is present. Further increase in the temperature to 308 K had only a small
effect on reducing the residual polarization of the films. It would be expected that any
internal polarization in the films would have vanished at a temperature of +50 K above
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221
270 nm
BST oii MgO at 78,278* 308 K
Trace 078_1
Trace 078 ^
B. 0.3
-40
-30
-20
-10
0
10
20
30
40
DC Bias (V)
Figure 5.27: Two cycles of the capacitance vs. DC bias for a 270 nm BST (60/40) film on MgO
at 78,278, and 308 K, showing varying amounts of hysteresis due to residual
polarization changes with temperature.
BST oh MgO a* 78,278,308 K j- 44 nm!
Trace 078_1
Trace 078 2
& 0.13
-10
0
10
DC Bias (V)
Figure 5.28: Two cycles of the capacitance vs. DC bias for a 44 nm BST (60/40) film on MgO
at 78,278, and 308 K, showing varying amounts of hysteresis due to residual
polarization changes with temperature.
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222
the Curie temperature (257 K). However, the presence o f significant residual polarization
combined with the observed shift of the permittivity maximum to higher temperatures
indicates that the tensile strain in these films has indeed affected the transition
temperature.
It seems likely that the phase transition between the ferroelectric and paraelectric
phase has become much more diffuse due to this strain-induced polarization effect. The
normal polarization fluctuations that occur at the transition temperature38,47 in bulk BST
are suppressed due to the tensile strain.
In addition, the broadening of the phase
transition may be related to relaxor-type behavior caused by defect dipoles created by
strain68'™.
The defect dipoles in BaxSr(i_x)Ti0 3 thin films have been experimentally measured
by J. Li et al.6i using a modified ellipsometry measurement. It was determined that the
linear electro-optic effect was present over a much broader range than expected (typically
only present in ferroelectric compositions) up to a composition of x=0.3, which was
attributed to the evidence of the existence of ferroelectric domains. It was also observed
that the quadratic electro-optic effect was dependent on composition, which suggested the
coexistence of paraelectric and ferroelectric phases. This behavior was described as a
relaxor-type effect since the coexistence of ferroelectric and paraelectric phases over a
broad range in composition at a fixed temperature is typical of relaxor ferroelectrics.
However, no mechanism for the existence of the ferroelectric domains was proposed.
In another study o f defect dipoles by Warren et al.
zq
they were experimentally
measured in Pb(Zr,Ti) 0 3 with electron paramagnetic resonance. The alignment of defect
dipoles along spontaneous polarization directions was attributed to a cooperative effect
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223
arising from lattice strain. It was also shown that defect dipoles can occur around oxygen
vacancies and other isolated defect centers. In addition, in a study by Zuccaro et al.70 it
was shown that defect dipoles are also associated with interstitials, and impurities at
interstitial lattice sites.
Therefore, defect dipoles are likely to exist in BST for the same reasons, defects,
oxygen vacancies, impurities, etc., which are all very common in thin films.
These
dipoles would then be a mechanism for the existence of residual polarization in the 270
nm and 44 nm films and the observed relaxor-type behavior. It is then possible that the
broadening of the phase transition is due to strain-dependent residual polarization around
defect dipoles in the film, which lead to the formation of ferroelectric domains above the
Curie temperature. Furthermore, the polarization caused by such dipoles may be the
reason for the suppression of the critical polar fluctuations that normally occur at the
phase transition38,47, leading to a single diffuse phase transition for BST thin films.
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224
C h apter Su m m a r y
Epitaxial (100) BST (60/40) thin films were grown on (100) LaAlQ3 and MgO
substrates with pulsed laser deposition.
Ideal PLD deposition conditions were
determined for epitaxial growth by examination of the film morphology with a variety of
characterization techniques.
The optimized PLD parameters yielded films that were
highly epitaxial, stoichiometric, and had a low surface roughness; they were 700 °C
(BST/LaA1 0 3 ) or 825 °C (BST/MgO), 100 mTorr O2 , 2 J/cm2 at 2 Hz, and a target-tosubstrate distance of 8.3 cm.
A series o f nine different films covering the thickness range of 22 nm to 1150 nm
were created on each substrate to vary the level of strain in the films. Films grown on
LaA 1 0 3 (4.4% smaller lattice parameter than BST (60/40)) developed an increasing
compressive strain with decreasing thickness.
Films on MgO (5.8% larger lattice
constant than BST (60/40)) had an increasing tensile strain with decreasing film
thickness. The thickest films of each series were near strain-free due to the formation of
increasing numbers of misfit dislocations at the growth temperature as the film thickness
increased.
Interdigitated capacitors were then patterned on each film through a
photolithographic process to create devices for the measurement of the microwave
dielectric properties over the frequency range of 1 to 20 GHz. The state of strain in the
films was then correlated with the capacitance, Q-factor, tunability, and permittivity. The
capacitance was relatively frequency independent and shown to decrease from just above
2 pF for the thickest films to 0.15 pF for the thinnest films on both substrates. Q-factors
were also relatively independent of film thickness and substrate type, with a range of 4 to
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225
20.
The low Q-factors are believed to be the result of large numbers of misfit
dislocations in the highly epitaxial films, with a possible contribution from metallization
losses or geometrical factors of the IDC structure.
One of the primary goals of this work was to determine the effect of strain of the
microwave tunability over a wide thickness range from <50 nm to over 1 pm. The
correlation of the tunability with the strain over this wide range was experimentally
investigated for the first time in this work. Comparisons were made between the two film
series at the midpoint frequency o f 10 GHz, since the properties were nearly frequency
independent.
Compressive strain states in BST films on LaAlCb caused a gradual
decrease in the tunability from 65% for the thickest films to 3% for the 22 nm film. The
tensile strain in the BST films on MgO was shown to be preferable for maintaining high
tunability over a wide thickness range. A maximum of 65% was again measured for the
thickest films, while the 22 nm film showed a much higher tunability of 30%.
The
tunability plotted as a function of misfit strain showed that the region of maximum
tunability exists from 0% to +0.07% tensile strain, which was in good agreement with
theoretical predictions based on LGD phenomenological models.
The reason for behavior of the tunability was attributed to the greater ionic
mobility in the unit cell for slightly tensile strain states. In addition, the degradation of
the tunability with increasing levels of strain was thought to be partly due to soft mode
phonon frequency shifts related to the strain in the unit cell. This soft mode hardening
which occurs in thin films has been shown to affect both the tunability and permittivity,
possibly by causing a shift in the phase transition temperature, and hence the region of
maximum dielectric response, away from the bulk BST (60/40) value of 257 K.
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226
The permittivity o f each film series also showed distinctly different behavior.
The dielectric constant o f films on LaA 1 0 3 decreased with thickness in much the same
manner as the tunability; a gradual drop toward zero. The dielectric constant of films on
MgO exhibited relative independence of film thickness, with a possible sharp increase for
very thin films. This strange behavior was attributed to the interaction of the shift and
broadening of the phase transition which occurred in such a manner as to keep the
permittivity constant at room temperature. The possibility of “dead layer” effects were
also discussed, but thought to be insignificant in all but very thin films due to the parallel
(rather than series) contribution to the measured properties for IDC structures due to the
electric field direction.
The in-plane field-induced charge was also examined as a function of film
thickness. The non-linearity of the dielectric response was found to decrease with film
thickness, but was dependent on the direction of the strain. Films on MgO showed a
clear non-linear response down to 22 nm due to the tensile strain states which was
directly related to the observed high tunability of the thinnest films. However, the nonlinearity nearly vanishes below 160 nm for films on LaA1 0 3 due to the compressive
strain, which correlates with the observed low tunability of those films. In addition, the
calculation o f the in-plane polarization was attempted, but unsuccessful due to the
unknown area over which the charge is distributed for each film thickness. Although, the
calculation was incorrect it did show that field distribution in the 22 nm and 44 nm films
may be complex, and possibly involve field penetration into the substrate.
Temperature measurements of the capacitance and permittivity of 44, 270, and
825
nm
films
on
MgO
showed
a
clear
shift
of the
maximum
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in
the
227
permittivity/capacitance to higher temperatures with decreasing film thickness or
increasing tensile strain. A shift o f up to +100-125 K occurred due to the +0.35% tensile
strain in the 44 nm film. The maximum also broadened with increasing strain, increasing
the temperature range o f the maximum dielectric response. This was observed through
the behavior o f the tunability with temperature, which was shown to be decreasingly
dependent on temperature as the film thickness decreased. These effects implied that the
temperature of the maximum was directly related to the phase transition temperature.
The shift of the transition temperature was believed to be the result of a complex
interaction of several mechanisms including soft mode hardening, electrostrictive
coupling, and residual polarization states.
Hysteresis measurements of the C -V curves were taken at 78, 278, and 308 K to
determine the change in the internal polarization below and above the Curie temperature
at 257 K. It was found that large internal polarization was present at low temperature
likely due to the spontaneous polarization states of the ferroelectric phase.
At
temperatures above the Curie point residual polarization was still present, evident through
the hysteretic behavior o f the C -V curves. This residual polarization was attributed to
the existence o f defect dipoles in the films created around defects such as oxygen
vacancies and impurities, both common in thin films. It was also proposed that the lattice
strain causes alignment o f the dipoles that result in the formation o f ferroelectric domains
which leads to a relaxor-type behavior observed as the broadening of the phase transition
with increasing strain.
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228
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233
CHAPTER 6 - CONCLUSIONS
In Chapter 3, it was stated that one of the most important factors that lead to the
difference between the properties of bulk and thin film materials is the strain in the
lattice. Through this investigation of the strain and thickness effects in BST thin films it
has been shown that the state of strain does have a great impact on the microwave
dielectric response. The wide thickness range studied in this work has provided good
insight on how the magnitude and direction of the strain in the films affects the behavior
of the microwave tunability, permittivity, and polarization.
At the beginning of this study, a list of questions were posed which were believed
to be most important issues for better understanding the effects of strain on the
microwave properties. Those questions are answered here based on the findings of this
thesis.
1. What is the effect of compressive and tensile strain states on the tunability and
permittivity at microwave frequencies?
The tunability was found to exhibit two different regimes of behavior based on
the strain state. The maximum tunability achieved for the thickest films of both the
BST/LaAl(> 3 and BST/MgO series was -65% due to the fact that those films were
nearly strain-free and had almost identical microstructures. Compressive strain in the
BST films on LaAlOa was shown to cause a large decrease in the tunability, and
while the tensile strain in BST on MgO also caused a decrease in the tunability, the
tunability was a factor of 10 greater for the 22 nm film on MgO (-30%).
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234
The compressive strain in BST on LaA 1 0 3 caused a proportional decrease in the
permittivity, in the same manner as the tunability.
However, the effect of large
tensile strains on the permittivity in BST films on MgO less than 200 nm is uncertain
due to inaccuracy in data extraction model for films below that thickness.
2. How does this effect scale with film thickness, from very thin films of 20 nm to thick
films o f over 1 micron?
The increasing in-plane compressive strain in BST films on LaA 1 0 3 reached a
maximum of -0.25% as the film thickness decreased to 22 nm. Films on LaA 1 0 3
(>400 nm) were under a slight tensile strain of up to +0.07%, which result in high
tunability near 65%. The large compressive strains which developed below 400 nm
were shown to cause a directly proportional drop in the tunability down to 3% at 22
nm. The permittivity was affected in much the same manner with decreasing film
thickness. It decreased gradually from around 1200 to near zero (estimated) as the
film thickness decreased toward zero.
The in-plane tensile strain in BST films on MgO was low (+0.05% to 0%) for
films >300 nm. The tunability reached a plateau of 65% at this thickness, since all
films greater in thickness were relatively strain-free. However, below 300 nm the
tunability dropped sharply due to the increasing tensile strain, but remained high at
-30% relative to films of the same thickness on LaA 1 0 3 . The permittivity remained
relatively constant at -1080 as thickness decreased from 1150 to 200 nm.
As
mentioned previously, the calculation of the permittivity was not accurate below 200
nm, and therefore the effect of large tensile strain on the permittivity is uncertain. It
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235
was hypothesized that very thin films on MgO may show a large increase in the
permittivity due to shift and broadening of the phase transition temperature, but more
accurate data extraction models need to be created for very thin films.
3. What is the preferable strain state, in any, for microwave device fabrication from BST
films?
It was clearly shown that near-zero strain, or slightly tensile strain states are
preferable for maintaining high tunability across a wide thickness range, especially in
very thin films. In addition, a near-zero to slightly tensile strain state allowed the
permittivity of films on MgO to remain high and relatively constant at ~1080 across a
thickness range o f 200 to 1150 nm. Therefore, it is concluded that a strain state of
0% to +0.07% is ideal for achieving the highest tunability from BST thin films using
interdigitated capacitors. It should be noted that in vertical capacitor structures, such
as parallel plate capacitors, the ideal strain state may be a tensile elongation in the
normal direction rather than the in-plane direction due the vertical direction of the
field in those structures.
4. Is there also a thickness effect involved for very thin films which will limit the
tunability and dielectric constant?
It was difficult to determine if there was a pure thickness effect in these films,
which limited the properties. The investigation of the in-plane field-induced charge
showed that the non-linearity o f the dielectric response decreased with film thickness,
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2 36
but was dependent on the strain state. In an attempted calculation of the polarization
from the in-plane charge data, it was observed that the polarization of the 22 and 44
nm films did not group with the other films (i.e. showed significantly different
behavior). This may be an indication that the field distribution in these very thin
film s is more complex and involve some degree of field infiltration into the substrate,
which may be considered to be evidence of a thickness effect. However, it is not
believed to have much influence on the microwave properties since it would have a
parallel (rather than series) contribution to the measured dielectric response. This is
supported by the drastically different properties observed for the 22 nm and 44 nm
film s on both substrates, which are attributed to the difference in the strain states.
5. How does strain affect the ferroelectric to paraelectric transition?
The paraelectric to ferroelectric phase transition (normally at -257 K) was shown
to shift to higher temperatures with increasing amounts of tensile strain (BST/MgO
series). The strain-free 825 nm film on MgO also showed a +30 K shift in the Curie
temperature. As the strain increased to +0.075%, the transition temperature shifted
by -+ 80-90 K, and at a tensile strain of +0.35% the transition temperature was
estimated to be +100-125 K above the bulk value. The phase transition was also
observed to broaden significantly with increasing strain. The shift and broadening
were thought to be from a complex interaction of several phenomena including soft
mode hardening, electrostrictive coupling, and defect dipoles.
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237
6. Do we observe the standard transitions for Bao.6 Sro.4 Ti0 3 , from rhombohedral to
orthorhombic to tetragonal to cubic, (typically occurring at ~ 150-165 K, -190-220 K,
and -250-278 K, respectively) over the studied temperature range of 78 K to 320 K
for thin films? If not, are the transitions suppressed due to strain?
The phase transitions normally present over the studied temperature range, as
listed above, were not observed in the measurement of the permittivity/capacitance
versus temperature.
Instead a single broad phase transition was observed which
shifted to higher temperatures with increasing in-plane tensile strain.
It was
concluded that tensile strain did have the effect of suppressing the phase transition by
causing it to broaden and shift, due to the phenomena listed in Question #5.
7. How does the internal polarization change with temperature as the measurement
temperature approaches the ferroelectric to paraelectric transition?
Measurements o f the C -V curves at 78, 278, and 308 K helped to tie the phase
transition to the observed maximum in the dielectric permittivity.
Significant
hysteresis was observed at low temperature in both the 270 nm and 44 nm films on
MgO, likely due to spontaneous polarization states of the ferroelectric phase. As the
temperature was increased to 278 K the hysteresis decreased but was still present
above the bulk phase transition temperature of 257 K.
Further increase in the
temperature to 308 K did not significantly reduce the hysteresis. The hysteresis was
believed to be caused by the formation o f ferroelectric domains around defect dipoles
which have been experimentally observed in ferroelectric thin films. These defect
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238
dipoles are the result of the displacement of charges associated with oxygen
vacancies, interstitial impurities, and other lattice defects.
In conclusion, the microwave properties of the BST thin films were found to be
greatly dependent on the magnitude and direction of the strain. The behavior seems to be
directly related to the shift and broadening of the phase transition between the
ferroelectric and paraelectric phases. The fundamental mechanisms through which strain
affects the phase transition, and in turn, the microwave properties must be further studied.
A better understanding of the complex interaction of phenomena such as soft mode
hardening, electrostrictive coupling, and the formation of ferroelectric domains around
defect dipoles will allow the fabrication of ferroelectric thin films such as BST with
optimal properties for microwave devices and many other microelectronic applications.
The next, and last, chapter lists some proposed future areas of exploration for
those continuing the study of BaxSr(i_X)Ti0 3 thin films.
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239
CHAPTER 7 - FUTURE WORK
The investigation of the microwave dielectric properties of BST (60/40) thin films
as a function o f misfit strain, film thickness, and temperature has revealed some
interesting behavior which could be the result of a number of phenomena, including
strain-effected phase transitions, soft mode hardening, electrostrictive coupling, and the
formation of ferroelectric domains around defect dipoles. As research groups continue to
study these effects, a better understanding of their complex interaction will be developed
to enable the use o f ferroelectric thin film materials such as BaxSr(i.X)Ti0 3 in next
generation microwave passive components. However, many years o f work are still ahead
before it will be possible to mass-produce reliable thin film microwave devices based on
ferroelectric materials.
Some suggestions for future work following this investigation of the strain and
thickness effects in BST thin films are:
1. Examination of the formation misfit dislocations in BST as a function of thickness
to understand how the concentration of such defects affects the tunability,
permittivity, and Q-factor.
2. Measurement of the shift of the phase transition temperature as a function of Sr
content to determine if strain affects the shift and broadening of the transition
differently depending on composition.
3. A study o f the thickness-dependent material properties of thin films to determine
if the bulk coefficients commonly used in thermodynamic phenomenological
models are really applicable.
The measurement of the elastic constants,
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240
electrostrictive coefficients, etc. of thin films may show that they are different
from bulk values.
4. A study comparing the results obtained in this thesis using interdigitated
capacitors versus the strain effects observed in the normal (or growth) direction of
the film using parallel plate capacitors.
5. Investigation o f the defect mechanisms in BST thin films which may lead to high
loss, or low Q-factor.
The determination of impurity concentrations, atomic
bonding states, and film surface/electrode interactions may all be important in
improving thin film microstructures to achieve higher Q-factors.
6. The transition between the ferroelectric and paraelectric phases should be further
investigated with temperature-dependent x-ray diffraction measurements to
determine how exactly the phase transition occurs under the influence of different
levels of strain.
Finally, I wish success to anyone continuing on this work and hope that these
proposed research topics will provide interesting studies that will further add to the
understanding of the microwave dielectric response of BST thin films.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
241
APPENDIX
Calculation of Film Permittivity by Conformal Mapping and Partial Capacitance Methods
Written by Dr. Jeffrey Pond and Dr. Steven Kirchoefer o f the U.S. Naval Research Lab
DECLARE
DECLARE
DECLARE
DECLARE
FUNCTION
FUNCTION
FUNCTION
FUNCTION
CH# (x#)
SH# (x#)
K# (x#, xxf)
ATAN2 (y, x)
Based on the papers:
1.
"Modelling of thin-filra HTS/ferroelectric interdigital
capacitors,"
S. Gevorgian, E. Carlsson, S. Rudner, L.-D. Wernlund, X. Wang,
and U. Helmersson, IEE Proceedings - Microwaves, Antennas, and
Propagation, vol. 143, no. 5, pp. 397-401, Oct. 1996.
2.
"CAD Models for Multilayered Substrate Interdigital Capacitors,"
S. Gevorgian, T. Martinsson, P. L. J. Linner, and E. Kollberg,
IEEE Trans, on Microwave Theory and Tech., vol. 44, no. 6,
p. 896, June 1996.
startover:
PI# = 3.141592653589793#
epsO# = 8.854E-18
’
1
epststn# = 100#
INS$ =
INPUT "ENTER the dielectric constant calculated by Touchstone
model (100) ", INS$
IF INS$ <> "" THEN epststn# = VAL(INS$)
h2# = .3#
INS$ = ""
INPUT "ENTER FE FILM THICKNESS (0.3 microns) ", INS$
IF INS$ <> "" THEN h2# = VAL(INS$)
Hsub# = 508#
INS$ = ""
INPUT "ENTER SUBSTRATE THICKNESS (508 microns (20 mils)) ", INS$
IF INS$ <> "" THEN Hsub# = VAL(INS$)
epssub# = 23.5#
INS$ = ""
INPUT "ENTER Substrate dielectric constant (23.5 for LAO) ", INS$
IF INS$ <> "" THEN epssub# = VAL(INS$)
epsflm# = 4000#
INS$ = ""
INPUT "ENTER FE film dielectric constant (4000) ", INS$
IF INS$ <> "" THEN epsflm# = VAL(INS$)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
242
t# = 1.25#
INS$ = ""
INPUT "ENTER METAL FILM THICKNESS (1.25 microns) ", INS$
IF INS$ <> "" THEN t# = VAL(INS$)
IF t# < .01# THEN t# = .01#
gapspace# = 10#
INS$ = ""
INPUT "ENTER GAP SPACE {10 microns) ", INS$
IF INS$ <> "" THEN gapspace# = VAL(INS$)
g# = gapspace# / 2#
gend# = g#
xfactor# = . 5 #
INS$ = ""
INPUT "ENTER END GAP FACTOR ( 0 . 5 ) ", INS$
IF INS$ <> "" THEN xfactor# = VAL(INS$)
fingerwidth# = 10#
INS$ = ""
INPUT "ENTER FINGER WIDTH (10 microns) ", INS$
IF INS$ <> "" THEN fingerwidth# = VAL(INS$)
s# = fingerwidth# / 2# + (t# / 2# / PI#) * (1# + LOG(4# * PI# *
fingerwidth# / t#))
length# = 80#
INS$ = ""
INPUT "ENTER FINGER OVERLAP LENGTH (80 microns) ", INS$
IF INS$ <> "" THEN length# = VAL(INS$)
n# = 8#
INS$ = ""
INPUT "ENTER THE NUMBER OF FINGERS (any integer (8)) ", INS$
IF INS$ <> "" THEN n# = VAL(INS$)
hi# = Hsub# + h2#
h3# = Hsub#
I
'Defining the hyperbolic arguements for the periodic structure (Ref.l)
I
argnll#
argnl2#
argn21#
argn22#
argn31#
argn32#
= PI#
= PI#
= PI#
= PI#
= PI#
= PI#
*
*
*
*
*
*
s# /
(s# +
s# /
(s# +
s# /
(s# +
(2# * hi#)
g # ) / (2#
(2# * h2#)
g # ) / (2#
(2# * h3#)
g # ) / (2#
* hi#)
* h2#)
* h3#)
I
'Defining the hyperbolic arguements for the outside edge fingers(Ref.2)
arg311#
arg312#
arg313#
arg321#
arg322#
arg323#
arg331#
=
=
=
=
PI#
PI#
PI#
PI#
= PI#
= PI#
= PI#
* s# / (2# * hi#)
* (s# + 2# k g#) / (2# * hi#)
* (s# + 2# * s# + 2# * g#) / (2# * hi#)
* s# / (2# * h2#)
* (s# + 2# *
g#) / (2# * h2#)
* (s# + 2# k s# + 2# * g#) / (2# * h2#)
-k s# / (2# k h3#)
•
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
arg332#
arg333#
= PI# * (s# + 2# * g#) / (2# * h3#)
=PI# * (s# + 2# * s# + 2# * g#) I (2# * h3#)
1
' Defining the hyperbolic arguements for the end gaps (Ref. 1)
I
I
argell#
argel2#
arge21#
arge22#
arge31#
arge32#
=PI#
= PI#
= PI#
= PI#
=PI#
=PI#
* xfactor#
* (xfactor#
* xfactor#
* (xfactor#
* xfactor#
* (xfactor#
* s#
* s#
* s#
* s#
* s#
* s#
/
+
/
+
/
+
(2# * hi#)
gend#) / (2# * hi#)
(2# * h2#)
gend#) / (2# * h2#)
(2# * h3#)
gend#) / (2# * h3#)
' For the periodic portion (Ref. 1):
f
kO# = s# / (s# + g # )
kOpr# = (1# - kO# A 2#) A .5#
' For the ouside edge fingers (Eqn. 10 of Ref. 1):
f
k03# = s# / (s# + 2# * g # ) * ((1# - ((s# + 2# * g#) / (s# + 2#
s# + 2# * g # ) ) A 2#) / (1# - (<s#) / (s# + 2# * s# + 2# * g # ) )
2#)) A .5#
k03pr# = (1# - k03# A 2#) A .5#
\
' For the endgap portion (Eqn. 15 of Ref. 1):
I
kOend# = xfactor# * s# / (xfactor# * s# + 2# * gend#)
kOendpr# = (1# - kOend# A 2#) A .5#
t
' Equation 5 of Ref. 1 gives (for the periodic portion):
I
kin# = (SH#(argnll#) / SH#(argnl2#)) * ((CH#(argnl2#) A 2# +
SH#(argnl2#)
A2#) / (CH#(argnll#) A 2# + SH#(argnl2#) A 2#))
.5#
klnpr# = (1# - kin# A 2#) A .5#
k2n# = (SH#(argn21#) / SH#(argn22#)) * ((CH#(argn22#) A 2# +
SH#(argn22#)
A2#) / (CH#(argn21#) A 2# + SH#(argn22#) A 2#))
.5#
k2npr# = (1# - k2n#
A 2#) A .5#
' This term is also calculated to compare to Touchstone's number for
' homogeneous substrate
k3n# = (SH#(argn31#) / SH#(argn32#)) *((CH#(argn32#) A 2# +
SH#(argn32#)
A2#) / (CH#(argn31#) A 2# + SH#(argn32#) A 2#))
.5#
k3npr# = (1# - k3n# A 2#) A .5#
'PRINT "kin = ", kin#, klnpr#
'PRINT "k2n = ", k2n#, k2npr#
'PRINT "k3n = ", k3n#, k3npr#
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
244
' Equation 11 of Ref. 1 gives {for the outside edge fingers):
kl3# = SH#(arg311#) / SH#(arg312#) * {{1# - SH#(arg312#) A 2# /
SH#(arg313#) A 2#) / {1# - SH#(arg311#) A 2# / SH#(arg313#) A
2#)) A .5#
kl3pr# = (1# - kl3# A 2#) A .5#
k23# = SH#(arg321#) / SH#(arg322t) * ({1# - SH#(arg322#) A 2# /
SH#(arg323#) A 2#) / (1# - SH#(arg321#) A 2# / SH#(arg323#) A
2#)) A .5#
k23pr# = (1# - k23# A 2#) A .5#
k33# = SH#(arg331#) / SH#(arg332#) * ((1# - SH#(arg332#) A 2# /
SH#(arg333#) A 2#) / (1# - SH#(arg331#) A 2# / SH#(arg333#) A
2#)) A .5#
k33pr# = (1# - k33# A 2#) A .5#
PRINT "kl3
= ",kl3#, kl3pr#
PRINT "k23
= ",k23#, k23pr#
PRINT "k33
= ",k33#, k33pr#
Equation 16
of
Ref. 1 gives (for the end gap contribution):
klend# = SH#(argell#) / SH#(argel2#)
klendpr# = (1# - klend# A 2#) A .5#
k2end# = SH#(arge21#) / SH#{arge22#)
k2endpr# = (1# - k2end# A 2#) A .5#
k3end# =
k3endpr#
PRINT "klend
PRINT "k2end
PRINT "k3end
SH#(arge31#) / SH#(arge32#)
= (1# - k3end# A 2#) A .5#
= ",klend#, klendpr#
= ",k2end#, k2endpr#
= ",k3end#, k3endpr#
Equation 4 of
qln# =
K#(kO#,
q2n# =
K#(kO#,
Ref. 1 gives:
(K#(kln#, klnpr#) * K#(kOpr#, kO#))
kOpr#))
(K#(k2n#, k2npr#) * K#(kOpr#, kO#))
kOpr#))
/ (K#(klnpr#, kin#)
*
/ (K#(k2npr#, k2n#)
*
I
' This term is also calculated to compare to Touchstone's number for a
' homogeneous substrate
I
q3n# = (K#(k3n#, k3npr#) * K#(kOpr#, kO#))
K#(kO#, kOpr#))
'
/ (K#(k3npr#, k3n#)
*
PRINT "qin = ", qln#, q2n#, q3n#
I
' Equation 9 of Ref. 1 gives:
*
ql3# = (K#(kl3#, kl3pr#) * K#(k03pr#, k03#)) / (K#(kl3pr#, kl3#)
* K#(k03#, k03pr#))
q23# = (K#(k23#, k23pr#) * K#(k03pr#, k03#)) / (K#(k23pr#, k23#)
* K # (k03#, k03pr#)}
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
245
' This term is also calculated to compare to Touchstone's number for a
' homogeneous substrate
I
q33# = (K#(k33#, k33pr#) * K#(k03pr#, k03#)) / (K#(k33pr#, k33#)
* K#{k03#, k03pr#))
PRINT "qi3 = ", ql3#, q23#, q33#
I
' Equation 14 of Ref. 1 gives:
»
qlend# = (K#(klend#, klendpr#)
* K#{kOendpr#, kOend#))
(K#(klendpr#, klend#) * K#(kOend#, kOendpr#))
q2end# = (K#(k2end#, k2endpr#)
* K#(kOendpr#, kOend#))
(K#(k2endpr#, k2end#) * K#(kOend#, kOendpr#))
/
/
I
' This term is also calculated to compare to Touchstone's number for a
' homogeneous substrate
f
q3end# = (K#(k3end#, k3endpr#)
* K#(kOendpr#, kOend#))
(K#(k3endpr#, k3end#) * K#(kOend#, kOendpr#))
/
'
PRINT "qiend = ", qlend#, q2end#, q3end#
I
' The effective dielectric constant for the periodic structure (Eqn. 3
' of Ref. 1)
I
epseffn# = 1# + qln# * (epssub# - 1#) / 2# + q2n# * (epsflm# epssub#) / 2#
I
' The effective dielectric constant for the side strips (Eqn. 31 of
' Ref. 2)
t
epseff3# = 1# + ql3# * (epssub# - 1#) / 2# + q23# * (epsflm# epssub#) / 2#
!
' The effective dielectric constant for the end gaps (Eqn. 13 of Ref.
' 1)
I
epseffend# = 1# + qlend# * (epssub# - 1#) / 2# + q2end# *
(epsflm# - epssub#) / 2#
'
PRINT "epseff = ", epseffn#, epseff3#, epseffend#
1
' The capacitance contribution from the periodic structure (Eqn. 2 of
' Ref. l")
I
cn# = (n# - 3#) * epsO# * epseffn# * (K#(kO#, kOpr#) / K#(kOpr#,
kO#)) * length#
I
' The capacitance contribution from the side strips (Eqn. 7 of Ref. 1)
I
c3# = 4# * epsO# * epseff3# * (K#(k03pr#, k03#) / K#(k03#,
k03pr#)) * length#
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
246
' The capacitance contribution from the end gaps (Eqn. 12 of Ref. 1)
I
cend# = 4# * n# * s# * (2# + PI#) * epsO# * epseffend# *
(K#(kOend#, kOendpr#) / K#(kOendpr#, kOend#))
PRINT "cterms(n, 3, end) = ", cnt, c3#, cend#
I
' The total capacitance from Eqn. 1 of Ref. 1 is (in pF):
I
c# = (c3# + cn# + cend#) * 1E+12
PRINT "Total Capacitance (pF) = ", c#
INS$ = ""
INPUT "Would you like to calculate again (y/n)?", INS$
IF UCASE$(MID$(INS$, 1, 1)) = "Y" THEN
PRINT " "
GOTO startover
ELSE
STOP
END IF
FUNCTION ATAN2 (y, x)
PI = 3.1415926535898#
IF x > 0! THEN angle = A T N {y / x)
IF x < 0! THEN angle = ATN(y / x) + PI
IF (x= 0!) AND (y > 0!) THEN angle = PI / 2
IF (x = 0!) AND (y < 0!) THEN angle = -PI/ 2#
IF (x = 0!) AND (y = 0!) THEN angle = 0!
IF angle > PI THEN angle = angle - 2 * PI
IF angle < -PI THEN angle = angle + 2 * PI
ATAN2 = angle
END FUNCTION
FUNCTION CH# (x#)
CH# = (EXP(x#) + EXP(-1# * x#)) / 2#
END FUNCTION
FUNCTION K# (x#, xx#)
I
'
'
'
'
'
'
'
The argument of the elliptic integral is x#. However,
when x# = k
(rather than x# = k) and k« < 1, numerical accuracylimits
k' =
(1 - kA2)A.5 = 1.
This results in y# = 1 - x# = 0 which causes a DIVIDE BY ZERO error.
To avoid this, if x# = 1 (due to this numerical truncation) then y#
is approximated by (xx# = k is passed as the second argument just for
this case):
(
y# = 1 - (1 - kA2)A0 .5
= 1 - (1 - 0.5*kA2)
= 0.5*kA2
'
f
1
aO#
al#
a2#
a3#
a4#
=
=
=
=
=
1.38629436112#
.09666344259#
.03590092383#
.03742563713#
.01451196212#
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
bO# =
bl# =
b2# =
b3# =
b4# =
IF x#
.5#
.12498593597#
.06880248576#
.03328355346#
.00441787012#
>= .999999999# THEN
y# = xx# A 2 / 2
ELSE
y# = 1# - x#
END IF
K# = (aO# + (al# + (a2# + (a3# + a4# * y#) * y#) * y#) * y#) + (bO#
(bl# + (b2# + (b3# + b4# * y#) * y#) * y#) * y#) * L0G(1# / y#)
END FUNCTION
FUNCTION SH# (x#)
SH# = (EXP(x#) - EXP(-1# * x#)) / 2#
END FUNCTION
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
248
CURRICULUM VITA
Jeffrey A. Bellotti
E d u c a tio n
•
Ph.D. in Ceramic Science and Engineering (March 2003), G.P.A. 3.78
Rutgers University, New Brunswick, NJ
Dissertation: “Strain and Thickness Effects on the Microwave Properties of
BaxSr(i_X)Ti0 3 Thin Films”
Thesis Advisors: Prof. Ahmad Safari, Dr. E. Koray Akdogan
•
M.S. in Ceramic Science and Engineering (May 2000)
Rutgers University, New Brunswick, NJ
•
B.S. in Ceramic Science and Engineering (May 1998), G.P.A. 3.88
Rutgers University, New Brunswick, NJ
T ec h n ic a l E x per tise
•
Fabrication of ferroelectric thin films by pulsed laser deposition in epitaxial,
polycrystalline, and amorphous states.
•
Electrical characterization of ferroelectric thin films at low frequencies (<40
MHz) and microwave frequencies (up to 20 GHz).
•
Microwave device patterning using photolithographic, multi-layer lift-off
processes.
•
Microwave device testing using vector network analysis at both room temperature
and cryogenic temperatures.
•
Single crystal x-ray diffraction o f thin films to determine growth orientation,
quality o f epitaxy, and state of strain/stress in all crystallographic directions using
conventional Bragg-Brentano geometry and omega-scan geometry with wide-area
detector for reciprocal space mapping.
•
Characterization o f thin films using atomic force microscopy, Rutherford
backscatter spectroscopy, and field-emission scanning electron microscopy.
•
Design and construction of high-vacuum systems for the purposes o f film
fabrication
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
249
R elated E x p e r i e n c e
Guest Researcher
U.S. Naval Research Laboratory, Washington, D.C., August 2001 - October 2002
Conducted experimental work using cleanroom facilities to photolithographically pattern
microwave devices on thin films, and subsequently characterize devices using microwave
vector network analyzer at room temperature and cryogenic temperatures.
P u blic a tio n s
“Tunable Dielectric Properties of BST Thin Films for RF/MW Passive
Components”
J. Bellotti, E. K. Akdogan, W. Chang, S. Kirchoefer, A. Safari
Integrated Ferroelectrics, Vol. 49, p. 113, (2002).
“Calibration of the Height and Radius of AFM Probe Tips by SrTiOa Pyramid
Crystals for Force Measurements and Local Electrical Transport Studies”
A. E. Semenov, I. N. Borodina, J. Bellotti, A. Safari, S. H. Garofalini
Ultramicroscopy (2002), in Press.
“Novel Dielectric Ceramics for RF/MW Applications”
A. Safari, J. Bellotti, M. Allahverdi, E. K. Akdogan
Materials Science and Engineering B (2002), in Press.
“Frequency Agile BST Thin Films for RF/Microwave Applications”
J. Bellotti, E. K. Akdogan, W. Chang, J. Pond, A. Safari
Ferroelectrics, Vol. 271, p. 131, (2002).
“Structural and Dielectric Characterization of SrTiC>3 and BST Thin Films for
Microwave Applications”
J. Bellotti, E. K. Akdogan, A. Safari
Proc. 12th International Symposium on Applications o f Ferroelectrics,
Vol. 2, p. 867, (2000).
“Extrinsic Loss Mechanisms in BST for Tunable RF/Microwave Passive
Components”
E. K. Akdogan, J. Bellotti, A. Safari
Proc. 12th International Symposium on Applications o f Ferroelectrics,
Vol. 1, p. 191, (2000).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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