close

Вход

Забыли?

вход по аккаунту

?

Processing, microstructure, and microwave dielectric properties of tunable (barium,strontium)titanate thin films

код для вставкиСкачать
Processing, Microstructure, and Microwave Dielectric Properties
of Tunable (Ba,Sr)Ti03 Thin Films
HuiDu
Doctoral Thesis
Department of Materials Science and Engineering
Carnegie Mellon University
Pittsburgh PA 15213
Thesis committee:
Prof. Marek Skowronski (Advisor, MSE, Carnegie Mellon University)
Prof. Paul Salvador (Advisor, MSE, Carnegie Mellon University)
Prof. Robert Davis (MSE, Carnegie Mellon University)
Prof. Mark De Graef (MSE, Carnegie Mellon University)
Prof. Mike Lanagan (MSE, Pennsylvania State University)
UMI Number: 3383408
INFORMATION TO USERS
The quality of this reproduction is dependent upon the quality of the copy
submitted. Broken or indistinct print, colored or poor quality illustrations
and photographs, print bleed-through, substandard margins, and improper
alignment can adversely affect reproduction.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if unauthorized
copyright material had to be removed, a note will indicate the deletion.
UMI
UMI Microform 3383408
Copyright 2009 by ProQuest LLC
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest LLC
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, Ml 48106-1346
Carnegie Mellon University
CARNEGIE INSTITUTE OF TECHNOLOGY
THESIS
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
TITLE
D o c t o r Of P h i l o s o p h y
Processing. Microstructure. and Microwave Dielectric Properties of Tunable
(Ba.Sr)TiO^ Thin Films
PRESENTED BY
Hui D u
ACCEPTED BY THE DEPARTMENT OF
Materials Science and Engineering
ADVISOR, MAJOR PROFESSOR
A,/fe^
APPROVED BY THE COLLEGE COUNCIL
DEPARTMENT HEAD
發hxi&\
'
*
癨it<\\too<\
DATE
DATE
Acknowledgements
This dissertation includes part of the work I carried out during my stay at
Carnegie Mellon University as a Ph.D candidate. I would like to take this opportunity to
acknowledge many of the people who assisted me during this time and in this endeavor.
I would like to express my gratitude to both my advisors, Prof. Marek Skowronski
and Prof. Paul A. Salvador, for their extensive time they have spent mentoring me.
Thanks to their consistent encouragement and care during these years and on this
research.
I am also indebted to my thesis committee members, Prof. Robert Davis, Prof.
Marc De Graef, and Prof. Mike Lanagan, for spending their precious time on reading and
discussing on my dissertation and for their help with data analysis. I would also like to
thank the committee members on my prior exams, including Prof. Gregory S. Rohrer and
Prof. Katayun Barmak, whose discussions helped properly lay the foundations for this
work. Thanks are also owed to Prof. Jim Bain, Prof. David E. Laughlin, and Prof. Lisa
Porter for their support and discussions during my tenure at Carnegie Mellon.
Many specific thanks are also owed to the following people who, by their
valuable support, helped make this work done possible.
Prof. Mike Lanagan and his group members, Steve Perini, Clinton Scarborough,
Jeffray L. Rankinen, not only helped to make the microwave frequency
measurements and analysis, but also they extended their hospitality to me during
my visits.
I would like to thank Prof. Mark Fanton, Dr. Joshua Robinson, Dr. Accord, and
Matthew Hollander at Perm State EOC for working on the IDC patterning.
iii
I must thank Dr. Steven W. Kirchoefer, Dr. Wontae Chang, and Dr. Lisa
Alldredge at Naval Research Laboratory for developing the software to extract the
useful dielectric properties and for their efforts for further in measuring the
dielectric properties, I would also thank Dr. Chang for discussions on theoretical
simulation work.
I would like to thank Dr. Eucker and Mr. Peters at the Institute for Crystal Growth
in Germany for generously supplying some of the high quality scandate
substrates.
I appreciate the help of Dr. Shanling Wang at Carnegie Mellon University for
doing focused ion beam (FIB) experiments to check some of the samples'
thickness values.
I would like to acknowledge the assistance of Dr. Oleg Maksimov on RBS
characterization, initial IDC, and split cavity measurements, in addition to
collaborations on MBE growth of other oxide materials.
I greatly appreciate the help and the efforts of Mr. Tom Nufher and Mr. Jason
Wolf were for their extensive time and efforts in training new users and
maintaining the TEM, AFM, and x-ray facilities.
I would like to acknowledge the supporting stuff in the Materials Science and
Engineering Department. Thanks to Ms. Jenna Bottles, Ms. Valerie Thompson,
and Ms. Jeanna Ossler for handling the huge amount of procurements and thanks
to Mrs. Suzy Smith, Mrs. Anita Connelly, and Mrs. Angie Pusateri for their
generous help whenever needed.
Current members of Prof. Salvador's and Prof. Skowronski's groups, including
Andy, Bala, Nitin, Sukwon, Sartak, Rumy, Kevin, Lu, Qiang, Sunwoo, Hongjae
for their great support and discussions.
I also want to thank Wei Wang, Binchen Wang, Xuan Zhang, Wanlin Wang (and
their families), Cong Wang, Li Huang, and the "Thunderstorm" drama group, as well as
many others missed in this list for making my stay at Carnegie Mellon memorable.
I would also like to thank my parents, parents-in-law, my wife Huichun, and my
son Andrew for their constant support and encouragement; they inspired me to work so
hard and carried me through the ups and downs of my graduate career.
Finally, I would love to thank the Lord for walking along with me giving the
vision, the health, the courage, the wisdom, the peace and joy.
v
Abstract
Barium strontium titanate (BST) materials have been extensively investigated for
their applicationability in microwave varactors of monolithic circuits. Compared to bulk
BST, thin films exhibited significant degradations in their dielectric properties, including
suppressed dielectric constants and ^inabilities, increased losses, and diffuse temperature
dependences of dielectric constant. To understand the causes of these degradations, Three
research lines were followed to conduct systematic experiments to test the hypotheses
that dislocation-associated inhomogeneous strains and lattice-mismatch-associated
homogeneous strains are the principle causes.
Over the issue of whether the principle slip-system was <100>{010} or < 110 > {110}
in relaxation process of BST epitaxial films, dislocation characteristics determined using
electron microscopy in (001)-, (110)-, and (lll)-oriented BST films support a two-stage
relaxation mechanism for BST films on SrTiC� A bowing out of inherited <110> type of
dislocations act as minor strain relaxation mechanism followed by film top surface
nucleation of <100> type for major strain relaxation. Results supported that <100>{010}
slip-system is easier-to-activate in BST.
To understand the dislocation-associated inhomogeneous strain effects, (001)oriented Bao.6Sr0.4Ti03 films were grown on GdScO3(110), Lao.3Sro.7Al0.65Tao.3503(100),
NdGaO3(110), LaAlO3(100), and MgO(100) using pulsed laser deposition under identical
conditions. The temperature dependences of in-plane dielectric properties measured using
interdigitated capacitors at 5 GHz were compared. Bulk-like dielectric properties were
observed in low-dislocation-density Bao.6Sr0.4TiC>3 films coherently-tensile-strained on
GdScCh. Degraded dielectric properties were observed in Bao.6Sro.4TiC�films with high
vi
dislocation densities on the other substrates. This supported that the dislocationassociated inhomogeneous strains caused the dielectric property degradation.
The homogeneous strain effects were investigated by comparing the in-plane
dielectric properties of coherently-strained Bao.6Sro.4Ti03(001) films grown on
GdScO3(110) and DyScC>3(110) under identical conditions. The compressively strained
Bao.6Sr0.4Ti03 films on DyScC>3 demonstrated dramatically degraded dielectric properties
compared to the bulk-like properties in Bao.6Sro.4Ti03 films on GdScCh while their
dislocation densities are similarly low. Landau-Devonshire theory based simulations
interpreted the compressive strain effects from DyScC>3. The results support that
compressive strain is a principle factor for dielectric property degradations.
From the above-described experimental and theoretical investigations, to achieve
bulk-like dielectric properties, it is necessary to minimize compressive strains in the
direction of measurement and the dislocation-associated inhomogeneous strains in BST
thin films.
va
TABLE OF CONTENTS
List of Figures
x
list of Tables
xx
Chapter 1 Introductions and Overview
1
Chapter 2 Backgrounds
14
2.1 Basics of electromagnetic waves and circuit
14
2.2 Competing technologies on microwave tuning
19
2.3 Candidate ferroelectric materials for varactors
21
2.4 Barium strontium titanate and factors related to the dielectric properties
24
2.5 Dislocation generation mechanisms
37
2.6 Summary: statement of the problem
41
References
42
Chapter 3 Hypotheses and Research Approaches
49
3.1 Experiment design and hypotheses
49
3.1.1 Strain relaxation mechanism study and slip-system identification
49
3.1.2 Correlation between dislocation concentration and dielectric properties...55
3.1.3 Correlation between homogeneous strain and dielectric properties
59
3. 2 Experimental techniques
60
3.2.1 Substrate treatment
60
3.2.2 Target preparation
61
3.2.3 Growth techniques
62
3.2.4 X-ray diffraction and reflectivity
65
3.2.5 Transmission Electron Microscopy (TEM)
67
3.2.6 Atomic force microscopy (AFM)
69
3.2.7 Reflection high energy electron diffraction (RHEED)
70
3.2.8 Microwave frequency electrical characterizations
72
References
75
Chapter 4 Film Growth and Structure Characterizations
79
4.1 Substrate processing
80
4.2 Thin film growth mode
90
4.3 X-ray characterization of epitaxial relationships between films and substrates.. 100
4.4 Strain relaxation mechanisms for differently oriented
films
112
4.4.1 TEM observations of (OOl)-oriented Bao.6Sro.4Ti03
films
114
4.4.2 TEM observations of(110)-orientedBao.6Sro.4Ti03
films
116
viii
4.4.3 TEM observations of (11 l)-oriented Bao.6Sro.4Ti03
films
124
4.4.4 Further investigations and discussion of the relaxation mechanism in BST
130
4.4.5 Summary of film relaxation mechanisms
138
4.5 Lattice parameters of
films
140
4.6 Film quality examination
143
4.7 Conclusions
145
References
149
Chapter 5 Dielectric Properties Related to Microstractures
153
5.1 Experimental procedures of microwave measurement
153
5.2 Dielectric properties of Bao.6Sro.4Ti03 films grown on GdScC<3(110)
155
5.3 Effects of inhomogeneous strain on dielectric properties
163
5.3.1 Inhomogeneous strain effect on the dielectric constant and tunability
163
5.3.2 Inhomogeneous strain effect on dielectric loss
166
5.3.3 Discussion on inhomogeneous strain effect on dielectric properties
169
5.4 Effects of homogeneous strains
172
5.4.1 Comparison of dielectric properties of Bao.6Sro.4Ti03 on GdScC>3 and
DySc03
172
5.4.2 Discussion of the homogeneous strain effect based on phenomenological
theory
175
5.5 Conclusions
180
References
183
Chapter 6 Summary of Conclusions and Future Perspectives
187
6.1 Summary of conclusions
187
6.2 Future Perspectives
192
6.2.1 Further investigation of homogeneous strain effect
192
6.2.2 Theoretical modeling
195
6.2.3 Investigation of stoichiometry effect
196
6.2.4 Investigation of other properties and functions
197
References
198
IX
LIST OF FIGURES
Fig.2.1 Schematics of (a) the parallel plate capacitor model and (b) the coplanar capacitor model
16
Fig.2.2 Schematics of (a) an ideal LC circuit and (b) an equivalent RLC circuit. These drawings
are taken from Wikipedia website
17
Fig.2.3 A schematics of the perovskite structure (a) and the dielectric constant of Ba^r^^T'iOs
changes
with the bias voltage (b). Image
(b) was adapted
from Heini et al.
430(2004),page758-761)
(Nature
23
Fig.2.4 Variation of the dielectric constant of a BST ceramic and a thin film as a function of
temperature from T .M. Shaw et al., Applied Physics Letter 75, 2129(1999)
26
Fig. 2.5 Expected shift in Tc of (100) SrTi03 (a)31 and BaTi03 (b)34 with biaxial in-plane strain,
based on thermodynamic analysis. The arrows indicate the predicted direction of the polarization
for strained SrTi03: in-plane for biaxial tensile strain and out-of-plane for biaxial compressive
strain. These figures were adapted from reference 31 and reference 34 respectively
30
Fig.3.1
63
Schematic of the setup of a pulsed laser deposition system
Fig.3.2 Ideal RHEED images for (A) an atomically flat substrate surface with low step density (B)
flat surface with high step density (C) Very rough surface, island-like
3D growth
mode
(transmission pattern) (D) polycrystalline film. This image was reproduced from Patrick Fisher's
thesis
72
Fig.3.3 The schematics of the planview (a) and the cross-section
(b) of an 8 digit (n=8)
IDC. Reproduced from Reference 37. L is the finger length, 2Sg is the finger width, 2g is the gap
width, h 1 and h2 refer to the thickness of the overall thickness and the thickness of the measured
thin film, t is the thickness of the electrodes, and tri and er2 are the two dielectric constant of
substrate and film respectively.
73
Fig.3.4 The HP8510 Network Analyzer (a) and the Cascade Microtech 11000 Probe Station (b)
used
in
frequency.
this
research
to
measure
the
dielectric
properties
at
microwave
74
Fig.4.1 AFM characterized surface morphology ofSrTiO3(100) substrate from Crystal after being
etched for different length of time: 10min (a), 3min (b), and 30sec (c) in BHF followed by
annealing at 1000癈 for 2 hours. Note the differing scales
83
Fig.4.2 AFM images of SrTiO3(100) substrate from obtained from Crystal after first being etched
for different lengths of time (a: 5 min, b: 4 min, and c: 2 min) in a HCI:HN03=3:1 solution and then
being annealed at 1000癈 for 2 hours. Note the different height scales
83
Fig.4.3 AFM images of SrTiO3(100) substrates obtained from /W77� after being etched for 40sec
in BHF (followed by an anneal at 1000癈 for 2 hours in air); (a) and (b) are images at two different
magnifications taken on the same sample imaged immediately after treatment, while (c) is an
image
taken
from
the
same
sample
after
it
was
exposed
to
air
for
month
a
84
Fig.4.4 RHEED patterns from a SrTi03 (100) surface after undergoing a surface treatment similar
to that used on the samples whose AFM images are shown in Fig. 4.3. (a) is the pattern along the
(110) azimuth and (b) is the pattern along the [100] azimuth
....84
Fig.4.5 AFM images of LaAI03 (100) (a) and NdGa03 (110) (b) surfaces after a BHF etch / high
temperature anneal surface treatment. Note the different scales..
85
Fig.4.6 1 ym * 1 urn area AFM images of GdScO3(110) (a) and DyScO3(110) (b) surfaces after
surface treatment after a BHF etch / high temperature anneal surface treatment.
Note the
different height scales
86
Fig.4.7 (a) and (b) are the RHEED patterns of treated GdSc03 from the azimuth of [110]
[001].
and
86
Fig.4.8 AFM images of (La018Sro,82)(AI059Taa4i)03(100) substrates: (a) after being etched for 3
min in an HCI:H20=1:1 solution; (b) after the same etch procedure and an anneal at 900癈 for 3
hours; and (c) after the same etch procedure and an anneal at 1100癈 for three hours. Note the
different scales
88
Fig.4.9 AFM images of surface morphology of MgO (100) substrates after being (a) annealed in
air at 1000癈 for 8 hours, and (b) in pure oxygen at 1050癈 for 3 hours and (c) annealed in air at
1350癈 for 4 hours (c). Note the differences of length and height scales
xi
89
Fig.4.10 AFM topographic images of the surfaces of Ba06Sr0477O3 films grown on LaAI03 (100)
and SrTi03 (100) with different thicknesses of 3, 50, and 150 monolayers
94
Fig.4.11 RHEED patterns of 300-monolayer thick Bao.6Sr0.47703 films grown on (a) LaAIO3(100)
and (b) (La0iBSro.82)(Alo59Ta04i)03(100); patterns were registered using15 kV electron energy
and taken along the [100] azimuths
94
Fig.4.12 Atomic force microscopy images from (a) treated GdScO3(110) substrates and (b,c)
Ba0eSr04TiO3(001)
films deposited on such substrates to (b) 25 nm and (c) 200 nm thicknesses.
The corresponding line scans are shown in (d) for the GdSc03 (110) surface and in (e,f) for
Bao6Sr04Ti03
(001) films deposited
on such substrates
to (e) 25 nm and (f) 200 nm
thicknesses
95
Fig.4.13 Atomic force microscopy topographic image of a 5*5 jjm2 area of a 300nm thick
Ba0.6Sro4Ti03 (001) film grown under 300mTorr
oxygen partial pressure
(with the other
parameters described in the text) on GdScO3(110). The rms roughness value of the surface is
0.88nm
96
Fig.4.14 The RHEED patterns of treated GdSc03 taken along the GdScO3[001] azimuth (a)
before growth and (b) after growth of a 200nm film taken along the Ba0eSr04TiO3[100]
azimuth
97
Fig.4.15 (a) AFM image of the surface of a Ba0,eSr0.4TiO3 film grown on MgO for a time equivalent
to a thickness of 3 monolayers (when grown in a layer-by-layer mode) . (b) The ex-situ RHEED
pattern of the film after 50nm of growth. The AFM image shows a 3D growth pattern with noncoalesced
growth
islands
and the RHEED pattern
shows a spotty pattern
,
consistent
with 3D
98
Fig.4.16 A bright field TEM cross sectional image from a Ba0eSro4Ti03(100)
film on a MgO(100)
substrate. The vertical dark contrast is indicative of the fact that the film grew in a 3D columnar
mode
99
Fig.4.17 AFM topographic images of Ba06Sr0.4TiO3 films grown
SrTi03(111) with different thicknesses of 3, 50, and 300 monolayers
Xll
(see text for details) on
100
Fig.4.18
(a)
Theta-2theta
x-ray
scans
of
BaoeSr0.4Ti03
films
grown
on
SrTiO3(100),
(Laoi8Sro82)(Alo.59Tao4i)03(100) and LaAIO3(100) under 300mTorr oxygen pressure and (b) the
typical phi scan of the {111} reflections of the films and the substrates
102
Fig.4.19 (a) Theta-2theta x-ray scans of Ba0.sSr04TiO3 films grown on MgO(100) under different
oxygen pressures of 1 mTorr, 35 mTorr, and 300 mTorr. In (a), the peaks marked S refer to those
of the substrates {hOO}, the peaks marked with F refer to those of the films (002), and the peaks
marked D refer to those of the films (111). The broad peaks underneath MgO(100) were from
substrates itself, (b) Bright field planview TEM image of the Ba06Sro,4Ti03 film grown under 300
mTorr
oxygen
partial
pressure.
The
inset
is
the
selected
area
diffraction
pattern
103
Fig.4.20 (a) Theta-2theta x-ray scans of Ba0.6Sr0.4TiO3 films grown on GdScO3(110)
under
ImTorr and 300mTorr oxygen pressures (see text for other details) and (b) the Phi scans for the
film's {111} reflections and the substrate's {202} reflections (the two theta and psi angles are:
substrate =39.969�, 54.7� and film 39.245�, 54.7�. The peaks marked with * are believed to be
Pendellosung
fringes arising from the films high quality and atomically
flat
interfaces...
106
Fig.4.21 Theta-2theta x-ray scans of Ba06Sro,4Ti03 films grown on DySc03 (110) under 1 mTorr
and 300 mTorr oxygen pressures (see text for other growth conditions)
Fig.4.22 Theta-2theta x-ray scans of Ba06Sr0ATiO3
and LaAI03(110)
under 300mTorr
oxygen
107
films grown on SrTiO3(110),
pressure
(other conditions
NdGaO3(100),
are given in
text)
the
109
Fig.4.23 (a) Pole figures of {101} reflections and (b) {002} reflections
for Ba0.eSro4Ti03 films
grown on theSrTiO3(110) substrate (growth conditions given in text)
Fig.4.24 Theta-2theta x-ray scans of Ba06Sr04TiO3
films grown on SrTi03(111),
709
NdGaO3(011),
and LaAI03(111) under 300 mTorr oxygen pressure (other conditions are given in the text). The
wide peak in the LaAI03 was from the substrate
Fig.4.25 (a) Pole figures of {002} reflections and (b) {111}
grown on the SrTi03(111) substrates
110
reflections for Ba06Sr0.4TiO3 films
770
xiii
Fig.4.26 Plan view TEM images of misfit dislocations registered using a two-beam bright-field
image where g (the second beam) is the (100) reflection for the image on the left (a) and the
(010) is the reflection for the image on the right (b). The arrows depict the direction of the g vector
in each image
115
Fig.4.27 Planview bright-field TEM image of the film-substrate interface of a relaxed epitaxial
(110)-oriented B3 06 Sr 04 77O 3 film deposited on SrTiO3(110) (see text for growth conditions). The
inset is the corresponding [110]-zone axis diffraction pattern, which gives the orientation of the
sample: the first peak to the right / left of the main spot is the (001)/(001)
peak above /below the main peak is the (110) /(HO)
reflection and the first
reflection
117
Fig.4.28 A planview TEM bright field image of the interface of 8a 06 Sr 04 77O 3 (770) grown on
SrTiO3(110) taken close to [110] zone axis at a higher magnification than that given in Fig. 4.27.
The arrow points along the [110 ]
direction
118
Fig.4.29 Schematic of the geometric arguments describing misfit dislocations slip systems in the
barium strontium titanate (110) film on SrTiO3(110) (see text for details), (a) shows the interface
plane as (110) in the standard unit cell, (b) shows two of the of the four {110}
specifically the (011) and (Oil).
planes,
AD and CF are the traces of these two slip planes with the
interface, corresponding to the [111]
and [111].
The other two sets of equivalent planes- COF
and ADG- are not shaded. For the case of the slip plane GFC, figure (c) shows the possible
Burger's vector direction's (GC) projection on the interface plane, or CH. CH is along the [112 J
direction, (d) shows the projection of the dislocation line (the trace) and Burger's vector directions
on the interface plane (110). KD corresponds to the Burger's vector projection of the dislocation
with trace AD, and CH corresponds to the Burger's vector direction of the dislocation with trace
CF
121
Fig.4.30 (a) is a planview bright-field TEM image of misfit dislocations on zone-axis of [110]. (b) is
a two-beam bright field image when g is the reflection (110).
xiv
(c) is a two-beam bright field image
when g is the reflection (111). The arrows in (b) and (c) point to the corresponding g vector
directions
722
Fig.4.31 The two beam bright field images of dislocations in the interface of Ba06Sro4Ti03(110)
and SrTiO3(110) under reflection of (110) (a) and (001) (b), respectively. The arrow points to the
direction of the reflections used.
123
Fig.4.32 Planview bright field TEM image of the inten'ace from the Ba06Sr04TiO3(111) film grown
on SrTi03(111). The inset is the corresponding [111] zone axis diffraction pattern; with the first
"circle" of spots are {110} reflections and the second "circle" of spots are {121} reflections.
The dashed line is a guide for the eyes to see that one of the < 121 > direction is parallel to one
of the long continuous misfit dislocation line directions
725
Fig.4.33 A higher magnification of the bright-field TEM image of the planview specimen showing
the interface of the Ba0eSr0ATiO3(111) films on SrTi03(111). The thick continuous lines are the
same as those observed in Fig. 4.32
726
Fig.4.34 (a) A high-resolution planview TEM image of the Ba0.6Sro4Ti03(111) epitaxial film grown
on a SrTi03(111) substrate (the growth conditions are given earlier). This image contains only the
film and two threading dislocations are pointed out with arrows, (b) An image formed by inverting
the fast Fourier transform of the image given in (a). Burger's circuits are drawn around the two
dislocations and the Burger's vectors are marked with black arrows. Both dislocations have
Burger's vector direction of <121> . The inset is the fast Fourier transform, which can be used to
identify the orientations. Note the first circle of spots in the FFT corresponds to the {110}
reflections and the second circle corresponds to the {121} reflections
727
Fig.4.35 Schematic of the slip system geometries for barium strontium titanate films grown on
SrTi03(111) substrates, (a) the (111) plane is shaded in the unit cell as the plane ABC. (b) the
three {100} planes OAB, OBC, and OAC are shaded and highlighted in a fashion indicating their
intersection with the (111) plane ABC. (c) the shaded planes ABGD, BCDF, and ACGF are
highlighted in the unit cell and they represent three {110} planes- respectively the (110), (011),
xv
and (101). (Glide on these systems produce pure in-plane screw components to the Burger's
vector and the traces are in < 110 > directions.) (d) the shaded planes OAE, OCD, and OBF,
represent the other three {110}
planes, respectively the (Oil),
(110),
and (101),
which are
perpendicular to the (111) planes. (The misfit dislocations can only climb to the (111) interface
and the traces are in the [112],
[121],
and [211 ] directions, (e) shows the traces from the
dislocation motion to the interface of the system shown in (d), highlighting the [112],
[121],
and [211 ] directions on the interface (111) plane, respectively the AE, CD, and FB directions.
129
Fig.4.36 Planview bright field TEM images from the (a) SrTiO3(100), (b) SrTiO3(110), and (c)
SrTi03(111)
substrates.
In
(c), the inset
shows
the selected
area
electron
diffraction
pattern
131
Fig.4.37 A bright-field TEM image of a slip-band that was observed in a SrTiO3(100) crystal. The
inset gives the selected
area electron diffraction pattern.
The slip band is along
direction
[100]
132
Fig.4.38 Schematic of the formation of misfit dislocations from dislocations inherited from the
surate. (a) the initial straight line is shown as dotted line, (b) when the accumulated stresses
overcome the dislocation tension, the dislocation starts to bow out as shown in the dotted line, (c)
when the dislocation bows to the interface, misfit dislocations are formed.
Fig.4.39 (a) bright field planview TEM image of the interface of (110)- Ba06Sr04TiO3
135
film grown on
NdGaO3(100). The image was taken under a condition close to Sa 0 6 Sr 0 4 Ti0 3 [110] zone axis, (b)
The two beam bright field image of the interface with g = (001); dislocation lines along
were revealed.
[110]
137
Fig.4.40 (a) theta-2theta x-ray diffraction scan of the Ba06Sr04TiO3 ceramic target used for PLD
growth, (b) theta-2theta x-ray diffraction scan of a Ba0,6Sr0,4TiO3 films grown on an annealed Si
xvi
substrate (the Si was treated thermally for 1200'C in air for 48 hours), illustrating some weak
texture
141
Fig.4.41 Planview bright-field
TEM images of of 120nm thick Ba0.6Sr0.4TiO3 films grown on
GdScO3(110), DyScO3(110), (LaaiaSro.82)(Alo.5gTao.4i)03(100), NdGaO3(110), LaAIO3(100), and
MgO(100). The samples are tilted to reveal the dislocation lines. The dislocation
calculated
by
counting
the
number
of
lines
per
unit
area
are
also
densities
given
in
the
images
144
Fig.5.1 Optical image of one of the IDC structure units used for dielectric measurent
microwave frequencies
Fig.5.2
,
at
154
High resolution x-ray diffraction rocking curve of (a) the (220) reflection of the
GdScO3(110) substrate and (b) the (004) reflection of Bao.6SrOATi03 film. Two peaks are observed
in each, representing the bi-crystal nature of the substrate within the x-ray
157
Fig.5.3 (a) The temperature dependence of dielectric constant under three different bias voltages
(OV, 15 V, and 30 V) applied on a 8 pm IDC gap. The inset in (a) shows the inverse dielectric
constant as a function of temperature, (b) The temperature dependence of tunability (using a
30 V bias). The inset in (b) shows the tunability as a function of applied bias voltage on the 8pm
IDC gap at T = 308 K.
158
Fig.5.4 Temperature dependence of dielectric loss measured at different bias voltages, 0 V, 15 V,
and
30 V. The
inset
shows
the
bias
voltage
dependence
of
dielectric
loss
308 K
at
161
Fig.5.5 Plot of Communication quality factor as function of temperature, using the tunability at
30V and the dielectric loss under no bias and loss under 30V bias
164
Fig.5.6 (a) Comparison of the temperature dependencies of the relative dielectric constants
(b) the relative tunabilities
for (001)-oriented
Ba0.eSro.4Ti03 films grown on
(Lao.iBSr0.s2)(Alo.s9Tao.4i)03(100), NdGaO3(110),
LaAIO3(100),
and
MgO(100).
and
GdScO3(110),
Note
the
measurement frequency was 5 GHz and the tunability was measured at 30 V applied on a 8
micron gap, equivalent to 37.5 kV/cm field
164
xvn
Fig.5.7 Temperature dependence of the dielectric losses measured at 5 GHz using IDC structure
for
120 nm Ba06Sr04TiO3
films grown
on GdScO3(110),
(La0i8Sr082)(Alos<)Tao4i)03(100),
NdGaO3(110), LaAIO3(100), and MgO(100)
166
Fig.5.8 Temperature dependence of the figure of merit, K', at 5 GHz using an IDC structure for
120
nm
Ba0.6Sro4Ti03
films
grown
on
GdScO3(110),
(La0isSr082)(Alo59Tao4i)03(100),
NdGaO3(110), LaAIO3(100), andMgO(IOO)
168
Fig.5.9 The (a) polarization distribution and (b) variation of the Curie temperature around a
b=a[100] edge dislocation at (0,0,0) in single-crystal
PbTi03
on an xz plane. Area shown
represents 20*20 nm cross section along the y direction (dislocation line). This figure is
reproduced from reference 35
169
Fig.5.10 The comparison of the temperature dependences of the relative dielectric constants (a)
and the relative tunabilities (b) for (OOI)-oriented Ba06Sr04TiO3
films grown on GdScO3(110) and
DyScO3(110)
173
Fig.5.11 The comparison of the temperature dependences of the dielectric loss (a) and the figure
of merit (b) for (001 )-oriented Ba06Sr04TiO3
films grown on GdScO3(110) and
DyScO3(110)
-.
173
Fig.5.12 The schematic depiction of barium strontium titanate film in-plane polarization related to
the in-plane tensile and compressive strains
174
Fig.5.13 The simulated temperature dependence of inverse dielectric constant (1/t-T)
and
dielectric constant (z(T)) based on Curie Weiss law in paraelectric phase of an ideal bulk
Ba0.eSro.4Ti03
178
Fig.5.14 Comparison of the simulated temperature dependence of inverse dielectric constant
(1/t-T) and dielectric constant (e-T) based on Curie Weiss law in paraelectric phase between an
ideal bulk Ba0eSr0.4TiO3 and a Ba0.6Sr04TiO3 film under compressive strain of 0.33%. Note that
the Curie temperature is shifted from 249K to 283K from bulk to strained film
Fig.6.1 Planview TEM image of the Ba05Sr05TiO3
179
film grown on GdScO3(110). The large area
examination did not find many dislocations in the whole TEM sample, indicating the film
dislocation density is as low as the substrate
194
xvin
Fig.6.2 The schematic drawing of the expected temperature dependence of the dielectric
constant from the set of BaxS/vx77'03 films with different Barium content x grown on DyScO3(110)
(a) and GdSc03(110) (b) as described in Table 6.2
xix
195
LIST OF TABLES
Table 2.1 Comparison of the properties of semiconductor GaAs diode varactors, MEMS
varactors, and ferroelectric varactors based on BST taken from Reference 6
21
Table 3.1 Misfit dislocation (MD) Burger's vectors and line characteristics predicted based on
< 100>{010} slip system and the film orientation geometry
53
Table 3.2 Misfit dislocation Burger's vectors and line characteristics predicted based on the
<110> {110} slip system and the film orientation geometry
53
Table 3.3 Comparison of x-ray diffraction rocking curve Full-Widths-Half-Maxima (FWHM) of
often-used substrates
55
Table 3.4 Structural and dielectric parameters of the often-used substrate materials
57
Table 3.5 Lattice and thermal mismatches of Ba06S/o 47703 on different substrates and the critical
thicknesses hc calculated based on force balance (FB) mode (Eq.2-18) 7 and energy balance
(EB) model (Eq.2-19),11 and the average distances between misfit dislocations for completely
relaxed film Dave
58
Table 4.1 Lattice parameters and high resolution x-ray rocking curve full width at half-maximum
(FWHM) of Ba06Sr0.4TiO3 films grown on different substrates. These films are deposited at
300mTorr oxygen pressure (the repetition rate was 1 Hz) with nominal thickness values of about
120 nm (except the film on DySc03 which is 300 nm)
142
Table 5.1 Summary of the strain states, FWHM of the film X-ray rocking curve, the peak dielectric
constant, the peak tunability, the corresponding temperatures, and the FWHM of the e-T peak..
165
Table 5.2 The relevant coefficients of in theoretical calculations of the dielectric constant vs.
temperature relationship of Ba0.6Sr0.4TiO3 grown on DyScO3(110)
178
Table 6.1 The in-plane lattice parameters of the GdScO3(110) and DyScO3(110) substrates and
the bulk lattice parameter of BaxSr^TiOs with different Ba content x
192
Table 6.2 The expected strain states of the BaxSr1.xTi03 grown on GdScO3(110) and
DyScO3(110)
193
xx
Chapter 1
Introduction and Overview
Electromagnetic waves have been serving as the foundation of the "wireless age"
in which we are living. Each individual wireless application has been assigned a specific
frequency range, known as a "band", to avoid interference. Owing to the rapid increase of
information volume in civilian and military communications, the lower frequency bands
will soon reach their full capacity. These increasing demands drive the electromagnetic
wave applications into the microwave frequency (0.3-300 GHz) and even millimeter
wave (Terahertz) range.1'2 The materials required to process these electromagnetic waves
should meet the needs correspondingly. For the ease of signal modulation and the
versatility of the circuit, capacitor devices that can be tuned by an electric field, which are
called varactors, are preferred.1'2 One approach to designing varactors is to develop
tunable dielectric materials that can be used as the functional dielectric in tunable
capacitors. Ferroelectric materials? such as BaTi03, (strained) SrTi03, and their solid
solutions? have dielectric permittivities that exhibit nonlinear dependencies on electric
fields; this triggered the idea of using ferroelectric compounds as the functional dielectric
in electronic components using varactors, such as oscillators, filters, modulators, and
amplifiers.3'4
Three important parameters for tunable dielectrics are the relative dielectric
constant, the dielectric loss, and the tunability.1'2 The relative dielectric constant (Sr),
which is often simply called dielectric constant of a material, is the ratio of its
permittivity 8 to the permittivity of vacuum Eo, i.e., sr = s/So^The permittivity is a
measufe of the ability of a media (material) to be polarized by an electric field.1'2 Because
1
the dielectric constant is directly related to the capacitance of devices,1'2 materials with
tunable dielectric constants can be used to fabricate varactors. Dielectric loss is
commonly described by tan 5, which is the ratio of the real current (which represents
power dissipation) to the charging current for a capacitor; loss is detrimental to signal
processing.1'2 The tunability nr is defined as the maximum percentage change in the
dielectric constant under an applied DC field;1 since the dielectric constant is directly
proportional to capacitance, the tunability of the dielectric constant is directly related to
the circuit tunability.2 For an ideal tunable dielectric material, the relative dielectric
constant and tunability should be high, while the dielectric loss should be low. 1,2's
The most promising candidates for room temperature tunable microwave
applications are the paraelectric phases of the perovskite ferroelectric material BaxSri.
x Ti0 3 ,
often called BST for short.2'5 Bulk polycrystalline ceramic discs have (relative)
dielectric constants that range from 6000 to 25,000, dielectric losses less than 1% (tan 8
<0.01), and relative ^inabilities of r^- 90%.2'6'7 Moreover, the temperature dependence of
the dielectric constant has a sharp peak around Curie temperature (the paraelectricferroelectric transition temperature) with a full width at half maximum (FWHM) of
around 10-50 K.7"10 In the paraelectric phase the dielectric constant follows the CurieWeiss Law, for which the inverse dielectric constant vs. temperature relation follows a
linear relation.6'10"12
For space applications, such as devices on satellites, space shuttles, and other
facilities, size and weight factors are critical concerns. To miniaturize devices, extensive
investigations were done on thin film dielectrics during the last several decades.
However, all films suffer from one or more of the following problems: 2'6'13'14
2
1. undesirably low dielectric constants and ^inabilities,
2. an order of magnitude higher dielectric loss than bulk ceramics, and
3. a diffuse temperature dependence of the dielectric constant, with much
lower peak values.
Multiple mechanisms have been proposed to explain the dielectric property
degradations in BST films, and these will be reviewed in Chapter II (which will present a
comprehensive background to this dissertation). The "dead-layer" model assumes that a
low-dielectric-constant interface layer, which is connected in series with the bulk film,
decreases the effective dielectric constant and tunability.15"19 The "dead layer" could be
caused by second phase formation,15'16'20 Thomas-Fermi screening effects,17'20 or
interfacial defects such as misfit dislocations. 19'21Another theory asserts that the
degradation is due to size effects in thin films, i.e. the film dielectric constant and
tunability are dependent on the size of the crystals (thickness of thin films), possibly
because the surface perturbations become dominant over bulk characteristics.17'22 Still
other discussions attribute the degradation to the presence of defects such as point
defect(including oxygen vacancies or antisite defects),16'23'24 dislocations,13'14'21'25 and
grain boundaries.17 Experimentally, it is extremely challenging to deconvolute the
abovementioned factors. Therefore, despite the enormous efforts expended to date (based
on the number of published papers on the topic), none of these theories have been
demonstrated to capture fully all aspects of the physical observations.17 It is the primary
goal of this thesis to understand the principle mechanism responsible for degraded
properties in thin film dielectrics and to use the understanding to improve thin film
dielectric properties.
3
One interesting experiment demonstrated that the samples of thin film dimensions
could exhibit bulk-like properties (and countered the size-effect theory) was performed
by Saad et al.18 They prepared a 75 nm thick BaTi03 sample directly from a bulk crystal
using a focused ion beam (FIB) milling technique.18 This 75 nm thick BaTiC>3 sample,
which had the same order of magnitude thickness as most thin films exhibiting degraded
properties, exhibited bulk properties.18 This experiment implicated factors associated
with thin film growth as the source of degradation, not the inherent size.
Compared with the free standing thin layer machined from bulk crystal, thin films
typically experience several types of strains, which can be classified as homogeneous and
inhomogeneous. The homogeneous strains usually arise from mismatches of the lattice
constants and thermal expansion coefficients between the film and substrates.
Homogeneous strains are known to affect the Curie temperature and dielectric constant of
ferroelectric materials,26"28 and therefore should affect the tunable dielectric properties.
However, volumetric homogeneous strains also drive dislocation formation, which offer
the ability to reduce the overall strain or stored energy.29,30
BST films have been widely grown on oxide substrates such as MgO,31'32 LaAlCh,33'34
and (Lao.i8Sr0.82)(Alo.59Tao.4i)03.35 Owing to large lattice mismatches between the films
and substrates (>2%) that lead to large homogeneous strains, misfit dislocations can be
generated for even very thin layers (~ 2 nm for 2% mismatch). During misfit dislocation
generation, residual threading dislocations are also generated, with densities on the order
of >10 n cm"2.26'33 Therefore, dislocation densities in thin films are several orders of
magnitude higher than those observed in single crystals of SrTi03 and BaTi03, which
have been reported to be on the order of 108 cm"2 or less.36 Although dislocations help
4
relax homogeneous strains, they themselves have inhomogeneous strain fields. '
Inhomogeneous strains around dislocation cores are believed to suppress the local
polarizations and decrease the dielectric constant, and therefore should affect the tunable
dielectric properties.14'21
Since both homogeneous and inhomogeneous strains are known to affect the
dielectric properties, more detailed investigations into their individual roles should
provide key insights into the nature of dielectric property degradation for thin films. The
first hypothesis of this research is that dislocations are a primary mechanism for the
severe degradation observed in the dielectric constant and tunability of thin films. The
second hypothesis of this research is that certain types of homogeneous strains also
provide a mechanism for degradation in the dielectric properties films (even when the
dislocation contents are lower than bulk values). In this research, the efforts will be
focused on detecting the relationship between dielectric properties and dislocationassociated homogeneous and inhomogeneous strains. Systematic and well-controlled
experiments will be designed to test this hypothesis.
To study the effect of dislocations on the dielectric constant and tunability, dielectric
films (here Bao.6Sr0.4TiC>3) must be generated with different dislocation densities under
controlled conditions. This is somewhat challenging because, since thin films directly
crystallize upon a substrate, the substrate provides several factors that determine the
dislocation density in thin films. The first factor is the dislocation density in the substrate
itself, as the film can inherit these dislocations directly during growth.29'30 This implies
that the ultimate film quality will be limited by the crystal quality of the substrate (i.e., its
5
dislocation density). To test if dislocations are primary players in determining the
dielectric constant, one needs to control for the substrate crystal quality.
The second substrate factor that controls dislocation density is the surface quality.
Substrates are generally single crystals (of a given quality) that are cut, oriented, and the
polished to yield an atomically smooth surface of a given crystallographic plane.
However, residual polishing damage on the substrate surface, such as indentations or
scratches (or even high surface dislocation contents), play a role in determining the films
dislocation content as they provide local stresses to help generate dislocations or high
local dislocation contents to be inherited. Therefore, substrate surface treatment must be
well controlled.37"39 In a similar fashion, growth mode must be controlled to avoid
variations in local surface stresses that assist dislocation generation.40
The third substrate factor that controls dislocation density in thin films is the
crystallographic mismatch between the film and substrate, including the lattice parameter
and thermal expansion mismatches.29'30 For epitaxial films, differences in the in-plane
periodicity of the film and substrate crystal lattices cause a strain to develop as they
attempt to match the bonding across the interface. For coherently strained thin films, this
strain can be stored volumetrically (homogeneously) by lattice expansion/compression.
Note that this means the homogeneous strain state of the film is substrate dependent. As
the thickness increases to a critical value, when the volumetric energy is larger than the
dislocation energies, misfit dislocations are generated to relax the strains.30 Although
these misfit dislocations can relax the entire film even if they exist only at the interface,
the mechanism by which they form? nucleation at the film surface and glide or climb to
the film-substrate interface? often leaves threading dislocations in the film because of
6
pinning. ' ' While threading dislocations may reduce their densities by reacting with
one another (and annihilating) or moving out of the film entirely (under proper
conditions41 such as annealing42), it is difficult to entirely remove them.
These last few paragraphs emphasize the critical role that substrates play in testing
the two hypotheses related to strain dependent dielectric property degradation. To control
the homogeneous strain state, substrates of similar crystal quality and opposite (and
small) lattice mismatches are required. To minimize or to control the density of
dislocations (and therefore the inhomogeneous strain state) in films one must control the
substrate dislocation density, substrate surface morphology, lattice and thermal expansion
mismatches, and dislocation reaction or motion.
Chapter 3 will present in detail the hypotheses and the experimental strategies to test
them First, the strain relaxation process during thin film growth of BST will be studied
to understand it and to allow us to control strain effects. Secondly, different substrates
will be used to obtain Bao.6Sro.4Ti03 films with different dislocation concentrations since
the substrates have different mismatches with Bao.6Sr0.4Ti03 and different dislocation
contents that are inherited by the film. The growth conditions will be maintained to
control oxygen vacancies, assuming the vacancy population is independent of substrate
strain and dislocation concentration. Thirdly, the nature of strain, compressive or tensile,
will be investigated on coherently strained films of similar crystal quality / dislocation
density, grown on GdScCh or DyScC>3. Finally, Chapter 3 will introduce the experimental
techniques used for growth and structural characterization, such as pulsed laser
deposition (PLD), four-circle x-ray diffraction, reflection high-energy electron diffraction
(RHEED), and transmission electron microscopy (TEM).
7
Chapter 4 will present and discuss the detailed growth and relaxation processes of BST
films on appropriate substrates. Substrate surface treatments will be optimized to obtain
smooth surfaces before film growth. AFM and RHEED characterizations will be used to
determine the surface structure of substrates and films. Growth conditions and growth
modes will be studied to assist the understanding of the film microstructures. Four-circle
X-ray diffraction will be used to characterize the epitaxial relationships between films
and substrates. Asymmetric reflections will be used to calculate the in-plane and out-ofplane lattice parameters. High resolution X-ray will be used to characterize the film
quality, i.e. the dislocation contents as reflected in the full width at half maxima of peaks
registered as rocking curves. Film strain relaxation processes will be studied to clarify the
slip system and relaxation mechanism in the Bao.6Sro.4TiC�films.
In Chapter 5, the relation between the crystal quality and the dielectric properties will
be discussed. Firstly, approaches for thin films microwave frequency measurements will
be reviewed. Secondly, the experimental measurement procedures will be presented in
detail. Thirdly, thin film dielectric properties will be discussed and correlated to their
crystal quality and strain states. Finally, Discussions based on the Landau-Devonshire
phenomenological theoretical models will be formulated to interpret the observed
experimental phenomena.
Based on the understanding generated in this research, future perspectives on
improving dielectric properties and device performance in ferroelectric thin films will be
proposed in Chapter 6. Besides providing the experimental and theoretical understanding
for thin-fiim varactor applications for tunable microwave circuits, this research will
provide fundamental understanding of film processing-structure-property relationships in
8
other related fields, such as micro-electro-mechanical system (MEMS),
ferroelectric
random access memory (FeRAM),44"46 pyroelectric uncooling infrared detection,47"49 and
electro-optical applications.50"53
References:
1
L. F. Chen and C. K.Ong, Microwave Electronics: measurement and material
characterization (John Wiley & Sons, Ltd.,, 2004).
2
A. K. Tagantsev, V. O. Sherman, K. F. Astafiev, J. Venkatesh, and N. Setter,
Journal of Electroceramics 11, 5-66 (2003).
3
M. DiDomenico, Jr., D. A. Johnson, and R. H. Pantell, Journal of Applied Physics
33, 1697-1706 (1962).
4
H. H. Walter, Journal of Applied Physics 27, 775-777 (1956).
5
P. Bao, T. J. Jackson, X. Wang, and M. J. Lancaster, J. Phys. D: Appl. Phys. 41
063001 (2008).
6
T. M. Shaw, Z. Suo, M. Huang, E. Liniger, R. B. Laibowitz, and J. D. Baniecki,
Applied Physics Letters 75, 2129-2131 (1999).
7
M. M. Saad, P. Baxter, R. M. Bowman, J. M. Gregg, F. D. Morrison, and J. F.
Scott, J. Phys.: Condens. Matter 16, L451-L456 (2004).
8
L. Benguigui and K. Bethe, Journal of Applied Physics 47, 2787-2791 (1976).
9
J. Zhai, X. Yao, X. Cheng, L. Zhang, and H. Chen, Materials Science and
Engineering B 94, 164-169 (2002).
10
H. V. Alexandru, C. Berbecaru, A. Ioachim, L. Nedelcu, and A. Dutu, Applied
Surface Science 253, 354-357 (2006).
9
O. G. Vendik, E. K. Hollmann, A. B. Kozyrev, and A. M. Prudan, Journal of
Superconductivity: Incorporating Novel Magnetism 12, 325-338 (1999).
H. V. Alexandru, C. Berbecaru, A. Ioachim, M. I. Toacsen, M. G. Banciu, L.
Nedelcu, and D. Ghetu, Materials Science and Engineering B 109,152-159
(2004).
C. L. Canedy, H. Li, S. P. Alpay, L. Salamanca-Riba, A. L. Roytburd, and R.
Ramesh, Applied Physics Letters 77,1695-1697 (2000).
D. Balzar, P. A. Ramakrishnan, P. Spagnol, S. Mani, A. M. Hermann, and M. A.
Matin, Jpn. J. Appl. Phys. 41, 6628-6632 (2002).
A. K. Tagantsev and G. Gerra, Journal of Applied Physics 100, 051607 (2006).
A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J. Hao, W. Si, and X. X. Xi,
Nature 404,373-376 (2000).
J. F. Ihlefeld, W. J. Borland, and J. P. Maria, Advanced Functional Materials 17,
1199-1203(2007).
M. M. Saad, R M. Bowman, J. M. Gregg, F. D. Morrison and J, F, Scott J. Phys.:
Condens. Matter 16, L451-L456 (2004).
C. Zhou and D. M. Newns, Journal of Applied Physics 82, 3081-3088 (1997).
A.K. Tagantsev, K.F. Astafiev, J. Venkatesh andN. Setter, Journal of
Electroceramics 11, 5-66 (2003).
S. P. Alpay, I. B. Misirlioglu, V. Nagarajan, and R. Ramesh, Applied Physics
Letters 85,2044-2046 (2004).
N. A. Spaldin, Science 304, 1606-1607 (2004).
10
W. J. Kim, W. Chang, S. B. Qadri, J. M. Pond, S. W. Kirchoefer, D. B. Chrisey,
and J. S. Horwitz, Applied Physics Letters 76,1185-1187 (2000).
W. J. Kim, H. D. Wu, W. Chang, S. B. Qadri, J. M. Pond, S. W. Kirchoefer, D. B.
Chrisey, and J. S. Horwitz, Journal of Applied Physics 88, 5448-5451 (2000).
S. S. Stemmer, N.D. Browning, C. Basceri and A.I. Kingon, Interface Science 8,
209-221 (2000).
J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W.
Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q.
Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, Nature 430, 758-761 (2004).
W. Chang, C. M. Gilmore, W.-J. Kim, J. M. Pond, S. W. Kirchoefer, S. B. Qadri,
D. B. Chirsey, and J. S. Horwitz, Journal of Applied Physics 87, 3044-3049
(2000).
C. Wontae, L. M. B. Alldredge, W. K. Steven, and M. P. Jeffrey, Journal of
Applied Physics 102,014105 (2007).
J. W. Matthews and A. E. Blakeslee, Journal of Crystal Growth 27,118-125
(1974).
R. People and J. C. Bean, Applied Physics Letters 47, 322-324 (1985).
A. C. Carter, J. S. Horwitz, D. B. Chrisey, J. M. Pond, S. W. Kirchoefer, and W.
Chang, Integrated Ferroelectrics 17, 273-285 (1997).
L. M. B. Alldredge, C. Wontae, W. K. Steven, and M. P. Jeffrey, Applied Physics
Letters 94, 052904 (2009).
W. Chang, J. S. Horwitz, A. C. Carter, J. M. Pond, S. W. Kirchoefer, C. M.
Gilmore, and D. B. Chrisey, Applied Physics Letters 74, 1033-1035 (1999).
11
I. B. Misirlioglu, A. L. Vasiliev, M. Aindow, S. P. Alpay, and R. Ramesh,
Applied Physics Letters 84,1742-1744 (2004).
D. Wang, Y. Wang, J. Dai, H. Chan, and C. Choy, Journal of Electroceramics 16,
587-591 (2006).
D. G. Schlom, Long-Qing Chen, C.-B. Eom, K. M. Rabe, S. K. Streiffer, and J.M. Triscone, Annual Revew of Materials Research 37, 589-626 (2007).
T. O. Iizuka, Yasumasa; Kikuchi, Makoto Japanese Journal of Applied Physics 4,
237 (1965).
Myung Yoon Um, Jae Kyeong Jeong, Bum Seok Kim, Hoon Joo Na, In Bok
Song, and H. J. Kim, Mat. Res. Soc. Symp. Proc. 719, F8.12.2 (2002).
M. R. Surowiec, H. S. Leipner, and J. Schreiber, Journal of Applied
Crystallography 22, 606-612 (1989).
C. J. Lu, L. A. Bendersky, K. Chang, and I. Takeuchi, Journal of Applied Physics
93,512-521(2003).
A. E. Romanov, W. Pompe, S. Mathis, G. E. Beltz, and J. S. Speck, Journal of
Applied Physics 85,182-192 (1999).
L. A. Knauss, J. M. Pond, J. S. Horwitz, D. B. Chrisey, C. H. Mueller, and T.
Randolph, Applied Physics Letters 69,25-27 (1996).
G. Wang, T. Polley, A. Hunt, and J. Papapolymerou, IEEE Antennas and Wireless
Propagation Letters 4, 217-220 (2005).
J. F. Scott, Japanese Journal of Applied Physics, Part 1: 38,2272-2274 (1999).
12
Y. Tsunemine, T. Okudaira, K. Kashihara, A. Yutani, H. Shinkawata, M. K.
Mazumder, Y. Ohno, M. Yoneda, Y. Okuno, A. Tsuzumitani, H. Ogawa, and Y.
Mori, Japanese Journal of Applied Physics, Part 1 43, 2457-2461 (2004).
H. Shu-chun, C. Hong-ming, W. Shich Chuan, and L. Joseph Ya-min, Journal of
Applied Physics 84, 5155-5157 (1998).
H. Zhiming, Z. Zhanhong, J. Chuping, Y. Jian, S. Jinlan, and C. Junhao, Applied
Physics Letters 77, 3651 -3653 (2000).
M. H. Charles, R. B. Howard, and L. A. Diane, in Uncooled thermal imaging with
thin-film ferroelectric detectors, 2008 (SPIE), p. 694025.
M. H. Charles, R. B. Howard, A. O. Robert, C. Mac, and S. McKenney, in
Uncooled thermal imaging at Texas Instruments, 1992 (SPIE), p. 17-26.
M. Gaidi, M. Chaker, P. F. Ndione, R. Morandotti, and B. Bessais, Journal of
Applied Physics 101,063107 (2007).
K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, in
Theoretical study of ferroelectric barium-strontium-titanate-based onedimensional tunable photonic crystals, 2007 (SPIE), p. 65560R.
K. Dai-Young, M. Seung Eon, K. Eun-Kyung, L. Su-Jae, C. Jong-Jin, and K.
Hyoun-Ee, Applied Physics Letters 82,1455-1457 (2003).
J. M. Marx, O. Eknoyan, H. F. Taylor, Z. Tang, and R. R. Neurgaonkar, Applied
Physics Letters 67,1381-1383 (1995).
13
Chapter 2
Background
This chapter addresses the theoretical and empirical background leading to the current
research. The first few sections begin with a foundational introduction on microwave
communications (�1), a discussion of competing microwave tuning technologies (�2),
and a list of candidate materials that are being investigated as varactors (�3). Section
2.4 focuses on the (Ba,Sr)Ti03 material system and reviews the factors that affect the
bulk and thin film dielectric properties, including composition (�4.1), stoichiometry and
doping (�4.2), strain (�4.3), "dead-layers," (�4.4), and defects (vacancies,
dislocations, etc..., �4.5). Following this introduction, the problems that face the use of
BST in applications will be discussed, and a case is made that solutions to problems are
important and realizable (�6).
2.1 Basics of electromagnetic waves and circuits
Electromagnetic waves were first postulated by James C. Maxwell, who ingeniously
unified the previous observations and theories about electricity, magnetism, and optics
with the now-famous Maxwell equations.1 Subsequently, Heinrich Hertz satisfactorily
demonstrated the existence of the electromagnetic waves by setting up an apparatus to
generate and detect waves. This "no use whatsoever" setup, as considered by Hertz
himself,2 started the technological revolutions that have marched forward to today's
"wireless age," where communication via waves spanning a broad range of the
electromagnetic spectrum enable devices such as cell-phones, satellites, television,
Bluetooth and infrared headsets and remote controls, etc... This basic electronic set-up is
now known as the "LC circuit", where "L" and "C" refer to the inductance (units of
14
Henrys, or H) and capacitance (units of Farads, or F) of the inductor and capacitor that
compose the basic circuit3
Inductance is a measure of the electromotive force that opposes the current
change that is flowing in an electric circuit.4 Conventionally, a solenoid is used as the
inductor. A solenoid is a long, thin coil, i.e. a coil whose length is much greater than the
diameter. Under these conditions, and without any magnetic material used, the magnetic
flux density B within the coil is practically constant and is given by:1'4
B = *f-
(Eq.2-1),
where ju0 is the permeability of free space (4rc * 10"7 H/m), TV is the number of turns, i is
the current, and / is the length of the coil. Ignoring end effects, the total magnetic flux ( $
through the coil is obtained by multiplying the flux density B by the cross-sectional area
A and the number of turns N:1A
, M0N2iA
0 = ?;
(Eq.2-2).
Since the inductance (L) is the constant of proportionality between ^and /, it follows that
the inductance of a solenoid is given by:1'4
M0N2A
L = ^-j?
If the solenoid has a magnetic core, the inductance can be given by:
L =
(Eq.2-3).
lA
Wr_
(Eq.2-4),
where fxr is the relative permeability, which is a parameter indicating the degree of
magnetization of a material within the solenoid in response to a magnetic field.
15
Capacitance is a measure of the amount of electric charge stored for a given
electric potential. The most commonly used capacitor is the parallel plate capacitor
(shown in Fig. 2.1a). The capacitance of this structure is given by:3
C = ere�
(Eq.2-5),
a
where, A is the area of the plate, d is the separation of the plates, and the 80 is the
permittivity of free space (�= 8.854xl0"12 Fm"1 ).3'4 Permittivity is a parameter that
describes the ability of a material to polarize in response to an electric field. er is called
relative permittivity, or the ratio of a material's permittivity (e) to that of free space (fc'o).
The relative permittivity is also called the relative dielectric constant or, more simply, the
dielectric constant.3 For parallel plate capacitors, the only permittivity that contributes to
charge storage is the permittivity arising from out-of-plane polarizations (normal to the
area A)5'6 Another type of capacitor structure is known as the coplanar capacitor
geometry (Fig. 2.1b), where the permittivity contributing to charge storage is mainly
from the in-plane polarizations (parallel to the area A), though the out-of-plane
polarizations play a minor role.5'7'8 The dielectric constant and capacitance values are
determined from the electrical properties of the coplanar capacitors using a series of
complicated models that take into account the electrode design and the electric field
distribution profile.3'8"10
(a)
Substrate
{1))
Fig.2.1 Schematics of (a) the parallel plate capacitor model and (b) the coplanar capacitor model
16
For an ideal LC circuit (Fig. 2.2a) having specific L and C values,3 the resonant
frequency (/) is given in Hz by:
f
(E 2 6X
-T?=i^m
"-
where a> is the radial frequency in radians per second.
However, in real applications, there is always some energy being converted to
heat and can be modeled as being equivalent to a resistor connected in the LC circuit
(Fig. 2.2b), resulting in a RLC circuit.3 In such a case the permittivity assumes a complex
form of:3
s = e'-je"
(Eq.2-7),
where E' and s" are the real and the imaginary part of the permittivity, respectively. The
imaginary portion of the dielectric constant is related to the dissipation (or loss) of energy
within the medium, while the real part of the permittivity is related to the energy stored in
the circuit. The dissipation factor, also called dielectric loss, is defined as tan5:
s"
tanS = ?
(Eq. 2-8).
Another parameter relating to loss is defined as the quality factor Q =l/tanS.
S j ^
o?,
ft
\\\
,
c:
i
s
oa
<>
(b)
Fig. 2.2 Schematics of (a) an ideal LC circuit and (b) an equivalent RLC circuit. These drawings
are taken from Wikipedia website.
17
LC circuits are used either for generating signals at a particular frequency, or for
picking out a signal at a particular frequency from a more complex signal.6 During the
last century, the number of applications using electromagnetic waves increased sharply.
The Federal Communications Commission (FCC) and the National Telecommunications
and Information Administration (NITA) have assigned a band (or frequency range) to
different applications,11 such as radio broadcasting, mobile phones, inter-satellite,
military radar, space search, etc... Taking mobile phone communications as an example,
the available lower frequency band width is becoming limited as the volume of the
information increases. Therefore, the frequency has tended to move to higher and higher
frequencies to accommodate the increased volumes. The microwave frequency range is
normally defined as the frequency range of 0.3-300 GHz, and is an important frequency
range for telecommunications.3'6'11 This research will focus on material dielectric
properties in the frequency range of 1-20 GHz.
From the Eq. 2-6, it is apparent that when one of the parameters L or C changes, the
resonant frequency of the system changes. That is, the system can be tuned by changing
either the inductance or capacitance, or both. For a bulk circuit, the LC frequency can be
mechanically tuned by either changing the number of coils in the inductor or changing
the effective area of the capacitor.12'13 When the device is miniaturized, mechanical
tuning becomes very limited and time consuming. Fast electrically tuned circuits
appropriate for small devices include, for example, semiconductor Schottky contacts,
tunable ferroelectric thin films, and micro-electro-mechanical-systems (MEMS).6 These
three techniques will be reviewed in the following section.
18
2.2 Competing technologies on microwave tuning
Since this research focuses on the capacitance tuning, we will only review the
techniques currently under research to tune capacitors. One kind of commercially
available tuning technology is called a heterostructure barrier varactor (HBV), which uses
p-n junctions.6'14 For a reverse-biased p-n junction, the depletion width can be changed
by the applied voltage; the thickness of the depletion width is proportional to the square
root of applied voltage. Since the capacitance is inversely proportional to the depletion
region thickness, the diode capacitance can be changed by the applied voltage (electric
field); the capacitance is inversely proportional to the square root of voltage.14 The
materials commonly used for this application are Si or the IH-IV family semiconductors,
such as GaAs and GaN.14
Micro-electrical-mechanical systems (MEMS) form the basis of another technology
that can be used for tuning at microwave frequencies. MEMS technology utilizes electrothermal, electrostatic, and piezoelectric effects to drive actuators that vary the
overlapping area or the gap between capacitor plates to realize capacitance tuning.15
This research focuses on a technique that uses the fact that ferroelectric materials
exhibit a non-linear dependence of their dielectric constant on the applied field.5'6'16 For
ferroelectric materials such as BaTiCh, SrTi03, and (Ba, Sr)TiC>3, their dielectric constant
decreases with an increase of applied electric field. The tunability, n, is defined as:
n-^L-
(Eq.2-9),'
where E'(0) and z'(EMay) are the real portions of the dielectric constant respectively under
zero and the maximum electric field (Emax), which should be just below the breakdown
field). Sometimes the relative tunability, nr, is used instead:
19
a? (0)
n
In the literature the convention , tunability is commonly used to refer to any dielectric
constant change under the bias of an in an applied electric field, not necessarily at the
breakdown voltage.17
A comparison of these three technologies have been summarized in Table 2.1.6
GaAs diode varactors have high tunability and are reliable. They have high quality
factors at the lower end of the microwave frequency. However, there is a linear decrease
of the quality factor as the frequency increases, which has limited the application of
GaAs varactors in tunable filters above 20 GHz.6 MEMS varactors are at the closest
functional equivalent to ferroelectric thin film varactors and are at a similar level of
developmental maturity.6 MEMS has the advantage of having very high quality factors;
however, the response speed is relatively slow as compared to that for both GaAs and
ferroelectric thin film varactors. In addition, in practice, reliability issues need to be taken
into consideration for MEMS varactors, these arise from environmental conditions, such
as air moisture, temperature, and background vibrations. Though ferroelectric varactors
currently have the drawbacks of having low quality factors and higher tuning voltage
requirements, their low cost, good reliability, fast tuning response speed, and high power
handling capability have attracted intense research.6
For a desirable ferroelectric varactor, the general features would be:6 1) a high
dielectric constant?the higher the better(though in some applications, the impedance
matching limit the value and some cases require temperature independent performances
are required),5'6'16 2) high tunability, >50%, 3) a high dielectric quality factor-ideally Q >
100 (or tcrnS < 1%), 4) a low cost for production, and 5) a reasonable reliability and
20
reproducibility. Although devices from bulk ferroelectric materials have been
demonstrated, the voltage required for tuning is very high.5 Though the higher values of
the desired features have been observed separately in different material systems or in
bulk devices, they have never been observed simultaneously in thin films and the reason
for the differences from bulk materials is unclear.5'6 Toward this end, ferroelectric
materials will be reviewed in the following section.
Table 2.1 Comparison of the properties of semiconductor GaAs diode varactors, MEMS
varactors, and ferroelectric varactors based on BST taken from Reference 66
Tunability (n)
Quality Factor
Tuning Voltage
Tuning Speed (s)
Reliability
Cost
Power Handling
GaAs Diode
Varactor
-2-6:1
-20-50 atlOGHz
<15V
~10_b
Good
High
Poor
MEMS Varactor
-1.5-3:1
Very High
<50V
>io-5
Poor
High
Good
Ferroelectric Varactor
(BST)
-2-4:1
-20-100 atlOGHz
<15V (parallel plate)
~10" y
Good
Low
Good
2.3 Candidate ferroelectric materials for varactors
As mentioned, the relative dielectric constant of a material is the ratio of its
permittivity to the permittivity of vacuum.3 The permittivity is a measure of the ability of
a material to be polarized by an electric field. BaxSri.xTi03 (BST), PbxSri.xTi03
(PST),6'18 PbZrxTii.x03 (PZT),19 and NaxK!.xNb03 (NKN)20 are the best known members
of the family of ferroelectrics that have the ABO3 perovskite structure (Fig. 2.3a). The
polarization in these materials is largely a result of the B ion displacement from the
center of oxygen octahedra (though Pb offers an additional mechanism owing to the
stereochemical activity of its lone pairs).21 When B cations move (or lone pairs arrange)
toward some anions, the positive and negative centers of charges in the unit cell are
21
displaced, resulting in local dipoles. When dipoles align without the application of an
electric field, the materials develops a spontaneous polarization and the polarization and
electric field relation becomes hystetic.21 When the direction of the polarization has
degenerate axes (and can be switched by the application of an electric field), this phase is
called a ferroelectric phase.
When no spontaneous polarization exists, the phase is often called a paraelectric.
For some paraelectric phases, the dielectric constant arises from the polarization
introduced by the electric field of the electromagnetic wave, and this polarization can be
tuned by an applied bias electric field.5 The ferroelectric-to-paraelectric phase
transformation temperature is called Curie temperature, or Tc3'5 Above (below) the Curie
temperature, the material is in the paraelectric (ferroelectric) state. Normally,
ferroelectrics exhibits a sharp increase of the dielectric constant in the vicinity of the
Curie temperature.6'22'23 For tunable microwave applications, the paraelectric phase is
desirable because the electric field has a one-to-one relation with the dielectric constant
(Fig. 2.3b), a characteristic that is convenient for device design and signal processing.5
Because of the hysteresis exhibited by ferroelectrics, two dielectric constants exist for
one applied electric field values, also, dielectric losses are increased by domain wall
friction, and therefore the ferroelectrics generally exhibit increased loss values.
The primary material used for ferroelectric varactors is BaxSri.xTi03 (BST), and it
is discussed in detail in the next section. Films of perovskite ferroelectrics PbxSri.xTiC>3
(PST) and PbZrxTii.x03 (PZT) exhibited properties that were comparable to BST films at
microwave frequencies and bulk properties are also appropriate for applications.6'19
22
However, these lead-based materials are generally avoided for productions and
applications owing to their environmental hazards.
Films of the perovskite NaxKi.xNb03 (NKN)6'20 have demonstrated high quality
factors, but their dielectric constants and tunabilities at microwave frequencies are not
comparable to barium strontium titanate films. Also, Na and K are volatile elements that
make device fabrication challenging and the materials are sensitive to environmental
conditions such as moisture.
Bias Voltage (V)
Fig. 2.3 A schematics of the perovskite structure (a) and the dielectric constant of BaxSr,.x7/03
changes with the bias voltage (b). Image (b) was adapted from Heini et al. (Nature 430 (2004),
page758-761).
In recent years, films of the pyrochlore Bi1.5Zn1.0Nb1.5O7 (BZN) have attracted
some attention, despite the fact that BZN is not a ferroelectric.24,25 300 nm films were
deposited on Pt/Si and tested using parallel plate structure. At 20 GHz, high quality
factors >100 were observed. However, the tunabilities of BZN were only about 30% at 1
MV/cm, a voltage that is already unrealistically high to be integrated with silicon.6
To date, there is still no other material that can comprehensively challenge (Ba,
Sr)Ti03 for ferroelectric varactor applications at microwave frequencies, so we have
focused on this material and will discuss these next.
23
2.4 Barium strontium titanate and factors related to the dielectric properties
A material's properties are determined by its composition, crystal structure,
processing history, and microstructure, all of which interact with each other, making it
challenging to dissociate the effects one from the others.
For bulk BST materials (single crystals22'23 or polycrystalline ceramics26'27),
researchers have focused on either compositional factors, such as stoichiometry and
doping, or processing conditions, such as growth or sintering conditions, and their effects
on the dielectric properties. For thin films, the factors are significantly more complicated,
owing to the fact that films are deposited on different substrate materials, and properties
of thin films are further influenced by interfaces,28'29 mismatch strains,30 (extended and
point) defects, and chemical inter-diffusion within the hetero-system.28'29'31"33 The
complexity of microstructures that result from heterostructure processing introduces more
variables that can impact final materials properties.
In this section I will first review the factors that affect both bulk and thin film
properties and will then review those factors specific to thin film varactors.
2.4.1 Composition and dielectric properties
Ferroelectric varactors are designed to operate near room temperature; as such,
the Curie temperature of the ferroelectric should be below room temperature. Since
BaTiC>3 has its Curie temperature at 390 K, it is not suitable for room temperature
applications.34'35 SrTKVs (STO) Curie temperature (if it exists) is close to 0 K.31,34
SrTi03 only exhibits high dielectric constants and tunabilities at cryogenic
temperatures.31'34 At room temperature, both the dielectric constant and tunability of
SrTi03 decrease to very low values.31'34 Investigations of BaxSri.xTi03 single crystals and
24
ceramics demonstrated that the Curie temperature decreased linearly with an increase of
Sr content (a decrease in x), following the relation: 26
TC(癈) � 120- 360(1 -x)
(Eq. 2-11).
Single crystal investigations have shown that BaTiCh has a first order phase
transformation, which appears as a sharp and narrow (Curie) peak in the temperature
dependent dielectric constant near the Curie temperature. When the Ba content decreases
to x < 40%, the phase transformation becomes more and increasingly more diffuse with
temperature, a characteristic that is consistent with a second order transformation.22'23
Bulk Bao.6Sro.4TiC>3 has its Curie temperatures around 250 K,26'36 an ambient
temperature dielectric constant as high as 7000 (measured in bulk ceramics), and a35
tunability of about 80% or more at microwave frequencies.5'27'36 Therefore, the BaxSri.
xTiCh solid solution is considered the most suitable material system for tunable
microwave applications at room temperature, and x ~ 60% (x=0.5~0.7) is considered the
best composition.5'6
BaxSri.xTi03 (x=0.5~0.7) dielectric films have therefore been intensely studied
over the last two decades.5'6'17'37"40 These thin films have much worse properties than bulk
ceramics. They demonstrated a much more diffuse e' vs. T relationship around the Curie
temperature Tc (Fig. 2.4); the FWHM of the Curie peak have been measured as more than
100-200K.41 The dielectric constant peak values have been measured to be two orders of
magnitude lower than those of bulk materials and have never been reported to exceed
3500.7 The tunability decreased to values below 50% for films. The dielectric losses are
often an order of magnitude higher (>10%) than those in bulk materials. Though, low
loss (O.005) values have been observed in BST thin films, the dielectric constant (40)
25
and tunability (7%) were unacceptably low for those films.
42
The cause of the significant
degradation in films has not been clarified 5,28,43,44
130000
'?i
'"*?
a
i''
" ? " " � "
<? ' ? � ' '
Ba^TSr^TiO^
� 1UO00
Ceramic
�
1000 J
Thin Film "*-"**?*-.
t-IOOnm
100
O
100 300 TOO 4CO S90 600 TOO
Temperature {!<}
Fig.2.4 Variation of the dielectric constant of a BST ceramic and a thin film as a function of
temperature from T M. Shaw et al., Applied Physics Letter 75, 2129(1999)
2.4.2 Doping, stoichiometry, and dielectric properties
Isovalent or aliovalent ion doping were investigated in BST bulk ceramics and
thin films to control the dielectric constant, the tunability, and the dielectric loss.6 Ba and
Sr deficiency has been reported in BST films and single crystals.45 In fact, Wontae et al.
purposely used a target with excess Ba and Sr to correct for this in pulsed laser deposited
films,45 the dielectric constant increased and the dielectric loss decreased.45 However,
with the increase of the B site excess, the tunability decreased.45 When an extreme
amount of excessive Ti02 was used, amorphous TiCh-rich grain boundaries phase were
observed, and these were believed to have a dilution effect to decrease the dielectric
constant, the tunability, and the loss.5'46
Mg2+ can take the position of Ba2+ and Sr^+ as an isovalent dopant, and its
introduction decreased the dielectric loss but also decreased the dielectric constant and
26
tunability.5 Fe3+and Nb5+ are ions that were believed to take the position of Ti4+ and act
as acceptors and donors respectively.45'47 Both dopants had the effect of decreasing the
dielectric loss of the films, but again they decreased the dielectric constant and tunability
significantly. Mn ions (such as Mn3+), W6+, and La3+ have also been used as dopant in
both bulk and thin film BST.48 The effects of dopants were explained to arise from their
causing more impact of the vacancies populations to be introduced or on the
compositional homogeity in the materials.47 Oxygen vacancies are positively charged
point defects and are viewed as donor dopants. These will be covered in more detail in
Section 2.4.5.
A detailed review of the doping effect was given by Bao et al..6 Simply put, there
has been no fundamental breakthrough for applications using doping techniques,
especially in thin films.
2.4.3 Strain and dielectric properties
It has been reported that the Curie temperatures of single crystal and
polycrystalline ceramic ferroelectrics decreased linearly with an increase of hydrostatic
pressure.49"51 When a thin film is grown on a substrate forming a heterostructure, these
films are usually experience strains. Such strains in films can be generally categorized
into homogeneous and inhomogeneous strains.
Homogeneous strains refer to those strains that act uniformly in the thin film,
generally, originating from lattice parameter and thermal expansion coefficient (TEC)
differences between the film and substrate. When a film is coherently strained (such that
the in-plane lattice periodicity of the film and substrate are identical, or coherent), the
homogeneous strains are equal to the combination of the lattice mismatch and the
27
corresponding TEC mismatch (when the lattice mismatch is referenced to a different
temperature). When misfit dislocations are generated to relax homogeneous strains from
the coherent mismatches, some homogeneous strains can remain in the films, these
strains are known as "residual strains." The residual strain can be estimated by
measurement of the lattice parameters as compared to bulk (or fully relaxed/strain free)
values.
Importantly, when dislocations are introduced into the film, strain fields also exist
around the dislocation cores that are somewhat localized and whose values vary as a
function of the distance from the dislocations core. These localized strains are called
inhomogeneous strains owing to their spatial dependency or non-uniformity. The extent
of the strain field around a dislocation core can be estimated as Vz the spacing between
dislocations (or can be more accurately calculated if necessary).52 For a dense array of
misfit dislocations, any strain field will be fairly isolated to the interface. On the other
hand, threading dislocations, which formed during the generation of misfit dislocations,
will affect the entire film and their importance will depend on the number and
distribution of threading dislocations.
Several theoretical calculations have predicted the temperature-strain phase
diagram of BaTiC>3 and SrTi03.34'53 It has been shown that both compressive and tensile
biaxial homogeneous strains, applied along <010> directions for (OOl)-oriented films,
should shift the Curie temperature to a higher value (Fig. 2.5).31'34For example, SrTiCVs
Curie temperature can be increased by 300 K, from ~ 0 K to room temperature, using
coherent in-plane strains along <010> directions applied by lattice matching to the
DySc03(l 10) substrate.
28
At the atomistic level, strains affect the displacement of Ti ions. ' The effect of
strains on the dielectric constant of a cubic material depends on the relative direction of
the strains and applied electric field.30'54 It is believed that the tensile strain enhances the
freedom of the Ti4+ center to move off center (in the direction of tensile strain) while
compressive strain suppresses it (in the directions of compressive strain). Because
mismatch strains are primarily in-plane strains, with a Poisson strain in the out of plain
direction, they have predictable effects on the dielectric constant. Since there are two
methods to measure dielectric properties, the effects of mismatch strains depend on the
measurement technique. In the parallel plate capacitor approach, the electric field is outof-plane. In the coplanar capacitor approach, the electric field is in-plane (Fig. 2).
Therefore, when the electric field is in-plane, one can expect that in-plane tensile strains
strengthen the polarization, leading to an increase in the dielectric constant and tunability,
and that compressive in-plane strains weaken the polarization, leading to a decrease in the
dielectric constant and tunability. When the electric field is applied out-of-plane for
measurement, the in-plane tensile strain will weaken the polarization in the out-of-plane
direction, and reduce the measured dielectric constant and tunability, and vice versa for
in-plane electric fields(and ignoring other effect or differences in the measurement
approaches).7'30'54
Ideally, when the mismatch strains are completely relaxed by misfit dislocations,
the effect of strains should be eliminated (or are confined to the interfacial region where
misfit dislocations are located). In reality, there are always some dislocations that thread
through the films, often arising from the process of misfit dislocation generation, even if
the film is relaxed on average. As such, there are always inhomogeneous strains in the
29
films around threading dislocation, the number of which depend on the number inhereited
from the substrate and the number generated on misfit dislocation formation. The
compressive part of the inhomogeneous strains around a dislocation core can cause local
depolarization.28 Such inhomogeneous strains affect the dielectric constant in all
measurement geometries in a non-uniform fashion.7
.All
..i.M.
J.KKJ--
-'.;.�,?<�
..,:;.
In pljne Mum f-t
Fig. 2.5 Expected shift in Tc of (100) SrTi03 (a)J1 and BaTi03 (bf* with biaxial in-plane strain,
based on thermodynamic analysis. The arrows indicate the predicted direction of the polarization
for strained SrTi03: in-plane for biaxial tensile strain and out-of-plane for biaxial compressive
strain. These figures were adapted from reference 31 and reference 34 respectively.
2.4.4 Dead-layer effect
As it has been stated, the dielectric constants and tunabilities of thin films are
dramatically lowered in comparison to bulk values. One interpretation of this degradation
is that regions called "dead-layers" exist in the film (near interfaces) that have suppressed
polarizations and, hence, extremely low dielectric constants. The proposed locations of
the "dead-layer" are at the electrode-film interface, the film substrate interface, or within
the films at locations such as grain boundaries.
30
One explanation of the "dead-layer" attributes its existence to the misfit
dislocations at thefilm-substrateinterface owing to the inhomogeneous strains around the
misfit dislocations, which may suppress the local polarizations within a finite thickness of
several nanometers (Approximately a thickness that is V2 the spacing of the misfit
dislocations).5'28'33'37'55 Another explanation proposes that the "dead-layer" is an intrinsic
effect; when the electric field penetrates into the metal electrodes, a screening effect of
the free charges influences the effective dielectric permittivity.5 Other proposed
mechanisms include possible chemical reactions between the ferroelectric film and the
substrate or between the electrode and the film, or a Schottky effect at the ferroelectric
film and electrodes.5'29 The reported "dead-layer" varied from sub-angstrom to tens of
nanometers owing to the different models of the "dead-layers." 5'32>37'56'57
When parallel plate structures are used (Fig.2. la), for dielectric constant
measurements, the three components of capacitance (the two interfacial capacitances, Q,
at both electrodes and the bulk (intrinsic) film capacitance, Cb) are connected in series;
and the effective capacitance, Ce, is:
? =?+? +?
(Eq. 2-12).
c. ct cb c,
From Eq.2-5, Eq. 2-12 becomes:
-^L
Ases0
=
^L_
+
_ ^
ASjEg Asbe0
+
^L_
(Eq.2-13),
Aets0
in which dtotai is the total thickness of the film, d< is the interface "dead-layer" thickness,
db is the bulk film thickness, ee is the effective dielectric constant, E, is the "dead layer"
dielectric constant, and Eb is the intrinsic bulk film dielectric constant. Plugging in the
numerical values of the "dead layer" thickness as d,~ 3nm and the "dead layer" dielectric
31
constant as et ~ 40, as argued by Chen et al.,5'56 and assuming both "dead-layers" are
identical, taking one of the largest bulk dielectric constants reported, �&
. ~ 15,000,5 and
while assuming the film thickness dtotai = 300nm, we can calculate the effective dielectric
constant from Eq. 2-14:
300
et
3
294
3
=? +
+?
40 15,000 40
_ ? lyI.
(Eq. 2-14).
From Eq. 2-14, the effective dielectric constant, Se = 1769. One can see that the
capacitor's effective dielectric constant, in this model, is dominated by the thin lowdielectric-constant, or the so-called "dead layers".32'33,44'55'58
When coplanar approaches are used, the gap separations between the top
electrodes are usually much larger than the films thickness. According to Tagantsev,5 this
coplanar geometry approximates the condition where the three contributions to
capacitance are connected in parallel , and are, therefore,
additive to the total
capacitance; as such, the "dead-layer" effect was negligible compared to the parallel plate
5 29
geometry. '
In an experiment to test the intrinsic size effects, a bulk single crystal of BaTi03
was ion milled to a thickness of 75 nm, which is comparable to thickness of many thin
films,40 Au metal electrodes were deposited on the two surfaces of the thinned crystal,
and the dielectric properties were measured.40 Interestingly, this structure displayed bulklike properties.40 The dielectric constants at the Curie peak was -25,000, and the CurieWeiss analysis demonstrated a first-order transformation behavior.59 These observations
are in contradiction with the "dead-layer" argument arising from the intrinsic electrodefilm interface (as well as some size effect arguments of suppressed polarization below ~
200nm).34 X-ray photoelectron diffraction (XPD)60 and X-ray Diffraction61 studies on
32
PbTiCh thin films also indicated that there no "dead-layer" existed at the surface of
ferroelectrics (based on the observation of ferroelectric distortion in a film of three unit
cell thick).34
Sinnamon et al. argued that grain boundaries could be the "dead layers" within the
films.57 However, this grain boundary argument can only explain a small portion of the
collected literature observations (it is not valid to most epitaxial films with no
boundaries). Also, there was no direct experimental proof supporting this argument
because it is challenging to dissociate the grain boundary effect from other factors.
Sirenco et al. attributed the decrease of the film dielectric constant to the profound
change from the bulk of the lattice dynamical properties, such as soft mode hardening,
again with little proof.33 In summary, the existence and nature of "dead-layers" in real
samples remains a controversial issue, expecially in attributing the ubiquitous
degradation of film properties to their existence.
2.4.5 Defects and dielectric properties
The degradation of thin film properties have also been attributed to defects in the
film and at the interfaces.33'44'55'62 For instance, Tagantsev et al. proposed that defects in
the films, including oxygen vacancies, dislocations, and grain boundaries, in the films
could be the reasons for the increase of the dielectric loss at microwave frequencies by
introducing novel, readily activated mechanisms for phonon/electric field interactions.5
Oxygen vacancies are considered the most common defects in BST thin films,
because most thin films have been grown under vacuum conditions with low oxygen
partial pressures (owing to the characters of physical or chemical vapor deposition
techniques). Oxygen vacancy chemistry and its concentration can be written as:
33
00**V0~+�+2e'
(Eq.2-15),
and the oxygen vacancy population can be written as:
[V"]*P;21/2"~2
�
expf--^J
kT
(Eq.2-16).
In Eqs. 2-15 and 2-16, [V"] is the concentration of oxygen vacancies v", Eais the
oxygen vacancy generation energy, k is Boltzmann constant, T is temperature, P^ is the
partial pressure of oxygen, and n is the electron concentration. This treatment assumes
the electroneutrolity of the crystal is governed by the charged species presented in Eq.215. From Eq. 2-16, the oxygen vacancy concentration experimentally depends on partial
pressure of oxygen and temperature during film growth or post-growth annealing.17
Experiments have been performed to investigate the effect of oxygen vacancies
on the dielectric constant, tunability, and loss.17, It should be noted that, since oxygen
vacancies are positively charged and act as donors in films, an increase of oxygen
vacancies provides electrons and reduces the resistivity of thin films; hence, the leakage
current and the dielectric losses increase with oxygen vacancy populations.63 Before
discussing the dielectric properties it is important to point out that, in (Ba, Sr)Ti03 thin
films, oxygen vacancies are believed to cause a lattice parameter expansion. Kim et al.
observed this unit cell volume expansion in thin films with a decrease of the deposition
oxygen pressure.17 As such, the lattice mismatch between the film and the substrate
would be different when the films are grown under different oxygen pressures.54 Kim
found that the dielectric properties were dependent on the in-plane to out-of-plane lattice
parameter ratio, or c/a. When the lattice distortion was minimized (c/a ~ 1), the film
demonstrated the highest dielectric constant and lowest dielectric loss.17 Unfortunately,
34
this investigation reported the properties only at one particular temperature point (room
temperature); therefore, the dielectric property picture is incomplete, especially in regards
to the effect on the Curie temperature and dielectric dispersion with temperature. More
importantly, without temperature dependent measurement one cannot rule out other
interpretations. For instance, the Curie temperature may have shifted, the temperature
point reported may now fall on the different regions of the dielectric constant vs.
temperature plot.
As discussed above, grain boundaries are also considered one of the potential
critical factors that can cause a dielectric constant decrease. A relationship between the
dielectric constant and the grain sizes were observed for both thin film and bulk
polycrystalline BST ceramics.57'64 The dielectric constant decreases with the decrease of
the grain sizes and increase of the concentration of grain boundaries. These observations
were explained by either an "intrinsic size effect" or a "dead-layer" effect of grain
boundaries.64 Models that considered grain boundaries "dead-layers" required that the
en
grain boundary layers be tens of nanometers in thickness.
High resolution TEM
revealed no distinct structural disturbance in the grain boundaries of stoichiometric (Ba,
Sr)TiC<3.57 In BST thin films with extreme excess TiC>2 (18%), Ti-rich amorphous areas
were observed at the grain boundaries due to TiCh segregation.46'65 However, this
observation cannot be generalized to explain the property degradations of films with
appropriate stoichiometry because of the complexity of TiC>2 doping effect.46
Nevertheless, closely spaced grain boundaries should be avoided in order to improve
dielectric properties. The concentration of grain boundaries can be controlled by
controlling the grain sizes. The grain size depends on the factors that affect the nucleation
35
rate and adatom mobility, such as supersaturation,
interfacial energy, growth
temperatures, and oxygen pressures.57'64
One of the most significant and experimentally qualitiable differences between
films and bulk materials is that the films have much higher dislocation densities when
grown on mismatched substrates, as is the case for BST deposited on conventional
substrates, including MgO, LaA103 and SrTi03. The dislocation densities in such films
are on the order of 10n~12/cm2,28'43'66"68 which is several orders of magnitude higher than
the dislocation density in the bulk SrTi03 and BaTi03 crystals (on the order of 108 /cm2
from the TEM observation of this research).69 Simulations based on Landau-Devonshire
thermodynamics have shown that the inhomogeneous strains around dislocations caused
polarization suppression within an area of 20x20 nm2; the Curie temperature was also
determined to be inhomogeneous in the same area around the dislocations.28 One
argument for the importance of the dislocations is based on the fact that the dielectric
constant was observed to increase by annealing thin films.5'70 Annealing, has been
reported to increase the dielectric constant. It was proposed that this dielectric property
improvement was due to the reduction of dislocation density during annealing.67
However, this dielectric property improvement can be explained also by considering
other strain relief mechanism or other chemical changes during annealing.66'71 Also, the
domain wall motion associated with the local ferroelectric phase may have caused the
increase of loss in thin films.72
Because these defects, such as oxygen vacancies, grain boundaries, and
dislocations are always conjugated and intertwined with other factors, such as strains and
stoichiometry, and the data reported in the literature are scattered, the mechanisms on
36
how individual defects affect the dielectric constant and tunability are not well
understood. Therefore, more systematic experiments with better control need to be done
to investigate the relation between these defects and the dielectric properties, including
dielectric constant, tunability, and dielectric loss, ultimately to engineer improved thin
film devices.
2.5 Dislocation generation mechanisms
During the initial stages of growth, epitaxial thin films tend to be coherent with
the substrate, meaning the in-plane periodicities of both are coherent. Strain accumulates
in the coherent films as the film thickness increases owing to the lattice mismatch
between the substrate and the film (the strain is proportional to the square of the
mismatch strain and the stored energy is proportional to the volume of the film).73'74
Misfit dislocations can relax the strain by rendering the film incoherent with the
substrate, but there is an energy cost to generate the misfit dislocations. When the film
thickness exceeds a critical value, misfit dislocations generation are energetically
favorable but there is still a barrier for their formation. One mechanism for misfit
generation is by the bowing of those preexisting dislocations inherited from the
substrates. Another mechanism is for the misfit dislocations to form by nucleation at the
surface of the film then to move to the interface to relax the strain energy.74
Two models are often adopted to calculate the critical thickness (hc), or the
thickness above which dislocations should be generated. One is the so-called the force
balance model, which uses the force balance relation between the shear stress and the
dislocation tension.73 The equation is written as:73
b (1-vcos2 a) _ h. + ]
K =^-777
17$
:
iO籘
(l + V)COSA
37
O
)
(Eq.2-17),
where b is the magnitude of Burger's vector,/is the lattice mismatch, v is the Poisson's
ratio, � is the angle between the dislocation line and the Burger's vector, and X is the
angle between the slip direction and that direction in the film plane that is perpendicular
to the line of the intersection of the slip plane and the interface.73
The other model is the so-called energy balance model, which uses the energy
balance relation between the strain energy of the film and the dislocation energy.74 The
resultant equation is written as:74
K=-[-?�
-Mn^ + J)
/ 4n(l + v)
b
(Eq2-18).
Introducing approximate values of those constants, the critical thickness has an
approximately inverse relation with the lattice mismatch, hc ~ 6/(10/).74 The dislocations
atfilm-substrateinterface should be aligned in a periodic fashion for the strain relaxation
and are referred to as misfit dislocations (MDs).73 During the MD formation process,
threading dislocations (TDs) and run through the interface through the film surface can
be left due to pinning or dislocation reactions.43'73"75
Regarding the slip system of perovskite (Ba, Sr)TiC>3 materials, there are a
number of conflicting reports that argue for either the <100>{010} slip-system or the
<110 >{1J0}16 slip-system, both on bulk materials and on thin films. For instance,
Yamanaka (2000) reported the dislocations in as-grown SrTiCh single crystals mostly
have <100> type Burger's vectors.77 Nishigaki (1991) observed dislocations with both
<100> and <110> Burger's vectors in SrTi03 single crystals that were plastically
deformed by indentation at 900癈 and 1100癈..78 In contrast, Brunner (2006) recently
studied SrTiC>3 deformed by means of compression along a <100> direction at room
temperature and their observations suggested that the dislocations were generated based
38
on the slip system of < 110 > {110} 79 Liu et al. (2006) studied plastically deformed (by
indentation) (001)- and (HO)-oriented BaTiCb single crystals at room temperature and
proposed the dislocations were generated based on the < 110 > {110} slip system.80
Most of the film relaxation mechanism studies were performed on [001]-oriented
films. There is no agreement on the film strain relaxation mechanism. However, Suzuki
et al. (1999) observed misfit dislocations with both <100> and 1/2<101> Burger's vectors
and line directions (traces) along <100> directions in the film-substrate interface, the
substrate was SrTiOs.
Two possible relaxation scenarios of the BaTiC>3 films were
proposed, which would allow for two types of Burger's vectors with only one type of
dislocation motion mechanism. In the first, the misfit dislocations could have glided from
the surface to the interface via the < 110 > {110} slip system and then recombined
(l/2<101>a +l/2<i07>a => <100>a) to form a dislocations of <100>a Burger's
vector.81 In the second, misfit dislocations with a <100> Burger's vector could have
climbed from the surface to the interface and then dissociated into misfit dislocations
with Burger's vectors of '/2<101>, <100>a =>l/2<101>a +1/2< 101 > a.81 Sun and coworkers62'82 observed that BaTiCh films grown on SrTi03 start to relax at a film thickness
of 2nm by misfit dislocation half-loops nucleating on the film surface; they relaxed
gradually with increased thickness until the film was completely relaxed at 20nm. They
proposed that the dislocations climbed to the interface because they observed <100> type
of dislocations infilm-substrateinterface. Examining the two models proposed by Suzuki
et al., one can find that the dislocation reactions are energetically feasible in either
direction.81 That being said, however, it is impossible to precisely determine the
relaxation mechanism by studying (OOl)-oriented films ex-situ.
39
Gliding is an abrupt process; in comparison, climbing is dynamically limited
depending on the slow processes of point defects (vacancies) diffusion.81 These two
different misfit dislocation generation motion mechanisms may affect the dependence of
the dielectric properties dependence on the film thickness. An accurate understanding of
the strain relaxation mechanism will assist the understanding of how homogeneous
strains and film thickness affect properties. A further study to clarify strain relaxation
mechanism in this family of materials is necessary.
Misfit dislocations in the interface are introduced to relax the homogeneous
strains originating from lattice mismatch or thermal expansion coefficient difference
between the film and the substrate. Threading dislocations, which run through the
thickness of the film, can be introduced in four possible manners: a. inherited from the
substrate,73 b. generated during the misfit dislocation generation process,43'73 c. generated
from substrate surface defects,83'84 and d. nucleation and coalescence of rotated
neighboring grains that are rotated slightly from one another.24'85 Therefore, critical
factors that affect the dislocation concentrations in films include the substrate crystal
quality itself, the substrate surface quality (based on treatment processes), the substrate
orientation, the film growth mode (again related to substrate), and the substrate-film
lattice mismatches.
2.6 Summary: statement of the problem
(Ba, Sr)Ti03, a promising candidate material for tunable microwave varactors,
has been the subject of extensive investigations for applications during recent decades.5'6
Compared to barium strontium titanate bulk materials, barium strontium titanate thin
40
films have degraded dielectric properties: dramatically lower dielectric constants and
^inabilities and higher dielectric losses.5'6'22'67 These property changes from bulk to thin
films have been attributed to interface effects (dead-layer),28'44 strain effects,30'68'86 and
defects28'68 associated with thin film processing. Meanwhile, these factors have not been
uncoupled in past experimental investigations. Therefore, our understanding of and
ability to control properties of barium strontium titanate thin films remains challenged.
It is believed that most of the factors that affect dielectric properties are associated
with dislocations, either directly or indirectly. From prior studies we know that when a
film is grown on a substrate, the homogeneous strains due to mismatch of lattice
parameters or TECs, either compressive or tensile, shift the Curie temperature to a higher
value than the material's corresponding bulk value (the latter of which is dependent on
composition only).26'31'34 Homogeneous strains can not only shift the Curie temperature,
but they also can affect the general peak dielectric constant values. Tensile strains parallel
to the wave electric field strengthen the polarizations in the film and increase the
dielectric constant, and compressive strains suppress the polarizations and decrease the
dielectric constant.30 This homogeneous strain energy increases as the film thickness
increases. When a critical thickness is reached, misfit dislocations will be generated to
release the homogeneous strain.74 Misfit dislocations will move to the interface and
impact interfacial effects, such as the "dead-layer" effect in the interfaces.28'33'44'55 During
the process of misfit dislocation development, threading dislocations are left in the film
due to either dislocation reaction or impurity pinning.43 Around threading dislocations
cores there exits inhomogeneous strains.28'43 Thin films have usually high concentrations
41
of dislocations, e.g. >10n/cm2;31 the lattices parameters, the polarizations, and the Curie
temperatures in the films can be highly distributed in local regions.
For thin films, dislocations are the factor that connects many of the other factors
that impact dielectric properties. Investigations focusing on the role dislocations offer an
opportunity to gain much improved understandings of and control over the dielectric
properties of barium strontium titanate thin films. This research makes the effort to
isolate the effect of homogeneous strains and inhomogeneous strains by controlling the
dislocation concentration and strain states using substrates with different mismatches
with the BST films. The detailed hypotheses and experiment design will be presented in
Chapter 3.
References
1
W. Halser, Introduction to the principles of electromagnetism (Addison-Wesley
Publishing Company, Reading, Massachusetts, 1971).
2
Hertz biography, digitized photographs, created by Institute of Chemistry,
Hebrew University of Jerusalem in July 30, 2004.
3
L. F. Chen and C. K.Ong, Microwave Electronics: measurement and material
characterization (John Wiley & Sons, Ltd., 2004).
4
F. W. Grover, Inductance calculations : working formulas and tables (Instrument
Society of America, New York, 1981).
5
A. K. Tagantsev, K. F. Astafiev, J. Venkatesh and N. Setter, Journal of
Electroceramics 11, 5-66 (2003).
6
P. Bao, X. Wang and M. J. Lancaster, J. Phys. D: Appl. Phys. 41 063001 (2008).
42
C. Wontae, M. G. Charles, K. Won-Jeong, M. P. Jeffrey, W. K. Steven, B. Q.
Syed, B. C. Douglas, and S. H. James, Journal of Applied Physics 87, 3044-3049
(2000).
S. S. Gevorgian, T. Martinsson, P. L. J. Linner, and E. L. Kollberg, IEEE
Transactions on Microwave Theory and Techniques 44, 896-904 (1996).
C. Nguyen, Analysis methods for RF, microwave, and millimeter-wave planar
transmission line structures (John Wiley & Sons, Inc., New York, 2000).
S. Gevorgian, C. E., S. Rudner, L. D. Wernlund, X. Wang, and U. Helmersson,
IEE Proceedings-Microwave and Antenna Propagation 143,397-401 (1996).
M. Golio, The RF and Mircowave Handbook (CRC Press, Boca Raton, London,
New York, Washington D.C., 2001).
R. A. Walton, Popular Electronics March, pp 53-55 (1968).
L. T. Muftuler, G. Gulsen, K. D. Sezen, and O. Nalcioglu, Journal of Magnetic
Resonance 155, 39-44 (2002).
I. Gutierrez, J. Melendez, and E. Hernandez, Design and Characterization of
Integrated Varactors for RF Applications (John Wiley & Sons Ltd,, West Sussex,
England, 2006).
M. V. Shakhrai, in Miroelectromechanical (MEMS) Varactors for Mobile
Communications, Erlagol, 2003, p. 3-9.
X. X. Xi, H. C. Li, W. Si, A. A. Sirenko, I. A. Akimov, J. R. Fox, A. M. Clark,
and J. Hao, Journal of Electroceramics 4, 393-405 (2000).
W. J. Kim, W. Chang, S. B. Qadri, J. M. Pond, S. W. Kirchoefer, D. B. Chrisey,
and J. S. Horwitz, Applied Physics Letters 76,1185-1187 (2000).
R. S. Katiyar, M. Jain, N. K. Karan, A. S. Bhalla, F. A. Miranda, and F. W. Van
Keuls, Integrated Ferroelectrics 71,11 - 19 (2005).
Q.-Y. Shao, A.-D. Li, Y.-D. Xia, D. Wu, Z.-G Liu, and N.-B. Ming, Journal of
Applied Physics 100,036102-3 (2006).
43
C. Wontae, A. C. Carter, S. H. James, W. K. Steven, M. P. Jeffrey, K. S.
Grabowski, and B. C. Douglas, Mat. Res. Soc. Symp. Proc. 493, 353 (1998).
M. E. Lines, A. M. Glass, Principles and applications of ferroelectrics and
related materials ^Oxford University Press, New York, 2001).
L. Benguigui and K. Bethe, Journal of Applied Physics 47, 2787-2791 (1976).
L. Benguigui, Physica Status Solidi (a) 46, 337-342 (1978).
C. J. Lu, L. A. Bendersky, K. Chang, and I. Takeuchi, Journal of Applied Physics
93,512-521 (2003).
J. Lu and S. Stemmer, Applied Physics Letters 83,2411-2413 (2003).
H. V. Alexandria, C. Berbecaru, A. Ioachim, L. Nedelcu, and A. Dutu, Applied
Surface Science 253, 354-357 (2006).
H. V. Alexandru, C. Berbecaru, A. Ioachim, M. I. Toacsen, M. G. Banciu, L.
Nedelcu, and D. Ghetu, Materials Science and Engineering B 109, 152-159
(2004).
S. P. Alpay, I. B. Misirlioglu, V. Nagarajan, and R. Ramesh, Applied Physics
Letters 85, 2044-2046 (2004).
A. K. Tagantsev and G. Gerra, Journal of Applied Physics 100, 051607 (2006).
W. Chang, C. M. Gilmore, W.-J. Kim, J. M. Pond, S. W. Kirchoefer, S. B. Qadri,
D. B. Chirsey, and J. S. Horwitz, Journal of Applied Physics 87, 3044-3049
(2000).
J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W.
Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q.
Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, Nature 430, 758-761 (2004).
J. Kim, J. Pak, K Nam, and G. Park, J. Electocerm 16, 495-498 (2006).
A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J. Hao, W. Si, and X. X. Xi,
Nature 404,373-376 (2000).
44
D. G. Schlom, Long-Qing Chen, C.-B. Eom, K. M. Rabe, S. K. Streiffer, and J M. Triscone, Annu. Rev. Mater. Res. 37, 589-626 (2007).
K. J. Choi, M. Biegalski, Y. L. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche,
Y. B. Chen, X. Q. Pan, V. Gopalan, L. Q. Chen, D. G. Schlom, and C. B. Eom,
Science 306,1005-1009 (2004).
J. Zhai, X. Yao, X. Cheng, L. Zhang, and H. Chen, Materials Science and
Engineering B 94, 164-169 (2002).
J. Q. He, E. Vasco, C. L. Jia, and R. H. Wang, Applied Physics Letters 87,
062901-3 (2005).
S. B. M. M. Jain, A. Martinez, R. S. Katiyar, F. W. Van Keuls, R.R. Romanofsky,
F. A. Miranda, Integrated Ferroelectrics 42, 343-355 (2002).
S. W. Kirchoefer, A. C. Carter, W. Chang, K. K. Agarwal, J. S. Horwitz, and D.
B. Chrisey, Microwave and Optical Technology Letters 18,168-171 (1998).
H. Zhiming, Z. Zhanhong, J. Chuping, Y. Jian, S. Jinlan, and C. Junhao, Applied
Physics Letters 77, 3651 -3653 (2000).
T. M. Shaw, Z. Suo, M. Huang, E. Liniger, R. B. Laibowitz, and J. D. Baniecki,
Applied Physics Letters 75, 2129-2131 (1999).
E. J. Cukauskas, S. W. Kirchoefer, and J. M. Pond, Journal of Applied Physics 88,
2830-2835 (2000).
I. B. Misirlioglu, A. L. Vasiliev, M. Aindow, S. P. Alpay, and R. Ramesh,
Applied Physics Letters 84,1742-1744 (2004).
C. Zhou and D. M. Newns, Journal of Applied Physics 82, 3081-3088 (1997).
C. wontae, J. S. Horwitz, J. M. Pond, S. W. Kirchoefer, and D. B. Chrisey, Mat.
Res. Soc. Symp. Proc. 526,205 (1998).
S. Stemmer, S. K. Streiffer, N. D. Browning, C. Basceri, and A. I. Kingon,
Interface Science 8,209-221 (2000).
45
S. Garcia, J. P. R. Font, R. J. Quinones, J. Heiras, and J. M. Siqueiros, Journal of
Electroceramics 6:2,101-108 (2001).
C. Wontae, S. H. James, K. Won-Jeong, M. P. Jeffrey, W. K. Steven, and B. C.
Douglas, Mat. Res. Soc. Symp. Proc. 541,699 (1999).
A. K. Goswami and L. E. Cross, Physical Review 171,549 (1968).
W. J. Merz, Physical Review 78, 52 (1950).
G. A. Samara, Physical Review 151, 378 (1966).
D. Hull and D. J. Bacon, Introduction to Dislocations (BPC Wheaton Ltd, 1984).
Y. L. Li and L. Q. Chen, Applied Physics Letters 88, 072905-3 (2006).
L. M. B. Alldredge, C. Wontae, W. K. Steven, and M. P. Jeffrey, Applied Physics
Letters 94, 052904 (2009).
M. Stengel and N. A. Spaldin, Nature 443, 679-682 (2006).
B. Chen, H. Yang, L. Zhao, J. Miao, B. Xu, X. G. Qiu, B. R Zhao, X. Y. Qi, and
X. F. Duan, Applied Physics Letters 84, 583-585 (2004).
L. J. Sinnamon, M. M. Saad, R M. Bowman, and J. M. Gregg, Applied Physics
Letters 81, 703-705 (2002).
K. Natori, D. Otani, and N. Sano, Applied Physics Letters 73, 632-634 (1998).
M. M. Saad, R. M. Bowman, J. M. Gregg, F. D. Morrison and J. F. Scott, J. Phys.:
Condens. Matter 16, L451-L456 (2004).
L. Despont, C. Koitzsch, F. Clerc, M. G. Gamier, P. Aebi, C. Lichtensteiger, J. M.
Triscone, F. J. G de Abajo, E. Bousquet, and P. Ghosez, Physical Review B
(Condensed Matter and Materials Physics) 73, 094110-6 (2006).
C. Lichtensteiger, J.-M. Triscone, J. Junquera, and P. Ghosez, Physical Review
Letters 94, 047603-4 (2005).
46
H. P. Sun, W. Tian, X. Q. Pan, J. H. Haeni, and D. G. Schlom, Applied Physics
Letters 84, 3298-3300 (2004).
M. S. Tsai and T. Y. Tseng, J. Phys. D: Appl. Phys. 32, 2141-2145 (1999).
Z. Zhao, V. Buscaglia, M. Viviani, M. T. Buscaglia, L. Mitoseriu, A. Testino, M.
Nygren, M. Johnsson, and P. Nanni, Physical Review B 70, 024107 (2004).
S. S. Stemmer, N.D. Browning, C. Basceri and A.I. Kingon, Interface Science 8,
209-221 (2000).
C. L. Canedy, H. Li, S. P. Alpay, L. Salamanca-Riba, A. L. Roytburd, and R.
Ramesh, Applied Physics Letters 77,1695-1697 (2000).
W. Chang, J. S. Horwitz, A. C. Carter, J. M. Pond, S. W. Kirchoefer, C. M.
Gilmore, and D. B. Chrisey, Applied Physics Letters 74,1033-1035 (1999).
D. Balzar, P. Spagnol, S. Mani, A. M. Hermann and M. A. Matin, Jpn. J. Appl.
Phys. 41, 6628-6632 (2002).
X. Guo, Z. Zhang, W. Sigle, E. Wachsman, and R. Waser, Applied Physics
Letters 87,162105-3 (2005).
O. Tikhomirov, H. Jiang, and J. Levy, Applied Physics Letters 77, 2048-20.50
(2000).
J.Y. Ha, J. W. Choi, C.Y. Kang, S. F. Karanenko, S. J. Yoon, D.-J. Choi, and H J. Kim, Japanese Journal of Applied Physics 44, LI 196-L1198 (2005).
A. K. Tagantsev, V. O. Sherman, K. F. Astafiev, J. Venkatesh, and N. Setter,
Journal of Electroceramics 11, 5-66 (2003).
J. W. Matthews and A. E. Blakeslee, Journal of Crystal Growth 27, 118-125
(1974).
R. People and J. C. Bean, Applied Physics Letters 47, 322-324 (1985).
A. E. Romanov, W. Pompe, S. Mathis, G. E. Beltz, and J. S. Speck, Journal of
Applied Physics 85, 182-192 (1999).
47
M. Dawber, K. M. Rabe, and J. F. Scott, Reviews of Modern Physics 77, 1083
(2005).
J. Yamanaka, J. Yoshimura, and S. Kimura, Journal of Electron Microscopy 49,
89-92 (2000).
J. Nishigaki, K. Kuroda, and H. Saka, Physica status solidi. A: Applied research
128,319-336(1991).
D. Brunner, Acta Meterialia 54,4999-5011 (2006).
D. Liu, M. Chief, and K. W. White, Acta Meterialia 54, 4525-4531 (2006).
T. Suzuki, Y. Nishi, and M. Fujimoto, Philosophical Magazine A 79, 2461-2483
(1999).
H. P. Sun, X. Q. Pan, J. H. Haeni, and D. G. Schlom, Applied Physics Letters 85,
1967-1969 (2004).
T. O. Iizuka, Yasumasa; Kikuchi, Makoto Japanese Journal of Applied Physics 4,
237 (1965).
Myung Yoon Urn, Jae Kyeong Jeong, Bum Seok Kim, Hoon Joo Na, In Bok
Song, and H. J. Kim, Mat. Res. Soc. Symp. Proc. 719, F8.12.2 (2002).
C. J. Lu, Applied Physics Letters 85,2768-2770 (2004).
L. Hao, A. L. Roytburd, S. P. Alpay, T. D. Tran, L. Salamanca-Riba, and R.
Ramesh, Applied Physics Letters 78,2354-2356 (2001).
48
Chapter 3
Hypotheses and Research Approaches
Chapter 2 presented the problem that ferroelectric films, such as BaxSri.xTi03,
exhibit lower dielectric constants and tunabilities and higher dielectric losses, all by one
or two orders of magnitude, compared to the bulk materials. A hypothesis was proposed
there that stated both the homogeneous and inhomogeneous strains associated with
substrate interactions and threading dislocations, respectively, are the primary factors that
have alter thin film properties compared to bulk properties. The overarching goals of my
research are as follows; 1) to understand the dislocation generation mechanism, since
understanding dislocation generation will help identify the type of dislocations and
perhaps help prevent their formation, 2) to understand the correlation between the
number of dislocations and the dielectric properties, as this test the hypothesis concerning
the important role of inhomogeneous strains, 3) to understand the effects of homogeneous
strains on the dielectric properties of thin films, especially when the dislocation
concentration is minimized so the effects can be isolated. In this chapter, the
experimental designs aiming to achieve these goals will be discussed (�1), and the
related experimental techniques will be introduced (�2) along with general details of
how such techniques were implemented.
3.1 Experimental design and hypotheses
3.1.1 Strain relaxation mechanism study and slip-system identification
49
Since no agreed-up film relaxation mechanism is found in the literature for (001)oriented (Ba, Sr)Ti03 films,1"3 the further study of relaxation mechanisms is necessary.
All of the previous studies on relaxation mechanisms were focused on (OOl)-oriented
(Ba,Sr)Ti03films.1"3Similar phenomena have been reported that misfit dislocations with
both Burger's vectors, <100>a and l/2<110>a, exist in the film-substrate interface as
observed based on by both planview and cross-sectional transmission electron
microscopy (TEM).1'3 Alternative misfit dislocation generation mechanisms have been
proposed.1 Misfit dislocations can be introduced either via dislocation climbing of
dislocations with Burger's vectors of a<100>, followed by dislocation dissociation
<100>a ?� '/2<101>a + 1/2<101>a, or via dislocation gliding of dislocations with
Burger's vector of <110>a followed by dislocation combination, !4<101>a + V2 < 101 > a
?? <100>a.1"3 This dislocation dissociation and combination are equally energetically
feasible (based on the energy of long-range strain fields), therefore, the strain relaxation
mechanism study on the (OOl)-oriented films cannot precisely determine the misfit
dislocation generation mechanism using ex-situ TEM characterization of the dislocations.
An accurate understanding of the slip system will provide a precise interpretation
of the dislocation Burger's vectors and how the inhomogeneous strains are distributed
around dislocations cores. With a precise knowledge of the dislocation characteristics and
the inhomogeneous strain distribution, during the experimental design of the dielectric
property comparisons can be improved along with an appropriate choices of film
thicknesses. In addition, understanding the slip system in this family of perovskite
structures are also of interest to geologists, because this structure from which the earth's
50
mantle are built.4'5 A precise understanding of the slip system could help geologists in
predicting earth quakes and in modeling them.4
The strain relaxation processes can be investigated on films of other orientations
(other than (100)) for whom the dislocation characters can be uniquely determined. This
approach can be used to elucidate the slip system and to generate an accurate
understanding of the strain relaxation mechanisms during Bao.6Sro.4Ti03 growth. Cubic
SrTiCh, LaAlC>3, MgO, and orthorhombic NdGa03 crystals with surface orientations
equivalent to perovskite (100), (110), and (111) are commercially available. Surface
morphologies of films grown on substrates of different orientations will be studied and
the growth conditions will be optimized to maintain the growth in a 2D layer-by-layer
mode. This growth mode study is designed to exclude the potential complexity of
multiple misfit dislocation generation mechanism that are related to the growth mode.6
Based on conventional models of dislocation generation, misfit dislocations
nucleate at the film surface after the critical thickness is reached and then they move to
the interface (by glide or climb).7 The direction of the observed dislocation line in the
interface must be the trace of the slip plane and the interface plane. In order to relax the
in-plane strain, the Burger's vectors of misfit dislocations must have an in-plane edge
component, i.e., A Burger's vector perpendicular to the dislocation line in the plane of the
interface. If the dislocations are pure screw dislocations or the in-plane projection of the
Burger's vector make them pure screw type, these dislocations cannot contribute to strain
relaxation.7"11 When the slip-plane that defines the dislocation is parallel to the interface
plane, and no other slip systems are in operation, the misfit dislocations can only climb
51
into the interface. That being said, the misfit dislocation characteristics can be predicted
based on the <100>{010} and < 110 > {110} slip systems respectively and their glide or
climb to the interface.
For (OOl)-oriented barium strontium titanate films, according to that relax using
the <100>{010} slip system, the two slip planes intersecting with the (001) interface
plane are (100) and (010). These planes are both perpendicular to the (001) interface
plane. These misfit dislocations have no possibility of gliding to the interface. To relax
strains, the misfit dislocations with <100> Burger's vectors must climb into the interface.
Such misfit dislocations should form a dislocation network with dislocation lines running
along <100> directions and that are perpendicular to each other. On the other hand, based
on films that relax via the < 110 > {110} slip system, the misfit dislocations can glide to
the interface on the four {110} planes: the (101), (101), (011), and (011). The traces of
these four {110} planes on the interface plane (001) form a network with lines along the
<100> directions that are (of course) perpendicular to each other.
For the case of (HO)-oriented barium strontium titanate films that relax via the
<100>{010} slip system, two {100} planes, (100) and (010), are tilted respect to the
interface plane (110) and have traces along [001] direction; misfit dislocations have the
possibility of gliding on these two planes. The slip plane (001) is perpendicular to the
interface plane (110). Misfit dislocations can only climb into the interface and have the
dislocation line traces along the [110] direction. [001] and [110] are perpendicular to each
other and form a rectangular network. On the other hand, films relaxing via the
52
< 110 > {110} slip-system, misfit dislocations can glide on four {110} planes: (101), (101),
(Oil), and (011); these planes have traces in the (110) interface plane along [111] and
[111] directions, which make a 109� angle respect to each other. One slip plane(110)is
perpendicular to (110) interface; therefore, the misfit dislocations can climb and have a
line direction trace along the direction [001].
Table 3.1 Misfit dislocation (MD) Burger's vectors and line characteristics predicted
based on <100>{010} slip system and the film orientation geometry.
Orientation
MD Burger's
Vector
(100)
a<100>
(110)
a<100>
MD Line Directions
and Motion Process
[100] & [010] by climb
[001] by glide
MD Line
Relations
90�
90�
[110] by climb
(111)
a<100>
[110] , [101], and [011] by glide
60�
Table 3.2 Misfit dislocation Burger's vectors and line characteristics predicted based on
the <110> {flO} slip system and the film orientation geometry.
(100)
MD
Burger's
Vector
a<110>
(110)
a<110>
Film
Orientation
MD Line Directions and Motion Process
Line
Relations
[1001 &[0101 by glide
90�
[111] and [111] by glide
(111)
a<110>
109�
[0011 by climb
[112],[121],and[211] b y C l i m b
60�
For the case of (11 l)-oriented films relaxing via the <100>{010} slip system, the
misfit dislocations can glide on the three <100> planes: (100), (010), and (001). These
53
three planes have traces on (111) interface plane along [Oil], [101], and [110] , having 60�
angles respect to each other. On the other hand, a similar strain relaxation via the
< 110 > {110} slip-system has several possibilities for six {110} planes. Three of them,
including (110), (101), and (011), have traces in the interface plane long [110] , [101], and
[011] directions. However, the possible Burger's vector directions for these are in the
same directions as the line directions correspondingly. As such, these dislocations are
pure in-plane screw dislocations and cannot contribute to the strain relaxation. The other
three {110} planes, including (110) , (101), and (011), are perpendicular to the (111) plane;
and they have their traces along the [112], [121], and [211]. Therefore, the misfit
dislocations cannot move to the interface by gliding; they can only move by climb.
The predictions described above for the possible misfit dislocation configurations
have been summarized in Table 3.1 and 3.2 for all the three orientations. Transmission
electron microscopy will be used to determine experimentally the dislocation
characteristics. The observations will be compared to the predictions to identify which
slip system is in operation.
Different relaxation mechanisms in differently oriented films will result in
different residual strain states in the films and sometimes even strain anisotropy. To
investigate the correlation between these strain states, strain anisotropy, and the dielectric
properties, such as Curie temperature, dielectric constants, and tunabilities would lead to
a deeper understanding over property engineering.
54
3.1.2 Correlation between dislocation concentration and dielectric properties
To study how dislocations influence the dielectric constant and tunability,
samples with different dislocations densities will be prepared, and their dielectric
constants and tunabilities will be measured and correlated to the dislocation densities. In
order to isolate the effect of dislocations, we need to keep other factors constant. First of
all, film compositions should be kept constant. Bao.6Sr0.4Ti03, with its bulk Curie
temperature slightly below 0癈, is considered suitable for room temperature tuning
applications.12 Bao.6Sro.4Ti03 will therefore be used as the film composition. Another
reason to choose Bao.6Sr0.4Ti03 is the fact that it has been frequently reported in the
literature, and these accumulated data can be used as references for current research.12'13
Table 3.3 Comparison of x-ray diffraction rocking curve Full-Widths-Half-Maxima (FWHM) of
often-used substrates.
Substrate
materials
GdSc0 3
(110)
DySc0 3
(110)
SrTiOj
(100)
LSAT
(100)
NdGaOj
(110)
LaA10 3
(100)
FWHM(�)
0.005
-0.008
0.005
-0.008
0.033
-0.045
0.007
-0.01
0.007
-0.01
0.015
MgO
(100)
0.016
Since films inherit dislocations from substrates, the substrates quality directly
affects the film quality. For coherently strained films, the dislocation densities of the
films are dependent on the dislocation density of the substrates. The full-width-at-halfmaximum (FWHM) of a rocking curve from high resolution x-ray diffraction has often
been used to quantitatively estimate the dislocation densities in single crystals or thick
55
films. ' Qualitatively, a higher rocking curve FWHM represents a higher concentration
of dislocations. The available substrates and their rocking curves are listed in Fig. 3.3.
For SrTi03 substrates, their rocking curves FWHM are of about 0.033-0.045�,
which corresponds to a dislocation density of about 4xl08/cm2 as characterized by TEM.
(110) GdSc03 and (110) DySc03 are two kinds of novel substrates that have been used to
grow high quality BaTi03 and SrTi03 films using MBE.16'17 They have yet to be used for
BaxSri.xTi03 solid-solution film growth. Both substrates have much more narrow rocking
curve FWHMs (0.005-0.007�) than SrTi03 substrates (Table 3.3). The dislocation
densities in GdSc03 and DySc03 have been determined to be a least two orders of
magnitude lower than in SrTi03 (by the etch pits counting method). At the same time,
GdSc03 and DySc03 have a pseudo-cubic-perovskite structure that will allow (001)oriented BaxSri_xTi03 films to grow epitaxially.
Based on the substrate lattice parameters, and their mismatches with
Bao.6Sr0.4Ti03 (See Table 3.4 and 3.5), the critical thicknesses values for films deposited
on different substrates were calculated based on the force balance model (Eq.2-18) and
the energy balance model (Eq. 2-19) discussed in Chapter 2; the results are given in Table
3.5 GdSc03 and DySc03 have small lattice mismatches with Bao.6Sr0.4Ti03 and the
calculated critical thickness is in the range of tens of nanometers to hundred of
nanometers (Table 3.5). It is possible to obtain coherently strained films on these
substrates. Therefore, it is possible to obtain films with dislocation densities as low as
those of the substrates. For microwave measurements to be made in the current research,
the film thickness needs to be larger than 50nm (Any thickness below this value causes a
numerical overflow.) Theoretically, it is possible to grow coherent films on substrates
56
such as SrTiCh, (Lao.i8Sro.82)(Alo.59Tao.4i)03 (commonly called LSAT), LaA103.
Experimentally, the critical thicknesses are so small that it is impossible to carry out
property measurements on those films based on the available techniques.
Table 3.4 Structural and dielectric parameters of the often-used substrate materials
Substrate
Space
Group
Lattice
Parameter
Relative
Permitivity
Dielectric Loss
Tand
(at 10GHz)
Thermal
Expansion
Coefficient a
(l<r6/K)
(A)
MgO
Pm3m
a = 4.210
9.8
<2xl0" 5
12.8
GdSc0 3
Prima
a = 5.755
b = 5.489
c = 7.936
3^= 3.968, 3.973
22
NA
a ? =6.7
a 22 = 11.5
a 3 3 =14.5
0^=10.9
DySc0 3
Prima
a = 5.720
b = 5.442
c = 7.890
a?c = 3.948, 3.945
21
NA
a n = 5.7
a 22 = 8.6
a33=ll
aav=8.4
SrTiOj
Pm3m
a = 3.905
300
5xl0" 4
9.4
LSAT
R3m
a = 3.868
22
2x10"4
10
NdGaOj
Prima
a = 5. 428
b = 5.493
c = 7.729
a^ = 3.862
23
7xl0" 3
a ? =11.9
a 22 = 6.6
a j3 =5.8
0^=7.8
LaA10 3
R3c
a = 3.793
25
3xlO"4@300K
11
Si
Diamond
a = 5.431
11.9
NA
2.5
Bao.6Sr04Ti03
Cubic(RT)
a = 3.959
10,000
(peak)
<0.01
10.5
Strain relaxation is the major source of dislocation generation for a mismatched
heterostructure. The bulk lattice parameter of our Bao.6Sr0.4Ti03 is about 3.956 A, from
the x-ray measurement of the PLD target. Candidate substrates-MgO, GdSc03, DySc03,
SrTi03, (Lao.i8Sro.82)(Alo.59Tao.4i)C>3, NdGaCh, and LaAlCV have different mismatches
with Bao.6Sr0.4TiC>3 as listed in Tables 3.4, and 3.5. For a completely relaxed film, the
57
average distances between misfit dislocations can be calculated by b/f, where b is the
magnitude of the Burger's vector,/is the mismatch. As listed in Table 3.5, this distance
is inversely proportional to the lattice mismatch, which means the higher is the mismatch,
the more misfit dislocations are needed to relax the strain. It is possible to grow a series
of films with different dislocation concentrations by varying the substrates and film
thicknesses.
Though Si is inexpensive and compatible with integrated circuit technologies,
films deposited directly on Si rarely grow epitaxially owing to large lattice mismatches;
instead, the films are usually poly crystalline or textured.18'19 Epitaxial films grown on Si
require buffer layers to bridge the lattice mismatch gap, which would unnecessarily
complicate the issues to be tackled in this work.20 Si will not be used as substrate in this
research. SrTi0 3 substrates have a dielectric constant of about 300; During dielectric
constant measurement, because the SrTi03 substrates contribute strongly to the dielectric
Table 3.5 Lattice and thermal mismatches of Ba06Sr0.4TiO3 on different substrates and the critical
thicknesses hc calculated based on force balance (FB) mode (Eq.2-18)
7
and energy balance
(EB) model (Eq.2-19),11 and the average distances between misfit dislocations for completely
relaxed film Dave.
Film
materials
Substrates
MgO
(110)GdScO3
(110)DyScO3
SrTi0 3
Bao.6Sr0.4Ti03
LSAT
(110)NdGaO3
LaA103
Misfit f Critical thickness
Dave(nm)** ATEC (10 6/k)
h
(nm)*
c
(%)
+6.3 1.08(FB),0.6(EB)
+0.2 100(FB), 31(EB)
-0.33 62.3(FB),12(EB)
-1.4 10.3(FB), 2.9(EB)
-2.3
5.3(FB),1.7(EB)
-2.5
4.7(FB),1.6(EB)
-4.3
2.1(FB),0.9(EB)
58
6.3
305
120
28.5
17.2
15.8
9.2
1.3
0.4
-3.1
-0.5
-1.5
-3.7
-0.5
response of the hereterstructure, it is difficult to extract the film dielectric constant from
the capacitance measured. Therefore, BST films grown on SrTi03 were not used in this
work for dielectric measurement, but they were used to understand the relaxation
mechanism to determine the microstructural relationship.
As mentioned in Chapter 2, strain can shift Curie temperature to higher
temperature values and can affect the dielectric constant.21 During film growth, films can
relax the homogeneous strains by the introduction of misfit dislocations. However, misfit
strains are difficult to relax completely for various reasons. For example, misfit
dislocations can be pinned by impurities or the formation of sessile junctions during the
moving into the interface.22 In addition, those strains introduced by thermal-expansion
coefficient differences at low temperature can be another form of residual strain, because
when the film is cooled down to a certain temperature after growth the dislocations
become immobile. In any analysis of dielectric properties, residual strain effects should
be considered.
3.1.3 Correlation between homogeneous strain and dielectric properties
Previous researches on strain effects have mainly focused on how strain affects
the Curie temperature.16'21'23 It is also believed that the compressive strain will suppress
the polarization of barium strontium titanate, which could lead to a decrease of the
dielectric constant and tunability. However, since coherently strained films have never
been achieved for barium strontium titanate solid solutions, the significance a role of
homogeneous strains play was still experimentally unknown and needs to be investigated.
SrTi03 films have, however, been grown on DyScC>3(110) substrates and, even with a
mismatch of 1.1%, a 50nm SrTiCh film was reported to be coherently strained.
59
Bao.6Sro.4TiC>3, which has a smaller mismatch of 0.33% with DyScC>3, should be
obtainable as a coherent film. Since the in-plane lattice parameter of DyScCh is smaller
than Bao.6Sr0.4Ti03, it will apply a compressive biaxial strain on Bao.6Sr0.4Ti03 films. The
in-plane lattice parameter of GdScO3(100) is slightly larger than that of Bao.6Sro.4Ti03,
Therefore, a coherent film with biaxial tensile strain is expected on the substrate.
Comparing coherently strained Bao.6Sro.4Ti03 films grown on these substrates would help
understand the role of tensile and compressive strains isolated from dislocation effect.
To understand, optimize, and control the film growth, AFM and reflection high
energy electron diffraction (RHEED) will be used to monitor the film growth mode. 4circle X-ray diffraction will be adopted to track the epitaxial relationship, lattice
parameters, and relaxation process. High resolution x-ray diffraction rocking curves will
be used to qualitatively estimate the crystalline quality. TEM will be used to determine
dislocation densities quantitatively.
3.2 Experimental techniques
3.2.1 Substrate treatments
Substrate with atomically flat surfaces and with clearly defined steps, achieved by
chemical etching and thermal annealing treatments, are believed to benefit the structural
perfection of the thin films grown upon them. In this research, the perovskite structure
substrate surface treatment of the perovskite substrates followed the method developed
by Kawasaki et al..24 Substrates were cleaned with acetone and methanol to remove the
grease and/or particles acquired during polishing, cutting, and handling. Substrates were
cleaned by five minutes in each solvent; more cycles were sometimes necessary
depending on the condition of the surface contamination. After the solvent cleaning,
60
substrates were ultrasonically cleaned in de-ionized (DI) water for 30 minutes; this is
believed to assist the formation of surface hydroxides which are supposed to decrease the
etching time and help to avoid the formation of deep trenches. After the water cleaning,
the substrates were subjected to acid etches for different time periods to investigate how
the surface morphology evolve with etch time. The acids used in this research included
buffered hydrofluoride (pH~4, semiconductor grade, Riedel-de Haen, AF875-125), a
hydrochloric acid (pH~l, Fisher chemicals, A144-212), and nitric acid (pH玪, Fisher
chemicals, A200-212) mixture in the ratio of 3:1 hydrocloric: nitric (pH=l), and a
hydrochloric acid/water mixture in a ratio of 1:1 (pH~l). After etching for a specific
duration of time, the samples were rinsed with water, methanol, and acetone, and then
dried with flowing clean air. Substrates were then loaded into a tube furnace for thermal
annealing. The annealing temperature ranged from 900-1100癈 to achieve ideal surface
morphologies. For the rock salt substrate MgO, the annealing was carried out in a box
furnace that was heated to 1450癈. Atomic force microscopy (AFM) and reflection high
energy electron diffraction (RHEED, introduced later) were used to characterize the
resultant morphologies.
3.2.2 Target preparation
The target used in this research was prepared using a conventional two step
ceramic sintering process.25 BaC03(99.995%, Aldrich) and SrTi03(99.995%, Aldrich)
powders were heat treated at 950癈 in tube furnace with flowing CO2 to remove
hydroxide and nitrate groups, and the TiC>2 (nanopowder, 99.99%, Aldrich) powder was
dried at 950癈 in air prior to use. After these heat treatments, these chemicals were
weighed immediately (after reaching room temperature) according to the cationic
61
stoichiometry of Bao.6Sro.4Ti03. The weighed powders were mixed with zirconia beads
and DI water in a plastic bottle. The mixing was done using a ball milling machine for 12
hours using a rotation speed of 3000 rotations per minute. After mixing, the paste was
dried, and pressed into pellets (using a uniaxial press) and then heated treated for 12
hours in ambient air at 1200癈 in a box furnace. After x-ray proved that the reaction was
complete, the pellets were ground into powders, and passed through a No. 40 (particle
size: 0.42 mm) sieve and was ball milled as done before for 48 hours. After the ball
milling, the paste was dried, passed through a No. 100 (Size ~ 0.149 mm) sieve, mixed
with organic binders (PVA at 2 wt%), and then pressed into pellets using uniaxial press.
The pellets were dried in furnace at 200癈 for 2 hours and then heated up to 1400癈 at
5癈/min and sintered for 12 hours at that temperature. The sintered target was cooled to
room temperature by 5癈/min, polished, and mounted onto a PLD target holder. Before
each deposition, the target was cleaned by ablating the surface at deposition conditions
for 10,000 pulses.
3.2.3 Growth techniques
Pulsed Laser Deposition (PLD) is the most commonly used technique for
preparation of tunable dielectric thin films owing to its low cost, simplicity, and
capability of maintaining stoichiometry.26 It consists of a target on a holder and a
substrate on a holder and heater housed in a vacuum chamber. A high power laser is
focused, using a set of optical components, onto the target surface causing ablated
material to form a forward-directed plume that deposits material onto the substrate
(Fig.3.1).26 Two PLD chambers were used in this research, one was a conventional PLD
system that has a maximum deposition oxygen pressure of 300mTorr while the other one
62
was a so-called Laser-MBE which is a hybrid system with both PLD and MBE system
that operated at a lower oxygen pressure (to allow for in-situ monitoring) and has a
maximum deposition oxygen pressure of lmTorr. For film growth in the Laser MBE
system, depositions were only carried out simply in the mode of low pressure without insitu monitoring. Another difference between the two chambers (systems) is that the
substrate-target distance of the Laser MBE system was always maintained at 75 mm
while that distance in the conventional PLD was maintained 60 mm. Moreover, substrates
were heated by a radiation heating by SiC radiating heater in the Laser MBE, while
substrate in the standard PLD were heated using a direct thermal contact with a resistive
heating element.
The Laser MBE system was equipped with a reflection high energy electron
diffraction (RHEED) system that allows for substrate surface characterizations and exsitu film growth mode study. RHEED characterization will be introduced later in �2.7.
The RHEED can operate from 15 kV to 30 kV for the accelerating voltage. All the
diffraction patterns collected in this research were collected when the acceleration
voltage was at 15 kV. The substrate holder can be rotated to a random position during the
imaging in search of the desired azimuth interested.
JQ
"'Heater
Substrate
RHEED/d
Screen | L
RHEED
?_Gun
Raster
Minor v* 4
Jvloleculai
Beam
Laser Beam
ffusion
Cells
Gas Injector
Fig. 3.1 Schematic of the setup of a pulsed laser deposition system.
63
Generally, film nucleation and growth can be categorized into three conventional
modes:27'28 a) three dimensional (3-D) island growth, b) continuous two dimensional fullmonolayer growth, and c) initial two dimensional full-monolayer growth followed by 3-D
island growth. However, after some time the 3D island growth can lead to coalescence
and even a conversion to the 2D mode.40 The mode in which the film grows depends on
the thermodynamic energy balance including contributions from the substrate and film
surface energies and on their interfacial energies.28 Kinetically, to achieve layer-by-layer
mode, growth conditions, such as the substrate temperature, laser energy, pulse rate, and
partial pressure of oxygen should be controlled. These parameters can influence the
mobility of adatoms or the super saturation rate, and hence influence the growth mode.26
Growth conditions will be optimized to achieve 2D growth of the Bao.6Sro.4Ti03 on the
selected substrates.
The substrate treatment processes for different substrates have been introduced in
�2.1, and the target preparation process has been introduced in �2.2. The laser used in
this research was a KrF laser (1=248 nm, pulse duration ~20 ns), the laser frequency was
varied over the range of 1-10 Hz. The laser energy used in this research was always
calibrated to be 2 J/cm2, Most of the BST films were deposited at a 1 Hz laser repetition
rate, except if otherwise pointed out. All films deposited below 1 mTorr were grown in
the Laser MBE chamber and those films deposited at lmTorr and above were grown in
the standard PLD chamber. Ultra high pure (UHP) oxygen gases (99.999%) were
introduced into the chamber by leakage valves to dynamically control oxygen pressure
during film growth. The substrate temperature was increased
to the deposition
temperature at a rate of 15 癈/min, most of the depositions were carried out with the
64
substrate temperature at 850癈, except when otherwise pointed out. After depositions
were done, the turbo pump valve was closed and the chamber was filled with UHP
oxygen to 400 Torr; the films was annealed at the deposition temperature for 5 minutes
before cooling down. The cooling rate was 20 癈/min (until inertial cooling took over).
Atomic force microscopy (AFM) and reflection high energy electron diffraction
(RHEED) were used to monitor the growth mode.
3.2.4 X-ray diffraction and reflectivity
A Philips X'pert x-ray diffractometer was used for most of the structural
characterizations of the thin films. A tube with a Cu anode is used to generate a beam of
x-rays, which contains photons with different frequencies. After passing through a series
of monochromators and filters, the x-ray beam becomes parallel and monochromatic with
wavelength A,=1.5418A (Cu Kxxi), or with Kct2 when the monochromators were not used.
When the beam hits a sample, it is diffracted and the diffracted beam obeys the Braggs'
law, or 2dSin6=nX, where d is the inter-plane spacing of the corresponding diffracting
planes, 6 is the incident angle of the x-ray beam, and n is an integer. A detector detects
the intensities of the diffracted x-rays at a known angle and this information is used to
infer structural information of the sample. Different scan modes can be used to determine
different crystallographic information; these modes are accessed by adjusting optics and
scanning parameters. The mostly commonly used modes, described with respect to the
optical train configurations, are lens mode, mirror mode, and high resolution mode.
The X'pert diffractometer is al so-called four-circle x-ray system, the four-circles
refers to the four degrees of freedom over which the sample can rotate: Omega, 2-Theta,
Phi, and Psi. In the lens mode, the intensity is very high and the resolution is low. The
65
most commonly used scan mode (in the lens mode) is the 0-20 scan. In this scan mode,
the x-ray tube is stationary, the sample moves by the angle 6 and the detector
simultaneously moves by the angle of 20. The output of the scan is displayed as a plot of
the intensity versus 20. Peaks show up in the plot when planes satisfy the Bragg
condition. The position of the peaks can be used to calculate the lattice parameters
(through the measurement of the interplanar spacings). Phi scans and Phi vs. Psi scans
(pole figure) are also used in thin film characterization (Where 26 and a> are fixed while
the other angles are scanned through) can to be used determine the epitaxial relationship
and in-plane rotation of grains.29
Another important scan mode is the Omega-Theta (co - 0) scan, also called a
rocking curve. In this scan, the detector is fixed at a 26 position while the sample is
rocked around a 0 (omega) position. Strains around dislocations, as well as any other
mosaicity, can cause a broadening of the diffraction peaks in rocking curves. When
registered in the lens optical mode, the rocking curve peaks includes a wide significant
broadening from machine itself, which can mask the structural information of the
material. High-resolution rocking curves which have very low instrumental broadenings
(12 arcseconds for our highest resolution optics) and can be used in an approximate for
quantitative crystal quality characterization.
The combination of the 6-26 scans and rocking curve scans gives information on
the orientation relationship between sets of lattice planes with different d values. This
combination scanning mode is called reciprocal space mapping (RSM). Reciprocal space
mapping of the asymmetric reflections that have non-zero in-plane and out-plane indexes
can provide information on strain relaxation.
66
When the mirror optical mode is used, a x-ray mirror is used to convert the x-ray
highly parallel, such an reflected x-ray beam can be used at low incident angles to detect
interference reflected from the film surface andfilm-substrateinterface. The interference
produces oscillations in the detected intensity vs. angle at low angles. This x-ray
reflectivity (XRR) spectrum can be used to determine the film interface roughness and
film thickness. This was used for growth rate calibration and thickness measurements.
During Bao.6Sro.4Ti03 film growth, an MgO substrate was often placed near by the
samples-of-interest at the same time as a sample on which XRR could be carried out. For
films below 60nm, this Bao.6Sro.4TiC>3/MgO sample was used for XRR characterization to
determine the thickness of the sample and the sample-of-interest. At the same time, the
deposition rate at that specific condition was calculated based on the number of laser
pulses that were used.
3.2.5 Transmission electron microscopy (TEM)
TEM is considered the most effective instrument to study defects in great details
with regard to spatial resolution and to crystallography. In TEM, an electron beam is
passed through a series of condenser lenses and is focused on a sample, where it is
diffracted. Both the atoms in the lattice and any defects present in the path of the electron
beam will modulate the amplitude and the phase of the primary and diffracted beams.
After going through a series of objective lenses and apertures, either reciprocal-space
diffraction patterns or real-space images can be obtained30
An image formed using the primary electron beam is called a bright field image.
An image that is formed using a diffracted beam is called a dark field image. In a dark
field image, only those planes that meet the Bragg condition can show bright contrast.
67
When there is only one strong diffraction beam shows up on the diffraction pattern, the
dark field image formed using this strong diffracted beam (reflection) is called Two
Beam Dark Field Image (TBDFI).5"'57 TBDFIs can be used to identify dislocation
characters. The Burger's vector of an edge dislocation can be determined by selecting
two reflections under which the dislocations vanish in the TBDFIs using the g籦=0
criterion, where g is the reflection vector, and b is the Burger's vector.31 Of course, when
the dislocation density is being counted, this needs to be considered to avoid the
vanishing of the dislocations interested. In characterizing thin films, one can view the
sample from the film top (plan-view) and from the side (cross-sectional) to collect
complete set of information about the character, distribution, and concentration of
dislocations.
Because the energy of the electron beam is somewhere between 100 - 400 keV
and because the beam must pass through the entire specimen, the specimen thicknesses
must be between 10 nm to 1 um depending on the interaction between the material and
electron beam. Samples were normally prepared by cutting, mechanical polishing, and
low angle ion milling to achieve a perforation; an electron transparent area then exist at
the edge of the perforation. Cross-sectional TEM samples were prepared by first cutting
the samples into 3 mm x 400 um bars. Two bars were then glued with film side facing
each other using gl epoxy. Polishing was completed using 30 um, 9 um, and 1 um
diamond films on both cross-sectional sides until the thickness was 20 urn. Then, the
sample was glued onto a copper grid. The sample was placed in a PIPS and ion milled
from both sides until perforation occurred at the interface. The ion milling energy used
ranged from 3.5 keV to 4.5 keV, with milling angles 5-8�. Planview TEM samples were
68
also prepared by direct thinning from the substrate side to a thickness of 20 um, which
was followed by ion milling till a perforation was obtained from the substrate side while
the film side was protected by removable wax. Then the samples were then cleaned in
acetone and methanol. Plasma cleaning was used to clean further the samples before
TEM observation. A Joel 2000EX was employed for conventional TEM analysis. A
Tecnai F20 was used for high resolution electron microscopy (HRTEM) analysis. Both
microscopes were operated with the acceleration voltage at 200 kV.
3.2.6 Atomic force microscopy (AFM)32,33
AFM is a very sensitive tool that can be used to detect surface morphology with a
high resolution in characterizing in the height profile. It consists of a microscale
cantilever that has a sharp tip to detect the specimen surfaces. When the sharp tip is close
enough to the sample surface, the atomic forces between the detector tip and the
specimen surface will cause deflection of the cantilever following Hooke's law. A
deflection can be measured using a piezoelectric strain gauge or laser diode detector. A
feedback mechanism is always used to maintain the distance between the tip and the
sample surface (using precise piezoelectric actuators).
The AFM can operate in different modes; the two most common modes are
contact mode and tapping mode. In contact mode, the force between the tip and the
surface is kept constant during scanning by maintaining a constant deflection. The tip
deflection is used as a feedback signal. Because of high noise and drift effects, low
stiffness cantilevers are used to boost the deflection signal. Contact mode suffers from tip
damages when it crashes into the surface features, sample surface damages by tip
dragging, and tip abrasion artifacts being introduced into the image. In tapping mode, the
69
cantilever is in an oscillatory fashion close to the resonance frequency by a piezoelectric
element mounted in the AFM tip holder. The amplitude of the oscillation decreases as the
tip gets closer to the sample surface. A piezoelectric actuator is used to control the height
of the cantilever to maintain the cantilever oscillation amplitude as the cantilever is
scanning the sample surface. This height change can be recorded and converted into
image of a height profile. Tapping mode can avoid the surface damage of the sample and
reduce the tip damage induced artifacts in the overall image, but it is slightly more
difficult in of an operational mode.
In this research, a Veeco model Dimension� 3100 AFM was used. All the images
were collected using tapping mode. The tapping tip used was made by Veeco, the Model
number is RTESP. The tip was an un-coated 1-10 Ohm-cm phosphorous doped Si tip.
The resonant oscillation frequency was between 267-348 kHz. The amplitudes used for
image collection were in the range of 1.3-1.9 V. The images were collected and
processed using software Nanoscope V613R1.
3.2.7 Reflection high energy electron diffraction (RHEED)34,35'40
RHEED utilizes a high energy electron beam with a low incident angle (1-5�) to
characterize the surface structures of crystals. The reflected electrons can only come from
the outermost (last unit cell) surface of the sample and are diffracted by the in-plane
surface periodicity. The diffracted beams interfere constructively at specific angles and
form patterns on a photoluminescent detector screen.
The diffraction pattern can be analyzed using an understanding of the geometry of
Ewald's spheres. In Figure 3.2, schematics are given of idealized RHEED patterns from
70
typical surfaces. First, an atomically flat, highly crystalline surface can be considered as
an ideal 2-D plane. The reciprocal lattice of a crystal surface is a series of infinitely long
thin rods extending perpendicular to the sample's surface. The image can be described as
a set of spots on a semi-circle and can be explained as the intersection in reciprocal space
of 1-dimensional rods intersecting with the Ewald's sphere (Fig. 3.2A). The surface
construction can be calculated quantitatively based on the electron energy, the spacing
between the spots, and the distance from sample surface to the screen. When the surface
step density increases, the in-plane coherency decreases; this broadens the thickness of
the 1-D reciprocal rods. The intersection of this rod with Eward's sphere changes from
spots to streaks and the corresponding RHEED image now consists of vertical (in the
partem) streaks instead of spots (Fig.3.2B). In addition, if the surface contains 3dimensional island-like features, the reciprocal lattice is no longer 1-D rods, the RHEED
pattern will be represented by a 2-dimensional array of points, similar to what is observed
in TEM (Fig. 3.2C). Finally, if the diffraction sample is polycrystalline, the image will be
composed of concentric circles analogous to the observations in both TEM and XRD of
polycrystalline samples. The diffraction principles are the same: the random orientation
of sample crystallites leaves only the 20 Bragg angle as a distinguishing feature of the
crystal, and so only the concentric circles representing allowed Bragg reflections are
observed. Note that, while in the figure these cases are shown to be distinct, in practice
images often exhibit characteristics of transition of two of these ideal patterns.
71
Fig. 3.2 Ideal RHEED images for (A) an atomically flat substrate surface with low step density
(B) flat surface with high step density (C) Very rough surface, island-like 3D growth mode
(transmission pattern) (D) polycrystalline film. This image was reproduced from Patrick Fisher's
thesis.
The RHEED used in this research was manufactured by Staib Instrument. A
differential pump is integrated with the Laser-MBE chamber, which allows the RHEED
to operate in an oxygen pressure of 1 mTorr. The accelerating voltage can operate in the
range of 15 kV to 30 kV. The detecting system including the phosphorous screen, CCD
camera, and image recording and processing software were manufactured from K-space
Associates. Inc.
3.2.8 Microwave frequency electrical characterizations36
There are two common approaches used to measure dielectric properties for
which electrodes are needed: the parallel plate capacitor approach and the coplanar
capacitor approach. While parallel plate structures can give very large capacitances, they
sometimes suffer from significant values of leakage current. Also, because the bottom
72
electrode always has a different lattice parameter and crystalline structure from that of the
dielectric film, growth of the dielectric on the base electrode increases the defect density
in the functional layer. Another concern is that the capacitance is so high that, at
microwave frequencies, the impedance will be too small to measure. Co-planar capacitors
are, therefore, of interest for dielectric property measurement at microwave frequencies.
'
2%
il
2g
J
'
T'"
2s,
?*
,
..."
n "TV"^
#
Zsi
?jr
U
J'
w
2%
2g
.q ? Id a d b ? o:r: t
F/g. 3.3 Tfte schematics of the planview (a) and the cross-section (b) of an 8 digit (n=8)
I DC. Reproduced from Reference 37. L is the finger length, 2Sg is the finger width, 2g is the gap
width, h 1 and h2 refer to the thickness of the overall thickness and the thickness of the measured
thin film, t is the thickness of the electrodes, and sri and er2 are the two dielectric constant of
substrate and film respectively.
To avoid the complexity introducing by using the bottom electrode, interdigital
capacitor structures were used to measure dielectric properties of Bao.6Sro.4Ti03 thin films
73
in this research. The geometry of such structures is shown in Fig. 3.3. To realize
measurable capacitance values, the separation between the co-planar plates, g, must be
very small (on the order of 10 fxm or less) and the area of the plates must be reasonably
large. Owing to the complexity of the electrode geometry, the electromagnetic wave
distribution is very complex. Models have been developed (or based on those proposed)
by Gevorgian et al.36"38 to calculate thin film properties from the reflection parameter Si i
measured using the interdigitated capacitor structures. The detailed derivations of these
models were discussed in the literatures.36"38
Fig. 3.4 The HP8510 Network Analyzer (a) and the Cascade Microtech 11000 Probe Station (b)
used in this research to measure the dielectric properties at microwave frequency.
Interdigitated capacitors (IDC) were fabricated on the Bao.6Sro.4TiC>3 films using a
lift-off lithography process.36 The electrodes consisted of three metal layers; they were
consisted of several nanometers of Ti as an adhesion layer, 1 micron of Ag as the main
conductor, and 50 nm of Au as a capping layer to protect from Ag oxidation.
The IDC configuration used for microwave frequency measurements consisted of
16 fingers of dimensions 80x10x8 um, where the finger length was 80 fj.m, the finger
width was 10 urn, and the finger gap was 8 urn. The fingers were aligned parallel to
Bao.6Sro.4TiC>3 in-plane <100> direction. A Cascade probe station (Fig. 3.4b) was used to
74
make the measurements in the temperature range of 213 K to 473 K, with T controlled by
Temptronic TP3000A. Flowing dry nitrogen was used to prevent condensation during
temperature measurements below 300 K. The vector network analyzer HP8510 (Fig.
3.4a) measured the Sll parameter from the IDC structure in the frequency range 1-20
GHz. Before sample measurement, open and short circuit measurements were used to
calibrate the system. The parallel resistor-capacitor models were used to determine the
microwave capacitance and device loss, and the dielectric constant was calculated using a
modified conformal-mapping partial-capacitance method (which incorporated the
dimension of the capacitors).16'37'39
References
1
T. Suzuki, Y. Nishi, and M. Fujimoto, Philosophical Magazine A 79, 2461-2483
(1999).
2
H. P. Sun, W. Tian, X. Q. Pan, J. H. Haeni, and D. G. Schlom, Applied Physics
Letters 84, 3298-3300 (2004).
3
H. P. Sun, X. Q. Pan, J. H. Haeni, and D. G. Schlom, Applied Physics Letters 85,
1967-1969 (2004).
4
P. Besson, J. P. Poirier, and G. D. Price, Phys Chem Minerals 23,337-344 (1996).
5
Z. Wang, S.-i. Karato, and K. Dujino, Physics of the Earth and Planetary Interiors
79,299-312(1993).
6
C. J. Lu, L. A. Bendersky, K. Chang, and I. Takeuchi, Journal of Applied Physics
93,512-521(2003).
7
J. W. Matthews and A. E. Blakeslee, Journal of Crystal Growth 27, 118-125
(1974).
75
F. R. Nabarro, Theory of Crystal Dislocations (Dover Publications, New York
1987).
F. R. N. Nabarro, Dislocations in solids (North-Holland Pub. Co., New York
1979).
D. Hull and D. J. Bacon, Introduction to Dislocations (BPC Wheaton Ltd, 1984).
R. People and J. C. Bean, Applied Physics Letters 47,322-324 (1985).
A.K. Tagantsev, K.F. Astafiev, J. Venkatesh and N. Setter, Journal of
Electroceramics 11, 5-66 (2003).
P. Bao, T. J. Jackson, X. Wang, and M. J. Lancaster, J. Phys. D: Appl. Phys. 41
063001 (2008).
E. Koppensteiner, A. A. Schuh, A. G. Bauer, A. V. Holy, A. G. P. Watson, and A.
E. A. Fitzgerald, Journal of Physics D: Applied Physics 28 Al 14-A119 (1995).
S. Danis, V. Holy, Z. Zhong, G. Bauer, and O. Ambacher, Applied Physics
Letters 85, 3065-3067 (2004).
J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W.
Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q.
Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, Nature 430, 758-761 (2004).
K. J. Choi, M. Biegalski, Y. L. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche,
Y. B. Chen, X. Q. Pan, V. Gopalan, L. Q. Chen, D. G. Schlom, and C. B. Eom,
Science 306,1005-1009 (2004).
G. Bhakdisongkhram, Y. Yamashita, T. Nishida, and T. Shiosaki, Japanese
Journal of Applied Physics 44, 7098-7102 (2005).
76
T. L. Chen, X. M. Li, W. B. Wu, S. D. Yao, and K. Wang, Journal of Crystal
Growth 285, 1-5(2005).
S.Jun and J. Lee, Ferroelectrics, 271 21-26 (2002).
D. G. Schlom, Long-Qing Chen, C.-B. Eom, K. M. Rabe, S. K. Streiffer, and J.M. Triscone, Annu. Rev. Mater. Res. 37,589-626 (2007).
A. E. Romanov, W. Pompe, S. Mathis, G. E. Beltz, and J. S. Speck, Journal of
Applied Physics 85, 182-192 (1999).
L. Benguigui, Physica Status Solidi (a) 46, 337-342 (1978).
M. Kawasaki, K. Takahashi, T. Maeda, R. Tsuchiya, M. Shinohara, O. Ishiyama,
T. Yonezawa, M. Yoshimoto, and H. Koinuma, Science 266,1540-1542 (1994).
J. Zhai, X. Yao, X. Cheng, L. Zhang, and H. Chen, Materials Science and
Engineering B 94,164-169 (2002).
D. B. Chrisey, Pulsed laser deposition of thin films (John Wiley & Sons, Inc. ,
1994).
L. B. Freund, Thin film materials : stress, defect formation, and surface evolution
(Cambridge University Press, New York 2003).
D. L. Smith, Thin-film deposition : principles and practice (McGraw-Hill, New
York 1995).
W. K. Simon, E. K. Akdogan, A. Safari, and J. A. Bellotti, Applied Physics
Letters 87,082906-3 (2005).
M. De Graef, Introduction to conventional transmission electron microscopy
(Cambridge University Press, New York 2003).
D. B. Williams and C.B. Carter, Transmission Electron Microscopy, Vol. IV
77
(Springer New York, 2004).
G. Kaupp, Atomic force microscopy, scanning nearfleld optical microscopy and
nanoscratching : application to rough and natural surfaces (Springer-Verlag,
Berlin, 2006).
F. J. Giessibl, Reviews of Modern Physics 75,949 (2003).
A. Ichimiya, Reflection high-energy electron diffraction (Cambridge University
Press, New York 2004).
P. Fisher, Thesis, Carnegie Mellon University, 2007.
L. F. Chen and C. K.Ong, Microwave Electronics: measurement and material
characterization (John Wiley & Sons, Ltd., 2004).
S. S. Gevorgian, T. Martinsson, P. L. J. Linner, and E. L. Kollberg, IEEE
Transactions on Microwave Theory and Techniques 44, 896-904 (1996).
S. Gevorgian, C. E., S. Rudner, L. D. Wernlund, X. Wang, and U. Helmersson,
IEE Proceedings-Microwave and Antenna Propagation 143, 397-401 (1996).
W. Chang, J. S. Horwitz, A. C. Carter, J. M. Pond, S. W. Kirchoefer, C. M.
Gilmore, and D. B. Chrisey, Applied Physics Letters 74, 1033-1035 (1999).
O. Maksimov, V. D. Heydemann, P. Fisher, M. Skowronski, P. A Salvador, Applied
Physics Letter 89,262903 (2006)
78
Chapter 4
Film Growth and Structure Characterization
This chapter will discuss thin film deposition and the development of
microstructural features, especially focusing on how dislocations, which are hypothesized
to negatively impact the dielectric properties. In particular, section 4.1 will discuss the
pre-growth surface engineering processes for all the substrates used in this research,
processes that are essential in developing two-dimensional growth modes and in
controlling the mechanisms of dislocation nucleation. AFM and RHEED were used to
characterize the substrate surfaces treated by chemical etching and thermal annealing. In
section 4.2, the growth mode of the films grown on different substrates will be discussed
based on results of ex-situ AFM and RHEED investigations used to characterize the
surface morphology at different stages of the film growth. Based on these observations,
processing conditions were identified where two dimensional growth was observed;
again, this allowed us to ensure growth and microstructural evolution of the different
films followed similar paths, enabling direct comparisons between films grown on
different substrates. Section 4.3 will present the epitaxial relationship between films and
substrates determined by 4-circle X-ray diffraction. Section 4.4 will focus on relaxation
mechanisms of epitaxial films grown in a two-dimensional fashion on substrates of
different orientations; the discussion focuses on resolving the conflicting data and
proposed mechanisms reported in the literature for similar films. It is important to
emphasize that one of the major outcomes of this dissertation is that inhomogeneous
strain fields associated with threading dislocations can be considered a major player in
dielectric property degradation of ferroelectric thin films. In principle by understanding
79
the dislocation formation / propagation mechanisms, one can engineer processing
methods to minimize such defects. Section 4.5 will present the in-plane and out-of-plane
lattice parameter measurement for all films grown under controlled conditions, whose
dielectric properties will later be correlated with the dislocation density and amount of
relaxation. In section 4.6, film quality, as determined by x-ray rocking curve widths and
total dislocation density, will be presented using results from both high resolution X-ray
and TEM. Section 4.7 will summarize the main conclusions from this chapter.
4.1 Substrate processing
An atomically flat surface with clearly defined steps for substrates, achieved by
chemical and thermal treatments, is believed to benefit the structural perfection of the
thin films grown upon such surfaces. For example, perovskite SrTi03 is often used as the
substrate for YBa2Cu307-s thin films (among many other perovskite films).1 It has been
found that the substrate surface engineering process can significantly affect the film
structural quality.1 SrTi03 substrates subjected to chemical and thermal treatments that
produced surfaces that were atomically flat with T1O2 terminations improved not only the
YBa2Cu307-8 film structural quality but also its electric properties.1 Since then much
research has focused on SrTiC>3 substrate surface chemistry and atomic reconstruction
because of its popularity as a substrate for oxide growth.2 In order to control the film
quality and to reduce the complexity of interfaces, all the substrates used in this research
have been investigated to optimize the conditions for the growth of (Ba, Sr)Ti03 thin
films. Some of the literature approaches suffer from unsatisfactory reproducibility either
owing to quality variation from different vendors or owing to the variation of the
chemical and thermal conditions of different labs. In current research, all factors that
80
affect crystal quality, such as vendors, acid pH values, thermal annealing temperature,
and annealing time-length, were carefully controlled.
Commercial
single
crystal
substrates
of
MgO,
NdGaCh,
SrTiCh,
(Lao.i8Sro.82)(Alo.s9Tao.4i)03 (LSAT), and LaA103 were obtained from MTI Corporation
(Richmond, CA, USA); and GdScC>3 and DyScC>3 were obtained from the Crystech
GmbH (Berlin, Germany).3'4 Some SrTi03 crystals were also obtained from Crystal
GmbH (Berlin, Germany) to compare processes for crystals from different vendors. The
surfaces of all these commercial crystals were within 0.02- 0.08� of specific low index
crystal planes? such as (100), (110), and (111)? and were polished by the vendor using
chemical-mechanical processes where the final polish used an alkaline solution
containing colloidal silica particles.5 The surface root mean square (rms) roughness
values of all the as-received substrates were � 0.1 nm and exhibited no obvious
morphological features.
4.1.1 SrTiO3(100) substrates
For SrTiC>3 substrates, different processing conditions and substrates from
different vendors were compared. In this discussion, we first focus on the SrTi03
substrates obtained from Crystal GmbH. After ultrasonic cleaning with acetone and
methanol for 5 minutes each, then all substrates were cleaned ultrasonically in DI water
for 30 minutes. Next, the substrates were etched for various times in acidic solutions
(whose detailed preparation is described in �2.1). For SrTiCh substrates obtained from
Crystal GmbH., both buffered hydrofluoric (BHF) (pH~4) solutions and HC1:HN03=3:1
solutions (pH~l) were explored as an etch.
81
Following Kawasaki's approach using BHF,1 the deionized (DI) water treated
substrates were etched in BHF for 10 minutes and then annealed at 1000癈 for 2 hours in
air. Square etch pits were observed with AFM (Fig. 4.1). The etch pits formed deep
trenches along the directions parallel to the sample edges, i.e., the <100> directions. The
trenches and pits were so deep that the surface roughness values after treatment were
unacceptably high (rms=Snm), and were not appropriate for thin film growth. With a
decrease in the etch time, the trenches and pits became fewer and shallower (as observed
with AFM). When the etch time was 30 seconds, the surfaces exhibited a rms roughness
of 0.3 nm and only a few pits. Clear steps were observed on such substrates; however, all
SrTiC>3(100) substrates from Crystal GmbH exhibited twisted steps, which indicated that
a high density of low-angle grain boundaries existed or uneven polishing took place.
Changes of miscut angle locally can change the local surface step spacing, and this
appears as step twisting. Similar phenomena were observed on Crystal GmbH samples
treated with an HC1:HN03=3:1 etch for different time periods (5, 4, and 2 minutes) after
ultrasonic cleaning in DI water for 30 minutes, and then dried and annealed at 1000癈 for
2 hours in air (Fig. 4.2a-c) . Though surface steps were observed, they were not straight
and had varying terrace widths.
SrTiO3(100) substrate wafers from MTI were also investigated. They were first
cleaned using acetone and methanol, then ultrasonically cleaned in DI water for 30
minutes. Substrates were then etched in a BHF (pH ~ 4) solution for 40 seconds, rinsed
with DI water, dried, and then subjected to a 1000癈 anneal for 2 hours in air. AFM
images of such surfaces are shown in Fig. 4.3 (a and b are for two different
magnifications of the same sample, while c is for a similar sample after being exposed to
82
laboratory air for 1 month); after treatment the surfaces are smooth and have fairly
straight surface steps of similar terrace widths. The steps were both single-unit-cell
(a)
* ?
20nm
I.MrlftM
*tjm
go
BHF 10min
CO
10nm
l.^h!
t9\im
(c)
0.0
5nm
l:HrlgM
BHF 3min
10.0|M�
BHF 30sec
Fig. 4.1 AFM characterized surface morphology of SrTiO3(100) substrate from Crystal after
being etched for different length of time: 10 min (a), 3 min (b), and 30 sec (c) in BHF followed by
annealing at 1000癈 for 2 hours. Note the differing scales.
(a)
-
??
?
2nm
- ? -
- ?
HCLHNOj 5min
- m
0�)
-?
3nm
-
HCI:HN0 3 4min
- m
(c)
-
--
?
3nm
- -ii
HCI:HN0 3 2min
Fig. 4.2 AFM images of SrTiO3(100) substrate from obtained from Crystal after first being etched
for different lengths of time (a: 5 min, b: 4 min, and c: 2 min) in a HCI:HN03=3:1 solution and then
being annealed at 1000癈 for 2 hours. Note the different height scales.
and half-unit-cell high, indicating two surface terminations. The surface rms roughness
value was ~ 0.2 nm. After the sample had been exposed to laboratory air for one month,
these clear steps disappeared (Fig 4.3c), which suggested that the treated substrate surface
deteriorated over time. Therefore, film growth was carried out only on substrates that
83
were freshly treated. RHEED patterns collected from such as-treated SrTiO3(100)
substrates (using 15 kV electron energy along the [110] and [100] azimuths) were best
described as spots on semicircles which further supports the idea that that the surfaces
were atomically flat. Moreover, The RHEED patterns indicate that the surface had a 1 x 1
periodicity relative to the bulk lattices.
(a)
B*
1nm
l;ttrlfltt
SAjUft
BHF 40sec
t o
0>)
V.tlti+t
1nm
i.Bps
*0
(�)
l:tki玀
3nm
1.珅f*
After a month
BH F 40sec
Fig. 4.3 AFM images of SrTiO3(100) substrates obtained from M77� after being etched for 40sec
in BHF (followed by an anneal at 1000癈 for 2 hours in air); (a) and (b) are images at two different
magnifications taken on the same sample imaged immediately after treatment, while (c) is an
image taken from the same sample after it was exposed to air for a month.
(a)
(b)
Fig. 4.4 RHEED patterns from a SrTi03 (100) surface after undergoing a surface treatment similar
to that used on the samples whose AFM images are shown in Fig. 4.3. (a) is the pattern along the
[110] azimuth and (b) is the pattern along the [100] azimuth.
84
4.1.2 Other perovskite (100)c substrates
Several other perovskite ABO3 substrates having the equivalent surface
orientation to the cubic (100) face (whose structure has alternating layers of AO and BO2
in this direction), including LaAlO3(100)c, NdGaO3(110), GdScO3(110), and
DyScO3(110) (the latter three are indexed in their orthorhombic settings), were treated
following the same procedures as used for SrTiO3(100). After ultrasonic cleaning with
acetone and methanol for 5 minutes each, the substrates were cleaned ultrasonically in DI
water for 30 minutes and etched in BHF (pH � 4), rinsed and dried, and annealed at
1000癈 in air for two hours.
(a)
0-0
1: Height
2nm
�
f.0 pm
0,0
1:MolnM
3nm
10,0 um
Fig. 4.5 AFM images of LaAIO3(100) (a) and NdGa03(110) (b) surfaces after a BHF etch / high
temperature anneal surface treatment. Note the different scales.
AFM images of the treated LaAlC>3(100) and NdGaO3(110) are shown in Fig.
4.5a, b, and those of GdScO3(110) and DyScO3(110) are shown in Fig. 4.6a, b. The
treated surfaces demonstrated clear single-unit-cell and half-unit-cell height steps. These
treated substrates all have rms roughness values below 0.2 nm. For LaAlC>3(100), the
steps are fairly uniform in width and slightly wavy in shape, though they run along an
average parallel direction. For NdGaC>3(110), the steps are also uniform in dimensions
and run along an average parallel direction, but the edges are very wavy and steps contain
holes. Also, the terrace widths on the NdGaC>3 are much wider than those on
85
LaAlO3(100) (note the different scales in the images) Both surfaces are useful for growth
of high quality films.
The RHEED pattern along the [110] azimuth of the treated GdSc03(l 10) substrate
is shown in Figure 4.7a. The pattern can be best described as sharp diffraction spots lying
on a semicircle with Kikuchi lines in the background, consistent with an atomically flat
surface with wide terraces as observed in the AFM topography. The pattern in Fig. 4.7b
was obtained along the [001] azimuth. Both surfaces exhibited diffraction spots that were
consistent with an unreconstructed ( l x l ) surface of an orthorhombic crystal having
bulk-like surface periodicities. The same phenomena were observed on DyScC>3(l 10) and
NdGa03(l 10) substrates.
(a)
2nm
(b)
5nm
Fig. 4.6 1 pm * 1 pm area AFM images of GdScO3(110) (a) and DyScO3(110) (b) surfaces after
surface treatment after a BHF etch / high temperature anneal surface treatment. Note the
different height scales.
Fig. 4.7 (a) and (b) are the RHEED patterns of treated GdSc03 from the azimuth of [110] and
[001].
86
4.1.3 Treatment of (Lao.i8Sro.82)(Alo.59Tao.4i)C>3(100) substrates
Surface treatment of (Lao.i8Sro.82)(Alo.59Tao.4i)C>3(100) proved to be more
complicated. The procedure used to treat SrTiC>3(100) (� 4.1.1) was first employed, but
no clearly defined steps were observed with AFM. Despite the previously published
reports that argued such a procedure could be successful,6 similar experiments carried out
in this work could not replicate the stepped surface morphology. Instead, a HC1:H20 =1:1
solution (�3.1) was used and was successful. After the (Lao.i8Sro.82)(Alo.59Tao.4i)03(100)
substrate was cleaned with acetone and methanol for 5 minutes each, dried, and
ultrasonically clean for 30 minutes in DI water, (Lao.isSro 82XAI0 59Tao4i)03 was etched in
a HCkFfcO =1:1 solution for 3 minutes. After it was rinsed and dried, the resulting
surface morphology is shown in Fig. 4.8a, where a smooth surface having indications of
poorly ordered steps are observed. Fig. 4.8b shows the AFM image of a treated
(Laoi8Sro.82)(Alo.59Tao.4i)03(100) surface that was subsequently annealed at 900癈 for
three hours in air. No clear steps were revealed (Fig. 4.8b) by this anneal, and the
surfaces look similar to the treated/un-annealed sample (Fig.4.8a), even with less obvious
ordered regions. Similarly etched substrates were exposed to anneals at 1000癈 and
1100癈 for three hours, and then were characterized with AFM. As seen in Fig. 4.8c,
surface steps were observed in the background but many particles were observed in the
foreground on the treated surfaces, and these particles could not be removed by ultrasonic
cleaning. These particles proved to be problematic during growth, as BST films grown on
the annealed substrates exhibited peaks in the X-ray pattern belonging to both the (001)
and
(111)
orientations.
On
the
other
hand,
BST
films
grown
on
(Lao.i8Sro82)(Alo.59Tao.4i)03(100) substrates that were only etched in a HCkFbO =1:1 for
87
one minute and that were not annealed did exhibit (lll)-oriented crystallites. Therefore,
it was determined that (Lao.i8Sro.82)(Alo.59Tao.4i)03(100) substrates would be treated using
the HChEbO =1:1 chemical treatment without a thermal treatment before growth. It
would be of
interest
to determine the
nature
of the particles
on the
(Lao.i8Sro.82)(Alo.59Tao4i)03(100) surface and their connection with the (lll)-oriented
BST grains, but that was beyond the scope of this work. Though the surface did not
exhibit evident unit-cell high steps of uniform widths and parallel step edges, the films
grown upon these substrates exhibited high-qualities consistent with the substrates
inherent structural quality. Therefore, this treatment was deemed sufficient for the current
purposes. It is not clear why our results differ from literature reports but, as pointed out in
�1.1, even the results for SrTiO3(100) surfaces are vendor and crystal dependent.
,
,? i
,�,
?
Fig. 4.8 AFM images of (Lao.i3Sr0.82)(Alo.59Tao.4i)03(100) substrates: (a) after being etched for 3
min in an HCI:H20=1:1 solution; (b) after the same etch procedure and an anneal at 900癈 for 3
hours; and (c) after the same etch procedure and an anneal at 1100癈 for three hours. Note the
different scales.
4.1.4 Rock salt MgO(lOO) substrates treatment
The highest-quality surface on MgO can be obtained by cleaving in vacuum.7
This is obviously not a practical choice for the growth system in this research. It was
difficult to obtain atomically flat surface for rock salt MgO, similar to that reported in the
88
literature.6 No etch was used for MgO in this work, but various thermal treatments were
explored to produce smooth surfaces. First, a thermal anneal was carried out at 1000癈
for 8 hours in air. No obvious difference was observed for the annealed MgO(lOO)
substrates when compared to the the as-received surface; the surface morphology of the
annealed sample is shown in Fig. 4.9a. Fig. 4.9b shows the surface of an MgO(lOO)
substrate after it was annealed at 1050癈 in pure oxygen; the surface seems slightly
rougher but some steps seem to have developed. Clear surface steps were finally achieved
by annealing the MgO(lOO) substrate at 1350癈 in air for 4 hours, as shown in Fig. 4.9c.
The rms roughness value was = 0,1 nm over a 1 um x 1 urn area. Though the surface
morphology is not as good that achieved by cleavage, it is of sufficient by annealing to
achieve a quality like in this research for thin film growth in this research.
on
liinsM
mown
0,0
i:HtiaM
t>.0wn
*�
KttnoM
M I B
Fig. 4.9 AFM images of surface morphology of MgO(100) substrates after being (a) annealed in
air at 1000癈 for 8 hours, and (b) in pure oxygen at 1050癈 for 3 hours and (c) annealed in air at
1350癈 for 4 hours (c). Note the differences of length and height scales.
4.1.5 Treatment of substrates of lower symmetry
For (OOl)-oriented substrates, it is fairly straightforward to achieve atomically
smooth surfaces using chemical etchants and thermal annealing, as discussed above and
reported extensively in the literature.1'6 Much less work has been carried out on the (110)
89
and (lll)-oriented perovskite substrates, though selective etching has been reported to
yield rough surfaces that are of worse morphological quality than the as-received
surfaces.8'9 Therefore, for (110)- and (lll)-oriented perovskite surfaces, they were used
as-received or as-etched in HC1:H20 = 1 solutions for less than one minute to remove the
surface
contaminations,
in
a
similar
fashion
to
that
done
for
(Lao.i8Sro.82)(Alo.59Tao.4i)03(100). We will comment later on the impact of this approach,
though the BST films quality was very good and did not seem to be impacted by the
absence of steps. All substrates discussed later were subjected to the final treatment
indicated in the above sections, and all SrTi03 crystals are from MTI.
4.2 Thin film growth mode
As it has been stated in Chapter 3, film growth modes can be categorized into
three types.10,11
1) The first is called the Frank-van der Merwe layer-by-layer growth mode.1011
In fact, there are distinct variations within the class of two-dimensional growth, which
can be divided into: (a) the step-flow mode and (b) the terrace-nucleation mode.1011 In
the step-flow mode (or growth),10'11 the adatoms (or ad-species if the species are larger
clusters, such as metal-oxide species) have sufficient time (energy) to migrate to the step
edges, which are low energy attachment sites, and sufficient energy to overcome
attachment barriers to the step edge. As such, step-flow growth maintains clean and sharp
surface steps and leads to a replication of the original surface morphology throughout
growth. In the terrace-nucleation mode,1011 all adatoms (or ad-species) are not mobile
enough to move to the step edges (though those within a diffusion length can) prior to the
arrival of sufficient enough material on the terrace to overcome barriers to 2D island
90
nucleation. As such 2D islands nucleate on the terraces, which greatly increase the
number and distribution of attachment sites for other arriving species. New adatoms have
sufficient time and energy to migrate to the island edges and, therefore, expand the
islands laterally until they all merge into a continuous layer, wherein the process begins
again. Though this terrace-nucleation mode can, in principle, lead to a replication of the
surface morphology of the substrate, this will occur only at the complete filling time (or
once a cycle). As described above, the difference in achieving either of these two modes
is strongly related to growth kinetics. Of course, some thermodynamic factors also play a
role in whether 2D growth occurs,10'11 (such as whether or not the surface is the lowest
energy facet or if the film has a preference to wet the substrate or not,) though we will not
focus on them here.
2) The second is called the Volmer-Weber 3-D island mode (or growth).10'11 This
3D mode occurs when the the adatoms form 3D islands, which are islands of heights
more than one monolayer or unit-cell (or growth unit). The driving force for 3D island
growth can be thermodynamic (so as to expose a different crystallographic facet or to
avoid wetting the substrate) or kinetic (if the attachment probability on the second, third,
and higher layers is appreciable compared to the probability of all species migrating to
step / 2D island edges).10'11 In this work, 3D island mode is avoided because it can lead
to different relaxation mechanisms than those that occur in 2D modes.12
3) The third is called the Stranski-Krastanov (SK) growth mode.1011 In SK mode,
the initial several monolayers grow in a 2D layer-by-layer mode, but the remaining layers
grow in a 3-D island mode.13 As this involves a 3D mode also, this growth mode was
91
avoided, even though it is sometimes difficult to distinguish in thicker films whether
islands formed from pure 3D or SK modes.
Film growth mode is dependent on both thermodynamic and kinetic factors,
which include contributions from the interface energy, the lattice mismatch, and the
chemical interactions between the film and the substrate (bonding),1011 as well as from
the growth conditions, including the substrate temperature, the oxygen pressure, the laser
repetition rate, and the laser energy (essentially supersaturation).13 In the current research,
substrates that have different chemical compositions and lattice mismatches with
Bao.6Sro.4Ti03 (or any barium strontium titanate composition) were used. Therefore we
carried out extensive growth mode investigations for barium strontium titanate film
growth on each substrate, to facilitate our gaining an understanding of how the film
microstructures are related to mismatch and substrate quality (as opposed to growth
modes) and to, later, correlate the existence of specific microstructural features or lattice
parameter varations to dielectric properties.
AFM (see �2.6) and RHEED (see �2.7) were employed for ex-situ monitoring
of the growth mode. The film surface morphologies were examined at different stages of
the films growth to track surface morphologies. Depositions were carried out in the
standard PLD system (see �2.3) over the range of oxygen pressure from 1 mTorr to
300mTorr. The substrate temperature was maintained at 850癈 for all growth. The laser
energy was calibrated to be 2 J/cm2 and the pulse rate was from 1-3 Hz. The target to
substrate distance was maintained at approximately 75 mm for the Laser MBE system
and 60 mm for the conventional standard PLD chamber. Films were cooled in 400 Torr
O2 at a rate of 20 癈/min. The film growth rate was calibrated using XRR at different
92
oxygen pressures. The two commonly used Bao.6Sro.4Ti03 film growth rates in this
research were found to be 0.24 A/pulse (at lmTorr) and 0.17 A/pulse (at 300 mTorr).
4.2.1 Film growth mode on SrTiO3(100), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100), and
LaAlO3(100)
AFM topographic images of the 3-, 50-, and 150-monolayer thick (monolayer
here is considered as 1 unit-cell or growth-unit in thickness) BST films grown on
SrTiO3(100) and LaAlC>3(100) are shown in Fig. 4.10. These films were deposited at 1
mTorr O2. The films maintained smooth surfaces during film growth with rms roughness
values smaller than a single-unit-cell height at all thicknesses indicating 2D growth. No
clear steps were observed on the film surface for any thickness; therefore, the films did
not grow in the step-flow mode, but by a terrace nucleation in a layer-by-layer mode (that
did not lead to step edge replication after island coalescence). RHEED patterns registered
at room temperature are shown in Fig. 4.11 for the as-grown barium strontium titanate
films on LaAlO3(100) and (Lao.i8Sro.82)(Alo.59Tao.4i)03(100) after growth of � 300monolayers. The patterns are best described as streaky patterns, which is further evidence
of smooth film surfaces indicating a layer-by-layer growth mode. The change in the
patterns from spots on a circle to streaks indicates the terrace edges are narrower and
steps are more uniformly distributed on the flat surfaces.
93
3 Monolayers
50 Monolayers
150 monolayers
1x1nm2Rms:0.125nm 1x1pm!Rm3:0.591nni
5nm
1x1|jm2Rms:0.118nm
1xlHm'Rms:0.294nm
5nm
10nm
1xlMmIRi玸:0.154nm 1x1pm2Rms:0.215nm
Fig. 4.10 AFM topographic images of the surfaces of barium strontium titanate films grown on
LaAIO3(100) and SrTiO3(100) with different thicknesses of 3, 50, and 150 monolayers.
Fig. 4.11 RHEED patterns of 300-monolayer thick barium strontium titanate films grown on (a)
LaAIO3(100) and (b)
(La0.iaSro.B2}(Alo.59Ta0.4i)03(100); patterns were registered using 15 kV
electron energy and taken along the [100] azimuths.
4.2.2 Film Growth mode on GdScO3(110), DyScO3(110) and NdGaO3(110)
Bao6Sro.4Ti03(001) films were grown on GdSc03 (110), DySc03 (110) and
NdGa03 (110) under 1 mTorr oxygen pressure in the Laser-MBE chamber. The laser
energy was calibrated to be 2 J/cm2, the repetition rate was 1 Hz. The substrate
temperature was maintained at 850癈 during deposition. The surface morphologies of
treated GdScO3(110) are shown in Fig. 4.12a as AFM images. Wide flat terraces are
94
visible and the step-heights correspond to half- or single-unit-cell high cubic
Bao.6Sro.4Ti03 (Fig.4.12a). This is ideal for 2D layer-by-layer growth of Bao6Sro.4Ti03.
Films were grown to three thicknesses (25 run, 60 nm, and 200 nm) and then
characterized for their surface morphology. Fig. 4.12b and 4.12c show the ex-situ AFM
topographs of respectively 25 nm and 200 nm thick Bao.6Sro.4Ti03 films deposited on
GdScC>3. These figures indicate that the films grew in a manner that continually
replicated the original terrace structure, since the film surfaces were similar in nature to
the substrate surfaces, with nearly identical terrace widths. A few islands were observable
on the terraces in both figures, although they are more evident in the 200 nm thick film.
The rms roughness values of the films did increase slightly with the film thickness,
although the films are still remarkably flat: the rms values were 0.13, 0.23, and 0.29 nm
for films 25, 60, and 200 nm thick, respectively.
Substrate
25nmfilm
Distance X (micron)
�
OitUnceX
(e)
200nmfilm
( cnic.on)
Distance X
2nm
(micron)
(I)
Fig. 4.12 Atomic force microscopy images from (a) treated GdScO3(110) substrates and (b,c)
Ba06Sr04TiO3 (001) films deposited on such substrates to (b) 25 nm and (c) 200 nm thicknesses.
The corresponding line scans are shown in (d) for the GdSc03 (110) surface and in (e,f) for
Bao6Sr04Ti03 (001) films deposited on such substrates to (e) 25 nm and (f) 200 nm thicknesses.
95
The AFM results indicate that the films grew in a 2-D nucleation layer-by-layer
mode, with a small probability that a second layer nucleates before the first layer is
completed. At the time when the film is 200 nm thick, the RMS roughness is still less
than 0.5% of the total thickness and the accumulated maximum terrace height is 4 unit
cells, although the vast majority is lower than this. The 2D layer-by-layer growth mode
results in all of the steps advancing at the same speed and the terraces and steps can be
replicated to the 200 nm thick film. Fig. 4.13 shows the AFM image of a 300 nm thick
Bao.6Sro4Ti03 film grown under 300 mTorr oxygen pressure (and all other values being
described above); though the surface steps are not obvious anymore, it still demonstrates
a rms roughness value of 0.88 nm, which is only 0.3% of the film thickness.
Fig. 4.13. Atomic force microscopy topographic image of a 5*5 pm2 area of a 300nm thick
Bao.6Sr0ATi03 (001) film grown under 300mTorr oxygen partial pressure (with the other
parameters described in the text) on GdScO3(110). The rms roughness value of the surface is
0.88nm.
Fig. 4.14b shows the RHEED pattern from the 200 nm thick Bao.6Sr0.4Ti03(001)
film along the [100] azimuth (the [010] had a similar pattern), which was parallel to the
substrate [001] azimuth (Fig. 14a). The film's RHEED pattern was best described as a
streaky pattern having diffuse spots lying on a semicircle with Kikuchi lines in the
96
background, consistent with a fairly fiat surface that has an slightly increased number of
steps compared to the substrate. The RHEED pattern became streakier as the growth
proceeded and streaks were observed for the 200 nm thick films; these results are
consistent with the result of AFM study and indicate that, although step-flow-growth is
occurring, some probability exists for terrace nucleation as well.
Fig. 4.14 The RHEED patterns of treated GdSc03 taken along the GdScO3[001] azimuth (a)
before growth and (b) aftergrowth of a 200nm film taken along the Ba0.6Sro.4Ti03[100] azimuth.
The RHEED patterns shown above are consistent with an epitaxial relationship
between
the
film
and
substrate,
where
the
[100]fiim||[001]SUbstrate
(and
[010]fiim| | [110] substrate)- Comparing the RHEED patterns, one notices that the spacing
between the spots in Fig. 12a is Vi that of the spacing between the streaks in Fig. 12b.
This arises from the fact that the substrate has a doubled in-plane lattice parameter
compared to that of the cubic (or tetragonal) Bao.6Sro.4TiC� The REScOz substrates adopt
an orthorhombically distorted perovskite structure whose unit cell has the dimensions of
V2ap, V2ap, 2ap (where ap is a cubic perovskite lattice parameter) while bulk
Bao.6Sro.4Ti03 adopts a cubic unit cell of dimensions ap, ap, ap (above the Curie
97
temperature). The RHEED patterns indicate that the surfaces of each material have a lxl
unreconstructed surface cell when compared to the bulk materials. Moreover, the choice
of substrate does not induce an apparent change in the surface unit cell of the film.
DyScO3(110) and NdGaO3(110) substrates have a similar orthorhombic structure
to GdScC>3 and their treated surface morphologies were similar to that of GdScC>3, all
possessing wide step terraces and clear step (see Fig. 4.12). Though the lattice
mismatches with Bao.6Sro.4Ti03 for NdGaC>3(110) and DyScCtyllO) are bigger than that
for GdScC>3(110), 2D layer-by-layer growth of Bao.6Sro.4Ti03 was observed on all three
substrates.
Such 2D layer-by-layer growth that can repeat substrate terraces has not been
observed in the literature for BST solid solutions. This benign growth mode will yield a
sharp film-substrate interface. As it will be discussed later, the high crystal quality with
narrow x-ray diffraction rocking curve and low dislocation density in this type of films
may be attributed to the 2D growth mode.
4.2.3 Films growth mode on MgO(lOO)
5x5um2 Rms: 1.49nm
Fig. 4.15 (a) AFM image of the surface of a Bao.6Sr0.4Ti03 film grown on MgO for a time
equivalent to a thickness of 3 monolayers (when grown in a layer-by-layer mode). (b) The ex-situ
RHEED pattern of the film after 50 nm of growth. The AFM image shows a 3D growth pattern with
non-coalesced islands and the RHEED pattern shows a spotty pattern consistent with 3D growth.
98
BST
MgO
200nm
Fig.4.16 A bright field TEM cross sectional image from a Ba0.6SroATi03(100) film on a MgO(100)
substrate. The vertical dark contrast is indicative of the fact that the film grew in a 3D columnar
mode.
The AFM topographic images of a Bao.6Sro.4Ti03 film grown on an MgO(lOO)
substrates (treated as described in �1.4) at oxygen pressure of 1 mTorr for a deposition
time (50 pulses) equivalent to 3 unit cell layers demonstrated is given in Fig.4.15a. The
film exhibits a rough surface with a rms roughness value of 1.49 nm, which is equivalent
to the height of several unit cells. The RHEED pattern from a similar film deposited to a
thickness of ~ 50 nm is shown in Fig. 4.15b. The pattern is best described as a spotty
pattern, which is consistent with 3D growth. Fig. 4.16 is a bright field image taken from a
cross-sectional TEM specimen (the sample was prepared as described in �2.5) and the
microscope was operated as described in �2.5 prepared from a 400nm thick
Bao.6Sro 4TiC>3 film grown under identical conditions to those above. Clear columnar
features are observed in the TEM image, also consistent with 3D growth. All these
observations suggested that the films on MgO grew in 3-D island mode over the entire
deposition sequence. Owing to the large lattice mismatch between Bao.6Sro.4Ti03 and
MgO, the observation of 3-D island growth is very common in the literature.1415 As will
be discussed later, the Bao.6Sro.4Ti03 films deposited on MgO exhibited more than one
99
orientations. The existence of the other orientations is consistent with the 3D-island
mode, which allows different orientations of grains to nucleate during film growth.14
4.2.4 Films grown on SrTi0 3 (lll)
3 monolayers
50 monolayers
1x1(jm2Rms:0.103nm 1x1|jm2Rms:0.247nm
300 monolayers
1x1|jm2Rms:0.443nm
Fig. 4.17 AFM topographic images of Ba0.6Sro.4Ti03 films grown (see text for details) on
SrTi03(111) with different thicknesses of 3, 50, and 300 monolayers.
AFM images of Bao.6Sro4Ti03 films grown on SrTi03(l 11) are shown in Fig. 4.17
for different stages of film growth. The films were grown under 1 mTorr oxygen pressure
with other conditions the same as the films grown on MgO. The film rms surface
roughness increased from ~ 0.1 nm to ~ 0.4 nm as the film thickness increased from 3 to
300 monolayers. However, these rms values are below or � equal to one unit cell height.
It is reasonable to believe that these films deposited upon SrTiC>3(l 11) substrates grew in
a 2D layer-by-layer mode throughout the deposition. The growth mode of Bao.6Sro.4Ti03
films on SrTi03(lll) has rarely been investigated, because it has rarely been used for
microwave varactor study.
4.3 X-ray characterization of epitaxial relationships between films and substrates
4.3.1 Epitaxial relationships of films grown on cubic (OOl)-oriented substrates
Epitaxy, in this research, is strictly defined as when the deposited film adopts the
identical orientation to that of the substrate (when considering the orientations of the
parent cubic perovskite aristotype) in both the in-plane and out-of-plane directions. Films
100
with a preferred orientation aligned with the substrate and the other orientations randomly
distributed will be considered "textured", not epitaxial. Also, because of the strict
definition given above, Bao.6Sro.4Ti03 films deposited on MgO, when the two crystals
have a single preferred in-plane and out-of-plane orientation relationship, will be
considered to be biaxially textured. Since the various substrates used in this research have
different chemical compositions and lattice mismatches with the Bao.6Sro.4TiC>3 (and other
BST compositions), their strain energy, interfacial energy, and bonding characteristics
may be different; these will impact the epitaxial relationships and defect characteristics.
The growth conditions, such as the substrate temperature, the oxygen pressure, and the
surface treatments, may also affect the epitaxial relationship (as discussed in � 4.1). To
understand the evolution of the microstructural features (and to engineer them), the
epitaxial relationship between the film and the substrate was investigated for each of
these substrates. In this research, symmetric theta-2theta scans were used to characterize
the out-of-plane (or growth direction) orientation and phi scans or pole figures of
asymmetric reflections (those containing an in-plane component) were used to
characterize the in-plane orientations; together these can be used to define the epitaxial
relationship.
4.3.1.1 Bao.6Sr0.4Ti03 on SrTiO3(100), (La0.i8Sro.82)(Alo.59Tao.4i)03(100) and LaA103
(100)
The theta-2theta scans of Bao.6Sro.4TiC>3 films grown on SrTiC>3(100),
(Lao i8Sro.82)(Alo.59Tao.4i)C>3(100), and LaAlC>3(100) at similar conditions as discussed in
�2.1 are shown in Fig. 4.18a (respectively from bottom to top). All of these films
exhibited peaks from only the (001) orientation; no peaks from other orientations were
101
observed. Fig. 4.18b shows the phi scans from Bao.6Sro.4Ti03 film on the SrTiC>3(100)
substrate. The (111) reflections of the film and substrate were well aligned (as were the
(110), which are not shown). It should be noted that the film and substrate peaks were
registered using different two-theta and psi angles: psi=54.7癴or (111) reflection and
psi=45� for (110) reflection. Similar results were found for Bao.6Sr0.4Ti03 films on
(Lao.i8Sro.82)(Alo.59Tao.4i)C>3 and LaA103 for both the (111) and (110) film peaks (not
shown). For all of these cubic substrates, the epitaxial relationship can be written as
(001)BST||(100)subs and [100]BST|| [100]subs (by consideration of the theta-2theta scans and
phi scans). These observations are consistent with literature report that the Bao.6Sro.4Ti03
films are easy to grow epitaxially on SrTiC>3(100), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100) and
LaAlO3(100). 12,16-18
(b)
subtil;
?
?
:
mm
w w.
i,
Wfffli
Lmonj
\ JWWWW
20
25
30
35
40
2 Theta (Degree)
45
50
55
?200 -150 -100 -50
0
50
Phi (Degree)
100 150 200
Fig, 4.18 (a) Theta-2theta x-ray scans of Ba0.6Sr0.4TiO3 films grown on SrTiO3(100),
(Lao.isSro,82)(Alo.5aTao.4i)03(100) and LaAIO3(100) under 300mTorr oxygen pressure and (b) the
typical phi scan of the {111} reflections of the films and the substrates.
4.3.1.2 Bao.6Sro.4Ti03 films grown on MgO(100)
There is always a challenge to avoid the formation of (11 l)-orientated regions
when Bao.6Sro.4Ti03 films are grown on MgO(100) substrates, owing in part to the large
lattice mismatch between Bao.6Sro.4TiC>3 and MgO substrate.14 Fig. 4.19a shows a theta102
2theta scans of Bao.6Sro.4Ti03 films grown on MgO(lOO) at different oxygen pressures of
5 mTorr, 35 mTorr, and 300 mTorr (the other deposition conditions are the same as
discussed in �2.1.1). From Fig. 4.19a, one can see that, though the majority constituent
of each film is (OOl)-oriented, all the films demonstrated peaks from (111) oriented
regions (marked with D) in the theta-2theta scans. These observations are consistent with
those reports in the literature.14
Fig. 4.19 (a) Theta-2theta x-ray scans of Bao.6Sr0ATi03 films grown on MgO(100) under different
oxygen pressures of 1 mTorr, 35 mTorr, and 300 mTorr. In (a), the peaks marked S refer to those
of the substrates {hOO}, the peaks marked with F refer to those of the films (002), and the peaks
marked D refer to those of the films (111). The broad peaks underneath MgO(100) were from
substrates itself, (b) Bright field planview TEM image of the Ba0.6Sr04TiO3 film grown under 300
mTorr oxygen partial pressure. The inset is the selected area diffraction pattern.
The 2theta locations of the film's (002) peak shifted to higher angles when the
growth oxygen pressure was increased, even though the films were all cooled down from
850癈 in an oxygen pressure of 200 Torr (note that the substrate peaks have been
aligned). This is consistent with the reports that the unit cell volume increases with a
decrease of the deposition oxygen pressure, which is often attributed to the introduction
of higher concentrations of oxygen vacancies (or other point defect) at low pressures.19,20
Recently it was shown that the lattice parameters and cation stoichiometry of SrTiC>3
103
were sensitive to changes in the growth conditions and that these defects were not
affected by the annealing pressure.20 In our work, we did not aim to distinguish or to
identify the point defects responsible for such lattice parameter variations.
Fig. 19b shows a bright field (BF) TEM image from a planview specimen of a
Bao.6Sro.4Ti03 film grown on MgO(lOO) (using the following conditions: 300 mTorr
oxygen partial pressure, and other conditions as described in �2.3). In the bright field
image, bright in-plane contrasts were observed approximately every 20 nm; this contrast
is likely related to the crystallite boundaries. The inset in Fig. 19b shows the selected area
electron diffraction pattern and is consistent with a highly textured, [001]-oriented film
(the [001] is pointing to the out-of-plane) with only a slight in-plane orientation
misalignment. All of these results are similar to literature reports14 and indicate that the
films deposited on MgO are very different from barium strontium titanate films grown on
perovskite substrates. Though Delage et al.14 used sub-oxidized barium strontium titanate
as a buffer layer to reduce the content of (lll)-oriented region, this method cannot be
used in this research, because the buffer layer will complicate the strain state and
introduced unpredictable factor during dielectric property comparison.
4.3.1.3 Bao.6Sro.4T/iO3 growth on orthorhombic perovskite substrates: GdScO3(110),
DyScO3(110), and NdGaO3(110)
For films grown on (110)-oriented orthorhombic perovskite substrates (equivalent
to the (OOl)-oriented cubic perovskite substrates), including GdScO3(110), DyScO3(110),
and NdGaC>3(110), out-of-plane theta-2theta x-ray scans showed that the films exhibited
(001) reflections close to (hhO) reflections from the orthorhombic substrates. Fig. 4.20a
shows two such patterns registered for the film grown on GdScO3(110) substrates. (It
104
should be noted that the growth condition has been described in �2.3: the film grown at
lmTorr had a thickness of 200 nm and the film grown at 300 mTorr had a thickness of
120 nm, as measured using cross-sectional TEM). The theta-2theta scans show that the
Bao.6Sro.4TiC>3 film grown at 1 mTorr has a lower Bragg angle for its (002) reflection than
for the substrate (220) and that the film grown at 300 mTorr has a Bragg angle for the
(002) reflection that overlaps with the substrate's (220) reflection. This indicates that the
Bao.6Sro.4TiC>3 film grown at 1 mTorr has a larger out-of-plane lattice parameter than that
of the Bao.6Sro.4Ti03 film grown at 300 mTorr, similar to that observed for films grown
on MgO in Fig. 4.19a. Quantitatively, the lattice parameter at 1 mTorr is 4.009 A and at
300 mTorr is � 3.957 A (though the (001) and (002) reflections of the film overlap with
the substrate peaks for the latter, the film (004) peak measured from high resolution x-ray
diffraction can be differentiate from the substrate (440) peak to calculate the out-of-plane
lattice parameter). Similar observations were made for the Bao.6Sro4Ti03 films grown on
DySc03(l 10) substrates, as shown in Fig. 4.21. As discussed above, this has been widely
explained by oxygen vacancy introduction at low pressures, though recent work indicates
that cation stoichiometry variation owing to PLD growth parameter variations is perhaps
a better explanation (see �3.1.2).
In Fig. 4.20a, two peaks are observed that are
symmetrically located on the two sides of the film's (002) Bragg peak. These peaks do
not correspond to any other orientations or phases. They are believed to be the
Pendellosung fringes21 from atomically flat interfaces and the high film quality, which
has rarely been observed infilmsbarium strontium titanate solid solution.
105
a)
?
f
I
BST/GdScO3(110)
;I _ 1
I
300 mTorr
(b)
I
I
Sub{202}
f
Film{11|l�
o
/V
B B ^iu M ^ | J^UM|Ull t jJLl|^|玥^|lb a iJ
'
20
25
30
35
40
45
50
55
*
-IOU-IUU
2 theta (Degree)
-OU
U
OU
IUU
?
?
IOU
Phi (Degree)
Fig. 4.20 (a) Theta-2theta x-ray scans of Bao.6Sr0.4Ti03 films grown on GdScO3(110) under
ImTorr and 300mTorr oxygen pressures (see text for other details) and (b) the Phi scans for the
film's {111} reflections and the substrate's {202} reflections (the two theta and psi angles are:
substrate =39.969�, 54.7" and film 39.245", 54.7". The peaks marked with * are believed to be
Pendellosung fringes arising from the films high quality and atomically flat interfaces.
Phi scans from the GdScC>3 {202} peaks (equivalent to the cubic {111}) and the
films {111} peaks are presented in Fig. 20b for the film grown at 1 mTorr. The film's
{111} reflections align with the substrate's {202} reflections. The film exhibits 4 peaks
of similar intensities while the substrate exhibits two strong and two weak peaks; this is
due to the lower symmetry / distortions in the GdScC^ orthorhombic lattice. The epitaxial
relation can be determined from these observations and can be written as:
(002)BsT||(220)GdScO3 and
[100]BsT||[H0]GdscO3. Bao.6Sr0.4Ti03 films grown
on
DyScO3(110) and NdGaC>3(110) have the same epitaxial relationship as that of the film
grown on GdScC>3 (phi scans are not shown below for them).
Fig. 4.20a shows the theta-2theta patterns registered for films grown on
DyScC>3(110) substrates in 1 mTorr and 300 mTorr O2. (It should be noted that the film
grown at ImTorr had a thickness of 100 nm and the film grown at 300 mTorr had the
thickness of 120 nm, as measured using growth rate calibration and cross-sectional TEM.
106
Other conditions were the same as described in �2.3). The theta-2theta scans show that
the Bao.6Sro.4Ti03 film grown at 1 mTorr has a lower Bragg angle for (002) than for the
substrate (220) and that the film grown at 300mTorr has a Bragg angle for the (002)
reflection that overlaps with the substrate (220). This indicates again that the
Bao.6Sro.4Ti03 film grown at 1 mTorr has a larger out-of-plane lattice parameter than that
of the Bao.6Sro.4Ti03 film grown at 300 mTorr. As mentioned above, the epitaxy observed
for Bao.6Sro.4TiC>3 on GdSc03(l 10) was also observed for Bao.6Sro 4TiC>3 on DyScC>3(l 10).
Finally, nearly identical observations were made for films grown on NdGa03 (at
these thicknesses). The lattice parameter was strongly influenced by deposition oxygen
pressure and the epitaxy was identical to that observed for films on GdScCb and DySc03.
4
f
C
t
I
'
15
20
25
?
?
?
?
-
'
30 35 40 45
2 Theta (Degree)
-
'
50
-
?
?
55
60
Fig. 4.21 Theta-2theta x-ray scans of Ba06Sr0.4TiO3 films grown on DySc03 (110) under 1 mTorr
and 300 mTorr oxygen pressures (see text for other growth conditions).
4.3.2 Epitaxial relationship of films grown on surfaces equivalent to cubic perovskite
(110)
Bao.6Sro.4Ti03 films were
grown
on cubic
SrTiO3(110),
pseudocubic
LaAlC>3(110), and orthorhombic NdGaC>3(100) substrates under the oxygen pressure of
300 mTorr (and other conditions were as described in �2.3). Their out-of-plane theta2theta scans are shown in Fig. 4.22. Bao 6Sro.4TiC>3 films grown on these substrates
107
demonstrated pure (HO)-oriented films. The positions of the (110) peaks on these
substrates was 31.912�, 31.908�, and 31.887� on SrTiOs, NdGa03, and LaA103,
respectively. Keeping in mind that the substrate patterns were calibrated using substrate
peak, these patterns show that the (110) peak shifted to lower angles (the out-of-plane d
spacing increased) as the substrate's two-theta position increased (lattice parameter
decreased). This is consistent with in-plane compressive strain and am out-of-plane
lattice parameter increases by the Poisson effect.
Pole figures are often used to give a more complete view of the epitaxial or
texture relationships between the film and the substrate, as it has been discussed in
�2.4. The pole figure22 of {101} reflections (under condition of where the (101)
reflection of the film has 2theta = 31.861�) from the film deposited on the SrTiO3(110)
substrate are given in Fig. 4.23a and show 5 peaks: the center peak is the out-of-plane
(110) peak, whose pole is parallel to the substrate normal, and the four reflections that are
located at a 60� angle (in psi) from the central (110) peak (and spaced ay 109� and 71� in
phi from each other); these peaks indicate that the film has a single epitaxial orientation.
The corresponding pole figure of the {002} reflections (2theta = 45.585�) from the same
film gave two peaks at an angle of 45� in psi from the substrate normal and with two fold
symmetry (180� in phi from each other). The narrow peaks in the pole figure indicate that
the films are extremely well aligned with the substrate. These observations (in
conjunction with similar observations for the other substrates and pole figures on the
substrate peaks, which are not shown) indicate that the films adopted an epitaxial
relationship with the substrate of
(110)BST||
(H0)NdGaO3, for theNdGaC>3 substrates, and
[100]BST||[100]SUbStrate, for cubic substrates LaA103(HO) and SrTiO3(110), and
108
(110)BsT||(100)NdGaO3 and [100]BST||[001]SUbstrate. Compared to the textured BST films
grown on NdGaO3(100) by Simon et al.,22 the epitaxial films deposited in this research
are attributed to the good substrate treatment.
20
25
30
35
40
2 theta (Degree)
45
SO
Fig. 4.22 Theta-2theta x-ray scans of Ba0.sSr0ATiO3 films grown on SrTiO3(110), NdGaO3(100),
and LaAI03(110) under 300mTorr oxygen pressure (other conditions are given in the text).
(�)
(|>)
'
\
'
"\
\
Fig. 4.23 (a) Pole figures of {101} reflections and (b) {002} reflections for Ba0.6Sr0.4TiO3 films
grown on the SrTi03(110) substrate (growth conditions given in text).
4.3.3 Epitaxial relationship of films grown surfaces equivalent to cubic perovskite
(111)
Bao.6Sro.4TiC>3 films were
grown
on cubic
SrTiC>3(lll),
pseudocubic
LaA103(lll), and orthorhombic NdGaO3(011) substrates under an oxygen pressure of
300 mTorr. Their out-of plane theta-2theta scans are shown in Fig. 4.24. Bao.6Sro4TiC>3
films grown on these substrates demonstrated pure (lll)-oriented films. The 2theta
109
positions of the out-of-plane (111) reflections of these films are 39.321�, 39.358�, and
39.375� on SrTi03(l 11), NdGaO3(011), and LaA103(l 11), respectively. These angles are
smaller than the bulk (111) 2theta = 39.397�, which means the out-of-plane d spacings
are larger than expected for the bulk Bao.6Sro.4Ti03 values, similar to the observations on
(100) and (110) substrates.
3
20
25
30
35
40
2 Theta (Degree)
45
50
Fig. 4.24 Theta-2theta x-ray scans of Ba0.6Sr0.4TiO3 films grown on SrTi03(111), NdGaO3(011),
and LaAI03(111) under 300mTorr oxygen pressure (other conditions are given in the text). The
wide peak in the LaAI03 was from the substrate.
(a)
(b)
A
?I
? -t '
Fig. 4.25 (a) Pole figures of {002} reflections and (b) {111} reflections for BaQ,eSroATi03 films
grown on the SrTi03(111) substrates.
110
The pole figures of the film {002} reflections (2theta = 45.733�) for films
deposited on SrTi03(lll) are shown in Fig. 4.25a and exhibit three peaks at a psi angle
of 54.7� with three fold symmetry when film, as expected. The pole figure of film
{111} reflections (2theta = 39.354�) from the same film is given in Fig. 4.25b and shows
four peaks: one is the out-of-plane peak whose pole is parallel to the substrate normal and
three are at a psi angle of 70.5� with three fold symmetry, as expected. The pole figures
of Bao.6Sro.4Ti03 films grown on NdGaO3(100) and LaAlO3(110) are similar, but not
shown. These observations (in conjunction with similar observations for the other
substrates and pole figures on the substrate peaks, which are not shown) evinced that the
films had the epitaxial relation of (11 1)BST||(1 1 l)substrate and [110] BST|I [HO]substrate for
cubic substrates SrTi03 and LaA103, and (lll)BST||(011)substiate and [100]BsT||[110]Substrate
for orthorhombic NdGaC>3.
4.3.4 Conclusions of epitaxial relationship
X-ray and planview TEM characterization of the Bao.6Sro.4Ti03 films grown on
MgO demonstrated that the films are textured with a preference of (OOl)-orientation. This
textured structure is believed to be due to the large lattice mismatch (6.7%) between
Bao 6Sro.4Ti03 and MgO. The textured structures were observed in the Bao.6Sro.4Ti03
films grown on MgO under oxygen partial pressures from lmTorr to 300mTorr. The
other (OOl)-oriented Bao.6Sr0.4Ti03 films grown on GdScO3(110), DyScO3(110),
SrTiO3(100), (Lao.i8Sr0.82)(Alo.59Tao.4i)03(100), and LaAlO3(100) (also grown under 1 to
300 mTorr oxygen partial pressure) have all demonstrated that the films were all
epitaxial to the substrates, which indicate that the chemical compositions and lattice
mismatches of these substrates are not barriers for the Bao.6Sro.4Ti03 films to grow
111
epitaxially. Bao.6Sro.4Ti03 films of other orientations, such as those deposited on surfaces
equivalent to the cubic (110) and (111) surfaces of SrTi03, LaAlCb, and NdGaC� are
also epitaxial to the corresponding substrates. Epitaxial films make it simpler to
investigate the strain relaxation mechanism and later the effects of dislocations on
dielectric properties. Importantly, the lattice parameter varies with oxygen pressure,
similar to that reported in the literature. To exclude this oxygen pressure effect, all the
films for dielectric property measurement were deposited at the same conditions
(including the same oxygen pressure).
4.4 Strain relaxation mechanisms for differently oriented films
As it has been discussed in Chapter 3, there is no agreed-up slip system in
(Ba,Sr)TiC<3 single crystals and no accepted film relaxation mechanism in (OOl)-oriented
(Ba, Sr)TiC�films. The phenomena observed in such films can be explained by either
climb of misfit dislocations with <100> Burger's vectors, followed by dislocation
dissociation, [100]a -> l/2[101]a + 1/2 [101] a,23 or by glide of misfit dislocations with
<101> Burger's vectors, followed by dislocation combination of l/2[101]a + 1/2 [101] a
?> [100]a.23"25 The dislocation dissociation and combination processes are energetically
equivalent from the E=Gb2 point of view. Therefore, it is impossible to precisely
determine the relaxation mechanism using ex-situ characterization of dislocations in
(OOl)-oriented films. In order to clarify the slip system / relaxation mechanisms in BST
materials, Bao.6Sro.4TiC>3 films were grown on (001)-, (110)-, and (lll)-oriented
substrates. The TEM observations will be compared to the predictions made for
dislocations based on two different slip systems and the crystal geometry. The relaxation
112
mechanisms for films of all three orientations, (001), (110), and (111), will be discussed
in this section.
The film growth conditions, growth mode, and film-substrate epitaxial
relationship have been presented earlier in this chapter. Films grown on all three
orientations are epitaxial to the substrates SrTiO3(100), SrTiO3(110), and SrTi03(lll).
Films deposited under the following conditions were used in the TEM analysis: 300
mTorr UHP oxygen, 2 J/cm2 laser energy and repetition rate 1 Hz, other parameters were
described in �2.3. As explained earlier, all films have a nominal thickness of 120 nm
and they were epitaxial and grew in a layer-by-layer mode, indicating that the relaxation
processes should be similar.
Cross-sectional TEM specimens were prepared from the samples by cutting the
samples into 3 mm x 400 um bars. The two bars were glued together with the film sides
facing each other using gl epoxy (Gatan, Warrendale PA). Polishing was completed
using 30 um, 9 um, and lum diamond films from both cross-sectional sides, until the
thickness was ~ 20 um. Then, the sample was glued onto a copper grid. PIPS ion milling
was then carried out from both sides to mill the sample just until a perforation occurred in
the interface where the two films met. The ion milling energy used ranged from 3.5 keV
to 4.5 keV, with milling angles of 5-8�.
Planview TEM samples were prepared by direct thinning of the substrate from the
substrate side to ~ 20 um. This was followed by ion milling (similar to that described
above) until a perforation occurred from the substrate side; the film side was protected
using a removable wax. Then, the samples were cleaned in acetone and methanol to
113
remove the wax. Plasma cleaning was used to further clean the sample before TEM
observation.
A Joel 2000EX was employed for conventional TEM analysis. A Tecnai F20 was
used for high-resolution transmission electron microscopy (HRTEM) analysis. Both
microscopes were operated with the acceleration voltage at 200 kV.
4.4.1 TEM observations of (OOl)-oriented Baiu,Sro4TiOj films
Fig. 4.26a shows a two-beam bright-field planview TEM image26 from the
interface of an epitaxial (OOl)-oriented Bao.6Sro.4Ti03 film grown on SrTiO3(100) (both
film and substrate are included in the image). The orientation was determined by
analyzing the selected area electron diffraction pattern (SAEDP), which is not shown.
The reflection used to generate the two-beam image in Fig. 4.26a (in addition to the main
beam) is the (100) reflection, which is parallel to the direction of the inset arrow. Fig.
4.26b shows a two-beam bright-field planview TEM image from the same sample using
the (010) reflection to generate the two-beam image, which is parallel to the direction of
the inset arrow; note that this reflection is perpendicular to the one used in Fig. 4.26a. In
both images, two types of dark contrasts on the uniform grey background can be
observed and are interpreted as arising from dislocations: continuous long dislocation
lines with thick contrast and short dislocation segments. The dislocation lines are along
the [010] and [100] directions in Fig. 4.26a and 4.26b, respectively; the line directions are
perpendicular to the reflection direction used to generate the images. The dislocations
parallel to the reflection direction are invisible in each image. The dislocation line
directions in the two images are perpendicular to each other and, when taken together,
form a rectangular network in thefilm-substrateinterface allowing for strain relaxation.
114
These two-beam bright-field images, taken using either the (100) or (010)
reflections, demonstrate that both conditions can make the dislocations, whose line
directions are parallel to the reflection direction, vanish. This means that the projection of
the Burger's vectors' in the interface plane satisfy the condition g玝=0. Considering the
g reflections used, both b=<100>a and b=<101>a satisfy these criteria. These
observations are consistent with those reported in the literature.23'25 As has been
discussed earlier, even if we confirm whether the misfit dislocations have [100] Burger's
vectors or [101] Burger's vectors, as has been done in previous research using high
resolution TEM,23 we still cannot accurately determine the relaxation mechanism using
this orientation, because the Burger's vector reaction l/2[101]a+l/2[101]a <� [100]a is
energetically equivalent in either the forward or reverse direction.23'25 These observations
serve as a baseline for comparison with similar observations for films grown on other
orientations and as a reference point indicating the similarity of our films to others
reported in the literature.
Fig.4.26 Plan view TEM images of misfit dislocations registered using a two-beam bright-field
image where g (the second beam) is the (100) reflection for the image on the left (a) and the
(010) is the reflection for the image on the right (b). The arrows depict the direction of the g vector
in each image.
115
One thing to note in these observations is that the long continuous dislocation
lines have a much wider separation between each other than the short segments. The
average distance between them is more than 500 ran. The in-plane lattice parameters
(calculated using X-ray diffraction for this 120 nm thick film) indicated that the film was
fully relaxed (a = b = 3.965 A a c = 3.962 A, for this (OOl)-oriented film). For a fully
relaxed Bao.6Sro.4Ti03(001) film on SrTiO3(100) substrate, which has a misfit of-1.4%
(using the value of the lattice parameter for our fully relaxed films deposited in these
conditions), the average distance between misfit dislocations should be approximately
20-30 nm, depending on the magnitude of the Burger's vector. The long continuous
dislocations, which have an average separation distance of ~ 500 nm, can only account
for less than 1/20 of the total misfit strain relaxation. The short dislocation lines that lie
between the continuous dislocation lines have average distance of about 25 nm. It is
reasonable to believe these dislocations account for the majority of the misfit strain
relaxation. These two sets of dislocations have different characteristics, such different
lengths and average distances; further investigations are needed to understand the
differences between these two sets of dislocations.
4.4.2 TEM observations of (HO)-oriented films
A low magnification, planview, on-zone-axis, bright-field TEM image taken from
a fully-relaxed epitaxial Bao.6Sro.4TiC>3(110) film on SrTiC>3(110) is shown in Fig. 4.27
(the growth conditions are as presented at the beginning of this section �4); the most
obvious contrast observed in the image arises from the dislocation network formed by
continuous long dislocation lines in the film-substrate interface. These misfit dislocation
lines lie along two directions that make a 109� angle with respect to each other. Using the
116
corresponding selected area electron diffraction pattern (SAEDP), shown in the inset and
described in the caption, the dislocation line directions can be identified as the
[111] and [111] directions.
1 pm
F/g. 4.27 Planview bright-field TEM image of the film-substrate interface of a relaxed epitaxial
(110)-oriented Ba0.6Sro.4Ti03 film deposited on SrTiO3(110) (see text for growth conditions). The
inset is the corresponding [110]-zone axis diffraction pattern, which gives the orientation of the
sample: the first peak to the right/left of the main spot is the (001)/'(001)reflection and the first
peak above / below the main peak is the (110)1(110) reflection.
Fig. 4.28 shows a planview bright-field TEM image, taken close to the zone axis,
taken under a higher magnification than that of Fig. 4.27. Short dislocation segments are
observed between the long continuous dislocation lines (the latter of which run along the
[111]and [111]directions). The line directions of the majority of the short segments are
along [110] direction.
117
Fig. 4.28 A planview TEM bright field image of the interface of Bao.6Sra4Ti03(110) grown on
SrTiO3(110) taken close to [110] zone axis at a higher magnification than that given in Fig. 4.27.
The arrow points along the [110] direction.
The predictions of the dislocation characteristics (line directions, angles between
traces in the film-substrate interface, Burger's vectors) based on the different relaxation
mechanisms (slip on different slip systems or climb) have been discussed in Chapter 3. In
this chapter, we will analyze the observations based on the graphical analysis shown in
Fig. 4.29. Fig. 4.29a shows (as the shaded plane) a (110) plane in a cubic structure (plane
ACDF). First we will consider the slip system <100>{010}, for Bao.6Sro.4Ti03(l 10) films
grown on SrTiC�110) substrates. Three {100} glide planes, including the (100), (010),
and (001), are operative in this system, meaning they intersect the (110) plane. In Fig.
4.29(a), these planes correspond to planes OCDG, OAFG, and OABC. Plane OCDG and
OAFG have traces on the interface plane along [001] direction (directions AF and CD)
and plane OABC has a trace along [110] direction (AC and DF). For the biaxial in-plane
strains applied by the substrate, only plane OCDG and OAFG can yield shear stresses
that have the possibility to drive dislocation glide to form misfit dislocations, since the
angle between these planes and the interface are not 90�. Since the (001) plane is
118
perpendicular to the (110) interface plane, there is no shear stress on this (001) plane;
dislocations can only move in this plane by climbing to the interface to release the strain.
Considering now the < 110 > {110} slip system, there are six {110} planes that
intersect the (110) and can operate to relieve misfit strain. The first is the interface plane
itself, or the ACDF plane. The second is the OBEG plane that is perpendicular to the
interface plane. The other four are the planes OAED, BCGF, OCEF, ABDG (in Fig.
4.29a) that are all inclined to the interface. Two of the inclined planes, BCGF (GCF in
Fig. 29b) and OAED (OAD in Fig. 29b), are shaded in Fig. 29b. Based on conventional
dislocation generation mechanisms, the misfit dislocations nucleate from the top surface
and then move to the interface; therefore, the interface plane cannot be the slip plane that
contributes to the misfit strain relaxation. Plane OBEG, which is perpendicular to the
interface, does not experience shear stresses; therefore, dislocations cannot glide on this
plane. Misfit dislocations can only move by climbing to the interface. Relaxation that
occurs by climb on this plane leave a trace in the interface plane along [001] direction
(AF direction). The inclined planes, ABDG, OCEF, BCGF, and OAED, corresponding to
(101), (101), (011), and (011), experience shear stresses under the biaxial misfit strains
and can relax by nucleation and glide of dislocations on these four {110} planes. These
four planes have their traces in the interface plane (110) along directions of [111]
and [111] directions, forming 109� angles with each other.
Now we will compare the predictions based on the two slip systems. Both systems
have the possibility of having dislocations with line vectors along the [001] directions?
one gliding on {100} planes and the other climbing on the (110) plane. The projections of
119
the two types of Burger's vectors on interface plane are both along [110] direction, which
are hard to identify from planview samples. Even if the Burger's vectors could be
determined, the same ambiguity arises based on the energetically equivalent dislocation
reactions already discussed for the (OOl)-oriented films. Therefore, analysis of the
dislocations running along the [001] does not help with identifying the basic relaxation
mechanism. One unique character of the <100>{010} system is that dislocation climb on
the (001) plane can yield a dislocation with a line direction (and trace in the interface
plane) along the [110] direction, which cannot happen in the < 110 > {110} slip system.
Dislocation glide based on the < 110 > {110} slip system can yield dislocations who leave
a trace along the [111] and [111] directions (AD and CF directions in Fig. 4.29d) forming a
109� degree angle (shown in Fig. 4.29d), and angle that cannot be realized based on
<100>{010} slip systems.
From the above TEM observations presented in Fig. 27 and Fig. 28, traces of
dislocations were observed along the [111] / [111] directions and the [110] direction.
However, the two sets of dislocations are distinctive from each other. The dislocations
along [111] / [111] directions are long continuous lines that are widely separated, while the
dislocations along the [110] direction are short segments. In addition, the average distance
between the long continuous dislocation lines are more than 200 nm, while the average
distance between the short dislocation segments along the [110] direction is about 30 nm.
Obviously, the continuous long dislocation lines lying along the [111] / [111] directions do
not contribute significantly to the majority of the misfit strain relaxation. Instead, the
120
short segments that are closely spaced to each other and run along the [110] direction
accommodate the vast majority of the misfit strain relaxation.
(c)
Cd>
Fig. 4.29 Schematic of the geometric arguments describing misfit dislocations slip systems in the
barium strontium titanate (110) film on SrTiO3(110) (see text for details), (a) shows the interface
plane as (110) in the standard unit cell, (b) shows two of the of the four {110} planes,
specifically the (011) and (Oil).
AD and CF are the traces of these two slip planes with the
interface, corresponding to the [111 J and fill
J. The other two sets of equivalent planes- COF
and ADG- are not shaded. For the case of the slip plane GFC, figure (c) shows the possible
Burger's vector direction's (GC) projection on the interface plane, or CH. CH is along the [112]
direction, (d) shows the projection of the dislocation line (the trace) and Burger's vector directions
on the interface plane (110). KD corresponds to the Burger's vector projection of the dislocation
with trace AD, and CH corresponds to the Burger's vector direction of the dislocation with trace
CF.
To analyze the Burger's vector on the dislocations along [111] / [111], one of the
slip planes corresponding to (011) plane, was chosen for analysis, as shown as plane CFG
in Fig. 29c. In plane CFG, the possible slip direction, or Burger's vector direction, would
121
be along the GC direction, corresponding to [Oil]. The projection of GC on the interface
plane would be CH, or along the [112] direction. From this geometrical analysis, [112] is
perpendicular to [111] (because their dot product is zero). As shown in Fig. 29d, there are
four equivalent planes that can yield misfit dislocations along [111] / [111]. Their Burger's
vectors will have projections either along [112] or [112] directions. It is possible to use
the two-beam condition in TEM with the reflections (111) or (111) as the second beam g
to test the Burger's vectors direction by the g籦=0 criterion.
Fig.4.30 (a) is a planview bright-field TEM image of misfit dislocations on zone-axis of [110]. (b) is
a two-beam bright field image when g is the reflection (111). (c) is a two-beam bright field image
when g is the reflection (111). The arrows in (b) and (c) point to the corresponding g vector
directions.
Fig. 4.30a shows a bright field image of the interface, close to zone axis; both sets
of dislocations along [111] and [111] are visible. When the (111) reflection (pointed out
with an arrow, along one set of the dislocation lines) is used for two-beam bright-field
imaging, as shown in Fig. 30b, one set of dislocations become very weak in intensity or
invisible. When the other (111) reflection is used for two-beam bright-field imaging, the
other set of dislocations becomes very weak in intensity or invisible (Fig. 30c). These
122
observations are consistent with the Burger's vectors being of the [110] type (see above).
Keep in mind that these dislocations to not provide a significant amount of the total
relaxation.
Fig. 4.31 The two beam bright field images of dislocations in the interface of Ba0.eSro.4Ti03(110)
and SrTiO3(110) under reflection of (110) (a) and (001) (b), respectively. The arrow points to the
direction of the reflections used.
For the short dislocation segments running along the [110] direction, a similar
analysis can be carried out. If they were generated by climb on the (001) plane, the
Burger's vector should be along [001] direction. Using the (110) reflection for g in the
two-beam TEM image, the dislocations should disappear; in contrast, using the (001)
reflection for g, the dislocation contrast should be strong. Such experimental observations
are presented in Fig. 31 and are consistent with this picture. In Fig. 31a, when the (110)
reflection was used to generate a two-beam bright-field image, the dislocation lines along
[110] vanish. In Fig. 31b, when the (001) reflection was used to generate a two-beam
bright-field image, the dislocations lines along the [110] exhibit a strong contrast. This is
consistent with the climb on the (001) plane of dislocations having a <100> type of
Burger's vector.
123
Dislocations along [001] directions have been observed in Fig. 4.31a under the
two beam condition using a reflection (110). As discussed earlier, these dislocations have
the possibility of being <110> and <100> types, studying their characters will still lead to
the circular argument of equally involving energetical degenerate dislocation reactions
(as presented in (OOl)-oriented films). Their existence is consistent with the x-ray
observation that the [110] direction is also relaxed. However, the Burger's vectors of this
set of dislocations are hard to identify precisely, so they will not be used to analyze the
relaxation mechanism.
Though relaxation seems to occur using both slip systems, the dislocations from
the<110>{110} slip system are not deemed to be primary players in the overall
mechanism to relax the strains, based on the spacing between such dislocations. Instead,
the dislocation that are generated by climb on the (001) plane with a Burger's vector
projection along the [001] are deemed to contribute to the major relaxation of the misfit
strains.
4.4.3 TEM observations of (lll)-oriented Bao.6Sro.4TiC>3 films
Observations on (110)-oriented films indicated that the <110> type of dislocations
were not the major mechanism for strain relaxation, instead <100> type of dislocations
play the major role. Relaxation mechanism in (lll)-oriented films will be studied as a
controlled experiment to check the consistency. A planview bright field TEM image
taken close to the zone axis from a fully-relaxed epitaxial Bao.6Sro.4TiC>3(lll) film on
SrTiC>3(l 11) is shown in Fig. 4.32 (the growth conditions were presented at the beginning
of this section �4) to show the interface of the film and substrate. The most obvious
contrast is the triangular network of long continuous lines interpreted as dislocations. The
124
long continuous misfit dislocation lines intersect each other at an angle 60�. Using the
[111] zone axis selected area electron diffraction pattern, given in the inset of Fig. 4.32
(and which was calibrated for the rotation between the diffraction pattern and the image),
the misfit dislocation lines were determined to be along the < 121 > directions. A second
contrast seems to exist at a finer lengths scale on the uniform grey background between
the long continuous dislocation lines.
Fig. 4.32 Planview bright field TEM image of the interface from the Ba0.6Sro.4Ti03(111) film grown
on SrTi03(111). The inset is the corresponding [111] zone axis diffraction pattern; with the first
"circle" of spots are {110} reflections and the second "circle" of spots are {121}
reflections.
The dashed line is a guide for the eyes to see that one of the < 121 > direction is parallel to one
of the long continuous misfit dislocation line directions.
A higher magnification bright field image of the interface is given in Fig. 4.33.
The thick continuous lines in this image are the same type of lines observed in Fig. 4.32.
The finer length scale contrast observed in Fig. 4.32 is observed to be short line segments
in Figure 4.33, which are scattered between the long continuous lines. The thick
continuous lines can be used as a reference for identification of directions when the
image is taken close to zone axis. Unfortunately, the short segments have their lines
following irregular directions, and some of them demonstrated features resembling to
bundles of dislocations. These lines have the possibility to be low angle grain boundaries,
125
which makes it challenging to precisely determine the characteristics of the dislocations
such as line directions and Burger's vectors. In order to understand the relaxation
mechanism, the threading dislocation can be used to characterize the dislocations,
because the threading dislocations should have the same Burger's vector as the misfit
dislocations have.
Fig. 4.33 A higher magnification of the bright-field TEM image of the planview specimen showing
the interface of the Bao.6Sro.4Ti03(111) films on SrTi03(111). The thick continuous lines are the
same as those observed in Fig. 4.32.
Because the line directions of the short misfit dislocations segments were not well
defined for the (11 l)-oriented films, threading dislocations (which are believed to exist as
the result of the nucleation and motion of dislocation from the surface to the interface)
were characterized using high resolution TEM (HRTEM). Fig. 4.34a shows a HRTEM
image taken from the (lll)-oriented Bao.6Sro.4Ti03 film (there is no substrate in this
image). The cores of two threading dislocation are pointed out by the arrows. Fig. 4.34b
shows the inversion of the fast Fourier transformation (FFT) of the original TEM image
(given as the inset of Fig. 4.34a), which simplifies the determination of a Burger's circuit
around the dislocation cores. The circuits show that both dislocations have Burger's
vectors of < 121 > directions (in this plane). Considering that the HRTEM only gives the
projection of the Burger's vector on the (111) plane, and by examining the geometries
126
given below in Fig. 4.35, one can determine the Burger's vector. <100> Burger's vectors
should have a projection along the < 121 > direction, as observed in Fig. 4.34b. <110>
Burger's vectors should have a projection along the < 110 > directions, which are not
observed in the image.
Fig. 4.34 (a) A high-resolution planview TEM image of the Bao.eSroAT^fl 11) epitaxial film
grown on a STO(111) substrate (the growth conditions are given earlier).This image contains only
the film and two threading dislocations are pointed out with arrows, (b) An image formed by
inverting the fast Fourier transform of the image given in (a). Burger's circuits are drawn around
the two dislocations and the Burger's vectors are marked with black arrows. Both dislocations
have Burger's vector direction of < 121 >. The inset is the fast Fourier transform, which can be
used to identify the orientations. Note the first circle of spots in the FFT corresponds to the
{110} reflections and the second circle corresponds to the {121} reflections.
To understand the above analysis, geometrical schematics of Bao.6Sro.4Ti03(lll)
films grown on SrTiOs(l 11) are presented in Fig. 4.35. As has been addressed in Chapter
3 and shown in Fig. 4.35 for (lll)-oriented Bao.6Sro.4Ti03 films grown on SrTi03(lll),
misfit dislocations based on the slip system <100>{010} have the possibility of gliding
127
on the three <10O> planes, specifically the (100), (010), and (001), corresponding
respectively to the planes OBC, OAC, and OAB in Fig. 4.35b. These three planes have
traces in the interface plane (111) along [011], [101], and [110] directions, corresponding
respectively to the BC, CA, and AB directions in Fig. 4.35b. These traces form a
triangular network of dislocations intersecting each other at 60� angles. In this case, the
possible Burger's vectors are the <100> directions, corresponding to OA, OB, and OC in
Fig. 4.35b. The projection of the Burger's vector in the interface plane (111) should be
along the < 121 > directions, which are respectively the AE, BF, and CD directions in
Fig. 4.35e. The observed traces of the long continuous dislocation lines are not in
agreement with this glide mechanism on this slip system. Instead the observation of
Burger's vector projection along < 121 > i n Fig. 4.34a and b are in agreement with this
dislocation glide mechanism. If we believe the two dislocations shown in Fig. 4.34
represent most of the short dislocation segments, it is reasonable that the majority of the
strains were relaxed by <100> type of dislocation glide.
Based on the < 110 > {110} slip system, there are six {110} planes that can operate.
Three of them, the (110), (101), and (011), are shown in Fig. 4.35c as shaded planes,
respectively the ABGD, ACGF, and BCDF planes. These three planes have traces in the
interface plane (111) along the [110], [101], and [011] directions. However, the possible
Burger's vector directions are in the same directions as the line directions, which makes
these dislocations pure screw type. Pure in-plane screw dislocations do not contribute to
the in-plane strain relaxation, and can be ignored in the relaxation mechanism. The other
three {110} planes, the (110), (101), and (011), are shown in Fig. 4.3 5d respectively as
128
(c)
(d)
(e)
Fig. 4.35 Schematic of the slip system geometries for barium strontium titanate films grown on
SrTi03(111) substrates, (a) the (111) plane is shaded in the unit cell as the plane ABC. (b) the
three {100} planes OAB, OBC, and OAC are shaded and highlighted in a fashion indicating their
intersection with the (111) plane ABC. (c) the shaded planes ABGD, BCDF, and ACGF are
highlighted in the unit cell and they represent three {110} planes- respectively the (110), (011),
and (101). (Glide on these systems produce pure in-plane screw components to the Burger's
vector and the traces are in <110>
directions.) (d) the shaded planes OAE, OCD, and OBF,
represent the other three {110} planes, respectively the (Oil),
(110), and (101), which are
perpendicular to the (111) planes. (The misfit dislocations can only climb to the (111) interface
and the traces are in the [112 J, [121J, and [211J directions, (e) shows the traces from the
dislocation motion to the interface of the system shown in (d), highlighting the [112J,
[121J,
and [211] directions on the interface (111) plane, respectively the AE, CD, and FB directions.
the planes AOE, BOF, and COD. These planes are all perpendicular to the (111) plane
and they have traces along directions, [112], [121], and [211], corresponding respectively
129
to the CD, BF, and AE directions in Fig. 4.34e, forming triangular misfit dislocation line
network at 60� to each other. In this case, this set of misfit dislocation cannot move to the
interface by glide, because of absence of shear stresses, but only by climb. The long
continuous lines observed along the [112], [121], and [211] directions are consistent with
these traces, which generally does not produce such long straight lines.23'24'27 However,
The number of this type of dislocations are low enough that they do not account for the
major strain relaxation. To understand how the two set of dislocations come into place,
further work needs to be done (as described next).
4.4.4 Further investigations and discussion of the relaxation mechanism in BST
4.4.4.1 Long Continuous Dislocations
From the above-described TEM observations for films of all three orientations,
two sets of distinct types of misfit dislocations were observed. One set of dislocations
were long continuous lines that were widely separated from each other, and therefore
cannot account for the majority of the strain relaxation for these fully relaxed films. The
other set of dislocations were short line segments (possibly loops) that are closely spaced
and that can account for the majority of strain relaxation in the relaxed films. On the
other hand, a simple complete picture did not develop from these experiments in as clear
a fashion as once could hope. Nevertheless, the simplest picture that can be presented
starts with the following: the long continuous dislocations are always consistent with the
< 110 > {110} system (we will return to discuss the short segments later). For the (110)oriented and (lll)-oriented films, this interpretation is unambiguous. Though the
interpretation is ambiguous for the (OOl)-oriented films, the "by-analogy" interpretation
is compelling. Interestingly, <110> dislocations can glide to the interface on this system
130
for the (001)- and (110)-oriented films, but they must climb to the interface for the (111)oriented films.
Because these long continuous dislocations do not appear to relax a significant
portion of the films misfit strain, we explored the possibility that these misfit dislocations
were inherited from the substrates.
Planview TEM specimens of the three orientations were prepared and Fig. 4.36 a,
b, and c gives respectively the bright-field TEM images of the SrTiC>3(100), SrTiO3(110),
and SrTi03(l 11) substrates. In SrTiC>3(100) (Fig. 4.36a), long line features were observed
and these lines are lying along <100> directions. If we compare the dislocations shown in
Fig. 4.35a to those long continuous lines in the film-substrate interface shown in Fig.
4.26a and b, we notice that the average distance between these lines in substrate is about
several microns while the average distance between the long continuous dislocations in
the film-substrate interface is about 200 nm. Obviously those long dislocation lines
observed in the film-substrate interface are higher in density than those that exist in the
substrate, though the types are consistent.
Fig. 4.36 Planview bright field TEM images from the (a) SrTiO3(100), (b) SrTi03(110), and (c)
SrTi03(111) substrates. In (c), the inset shows the selected area electron diffraction pattern.
131
The (110) substrate is very defective. Fig. 4.36b gives the bright field image of a
SrTiO3(110) substrate. The dislocations in the SrTiO3(110) substrates do not follow a
regular pattern of line directions, unlike those in the (100) and (111) SrTi03 substrates.
This can be explained if the region imaged in Fig 4.36b is from a slip-band region. In
fact, slip-bands were also observed in the SrTiO3(100) crystal, an example of which is
shown in Fig. 4.37. A high density of dislocations was observed to be concentrated
within a thick band in that image. The dislocation density around these areas is several
orders of magnitude higher than in the rest of the crystal and the dislocations are curved
and entangled, for both the (110)- and (OOl)-oriented crystals.
Fig. 4.37 A bright-field TEM image of a slip-band that was observed in a SrTiO3(100) crystal. The
inset gives the selected area electron diffraction pattern. The slip band is along [100] direction.
Such slip bands are believed to be generated during crystal growth. Owing to the
strain fields generated in the Verneuil growth method, which is typically used for SrTiC>3
single crystal growth,28 the crystal deformed along many parallel slip planes in a specific
region of the crystal at growth temperature or during cooling; these deformed regions are
called slip-bands.29 It can be seen the plane the slip happened on was (100) plane. When
the crystal is cut to expose the (110) plane, it has high possibility to cut through the slip
132
band and leaving high dislocation density in the crystal. When the defects in substrate are
compared to those in the film- SrTiO3(110) interface, those long continuous misfit
dislocation lines that form 109� network are not observed in the substrate itself, neither
are those short segments along [110] directions. It is reasonable to believe that these
dislocation features observed in the interface came from the strain relaxation process
during growth, though the dislocations may have been inherited from the substrate.
When the SrTi03(lll) substrate is examined as shown in Fig. 4.36c, dislocation
lines are observed, and their line directions are identified along [112], [121], and , [211]
using selected area electron diffraction (whose pattern is given as the inset). Actually,
these defects can be understood as the projection of those line features observed in
SrTiC>3(100) along <100> directions. When <100> directions project on (111) plane, the
projections will be [112],[121], and [211]. Again, because the dislocations in substrates
are short segments while the ones in the film-substrate are much longer, and increase in
the density of these types of dislocations occurs on film growth, but they do not
correspond to the major strain relaxation mechanism. And those short curly segments
observed infilm-substrateinterface are absent from the substrate itself, which means they
definitely are formed during film growth.
From the length and density differences between the two sets of misfit
dislocations, it is reasonable that they came from different generation mechanisms. A
model can be proposed to explain this is: these <110> types of dislocations arise from
pre-existing dislocations inherited from the substrate. When Bao.6Sro.4Ti03 films were
grown on SrTiCb substrates, the <110> dislocations were inherited into the films,
133
generally as straight segments to reduce the line tension. As the film thickness increases,
stresses accumulate; when the shear stress overcomes the tension of the dislocations, the
dislocation can bow and move to the interface forming misfit dislocations and increasing
the overall dislocation density.30 The schematic of the process is presented in Fig. 4.38.
This mechanism has been discussed in Matthew and Blakeslee's paper.30 Existence of
<110> dislocations has been discussed in the literature, and their density is supposed to
be low,28 which is consistent with the low density of this type of dislocations observed in
this research. Furthermore, as Sun's papers have shown,24'27 long continuous lines came
into being at the very beginning of growth (or relaxation) and then those short segments
appeared, consistent with this proposed mechanism. On the other hand, these dislocations
glide to the interface for the (OOl)-oriented films, but they climb to the interface for the
(110)- and (11 l)-oriented films. This argues that climb can be a significant contributor to
dislocation motion for relaxation in these films and that the length of the dislocation line
is more related to where it originated then how it moved (long lines are inherited and
short lines nucleate from the surface).
When the inherited dislocations are used up or they no longer able to move owing
to increased critical stresses (forces) for motion, this mechanism will stop working. The
accumulated strain energy will continue to increase as the film thickness increases. Then,
a much higher number of misfit dislocations have to be introduced to relax the strain and
a new mechanism kicks in: dislocation nucleation from the film top surface and their
motion to the interface to form misfit dislocations.30'31
134
/b
a
Film
\,f__
Substrate
Fig. 4.38 Schematic of the formation of misfit dislocations from dislocations inherited from the
surate. (a) the initial straight line is shown as dotted line, (b) when the accumulated stresses
overcome the dislocation tension, the dislocation starts to bow out as shown in the dotted line, (c)
when the dislocation bows to the interface, misfit dislocations are formed.
4.4.4.2 Short Line Segment Dislocations
As stated above, no clear picture developed for the nature of the short dislocation
lines except that these dislocation lines accounted for the majority of the relaxation of the
misfit strains. Essentially, it is believed that the short dislocations nucleated at the surface
of the films and move to the substrate interface to relax the misfit strain (this will be
confirmed later based on evidence obtained on films with low concentrations of inherited
defects). Unraveling the nature of these dislocations has proven challenging. On
SrTiC>3(100) substrates, the short-segment misfit dislocations in the (OOl)-oriented
barium strontium titanate epitaxial film cannot be distinguished in terms of their
formation mechanism; they can be consistent with either slip system. On SrTiO3(110)
substrates, the short-segment misfit dislocations in the (HO)-oriented epitaxial
Bao.6Sro 4T1O3 film are consistent with the <100>{010} system where the dislocations
135
climb to the interface, which is also a possible mechanism for relaxation of the (001)oriented film.
On SrTi03(lll) substrates, the short-segment misfit dislocations in the (111)oriented epitaxial Bao.6Sro.4Ti03 film are complex, however the observation of that
threading dislocations have a Burger's vector projection on the (11 l)-plane along < 121 >
directions which indicates that the misfit dislocations should belong to the <100>{010}
family. If <100>{010} slip system is active, then the simplest story is that the short
segments belong to the <100>{010} family on all three orientations and their motion
occurs by both glide and climb, depending on the orientation.
The proposed model is supported by the comparison experiment carried out for
(HO)-oriented Bao.6Sro.4Ti03 films grown on NdGaO3(100) substrates, described now.
NdGaO3(100) is a very high quality crystal, similar to GdScC>3 in terms of its rocking
curve width, which is an indication of the dislocation density. Therefore, very few
dislocations are expected to be inherited from the substrate. Fig. 4.39a gives the bright
field image of the interface of a (HO)-oriented Bao.6Sro.4Ti03 film on a NdGaC>3(100)
substrate, taken close to the Bao.6Sro.4Ti03[110] zone axis. In this film, there are no long
continuous lines, unlike those observed in (HO)-oriented Bao.6Sro 4TiC>3 on SrTiC>3(110)
that made a 109� angle with one another. The two beam bright field image corresponding
to reflection of (001), given in Fig.4.39b, demonstrated that the dislocation lines along
[110] still exist as short segments, consistent with the slip system <100>{010} and climb
to the interface, similar to the short segments in the films deposited on SrTi03(l 10).
136
Fig. 4.39 (a) bright field planview TEM image of the interface of (110)- Bao.6Sro.47703 film grown
on NdGaO3(100). The image was taken under a condition close to Bao.eSro.4Ti03 [110] zone axis.
(b) The two beam bright field image of the interface with g = (001); dislocation lines along [110]
were revealed.
As it has been discussed above, this set of dislocations are consistent with the
<100> dislocations that moved to the interface by climb. This set of observations is
consistent with the model proposed that the long continuous lines are from the bowing
out of inherited <110> type of dislocations and the short segments are formed by
nucleation of <100> types at the top surface and their climb to the interface.
This two-step relaxation mechanism is consistent with the report that the majority
of the misfit dislocations have <100> Burger's vectors, as characterized using crosssectional HRTEM.23 This model can explain why both <100> and <110> type of misfit
dislocations were observed in the BaTiCh films grown on SrTiC>3 and the majority of the
HRTEM identified misfit dislocations were <100> type.23 This model does not need to
involve the complex dislocation reaction process described previously (which ignores the
137
nature of the core of the dislocations which could shift the energetic of the reactions in
the specific directions37) and is consistent across orientations.
4.4.5 Summary of film relaxation mechanisms
The misfit dislocations in the interfaces of Bao.6Sro.4TiC>3 films grown on three
differently oriented SrTiC>3 substrates, (001), (110), and (111) have been investigated.
The misfit dislocation characteristics were compared to the predictions made based on the
geometry of two slip-systems, the <100>{010} and the <110>{110}, and the interface
planes. The TEM results show that two sets of dislocations were observed for all films
grown on SrTiC>3. One set of dislocations were observed as long continuous lines that
were widely separated and accounted for only a small fraction of the misfit strain
relaxation. The second set of dislocations was observed as small line segments that were
closely separated and accounted for the majority of the misfit strain relaxation. The
simplest interpretation of these observations is as follows. The first set of (long
continuous) dislocations belong to the
< 110 > {110} slip system, which was
demonstrated in an unambiguous fashion on the (110)- and (lll)-oriented films, and is
one of two possible explanations for the (OOl)-oriented films. On the (110)- and (111)oriented films, these dislocations glide to the interface on the (HO)-oriented films while
they climb to the interface on the (lll)-oriented films, indicating both motion processes
can be active during the relaxation process. Therefore, <110> types of dislocations
should have no problem gliding to the interface on the (OOl)-oriented films. The second
set of (short segmented) dislocations belong to the <100>{010} system. This was
demonstrated unambiguously for the (HO)-oriented films, is one of the ambiguous
138
interpretations on the (OOl)-oriented films, and agreed with the Burger's vector analysis
of threading dislocations on the (lll)-oriented films (though their traces in the interface
plane were too complex to interpret simply). On the (OOl)-oriented films, these
dislocations climb to the interface, on the (HO)-oriented films these dislocations climb
for one set of parallel dislocations and glide for the other set of parallel dislocations (that
are normal to the first set), and on the (11 l)-oriented films these dislocations glide to the
interface. All of these observations indicate that the process of dislocation motion, either
glide or climb, does not control the type of dislocation observed in the interfaces. The
existence of both types of dislocations also argues that the energetics are close for the two
systems and that the formations mechanism (inheritance or nucleation) controls the type
of dislocations observed. It appears that the nucleation of <100>{010} dislocations is
preferred on all orientations (whether it is thermodynamic or kinetic remains unclear).
Observations of similar films grown on higher quality (lower dislocation content)
substrates of similar orientations allowed for the removal of the observation of the first
set of (long continuous inherited) dislocations but retained the primary misfit dislocations
accounting for strain relaxation, and these were still consistent with the <100>{010}
family.
By studying the relaxation mechanisms of Bao.6Sro.4Ti03 films grown on different
orientations, it has been found that the defects in substrates affect the relaxation process.
The defects inherited from the substrates can participate in the strain relaxation process
and affect the defect characteristics. When substrates are chosen for the purpose of
dielectric property comparison, it is helpful on screening the appropriate substrates during
139
the experiment. In (HO)-oriented Bao.6Sr0.4Ti03 films, understanding the relaxation
mechanism will help to understand the in-plane strain anisotropy. The strain anisotropy
might affect the dielectric properties because of the coupling between strain and
polarization.22 However as a control experiment to study the effect of homogeneous and
inhomogeneous strains on dielectric properties, it is ideal to minimize the complexity
involved. In (HO)-oriented Bao.6Sro.4Ti03 films, the strain anisotropy related the
relaxation mechanism would further complicate the issue. For (111) orientation, the
dislocation geometry makes them mixed dislocations in the plane of the substrate. The
screw component will make the strain analysis complicated when it is correlated to
dielectric properties. In the dielectric property experiments, to understand how
dislocation density and homogeneous strain affect the dielectric properties, (OOl)-oriented
films were used. In (OOl)-oriented films, the relaxation process in the two in-plane
directions are isotropic and involve pure edge dislocations in-plane. For the purpose of
experimental control, understanding the <100> dislocation climb mechanisms during
strain relaxation is also helpful to consider the kinetic process of dislocation climbing
during experimental design.
4.5 Lattice parameters of films
To determine the bulk lattice parameter of the Bao.6Sro.4Ti03 target, the
Bao.6Sro.4Ti03 ceramic target used for the film growth was characterized using X-ray
diffraction. Fig. 4.40a shows the XRD pattern from the ceramic target. The measured
lattice parameter from the Bao.6Sro.4Ti03 ceramic target is 3.954�002 A (unit cell
volume ~ 61.817 A3). This is slightly smaller than expected from the theoretical
calculation 3.996x0.6+3.905x0.4=3.960 A.
140
Substrate Si
(b)
110)(111)(200)
I
20
30
40
50
GO
70
80
90
20
2 Theta( Degree)
30
40
50
60
70
SO
2 Theta (Degree)
Fig. 4.40 (a) theta-2theta x-ray diffraction scan of the Bao.6Sro4Ti03 ceramic target used forPLD
growth, (b) theta-2theta x-ray diffraction scan of a Bao.6Sro.4nO3 films grown on an annealed Si
substrate (the Si was treated thermally for 1200癈 in air for 48 hours), illustrating some weak
texture.
As has been discussed, the deposition oxygen pressure affects the lattice
parameter of the films owing to increased populations of point defects and, possibly, nonstoichiometry. To determine the strain-free (free-standing) lattice parameter of films
deposited at specific oxygen pressures, Bao.6Sro.4Ti03 films were grown at 300 mTorr
oxygen pressure (UHP O2, other conditions have been described in �2.3) on Si
substrates which had been annealed in air at 1200癈 for 48 hours to oxidize the top Si
layer into amorphous layer. Fig. 4.40b shows the XRD pattern of one such film. Though
the intensity ratios between theta-2theta reflections were not exactly as the peak ratios
from the ceramic target (Fig. 4.40a), indicating that the film was slightly textured, we
assume the measured lattice parameters were close to thefree-standingcondition;21 it will
be used as a rough reference to estimate the strain state in the epitaxial films grown on
other substrates under the same conditions. The calculated "free-standing" Bao.6Sro.4TiC>3
lattice parameter is about 3.959�002 A (unit cell volume -62.052 A3), which is slightly
bigger than the lattice parameter calculated from the ceramic Bao.6Sro.4TiC>3 target
141
(3.954�002A). The unit cell volume difference can be attributed to the generation of
point defects, possibly oxygen vacancies, cation vacancies, anti-site defects, or
complexes of these items.20 Annealing did not change the lattice parameter significantly,
indicating that the defects are not likely simple isolated oxygen vacancies.
Table 4.1 Lattice parameters and high resolution x-ray rocking curve full width at half-maximum
(FWHM) of Bao.6Sr0.4Ti03 films grown on different substrates. These films are deposited at
300mTorr oxygen pressure (the repetition rate was 1 Hz) with nominal thickness values of about
120 nm (except the film on DySc03 which is 300 nm).
Substrate
Material
Filmc
Film a
(A)
(A)
MgO(100)
GdScO3(110)
3.953
3.957
DyScO3(110)
LSAT(100)
NdGaO3(110)
LaAIO3(100)
3.970
3.962
3.962
3.958
3.965
3.965
3.968
3.944
3.959
3.958
3.957
Film c/a
Unit Cell
Volume
3
Residual
Strains
0.996
0.998
62.146
62.256
1.006
1.001
1.001
1
61.754
62.099
62.068
61.974
(A )
FWHM of Film
Rocking Curve
+0.2
+0.2
FWHM of
Substrate
Rocking Curve (�)
0.034
0.006
-0.33
=0
=0
=0
0.004
0.011
0.006
0.06
0.005
0.016
0.02
0.183
(%)
n
0.617
0.008
Lattice parameters of 120 nm thick Bao.eSro/TiOs films grown on different
substrates (expect for the 300 nm film grown on DyScCb due to laser window change) at
300 mTorr oxygen pressure were measured using x-ray diffraction theta-2theta scans of
symmetric (psi = 0) and asymmetric (psi ^ 0) reflections, or reflections containing both
out-of-plane and in-plane components. The precision of the measurement was about
�002 A. The film Bragg angles used to calculate lattice parameters were calibrated
using substrate peaks as references. The in-plane and out-of-plane lattice parameters of
films are listed in Table 4.1. In-plane lattice parameters of Bao.6Sro.4Ti03 films grown on
both GdScO3(110) and DyScO3(110) matched those of the substrates (within
experimental error of �002 A), indicating that the films were still fully strained. The
Bao.6Sro 4TiC>3 film on GdScCb is under +0.2% tensile strain and the film grown on
142
DyScC>3 is under -0.33% compressive strain. The films grown on MgO almost have the
same in-plane lattice parameter as the Bao.6Sro.4Ti03 film grown on GdScOs. The unit cell
volumes of the Bao.6Sro.4Ti03 films grown on GdScC>3 and MgO are bigger than the bulk
Bao.6Sro.4TiC>3 unit cell volume of 62.052 A3. The in-plane lattice parameter of
Bao.6Sr0.4Ti03 films grown on DyScC>3 has a smaller unit cell volume of 61.754 A3 than
that of bulk Bao.6Sro.4Ti03, 62.052 A3, and the c/a>l, which is consistent with the
presence of compressive biaxial strain.22"25 For Bao.6Sro.4TiC>3 films grown on
(Lao.i8Sro.82)(Alo.59Tao.4i)03, NdGa03, and LaA103, the in-plane lattice parameters are
close to the free-standing value and c/a ~ 1. The strains are almost fully relaxed at this
thickness.
4.6 Film quality examination
In the literature, rough threading dislocation density estimates have been
calculated by plotting high resolution X-ray rocking curve full-width-at-half-maximum
values as a function of the corresponding Bragg angles.18'26 This approach has often been
applied to semiconductor films that have film thicknesses of above 1 or 2 microns in
which the x-ray peak broadening caused by film thickness effect, or the so-called Scherer
effect, can be neglected.26"28 For the films in current study with thickness ranging from 50
to 300nm, the film size effect is unclear for those reflections containing both in-plane and
out-of-plane components; therefore, the process of calculating dislocation density using
x-ray rocking curves is complicated.27,28 Nevertheless, high resolution x-ray rocking
curves were used as a qualitative comparative parameter of film crystalline quality when
the film thickness was kept constant and the same reflections were used.27 Table 4.1 lists
the rocking curve widths measured from the Bao.6Sro.4Ti03 films grown on different
143
substrates. They generally follow the expected trend that the higher was the mismatch,
the larger the FWHM of the rocking curve.
BST/GdScOj (110)
6xl0 9 /cm 2
BST/DyScO3(110)
2xl0 1 0 /cm 2
BST/LSAT(100)
1.5xlO u /cm 2
Fig. 4.41 Planview bright-field TEM images of of 120nm thick Bao.6Sro.4nO3 films grown on
GdScO3(110), DyScO3(110), (Lao.18Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), LaAIO3(100), and
MgO(100). The samples are tilted to reveal the dislocation lines. The dislocation densities
calculated by counting the number of lines per unit area are also given in the images.
Planview TEM was used to determine the dislocation densities and to compare
these with the rocking curve FWHMs. The planview TEM samples were prepared by
mechanical polishing from substrate side using SiC sand papers. After the thickness
reached 20um, the samples were glued on copper grid and ion milled from the substrate
side till perforation. During the process, the film side was protected from contamination
using wax, which was removed after sample preparation.
Fig. 4.41 gives the representative planview TEM images of the Bao.6Sro.4Ti03
films grown
on
GdScO3(110),
DyScO3(110),
(Lao.i8Sro82)(Alo59Tao.4i)03(100),
NdGaO3(110), LaAlO3(100), and MgO(lOO). The dominant types of dislocations were
144
threading ones extending along the growth direction (or the sample surface normal). The
samples were intentionally tilted in TEM to reveal dislocation lines. The dislocation
densities in the films were determined by taking the average of counts from five images
taken on each sample. The dislocation concentration in Bao.6Sro.4Ti03 film grown on
GdScC>3(110) is about 6xl09cm"2. The dislocation concentrations in Bao.6Sro.4Ti03 films
grown on DySc03(l 10) is about three times higher than the films on GdScC>3, or 2xl0 10
cm"2. For Bao.6Sro.4Ti03 films grown on (Lao.i8Sro.g2)(Alo.59Tao.4i)03(100), NdGaO3(110)
and LaAlO3(100), their dislocation concentrations are on the order of 1011 cm"2, which are
one or two orders of magnitude higher than that in Bao.6Sro.4Ti03 films grown on
GdScCb. For Bao.6Sro.4TiC>3filmsgrown on MgO, the films are textured; therefore, grain
boundaries are observed in both the planview TEM sample (Fig. 4.41 and Fig. 4.19) and
cross-sectional TEM image (Fig. 4.16). The complex image contrasts in the planview
TEM images make it impossible to count dislocations with any reasonable precision.
The dislocation densities are listed in Fig. 4.41. Comparing these numbers with
the rocking curve FWHMs listed in Table 4.3, one can find a monotonic relationship
between the two. Both values also increase with the increasing lattice mismatch. Films
discussed here will be useful
in distinguishing between homogeneous and
inhomogeneous strain effects on properties.
4.7 Conclusions
In this chapter, substrate treatment processes were studied and optimized for the
film growth by chemical etching and thermal annealing. For substrates SrTiO3(100),
LaAlO3(100), GdScO3(110), DyScO3(110) and NdGaO3(110), atomically flat surfaces
were produced by 40 second BHF etch followed by 1000癈 annealing for 2 hours in air.
145
(Lao.i8Sro.82XAlo.59Tao.4OO3 is good for growth just by etching for 1 minute in
HC1:H20=1. Various annealing conditions have been attempted on MgO substrates and it
was found that clear steps are achieved when the substrate is annealed at 1350癈
annealing in air for 4 hours.
Bao.6Sro.4Ti03 thin films have been deposited on the treated substrates using
pulsed laser deposition. Their growth modes were investigated at different growth
conditions using ex-situ AFM and RHEED. Bao.6Sro.4Ti03 films growth on MgO always
occurred in 3-D island growth mode due to the large lattice mismatch; columnar
structures were observed in cross-sectional TEM images. Bao.6Sro.4Ti03 films deposited
on
GdScO3(110),
DyScO3(110),
SrTiO3(100),
(Lao.i8Sro.82)(Alo.59Tao.4i)03(100),
NdGaO3(110), and LaAlCtylOO), in general, had rms roughness values lower than a
Bao 6Sro.4Ti03 unit cell height, indicating 2D nucleation layer-by-layer mode. (110),
(lll)-oriented Bao.6Sro.4Ti03 films were also deposited on corresponding orientation of
LaA103, SrTi03 and NdGa03 substrates. They all demonstrated low surface roughness
indicating 2D terrace nucleation layer-by-layer growth mode.
Epitaxial relationships were investigated using both out-of-plane X-ray diffraction
theta-2theta scans and phi scans (or pole figures) of asymmetric reflections containing inplane components. Bao.6Sro.4Ti03 films grown on MgO were (OOl)-textured, containing
some regions of (lll)-orientated film. All the other (OOl)-oriented films grown on
GdScO3(110),
DyScO3(110),
SrTiO3(100),
(Lao.i8Sro.82)(Alo.59Tao.4i)03(100),
NdGaO3(110), and LaAlO3(100) substrates were epitaxial to the substrates at the
deposition oxygen pressure ranging from 1 mTorr to 300 mTorr. All the (110) and (111)oriented films grown on SrTi03, LaA103, and NdGa03 were epitaxial to the substrates
146
when they were deposited at 300mTorr. Epitaxial films make it simpler to investigate the
strain relaxation mechanism and later the dislocation effect on dielectric properties.
Bao.6Sro.4Ti03 film strain relaxation mechanisms in (001)-, (110)-, and (111)oriented Bao.6Sro.4Ti03 films were discussed by comparing the experimentally observed
dislocation characteristics to the predictions made based on the film geometry and two
possible slip-systems. Two sets of dislocations were observed for those films grown on
SrTiC>3(100), SrTi03(l 10), and SrTiC>3(l 11). One set was observed to be long continuous
lines that were widely separated and accounted for a small fraction of strain relaxation.
These dislocations were consistent with < 110 > {110} slip system; for the (110)- and
(11 l)-oriented films this was unambiguous, but the standard level of ambiguity remained
for the (OOl)-films. Depending on the orientation, these dislocations either glided or
climbed to the interface. It is believed that these dislocations are inherited from the
SrTi03 substrates; indeed, higher quality substrates having fewer dislocations did not
exhibit this set of dislocations. The second set was observed to be short segments that
were closely spaced and accounted for the majority of the misfit strain relaxation. These
dislocations were consistent with the <100>{010} system on all orientations, including
other substrates than SrTi03. It is believed that the second set of dislocations nucleate
from the film's top surface, and then they move to the interface by glide or climb,
depending on the orientation. It is believed that the formation mechanism (inheritance or
nucleation) dictates the type of dislocation instead of the motion process, since both glide
and climb are observed for both systems. Understanding the relaxation mechanism helps
with the experiment design on substrate choices, substrate orientation selection and the
147
control of the film thicknesses to make the property vs. microstructure correlation
analysis easier.
120 nm thick (OOl)-oriented Bao.6Sro.4Ti03 films were grown on GdScO3(110),
DyScO3(110),
SrTiO3(100),
(LacsSro^XAWTa^OO^lOO),
NdGaO3(110),
and
LaAlO3(100) for dielectric property measurement. The in-plane and out-of-plane lattice
parameters of these films were measured. Bao.6Sro4Ti03 films grown on GdSc03 and
DySc03 were coherently strained to the substrates within the limit of measurement
technique; Bao.6Sro.4Ti03 on GdSc03 was under +0.2% tensile strain and BST on DySc03
was under -0.33% compressive strain. Room temperature lattice parameter measurement
demonstrated that the Bao.6Sro.4Ti03 film grown on MgO was also under tensile strain
(+0.2%), the same as the Bao.6Sro.4Ti03 films grown on GdSc03. The lattice parameter
measurements
indicate
that
the
Bao 6Sr0.4TiO3
films
grown
on
(Lao.i8Sro.82)(Alo.59Tao.4i)03, NdGa03, and LaA103 were fully relaxed.
The film crystalline quality and dislocation, concentrations were estimated using
high resolution X-ray diffraction and TEM. Bao.6Sro.4Ti03 films grown on GdSc03(l 10)
had the lowest dislocation concentrations, 6x109 cm"2. The dislocation concentration in
Bao.6Sro4Ti03 films grown on DyScO3(110) was 2x1010 cm"2, which is about three times
higher
than
the
films
on
GdSc03.
For
Bao.6Sro.4Ti03 films grown
on
(Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), and LaAlO3(100), their dislocation
11
0
concentrations were on the order of 10 cm", which are one or two orders of magnitude
higher than that in Bao.6Sro4Ti03 films grown on GdSc03. Both the rocking curve
FWHMs and dislocation concentrations increased as the lattice mismatch increased,
148
which is consistent with the hypothesis. The correlation between film microstructures and
dielectric properties will be discussed in the next chapter.
References
1
M. Kawasaki, K. Takahashi, T. Maeda, R. Tsuchiya, M. Shinohara, O. Ishiyama,
T. Yonezawa, M. Yoshimoto, and H. Koinuma, Science 266,1540-1542 (1994).
2
E. Heifets, E. A. Kotomin, and J. Maier, Surface science 462,19-35 (2000).
3
R. Uecker, H. Wilke, D. G. Schlom, B. Velickov, P. Reiche, A. Polity, M.
Bernhagen, and M. Rossberg, Journal of Crystal Growth 295, 84-91 (2006).
4
R. Uecker, B. Velickov, D. Klimm, R. Bertram, M. Bernhagen, M. Rabe, M.
Albrecht, R. Fornari, and D. G. Schlom, Journal of Crystal Growth 310, 26492658 (2008).
5
D.-G. Liu, M. Tsai, W. Yang, and C.-Y. Cheng, Journal of Electronic Materials
30, 53-58 (2001).
6
K. Rabe, C. H. Ann, and J. M. Triscone, Physics of Ferroelectrics: a Modern
Perspective (Springer-Verlag, Berlin Heidelburg, 2007).
7
N. Ikemiya, A. Kitamura, and S. Hara, Journal of Crystal Growth 160, 104-110
(1996).
8
C. Duriez, C. Chapon, C. R. Henry, and J. M. Rickard, Surface Science 230, 123136 (1990).
9
V. E. Henrich, Surface Science 57, 385-392 (1976).
10
L. B. Freund, Thin film materials : stress, defect formation, and surface evolution
(Cambridge University Press, New York 2003).
149
D. L. Smith, Thin-film deposition : principles and practice (McGraw-Hill, New
York 1995).
C. J. Lu, L. A. Bendersky, K. Chang, and I. Takeuchi, Journal of Applied Physics
93,512-521(2003).
M. H. Grabow and G. H. Gillmer, Semiconductor-based heterostructures :
interfacial structure and stability (Metallurgical Soc.? Warrendale, PA? 1986).
T. Delage, C. Champeaux, A. Catherinot, J. F. Seaux, V. Madrangeas, and D.
Cros, Thin Solid Films 453-454,279-284 (2004).
P. Bao, T. J. Jackson, X. Wang, and M. J. Lancaster, J. Phys. D: Appl. Phys. 41
063001 (2008).
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, Applied Physics Letters 76, 19201922 (2000).
W. Chang, J. S. Horwitz, A. C. Carter, J. M. Pond, S. W. Kirchoefer, C. M.
Gilmore, and D. B. Chrisey, Applied Physics Letters 74,1033-1035 (1999).
I. B. Misirlioglu, A. L. Vasiliev, M. Aindow, S. P. Alpay, and R. Ramesh,
Applied Physics Letters 84,1742-1744 (2004).
W. J. Kim, W. Chang, S. B. Qadri, J. M. Pond, S. W. Kirchoefer, D. B. Chrisey,
and J. S. Horwitz, Applied Physics Letters 76,1185-1187 (2000).
O. Tsuyoshi, S. Keisuke, Y. Takahisa, and L. Mikk, Journal of Applied Physics
103,103703 (2008).
T. S. Uragami, Journal of the Physical Society of Japan 28,1508-1527 (1969).
150
W. K. Simon, E. K. Akdogan, A. Safari, and J. A. Bellotti, Applied Physics
Letters 87, 082906-3 (2005).
T. Suzuki, Y. Nishi, and M. Fujimoto, Philosophical Magazine A 79, 2461-2483
(1999).
H. P. Sun, X. Q. Pan, J. H. Haeni, and D. G. Schlom, Applied Physics Letters 85,
1967-1969 (2004).
Y. L. Qin, C. L. Jia, K. Urban, J. H. Hao, and X. X. Xi, J. Mater. Res. 17, 31173126(2002).
M. De Graef, Introduction to Conventional Transmission Electron Microscopy
(Cambridge University Press, Cambridge, 2003).
H. P. Sun, W. Tian, X. Q. Pan, J. H. Haeni, and D. G. Schlom, Applied Physics
Letters 84, 3298-3300 (2004).
J. Yamanaka, J. Yoshimura, and S. Kimura, Journal of Electron Microscopy 49,
89-92 (2000).
T. M. Matsunaga and H. Saka, Philosophical Magazine Letters 80, 597-604
(2000).
J. W. Matthews and A. E. Blakeslee, Journal of Crystal Growth 27, 118-125
(1974).
R. People and J. C. Bean, Applied Physics Letters 47,322-324 (1985).
C. Wontae, M. G. Charles, K. Won-Jeong, M. P. Jeffrey, W. K. Steven, B. Q.
Syed, B. C. Douglas, and S. H. James, Journal of Applied Physics 87, 3044-3049
(2000).
151
L. M. B. Alldredge, C. Wontae, W. K. Steven, and M. P. Jeffrey, Applied Physics
Letters 94, 052904 (2009).
C. L. Canedy, H. Li, S. P. Alpay, L. Salamanca-Riba, A. L. Roytburd, and R.
Ramesh, Applied Physics Letters 77,1695-1697 (2000).
D. Brunner, Acta Metrialia 54,4999-5011 (2006).
L. Hao, A. L. Roytburd, S. P. Alpay, T. D. Tran, L. Salamanca-Riba, and R.
Ramesh, Applied Physics Letters 78,2354-2356 (2001).
D. Hull and D. J. Bacon, Introduction to Dislocations (BPC Wheaton Ltd, 1984).
P. D. Healey, M. G. K. Bao, J. E. Ayers, and F. C. Jain, Acta Cryst. A51,498-503
(1995).
E. Koppensteiner, A. A. Schuh, A. G. Bauer, A. V. Holy, A. G. P. Watson, and A.
E. A. Fitzgerald, Journal of Physics D: Applied Physics 28 Al 14-A119 (1995).
J. E. Ayers, Journal of Crystal Growth 135, 71-77 (1994).
152
Chapter 5
Dielectric Properties Related to Microstructures
This chapter addresses the dielectric property measurements of thin films. The
results are discussed in relation to the structural film characteristics, such as strain and
defects. The IDC electrode fabrication process and the dielectric property measurement
methodology will be introduced (�1). Bulk-like microwave dielectric properties will be
demonstrated in thin Bao.6Sro.4Ti03 films coherently grown on GdScO3(110) (�2). The
dielectric properties of the films grown on conventional large-lattice mismatch substrates,
such as MgO(lOO), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), and LaA103 will be
compared to the Bao.6Sro4Ti03 films on GdScO3(110) in �3. In �4, the homogeneous
strain effect will be discussed based on the comparison of dielectric properties of the
Bao.6Sro4TiC>3 films coherently grown on GdScO3(110) and DyScO3(110) (�4.1), with
the phenomenological theory behind these observations described in �4.2. The last
section (�5) will summarize the observations made and conclusions drawn.
5.1 Experimental procedures of microwave measurements
The dielectric properties at microwave frequencies have been determined using
interdigitated capacitor (IDC) structures.1 The electrodes were patterned using a lift-off
lithography process.2 The lay-out of the IDC structures is shown in Fig. 5.1. The masks
were designed to allow several IDC configurations to be patterned simultaneously. IDC
finger lengths used in this research were 80 um with finger widths of 5 um or 10 um. The
IDCs had either 8 fingers or 16 fingers. The gap between the fingers varied from 4 um to
10 um, with 2 um increments. Multiple layers of metals were deposited as top electrodes
using electron beam deposition (EBD) method. A thin Ti layer of 50 nanometers was
153
deposited on the oxide film in order to improve the adhesion.3'4 Following that, a 1.5
micron thick Ag layer was deposited to reduce the resistive losses. This layer was capped
with a 100 nm gold layer to prevent silver oxidation.3
Fig. 5.1 Optical image of one of the IDC structure units used for dielectric measurent at
microwave frequencies.
A HP8510 two-port vector network analyzer (Fig. 3.4a) was used to generate the
microwave frequency signal and to measure the reflection parameter Sn from the
interdigitated capacitor. A Cascade Microtech 1100 Probe Station and a Temptronic
TP3000A temperature measurement system (Fig. 3.4b) were used to carry out the
measurements in the temperature range of -65癈 to 200癈. The stage was purged with
nitrogen to prevent water vapor condensation at temperatures below 30癈. A separate DC
voltage source was used to apply the DC bias to measure the dependence of the dielectric
constant on electric fields. Coplanar strip-line standards from Agilent were used for
initial short and open circuit calibrations. Microprobes with two fingers from Signatone
were connected with one port to measure the Si i parameter in the range of 1 GHz to 20
GHz. The measured reflectivity parameters Sn were imported into Labview simulation
154
software developed based on Gevorgian's IDC single-layer and multilayer models to
extract the capacitance, dielectric constant, and dielectric loss.1'4'5
IDC
structures
were
also
patterned
on
bare
MgO,
LaA103,
(Lao.i8Sro.82)(Alo.59Tao.4i)03, and SrTiC�substrates to have their dielectric constants
measured. For each of the IDC configurations, three different capacitors were used; the
measured data were averaged and compared to the literature values. The results were
within 10% of data found in literature, which is considered acceptable for the IDC
technique used.6
Detailed experimental procedures of film growth have been described in Chapter
4. Bao.6Sro.4Ti03 films were grown on MgO(lOO), GdScO3(110), DyScO3(110),
(Lao.i8Sro82)(Alo.s9Tao.4i)03(100), NdGaO3(110), and LaAlO3(100) substrates. The
oxygen pressure used during deposition was kept at 300 mTorr for all films discussed
below. The intention was to keep oxygen vacancy (or other point defects) concentration
constant and to focus only on the impact of structure-related factors on dielectric
properties. The in-plane and out-of-plane lattice parameters of the films were measured
using a 4-circle x-ray system to monitor the strain state as discussed in �5. The
crystalline quality and dislocation density of these films were determined by TEM
(Section �6). The dielectric properties presented in this chapter was measured using
80x10x8 16 finger IDCs and frequency of 5GHz.
5.2 Dielectric properties of Bao.6Sro.4TiC>3 films grown on GdScC>3(110)
It is known that the lattice parameter of Bao.6Sro.4Ti03 depends on oxygen
pressure during deposition.7 In order to get precise understanding of the film strain state,
the lattice parameter of the materials grown at the specific oxygen pressure of interest
155
must be measured for a strain-free sample. This was accomplished by the following
procedure: polycrystalline Bao.6Sro.4Ti03 films were grown on a Si substrate that had
been annealed in air at 1200 癈 for 48 hours in order to get an amorphous top surface
layer to achieve a free-standing lattice parameter for a Bao.6Sro.4Ti03 film grown upon it.
The measured free-standing lattice parameter of Bao.6Sro.4TiC>3 in this research is
a = 3.959�002 A. GdScC>3 is an orthorhombic perovskite with lattice parameters a =
5.755 � 0.003 A, 6=5.489 � 0.003 A, and c = 7.936 � 0.003 A.8 The (110) plane of
GdScC>3 has a nearly square mesh with in-plane lattice periodicities of d00l= 3.967 and
d^ = 3.970 A, values which are = 0.2% larger than the a of Bao.6Sro.4TiC>3. Using the
models proposed by Matthew and Blackeslee9 and by People and Bean,10 the respective
calculated critical thicknesses for Bao.6Sro.4Ti03filmson GdScC>3(l 10) are ~ 100 nm and
20 nm. Such unrelaxed films would be in a slight (=0.2%) homogeneous tensile strain
state, which is believed to be beneficial for dielectric constant and tunability when the
dielectric constant is measured in-plane.11
As discussed in Chapter 4, Bao.6Sro.4Ti03 films were deposited on chemically and
thermally treated GdScO3(110) using pulsed laser deposition (PLD). 120 nm-thick
Bao.6Sro.4Ti03 films were grown on GdScO3(110) substrates at 300 mTorr O2 pressure,
characterized structurally and for their dielectric properties. X-ray diffraction (XRD)
confirmed
that the film-substrate epitaxial relationship
was, as expected,12
BST(001)[100]||GdScO3(110)[001]. The in-plane (a,a') and out-of-plane (c) lattice
parameters of the films were measured using both symmetric and asymmetric reflections
to be o=3.965�002 A, a'=3.968�002 A, and c=3.957�002 A. The a and a' values
are the same as the substrate in-plane lattice parameter within the measurement error,
156
which indicates that the films are coherently strained with the substrate and the c/a ratio
of 0.998 indicates that the film was under a slight biaxial tensile strain.
a
b
5"
.. _. _
... _
._
._
i
�
I
L)*rlim><w0J> � M *
tWIIHrttOHMJ
d^lAA^kLA^kkLu^rfJ^AAdJ^AAAlAAAAiAA
-150-100 -50 0
50 100 150
Omega (Arc seconds)
-150-100 -50 0 50 100 150
Omega (Arc Seconds)
Fig. 5.2 High resolution x-ray diffraction rocking curve of (a) the (220) reflection of the
GdScO3(110) substrate and (b) the (004) reflection of Bao.eSro.4Ti03 film. Two peaks are observed
in each, representing the bi-crystal nature of the substrate within the x-ray.
Fig. 5.2a presents the high resolution XRD rocking curve of the (220) reflection
of a GdScO3(110) substrate (Fig. 5.2a) and the (004) reflection of a Bao.6Sro.4Ti03 film
(Fig. 5.2b). The rocking curve of the substrate has two peaks separated by 50 arc seconds,
where each peak has a FWHM of less than 25 arc seconds (a value that includes 12 arc
seconds of instrumental broadening). The two peaks are due to the presence of two
slightly misoriented grains within the beam footprint. The rocking curve of the film
demonstrates that the film inherits the bi-crystal structure from the substrate; the FWHM
of film rocking curves are also = 25 arc seconds, basically the same as that of the GdScC>3
substrate. The small FWHM indicates the high crystalline quality of Bao.6Sro.4TiC>3 film
grown at high pC>2, similar to that grown at lower pressures12 and for SrTi03.4 This is the
narrowest rocking curve that has been reported for solid solution BST thin films. Also,
the rocking curve width of these films (~ 25 arc seconds) is lower than the rocking curves
157
widths measured from commercially available single crystals of BaTiC>3 and SrTi03
(hundreds of arc seconds in width).13
a
b
8000
:r. A
7000
a * 6000
|
A 30V
5000
'
1
g 4000
O
� 3000
Z
JK 2000
?30-20-10 0 10 20 30
Bias Voltage (V)
� 1000
^
-
?
-
?
'
?
?
-
-
?
?
?
?
-
�
-
?
-
0
250
300
350
400
250
Temperature (K)
300
350
400
Temperature (K)
Fig. 5.3 (a) The temperature dependence of dielectric constant under three different bias voltages
(0 V, 15 V, and 30 V) applied on a 8 pm IDC gap. The inset in (a) shows the inverse dielectric
constant as a function of temperature, (b) The temperature dependence of tunability (using a
30 V bias). The inset in (b) shows the tunability as a function of applied bias voltage on the 8pm
IDC gap at T = 308 K..
The dielectric properties were measured using interdigitated capacitors (IDCs) in
the frequency range of 1-20 GHz and the temperature range of 250 - 450 K. Fig. 5.3a
gives the temperature dependence of the relative dielectric constant measured at 5 GHz
under different bias voltages (equivalent electric fields for 8 um gap fingers): 0 V (0
Vcm-1), 15 V (18.75 kVcm"1), and 30 V (37.5 kVcm"1). At zero bias, the relative
dielectric constant peaks at more than 7000 at 308K, and the sr-T curves exhibit a narrow
FWHM of 30 K around the peak. These values are comparable to those observed in bulk
BST ceramics and single crystals.14"18 The Curie temperature of Tc=308 K (using the peak
temperature as Tc) is 59 K higher than the reported Tc=249 K for bulk Bao.6Sr0.4Ti03
ceramics.1819 This shift in Tc is likely due to a homogeneous strain effect, which is
158
similar to shifts reported for SrTiC>3 and BaTi03 thin films.413'20 With an increase of the
applied voltage, sr. decreases and the peaks become broader; the peak shifts to by 20K
toward higher temperature for every 15 V. The Tc shift under bias voltage is due to
electrostriction (the applied electric field increases the strain level leading to the increase
of the Curie temperature1113).
The inset given in Fig. 5.3a is a plot of the inverse dielectric constant as a function
of temperature. At temperatures much higher than Tc where the film is in the paraelectric
state, the data can be fitted to a linear relationship that follows the Curie Weiss law. The
Curie constant (C) and the characteristic temperature {Te) were determined to be C =
5x104 K and Te = 305 K. The Curie constant is half the value (lxlO5 K) observed in bulk
Bao.6Sro.4Ti03 materials.18'21'22 The reason for the lower C value remains unclear. In the
vicinity of the Curie temperature, the values of 1/s smoothly deviate away from the Curie
Weiss values, consistent with the behavior indicative of a second order phase
transformation. That Te ~ Tc is also consistent with a second order transition.23 It is
believed that BaxSri.xTi03 single crystals with x>50% exhibit a first order phase
transformation, in which the inverse dielectric constant abruptly deviates from Curie
Weiss behavior and Te < Tc.24 However, similar Ba^SrojTiC^ doped with 0.01 to 0.1
mol% Nb5+ was observed to exhibit a second order transition.25 The second order
character observed in this experiment could, therefore, be a result of significant point
defect populations, such as oxygen vacancies.
The relative tunability at a given voltage and temperature can be defined as:26
( ^ = f^Z2zZ2
159
(1),
where er(0,T) and s^V,T) are the relative dielectric constants at a temperature T under
bias voltages of zero and V, respectively. Figure 5.3b shows the relative tunability at the
maximum applied voltage versus temperature, or nr(30 V,T). The relative tunability
reaches a peak value of 92% at 308 K (the same temperature as the dielectric constant
peak), a value that is comparable to the highest tunability observed in bulk ceramics and
single crystals.26"28
The bias voltage dependence of dielectric constant was measured at 308 K by
increasing the bias voltage from -30 V to +30 V and then back to -30 V. From these
measurements, the relative tunability nr(V,308 K) was determined and is given as the
inset in Fig. 5.3b. No hysteresis was observed at 308K, indicating the spontaneous
polarization at Tc = zero, as expected for a second order transition. It can be seen from the
inset that more than 80% of the tuning happens below 15 V, which will benefit
applications.
Fig. 5.4 gives the temperature dependence of (device) dielectric loss, given as
tan8, measured at 5 GHz under different bias voltages. At a 0 V bias, the dielectric loss
curve exhibits a peak of 0.38 at 298 K (a temperature that is slightly below the
temperature of the dielectric peak); with increase of the temperature, the loss drops
sharply to about 0.05 at 325 K and then gradually increases. The behavior at bias voltages
of 15 and 30 V are similar to each other; the loss decreases from 250 K to ~ 350 K and
then gradually increases with increasing temperature. The inset gives tand. as a function
of bias voltage at 308 K. The dielectric loss decreases sharply with applied voltage from
0 V to ~ 10 V and then increases slowly as the voltage is increased further.
160
0.40
.
OM
A
? ov
"|M�
jl
T籎ttX
0.3S ? �V
130V
/
MS 0.30
" 0.25
1
'
?
?
\
*'"
| M�
1 &>�
^
?-JL-.
-IB ? � -10 0 10 20 JO
BlttVatug�(V|
?*
i:::
0.05
0.00
*
?-*??
?
250
300
350
Temperature (K)
400
Fig. 5.4 Temperature dependence of dielectric loss measured at different bias voltages, 0 V,
15 V, and 30 V. The inset shows the bias voltage dependence of dielectric loss at 308 K.
The device loss comes from a combination of BST film loss and electrode loss.
The loss from BST film includes the intrinsic dielectric loss (tan8int) and the conduction
loss (tan8c). The device dielectric loss can be expressed as:16'29
tan 8 =. tan Sjm + tan Sc
(2).
The intrinsic loss of paraelectric phase can be expressed as:[9,40]
tan 8^,
1
tanSl
[l + j3(tanl3)E2]' /3
(3),
where tanS癿 is the intrinsic loss with no bias field, E, and /? is a constant derived from
Landau-Devonshire theory. The conduction loss can be expressed as:16'29
1
tan 8? =
coRC
(4),
where co is the measurement frequency, R is the resistance of the sample, and C is the
geometrical capacitance (effective capacitance from the measurement) of the specimen.
These mechanisms can be used to understand observations in Fig. 5.4.
The dielectric loss peak observed slightly below Curie temperature in the 0 V
curve has been observed in barium strontium titanate bulk polycrystalline ceramics and
161
other ferroelectric materials. This characteristic is often attributed to viscous domain wall
motion and its associated internal friction that dissipates electrical energy (to mechanical
and thermal energy).16'30-32 With an increase in the temperature, the dielectric loss at 0 V
decreases quickly to about 0.05, because above the Curie temperature the paraelectric
phase has no domains.30 While this mechanism of intrinsic loss decreases, the conduction
loss increases with increasing temperature and ultimately dominates at high temperatures.
The loss increases with temperature because the conductivity of the barium strontium
titanate film increases with temperature.33 Therefore, the measured loss increases when
the temperature goes above 350-380 K, for all bias voltages. In regard to the field
dependence of the tand vs. T curves, the most obvious effect is that there is no peak for
15 and 30 V bias, as observed elsewhere.16 Also, the low-T portion of the curves also
exhibit a field dependence offset from each other similar to the conduction loss region.16
At 308 K, the loss decreases with increasing field in either direction from 0 V, as
expected from Equation (3). At higher bias voltages, however, the conductivity of the
barium strontium titanate film starts to increase with increasing electric field, resulting in
an increasing loss.34
For application purposes, one must consider the trade-offs between the tunability
and the losses. The communication quality factor (K) has been used as a comprehensive
figure of merit and is defined as:26
(*-0 2
K__
(5)
玹an<5(0ntan<J(30n
in which tan5(0 V) and tan8(30 V) are the dielectric loss under zero and 30 V bias, and
n is defined as the tunability (note the difference from the relative tunability):
162
sr(OV)
n=
sr(30V)
(6)
Fig. 5.5 gives the communication quality factors K as a function of temperature;
K peaks at the value of 500 at 320 K. This is over a 50% increase from the highest
reported values for thin film varactors.26 A value of 900 is considered appropriate for
phase shifter applications.26 Further decreases in the dielectric losses, either by decreasing
the electrode or barium strontium titanate conduction losses, could push these values into
an acceptable range.
300
350
400
Temperature (K)
Fig. 5.5 Plot of Communication quality factor as function of temperature, using the tunability at
30V and the dielectric loss under no bias and loss under 30V bias.
5.3 Effects of inhomogeneous strains on dielectric properties
5.3.1 Inhomogeneous strain effects on the dielectric constant and tunability
Bao6Sro.4Ti03 films were grown on MgO(100), (Lao.i8Sr082)(Alo.59Tao.4i)C>3(100),
NdGaC>3(110), and LaAlOs(lOO) substrates under exactly the same conditions as the
Bao.6Sro4Ti03 films on GdScC>3(110). The results of the dielectric constant measurement
versus temperature are summarized in Fig. 5.6a and are also compared to that of the
Bao.6Sro.4Ti03 films on GdSc03(l 10). The dielectric properties and structural information
are summarized in Table 5.1. The dielectric constant peaks of Bao.6Sro 4TiC>3filmsgrown
163
on substrates other than GdScC>3 have much wider widths (FWHM > 95 K), and much
lower maximum values than those observed in Bao.eSro/TiOs films on GdScC>3. The
maxima of the dielectric constant of the films follow the order BST/GdScO3(7099) >
BST/(Lao.i8Sro.82)(Alo.59Tao.4i)03 (1654) > BST/NdGa03 (1174) > BST/LaA103 (874) >
BST/MgO(630). By comparing this order to that of films' x-ray rocking curve widths
(listed in Table 5.1), one can find that the maximum of the dielectric constant decreases
as the rocking curve FWHM (or dislocation density) increases. Also, the e(T) peaks
become wider as the FWHM of the rocking curve and dislocation density increase.
100
8000
(a)
A
g 6000
o
-?-GdScO^HO)
-�-LSAT(100)
- A - N d G 30,(100)
-T-La籌O,<100>
?�-M(jO<10<�
J> 5000
|
4000
I 2000
& 1000
�
� 60
'
T T
\
-�-LSAT(100)
-A-NdGaOjdlO)
-Y-LaAIO,(100)
MgO
J�
40
J
a 3000
-?-GdScO^HO)
<b)
lity
| 7000
/
/
.^
?"--.
� 20
~�-^
0
250
300
350
Temperature (K)
400
450
250
300
350
Temperature (K)
400
450
Fig. 5.6 (a) Comparison of the temperature dependencies of the relative dielectric constants and
(b) the relative tunabilities for (OOI)-oriented Sa06Sro477'03 films grown on GdScO3(110),
(Lao.igSro.82)(Alo.59Tao.4i)03(100),
NdGaO3(110), LaAIO3(100), and
MgO(100). Note the
measurement frequency was 5 GHz and the tunability was measured at 30 V applied on a 8
micron gap, equivalent to 37.5 kV/cm field.
Fig. 5.6b gives the temperature dependencies of the relative tunabilities for
Bao.6Sro.4Ti03 films on GdScO3(110), MgO(100), (Lao.i8Sro.82)(Alo59Tao.4i)03(100),
NdGaO3(110), and LaAlO3(100) substrates. The relative tunabilities were calculated
using the dielectric constants measured at zero bias and 30 V bias. The tunabilities follow
the same general trend of peak values decreasing when the dislocation density increases,
164
The only exception is the Bao.6Sro.4Ti03 film on LaAlC>3, which has a higher tunability
than the Bao.6Sro.4Ti03 film on (Lao.i8Sro.82)(Alo.59Tao.4i)03. Overall, the relative
^inabilities
of
the
Bao.6Sro.4TiC>3
films
grown
on
MgO(lOO),
(Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), and LaAlO3(100) substrates are lower
than that of Bao.6Sro.4Ti03 films grown on GdScC>3(l 10). From the dielectric constant and
the tunability comparison between Bao.6Sro.4Ti03 films grown GdScC>3 and Bao.6Sro.4Ti03
films grown on MgO(lOO), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), and
LaAlC>3(100) substrates, it can be concluded that the film quality, essentially the
dislocation density, has played an important role in the dielectric constant and tunability
degradation.
Table 5.1 Summary of the strain states, FWHM of the film X-ray rocking curve, the peak dielectric
constant, the peak tunability, the corresponding temperatures, and the FWHM of the t-T peak.
Substrates
TEM Dislocation
Density(/cm2)
FWHM of
Film Rocking
Curve(�)
Peak Values
-T/ nr-T Peak
Position(K/K)
FWHM of
er-T Peak
(K)
GdScO3(110)
6xl0 9
0.008
7099/92.4%
308/303
32
MgO(lOO)
textured
0.617
630/31.7%
253/253
155
LSAT(IOO)
1.5x10"
0.016
1654/55.4%
353/343
95
NdGa03(l 10)
2.1x10"
0.02
1174/52.3%
363/353
98
LaAlO3(100)
2.4x10"
0.183
874/60.6%
303/273
124
Er-T/nr-T
5.3.2 Inhomogeneous strain effect on dielectric loss
Fig. 5.7 gives the temperature dependence of dielectric loss measured at 5GHz
from
the
120
nm
Bao 6Sro.4Ti03
films
grown
on
GdScC>3(110),
(Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), LaAlO3(100) and MgO(100). The peak
165
of the dielectric loss in the Bao.6Sro.4TiC>3 film grown on GdScC>3(l 10) has been discussed
earlier in Section 5.2.1. All temperature dependencies of dielectric loss have some
correlation with the Curie temperature. The losses of all the films reach maxima below
Curie temperature and then drop in different magnitudes when the temperature increases
above the Curie temperature. If the measurement temperature range is high enough above
the Curie temperature, the dielectric losses starts to increase.
0.40
i
0.30
ctri
0.35
0.20
IA
o
2
I
.
:
??--GdScO,(110)
- LSAT(100)
??- A - -NdGaO,(110)
?A
??- - LaAIO,(100)
- MgO(100)
U*^.
0.25
?
.A
y * ?^
I
?
0.15
a
x*?^
?
0.10
?
?^.
^?-?-?-�-
0.05
250
300
350
Temperature (K)
400
450
Fig. 5.7 Temperature dependence of the dielectric losses measured at 5 GHz using IDC structure
for 120 nm Ba0.6Sro.4Ti03 films grown on GdScO3(110), (Lao.iaSro.ad(^o.59Tao.4i)03(100),
NdGaO3(110), LaAIO3(100), and MgO(100).
The sharp loss peak slightly below the Curie temperature is believed to be due to
the increase of the internal friction related to the increase of domain walls and domain
wall motion.16'30"32 The loss in the film on GdScC>3 drops sharply above the Curie
temperature, where the ferroelectric phase transformed into paraelectric phase and no
domain walls should exist.16'30"32 After the loss related to domain wall motion drops to
the minimum, the conduction loss starts to increase for Bao 6Sr0.4TiO3,33 and eventually it
dominates the overall loss. The same trend has been observed in the films on LaAlCb and
MgO. For Bao.6Sro 4TiC>3 grown on (Lao.i8Sro.82)(Alo.59Tao.4i)03 and NdGaC� the
166
temperature dependencies of the loss are almost identical. Since their Curie temperatures
are higher than for other films, the increase of loss at high temperatures does not show
up, but the trend of loss decrease above Curie temperature is consistent with all the other
films.
From the comparison of the temperature dependencies of the dielectric losses of
these films, it can be found that the Bao.6Sro.4Ti03 film with a low dislocation density,
such as the Bao6Sro4TiC�film on GdScOs, has a very sharp loss peak while the
Bao.6Sro.4TiC>3 films with two or more orders of magnitude higher dislocation densities,
such as Bao.6Sro.4Ti03 films on (Lao.i8Sro.82)(Alo.59Tao.4i)03, NdGaC>3, LaAlC>3, and MgO,
the temperature dependencies of the loss peaks are widely spread. This wide spread of the
loss can be attributed to the inhomogeneous strains associated with dislocations. The
inhomogeneous strains can spread out the local Curie temperatures distribution, as
observed in the temperature dependencies of dielectric constant. When the Curie
temperature is spread out, the phase transformation happens in a diffuse fashion, in which
the domain walls and domain wall motion (or equivalent to the changes of local
polarization magnitudes or spatial cohesion of the polarization vectors) can exist over a
considerable temperature range; therefore, the dielectric loss related to domain wall
motion can be maintained at a high level over such a wide range.
Figures of merit are often assigned to different materials to illustrate their
suitability for device design. The figure of merit {K') for phase shifter applications is
often defined as:26
K' =
(7),
tan�(0F)
167
in which n is defined by equation (6). The K' for different films is presented in Fig. 5.8.
It is evident, that as the losses were spread out respect to temperature, even with
relatively high tunability in the film, the figure of merit is flattened out by the high
dielectric loss at a high level of above 10% throughout the whole temperature range. This
is undesirable for device applications. The K' values of the Bao.6Sro.4TiC>3 film grown on
GdScC>3, despite the fact that the loss peaks just below Curie temperature, are higher than
for any other films; at the maximum, it exhibits a figure of merit 6 to 7 times higher than
the values for the other films.
70
60
50
-?-GdScO s (110)
- ? - LSAT(100)
-A-NdGaO,(110)
- V - LaAIO,(100)
-*- MgO(100)
40
?5 30
�
�20
il
10
0
:, ?. r r s *?: �*****-**?
250
?
300
350
400
Temperature (K)
?
?
?
450
Fig.5.8 Temperature dependence of the figure of merit, K', at 5 GHz using an IDC structure for
120 nm Ba0.eSro.4Ti03 films grown on
GdScO3(110),
(La0.i8Sr0.82)(Alo.59Tao.4i)03(100),
NdGaO3(110), LaAIO3(100), and MgO(100).
5.3.3 Discussion on inhomogeneous strain effects on dielectric properties
As it has been discussed in Chapters 2 and 3, inhomogeneous strains, which are
associated with point and extended defects, such as vacancies, dislocations, and grain
boundaries, exist in all of the Bao.6Sro.4Ti03 films.35"37 The localized strains affect the
local materials dielectric properties.35"37 Simulations based on Landau-Devonshire theory
168
were done to analyze the strain distribution and depolarization field around dislocation
cores of both misfit and threading dislocations.35 The polarization mapping around
dislocation core with Burger's vector <100> (shown in Fig. 5.9a) demonstrated that the
compressive strain on one side of the dislocation core locally depresses the polarization.
M
to?
V
I
w
10Distant on a(nHi)
i
I
i
OS B
m
_iSiS
<4*
I'
E
c
101C
on S"
tea E
I
P
ai3t>naeanx(naij
Fig. 5.9 The (a) polarization distribution and (b) variation of the Curie temperature around a
b=a[100] edge dislocation at (0,0,0) in single-crystal PbTi03 on an xz plane. Area shown
represents 20*20 nm cross section along the y direction (dislocation line). This figure is
reproduced from reference 35.
The tensile strains on the opposite side of the dislocation core can enhance the
polarization, increasing dielectric constant. Note that the Burger's vector of dislocations
dominant in the films studied in this research should be <100> type. The dielectric
measurements using IDC structures are dependent on the in-plane polarizations. The two
sides of the threading edge dislocation can be considered as two capacitors connected in
169
series,. Therefore the effective dielectric constant will be limited by the capacitor with
low dielectric constant when the geometrical factors are close to each other.
The area affected by the strain field of a single dislocation was estimated to be 20
x 20 nm2.35 For a film with threading dislocation density of around 2xlO u /cm2, the
average distance between dislocations is about 20nm and is comparable to the size of the
strain field depressing the dielectric constant.35 This means that the suppressed areas will
overlap and a large fraction of the film material will exhibit lowered polarization. This
causes the whole film's general polarization to be suppressed and dielectric constant to
decrease.
It is well established that homogeneous strains can shift the position of the Curie
temperature j ^ 4 - 2 0 ' 3 5 - 3 8 The area around the dislocation core is under a different strain
state, which will shift the Curie temperature either up or down depending whether the
film is in tension or compression.35'38 This will spread out the Curie temperature
distribution. As shown in Fig. 5.9b, the local phase transformation temperature (Tc) had
also been calculated
around a dislocation core in PbTi0335'36 and observed
experimentally in other ferroelectrics.38'39 This effect appears to be responsible for the
increased width of Curie peaks of Bao.6Sro.4Ti03 films. One should note that point defects
also can affect temperature dependence of dielectric properties. In this research, the all
films were deposited under the same growth conditions, in particular the same oxygen
partial pressure, and they should have similar concentrations of point defects.40 The large
differences in their dielectric constants and tunability are unlikely to be due to the
differences in point defect concentrations. The tensile strain in Bao.6Sro.4TiC>3 films grown
on GdScC<3 may have contributed to the high dielectric constant and tunability of the
170
film. However, the Bao.6Sro.4TiC>3 films on MgO have the similar strain state but
significantly degraded properties. Bao.6Sro.4Ti03 films on MgO were textured with the
high density of grain boundaries; the grain boundaries may have degraded the dielectric
constant compared with those films grown on (Lao.i8Sro.82)(Alo.59Tao.4i)C>3, NdGa03 and
LaA103. No high angle grain boundaries were observed in the Bao6Sro.4TiC>3filmsgrown
on GdScC>3, (Lao.i8Sro.82)(Alo.59Tao4i)03, NdGaCb, and LaA103 within the detection limit
of planview TEM.
As is evident from Fig. 5.7, the Bao.6Sro.4Ti03 film with a low dislocation density
had a very sharp loss peak while Bao.6Sro.4Ti03 films with dislocation density above 10 n
/cm , such as Bao.6Sro.4Ti03 films on (Lao i8Sro.82)(Alo.59Tao.4i)03, NdGaC>3, LaAlC>3, and
MgO, exhibited wide peaks in the loss spectrum. These characteristics also can be
explained by the inhomogeneous strains associated with dislocations. When the Curie
temperature is spread out (Fig. 5.9), the phase transformation occurs in a diffused
fashion. The ferroelectric domains can exist at elevated temperatures and the domain wall
motion can contribute to the total loss in a wide temperature range. The comparison of
figures of merit demonstrated that the spread out of the loss will lower the figure of merit
by maintaining it in a low level.
In this section, it is demonstrated that films with high dislocation densities (lower
crystalline quality as determined by X-ray diffraction and TEM) have degraded dielectric
properties. Simulation results based on Landau theory reported by Alpay et al. can
explain the correlation between dielectric properties and inhomogeneous strains
associated with dislocations.35 However, it does not necessarily mean that low dislocation
concentration (high crystalline quality) will yield bulk-like properties. This question will
171
be answered by comparing dielectric properties of films grown on GdScC>3 and DyScC>3
substrates.
5.4 Effects of homogeneous strains
5.4.1 Comparison of dielectric properties of Bao.6Sro.4Ti03 on GdScC>3 and DyScC>3
Bao 6Sro.4Ti03 films were grown on DyScO3(110) and GdScO3(110) substrates at
850癈 and oxygen pressure of 300 mTorr. The Bao.6Sro.4Ti03/DySc03 film thickness was
measured to be 300 nm. Even though this thickness is above the theoretical critical
thickness, the measured in-plane lattice parameter demonstrated that the films are
coherently strained to the substrate with a compressive strain of -0.33% as shown in
Table 4.3. The measured rocking curve width of the film is 0.007�, comparable to that of
Bao.6Sro4TiC>3filmsgrown on GdScC>3(l 10) (Table 4.3). The planview TEM also showed
that the dislocation density in the Bao.6Sro.4Ti03 film on DyScC>3(110) was 2xl0 10 cm"2
which is about three times the dislocation density, 6x109 cm"2, in Bao.6Sro.4TiC>3 films
grown on GdScQ3( 110).
100
7000
-?-GdScO,(110)
-?-DySeO^HO)
. (a)
6000
4000
3000
2000
1000
200
??
.,�?*.
-?-GdScO,(110)
-?-DyScO,(110)
3-80
A
J \
5000
a
(*>)
40
& 20
^-,
.----.????-.*
250
.
300
350
Temperature <K)
..?"-??
400
450
01?
200
250
300
350
Temperature (K)
400
450
Fig. 5.10 The comparison of the temperature dependences of the relative dielectric constants (a)
and the relative tunabilities (b) for (001)-oriented Ba0.6Sro.4Ti03 films grown on GdScO3(110) and
DyScO3(110).
172
0.40
0.35
70
: (�)
0.30
J 0.25
� 0.20
. ???
8
� 0.15
A4
-?-GdScO^IIO)
-?-DyScO,'(110)
s
?*
\
5
so
I40
I 30
I 20
10
200
250
300
350
Temperature (K)
:
/ \
V
s.
0.10
0.05
0.00
- ? - BST/GdScO,
-?-BST'DyScO,
60
400
450
0
250
300
350
400
Temperature (K)
450
Fig. 5.11 The comparison of the temperature dependences of the dielectric loss (a) and the figure
of merit (b) for(001)-oriented Ba0.6Sro.4Ti03 films grown on GdScO3(110) and DyScO3(110).
Fig. 5.10a gives the comparison of the temperature dependence of dielectric
constant (e(T)) between Bao.6Sro.4Ti03 films grown on DyScC>3 and on GdScC>3. The
dielectric constant maximum of Bao 6Sro.4Ti03/DySc03 only reaches 375 at 283 K, even
lower than that for Bao.eSro^TiOs/MgO. The e(T) FWHM is about 167 K, also wider than
that of Bao.6Sro.4Ti03 on MgO (155 K). The maximum relative tunability (Fig. 5.10b) is
about 40%. Compared to Bao.6Sro.4TiC�films on GdScCb, the films on DyScCb have
demonstrated much lower dielectric constant and tunability. Compared to Bao.6Sro.4TiC�films on MgO, (Lao.i8Sro.82)(Alo.59Tao.4i)03, NdGaCb, and LaAlCh, the films on DyScC�are worse than films which have two orders of magnitude higher dislocation densities.
Fig. 5.11 shows the dielectric loss (a) and figure of merit (b) of Bao 6Sro.4Ti03 films
grown on DyScC>3 and on GdSc03. The loss follows the temperature dependence trend
for all other films: maximum slightly below Curie temperature followed by drop as the
phase transformation is finished. As the temperature increases further, the conduction
loss becomes dominant and increases again. In general, the dielectric loss for
Bao.6Sro.4TiC�films grown on DyScC>3 is high (>15%). In addition to the decrease of the
tunability, the figure of merit remains at 15 or so as shown in Fig. 5.11b. Considering that
173
the dislocation density in Bao 6Sr0 4TiC�DyScC)3 was only three times higher that that of
films on GdScCb, the dramatic differences in dielectric properties indicates that there
must be another important factor affecting the properties.
Compressive
Fig. 5.12 The schematic depiction of barium strontium titanate film in-plane polarization related to
the in-plane tensile and compressive strains.
As has been discussed in Chapter 4, the lattice parameter measurement
demonstrated that both the Bao.eSro^TiCb films on GdScO3(110) and DyScO3(110) are
coherently strained to the substrates. The difference was that the films on GdScO3(110)
were in tension (+0.2%) and the films on DyScC�110) were compressively strained (0.33%). Intuitively, it can be understood as depicted in Fig. 5.12, that when the film is
under in-plane tensile strain, the strain opens up the space for the displacement of Ti4+ ion
in the perovskite unit cell and, therefore, enhances the in-plane polarizations and the
dielectric constant. When the film is under compressive strain, the space for in-plane
displacement is more restricted, i.e. the strain suppresses the polarizations and decreases
the dielectric constant. To understand the strain effect, the Landau-Ginsburg-Devonshire
phenomenological theory is discussed in the next section.
5.4.2 Discussion of the homogeneous strain effect based on phenomenological theory
Chang et al., derived the correlation between the dielectric constant and strains at
a specific temperature in paraelectric phase based on Landau Devonshire theory.11'41"43 In
this research, this result will be extended to investigate the strain effect on the dielectric
174
constant vs. temperature relationship in paraelectric phase. For the ease of understanding,
the derivation process discussed in Chang's paper is summarized below.
According to the phenomenological theory developed by Devonshire for
BaTiOs,11'41"43 "the Gibbs free energy (G) of a stress-free ferroelectric subjected to an
external electric field (E) can be expressed as:
G(T,Pi) = F(T,Pi)-EiPi
(8),
where F is the Helmholtz free energy of a strain-free ferroelectric, and Pt is the
polarization. When a stress is applied to the ferroelectrics, the Helmholtz free energy
should include the factor of strain (x;) as:11
F(T,PltXj)
= F0 + 盿(P2
2
+ \d{P2P2
+ P2P2 + P2P2 ) + i c ? (x,2 + x\ + x] )
+ Cl2 (XlX2
+ X{X3
+ P22 + P2) + -B{P:
4
+ P24 + P34) + � r (/> 6 + P26 + P36)
6
+ X2X3 ) + T"<-44 V*l """ ?"'2 ~*~ X3 )
+ Gu {xxPx2 + x2P22 + xzP2) + G12 {xx (P2 +P2) + x2 (P2 + P2) + x3 (P,2 + P22)}
+ GM(x4PIP3+x3P1P3+x6P2P1)
+ ...
where Fo is a function of temperature alone, a, /?, y, and S are the free-energy expansion
coefficients, and c,-y and Gy are the elastic constants and the stress-polarization related
electrostrictive coefficients, respectively."
For an epitaxial film clamped by a substrate, the following assumption can be
introduced:11
(1) The equi-biaxial in-plane strains, xj and X2, in the film are controlled by the substrate.
(2) The out-of-plane stress is zero because of the free surface.
(3) For measurements using IDC structure, the electric field is applied in one direction,
therefore, there is only one polarization direction, P.
(4) The polarization is parallel to the electric field.
175
The Gibbs free energy for a ferroelectric thin film can be simplified to:11
G(T,Pi,xJ)
=
F(T,Pi,xJ)-EP
= F0 + -aP2
+ -/3P4 + -yP6 + -cn(x2
+ x\ + x2) + c12 (xxx2 + *,*3 + x2x3)
+ -TC44 (A + A + A ) + TC44 (^l2 + A + A)
+ [Gux,+Gl2(x2+xi)]P2-EP
(10).
Since the Gibbs free energy G must be at the minimum for a stable state of the
ferroelectric at a constant temperature {dGI dP=0), then equation (10) becomes:11
? -E = aP + pP3 +yP5 + 2[Gux, +Gu(x2 +x,)]P-E = 0
(11).
dP
The fifth and higher order of polarization P can be neglected. In addition, we can assume,
P-eE in the case of small electric fields E or in the case of relatively large electric fields
for a paraelectric state of a ferroelectric.11 Then, by differentiating Equation (11) with
respect to P, we can get:' l
BF 1
? = - = a + 3/KeE)2+2[Gnx1+Gu(x2+x3)]
dP
(12).
s
The first-order coefficient a is a function of temperature. When there is no external
electric field, in paraelectric phase of a stress-free ferroelectric, Equation (12) becomes:11
^aJlzI^l
S
(13),
C
in which C is the Curie-Weiss constant, T$ is a characteristic temperature, Te = Tc for
second order phase transformation and Te < Tc for first order phase transformation. For
strains, X2+X3= [l-la/cu]
jcy.For an epitaxial ferroelectric film with no external electric
field, Equation (12) can be expressed as follows:
I = fcZkl +2[Gn +Gl2(\-^)]Xl
6
C
Cu
176
(14).
In Equation (14), the stress-polarization-related electrostriction coefficients Gn and Gn
can be obtained from equation:
n
Gv=caQv
(i,j,k = \,2,...,6)
(15),
where Qkj are the strain-polarization-related electrostriction coefficients. Both c^ and Qkj
of SrTi03 and BaTi03 are listed in Chang's paper and references therein. When
considering (Ba, Sr)Ti03 solid solution, these parameters are calculated assuming there is
a linear relation between the parameter and Ba/Sr ratio.11 The data used for the later
calculation
are listed in Table 5.2. Using the coefficient
Gu=c1]Q11+c12QI2=
in Table 5.2,
-2.541xl010 Nm2C2, G12 = cuQ12 + c12Q22 = cnQi2 + c12Qu = -
3.397* 109Nm2C2. 2{GU +G12[l-2(c12/cn)]}x,
= -5.103xl010Nm2C2.
Table 5.2 The relevant coefficients of in theoretical calculations of the dielectric constant vs.
temperature relationship of Bao.6Sr0.4Ti03 grown on DyScO3(110).
Parameters
Description
Quantity
TC(K)
C(105K)
Bulk Curie temperature
Bulk Curie constant
249
1
Qn(m4/C2)
Electrostriction coefficient
-0.1
Q12(m4/C2)
Electrostriction coefficient
0.034
11
Elastic constant
Elastic constant
3.042
1.474
2
Cn(10 N/m )
c12(10"N/m')
177
0.0020
(a�
?
0.0016
1-- ? - I d e a l Bulk Ba
fleSr
(LS
Dielec
5?g 0.0008
sr
1
-?*
Li M ? *
W
| 20000
o
O
.� 15000
m
.*
m'
.
???Ideal Bulk Ba?,Sr? T i O .
. j *
?
mW
M'
ff
. '%
% 10000
*
m*
M
'
.'
S
mm
?
? \
9
Mm
0.0004
0.0000
TiO J
LA
_j
? 0.0012 .
(b)
25000 -- ??
m
5000
\
- ?
a.
250
300
350
400
Temperature (K)
450
250
300
350
400
Temperature IK)
450
Fig. 5.13 The simulated temperature dependence of inverse dielectric constant (1/t-T) and
dielectric constant (e(T)) based on Curie Weiss law in paraelectric phase of an ideal bulk
Ba0.eSro.4Ti03.
If we take an ideal bulk Bao.6Sro.4TiC>3, assuming C is lxlO5 K, the commonly
reported value, ' ' the bulk Curie temperature Tc is about 249 K and Te is close to
r c , 1819 In the paraelectric phase, the dielectric constant will follow the Curie Weiss Law:
1
(r-249)
?=a =s
,,,,
(16).
T?-
105
The inverse of the dielectric constant (1/s) vs. temperature (7) and e(T) are plotted in Fig.
5.13.
When the strain value, x = -0.33% for Bao.6Sro.4Ti03 on DySc03, is inserted into
Equation (14), one gets: 2{Gu+G12[l-2(cI2/cu)]}x,
=0.001492. If the Curie
temperature shift to 283 K is considered, the inverse of dielectric constant (1/s) and
dielectric constant (e) are plotted as a function of temperature and compared to those of
the ideal bulk plots as shown in Fig. 5.14. The compressive strain raises the inverse of the
dielectric constant at each temperature point by 0.001492; therefore, the dielectric
constant is lowered significantly. For an ideal bulk BST that follows Curie Weiss law, the
178
dielectric constant increases to infinity at the Curie temperature. When the material is
strained, the maximum value around the Curie temperature Tc will be limited by the
constant introduced by the strain; therefore, the dielectric constant does not diverge. For
Bao.6Sro.4TiC<3 films with -0.33% compressive strain, the simulated dielectric constant
maximum value at Curie temperature is about 670.
(a)
0.0028
25000
- ? - I d e a l bulk
S 0.0024 - ? - -0.33% strained
1A
?*
c
(5 0.0020
-
(b)
?
� 20000
� 0.0016
o
S 0.0012
o 15000
;
ric
- ? - I d e a l bulk
???-0.33% strain
?1
a
8 IOOOO
$ 0.0008
a
:
\
5000
� 0.0004
CL
^ 0.0000
?�..,
......"wSMSSlSI^gagigsan^:
0
250
300
350
400
Temperature (K)
450
250
300
350
400
Temperature (K)
450
Fig. 5.14 Comparison of the simulated temperature dependence of inverse dielectric constant
(1/E-T)
and dielectric constant (e-T) based on Curie Weiss law in paraelectric phase between an
ideal bulk Bao.6Sro.4Ti03 and a Ba0.6Sro.4Ti03 film under compressive strain of 0.33%. Note that
the Curie temperature is shifted from 249 K to 283 K from bulk to strained film.
Equation (12) can be used to simulate the effect of strain on the relative dielectric
tunability, if ft can be calculated from bulk tunability measurement. From Chang's
simulation results,11'44 the compressive stress decreases the tunability.11'44 This is
consistent with the observation that the tunability for Bao.6Sro4Ti03 films grown on
DySc03 is below 40%.
To summarize, simulations based on the phenomenological theory predict that the
compressive strain equal in magnitude to the strain in films grown on DyScC>3 can reduce
the dielectric constant from tens of thousands to several hundreds. The dielectric property
179
degradation observed in Bao.6Sro.4Ti03 films grown on DyScC>3 can be understood
qualitatively through this phenomenological analysis. The fact that the observed value is
lower than the simulated dielectric constant might be due to the presence of defects such
as dislocations. Also the observed experimental values of Curie Weiss constant was
2xl0 4 K for Bao.6Sro.4TiC>3 films grown on DySc03, which is lower than the value of bulk
barium strontium titanate, lxlO5 K,45 this Curie Weiss constant decrease remains to be
understood.
5.5 Conclusions
In this research, bulk-like dielectric constants and tunabilities were observed in
high quality Bao.6Sro.4Ti03 thin films grown on GdSc03(l 10) substrates. These properties
were attributed to the improved film crystal quality (absence of random strain fields
associated with extended defects) and the presence of homogeneous 0.2% tensile strain,
achieved by growth on nearly lattice-matched GdScCb substrates. Though the device
losses need to be further decreased, the observation of bulk-like dielectric constants and
tunabilities provides new perspectives on the relative importance of "dead layers" or
intrinsic size effects compared to inhomogeneous strains from extended defects on
dielectric property degradation in barium strontium titanate thin films. The demonstration
of bulk-like tunable microwave dielectric properties in thin films also benefits research
on related functional properties of ferroelectric titanates.
Bao.6Sr0.4Ti03 films were grown on MgO(lOO), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100),
NdGaO3(110), and LaAlC>3(100) under the same controlled conditions and compared to
the Bao.6Sro.4TiC�films grown on GdScO3(110). The relative dielectric constant and
relative tunability in these films were significantly lower than that of the Bao.6Sro.4TiC>3
180
films on GdScC>3. The dislocation densities in Bao.6Sro.4Ti03 films grown on MgO(lOO),
(Laoi8Sro82)(Alo59Tao4i)03(100), NdGaO3(110), and LaAlO3(100) are in the range of
1.5-2.7* lo11 cm"2, about two orders of magnitude higher than that in the Bao.6Sro.4Ti03
films grown on GdScC�and DySc03. The dielectric constant vs. temperature relationship
and tunability vs. temperature relationship demonstrated that the peak e(T) value
decreased and the peak width widened as the rocking curve FWHM increased and the
dislocation concentration increased. The observations were consistent with the simulation
results based on Landau theory. It appears that the compressive inhomogeneous strains
around the cores of dislocations have locally suppressed the polarizations; as the
dislocation concentration increases to the level of 1011 cm"2, the suppressed areas start to
overlap and the strain field around dislocations should have occupied significant fraction
of the film volume; therefore, the effective dielectric constant decreased. Bao.6Sro.4Ti03
films grown on MgO, even though these were homogeneously tensile strained, exhibited
degraded dielectric properties owing to the high dislocation concentration and high
density of grain boundaries. This indicates that the tensile strain is not sufficient to
achieve bulk-like dielectric properties.
Coherently strained Bao.6Sro.4TiC>3 films were grown on DyScO3(110) under the
same growth conditions as GdSc03 except the thickness difference. Planview TEM
showed that the dislocation concentration in Bao.eSro 4Ti03/DySc03 was only three times
that present in Bao.eSro^TiCVGdScCb. The relative dielectric constant and the relative
tunability
measurement
demonstrated
significant
degradation
of
the
Bao.6Sro.4TiC>3/DySc03 properties. The differences between dielectric properties in
Bao.6Sro.4TiC>3 film on DyScCb and on GdScC>3 were believed to be due to the
181
compressive strains from the DySc03 substrates. Simulations based on phenomenological
theories have shown that a compressive strain of-0.33%, can reduce the Bao.6Sro.4Ti03's
dielectric constant from tens of thousands to several hundreds. This can qualitatively
explain the degradation of the dielectric properties observed in Bao.6Sro.4TiC>3 films on
DyScC>3. From the comparison of the dielectric properties of Bao.6Sr0.4Ti03/DySc03 to
that of the Bao.eSro^TiCVGdScCb, it can be seen that the compressive strain by itself can
significantly degrade the dielectric properties.
In this research, the high quality Bao.6Sro.4Ti03 films grown on closely lattice
matched substrates with low dislocation density allow the separation of the effect of the
dislocations and the uniform strains. By systematic study of the inhomogeneous strains
associated with dislocations and the homogenous strains when the dislocation
concentration is minimized, we can draw the conclusion that (1) inhomogeneous strains
around dislocation cores are detrimental to the relative dielectric constant and the relative
tunability, (2) uniform compressive strain can degrade the dielectric properties, and (3)
both high crystal quality and tensile strain are necessary, but neither of them is sufficient,
to achieve bulk-like dielectric properties.
References
1
S. S. Gevorgian, T. Martinsson, P. L. J. Linner, and E. L. Kollberg, IEEE
Transactions on Microwave Theory and Techniques 44, 896-904 (1996).
2
P. Carlberg, M. Graczyk, E. L. Sarwe, I. Maximov, M. Beck, and L. Montelius,
Microelectron. Eng. 67-68,203-207 (2003).
3
J. H. Haeni, Thesis, Pennsylvania State University, 2002.
182
J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W.
Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q.
Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, Nature 430,758-761 (2004).
S. Gevorgian, C. E., S. Rudner, L. D. Wernlund, X. Wang, and U. Helmersson,
IEE Proceedings-Microwave and Antenna Propagation 143,397-401 (1996).
P. K. Petrov, N. M. Alford, and S Gevorgian, Meas. Sci. Technol. 16, 583-589
(2005).
W. J. Kim, W. Chang, S. B. Qadri, J. M. Pond, S. W. Kirchoefer, D. B. Chrisey,
and J. S. Horwitz, Applied Physics Letters 76, 1185-1187 (2000).
M. D. Biegalski, J. H. Haeni, S. Trolier-McKinstry, D. G. Schlom, C. D. Brandle,
and A. J. V. Graitis, Journal of Materials Research 20, 952-958 (2005).
J. W. Matthews and A. E. Blakeslee, Journal of Crystal Growth 27, 118-125
(1974).
R. People and J. C. Bean, Applied Physics Letters 47,322-324 (1985).
W. Chang, C. M. Gilmore, W.-J. Kim, J. M. Pond, S. W. Kirchoefer, S. B. Qadri,
D. B. Chirsey, and J. S. Horwitz, Journal of Applied Physics 87, 3044-3049
(2000).
H. Du, P. J. Fisher, M. Skowronski, P. A. Salvador, and O. Maksimov, Journal of
Crystal Growth 310, 1991-1998 (2008).
D. G. Schlom, Long-Qing Chen, C.-B. Eom, K. M. Rabe, S. K. Streiffer, and J.M. Triscone, Annual Revew of Materials Research 37,589-626 (2007).
M. M. Saad, P. Baxter, R. M. Bowman, J. M. Gregg, F. D. Morrison, and J. F.
Scott, Journal of Physics.: Condensed Matter 16, L451-L456 (2004).
183
T. M. Shaw, Z. Suo, M. Huang, E. Liniger, R. B. Laibowitz, and J. D. Baniecki,
Applied Physics Letters 75,2129-2131 (1999).
J. Zhai, X. Yao, X. Cheng, L. Zhang, and H. Chen, Materials Science and
Engineering B 94,164-169 (2002).
J. D. Baniecki, R. B. Laibowitz, T. M. Shaw, P. R. Duncombe, D. A. Neumayer,
D. E. Kotecki, H. Shen, and Q. Y. Ma, Applied Physics Letters 72, 498-500
(1998).
H. V. Alexandra, C. Berbecaru, A. Ioachim, L. Nedelcu, and A. Dutu, Applied
Surface Science 253,354-357 (2006).
H. V. Alexandra, C. Berbecaru, A. Ioachim, M. I. Toacsen, M. G. Banciu, L.
Nedelcu, and D. Ghetu, Materials Science and Engineering B 109, 152-159
(2004).
K. J. Choi, M. Biegalski, Y. L. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche,
Y. B. Chen, X. Q. Pan, V. Gopalan, L. Q. Chen, D. G. Schlom, and C. B. Eom,
Science 306,1005-1009 (2004).
N. A. Pertsev, A. G. Zembilgotov, S. Hoffmann, R. Waser, and A. K. Tagantsev,
Journal of Applied Physics 85,1698-1701 (1999).
S. Hoffinann and R. Waser, Le Journal de Physique IV 08, Pr9-221-Pr9-224
(1998).
K. Rabe, C. H. Ahn, and J. M. Triscone, Physics of Ferroelectrics: A Modern
Perspective, Vol. 105 (Springer-Verlag, Berlin Heidelburg, 2007).
L. Benguigui and K. Bethe, Journal of Applied Physics 47,2787-2791 (1976).
184
S. Garcia, J. P. R. Font, R. J. Quinones, J. Heiras, and J. M. Siqueiros, Journal of
Electroceramics 6:2,101-108 (2001).
A. K. Tagantsev, V. O. Sherman, K. F. Astafiev, J. Venkatesh, and N. Setter,
Journal of Electroceramics 11, 5-66 (2003).
A. C. Carter, J. S. Horwitz, D. B. Chrisey, J. M. Pond, S. W. Kirchoefer, and W.
Chang, Integrated Ferroelectrics 17,273-285 (1997).
L. C. Sengupta and S. Sengupta, Materials Research Innovations 2, 278-282
(1999).
M. J. Kenneth, Journal of Applied Physics 33,2826-2831 (1962).
X. B. Chen, C. H. Li, Y. Ding, Z. F. Zhang, H. M. Shen, J. S. Zhu, and Y. N.
Wang, Physica Status Solidi (a) 179,455-461 (2000).
W. P. Lu, X.Y. Mao, and X. B. Chen, Journal of Applied Physics 95, 1973-1976
(2004).
Y. N. Huang, Y. N. Wang, and Z. X. Zhao, Physical Review B 49,1320 (1994).
S. Der-Chi, C. Bi-Shiou, K. Meng-Wei, C. Jyh-Shin, C. S. C. Bruce, J. ChuehKuei, W. Mei-Fang, and C. Huang-Chung, Electrochemical and Solid-State
Letters 6, G55-G58 (2003).
H. Schroeder and S. Schmitz, Material Research Society Symposium Proceeding
748, U6.2.1(2003).
S. P. Alpay, I. B. Misirlioglu, V. Nagarajan, and R. Ramesh, Applied Physics
Letters 85, 2044-2046 (2004).
I. B. Misirlioglu, A. L. Vasiliev, M. Aindow, S. P. Alpay, and R. Ramesh,
Applied Physics Letters 84,1742-1744 (2004).
185
D. Balzar, P. A. Ramakrishnan, and A. M. Hermann, Physical Review B 70,
092103 (2004).
O. Tikhomirov, H. Jiang, and J. Levy, Applied Physics Letters 77, 2048-2050
(2000).
Y. Zheng and C. H. Woo, J. Phys. D: Appl. Phys. 41,175403 (2008).
W. Chang, J. S. Horwitz, A. C. Carter, J. M. Pond, S. W. Kirchoefer, C. M.
Gilmore, and D. B. Chrisey, Applied Physics Letters 74,1033-1035 (1999).
A. F. Devonshire, Philosophical Magazine (Series 7) 40,1040 -1063 (1949).
A. F. Devonshire, Philosophical Magazine (Series 7) 42,1065-1079 (1951).
A. F. Devonshire, Advances in Physics 3, 85 -130 (1954).
C. Wontae, L. M. B. Alldredge, W. K. Steven, and M. P. Jeffrey, Journal of
Applied Physics 102, 014105 (2007).
B. Wang and C. H. Woo, Journal of Applied Physics 100, 044114-5 (2006).
186
Chapter 6
Summary of Conclusions and Future Perspectives
In this chapter, Section 6.1 summarizes the observations and conclusions of this
research. Section 6.2 will propose future perspectives for extension of this project with
the goal of improving the understanding.
6.1 Summary of Conclusions
In this research, systematic investigations have been carried out to understand the
correlation between the microwave dielectric properties and the inhomogeneous strains
associated with dislocations and the homogeneous strains associated with lattice
mismatch in (Ba, Sr)TiC>3 thin films. To understand the microstructure, the growth modes
of Bao.6Sro4Ti03 grown on different substrates under different conditions were
investigated. The slipTsystem in (Ba, Sr)TiC>3 was revisited by studying the misfit
dislocation generation mechanisms of (001)-, (110)-, and (lll)-oriented Bao 6Sro.4Ti03
films. To systematically investigate the dielectric properties vs. dislocation density and
strain relation, Bao.6Sro.4TiC>3 films have been grown on substrates such as MgO(lOO),
GdScO3(110), DyScO3(110), (Lao.i8Sro.82)(Alo59Tao.4i)03(100), NdGaO3(110), and
LaAlO3(100) under the same controlled conditions. The dielectric properties were
measured using IDC structures at microwave frequencies. These properties were
correlated to the film dislocation densities and strain states. Phenomenological theoretical
analyses were used to explain the observations.
The substrates surface engineering processes using chemical etching and thermal
annealing were investigated by AFM and RHEED in order to optimize the Bao.6Sr0.4Ti03
films growth. For cubic or pseudo-cubic perovskite substrates, such as SrTiC�100),
187
LaAlO3(100), GdScO3(110), DyScO3(110), and NdGaO3(110), atomically flat surfaces
have been achieved by BHF etching followed by annealing at 1000癈 in air for two
hours. However, this approach did not work well for either (Lao.i8Sro.82)(Alo.59Tao.4i)03,
which has a very complex chemical composition, or MgO(lOO) which has a rock salt
structure. For (Lao.igSro.82)(Alo.59Tao.4i)03, the method used for ordinary perovskites
introduced particles on the substrate surfaces which caused disorientations in the
Bao.6Sro.4T103 films. (Lao.i8Sro.82)(Alo.59Tao.4i)03 substrates were used for direct
deposition after light acid (HC1:H20=1:1) etching for 1 minute. For MgO, annealing in
flow of pure oxygen caused step bunching and surface roughening on MgO crystal
surfaces; substrate annealing at 1350癈 in air for 4 hours yielded clear steps on the
substrate surfaces.
The growth modes of the films were studied by characterizing the surface
morphologies at different film growth stages. The purpose of this step was to assure the
same strain relaxation mechanism and control of the microstructure. Bao.6Sro.4Ti03 films
grown on SrTiO3(100), (110), and (111) exhibited 2D nucleation layer-by-layer growth
mode. Growth modes were also studied on (OOl)-oriented Bao.6Sro.4Ti03 films grown on
MgO(lOO),
GdScO3(110),
DyScO3(110),
(Lao.i8Sro82)(Alo.59Tao.4i)03(100),
NdGaO3(110), and LaAlO3(100). The Bao.6Sro.4Ti03 films grown on MgO(lOO) always
adopted a 3D island growth mode. This is attributed to the large mismatch between
Bao.6Sro4Ti03 lattice and the MgO lattice. Bao.6Sro.4Ti03 films grown on GdScO3(110),
DyScO3(110), (Lao.i8Sr0.82)(Alo.59Tao.4i)03(100),
NdGaO3(110),
demonstrated 2D nucleation layer-by-layer growth mode.
188
and
LaAlO3(100)
Bao.6Sro.4Ti03 film strain relaxation mechanisms in (001)-, (110)-, (lll)-oriented
Bao.6Sro.4TiC>3 films were discussed by comparing the experimentally observed
dislocation characteristics to the predictions made based on the film geometry and slipsystems. Two sets of dislocations were observed for films grown on SrTiC>3(100),
SrTiC>3(110), and SrTiC>3(lll). One set of long continuous lines that were far apart
played a relatively unimportant roll for the major strain relaxations and the other set of
short segments that were close to each other and played a major role on relaxing most of
strains. Using the unique features of (HO)-oriented films grown on SrTiO3(110), for
which the long continuous dislocations forming 109� network can only be consistent
with consistent with the < 110 > {110} slip system, and the short segments lying along the
[110] direction could only be generated by <100> type of dislocation climbing. A
relaxation model was proposed for which the films inherit <110> type of dislocations
from the substrate and these dislocations bow out forming misfit dislocations. When
these "inherited" dislocations are used up, they are not sufficient to relax all the mismatch
strain. Another set of dislocations has to nucleate from the film top surface and then
move to the interface forming misfit dislocations. Since dislocations with the <110>
Burger's vector take more energy to nucleate, <100> types of dislocations are preferred
for nucleation and play a major role in strain relaxation. This is supported by the absence
of <110>-type of misfit dislocations at the interface of (HO)-oriented Bao.6Sro.4Ti03 film
grown on NdGaO3(110) substrate, which has a very few dislocations for the film to
inherit. Dislocations in Bao.eSro/TiOs films on SrTiC>3(100) and SrTiC>3(lll) support the
same mechanism. Understanding the relaxation mechanism helps with the experiment
189
design on substrate choices, substrate orientation selection and the control of the film
thicknesses to make the property vs. microstructure correlation analysis easier.
120 nm thick Bao.6Sro.4TiC>3 films were deposited on different substrates
including MgO(lOO), GdScO3(110), SrTiO3(100), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100),
NdGaC>3(110), and LaAlC>3(100). The dielectric properties were measured and correlated
with the dislocation concentrations and the homogeneous strain states. The Bao.6Sro.4Ti03
films grown on GdScCb were coherently tensile strained and the films have high
crystalline quality. The rocking curve FWHM of the Bao.eSro/TiCh films grown on
GdScC>3 was about 25 arc seconds, which is the best crystal quality that has been reported
for (Ba, Sr)Ti03 solid solution films. This is one of the lowest widths observed on
commercially available substrates, such as single crystals of SrTiC>3 and BaTiC^.1 The
temperature dependence of the relative dielectric constant and the relative tunability in
Bao 6Sro.4TiC>3 on GdScC>3 has been measured at 5 GHz frequency. The relative dielectric
constant peak value at Curie temperature reached 7000 and the relative tunability peaked
at 92%. The FWHM of the dielectric constant vs. temperature plot is about 30 K. These
dielectric properties are comparable to the bulk properties observed in BST ceramics.2"4
The minimum dielectric loss under zero bias could reach 0.05 and the communication
quality factor reached its maximum of 500. This corresponds to about 50% increase from
the previous reports.
The dielectric properties of Bao.6Sro.4Ti03 films grown under the same conditions
on MgO(100), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), and LaAlO3(100) were
compared to the Bao.6Sro.4TiC>3 films grown on GdScO3(110). The relative dielectric
constant and relative tunability of these films were significantly lower than the
190
Bao.6Sro.4Ti03 films on GdScC>3. The dislocations in Bao.6Sro.4TiC>3 films grown on
MgO(lOO), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), and LaAlO3(100) were
present in densities above 10ncm"2, which is about two orders of magnitude higher than
the dislocation density in Bao.6Sro.4TiC>3 films on GdScC>3. The dielectric constant and
tunability vs. temperature relationships demonstrated that the peak value decreased as the
rocking curve width and the dislocation density increased. Simulation work in the
literature demonstrated that the compressive inhomogeneous strains around the cores of
dislocations have locally suppressed the polarizations and spread out the distribution of
Curie temperatures, therefore, decreased the local dielectric constant.5 As the dislocation
concentration increases to the level of 1011 cm"2, the areas of lower dielectric constants
overlap thereby decreasing the dielectric constant in general and caused the broadening of
the dielectric constant vs. T relation. The observations in this research are consistent with
the understanding of the simulation. For Bao.6Sr0.4Ti03 films on MgO, even though the
film was in tension, the dielectric constant and tunability were still degraded indicating
that the tensile strain is not sufficient to achieve bulk-like properties.
Effects of homogeneous strain were assessed by comparing the dielectric
properties of coherently strained high quality Bao 6Sro.4Ti03 films on DySc03(l 10) to that
of Bao.6Sro.4TiC>3 film on GdScC<3. The observation demonstrated that even though the
dislocation density between the two types of films differed by only a factor of three,
significant degradation was evident in the dielectric constant and tunability in the
BST/DyScC>3. The differences between dielectric properties in Bao.6Sro.4TiC<3 film on
DySc03 and on GdSc03 were believed to be due to the homogeneous compressive strains
induced by the DyScQ3 substrates. Simulations based on phenomenological theories have
191
showed that a compressive strains of-0.33%, equivalent to the strain from DySc03, could
decrease the dielectric constant of ideal bulk BaoeSro/riCh from tens of thousands to
several hundreds. This can qualitatively explain the degradation of the dielectric
properties observed in Bao.6Sro.4Ti03filmson DyScC>3.
From this research, conclusion can be drawn that: (1) both inhomogeneous strains
associated with dislocations and homogeneous compressive strains can cause the
degradation of the dielectric properties, (2) to achieve bulk-like properties, both the
absence of homogeneous compressive strains and low dislocation density are necessary;
however, neither of them is sufficient by itself.
6.2 Future Perspectives
6.2.1 Further investigation of homogeneous strain effect
As it has been discussed in Chapter 2, the lattice parameter of BaxSri.xTi03 has an
almost linear dependence on the Ba content x. ' The bulk lattice parameter can be
calculated using the following equation: 3.996x +3.905(l-x) A in which 3.996 A is the
lattice parameter of BaTiC"3 and 3.905 A is the lattice parameter SrTiC>32'3,6"8 In order to
further understand the effect of homogeneous strain effect. BaxSri.xTi03 films with
different Ba ratio x can be grown on GdScC>3 and DyScC>3 with the composition of x=0,
0.5, 0.6, 0.7, and 0.8. The corresponding bulk lattice parameters are listed in Table 6.1.
Table 6.1 The in-plane lattice parameters of the GdScO3(110) and DyScO3(110) substrates and
the bulk lattice parameter of BaxSri-xTi03 with different Ba content x.
GdScO3(110)
DyScO3(110)
3.968A
3.947A
3.965A
3.945A
Bao.8Sro.2Ti03
Bao7Sro.3Ti03
Bao.6Sro.4Ti03
Bao5Sro.5Ti03
SrTi03
3.978A
3.968A
3.959A
3.950A
3.905A
192
The mismatch between the BaxSri.xTiC>3 film and the substrate can be calculated
and the expected strain states can be estimated for coherently strained films. As is evident
from Table 6.2, when x increases from 0 to 0.8, the strain state in the films on DyScOs
and GdSc03 will change from tensile to lattice-matched to compressive; vertically, the
comparison between the different strain states for the same film stoichiometry can be
carried out.
Table 6.2 The expected strain states of the BaxS/vx77'03 grown on GdScO3(110) and
DyScO3(110).
SrTi03
Ba0.5Sro.5Ti03
Ba06Sro.4Ti03
BaoySrosTiOj
Bao.8Sra2Ti03
DyScO3(110)
Tensile
Matched
Compressive
Compressive
X
GdScOj(HO)
X
Tensile
Tensile
Matched
Compressive
This set of samples has been deposited at the same controlled growth conditions
and the film thicknesses were 50 nm. X-ray diffractions and reflectivity have proved the
existence of the 50 nm film. The planview TEM image taken from the Bao sSro.sTiOs film
grown on GdScC>3 (Fig. 6.1) showed that no dislocations were observed in the area of
about 1 urn2. Actually within the whole electron transparent area of the TEM sample,
very few dislocations were observed; those few dislocations might be just those inherited
from the substrate. It is reasonable to believe that these films are still coherently strained.
From the lattice mismatch calculation, the lattice mismatch between the Bao.5Sr0 ST1O3
film and the GdScCb substrate is of 0.46%, even though 50 nm thickness already exceeds
the critical thicknesses calculated based on models proposed by Matthew and Blackeslee9
and by People and Bean,10 the film is still coherently strained to the substrate. This
mismatch among this set of samples is the largest except SrTi03 on DySc03. For SrTiC>3
193
on DyScC>3, Haini et al. has proved that the SrTi03 films deposited using MBE on
DyScC>3 was still coherently strained at 50 nm thickness with a mismatch of 1.1%.7 It is
reasonable to believe that the other films with mismatches smaller than 0.46% are still
coherently strained. The high resolution rocking curve FWHM on all of these films have
shown that all of these films have the same quality as the substrates.
*!*?*??;&&';#
? - , ' 0 ???
-';/''W.
200 nm
Fig. 6.1 Planview TEM image of the Bao.5Sro.5nO3 film grown on GdScO3(110). The large area
examination did not find many dislocations in the whole TEM sample, indicating the film
dislocation density is as low as the substrate.
Considering the strain effect on the Curie temperature, and based on our modeling
on the effect of strains on the dielectric constant, the hypothesized temperature
dependence of the dielectric constant will be close to what is depicted in the schematic
drawing in Fig. 6.2. The dielectric constant will be enhanced for those films under tensile
strain, and suppressed for those films under compressive strain. The dielectric
measurement will be carried out and compared to the predictions we have made based on
our hypotheses. This set of experiment will exclude the effect of dislocations make the
argument stronger.
194
BST50:50 STO BST60:4Q BST70:3Q
*?*
c
(a)
S jj
a
m
c
O
u
u
tj
J)
Si
a
i
210K
i i
285K 310K 405K
Temperature
BST70:30 BSTS0:SO
BST60:40
BSi80:20
+?*
c
(Z
to
c
O
u
_u
*?*
u
a
a
a
285K 290K
310K
380K
Temperature
Fig. 6.2 The schematic drawing of the expected temperature dependence of the dielectric
constant from the set of Ba^Sr^TiOs films with different Barium content x grown on DyScO3(110)
(a) and GdScO3(110) (b) as described in Table 6.2.
6.2.2 Theoretical modeling
In the literature, simulations have been done on the homogeneous strain effect on
the polarizations and Curie temperatures around dislocation cores based on LandauDevonshire thermodynamic theory.5 A statistical model can be formulated based on the
simulation results. Density of dislocations and the overlapping of inhomogeneous strain
fields can be introduced into consideration. It might be able to give predictions on how
the polarizations or dielectric constants change as a function of temperature. The
predictions can be compared to experimental observations.
During our study on the homogeneous and inhomogeneous strain effects, the
Curie Weiss plot found lower Curie Weiss constant than those reported for counterpart of
195
bulk and thin films. If the experiments in �2.1 could be carried out, the experimental
results can be used a reference for theoretical study on what factors could have affected
the Curie Weiss constant. In the literature, there are still arguments between the idea on
whether compressive strains increase or decrease the Curie temperature.. Experimental
results from �2.1 may be an experimental proof when the impacting factors are
minimized and well controlled.
6.2.3 Investigation of stoichiometry effect
High quality coherently strained BST films grown on GdScCb give the possibility
to look into the effect of stoichiometry effects, such as oxygen vacancy effects, cation
vacancy effects, and doping effects, with the minimal complexity. Bao.6Sro.4Ti03 films
can be grown on GdScC>3(110) under different oxygen pressures. Lattice parameters can
be measured to track the strain state. This set of experiments can help the understanding
of the coupling between oxygen vacancies and strain effects.
Cation vacancy effects and extrinsic doping effects have also been investigated on
bulk and thin film of barium strontium titanate. Further experimental work can be done
for the BST films grown on GdScC� to change the stoichiometry of A site or B site
cations, or add extrinsic dopants to modify the composition of the deposition target to
understand how these factors would influence the temperature dependence of the
dielectric properties, including dielectric constant, tunability and loss.
In summary, the ability to deposit high quality barium strontium titanate films
grown on GdScC"3(l 10) which possesses the bulk like properties, allows one to use them
as a reference to design a series of experiments to understand the major factors that
deteriorate the dielectric properties of barium strontium titanate thin films. At the same
196
time, the results can be used in turn to examine the phenomenological predictions. The
observation will trigger further deeper understanding of the phenomenological theories.
6.2.4 Investigation of related properties and functions
The most important new direction for the varactor applications is to generate an
understanding of where loss mechanisms arise in the thin films that have otherwise bulklike properties. The results given herein show that the dielectric constant, the dielectric
tunability. and the temperature dependences of those values can be bulk-like by
controlling the strains in thin films. However, the dielectric loss are still larger in all the
films investigated here as compared to bulk material. To generate films with figures of
merits high enough for applications, it is essential that loss mechanisms be understood
and to decrease the overall loss values. The understanding and results obtained from this
research inspired a further deeper understanding of this family of ferroelectric materials
with multiple functions for multiple applications, barium strontium titanate material is
lead-free and environmentally benign. Its dielectric properties enable this material to
work as functional layer for tunable capacitors; these have been investigated here in this
research. However, its pyroelectric properties which can be used for infrared detectors,
night vision,11"13 its piezoelectric properties which can be used for transducers,14 its
ferroelectric properties which enable non-volatile random access memories,15"17 and its
electro-optic properties which benefit electronic controlled optical devices,18"21 are all
impacted by dislocations but were not investigated in this research. It would be
interesting to look into how such high-quality barium strontium titanate films would
improve the performances on these related functions.
197
References:
1
D. G. Schlom, Long-Qing Chen, C.-B. Eom, K. M. Rabe, S. K. Streiffer, and J.M. Triscone, Annu. Rev. Mater. Res. 37, 589-626 (2007).
2
H. V. Alexandria, C. Berbecaru, A. Ioachim, L. Nedelcu, and A. Dutu, Applied
Surface Science 253,354-357 (2006).
3
H. V. Alexandru, C. Berbecaru, A. Ioachim, M. I. Toacsen, M. G. Banciu, L.
Nedelcu, and D. Ghetu, Materials Science and Engineering B 109,152-159
(2004).
4
J. Zhai, X. Yao, X. Cheng, L. Zhang, and H. Chen, Materials Science and
Engineering B 94,164-169 (2002).
5
S. P. Alpay, I. B. Misirlioglu, V. Nagarajan, and R. Ramesh, Applied Physics
Letters 85,2044-2046 (2004).
6
K. J. Choi, M. Biegalski, Y. L. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche,
Y. B. Chen, X. Q. Pan, V. Gopalan, L. Q. Chen, D. G. Schlom, and C. B. Eom,
Science 306,1005-1009 (2004).
7
J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W.
Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q.
Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, Nature 430, 758-761 (2004).
8
J. H. Haeni, Thesis, Pennsylvania State University, 2002.
9
J. W. Matthews and A. E. Blakeslee, Journal of Crystal Growth 27,118-125
(1974).
10
R. People and J. C. Bean, Applied Physics Letters 47,322-324 (1985).
198
H. Zhiming, Z. Zhanhong, J. Chuping, Y. Jian, S. Jinlan, and C. Junhao, Applied
Physics Letters 77, 3651-3653 (2000).
M. H. Charles, R. B. Howard, A. O. Robert, C. Mac, and S. McKenney, in
Uncooled thermal imaging at Texas Instruments, 1992 (SPIE), p. 17-26.
M. H. Charles, R. B. Howard, and L. A. Diane, in Uncooled thermal imaging with
thin-film ferroelectric detectors, 2008 (SPIE), p. 694025.
G. Wang, T. Polley, A. Hunt, and J. Papapolymerou, IEEE Antennas and Wireless
Propagation Letters 4,217-220 (2005).
J. F. Scott, Japanese Journal of Applied Physics, Part 1: 38,2272-2274 (1999).
Y. Tsunemine, T. Okudaira, K. Kashihara, A. Yutani, H. Shinkawata, M. K.
Mazumder, Y. Ohno, M. Yoneda, Y. Okuno, A. Tsuzumitani, H. Ogawa, and Y.
Mori, Japanese Journal of Applied Physics, Part 1 43, 2457-2461 (2004).
H. Shu-chun, C. Hong-ming, W. Shich Chuan, and L. Joseph Ya-min, Journal of
Applied Physics 84, 5155-5157 (1998).
M. Gaidi, M. Chaker, P. F. Ndione, R. Morandotti, and B. Bessais, Journal of
Applied Physics 101,063107 (2007).
K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, in
Theoretical study of ferroelectric barium-strontium-titanate-based onedimensional tunable photonic crystals, 2007 (SPIE), p. 65560R.
K. Dal-Young, M. Seung Eon, K. Eun-Kyung, L. Su-Jae, C. Jong-Jin, and K.
Hyoun-Ee, Applied Physics Letters 82,1455-1457 (2003).
J. M. Marx, O. Eknoyan, H. F. Taylor, Z. Tang, and R. R. Neurgaonkar, Applied
Physics Letters 67,1381-1383 (1995).
199
icinity of the Curie temperature, the values of 1/s smoothly deviate away from the Curie
Weiss values, consistent with the behavior indicative of a second order phase
transformation. That Te ~ Tc is also consistent with a second order transition.23 It is
believed that BaxSri.xTi03 single crystals with x>50% exhibit a first order phase
transformation, in which the inverse dielectric constant abruptly deviates from Curie
Weiss behavior and Te < Tc.24 However, similar Ba^SrojTiC^ doped with 0.01 to 0.1
mol% Nb5+ was observed to exhibit a second order transition.25 The second order
character observed in this experiment could, therefore, be a result of significant point
defect populations, such as oxygen vacancies.
The relative tunability at a given voltage and temperature can be defined as:26
( ^ = f^Z2zZ2
159
(1),
where er(0,T) and s^V,T) are the relative dielectric constants at a temperature T under
bias voltages of zero and V, respectively. Figure 5.3b shows the relative tunability at the
maximum applied voltage versus temperature, or nr(30 V,T). The relative tunability
reaches a peak value of 92% at 308 K (the same temperature as the dielectric constant
peak), a value that is comparable to the highest tunability observed in bulk ceramics and
single crystals.26"28
The bias voltage dependence of dielectric constant was measured at 308 K by
increasing the bias voltage from -30 V to +30 V and then back to -30 V. From these
measurements, the relative tunability nr(V,308 K) was determined and is given as the
inset in Fig. 5.3b. No hysteresis was observed at 308K, indicating the spontaneous
polarization at Tc = zero, as expected for a second order transition. It can be seen from the
inset that more than 80% of the tuning happens below 15 V, which will benefit
applications.
Fig. 5.4 gives the temperature dependence of (device) dielectric loss, given as
tan8, measured at 5 GHz under different bias voltages. At a 0 V bias, the dielectric loss
curve exhibits a peak of 0.38 at 298 K (a temperature that is slightly below the
temperature of the dielectric peak); with increase of the temperature, the loss drops
sharply to about 0.05 at 325 K and then gradually increases. The behavior at bias voltages
of 15 and 30 V are similar to each other; the loss decreases from 250 K to ~ 350 K and
then gradually increases with increasing temperature. The inset gives tand. as a function
of bias voltage at 308 K. The dielectric loss decreases sharply with applied voltage from
0 V to ~ 10 V and then increases slowly as the voltage is increased further.
160
0.40
.
OM
A
? ov
"|M�
jl
T籎ttX
0.3S ? �V
130V
/
MS 0.30
" 0.25
1
'
?
?
\
*'"
| M�
1 &>�
^
?-JL-.
-IB ? � -10 0 10 20 JO
BlttVatug�(V|
?*
i:::
0.05
0.00
*
?-*??
?
250
300
350
Temperature (K)
400
Fig. 5.4 Temperature dependence of dielectric loss measured at different bias voltages, 0 V,
15 V, and 30 V. The inset shows the bias voltage dependence of dielectric loss at 308 K.
The device loss comes from a combination of BST film loss and electrode loss.
The loss from BST film includes the intrinsic dielectric loss (tan8int) and the conduction
loss (tan8c). The device dielectric loss can be expressed as:16'29
tan 8 =. tan Sjm + tan Sc
(2).
The intrinsic loss of paraelectric phase can be expressed as:[9,40]
tan 8^,
1
tanSl
[l + j3(tanl3)E2]' /3
(3),
where tanS癿 is the intrinsic loss with no bias field, E, and /? is a constant derived from
Landau-Devonshire theory. The conduction loss can be expressed as:16'29
1
tan 8? =
coRC
(4),
where co is the measurement frequency, R is the resistance of the sample, and C is the
geometrical capacitance (effective capacitance from the measurement) of the specimen.
These mechanisms can be used to understand observations in Fig. 5.4.
The dielectric loss peak observed slightly below Curie temperature in the 0 V
curve has been observed in barium strontium titanate bulk polycrystalline ceramics and
161
other ferroelectric materials. This characteristic is often attributed to viscous domain wall
motion and its associated internal friction that dissipates electrical energy (to mechanical
and thermal energy).16'30-32 With an increase in the temperature, the dielectric loss at 0 V
decreases quickly to about 0.05, because above the Curie temperature the paraelectric
phase has no domains.30 While this mechanism of intrinsic loss decreases, the conduction
loss increases with increasing temperature and ultimately dominates at high temperatures.
The loss increases with temperature because the conductivity of the barium strontium
titanate film increases with temperature.33 Therefore, the measured loss increases when
the temperature goes above 350-380 K, for all bias voltages. In regard to the field
dependence of the tand vs. T curves, the most obvious effect is that there is no peak for
15 and 30 V bias, as observed elsewhere.16 Also, the low-T portion of the curves also
exhibit a field dependence offset from each other similar to the conduction loss region.16
At 308 K, the loss decreases with increasing field in either direction from 0 V, as
expected from Equation (3). At higher bias voltages, however, the conductivity of the
barium strontium titanate film starts to increase with increasing electric field, resulting in
an increasing loss.34
For application purposes, one must consider the trade-offs between the tunability
and the losses. The communication quality factor (K) has been used as a comprehensive
figure of merit and is defined as:26
(*-0 2
K__
(5)
玹an<5(0ntan<J(30n
in which tan5(0 V) and tan8(30 V) are the dielectric loss under zero and 30 V bias, and
n is defined as the tunability (note the difference from the relative tunability):
162
sr(OV)
n=
sr(30V)
(6)
Fig. 5.5 gives the communication quality factors K as a function of temperature;
K peaks at the value of 500 at 320 K. This is over a 50% increase from the highest
reported values for thin film varactors.26 A value of 900 is considered appropriate for
phase shifter applications.26 Further decreases in the dielectric losses, either by decreasing
the electrode or barium strontium titanate conduction losses, could push these values into
an acceptable range.
300
350
400
Temperature (K)
Fig. 5.5 Plot of Communication quality factor as function of temperature, using the tunability at
30V and the dielectric loss under no bias and loss under 30V bias.
5.3 Effects of inhomogeneous strains on dielectric properties
5.3.1 Inhomogeneous strain effects on the dielectric constant and tunability
Bao6Sro.4Ti03 films were grown on MgO(100), (Lao.i8Sr082)(Alo.59Tao.4i)C>3(100),
NdGaC>3(110), and LaAlOs(lOO) substrates under exactly the same conditions as the
Bao.6Sro4Ti03 films on GdScC>3(110). The results of the dielectric constant measurement
versus temperature are summarized in Fig. 5.6a and are also compared to that of the
Bao.6Sro.4Ti03 films on GdSc03(l 10). The dielectric properties and structural information
are summarized in Table 5.1. The dielectric constant peaks of Bao.6Sro 4TiC>3filmsgrown
163
on substrates other than GdScC>3 have much wider widths (FWHM > 95 K), and much
lower maximum values than those observed in Bao.eSro/TiOs films on GdScC>3. The
maxima of the dielectric constant of the films follow the order BST/GdScO3(7099) >
BST/(Lao.i8Sro.82)(Alo.59Tao.4i)03 (1654) > BST/NdGa03 (1174) > BST/LaA103 (874) >
BST/MgO(630). By comparing this order to that of films' x-ray rocking curve widths
(listed in Table 5.1), one can find that the maximum of the dielectric constant decreases
as the rocking curve FWHM (or dislocation density) increases. Also, the e(T) peaks
become wider as the FWHM of the rocking curve and dislocation density increase.
100
8000
(a)
A
g 6000
o
-?-GdScO^HO)
-�-LSAT(100)
- A - N d G 30,(100)
-T-La籌O,<100>
?�-M(jO<10<�
J> 5000
|
4000
I 2000
& 1000
�
� 60
'
T T
\
-�-LSAT(100)
-A-NdGaOjdlO)
-Y-LaAIO,(100)
MgO
J�
40
J
a 3000
-?-GdScO^HO)
<b)
lity
| 7000
/
/
.^
?"--.
� 20
~�-^
0
250
300
350
Temperature (K)
400
450
250
300
350
Temperature (K)
400
450
Fig. 5.6 (a) Comparison of the temperature dependencies of the relative dielectric constants and
(b) the relative tunabilities for (OOI)-oriented Sa06Sro477'03 films grown on GdScO3(110),
(Lao.igSro.82)(Alo.59Tao.4i)03(100),
NdGaO3(110), LaAIO3(100), and
MgO(100). Note the
measurement frequency was 5 GHz and the tunability was measured at 30 V applied on a 8
micron gap, equivalent to 37.5 kV/cm field.
Fig. 5.6b gives the temperature dependencies of the relative tunabilities for
Bao.6Sro.4Ti03 films on GdScO3(110), MgO(100), (Lao.i8Sro.82)(Alo59Tao.4i)03(100),
NdGaO3(110), and LaAlO3(100) substrates. The relative tunabilities were calculated
using the dielectric constants measured at zero bias and 30 V bias. The tunabilities follow
the same general trend of peak values decreasing when the dislocation density increases,
164
The only exception is the Bao.6Sro.4Ti03 film on LaAlC>3, which has a higher tunability
than the Bao.6Sro.4Ti03 film on (Lao.i8Sro.82)(Alo.59Tao.4i)03. Overall, the relative
^inabilities
of
the
Bao.6Sro.4TiC>3
films
grown
on
MgO(lOO),
(Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), and LaAlO3(100) substrates are lower
than that of Bao.6Sro.4Ti03 films grown on GdScC>3(l 10). From the dielectric constant and
the tunability comparison between Bao.6Sro.4Ti03 films grown GdScC>3 and Bao.6Sro.4Ti03
films grown on MgO(lOO), (Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), and
LaAlC>3(100) substrates, it can be concluded that the film quality, essentially the
dislocation density, has played an important role in the dielectric constant and tunability
degradation.
Table 5.1 Summary of the strain states, FWHM of the film X-ray rocking curve, the peak dielectric
constant, the peak tunability, the corresponding temperatures, and the FWHM of the t-T peak.
Substrates
TEM Dislocation
Density(/cm2)
FWHM of
Film Rocking
Curve(�)
Peak Values
-T/ nr-T Peak
Position(K/K)
FWHM of
er-T Peak
(K)
GdScO3(110)
6xl0 9
0.008
7099/92.4%
308/303
32
MgO(lOO)
textured
0.617
630/31.7%
253/253
155
LSAT(IOO)
1.5x10"
0.016
1654/55.4%
353/343
95
NdGa03(l 10)
2.1x10"
0.02
1174/52.3%
363/353
98
LaAlO3(100)
2.4x10"
0.183
874/60.6%
303/273
124
Er-T/nr-T
5.3.2 Inhomogeneous strain effect on dielectric loss
Fig. 5.7 gives the temperature dependence of dielectric loss measured at 5GHz
from
the
120
nm
Bao 6Sro.4Ti03
films
grown
on
GdScC>3(110),
(Lao.i8Sro.82)(Alo.59Tao.4i)03(100), NdGaO3(110), LaAlO3(100) and MgO(100). The peak
165
of the dielectric loss in the Bao.6Sro.4TiC>3 film grown on GdScC>3(l 10) has been discussed
earlier in Section 5.2.1. All temperature dependencies of dielectric loss have some
correlation with the Curie temperature. The losses of all the films reach maxima below
Curie temperature and then drop in different magnitudes when the temperature increases
above the Curie temperature. If the measurement temperature range is high enough above
the Curie temperature, the dielectric losses starts to increase.
0.40
i
0.30
ctri
0.35
0.20
IA
o
2
I
.
:
??--GdScO,(110)
- LSAT(100)
??- A - -NdGaO,(110)
?A
??- - LaAIO,(100)
- MgO(100)
U*^.
0.25
?
.A
y * ?^
I
?
0.15
a
x*?^
?
0.10
?
?^.
^?-?-?-�-
0.05
250
300
350
Temperature (K)
400
450
Fig. 5.7 Temperature dependence of the dielectric losses measured at 5 GHz using IDC structure
for 120 nm Ba0.6Sro.4Ti03 films grown on GdScO3(110), (Lao.iaSro.ad(^o.59Tao.4i)03(100),
NdGaO3(110), LaAIO3(100), and MgO(100).
The sharp loss peak slightly below the Curie temperature is believed to be due to
the increase of the internal friction related to the increase of domain walls and domain
wall motion.16'30"32 The loss in the film on GdScC>3 drops sharply above the Curie
temperature, where the ferroelectric phase transformed into paraelectric phase and no
domain walls should exist.16'30"32 After the loss related to domain wall motion drops to
the minimum, the conduction loss starts to increase for Bao 6Sr0.4TiO3,33 and eventually it
dominates the overall loss. The same trend has been observed in the films on LaAlCb and
MgO. For Bao.6Sro 4TiC>3 grown on (Lao.i8Sro.82)(Alo.59Tao.4i)03 and NdGaC� the
166
temperature dependencies of the loss are almost identical. Since their Curie temperatures
are higher than for other films, the increase of loss at high temperatures does not show
up, but the trend of loss decrease above Curie temperature is consistent with all the other
films.
From the comparison of the temperature dependencies of the dielectric losses of
these films, it can be found that the Bao.6Sro.4Ti03 film with a low dislocation density,
such as the Bao6Sro4TiC�film on GdScOs, has a very sharp loss peak while the
Bao.6Sro.4TiC>3 films with two or more orders of magnitude higher dislocation densities,
such as Bao.6Sro.4Ti03 films on (Lao.i8Sro.82)(Alo.59Tao.4i)03, NdGaC>3, LaAlC>3, and MgO,
the temperature dependencies of the loss peaks are widely spread. This wide spread of the
loss can be attributed to the inhomogeneous strains associated with dislocations. The
inhomogeneous strains can spread out the local Curie temperatures distribution, as
observed in the temperature dependencies of dielectric constant. When the Curie
temperature is spread out, the phase transformation happens in a diffuse fashion, in which
the domain walls and domain wall motion (or equivalent to the changes of local
polarization magnitudes or spatial cohesion of the polarization vectors) can exist over a
considerable temperature range; therefore, the dielectric loss related to domain wall
motion can be maintained at a high level over such a wide range.
Figures of merit are often assigned to different materials to illustrate their
suitability for device design. The figure of merit {K') for phase shifter applications is
often defined as:26
K' =
(7),
tan�(0F)
167
in which n is defined by equation (6). The K' for different films is presented in Fig. 5.8.
It is evident, that as the losses were spread out respect to temperature, even with
relatively high tunability in the film, the figure of merit is flattened out by the high
dielectric loss at a high level of above 10% throughout the whole temperature range. This
is undesirable for device applications. The K' values of the Bao.6Sro.4TiC>3 film grown on
GdScC>3, despite the fact that the loss peaks just below Curie temperature, are higher than
for any other films; at the maximum, it exhibits a figure of merit 6 to 7 times higher than
the values for the other films.
70
60
50
-?-GdScO s (110)
- ? - LSAT(100)
-A-NdGaO,(110)
- V - LaAIO,(100)
-*- MgO(100)
40
?5 30
�
�20
il
10
0
:, ?. r r s *?: �*****-**?
250
?
300
350
400
Temperature (K)
?
?
?
450
Fig.5.8 Temperature dependence of the figure of merit, K', at 5 GHz using an IDC structure for
120 nm Ba0.eSro.4Ti03 films grown on
GdScO3(110),
(La0.i8Sr0.82)(Alo.59Tao.4i)03(100),
NdGaO3(110), LaAIO3(100), and MgO(100).
5.3.3 Discussion on inhomogeneous strain effects on dielectric properties
As it has been discussed in Chapters 2 and 3, inhomogeneous strains, which are
associated with point and extended defects, such as vacancies, dislocations, and grain
boundaries, exist in all of the Bao.6Sro.4Ti03 films.35"37 The localized strains affect the
local materials dielectric properties.35"37 Simulations based on Landau-Devonshire theory
168
were done to analyze the strain distribution and depolarization field around dislocation
cores of both misfit and threading dislocations.35 The polarization mapping around
dislocation core with Burger's vector <100> (shown in Fig. 5.9a) demonstrated that the
compressive strain on one side of the dislocation core locally depresses the polarization.
M
to?
V
I
w
10Distant on a(nHi)
i
I
i
OS B
m
_iSiS
<4*
I'
E
c
101C
on S"
tea E
I
P
ai3t>naeanx(naij
Fig. 5.9 The (a) polarization distribution and (b) variation of the Curie temperature around a
b=a[100] edge dislocation at (0,0,0) in single-crystal PbTi03 on an xz plane. Area shown
represents 20*20 nm cross section along the y direction (dislocation line). This figure is
reproduced from reference 35.
The tensile strains on the opposite side of the dislocation core can enhance the
polarization, increasing dielectric constant. Note that the Burger's vector of dislocations
dominant in the films studied in this research should be <100> type. The dielectric
measurements using IDC structures are dependent on the in-plane polarizations. The two
sides of the threading edge dislocation can be considered as two capacitors connected in
169
series,. Therefore the effective dielectric constant will be limited by the capacitor with
low dielectric constant when the geometrical factors are close to each other.
The area affected by the strain field of a single dislocation was estimated to be 20
x 20 nm2.35 For a film with threading dislocation density of around 2xlO u /cm2, the
average distance between dislocations is about 20nm and is comparable to the size of the
strain field depressing the dielectric constant.35 This means that the suppressed areas will
overlap and a large fraction of the film material will exhibit lowered polarization. This
causes the whole film's general polarization to be suppressed and dielectric constant to
decrease.
It is well established that homogeneous strains can shift the position of the Curie
temperature j ^ 4 - 2 0 ' 3 5 - 3 8 The area around the dislocation core is under a different strain
state, which will shift the Curie temperature either up or down depending whether the
film is in tension or compression.35'38 This will spread out the Curie temperature
distribution. As shown in Fig. 5.9b, the local phase transformation temperature (Tc) had
also been calculated
around a dislocation core in PbTi0335'36 and observed
experimentally in other ferroelectrics.38'39 This effect appears to be responsible for the
increased width of Curie peaks of Bao.6Sro.4Ti03 films. One should note that point defects
also can affect temperature dependence of dielectric properties. In this research, the all
films were deposited under the same growth conditions, in particular the same oxygen
partial pressure, and they should have similar concentrations of point defects.40 The large
differences in their dielectric constants and tunability are unlikely to be due to the
differences in point defect concentrations. The tensile strain in Bao.6Sro.4TiC>3 films grown
on GdScC<3 may have contributed to the high dielectric constant and tunability of the
170
film. However, the Bao.6Sro.4TiC>3 films on MgO have the similar strain state but
significantly degraded properties. Bao.6Sro.4Ti03 films on MgO were textured with the
high density of grain boundaries; the grain boundaries may have degraded the dielectric
constant compared with those films grown on (Lao.i8Sro.82)(Alo.59Tao.4i)C>3, NdGa03 and
LaA103. No high angle grain boundaries were observed in the Bao6Sro.4TiC>3filmsgrown
on GdScC>3, (Lao.i8Sro.82)(Alo.59Tao4i)03, NdGaCb, and LaA103 within the detection limit
of planview TEM.
As is evident from Fig. 5.7, the Bao.6Sro.4Ti03 film with a low dislocation density
had a very sharp loss peak while Bao.6Sro.4Ti03 films with dislocation density above 10 n
/cm , such as Bao.6Sro.4Ti03 films on (Lao i8Sro.82)(Alo.59Tao.4i)03, NdGaC>3, LaAlC>3, and
MgO, exhibited wide peaks in the loss spectrum. These characteristics also can be
explained by the inhomogeneous strains associated with dislocations. When the Curie
temperature is spread out (Fig. 5.9), the phase transformation occurs in a diffused
fashion. The ferroelectric domains can exist at elevated temperatures and the domain wall
motion can contribute to the total loss in a wide temperature range. The comparison of
figures of merit demonstrated that the spread out of the loss will lower the figure of merit
by maintaining it in a low level.
In this section, it is demonstrated that films with high dislocation densities (lower
crystalline quality as determined by X-ray diffraction and TEM) have degraded dielectric
properties. Simulation results based on Landau theory reported by Alpay et al. can
explain the correlation between dielectric properties and inhomogeneous strains
associated with dislocations.35 However, it does not necessarily mean that low dislocation
concentration (high crystalline quality) will yield bulk-like properties. This question will
171
be answered by comparing dielectric properties of films grown on GdScC>3 and DyScC>3
substrates.
5.4 Effects of homogeneous strains
5.4.1 Comparison of dielectric properties of Bao.6Sro.4Ti03 on GdScC>3 and DyScC>3
Bao 6Sro.4Ti03 films were grown on DyScO3(110) and GdScO3(110) substrates at
850癈 and oxygen pressure of 300 mTorr. The Bao.6Sro.4Ti03/DySc03 film thickness was
measured to be 300 nm. Even though this thickness is above the theoretical critical
thickness, the measured in-plane lattice parameter demonstrated that the films are
coherently strained to the substrate with a compressive strain of -0.33% as shown in
Table 4.3. The measured rocking curve width of the film is 0.007�, comparable to that of
Bao.6Sro4TiC>3filmsgrown on GdScC>3(l 10) (Table 4.3). The planview TEM also showed
that the dislocation density in the Bao.6Sro.4Ti03 film on DyScC>3(110) was 2xl0 10 cm"2
which is about three times the dislocation density, 6x109 cm"2, in Bao.6Sro.4TiC>3 films
grown on GdScQ3( 110).
100
7000
-?-GdScO,(110)
-?-DySeO^HO)
. (a)
6000
4000
3000
2000
1000
200
??
.,�?*.
-?-GdScO,(110)
-?-DyScO,(110)
3-80
A
J \
5000
a
(*>)
40
& 20
^-,
.----.????-.*
250
.
300
350
Temperature <K)
..?"-??
400
450
01?
200
250
300
350
Temperature (K)
400
450
Fig. 5.10 The comparison of the temperature dependences of the relative dielectric constants (a)
and the relative tunabilities (b) for (001)-oriented Ba0.6Sro.4Ti03 films grown on GdScO3(110) and
DyScO3(110).
172
0.40
0.35
70
: (�)
0.30
J 0.25
� 0.20
. ???
8
� 0.15
A4
-?-GdScO^IIO)
-?-DyScO,'(110)
s
?*
\
5
so
I40
I 30
I 20
10
200
250
300
350
Temperature (K)
:
/ \
V
s.
0.10
0.05
0.00
- ? - BST/GdScO,
-?-BST'DyScO,
60
400
450
0
250
300
350
400
Temperature (K)
450
Fig. 5.11 The comparison of the temperature dependences of the dielectric loss (a) and the figure
of merit (b) for(001)-oriented Ba0.6Sro.4Ti03 films grown on GdScO3(110) and DyScO3(110).
Fig. 5.10a gives the comparison of the temperature dependence of dielectric
constant (e(T)) between Bao.6Sro.4Ti03 films grown on DyScC>3 and on GdScC>3. The
dielectric constant maximum of Bao 6Sro.4Ti03/DySc03 only reaches 375 at 283 K, even
lower than that for Bao.eSro^TiOs/MgO. The e(T) FWHM is about 167 K, also wider than
that of Bao.6Sro.4Ti03 on MgO (155 K). The maximum relative tunability (Fig. 5.10b) is
about 40%. Compared to Bao.6Sro.4TiC�films on GdScCb, the films on DyScCb have
demonstrated much lower dielectric constant and tunability. Compared to Bao.6Sro.4TiC�films on MgO, (Lao.i8Sro.82)(Alo.59Tao.4i)03, NdGaCb, and LaAlCh, the films on DyScC�are worse than films which have two orders of magnitude higher dislocation densities.
Fig. 5.11 shows the dielectric loss (a) and figure of merit (b) of Bao 6Sro.4Ti03 films
grown on DyScC>3 and on GdSc03. The loss follows the temperature dependence trend
for all other films: maximum slightly below Curie temperature followed by drop as the
phase transformation is finished. As the temperature increases further, the conduction
loss becomes dominant and increases again. In general, the dielectric loss for
Bao.6Sro.4TiC�films grown on DyScC>3 is high (>15%). In addition to the decrease of the
tunability, the figure of merit remains at 15 or so as shown in Fig. 5.11b. Considering that
173
the dislocation density in Bao 6Sr0 4TiC�DyScC)3 was only three times higher that that of
films on GdScCb, the dramatic differences in dielectric properties indicates that there
must be another important factor affecting the properties.
Compressive
Fig. 5.12 The schematic depiction of barium strontium titanate film in-plane polarization related to
the in-plane tensile and compressive strains.
As has been discussed in Chapter 4, the lattice parameter measurement
demonstrated that both the Bao.eSro^TiCb films on GdScO3(110) and DyScO3(110) are
coherently strained to the substrates. The difference was that the films on GdScO3(110)
were in tension (+0.2%) and the films on DyScC�110) were compressively strained (0.33%). Intuitively, it can be understood as depicted in Fig. 5.12, that when the film is
under in-plane tensile strain, the strain opens up the space for the displacement of Ti4+ ion
in the perovskite unit cell and, therefore, enhances the in-plane polarizations and the
dielectric constant. When the film is under compressive strain, the space for in-plane
displacement is more restricted, i.e. the strain suppresses the polarizations and decreases
the dielectric constant. To understand the strain effect, the Landau-Ginsburg-Devonshire
phenomenological theory is discussed in the next section.
5.4.2 Discussion of the homogeneous strain effect based on phenomenological theory
Chang et al., derived the correlation between the dielectric constant and strains at
a specific temperature in paraelectric phase based on Landau Devonshire theory.11'41"43 In
this research, this result will be extended to investigate the strain effect on the dielectric
174
constant vs. temperature relationship in paraelectric phase. For the ease of understanding,
the derivation process discussed in Chang's paper is summarized below.
According to the phenomenological theory developed by Devonshire for
BaTiOs,11'41"43 "the Gibbs free energy (G) of a stress-free ferroelectric subjected to an
external electric field (E) can be expressed as:
G(T,Pi) = F(T,Pi)-EiPi
(8),
where F is the Helmholtz free energy of a strain-free ferroelectric, and Pt is the
polarization. When a stress is applied to the ferroelectrics, the Helmholtz free energy
should include the factor of strain (x;) as:11
F(T,PltXj)
= F0 + 盿(P2
2
+ \d{P2P2
+ P2P2 + P2P2 ) + i c ? (x,2 + x\ + x] )
+ Cl2 (XlX2
+ X{X3
+ P22 + P2) + -B{P:
4
+ P24 + P34) + � r (/> 6 + P26 + P36)
6
+ X2X3 ) + T"<-44 V*l """ ?"'2 ~*~ X3 )
+ Gu {xxPx2 + x2P22 + xzP2) + G12 {xx (P2 +P2) + x2 (P2 + P2) + x3 (P,2 + P22)}
+ GM(x4PIP3+x3P1P3+x6P2P1)
+ ...
where Fo is a function of temperature alone, a, /?, y, and S are the free-energy expansion
coefficients, and c,-y and Gy are the elastic constants and the stress-polarization related
electrostrictive coefficients, respectively."
For an epitaxial film clamped by a substrate, the following assumption can be
introduced:11
(1) The equi-biaxial in-plane strains, xj and X2, in the film are controlled by the substrate.
(2) The out-of-plane stress is zero because of the free surface.
(3) For measurements using IDC structure, the electric field is applied in one direction,
therefore, there is only one polarization direction, P.
(4) The polarization is parallel to the electric field.
175
The Gibbs free energy for a ferroelectric thin film can be simplified to:11
G(T,Pi,xJ)
=
F(T,Pi,xJ)-EP
= F0 + -aP2
+ -/3P4 + -yP6 + -cn(x2
+ x\ + x2) + c12 (xxx2 + *,*3 + x2x3)
+ -TC44 (A + A + A ) + TC44 (^l2 + A + A)
+ [Gux,+Gl2(x2+xi)]P2-EP
(10).
Since the Gibbs free energy G must be at the minimum for a stable state of the
ferroelectric at a constant temperature {dGI dP=0), then equation (10) becomes:11
? -E = aP + pP3 +yP5 + 2[Gux, +Gu(x2 +x,)]P-E = 0
(11).
dP
The fifth and higher order of polarization P can be neglected. In addition, we can assume,
P-eE in the case of small electric fields E or in the case of relatively large electric fields
for a paraelectric state of a ferroelectric.11 Then, by differentiating Equation (11) with
respect to P, we can get:' l
BF 1
? = - = a + 3/KeE)2+2[Gnx1+Gu(x2+x3)]
dP
(12).
s
The first-order coefficient a is a function of temperature. When there is no external
electric field, in paraelectric phase of a stress-free ferroelectric, Equation (12) becomes:11
^aJlzI^l
S
(13),
C
in which C is the Curie-Weiss constant, T$ is a characteristic temperature, Te = Tc for
second order phase transformation and Te < Tc for first order phase transformation. For
strains, X2+X3= [l-la/cu]
jcy.For an epitaxial ferroelectric film with no external electric
field, Equation (12) can be expressed as follows:
I = fcZkl +2[Gn +Gl2(\-^)]Xl
6
C
Cu
176
(14).
In Equation (14), the stress-polarization-related electrostriction coefficients Gn and Gn
can be obtained from equation:
n
Gv=caQv
(i,j,k = \,2,...,6)
(15),
where Qkj are the strain-polarization-related electrostriction coefficients. Both c^ and Qkj
of SrTi03 and BaTi03 are listed in Chang's paper and references therein. When
considering (Ba, Sr)Ti03 solid solution, these parameters are calculated assuming there is
a linear relation between the parameter and Ba/Sr ratio.11 The data used for the later
calculation
are listed in Table 5.2. Using the coefficient
Gu=c1]Q11+c12QI2=
in Table 5.2,
-2.541xl010 Nm2C2, G12 = cuQ12 + c12Q22 = cnQi2 + c12Qu = -
3.397* 109Nm2C2. 2{GU +G12[l-2(c12/cn)]}x,
= -5.103xl010Nm2C2.
Table 5.2 The relevant coefficients of in theoretical calculations of the dielectric constant vs.
temperature relationship of Bao.6Sr0.4Ti03 grown on DyScO3(110).
Parameters
Description
Quantity
TC(K)
C(105K)
Bulk Curie temperature
Bulk Curie constant
249
1
Qn(m4/C2)
Electrostriction coefficient
-0.1
Q12(m4/C2)
Electrostriction coefficient
0.034
11
Elastic constant
Elastic constant
3.042
1.474
2
Cn(10 N/m )
c12(10"N/m')
177
0.0020
(a�
?
0.0016
1-- ? - I d e a l Bulk Ba
fleSr
(LS
Dielec
5?g 0.0008
sr
1
-?*
Li M ? *
W
| 20000
o
O
.� 15000
m
.*
m'
.
???Ideal Bulk Ba?,Sr? T i O .
. j *
?
mW
M'
ff
. '%
% 10000
*
m*
M
'
.'
S
mm
?
? \
9
Mm
0.0004
0.0000
TiO J
LA
_j
? 0.0012 .
(b)
25000 -- ??
m
5000
\
- ?
a.
250
300
350
400
Temperature (K)
450
250
300
350
400
Temperature IK)
450
Fig. 5.13 The simulated temperature dependence of inverse dielectric constant (1/t-T) and
dielectric constant (e(T)) based on Curie Weiss law in paraelectric phase of an ideal bulk
Ba0.eSro.4Ti03.
If we take an ideal bulk Bao.6Sro.4TiC>3, assuming C is lxlO5 K, the commonly
reported value, ' ' the bulk Curie temperature Tc is about 249 K and Te is close to
r c , 1819 In the paraelectric phase, the dielectric constant will follow the Curie Weiss Law:
1
(r-249)
?=a =s
,,,,
(16).
T?-
105
The inverse of the dielectric constant (1/s) vs. temperature (7) and e(T) are plotted in Fig.
5.13.
When the strain value, x = -0.33% for Bao.6Sro.4Ti03 on DySc03, is inserted into
Equation (14), one gets: 2{Gu+G12[l-2(cI2/cu)]}x,
=0.001492. If the Curie
temperature shift to 283 K is considered, the inverse of dielectric constant (1/s) and
dielectric constant (e) are plotted as a function of temperature and compared to those of
the ideal bulk plots as shown in Fig. 5.14. The compressive strain raises the inverse of the
dielectric constant at each temperature point by 0.001492; therefore, the dielectric
constant is lowered significantly. For an ideal bulk BST that follows Curie Weiss law, the
178
dielectric constant increases to infinity at the Curie temperature. When the material is
strained, the maximum value around the Curie temperature Tc will be limited by the
constant introduced by the strain; therefore, the dielectric constant does not diverge. For
Bao.6Sro.4TiC<3 films with -0.33% compressive strain, the simulated dielectric constant
maximum value at Curie temperature is about 670.
(a)
0.0028
25000
- ? - I d e a l bulk
S 0.0024 - ? - -0.33% strained
1A
?*
c
(5 0.0020
-
(b)
?
� 20000
� 0.0016
o
S 0.0012
o 15000
;
ric
- ? - I d e a l bulk
???-0.33% strain
?1
a
8 IOOOO
$ 0.0008
a
:
\
5000
� 0.0004
CL
^ 0.0000
?�..,
......"wSMSSlSI^gagigsan^:
0
250
300
350
400
Temperature (K)
450
250
300
350
400
Temperature (K)
450
Fig. 5.14 Comparison of the simulated temperature dependence of inverse dielectric constant
(1/E-T)
and dielectric constant (e-T) based on Curie Weiss law in paraelectric phase between an
ideal bulk Bao.6Sro.4Ti03 and a Ba0.6Sro.4Ti03 film under compressive strain of 0.33%. Note that
the Curie temperature is shifted from 249 K to 283 K from bulk to strained film.
Equation (12) can be used to simulate the effect of strain on the relative dielectric
tunability, if ft can be calculated from bulk tunability measurement. From Chang's
simulation results,11'44 the compressive stress decreases the tunability.11'44 This is
consistent with the observation that the tunability for Bao.6Sro4Ti03 films grown on
DySc03 is below 40%.
To summarize, simulations based on the phenomenological theory predict that the
compressive strain equal in magnitude to the strain in films grown on DyScC>3 can reduce
the dielectric constant from tens of thousands to several hundreds. The dielectric property
179
degradation observed in Bao.6Sro.4Ti03 films grown on DyScC>3 can be understood
qualitatively through this phenomenological analysis. The fact that the observed value is
lower than the simulated dielectric constant might be due to the presence of defects such
as dislocations. Also the observed experimental values of Curie Weiss constant was
2xl0 4 K for Bao.6Sro.4TiC>3 films grown on DySc03, which is lower than the value of bulk
barium strontium titanate, lxlO5 K,45 this Curie Weiss constant decrease remains to be
understood.
5.5 Conclusions
In this research, bulk-like dielectric constants and tunabilities were observed in
high quality Bao.6Sro.4Ti03 thin films grown on GdSc03(l 10) substrates. These properties
were attributed to the improved film crystal quality (absence of random strain fields
associated with extended defects) and the presence of homogeneous 0.2% tensile strain,
achieved b
Документ
Категория
Без категории
Просмотров
0
Размер файла
2 707 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа