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Ferroelectric multilayers and heterostructures for high performance tunable microwave devices applications

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Ferroelectric Multilayers and Heterostructures for High
Performance Tunable Microwave Devices Applications
Shan Zhong, Ph.D.
University of Connecticut, 2007
Ferroelectric multilayers and heterostructures have attracted a significant amount
o f interest in the past decade due to their unique properties compared to their
homogenous counterparts. A num ber o f peculiar phenomena, such as gigantic dielectric
permittivity, enhanced spontaneous polarization, high dielectric tunability, and special
phase transformation characteristics have been discovered in various ferroelectric
heterostructures.
This study is a theoretical and experimental effort to understand the potential
applications o f ferroelectric multilayers in high performance tunable devices and
transducers. A comprehensive non-linear thermodynamic modeling incorporating theory
o f elasticity and principles o f electrostatics is developed to analyze interlayer coupling,
interface effects, and the role o f internal stresses in ferroelectric multilayers and
heterostructures. The theoretical results are then utilized to guide the deposition o f
ferroelectric multilayers with high dielectric tunability, low dielectric loss, and
temperature insensitive dielectric permittivity, which have potential applications in next
generation tunable microwave devices. The experimental results are then explained in the
context o f the developed theory. Theoretical and experimental results also indicate that
the piezoelectric response can be enhanced significantly due to a built-in potential and the
commensurate strain field.
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Ferroelectric Multilayers and Heterostructures for High
Performance Tunable Microwave Devices Applications
Shan Zhong
B.S., Shanghai Jiao Tong University, 2003
M.S., University of Connecticut, 2005
A Dissertation
Submitted in Partial Fulfillment of the
Requirement for the Degree of
Doctor of Philosophy
at the
University of Connecticut
2007
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UMI Number: 3276657
Copyright 2007 by
Zhong, Shan
All rights reserved.
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Copyright by
Shan Zhong
2007
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APPROVAL PAGE
Doctor o f Philosophy Dissertation
Ferroelectric Multilayers and Heterostructures for High
Performance Tunable Microwave Devices Applications
Presented by
Shan Zhong, B.S., M.S.
Major Advisor
S. Pamir Alpay
Associate Advisor
Harold D. Brody
Associate Advisor
Rampi Ramprasad
University o f Connecticut
2007
ii
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Acknowledgements
I would like to express my sincere appreciation to my advisor, Prof. S. Pamir
Alpay, who brought me into this research field. It is my great pleasure to work for him. I
really appreciate his philosophy o f graduate student training. His enthusiasm and the
drive for perfection have been the primary motivations in this work. I have benefited
from his vast knowledge in materials science and his expertise in thermodynamics.
W ithout his guidance, patience and encouragement, I would not have finished this work.
More importantly, he is not only a great mentor, but also a good friend.
I would like to thank my advisor committee members, Prof. Harold D. Brody,
Prof. Rampi Ramprasad, and Prof. Bryan D. Huey who was my associate advisor for M.S.
degree, for their critical reviews and important suggestions on this work.
I also want to express my special thanks to our collaborators, , Dr. Joseph, V.
Mantese from United Technologies Research Center, Prof. Alexander L. Roytburd from
University o f Maryland, and Drs. M elanie Cole from Arm y Research Laboratories, for
their collaborations and insightful discussions. Their wonderful work makes all these
research possible.
It is always fun to work with my group members. I absolutely enjoyed my fouryear working in Functional Materials Group with Gursel Akcay, Dr. Bure Misirlioglu,
Bamidele S. Allimi, Kevin Rankin, Sarah Winiarz, and Baris Okatan. I would like to
thank my friends in our department, Ramesh Nath and Dianying Chen. I also would like
to express my gratitude to all the staffs in our department and IMS, Dr. Daniel Goberman,
Mr. Jack Gromek, Ms. Cathy M cCrackan, Ms. Kimberly Post, Ms. Deborah Perko, Ms.
Nancy Kellerann, Ms. M aria Mejias, for their professional support and assistance.
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Finally, I would like to express my deepest appreciation to my parents for their
continuous faith in me and endless supports throughout my graduate study. I also would
like to dedicate this work to my beloved wife, Yiqing. Without her love, unselfish
support, and patience, I would never have finished this dissertation.
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Table of Contents
Chapter 1 Introduction..................................................................................................................... 1
1.1 Homogeneous Ferroelectrics............................................................................................... 1
1.1.1 Spontaneous Polarization..............................................................................................4
1.1.2 Hysteresis L oop.............................................................................................................. 5
1.1.3 Phase Transition and Dielectric A nom aly................................................................. 7
1.2 Heterogeneous Ferroelectrics..............................................................................................9
1.2.1 Multilayers and Superlattices....................................................................................... 9
1.2.2 Polarization Graded Ferroelectrics............................................................................13
1.3 Tunable M icrowave D evices............................................................................................. 16
1.4 O bjective............................................................................................................................... 20
Chapter 2 Therm odynam ics......................................................................................................... 21
2.1 Ferroelectric (FE)-Paraelectric (PE) B ilayer................................................................. 21
2.1.1 Compositionally Symmetry B reaking......................................................................26
2.1.2 Dielectric R esponse.....................................................................................................28
2.1.3 T unability...................................................................................................................... 34
2.1.4 High Capacitance Oxide/Ferroelectric/Oxide Stacks........................................... 39
2.2 Interface E ffects.................................................................................................................. 46
2.3 M ultilayer H eterostructures............................................................................................... 53
Chapter 3 Experim ental................................................................................................................. 56
3.1 Thin Film Fabrication......................................................................................................... 57
3.2 C haracterization...................................................................................................................58
3.3 Electrical M easurem ent...................................................................................................... 66
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3.4 Comparison with T heory....................................................................................................78
3.5 PFM M easurem ent..............................................................................................................81
Chapter 4 Conclusion and Future W o rk ..................................................................................... 88
References........................................................................................................................................ 90
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List of Tables
Table 3.1 A comparison o f the dielectric properties, TCC, and the percent change o f
permittivity with respect to 20°C for heterogeneous and uniform composition
BST thin films. Tabulated data are from the technical literature and from this
study.............................................................................................................................74
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List of Figures
Figure
1.1 Illustration o f the crystallographic relationship among piezoelectric,
pyroelectric, and ferroelectric m aterials.................................................................. 2
Figure 1.2 The unit cells for a typical ABO 3. (a) Cubic prototypic phase above the Curie
temperature; (b) Tetragonal phase below the Curie temperature. [8 ] ................5
Figure 1.3 Schematic illustration o f Sawyer-Tower circuit for measuring o f ferroelectric
hysteresis loop.............................................................................................................. 6
Figure 1.4 A P-E hysteresis loop in ferroelectrics......................................................................7
Figure 1.5 Temperature dependence o f the dielectric constant in BaTi 0 3 . [1 0 ].................. 9
Figure 1.6 (a) The measured real (solid line) and imaginary (dotted line) parts o f the
dielectric constant for the sample PbTi 0 3 /Pbi_xLaxTi 0 3 with periodicities o f
40 nm at FaC=0 V as a function o f frequency on a logarithmic scale, (b) The
calculated real (solid line) and imaginary (dotted line) parts o f the dielectric
constant at Fdc=0 V as a function o f frequency as a logarithmic scale. [30] • 11
Figure 1.7 C -V curves o f the superlattice with a BTO 2/STO 2 periodicity, (Ba 0.5,
Sro.5)T i0 3 (BST), S rT i0 3 (STO), and B aT i0 3 (BTO) capacitors. [1 5 ]...........12
Figure 1.8 P -E hysteresis loops o f the BT/ST superlattice with the stacking periodicity o f
15/3 and the BT single-phase film prepared using the same deposition
conditions as the superlattices. [14]....................................................................... 13
Figure 1.9 Unconventional hysteresis phenomenon in D vs. E plots, obtained at 37.5°C by
excitation w ith a 35-V, 50-Hz triangular wave. This behavior was observed in
a 9.8-pm -thick KTN film [37],............................................................................... 14
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Figure 1.10 Schematic variation in the dielectric permittivity o f a ferroelectric above the
ferroelectric phase transformation tem perature....................................................18
Figure 2.1 (a) Two freestanding ferroelectric layers and the initial polarization in layers 1
and 2 are P0<i and Po,2, respectively, (b) A bilayer constructed by joining the
layers in (a), sandwiched between metallic top and bottom electrodes, (c) a
heteroepitaxial bilayer made up o f the bilayer in (b) on a thick substrate. Due
to interlayer coupling, Pi<Po,i and P 2 >Po,2 . ......................................................... 22
Figure 2.2 Free energy potentials as a function o f polarization for an equal-ffaction
B T -B ST 90/10 bilayer: (a)^=0, (b) ^ 0 .0 1 , (c) #=0.1, and (d) # = 1 ................27
Figure 2.3 Dependence on ST fraction, a ST, o f polarization in BT layer under different
external fields (E=0, £j=100 kV/cm, E2=200 kV/cm) and the polarization
difference, AP=Pm-Psy: (a) and (b) for constrained B T -S T bilayer;
xbt—
2.28% and
xst=0%
(solid squares: first-principles results from Ref.
[113]); (c) and (d) for unconstrained B T -S T bilayer......................................... 30
Figure 2.4 Relative mean dielectric constant as a function o f volume faction,
cist:
(I) for
unconstrained B T -S T bilayer; (II) for strained heteroepitaxial B T -S T bilayer,
xbt=
- 2.28% an d xsT = 0% ....................................................................................................32
Figure 2.5 Dielectric response o f an unconstrained B T -ST bilayer as a function o f
volume fraction o f ST for different #. The inset shows the dielectric response
o f B T -S T bilayer with #=0.1 and #=1 in more detail......................................... 33
Figure 2.6 (a) Relative dielectric responses o f freestanding (FS) and heteroepitaxial (HE,
xbt= -2 .5 6 %
and
xst=0% )
B T -S T bilayers as a function o f ST fraction, (b)
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Dielectric tunabilities o f BT-ST bilayers as a function o f ST fraction under
100 kV/cm external field ......................................................................................... 36
Figure 2.7 (a) Dielectric tunabilities o f freestanding B T -ST bilayers as a function o f
external field for various ST fractions, (b) Dielectric tunabilities o f
heteroepitaxial B T -S T bilayers (x q t = - 2 .56 % and
x s t = 0 %)
as a function o f
external field for various ST fractions.................................................................. 37
Figure 2.8 A freestanding DE/FE/DE stack sandwiched between metallic electrodes. The
thickness o f the FE and DE layers are h\ and hi, respectively, and h is the
total thickness.............................................................................................................41
Figure 2.9 Critical fraction o f DE/BST/DE stacks as a function o f the (bulk) dielectric
constant o f DE layer. Results for BaTiCb (BT), Bao.9Sro.iTi0 3 (BST 90:10)
and Bao.8Sro.2Ti 0 3 (BST 80:20) as the FE layer are shown...............................44
Figure 2.10 Critical fraction o f DE/PZT/DE stacks as a function o f the dielectric constant
o f DE layer. Results for PbTiC>3 (PT), Pbo.8Zro.2Ti 0 3 (PZT 80:20) and
Pbo.sZro.sTiOs (PZT 50:50) as the FE layer are shown.......................................45
Figure 2.11 Normalized polarization change as a function o f thickness in the vicinity o f
the interface for a bilayer consisting o f two ferroelectrics, A and B: £a,\<4a,2 ,
6 ,i<&, 2; £a>i/<*a , = £ b,/<Sb,,>*=1.2....................................................................50
Figure 2.12 Polarizations in BT layer as a function o f ST fraction for different
thicknesses: (a) sharp interface
interface
(£ b t= 3
nm,
£ st= 0 .8
(£ b t= T
nm,
£ st= 0 .5
nm); (b) diffusive
n m ).......................................................................... 51
x
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Figure 2.13 Critical fraction as a function o f total bilayer thickness. The dashed line
shows the continuum limit from Ref. [120] and the solid line is a guide for
the e y e ......................................................................................................................... 53
Figure 2.14 The theoretical average dielectric response as a function o f temperature for
three compositionally graded BaYSri_xTi 0 3 systems with the same nominal
average com position................................................................................................. 55
Figure 3.1 Schematic diagram o f the thin film multilayer material design......................... 57
Figure 3.2 X-ray diffraction patterns o f the (a) multi-anneal and (b) single annealed
layered BST thin films. For comparison, the XRD pattern o f the (c)
homogenous uniform composition BST60/40 annealed at 750°C is also
displayed.....................................................................................................................61
Figure 3.3 AFM micrographs showing the plan view surface morphology o f the (a) single
annealed and the (b) multi-annealed BST film structure.
The AFM 3-D
images o f the single annealed film are shown in (c) and the multi annealed
film structure is shown in (d). The scanned area was 1 pm2. ........................... 64
Figure 3.4 FESEM cross-sectional images o f the annealed m ulti-layer films fabricated via
the (a) single anneal and (b) m ulti-anneal process protocol............................. 66
Figure 3.5 The RBS spectra, (a) the single anneal and (b) multi anneal layered BST films.
The large dashed and continuous smooth lines represent the RBS simulation
via RUMP [145] and the small dotted lines represent the experimental data
points............................................................................................................................6 6
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Figure 3.6 The room temperature tunability results as a function o f applied electric field
for the m ulti-layer BST films (open circles) and uniform paraelectric
BST60/40 (filled squares) thin film s......................................................................71
Figure 3.7 The temperature dependence o f the dielectric response for (a) the three time
annealed m ulti-layer BST film and (b) homogenous uniform composition
paraelectric (BST60/40) BST film m easured at 1 M H z.................................... 72
Figure 3.8 The temperature dependence o f the dielectric tunability for the multilayer BST
film from 90 to -10°C. The symbols on the plot represent the following
temperatures: 90°C (open circles), 80°C (open squares), 60°C (open
diamonds), 40°C (crosses), 20°C (filled circles), and -10°C (open triangles).
...................................................................................................................................... 78
Figure 3.9 Tunability o f the BST multilayer as a function o f external electric field at
different temperatures (solid line: calculation results from theory; solid
squares: experimental m easurem ents).................................................................. 80
Figure 3.10 (a) The AFM topography and PFM amplitude images taken at 2, 6 and 10V
for the homogenous BST film, (b) The same images obtained for the
multilayer graded sample......................................................................................... 84
Figure 3.11 The calculated average piezoresponse o f PFM images obtained at each
voltage step versus AC voltage for the multilayer and homogeneous sample.
Error bars are too small to be visualized: on average, the 95% confidence o f
the measurements is less than 3% .......................................................................... 87
Xll
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Chapter 1 Introduction
1.1 Homogeneous Ferroelectrics
The crystalline structure o f solid-state materials can be classified into 7 crystal
systems, which are cubic, tetragonal, orthorhombic, monoclinic, triclinic, trigonal, and
hexagonal.[l]
W ithin these 7 systems, there are 32 point groups, 20 o f which are piezoelectric.
The piezoelectric phenomenon was first discovered by Curie brothers in 1880 [2], W hen
piezoelectric crystal is subjected to external mechanical stress (ay), electric charges form,
which correspond to a macroscopically polarization (Pi). The quantity o f the electric
charge is proportional to the magnitude o f the mechanical stress (tensile or compressive),
such that Pl= dijk-oij, where dyk are the piezoelectric coefficients. The charges generated by
tensile stress are o f opposite sign to those generated by compressive stress.
Within the 20 piezoelectric point groups, 10 have a spontaneous electric
polarization (Ps) due to their symmetry, as illustrated in Figure 1.1. These are termed
polar materials and exhibit the pyroelectric effect, APs =P'AT, where p is the pyroelectric
coefficient, i.e., a change in polarization with a change in temperature. The ten polar
point groups are 1, 2, m, 2mm, 4, 4mm, 3, 3m, 6 , and 6 mm. Ferroelectrics are a subgroup
o f polar materials and are defined as those materials which possess a spontaneous
polarization that can be reoriented upon the application o f an electric field (E).
Ferroelectricity was first reported for Rochelle salt (NaKX^FLiCVdFlaO) in 1921,
and for potassium dihydrogen phosphate (KH2PO4, KDP) in 1935 [3], In these materials,
the origin was attributed to an order-disorder transition, i.e., protons in the hydrogen bond
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ordered leading to a dipole moment and spontaneous polarization. This is quite similar to
magnetic ordering in ferromagnetic materials. Later, BaTiCb and other oxides were
reported as ferroelectric materials. The origin o f ferroelectricity in these materials is
believed to be related to ionic displacements relative to the paraelectric state. Ionic shifts
introduce a dipole and hence a spontaneous polarization. This second class o f
ferroelectrics is term ed “displacive” ferroelectrics, and they have been the subject o f
studies for many years. For example, by 1990, there were more than 200 pure compounds
identified as ferroelectrics [4].
Nmiccntrusx inm ctric
( 'cii I r n \\ m metric
(mm-piczoclcctric)
20 Piezoelectric
S ub gro up
F erroelectric
Perovskite
T ype Oxide
Figure 1.1 Illustration of the crystallographic relationship among piezoelectric, pyroelectric, and
ferroelectric materials.
The m ost pronounced structural feature for oxide ferroelectrics is the oxygen
octahedron building block. There are three m ajor families o f oxide ferroelectrics, in
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which the origin o f ferroelectricity is related to the displacement o f ions through the
deformation, rotation, or tilt o f these oxygen octahedra.
(1)
Perovskites
Materials with the perovskite structure (ABO3), shown in Figure 1.2, constitute the
largest class o f oxide ferroelectrics. M ost o f the technologically useful ferroelectric
materials are within this class. For example,
BaTi 0 3 (BT), which was applied commercially in the ceramic industry after its
first discovery in 1945. It has been the subject o f research for more than 50 years and is
still being investigated and developed. Pb(Zr,Ti )0 3 (PZT) is the m ost widely used
piezoelectric material, and is also a candidate for Non-Volatile Random Access
Memories (NVRAM). (Ba,Sr)Ti 0 3 (BST) is a crystalline solution o f BT and SrTiCb (ST),
where the Curie point and dielectric constant can be varied by Sr concentration. It is a
potential candidate for future DRAM (Dynamic Radom Access Memories) applications
and frequency agile materials with voltage tunable capacitance. Pb(Zni/ 3N b 2/3)C>3 (PZN)
and Pb(Mgi/3N b 2/3)03 (PMN) are relaxor materials. Their crystalline solutions with
PbTiC>3, i.e., PZN-PT and PMN-PT, are another family o f ferroelectric materials that
draws significant interests. By adjusting the concentration o f PbTiCb, morphotropic phase
boundary (MPB) compositions can be developed, e.g., PZN-PT (8.5% PT) and PMN-PT
(35% PT). MPB compositions exhibit large field-induced strains (>1%) and are leading
candidates for the next generation o f transducer materials [5], although there has been
much debate about that the MPB compositions are not a stable phase but a phase mixture
[6],
(2)
Tungsten bronze type oxides
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This class o f structures and compositions are o f interest for electro-optic
properties and photo-refractive applications, including holographic information storage.
(Sr,Ba)Nb 2C>6 is a good example.
(3)
Bism uth oxide-layered structures
This is another large family o f ferroelectric oxides. Recently, it has been the
subject o f numerous studies mainly due to its excellent resistance to fatigue and nontoxic
(no lead). The leading candidate is SrBi2Ta 209 (SBT) that is currently being used in
NVRAM applications in various integrated systems, such as smart cards.
There are other oxide ferroelectric structures, including pyrochlore, nitrites,
nitrates, etc. [3,7].
1.1.1 Spontaneous Polarization
M ost o f oxide ferroelectric materials that are o f practical interest have perovskite
structure with the chemical formula ABO 3. Typical ferroelectric materials that possess
perovskite structure are BaTiC>3, PbTiCb, PbZrC>3 and their solid solution such as BaxSri.
xTiC>3, PbxSri.xTiC>3, and PbZri_xTix0 3 . Figure 1.2(a) illustrates the perovskite structure
where the BC>6 octahedra are linked in a regular cubic array forming the high symmetry
m3m prototype for many ferroelectric materials. The small 6 -fold coordinated site in the
center o f the octahedron is filled by a small highly charged (3, 4, 5 or 6 valent) cation B
and the larger 12 fold coordinated “interstitial” site between octahedral carries a larger
mono, di or trivalent cation A. The oxygen ions sit at the face-centers o f the cubic cells.
This perovskite structure can be visualized to be composed o f positive and
negative ions. Below its transition temperature, so-called Curie point, the center o f
positive ions does not coincide with the center o f the negative charges. For example, as
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shown in Figure 1.2(a), above the Curie temperature, the prototype crystal structure is
cubic, with B4+ ion at the cubic center, O2' ions at the face centers, and A 2+ ion at the
cubic comers. W hen the temperature is below the Curie point, the structure is slightly
deformed, with A2+ and B4+ ions displaced relative to the O2' ions, thus creating a dipole,
as shown in Figure 1.2(b). Each pair o f these positive and negative ions forms a dipole,
which essentially forms a spontaneous polarization (dipole moment per unit volume).
a—
(a)
a
—y
(b)
Figure 1.2 The unit cells for a typical A B 03. (a) Cubic prototypic phase above the Curie
temperature; (b) Tetragonal phase below the Curie temperature. [8]
1.1.2 Hysteresis Loop
The most important feature o f ferroelectric materials is the ferroelectric hysteresis
loop. It can be measured by a Sawyer-Tower circuit (Figure 1.3) [9]. An a.c. signal is
applied across a pair o f electrodes on a ferroelectric crystal sample C f placed on the
horizontal plates o f an oscilloscope. Thus, the quantity shown on the horizontal axis is
proportional to the field across the sample. A linear capacitor C q is connected in series
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with the sample. The voltage across C q is proportional to the polarization o f the sample
Cf. This voltage is displayed by the vertical plates o f the oscilloscope. I f a small electric
field is applied first, we will have only a linear response between P and E, because the
field is not large enough to switch any domain and the crystal will behave as a normal
dielectric material (paraelectric), which corresponds to the segment OA o f the curves in
Figure 1.4. As E increases, a num ber o f the negative domains (which have a polarization
opposite to the direction o f the field) will be switched over in the positive direction
(along the electric field) and the polarization will increase dramatically (segment AB)
until all the domains are aligned in the positive direction (segment BC). This is a state o f
saturation where the crystal is composed o f just a single domain. The process is also
called “poling”.
Scope
A.C.
Figure 1.3 Schematic illustration of Sawyer-Tower circuit for measuring of ferroelectric
hysteresis loop.
As the electric field decreases, the polarization will decreases to point D but does
not return back to zero. W hen the field is zero, some o f the domains will remain aligned
in the positive direction and the crystal will exhibit a remanent polarization Pr. The
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extrapolation o f the linear segment BC o f the curve back to the polarization axis
represents the value o f the spontaneous polarization Ps.
p‘
\
B
ps
Pz D /
F/
/
/
/
/* c
°
G
/
E
H
Figure 1.4 A P-E hysteresis loop in ferroelectrics.
W hen the electric field increases in the negative direction, the polarization starts
to decrease. At certain value (point F in the figure), the polarization is zero. The strength
o f the electric field required to reduce the polarization to zero is called the coercive field
Ec. Further increasing the negative field will completely reverse the polarization in the
crystal. The same cycle can be done by the field once again. Finally the relation between
P and E is represented by a hysteresis loop (C D FG H C ) as shown in Figure 1.4.
1.1.3 Phase Transition and Dielectric Anomaly
Temperature o f the phase transition called Curie point T(; is another important
characteristic o f ferroelectrics. W hen the temperature is below Curie point, the
ferroelectric crystal undergoes a structural transition from a paraelectric phase to a
ferroelectric phase. The crystal exhibits no ferroelectricity when the temperature is higher
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than Curie point; on the other hand, the crystal exhibits ferroelectricity below the Curie
point. If there are two or more ferroelectric phases in a crystal, such as BaTi 0 3 , the Curie
point only corresponds to the temperature where a paraelectric-ferroelectric phase
transition occurs. The temperature where a ferroelectric phase transforms to another
ferroelectric phase is called transition temperature.
The crystal’s properties show anomalies when the temperature is close to the
Curie point accompanying a structural change. As an example, the dielectric constant
shows a maximum on transition to the ferroelectric phase. Figure 1.5 shows such
dielectric anomaly o f BaTiC>3 [10]. For most o f ferroelectrics, the temperature
dependence o f the dielectric constant above the Curie point obeys the Curie-W eiss law,
such that:
£ =£«+- ¥ ~ r {T>Tc)
(1-1}
where C is the Curie constant and To is the Curie-W eiss temperature which is defined as
the temperature at which the extrapolated curve o f the inverse dielectric constant
intersects the temperature axis. To generally is different from Tc. In the case o f a firstorder phase transition, 7q< Tc, while for the second order phase transition To— Tc-
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Figure 1.5 Temperature dependence of the dielectric constant in BaTiCE [10]
1.2 Heterogeneous Ferroelectrics
1.2.1 Multilayers and Superlattices
The rapid development o f thin film depositions and the progresses in interfacial
quality control make it possible to produce ferroelectric superlattices and multilayers.
Physical vapor deposition (PVD), chemical vapor deposition (CVD), and chemical
solution deposition (CSD) are three major thin film deposition techniques which are
widely used in both scientific research and industrial manufacturing.
PVD method usually includes sputtering, electron beam evaporation, pulsed laser
deposition (PLD) [11-19], m olecular beam epitaxy (MBE) [20-23], laser-assisted MBE
[24,25] and atomic layer MBE [26-28]. Generally, the principle o f PVD method is that
the materials to be deposited are evaporated physically to form a thin film on the
substrate. The methods involved to evaporate the materials usually include an electric
resistant heating unit, a high energy electron beam, a plasma, or an energetic laser beam.
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In CVD based methods, the volatile m olecular species that contains elements o f the
compound to be deposited are transported to a reactor. The absorbed species on the
substrate surface react to form the film o f the material. The techniques based on the
principles o f CVD include metal-organic CVD (MOCVD) [29,30], atomic layer MOCVD
(ALMOCVD), metal-organic MBE (MOMBE), plasma enhanced CVD (PECVD) and
laser-assisted CVD (LCVD) [31]. Advantages o f the CVD processes are that the
deposited films are dense with good step coverage, which makes CVD one o f the
industrial standard thin film deposition methods. Deposition can be achieved at low
temperatures on selected areas which benefits the device fabrication. The CSD method,
which is also widely used in industry, includes precursor preparation, precursor formation
and film formation [32]. CSD is generally divided into metal-organic solution deposition
and sol-gel deposition. The principle o f CSD is that precursor solution is deposited on
substrate using spin coating machine and as-deposited film is pyrolyzed in furnace. The
advantages o f CSD are the lost operation cost and the capability to deposit on large
substrate.
Many ferroelectric oxide systems have been successfully deposited into
superlattices and m ultilayered heterostructures. A series o f interesting properties have
been discovered, which serve as a great m otivation for scientific and technological
explorations. First o f all, a dramatic enhancement o f dielectric response is most
commonly observed in multilayer and superlattice structures. The permittivities are
usually significantly greater than those possessed by single-layer solid-solution thin films,
with the same global composition as that o f the combined superlattice and multilayer
components. Dielectric permittivities with order o f 103 are widely reported [11,17,26,32],
10
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In 1996, Erbil et al [30] first reported that at low frequency, colossal real permittivities as
high as 420,000 were found in PbTi 0 3 -Pbo.72Lao.28Ti 0 3 superlattice with periodicities o f
40 nm and total thickness o f 400 nm, as shown in Figure 1.6. The mechanism o f this
phenomenon was also proposed by the same group as a result o f the motion o f pinned
domain-wall lattices at low electric fields and sliding-mode motion at high electric fields
[29,30]. Following that, a group from Japan also observed the extremely high dielectric
permittivity o f the magnitude o f 104- 105 in three different perovskite superlattice systems,
such as B aT i0 3/S rT i0 3 [20,21], B aT i0 3/B aZ r0 3 [20] and S rZ r0 3/S rT i0 3 [22,23].
5
experiment
4
3
3
2 %
2
t
0
theory
4
3
2
1
0
10-1
1
to
102
Frequency (kHz)
103
Figure 1.6 (a) The measured real (solid line) and imaginary (dotted line) parts of the dielectric
constant for the sample PbTi0 3/Pbi.xLaxT i0 3 with periodicities of 40 nm at Vac=0 V as a function
of frequency on a logarithmic scale, (b) The calculated real (solid line) and imaginary (dotted line)
parts of the dielectric constant at Fdc=0 V as a function of frequency as a logarithmic scale. [30]
11
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Moreover, other studies found that a decrease in the num ber o f m odulated unit
cells (so-called periodicities) leads to the enhancement o f the dielectric and ferroelectric
properties in superlattice [13,16,17,19,26,33]. High dielectric tunabilities as high as 94%
in BaTiCVSrTiCh system (see in Figure 1.7) were also observed in certain ferroelectric
superlattices [15]. Another interesting phenomenon which has been extensively studies is
that the temperature migration o f the dielectric peak with frequency, reminiscent o f
dielectric response o f relaxors [12,34-36].
60
(Ba#5,SrM)TIOa
SO
SrTlO.
BaTiO
Superlattice
•2
0
2
4
Applied Voltage (V)
Figure 1.7 C -V curves of the superlattice with a B T02/ST02 periodicity, (Bao.s, Sr05)TiO3 (BST),
SrTi03 (STO), and BaTi03 (BTO) capacitors. [15]
An enhancement in the remanent polarization is also a common feature observed
in superlattice structures, see e.g., Shimuta et al [14], In their work, superlattices o f
BaTi 0 3 and SrTi0 3 , with three unit cells o f each in the superlattice period, demonstrated
a remanent polarization greater than that o f single-phase BaTi 0 3 thin films, see Figure 1.8.
So-called “asymmetric superlattices” (with more B aT i0 3 than S rT i0 3 in superlattice
period) showed an even more dramatic response, with the maximum observed Pr more
12
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than three times that o f single-phase BaTi 0 3 thin films, and approaching that o f bulk
BaTiOs.
Electric field [MV/cm]
Figure 1.8 P -E hysteresis loops of the BT/ST superlattice with the stacking periodicity of 15/3
and the BT single-phase film prepared using the same deposition conditions as the superlattices.
[14]
1.2.2 Polarization Graded Ferroelectrics
In 1991, Schubring et al firstly observed an asymmetric dielectric hysteresis loop
in compositionally graded KTai.xNb x0 3 (KTN) thin films prepared via metal-organic
deposition [37]. In contrast to the symmetric hysteresis loop with respect to the
polarization and applied electric field axes in homogenous ferroelectric materials, they
found a charge offsets along the axis o f electric displacement (or polarization) (Figure 1.9).
It was believed that the polarization gradient resulting from the composition gradient,
which arises as a result o f the growth process, is the origin o f this abnormal phenomenon.
Following this original finding, researchers found that the polarization gradient can also
13
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be introduced by the other ways, such as temperature gradient [38,39] and strain gradient
[40,41],
A series o f further investigations revealed more unique phenomena in polarization
graded ferroelectrics, such as built-in potential which is dependent on the gradient o f
polarization [37,42], small temperature dependence o f dielectric properties which has
potential applications in temperature insensitive ferroelectric devices [38,43], and
gigantic pyroelectric response which is o f great interest for infrared detector applications
[44], These fascinating properties spawned further experimental works to extend to
various ferroelectric material systems via different deposition techniques.
P
eno
±1
0 f*
(■»*1.0? V/
Figure 1.9 Unconventional hysteresis phenomenon in D vs. E plots, obtained at 37.5°C by
excitation with a 35-V, 50-Hz triangular wave. This behavior was observed in a 9.8-pm-thick
KTN film [37],
Two major thin film deposition techniques have been utilized to prepare
polarization graded ferroelectric thin films. The first one is CSD. It essentially starts from
an either sol-gel based [45-56] or metal-organic [37,41,57-59] based precursor solution.
Each layer is spun on the substrate via a spin coater, and then the film is pyrolysed in
14
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order to form the desired oxides, and a post annealing treatment may be needed to
improve the crystallinity. The CSD is cost-effective and very easy to deposit film on
substrates o f large areas. However, the films are usually polycrystalline. The second
major method is Pulsed Laser Deposition (PLD) [60-74], which is one o f the Physical
Vapor Deposition (PVD) methods. A highly energized pulsed laser beam blasts over the
surface o f a target to form a plasma plume which eventually will be deposited on the
heated substrate. The process is carried out in a vacuum chamber. These techniques
enable researchers to easily prepare polarization graded thin films using different
ferroelectric
materials,
such
as
BST,
Ba(Zr,Ti)C >3
(BZT),
(Ba,Sr)(Zr,Ti) 0 3 ,
(Ba,Sr)Bi 4Ti40 i5, PZT, (Pb,Sr)T i03, (Pb,L a)Ti03, (Pb,La)(Zr,Ti)03, and (Pb,C a)T i03.
Other than PLD, r f magnetron sputtering m ethod has also been used to prepare
polarization graded thin film [44],
Besides the thin film form, more recently, Buscaglia et al synthesized B aT i0 3
core-shell particles with local compositional gradient [75], They grew a shell o f SrTi 03
or BaZr 0 3 on the surface o f BaTi 0 3 spherical templates suspended in aqueous solution.
Therefore, a radial compositional gradient within the single grains was formed after the
sintering.
There have been a number o f theoretical attempts to explain the origin o f the
unusual properties o f polarization graded ferroelectrics. A Slater model, where the free
energy is expressed in terms o f ion displacement relative to a central charge, was one o f
the first approaches. It qualitatively described some o f the phenomena known in
polarization graded ferroelectrics [43]. Studies based on the Transverse Ising Model
(TIM) have been reported to calculate the polarization profile, dielectric properties, and
15
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pyroelectric properties in composition graded and temperature graded ferroelectrics [7680]. Temperature and compositional graded ferroelectrics have also been studied using
basic electrostatic considerations [81-85]. This shift o f the hysteresis loop was also
attributed to an asymmetry in the leakage currents o f the structure [86,87]. Later, a
thermodynamic study showed that compositional variation across a ferroelectric bilayer
can result in broken spatial inversion symmetry [8 8 ]. This leads to the inescapable
conclusion that in insulating polarization graded ferroelectrics there exists a internal
potential that will self-pole the material due to the electrostatic coupling between layers..
Recently, a modified Landau-Ginzburg formalism, which took into account
electrostatic and elastic interactions, provided a unified approach to three different types
o f polarization graded ferroelectric system [89]. It was shown to be in good quantitative
agreement w ith the published experimental results [90]. It also predicts the both static [91]
and dynamic [92] pyroelectric responses in polarization graded ferroelectrics. Other form
o f Landau-Ginzburg theory was also reported in the literature, which divided the
polarization graded structure into finite num ber o f discrete layers and include the
interfacial energy for each layer [93].
1.3 Tunable M icrowave Devices
Ferroelectric materials have been found to be particularly important for
applications in piezoelectric, pyroelectric, microwave, linear and nonlinear optical
devices. This study will mainly focus on the applications o f ferroelectric materials on
tunable microwave devices. The principle lies in the strong nonlinear change o f dielectric
permittivity in ferroelectric materials upon the application o f an external electric field.
16
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Since the first demonstrations o f ferroelectric materials based m icrowave devices was
presented 45 years ago [94,95], their properties have been studied intensively. However,
it is only in the past decade that the real applications begin to emerge due to the
progresses related to both devices electronics and materials. Over the past years there has
been a fast growth in the development o f tunable dielectric materials for a variety o f
frequency agile radio frequency (rf) and microwave device applications including tunable
filters, voltage controlled oscillators, varactors in transmission lines, nonlinear medium in
frequency triplers and phase shifters [96-98].
The tunability (i.e., the degree o f variation in the dielectric constant as a function
o f the applied electric field) is the key design param eter o f tunable devices although
sometimes parameters incorporating the loss tangent to the field-dependent variation o f
the dielectric response (such as the Figure o f Merit, FOM, and the Commutation Quality
Factor K) are also used [99,100]. The most common definition o f the tunability rj is:
v=
(1.2)
s r (E = 0)
where sr(E) is the relative dielectric permittivity at an applied electric field E and er (E—0)
is the small-signal dielectric permittivity. Ideally, a large tunability accompanied by a
small dielectric loss is desired. Capacitors with high tunability can reduce the physical
dimensions and circuit losses o f a transmission line structure, and increase the conversion
efficiency o f frequency triples [101]. For phase shifter applications, a low dielectric loss
tangent (ideally 0.01 or less) is desired to decrease the insertion loss and hence increase
the phase shifting per decibel o f loss [ 102 ].
The non-linearity in the dielectric response with respect to an applied field is due
to the non-linear variation in the induced polarization, unique to ferroelectric crystals. For
17
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regular dielectric insulators such as SiC>2, Si3N 4, and Ta 2C>5, the permittivity does not
change significantly with an applied field. On the other hand, the dielectric response o f a
ferroelectric material to an applied field is shown schematically in Figure 1.10, above the
ferroelectric-paraelectric transformation temperature 7c. The high permittivity o f
ferroelectrics in the paraelectric state is a result o f interplay between microscopic internal
poling fields that are weaker than the thermal vibrations o f atoms [99]. A polarized state,
however, can be easily induced by an applied field. This results in high permittivities
especially near the transformation temperature. The ferroelectric state is characterized by
a hysteresis, attributed to domain phenomena. For relatively high frequencies, the
reversible domain wall motion in the ferroelectric state may result in unwanted delays in
the dielectric response as well as in an increase in the dielectric loss. Therefore, for
microwave application, the ferroelectric should be in its paraelectric state above 7c where
there is no spontaneous polarization and thus does not contain electrical or structural
domains
E
Figure 1.10 Schematic variation in the dielectric permittivity of a ferroelectric above the
ferroelectric phase transformation temperature.
Dielectric losses arise in ferroelectric crystals due to three predominant sources:
( 1) an intrinsic loss attributed to m ulti-phonon scattering, (2 ) a loss associated with the
18
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conversion o f the microwave field into acoustic oscillations by regions with residual
ferroelectric polarization, and (3) extrinsic losses due to motion o f charged defects such
as interstitials and vacancies resulting in acoustic waves at the frequency o f the applied
field [103]. The major challenge for utilizing these materials is the requirement for
simultaneous maximization o f the tunability and minimization o f the dielectric loss.
Researchers have succeeded in reducing losses by using metallic acceptor dopants that
reduce the dielectric losses to levels below 0.01 [102,104,105]. The positively charged
metallic ions combine with oxygen vacancies, which are believed to be the main source
o f dielectric degradation in thin film ferroelectric materials, and neutralize their
contribution to the extrinsic loss. In this study, we will mainly focus on using dielectric
oxide layer to reduce the device dielectric loss.
For practical tunable microwave devices, high dielectric tunability, low
microwave loss, and good temperature stability are required for optimum performance
and long-term reliability. Recently, much work has focused on optimizing the uniform
composition BST thin film material design (i.e., via doping, thickness variations, buffer
layers, stoichiometry and stress modification, etc.) and process science protocols in order
to develop thin films which possess low dielectric loss and high tunability. Although
much success has been achieved in optimizing these two material properties, less
attention has been devoted to optimizing temperature stability. There is significant
concern that in practical applications o f such tunable devices, in particular BST based
phase shifters for electronically scanned antennas (ESAs), that the phase shifter
performance will be compromised due to the temperature dependence o f the device
capacitance. Specifically, the capacitance o f the BST based device is strongly influenced
19
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by temperature changes because the dielectric constant (er) o f a single composition
paraelectric BST films (e.g., Bao.sSro.sTiOa) follows the Curie-W eiss law.
In fielded
applications, antenna systems are exposed to a broad range o f harsh operational
environments, i.e., variable ambient temperatures, and spurious changes in the device
capacitance that stem from ambient temperature fluctuations will disrupt the phase shifter
performance via device-to-device phase shift and/or insertion loss variations leading to
beam pointing errors and ultimately communication disruption and/or failure in the
ability to receive and transmit the information. Thus, to ensure device performance
consistency and reliability temperature stable devices are essential for fielded ESA
systems.
1.4 Objective
This study is to develop a thermodynamic modeling to analyze the ferroelectric
multilayered heterostructures and predict the properties o f ferroelectric multilayered
heterostructures to guide the fabrication o f high performance ferroelectric multilayers and
heterostructures for tunable microwave devices applications.
20
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Chapter 2 Thermodynamics
In order to understand the interlayer coupling o f multilayered heterostructures, we
first start with a simple bilayer. Based on the analysis o f bilayer, we then extend the
modeling to multilayered heterostructures to provide guidance for thin film depostions.
2.1 Ferroelectric (FE)-Paraelectric (PE) Bilayer
Consider two uncoupled, unconstrained FE layers with equal lateral dimensions,
shown in Figure 2.1(a). In its m ost general form, the energy density o f layers 1 and layer 2
in their uncoupled, unconstrained state can be expressed as:
Fx = F 0>1 + \ a P ? + ± bP * + X
-c P ? ,
2
4
6
F2 - F0 2 + ± d P 22 + -e P * + ~ J P 26
2
4
6
(2.1)
where F()j is the energy o f layer i in its high-temperature PE state, P { are the polarizations
o f layers 1 and 2, and a, b, c, d, e, and/ are Landau coefficients, a and d are temperature
dependent with their temperature dependency given by the Curie-W eiss law, i.e., cr=(TTc,i)/£0Ci and d-(J-Tc,i)le^C i where s0 is the permittivity o f free space, 7c,; and C, are the
Curie-W eiss temperature and constant o f layer i. The other coefficients for both materials
are assumed to be temperature independent. The spontaneous polarization for each layer
(Po.i and P 0,2 for layers 1 and 2 , respectively) is given by the condition o f thermodynamic
equilibrium, 8Fj I dPi = 0 .
Suppose layer 1 with thickness h\ is joined with layer 2 with thickness hi and the
bilayer is sandwiched between metallic electrodes [Figure 2.1(b)]. A FE superlattice
consisting o f sets o f identical bilayers with the same short circuit conditions can be
treated analogously. The relative volume fraction o f layer 2 is a=hi!h. We will assume
21
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that both h\ and hi are much larger than the characteristic correlation lengths o f each layer.
When these layers are coupled, the actual polarization o f each layer is expected to be
different from its “decoupled” value due to the electrical interaction between the layers.
The internal electric fields ED,\ and ED<2 in layer 1 and layer 2 due to the polarization
mismatch establish new polarization states, i.e., P i and P 2 in layer 1 and 2 , respectively,
see Figure 2.1(b). The internal electric fields Ed are related to the difference in
polarization o f each layer and can be determined through the Maxwell relations VxED=0
and V-ED=(l/£b)(p/^V-P) where pj is the free charge density. For perfectly insulating
bilayers, the internal fields in each layer are given by [106]
£n
(2.2)
( P ,- < P >) = — (P 2 - Pj)
£(\
E d ,2 ~ ' - ( P 2 - < P > ) = —
( P , - P 2)
(2.3)
where < P >= (1 - a )P x + aP2 is the average polarization.
Electrode
J L;i\ cr 2 f
l.u\er2t
|
I a\yer 2 ^
P,
P2
h
Layer 1 j
I
Electrode
(a)
(b)
Substrate
(C)
Figure 2.1 (a) Two freestanding ferroelectric layers and the initial polarization in layers 1 and 2
are P 0,1 and P 0,2, respectively, (b) A bilayer constructed by joining the layers in (a), sandwiched
between metallic top and bottom electrodes, (c) a heteroepitaxial bilayer made up of the bilayer in
(b) on a thick substrate. Due to interlayer coupling, Pi<Po,i and P 2>Po,2.
22
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It is clear that E d ,i > 0 enhances the polarization o f layer 2 whereas E d , i attempts to
decrease the polarization o f layer 1 since it lies anti-parallel to the polarization vector
(ED,i<0). Therefore, in equilibrium, it is expected that Pi<Po,i and P 2 >Po,2 so as to
decrease the initial polarization difference.
The total free energy functional incorporating the potential energies o f the internal
fields E d , i and E d ,2 is given by:
Fz = ( l - a ) [ F l (Pl ) - E P 1 - ^ E D^Pl ] + a[F2(P2) - E P 2 - ^
D2P2] + l f -
1
£
F
= (1 - a)[P ] (P ,) ■- PP, ] + a[F2 (P 2 ) - EP2} + - «(1 - a )
(P, - P2) 2 + - f 2
£0
h
(2A)
where E is an applied electrical field parallel to the polarization and Fs is the energy o f
the interfaces between the layers. We assume that the layers are relatively thick compared
to the correlation length o f ferroelectricity which is o f the order o f 1 nm [107]. Therefore,
we can neglect the interface energy Fs/h even for thin bilayers with thickness o f about
100 nm. This simplification does not affect polarization and the stress state within the
individual layers. The polarization is given by the continuity o f the normal component o f
the electrical displacement across the interfaces in each layer [108], The polarizations
beyond the interface area are constant in each layer and do not depend on distribution o f
polarization near the interface.
Similarly, due to the condition o f mechanical
compatibility across the interfaces, the internal stresses arising from the misfit between
the films and the substrate are homogeneously distributed throughout the volume o f the
individual layers if these layers are free o f dislocations and other defects [109], In Eq.
(2.4) we have introduced a coefficient £ which is essentially a measure o f the free charge
density with respect to the bound charge at the interlayer interface such that
23
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£ = 1 - p f / p b, where pb is the bound charge density. The two limiting values, f= l and
^==0 correspond to perfect insulating and semiconducting FE bilayers, respectively. The
latter condition implies that there are sufficient free charges with high mobility to
compensate for the internal fields due to the polarization mismatch. Thus, for £=0 (and
for £< 0 ), there is no electrostatic contribution to the total free energy due to the internal
electrical field.
The equilibrium polarization o f each layer is given by the simultaneous solution
o f the equations o f state dF\ /dP1 = 0 and dFz / dP2 = 0 :
§
=£ +^ ( /W
Wxj
£Q
,) ,
&i2
(2-5)
£q
In the absence o f an external electric field (E=0), the thermodynamic potential for
each layer can be extracted from the total free energy as:
w
) =
^
2)
f 0,
+ |<
+ i
cp?
(
= ^0,2 ^ - d P i + je P 24 + 7 ^ 2 6 - \ & DaPi
Z
4
o
Z
2-6)
(2.7)
The analysis can be extended to a heteroepitaxial bilayer grown on a thick cubic
substrate [Figure 2.1(c)] by incorporating the elastic energy o f the internal stresses that
results in renormalized Landau coefficients [110]:
,
a = a —x ,
4 0 12j
V 1+ V 1
4012,2
,
0
4Qu l
= b-\---------------- ,
(2.8)
s m + s l2,
,
4 Q,12,2
d - x 2--------------- , e =e-\-----------------,
11,2
12,2
°11,2T °12,2
24
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(2.9)
where Syj and Qyj are the elastic compliances at constant polarization and electrostrictive
coefficients o f material i, respectively. x,=(as-a,)/as are the (polarization-free) misfit
strains o f layer i with respect to substrate, where o, are the unconstrained equivalent cubic
cell constants o f layer i and as is the lattice parameter o f the substrate. For a
pseudomorphic bilayer w ith h<hp where hp is the critical thickness for misfit dislocations,
these misfit strains are not independent and the relation between them is given by
x 2 = l - [ a 2( l - x 1) / a 1].
In order to quantify the interlayer coupling effect explicitly, we can rearrange Eq.
(2.4) and normalize the coefficients,
Ft = ( ! - « ) Fx(Px) + ^ a P 2 + a F2(P2) + ^ ( l - a ) P 2 + Fel~ JP xP2
2sa
2 sn
= 0 - « ) F 01 + - d P x2 + —b P 2 + - c P 2
(2.10)
+ a F q,i + ~ d P 2 + -j e P 2 + ^ f P 2 + Fel- J P xP2
where the normalized coefficients given by:
a +— a
£o
£
a' H
a
sn
dH
d ' -1
E
E
unconstained
(2.11)
heteroepitaxial
(1 —a )
unconstrained
(1 - a )
heteroepitaxial
(2.12)
and b =b, e =e for the unconstrained bilayer and b = b ’ , e = e for the heteroepitaxial
bilayer. F ei is the elastic energy o f the polarization-free misfit:
Fel =
(2.13)
*^11,1 “*'‘^12,1
^11,2 “*“‘^12,2
25
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which is absent for the unconstrained bilayer.
The last term in Eq. (2.10) is the interlayer coupling and J is the coupling
coefficient given by:
(2.14)
/ = a(l-a)—
Unlike previous approaches, the coupling coefficient is explicitly identified in the
present study, indicating that the coupling between layers can be controlled by either the
fraction o f each layer or by modifying the free carrier content quantified by coefficient £
For example, if there are sufficient free charge carriers within the material that are mobile,
£ is zero and the bilayer is decoupled and behaves as if it is in a series connection (i.e.,
with an electrode layer between the ferroelectric layers). We note that the interlayer
interactions also modify first Landau coefficients via Eq. (2.11) and (2.12) and hence
may alter phase transformation characteristics. These results will be discussed elsewhere.
2.1.1 Compositionally Symmetry Breaking
It is clear that the electrostatic energy o f the internal fields in Eqs. (2.6) and (2.7)
serves to introduce a symmetry-breaking element in the otherwise symmetric Landau
potentials having even powers o f the polarization. Consider the example o f an equifraction (a = l/2 ), stress-free BaTiCL-Bao.gSro.iTiCb (BT-BST90/10) bilayer. In Figure 2.2,
we plot the normalized free energy as a function o f the net polarization o f each layer. The
“degree” o f symmetry-breaking strikingly varies with the variations in the density o f free
charges in the bilayer. For instance, for ^=0 [Figure 2.2(a)], the two layers are electrically
screened from one another and can act essentially independent and are unrelated entities.
26
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This is due to the complete compensation o f the electrical field resulting from bound
charges at the interlayer interface through free charges. An equivalent construction o f this
condition would be two ferroelectric layers with a metallic electrode between them, i.e.,
two dielectrics with a series connection. Both layers display typical symmetric double
well potentials, whose minima correspond to two energetically identical FE ground states.
The equilibrium polarizations o f the layers assume their values in single-crystal form.
Due to the free charges, a relative large polarization difference AP (for BT-BST90/10
bilayer, AP~ 0.056 C/m2) can be m aintained between the two layers.
3
3
id
4
1
C
0)
0)
iB ST
£
£
4-
3N
IM
io
z
BST
I
o
BT
-0.4
-
0.2
0.0
0.2
0.4
BT
z
-
0.2
P o l a r i z a t i o n ( C /m 3)
0 JO
0.2
0.4
P o l a r i z a t i o n ( C / m 3)
3
3
§»
ip
§5
iU
s
BST
S
lb t
4=
TJ
(V
N
BT
rt
O
z
BST
O
-0.4
-
0.2
0.0
0.2
0.4
z
P o l a r i z a t i o n ( C /m 3)
-
0.2
0 JD
0.2
0.4
P o la riz a tio n (C /m )
Figure 2.2 Free energy potentials as a function of polarization for an equal-ffaction BT-BST
90/10 bilayer: (a)*g=0, (b) ^=0.01, (c) ^=0.1, and (d) £=1.
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The electric coupling between layers due to the polarization mismatch is evident
for non-zero values o f £ where this coupling is enhanced with increasing £ i.e., a
reduction in the free charges. Figure 2.2 (b)-(d) show that the otherwise symmetric double
wells o f BT and BST90/10 are skewed towards one FE equilibrium state with P > 0. The
other FE ground state with P <0 becomes metastable. The strongest value o f electrical
coupling between the layers corresponds to a bilayer made up o f two completely
insulating FEs, i.e., no free charges, £=1. This results in only one stable FE ground state
in both layers and a small polarization difference between two layers (A /M ).037 C/m2).
The other FE ground state becomes unstable due to the electrical interaction between the
layers. This shows that the initial “uncoupled” polarization gradient in insulating graded
FEs becomes smoother due to the electrostatic interactions between the layers thus
resulting in a smaller polarization difference that seeks to minimize the internal electric
field. The above results are consistent with both the ab initio and density functional
theory calculations [ 111 , 112 ] wherein they also concluded that compositional variations
result in a broken inversion symmetry that likewise leads to asymmetric thermodynamic
potentials. W e show that whenever the free charge density is less than the bound charges
density, an internal potential arises from the compositional inhomogeneity always
resulting in asymmetric potentials.
2.1.2 Dielectric Response
Using the equilibrium polarization o f each layer given by dFT /8P1 = 0 and
dFz / dP2 = 0 , the (small-signal) average dielectric response o f a perfectly insulating
bilayer (if=l) can be determined as:
28
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where < P >= (1 - a )P t + aP2 is the average polarization, SPi = f*(£) - Pt{E = 0) as
0,
and P,- satisfying Eqs. (2.5).
We have solved Eqs. (2.5) for the case o f BT and ST as the FE and PE layers,
respectively. This combination has been a system o f choice in many experimental
investigations. ST is an “incipient” ferroelectric that is paraelectric at room temperature
(RT). The Landau coefficients and elastic constants for BT [110] and ST are wellestablished that allows us to carry out a numerical quantitative study. We consider a
heteroepitaxial (001) S T -B T bilayer on a thick (001) ST substrate such that
Eq. (2.8) and (2.9) at RT. The strain in the BT layer is
x
Bt= - 2 .2 8 % .
x st
= 0 %
in
The equilibrium
polarization o f a BT film at this strain level is 0.38 C/m2. The spontaneous polarization in
the BT layer in the S T -B T bilayer for E=0 decreases from this value with increasing
volume fraction o f the ST layer until it completely vanishes at a critical relative thickness
of
« st= 0 .6 6
(Figure 2.3(a)). Figure 2.3(b) plots the difference between polarizations in the
coupled BT and ST layers AP=Pbt~Pst- AP is small (typically less than 1% o f the
polarization o f BT) indicating that the induced polarization in the ST layer almost equals
to polarization in BT layer. As the relative fraction o f the ST layer increases, there is a
commensurate rise in the depoling field in the BT layer as well as a drop in the internal
field in the ST layer that induces polarization. Eventually, a critical relative thickness is
reached at asT=0.66 which corresponds to Pi=P2=0, the only solutions o f Eqs. (2.5) for
asj>0.66. The equilibrium polarization in BT layer and the polarization difference
between two layers for a completely relaxed and unconstrained system has similar
29
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behavior as shown in Figure 2.3(c) and (d). Without the biaxial internal stress, the
polarization in the BT is -0 .2 7 C/m 2 for asx-O and disappears at a critical relative
thickness orsT=0.14.
30
0-20
15
6 10
5
£=100 kV/cm
0.2
0.4
1,0
0.6
0.00
0
Volume fraction of ST* am (%)
40
60
80
Volume fraction of ST,
100
(%)
im
40
ir
35
0,5
30
.5 ^
25
I
20
%
0.4
15
10
0.1
5
0
0
20
40
60
80
100
Volume fraction of ST, crST(%)
0
20
40
60
80
100
Volume fraction of ST, agT(%)
Figure 2.3 Dependence on ST fraction, «Sx, of polarization in BT layer under different external
fields (E=0, £i=100 kV/cm, £ 2=200 kV/cm) and the polarization difference, AP=Pa r PsT- (a) and
(b) for constrained BT-ST bilayer; xBt=-2.28% and xST=0% (solid squares: first-principles results
from Ref. [113]); (c) and (d) for unconstrained BT-ST bilayer.
The dielectric responses o f the heteroepitaxial and unconstrained B T -S T bilayers
are presented in Figure 2.4 that display an anomaly at the critical relative thicknesses. To
explain the behavior o f polarization and dielectric constant o f a bilayer, we considered
30
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analytical solutions o f Eqs. (2.5). For <*=1, using a linear approximation for internal field
o f layer 2 such that dF2 / dP2 = ~2a2(P2 - P0 2) for a2<0 (FE state) or dF2!dP2 - a 2P2 for
a2> 0 (PE state) together with the approximation
(2.16)
dF] / dPx = axPx + bxPx3
transform Eq. (2.5) into
2s,
-P i 1 —
2sxa
1+ (1 - a)s,2
a P0,2
1 0,1
1+ (1 - a)s2
(2.17)
where P^x = - a x/b x , s x = - l / ( 2 e 0ax) and £2 = - \ / ( 2 e 0a2) (or s 2 = l/( s 0a2) in the PE
state) are the dielectric constants o f the constitutive layers. For a F E -P E bilayer Po^=0
and thus:
P i= ± P o .J1
2sxa
1+ (1 - a ) s 2
(2.18)
which vanishes at a critical relative thickness a* = (1 + s 2)/(2 s x + e2) that results in <P>=0.
For a F E -F E bilayer P i decreases but does not disappear for all fractions o f layer 2 since
P 0,2>0 .
31
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6
o
5
a
§
S
~
§
ts
4
1
8
2
'c
<y s
*
|
"aJ
■-S
3
2
1
0
20
40
60
80
100
Volume fraction of ST, agT(%)
Figure 2.4 Relative mean dielectric constant as a function of volume faction, a ST: (I) for
unconstrained BT-ST bilayer; (II) for strained heteroepitaxial BT-ST bilayer, x1!T=-2.28% and
X s t= 0 % .
To discuss the effect o f free charge carriers, fraction-dependent dielectric
response o f unconstrained BT-ST bilayer for various c are plotted in Figure 2.5. It is clear
that the critical relative fraction depends on the density o f free charges which shifts the
PE to PE transition to higher volume fraction o f ST with increasing £. We also note that
magnitude o f the singularity at the critical fraction is reduced with more free charges.
32
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"I 'I I I )' I1 I I "I I V I
14
M
20
0
20
40
60
80
100
Volume fraction of ST, #ST(%)
Figure 2.5 Dielectric response of an unconstrained BT-ST bilayer as a function of volume
fraction of ST for different £ The inset shows the dielectric response of BT-ST bilayer with
^=0.1 and c=\ in more detail.
The analogy with temperature dependence o f polarization and dielectric response
as well as with smearing o f the dielectric anomaly under an applied electric field is
obvious (Figure 2.3). However, the effect o f the depolarizing field is not equivalent to the
effect o f temperature. Therefore, using the expansion o f tree energy [Eq. (2.10)] does not
mean that the phase transition in bulk ferroelectrics is a second order transformation. For
example, BT in constrained layer undergoes a second order phase transformation, while
in bulk BT the transformation is first order. Although a single-domain state near the
transformation temperature is unstable with respect to the formation o f 180° domains
[114], it can be metastable far from this temperature, especially for thin constrained
ferroelectric films. Comparison o f results o f our scale independent analysis in bilayers
with results o f first principal calculations for superlattices allows one to conclude that the
33
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effects o f electrostatic interactions considered above should be observed in thin films as
well. The polarization o f superlattices with period equaling five atomic planes [113]
shown in Figure 2.3(a) (solid squares) demonstrates a similar dependence on the layer
fraction as a macroscopic ferroelectric-paraelectric bilayer. A critical fraction o f -0 .9 can
be expected on the basis o f extrapolation o f microscopic data to the zero polarization
(dashed line in Figure 2.3(a)). It is clear that increasing the period o f the superlattices
should decrease the deviation between the results o f macroscopic and microscopic
analysis.
The stability o f single domain states in films obviously warrants further
theoretical consideration. However, there are several experimental results supporting the
results o f this study. Experimental observations where an average relative dielectric
response o f - 5 0 0 was reported for a B T -S T superlattice with asr=0.5 and one stacking
period [11] can be related to the properties o f a partially relaxed bilayer. Extremely high
dielectric permittivities in P b T i0 3 - P b ^ L a /T iO j [30] and SrZrC>3-SrTiC )3 superlattices
[23] have been reported in the literature that is in agreement with the conclusions o f this
work.
2.1.3 Tunability
The tunability o f the bilayer can be expressed as [99,100]:
77 = 1 —
< s R > (E )
< s R > (E
=
0)
x 100%
(2.19)
where < sr > (E ) is the dielectric response in the presence o f an external electric field E.
34
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We consider a BT-ST bilayer as an example heteroepitaxial system. Two cases
are considered in this study. One is a freestanding BT-ST bilayer, sandwiched between
m etallic electrodes [Figure 2.1(b)]. The other is a heteroepitaxial BT-ST bilayer grown on
a thick
x st
(0 0 1 )
= 0 % .
ST substrate with pseudomorphic electrodes [Figure 2.1(c)] such that
The lattice parameters o f BT and ST are
Thus, the strain in the BT layer will be
x
0 .4 0 0 5
Bt = - 2 . 5 6 % .
and
0 .3 9 0 5
nm, respectively.
As shown in Figure 2.6(a), the
dielectric response exhibits an anomaly in the vicinity o f a critical fraction
-6 9 %
(-1 4 %
ST and
ST for the freestanding and heteroepitaxial bilayer, respectively).
With the application o f an external electric field, we can analyze the dielectric
tunability o f the bilayer via Eq. (2.19). Figure 2.6(b) plots the tunabilities o f both
structures at 100 kV/cm as a function o f the relative volume fraction o f ST layer. Both
cases show extremely high dielectric tunabilities, rjmax=~91%, around the dielectric
anomaly. Such a high tunability has not been observed from homogeneous thin film FEs
primarily because o f degradation due to internal stresses and the clamping effect o f the
substrate [115,116], The electric field dependence o f the dielectric tunabilities for both
cases is shown in Figure 2.7(a) and (b). For each ST fraction, the tunability increases with
the increasing o f external field. At the relative critical fraction, it is shown that the
bilayers have extremely high tunabilities even in the presence o f small external fields;
thus further simplifying the silicon IC elements necessary to control microwave and
millimeter wave tuning devices.
35
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FS
m
0
40
20
60
80
Relative fraction of ST (° /
100
0
20
40
60
80
Relative fraction of ST (%)
100
100
Figure 2.6 (a) Relative dielectric responses of freestanding (FS) and heteroepitaxial (HE,
x
Bt = - 2 . 5 6 %
and x S t = 0 %
)
BT-ST bilayers as a function of ST fraction, (b) Dielectric tunabilities
of BT-ST bilayers as a function of ST fraction under 100 kV/cm external field.
36
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100
69%
60
40
75%
20
60%
.50%
■85%
0
0
20
40
60
80
Electric field (kV/cm)
10%;
100
FreestandingJ
»..... i-ttm
tfII IM
If’l"
20
40
60
80
Electric field (kV/cm)
100
Figure 2.7 (a) Dielectric tunabilities of freestanding BT-ST bilayers as a function of external
field for various ST fractions, (b) Dielectric tunabilities of heteroepitaxial BT-ST bilayers
( x Bt = - 2 . 5 6 %
and x St = 0 % ) as a function of external field for various ST fractions.
Unlike homogeneous films, which show smaller the high tunabilities compared to
this analysis because o f internal stresses, FE multilayers and superlattices can
37
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experimentally
achieve near theoretical performance
(>90%
tunability) because
electrostatic interactions between the layers induce polarization in the paraelectric layer,
thus m aking them ideal for practical applications.
Moreover, a straightforward extension o f this analysis shows that >90% tunability
may still be achieved when the ST layer is replaced by a linear dielectric such as silicon
dioxide or silicon nitride layer. The critical FE volume fraction, however, depends on the
room temperature relative dielectric constant o f the linear dielectric. For a linear
dielectric forming a bilayer with a 100 nm thick BT freestanding film, the critical BT
layer fraction around which the high tunability should occur varies from 99.7% to 95% as
the dielectric response o f the linear dielectric changes from 4 to 40. Such versatility in the
structure formation, together with the ability to incorporate standard IC silicon films into
the design permit the device designer to construct elements that simultaneously have high
tunability and very low electrical leakage; crucial elements for low power consumption
devices [117]. In addition, the heteroepitaxial structures described above should have
inherently lower loss and temperature variation. The loss should be smaller in the bilayer
structures because the polarization in the ST layer is induced, and therefore does not
switch under small applied fields, while the temperature dependence should be flattened
over that o f the homogeneous film as the bilayer structure introduces a dielectric layer
into the structure whose permittivity is virtually independent o f temperature. These
predictions are in qualitative agreement with recent experimental results where the loss o f
ferroelectric memory elements have been shown to be reduced by growing top and
bottom paraelectric buffers prior to metallization [118].
38
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2.1.4 High Capacitance Oxide/Ferroelectric/Oxide Stacks
As the critical dimensions o f integrated circuits (ICs) continue to shrink into the
nanometer range, it becomes increasing more difficult for IC manufacturers to use
conventional silicon-based materials to form the high capacitance, on-chip elements
necessary for DRAM and filter applications. While a num ber o f non-traditional dielectric
(DE) materials have been investigated, including Ta2C>5, FHD2, AI2O3, ZrC>2, and BST,
such materials are problematic; not only because their compatibility with convention IC
processing m ust be proven, but because current deposition m eans can often produce
interface traps, high leakage, and low breakdown strength devices [119]. It is thus highly
desirable to maintain as m uch o f the current silicon-based capacitive element structures
as possible while increasing their overall storage capacity.
We consider various dielectric-ferroelectric-dielectric (DE/FE/DE) multilayer
structures as replacem ent elements for the simple DE layers m ost commonly used in IC
processing. M ultilayer FE heterostructures are considered as alternative charge storage
components because o f their extraordinarily high dielectric response [3]. We show that
conventional IC dielectrics such as silicon dioxide, silicon nitride, and silicon oxynitride
may be incorporated in these structures to produce low leakage and high breakdown
strength, while the FE acts to polarize these dielectrics, thereby producing an overall a
high capacitive structure. We will concentrate on oxide dielectrics although the analysis
is equally valid for all linear dielectrics. The theoretical analysis builds upon a previously
developed formalism for FE/FE and FE/paraelectric (PE) bilayers and superlattices [120],
This model was employed to explain the gigantic dielectric response in such
heterostructures [23,30] and predicts a dielectric anomaly at a critical layer fraction o f the
39
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PE material at which the dielectric tunability is also maximized [121]. Similar theoretical
results regarding the enhancement o f the dielectric permittivity were predicted for FE thin
films with “dead” layers at the interface with the electrodes [122].
Consider a DE/FE/DE stack that consists o f a FE layer o f thickness o f h\
sandwiched between two DE layers o f thickness /z2 and /?3 with top and bottom metallic
electrodes, as shown in Figure 2.8. The dielectric layer can be any low-loss dielectric
material, such as S i0 2, Si3N 4, or H f0 2 [123], W e will assume for simplicity that the
trilayer is symmetric, i.e., the DE layers have the same thickness h2= h 2. The total energy
density o f this configuration can be written as:
Fz = { \ - 2 a \ F l (Pl ) ~ E D;iPl - E P l + '2.C& F2(P2) - \
e d <2P2 - E P 2
Fc
(2.20)
h
where a = h2th is the relative thickness o f the DE layer, h = h \+ 2 h 2 is the total thickness o f
the multilayer heterostructure, P\ and P 2 are the polarizations the FE and DE layers,
respectively, and E is an applied electric field parallel to the polarization. ED%\ and E d,2
are the internal fields in the layers that arise from the interlayer polarization mismatch
[120], The last term Fs is the sum o f the surface energies o f the interlayer interfaces that
contain the contribution by the interface defect structures and traps. This surface energy
can be neglected if the individual layers are sufficiently thick, o f the order o f ten
nanometers [120], since the strength o f the electrostatic and elastic fields o f the interface
diminishes rapidly away from interface [124],
40
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Figure 2.8 A freestanding DE/FE/DE stack sandwiched between metallic electrodes. The
thickness of the FE and DE layers are h\ and hi, respectively, and h is the total thickness.
In Eq. (2.20), F\(P\) is the free energy density o f the FE layer that can be
expressed as a Landau expansion, such that:
W i ) = ^o,i + ^ a 1E12 e - U
2
4
f I4 +
(2.21)
6
where F 0j is the free energy o f the FE in the PE state,and a\, b\, and c\ are Landau
coefficients o f bulk FE. For a linear DE, the free energy Fi{Pi)o f the DE layers
is given
by:
( 2 .22)
F1(P1) = \ a 2P l = — ^— P22
I
Ls §er
where ai and £r are the (uncoupled) dielectric stiffness and relative dielectric constant o f
the DE, respectively.
The spontaneous polarization o f the layers in their uncoupled state (Po,>) follow
from the condition o f thermodynamic equilibrium, dFl / dPj = 0 such that:
,
- b . + J b ,2 - 4 a .c ,
,
Pol =
Y -------- — , Po.2 = 0
2c,
(2.23)
41
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W e note that the internal stresses that might arise from the lattice misfit in
heteroepitaxial stacks or the thermal expansion mismatch can be incorporated into the
free energy densities via re-normalized Landau coefficients [110,125], For the sake o f
simplicity, we will assume in this point that the layers are completely relaxed and the
trilayer structure is not clamped by a thick substrate.
The actual polarization o f the layers in the DE/FE/DE stack should obviously
differ from Poj because o f the electrostatic interaction between the layers due to the
internal electric fields E d ,\ and E d , 2 - For perfectly insulating bilayers [88,120]:
1
2a
Ed,, = ------(Pl ~ < P >) = — (P2 - P J
*o
£o
(2.24)
E d ,2 =
(2.25)
( P i - < P >) = ^ SL(Pl ~ P 2)
£o
£o
where <P>=( 1-2a)P\+2aP2 is the average polarization. E d ,2 induces polarization in the
DE layers whereas En,\ attempts to decrease the polarization o f FE layer as to minimize
the initial polarization difference, AP=P0j . The polarization in each layer is given by the
simultaneous solution o f equations o f state, dFj/dPf=0. It is expected that Pc,\<Po,\ and
Pc,2>0 in the trilayer, where Pc,\ and Pc,2 are the equilibrium polarizations in the FE and
DE layers, respectively, and correspond to the solutions o f 8Fx/dPf=0.
The (small-signal) average dielectric response o f the DE/FE/DE heterostructure
along the direction o f the polarization is:
1 d < Pc >
?0
where
dE
1
,
SSPC,
§Pr
(l-2a)
- + 2a E
E
< / >c > = ( l - 2 a ) P c , i + 2 « / ’c,2
(2 .26)
is the equilibrium average polarization o f the stack and
8PCl = PCl (E ) - PCi (E = 0) as £ ’->0. The average dielectric constant o f the trilayer is
42
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expected to increase substantially at a critical DE fraction similar to FE/PE bilayers as the
dielectric layer polarizes to ever larger values [120]. This behavior resembles the Z-type
anomaly near a phase transformation. The reason for this behavior is that for larger
fractions o f the DE layer, £fr,i completely suppresses ferroelectricity in the FE layer.
Beyond this critical fraction, the FE layer can no longer induce polarization in the DE
layers.
We considered two materials systems as the FE layer: Bai.xSrxT i0 3 (BST) with
0<x<0.2 and Pbi^Zr/TiCb (PZT) with 0<x< 0.5. In the specified composition range, these
FE materials have the prototypical perovskite lattice which transform from the PE cubic
to FE tetragonal crystal structure upon cooling and are FE at room temperature (RT) at
which the calculations were carried out. The polarization in each layer is calculated from
the condition o f thermodynamic equilibrium dFx/dP,= 0 and the dielectric response is
determined from Eq. (2.26).
A series o f calculations were carried out to determine the critical fraction o f the
DE layer where the gigantic average dielectric response is expected for BST and PZT
stacks as a function o f the uncoupled (or bulk permittivity) sR o f the DE layer. These
results
are
plotted
in
Figure
2.9
and
Figure
2.10.
As
an
example,
in
a
Si02/Bao.8Sro.2Ti0 3 /Si02 stack, where SiC>2 is a typical gate material with f«=4, the
anomaly in <er> o f the trilayer is around 0.05%. A SiCb/BT/SiCb trilayer shows a higher
critical fraction, -0.15% , compared to the BST stack. This is because BT has a higher
initial polarization and thus there is a larger initial polarization difference between the FE
and the DE. Likewise, the critical fractions in Si02/PZT/SiC>2 are higher than those in
Si02/BST/Si02 stacks (Figure 2.10). Furthermore, it is clear from Figure 2.9 and Figure
43
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2.10 that the larger the bulk £jjof the DE, the larger the critical fraction will be due to a
higher induced polarization by the internal electrical field in the DE. We also m ark in
these plots the bulk £r o f typical linear DEs [123] to provide an estimate as to where the
critical layer fraction is expected for the maximum dielectric response.
5
Ta,0,
u io
S i0 2 SijN
4
I i0 2
BT
BST 90:10
S
©
3
<8
2
BST 80:20
im
1
U
0
1
10
100
D ielectric constant o f dielectric layer
Figure 2.9 Critical fraction of DE/BST/DE stacks as a function of the (bulk) dielectric constant of
DE layer. Results for BaTi03 (BT), Bao.9Sr0.iTi03 (BST 90:10) and Bao.8Sro.2Ti03 (BST 80:20) as
the FE layer are shown.
In addition to the obvious advantage o f higher charge storage capabilities due to
the extremely high dielectric response, another technologically important implication o f
oxide/FE heterostructures is that they offer an efficient way to reduce dielectric loss and
leakage. The DE oxide serves as a buffer between the FE and the m etallic electrodes. The
elimination o f these metal-FE interfaces would significantly reduce charge injection from
44
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the metal into the FE or leakage o f charges from the FE into the metal that results in
deterioration in the dielectric properties o f simple FE capacitors. This has been one o f
the long-standing problems that has prevented the use o f high dielectric constant FEs
such as BST in charge storage applications. Indeed, low dielectric losses have been
reported experimentally in BST films on S i02, Ti-Al, and Teflon buffer layers
[118,126,127]. Furthermore, the concepts developed here also imply that multiple
oxide/FE stacks with a systematic variation in the FE layer composition would result in a
heterostructure with a high dielectric response that remains constant over a relatively
large temperature range.
20
PT
Tii.O,
Si02 SijN
MfO,
16
BS
©m
•m
TiO,
PZT 80:20-
12
u
©
8
PZT 50:50 -
03
(J
•■c
•wm
m
U
4
0
1
100
10
D ielectric constant o f dielectric layer
Figure 2.10 Critical fraction of DE/PZT/DE stacks as a function of the dielectric constant of DE
layer. Results for PbTi03 (PT), Pbo.sZro^TiCf (PZT 80:20) and Pbo.sZro.sTiCh (PZT 50:50) as the
FE layer are shown.
45
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2.2 Interface Effects
Artificial ferroelectric heterostructures such as bilayers, superlattices, and graded
films have attracted a great deal o f interest due to their unusual behavior compared to
their constituents in bulk or single-crystal form. Increases in the remnant polarization and
extremely high dielectric response have been reported in a variety o f FE-PE and FE- DE
systems [14,19,30,37,128-131]. It was also shown experimentally that losses and leakage
can be improved in ferroelectric memory elements by growing top and bottom dielectric
buffers before the growth o f the metallic electrodes [118]. Theoretically, the observed
phenomena in these heterostructures have been explained through an interlayer coupling
using a parametric coefficient or via electromechanical coupling that arises from internal
stresses [113,132-134], The large dielectric response has also been attributed to MaxwellW agner effects where defect-related transport plays a major role [34]. The interplay
between the internal fields results in the suppression o f polarization in FE and PE (or DE)
layers at a critical layer fraction. At this critical fraction, a gigantic dielectric response is
also predicted.
The
developed theoretical model o f interlayer coupling
in
ferroelectric
heterostructures was based on continuum relations and holds for relatively thick bilayers
with layer thickness much larger than the correlation length o f ferroelectricity and defectfree, morphologically smooth interlayer interfaces [120], Potential applications o f these
heterostructures as high-capacity stacks for on-chip charge storage devices or as memory
elements would require a scaling down o f the layer thicknesses and it is clear that the
interlayer structure and interface defects would play a significant role in such
heterostructures. Building upon our prior results, we employ a thermodynamic approach
46
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for a FE-PE bilayer that incorporates the presence o f polarization gradients at the
interface to show that the interface plays a significant role on the properties o f thin
bilayers. The analysis shows that although the interfacial effects influence the critical
fraction o f the PE layer at which a huge dielectric response is expected, this transition
from a polarized bilayer is still there for heterostructures with a thickness larger than the
correlation length. For ultra-thin films, the polarization gradients that emanate from the
interlayer interfaces may completely suppress ferroelectricity.
Consider a single-domain FE layer and a PE layer with equal lateral dimensions
between metallic electrodes. The thickness o f the FE and PE layers are L\ and T2,
respectively, such that the total thickness L=L\+L 2 . The spontaneous (and induced)
polarization is along a z-axis normal to the interlayer interface located at z=0. The free
energy density o f such a configuration can be expressed as [135-139]:
F = FP +
- E d P dz
2
(2.27)
where Fp is the combined polarization-free energy o f the two materials in the paraelectric
state and P=P(z) is the polarization. In Eq. (2.27), a,,
and c, are the dielectric stiffness
coefficients o f layer i (z=l,2). A t are the Ginzburg coefficients and they can be estimated
as Aj ~ \a \- f,2 where
is the correlation length o f layer i [138]. E ^ z ) is the internal
“built-in” electric field due to polarization variations such that:
(2.28)
o
47
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where P is the average polarization o f the entire heterostructure. The last two terms o f
Eq. (2.27) describe the interfacial energy where P_0 and P+0 are the polarizations o f the
two layers at the interface, i.e., at z= -0 and z=+0, respectively, and S{ are the
extrapolation lengths o f layers i. W e assume stress-free and unclamped layers throughout
the calculations although these contributions can be easily incorporated into the free
energy functional using re-normalized dielectric stiffness coefficients [110], We do so to
assure that the effect o f interfaces is clearly observable from the calculations since even
small strains can modify the polarization o f individual layers quite drastically. This also
enables us to compare the properties o f the layers to their bulk forms more clearly.
Minimization o f Eq. (2.27) with respect to P yields:
rl^p
Ai
1
_
= 2 atP + 4 bsP 3 + 6 c ,P 5 + — ( P - P )
s ()
dz
(2.29)
with the boundary conditions:
dP
dP_
dz z=-L\
dz
(2.30)
= 0
z=+L->
corresponding to complete charge compensation at the electrode interfaces and
f£± J-P
dz 8 :
(2.31)
=0
z=± 0
which ensure that the polarization is continuous across the FE-PE interface.
We carry out a numerical analysis for bilayers consisting o f BT as the FE layer
and ST as the PE layer since the thermodynamic coefficients o f BT and ST are wellestablished [110]. In our calculations, discrete elements (Az) were taken 0.4 nm,
corresponding approximately to the size o f a BT unit cell. In order to illustrate the
48
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“strength” o f the interfacial effect, two sets o f values o f the correlation lengths ( ) for
BT and ST were taken: 1 nm and 0.5 nm; 3 nm and 0.8 nm, respectively for BT and ST.
The ratio S j ^ t was taken to be 1.41 for both cases [136], In Figure 2.11 we show
schematically the polarization variation in the vicinity o f the interface which follows
from Eq. (2.27). The polarization variation extends over a comparatively larger region in
the case for the larger correlation length (which results in a smaller local polarization
difference due to the increase in the strength o f the depoling field). Thus, variations in
this param eter allow the modeling o f the role o f the interface characteristics [136],
Polarization and related electrical properties are a strong function o f the correlation
length as it describes the extent o f fluctuations o f the polarization and is a function o f
temperature (and internal/external stresses which alter Tc through Clausius-Clapeyron
type relations) [140], We note that defects in FE materials such as vacancies (which are
invariably electrically charged) and interfacial dislocations [141] have highly localized
non-linear electrostatic fields around them that are created via the electrostrictive
coupling o f the eigenstrain o f the defect and the spontaneous polarization. The strength o f
the electrostatic and elastic fields o f the interface diminishes rapidly away from interface
[124], Thus, the analysis presented in this study provides an estimate to an extremely
complicated problem since the exact variation o f the polarization near the interface is
unknown.
Figure 2.12(a) and (b) plot the polarization in the BT layer as a function o f the ST
fraction for 4 different total bilayer thicknesses and two sets o f £(. . As L decreases, the
polarization in the BT (as well as the ST layers, not shown) decreases due to the increase
o f the contribution o f the interfacial energy to the total energy, i.e., the length scale o f the
49
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polarization variation near the interface becomes comparable to L. For £<200 nm,
bilayers with larger correlation and extrapolation lengths [Figure 2.12(b)] have smaller
polarizations compared to the same thicknesses with smaller correlation and extrapolation
lengths [Figure 2.12(a)] since the more diffuse interface introduces larger depolarization
fields through the electrostatic coupling. M oreover, from Figure 2.12, it is clear that the
critical fraction o f ST at which the polarization in the bilayer is suppressed due to the
depolarization field arising from the interlayer coupling, changes as a function o f L.
B
_
o
+
Distance from the interface
Figure 2.11 Normalized polarization change as a function of thickness in the vicinity of the
interface for a bilayer consisting of two ferroelectrics, A and B: £a,i<£a,2, £b,i<£b,2;
50
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0.3
f
=1 n m , £e = 0 .5 nm
40 nm
80 nm
200 nm
400 mil
0.0
0
5
10
20
15
ST fraction (%)
0.3
" f " ' .... » ........> r i |lll,llr r i||lln r | - ......................
|M
4 = 3 n m , 4 r =0.8 n m
r O 0.2
5
6
^ 0 .1
•40 nm
• 80 nm
200 nm
•400 nm
1
0.0
5
10
15
20
ST fraction (%)
Figure 2.12 Polarizations in BT layer as a function of ST fraction for different thicknesses: (a)
sharp interface (Cbt= 1 nm, Csi=0.5 nm); (b) diffusive interface (£bt=3 nm, fsT=0.8 nm).
To display the effect o f the interlayer interface more clearly, we plot the critical
ST fraction as a function o f the total bilayer thickness in Figure 2.13. The dashed line
represents the result for thick bilayers in the continuum limit [120]. The critical fraction
increases as a function o f L and levels o ff around 200 nm at ~17% for both sets o f £,-•
51
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This is quite similar to the strain relaxation in epitaxial films with increasing film
thickness via misfit dislocation formation [142], For a “sharper” interface, the critical
fraction decreases only slightly as L decreases from -2 0 0 nm. On the other hand, for a
more “diffuse” interface, the critical fraction drops markedly as L decreases. This is
because the polarization varies along a larger length scale at the interface in comparison
to the “sharper” interface. In either case, the impact o f the interface becomes less
prominent and can be neglected in bilayers for L >200 nm. We note that the small
difference between the critical fractions o f the continuum limit calculations and the
bilayer thicker than -2 0 0 nm arise from the fact that in the previous model the
equilibrium Ginzburg fluctuations in the polarization were ignored [120,143].
Results presented in this work have several implications. The thermodynamic
model in the continuum limit clearly establishes that the internal electric field due to
polarization mismatch between FE-FE, FE-PE, and FE-DE bilayers and heterostructures
is the cause o f unique electrical properties including polarization enhancement and high
dielectric response [120]. This is in accordance with our current approach where
polarization gradients at the interlayer interfaces do not have much o f an impact for
relatively thick bilayers with L>200 nm. However, thinner bilayers typically with T<100
nm should display a marked degradation in polarization with increasing ST fraction. This
reduction occurs at m uch smaller ST fractions if the polarization variations at the
interfaces persist at longer length scales away from the interface. For these cases, the
polarization is controlled by the nature o f the interface rather than the global
thermodynamic driving forces. Therefore, the impact o f the interface cannot be neglected
52
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in designing ultra-thin bilayers as the interfacial region where polarization gradients exist
due to defects now represent a considerable volume o f the material.
Roytbimi e t
*
•
200
0
al
*
^ = 3 nm , £st=0.8 nm
^ ,= 1 nm , 4 = 0 . 5 nm
400
600
1000
800
Total thickness (nm)
Figure 2.13 Critical fraction as a function of total bilayer thickness. The dashed line shows the
continuum limit from Ref. [120] and the solid line is a guide for the eye.
2.3 M ultilayer Heterostructures
Using the analysis o f bilayer structures as a building block, we can extend the
formalism to a multilayer heterostructure or a graded construct. In either case, the free
energy density can be expressed through:
- a tP* +-b,P* +-c,P? +
2 1 '
4
6
dP
\d z
\2
-
e
^
-
ep,
dz + Fv
(2.32)
where Fo is the energy in the PE state and P (z) is polarization in layer i. Fs is the
interfacial energy due to the polarization variation across the interlayer interfaces
between layers and can be neglected for layer thicknesses much larger than the
53
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correlation length o f ferroelectricity (-1-10 nm). In Eq. (2.32), «, and bt are
renormalized dielectric stiffness coefficients given by [ 110 ]:
4 ’ Qua
t
,
,
, bt = b ,+
S u j + S 12,i
2 • Ql2i
(2.33)
Sm + S l v
where um is the misfit strain. We note here that if the sample is poly crystalline, the above
relations would still hold if um is replaced by the thermal strain,
ut- For
epitaxial films, um
contains the contribution o f the thermal strain since it is defined as the difference in the
lattice parameters o f the film and the substrate. In Eq. (2.32), A t are the Ginzburg
coefficients o f layer i. Ai can be estimated as At = \at | •
where
is the correlation
length o f layer i. E is the external electric field and Edj is the internal “built-in” electric
field due to polarization variations such that [106]:
(2.34)
E d J = - — {Pt - P )
where P is the average polarization o f the entire multilayer. The equilibrium polarization
can be determined by the equation o f state (<9/\. / dPi - 0) that yields an Euler-Lagrange
relation with {dPt /d z )|z=0ji= 0 as the boundary conditions. The average dielectric
permittivity follows from:
(L
Vl
Z (E ) = L J{ l/[^ (z ) + l]]tfe
Vo
-1
(2.35)
J
where x i z ) = [Pi(E + E E ) - P i (E )]/(A E ■s 0) is the small-signal dielectric permittivity.
The tunability, 77(E), in the presence o f an external electric field, E, can thus be
determined from:
54
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tj( E )
= Z ^E
(2.36)
x 100%
,
x
{E = 0)
The above outlined methodology allows us to calculate the temperature
dependence o f the average dielectric susceptibility for different BST multilayered or
graded heterostructures, as shown in Figure 2.14. The maximum is broadened as a result
o f systematic compositional grading, since these layers have different transition
temperatures. It is not surprising that the extent o f the broadening o f the susceptibility
displays a close relationship with the imposed compositional gradient. The dielectric
susceptibility is significantly flattened with respect to the temperature for B ST 100/0BST50/50 compared to BST80/20-BST70/30, and it is less pronounced for the
BST90/10-BST60/40. A steeper composition gradient can give rise to broader maximum
o f the dielectric susceptibility.
8
BST100/0-BST50/50
— —BST90/10-BST60/40
- * BST80/20-BST70/30
7
©
!—I
*'
'w
a
Xfl
S3
5
ft
4
O
<*)
cu
u
3
s&>
%
•pH
2
1
©
0
-20
0
20
40
60
80
100
120
140
Tem perature ( C)
Figure 2.14 The theoretical average dielectric response as a function o f temperature for three
compositionally graded Ba^Sr^/riCh systems with the same nominal average composition.
55
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Chapter 3 Experimental
Based on the theoretical results presented in Section 2.3, it is clear that a
multilayer heterostructure can be devised that is highly tunable and this tunability can be
sustained over a large temperature interval. This is an ideal combination for devices such
as phase shifters and antennas to be employed in telecommunications as described in the
Section 1.3. Out theoretical calculations can thus provide a recipe to make multilayer or
graded constructs o f BST films for this particular application. In collaboration with the
Army Research Laboratories in Aberdeen, MD, we pursued a joint experimental and
theoretical program to identify materials systems for high performance tunable
microwave device applications. For the fabrication o f these heterostructures, our
theoretical results were employed as a guide.
The multilayer thin film material design consisted o f three distinct compositional
layers (-220 nm nominal thickness), namely, Bao.6oSro.4oTi0 3 (BST60/40), BST75/25,
and BST90/10 which were sequentially deposited onto the PtSi substrates. A schematic
o f the thin film multilayer material design is shown in Figure 3.1. These compositions
were chosen to maximize the strength o f the composition gradient. As it was shown in a
theoretical study, the temperature sensitivity o f the dielectric response in a graded or
m ultilayer ferroelectric heterostructure can be tailored by adjusting the degree o f the
compositional variations [144], The ferroelectric phase transformation temperature o f
BST 60/40 is just below room temperature (5°C). Therefore a systematic compositional
variation from BST 60/50 to 90/10 would provide a wide range to minimize the
temperature sensitivity without sacrificing from leakage characteristics (BaTiOa typically
56
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has high dielectric losses) or from the dielectric response (for compositions with Sr less
than BST 60/40).
Electrodes
Si substrate
Figure 3.1 Schematic diagram of the thin film multilayer material design.
3.1 Thin Film Fabrication
The compositionally-multilayered thin films were fabricated on Pt coated high
resistivity Si substrates (PtSi) via the industry standard metalorganic solution deposition
(MOSD) technique using carboxylate-alkoxide precursors. The precursor solutions for
the BST films were prepared using barium acetate (Ba(CH3COOH)2), strontium acetate,
(Sr(CH 3COOH) 2), and titanium (IV) isopropoxide (Ti(C 4H(>C))4) as starting materials.
Glacial acetic acid and 2-methoxyethanol (H3COOH2CH2OH) were used as solvents.
The viscosity and surface tension o f the solution was adjusted by varying the 2methoxyethanol content. A detailed description o f the MOSD precursor solution
preparation and film deposition technique was reported elsewhere [104,105].
The multilayer material design was integrated via two process science protocols,
namely, a single-anneal and a multi-anneal. The single anneal multilayer integration
process consisted o f sequentially depositing three coats o f each distinct compositional
film layer, (i.e., BST60/40, BST75/25, and BST90/10), onto the PtSi substrate. After each
57
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individual spin-on film coating, the sample was pyrolyzed at 350°C for 10 min. in order
to remove the organic addenda. After all film coatings making-up the complete tri-layer
compositional material design were deposited and pyrolyzed, the tri-layer thin film
material structure was then post-deposition annealed one time at 750°C for 60 min. in
flowing oxygen. Alternatively, the multi-anneal process protocol consisted o f depositing
three coats o f each layer composition onto the substrates, whereby after each individual
spin-on film coating the sample was pyrolyzed at 350°C for 10 min. and subsequently
post-deposition annealed at 750°C for 60 min. in flowing oxygen. Thus, for the multi­
anneal process protocol the material design structure was exposed to three post­
deposition anneals at 750°C, such that each distinct layer composition was fully
crystallized prior to the deposition o f the next compositional layer.
3.2 Characterization
The crystal structure and surface morphology o f the films were assessed by
glancing angle X-ray diffraction (GAXRD) and atomic force microscopy (AFM) using a
Rigaku diffractometer with Cu Ka radiation at 40 kV and a Digital Instruments
Dimension 3000 tapping mode AFM, respectively. A Hitachi S4500 field emission
scanning microscope (FESEM) was utilized to assess the cross-sectional and plan-view
film microstructure. Rutherford backscattering spectroscopy (RBS) was employed to
assess film composition, areal thickness and interface quality. The RBS measurements
were obtained using a 2-MeV He+ ion beam from a NEC 5SDH-2 tandem positive ion
accelerator. All spectra were fitted and interpreted using the program RUM P [145],
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The XRD patterns o f the single-anneal and multi-anneal layered BST films are
shown in Figure 3.2. For comparison purposes, the XRD pattern o f a homogenous uniform
composition BST60/40 is also displayed in Figure 3.2. The layered BST films,
independent o f the annealing process, exhibited a random polycrystalline perovskite
structure. There was no evidence o f secondary phase formation, as no peaks other than
the peaks o f (100), (110), (111), (200), (210), and (211) BST were observed. For both the
single- and multi-anneal BST heterostructures there was a slight shift o f the X-ray peaks
to lower angles (corresponding to larger interplanar spacings) with respect to that o f
homogenous composition BST60/40. This down shift in the peak position is indicative o f
the fact that the lattice param eter o f the m ultilayered BST films based on the (110) XRD
peak (^multi-anneal 3.9875 A and a singie anneai= 3.9863 A) was slightly larger than that for the
uniform composition BST film (auniform b s t = 3.964 A). This larger lattice parameter o f
the multilayer BST films may be explained by the fact that the lattice param eter o f the
multilayer structure is an average o f the individual lattice parameters o f each
compositional layer whereby the lattice param eter increases as the Ba/Sr ratio is
increased from the first compositional layer, BST60/40 (aBST6o/4o= 3.9650 A) to that o f
the surface compositional layer, BST90/10
4.0lA ). Our X-ray
( a B sT 90/io =
6 b s t 90/io =
3.98 A, and
c B s t 9 o /io =
results are consistent with experimental w ork by Tian et al. [52]
wherein it was demonstrated for single composition BST films, that there was a
significant down shift o f the XRD peaks to lower angles as the Ba/Sr ratio was elevated
from BST70/30 to BST90/10. This study also showed that the XRD peaks for
compositionally graded BST (BST70/30 - BST80/20 - BST90/10) were down shifted to
lower angles with respect to that o f the uniform composition BST70/30 films, which is
59
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consistent with our results for compositionally layered BST films. Similar observations
were reported by Zhang et al. [146] where XRD peak down shifts to lower angles for
graded BST (BST60/40 - BST70/30 - BST80/20 - BST90/10 - B aT i0 3) films with respect
to uniform composition BST60/40 films were observed. It is also noteworthy to mention
that this increase in the lattice param eter may also result from surface/interface defects
and thermal strains that develop as the heterostructure is cooled down from the annealing
temperature. It has been noted that the uneven distribution o f Ba/Sr ratio in graded films
has resulted in noticeable interface regions, and as a result a non-linear strain field forms
through the thickness o f the heterostructure due to the variation in the lattice parameter
from the bottom to the top surface and the thermal strain. Combined with the localized
strains o f the defect structure near and at the interfaces, there is a highly non-uniform
internal strain distribution in these multilayer constructs. [147-149]
In addition to the X-ray peak down shifts, the X-ray data revealed differences in
the full-width-half-maximum (FWHM) o f the X-ray peaks for the BST films exposed to
the two annealing processes. Specifically, the FW HM o f the m ultilayer BST (110) peak
was slightly broadened/larger for the single-annealed film (0.522) with respect to that o f
the m ulti-annealed m ultilayer structure (0.365), suggesting that the grain size o f the
multi-annealed film possessed a larger grain size than the single-annealed films. This
result is supported by the AFM results which determined that the grain size o f the multi­
annealed films (-8 0 nm) was larger than that o f the single annealed films (-45 nm). The
enhanced grain size o f the multi-annealed layered BST thin films is most likely due to the
extended effective annealing exposure time (3 hours for multi-anneal process vs. 1 hour
for single anneal process). In other words, the layered BST structure showed an increase
60
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in grain size with increased annealing time (i.e., the multi-anneal process was exposed to
3 hours annealing time vs. single anneal process which was exposed to only 1 hour total
annealing time), which is entirely consistent with the X-ray diffraction studies. Initially,
grain nucleation and growth are expected with the on-set o f film annealing temperature
and time because o f the amorphous to crystalline phase transformation and the increase in
surface mobility, thus allowing the films to decrease their total energy by growing larger
grains and decreasing their grain boundary area. In addition, the extended temporal
exposure at the designated post depositional annealing temperature would allow
continued grain growth whereby smaller grains would to continue to grow and coalesce
into larger grains as the film is exposed to each subsequent post deposition anneal. Thus
the multi-anneal process protocol, with its longer anneal-exposure time, resulted in the
formation o f larger grains with respect to the single-anneal process for the layered BST
thin films.
( 110 ),
(1 1 1 )
Pt
Jliy
20
J
30
L Jt
40
Angle (26)
A.
50
il_
60
Figure 3.2 X-ray diffraction patterns o f the (a) multi-anneal and (b) single annealed layered BST
thin films. For comparison, the XRD pattern o f the (c) homogenous uniform composition
BST60/40 annealed at 750°C is also displayed.
61
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The surface morphology o f the multilayer BST thin under both processing
conditions was assessed via tapping mode AFM over a l x l pm2 scan area (Figure 3.3).
The param eter o f film surface roughness is very important since the dielectric properties
are strongly influenced by the quality o f the interface between the top electrode and the
film [104,150]. It is well known that film-electrode interface roughness exacerbates the
leakage characteristics, thereby resulting in reliability and lifetime issues [151-153]. The
AFM images o f the films show that the layered BST structures exhibited a dense
microstructure and no cracks, pin-holes, or other surface defects were observed. A larger
grain size with a more uniform and well-developed microstructure was observed for the
film fabricated via the multi-anneal process protocol. This result is consistent with the
XRD findings based on the FW HM data. The surface roughness (Figure 3.3), as quantified
by AFM was found to be higher for the larger grain size multi-anneal processed films
(3.479 nm) with respect to the single annealed multilayered film (2.640 nm). This
elevated value o f surface roughness for the multi-annealed films is m ost likely due to the
fact that as each o f the compositional layers is annealed and crystallized it exhibits a
rougher surface than the as-pyrolysed or as-deposited layers. This newly crystalline
surface now serves as the substrate for the next overlying compositional layer and this
overlayer will inherit the surface roughness o f the underlying crystalline film surface.
This is referred to as the “crystalline film overgrowth" effect [154]. In this manner, the
surface roughness o f the top or capping BST90/10 layer is enhanced due to the inherited
roughness from the underlying crystalline film layers. Thus, since the multi-anneal
process produced distinct crystalline surfaces o f each compositional layer, (i.e.,
62
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BST60/40, BST75/25, and BST90/10), whereby each annealed crystalline surface served
as the substrate for the next over-layer, it is expected that the surface o f the multi­
annealed layered BST films would be rougher than that o f the single annealed films
where a smooth amorphous pyrolyzed compositional surface separates each BST
compositional layer. Nonetheless, both films possess surface roughness values that are
within the acceptable range for device applications. Thus the resultant difference in
leakage characteristics should be negligible and neither annealing process should degrade
the device reliability.
Cross-sectional field emission scanning electron microscopy (FESEM) images o f
the multilayer films are shown in Figure 3.4. The FESEM micrographs demonstrated that
both the single- and m ulti-annealed multilayer BST films possessed a dense, wellcrystallized microstructure with a uniform cross-sectional thickness o f -2 2 5 nm. The
films were polycrystalline and were composed o f granular multi-grains randomly
distributed throughout the film thickness. The FESEM micrographs showed a distinct
structural delineation between the film and the PtSi substrate and no amorphous layer or
voiding/defects was observed. It is interesting to note that regardless o f the annealing
process protocol employed, the FESEM images do not reveal the presence o f visible
internal interfaces throughout the thickness o f the film, i.e., there are no structurally
visible internal interfaces which separate the individual layer compositions from one
another. FESEM characterization suggests that both films are similar in that they appear
homogenous
in
nature
lacking
structural
interface
delineation
o f the
compositional layers.
63
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internal
Figure 3.3 AFM micrographs showing the plan view surface morphology of the (a) single
annealed and the (b) multi-annealed BST film structure. The AFM 3-D images of the single
annealed film are shown in (c) and the multi annealed film structure is shown in (d). The scanned
area was 1 pm2.
The thickness o f the multilayered films and their compositional structure was
characterized by RBS. In order to avoid the interference or overlap o f the Pt and Ba peaks,
which would occur on PtSi substrates [105], the RBS data was m easured on multilayered
BST films deposited on M gO substrates exposed to both annealing processes. In addition,
to further diminish the effect o f the overlap o f the different elements and to accurately
interpret the spectra, the RBS simulated model was compared to data collected at angles
both normal to the beam (i.e., beam straight onto the sample) and then tilted away from
the detector at 60°. The RBS spectra, m easured with a 1.2 MeV He+ ion beam, o f the
64
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single-anneal and multi-anneal layered heterostructures are shown in Figure 3.5. The
simulated model was found to fit both the tilted and normal spectra, thus the results are
quite definite, accurate, and reliable. The RBS measured compositional gradients o f the
Ba and Sr elements in the m ultilayered films along the thickness direction clearly confirm
the films compositional differences with respect to annealing protocols employed.
Specifically, the RBS data showed that the single-annealed multilayer BST films have a
uniform Ba/Sr composition o f BST78/22 throughout the thickness o f the film. In contrast,
the multilayer film which was exposed to three post-deposition anneals was found to
consist o f three distinct compositional layers, namely, BST63/37, BST78/22, and
BST88/12. The RBS results suggest that the single anneal process protocol caused
extensive interdiffusion within the BST film and ultimately resulted in a uniform
homogenous composition BST thin film. On the other hand, the multi anneal process had
no interdiffusion within the film and thus it consisted o f three layers, each with a distinct
BST composition. The RBS characterization determined the film thickness to be -2 2 0
nm for both annealing protocols. This is in close agreement with the thickness
determination obtained from the cross-sectional FESEM results. Since the single-anneal
process resulted in a uniform homogeneous composition BST78/22 film it will no longer
be considered a candidate for a temperature stable material design. Hence, this film was
not characterized for dielectric properties as a function o f temperature.
65
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Figure 3.4 FESEM cross-sectional images of the annealed multi-layer films fabricated via the (a)
single anneal and (b) multi-anneal process protocol.
Energy (MeV)
0.8
120
Uniform 220 nm
BST 78/22
100
Energy (MeV)
1.2
1.0
158Q
:
.ft. Surface
0.8
0.6
1.2
Layered BST
100 ■ 74 nm BST 88/12
■ 74 nm B5T?8fiffl
? 80 L 74 nm BST 6 3 3 7
S4U 80
Ba
60
40
88/12
20
150
W
200
250
300
Channel
350
400
450
150
(b)
200
250
300
Channel
350
40)
450
Energy (MeV)
Figure 3.5 The RBS spectra, (a) the single anneal and (b) multi anneal layered BST films. The
large dashed and continuous smooth lines represent the RBS simulation via RUMP [145] and the
small dotted lines represent the experimental data points.
3.3 Electrical M easurement
The electrical measurements were achieved in the metal-insulator-metal (MIM)
capacitor configuration, with Pt as both the top and bottom electrodes. Details o f the
66
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device test structure configuration are discussed elsewhere [105]. The film capacitance,
Cp, and dissipation factor, tanS, were measured with a HP 4194A impedance/gain
analyzer. The dielectric constant, sr, was calculated from the capacitance measured at 100
kHz without bias voltage. The tunability, AC/Co where AC is the change in capacitance
relative to zero-bias capacitance Co, was measured as a function o f applied bias from 0 to
444 kV/cm. The measurements were performed as cycle sweeps (negative voltage to
positive voltage back to negative voltage) to check for any possible hysteretic behavior.
The temperature dependence o f the planar dielectric properties were measured using an
in-house temperature measurement apparatus whereby a HP 4194A impedance analyzer
and a temperature control box equipped with a Peltier thermoelectric module heating
stage, inert ambience, and automated computer control. The dielectric properties
(dielectric loss and capacitance-voltage measurements) were assessed from 90°C to -10°C
in incremental temperature steps o f 10°C.
The maximum rate o f cooling/heating the
samples was less than l°C/m in with a settling time o f 30 m in at each designated
measurement temperature.
In order to appreciate the effect o f compositional layering on the room
temperature-dielectric
response
a uniform
homogenous
composition
paraelectric
BST60/40 film, prepared using the same experimental MOSD parameters as the
multilayer BST films, was characterized and compared to that o f the layered BST
compositional design. Our experimental observations clearly demonstrated that the room
temperature dielectric properties for the m ultilayer and the single composition BST film
were distinctly different. Specifically, the multilayer film exhibited a higher permittivity
(e,.=360) and lower dissipation factor (tan<5=0.012) with respect to that o f the uniform
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
composition BST film (er=176, tan<5=0.024). The higher permittivity is expected in the
multilayered BST films due to the presence o f the ferroelectric BST75/25 and BST90/10
layers, which possess higher permittivities (and higher tunabilities) with respect to
uniform composition paraelectric BST60/40. The dielectric response can be further
improved by electrostatic interactions between layers [120]. It has been reported and
experimentally demonstrated that permittivity, hence tunability, for single layer uniform
composition BST increases with increasing Ba/Sr content [65]. Similarly, others have
reported elevated dielectric constants, 426 to 1650, for compositionally graded BST films
prepared by PLD [62,65,155] and 300-320 for graded film prepared by sol-gel methods
[52,146,156],
Unfortunately, the literature reports for dielectric loss o f compositional graded
films are not as consistent as the reported values for permittivity. Low frequency, 100
kHz to 1 MHz, room temperature m easured dielectric losses have been reported as low as
0.007 [62] for PLD compositionally graded BST (BaTiC >3 - BST90/10 - BST80/20 BST75/25) films on MgO substrates to extremely high values o f 0.05 [146] for
compositionally graded BST sol-gel films (BST60/40 - BST70/30 - BST80/20 BST/90/10 - BaTiC>3) on PtSi substrates. However, several research groups have reported
dielectric losses which cluster between values o f 0.02 to 0.03.[52,65,155] The dielectric
loss value, tan<5= 0.012, which we obtained for our compositionally m ultilayer BST thin
film was quite low with respect to the reported literature values for graded BST films.
Additionally, the fact that our multilayer films also possessed lower loss than the single
composition BST60/40 films prepared by same method on the same substrate was also
surprising. The reasons for this are not well understood. However, it can be speculated
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
that the lower loss o f our compositionally multilayer BST films with respect to both
uniform and continuously graded composition BST films may result from the fact that the
defects within the film are no longer mobile and are trapped at the compositionallydistinct interfaces to compensate for the polarization difference between the layers
[120,157], Thus, this defect trapping at the compositional interfaces may immobilize
defects such that they do not reach the electrodes, thereby allowing the film to possess an
improved dielectric loss over films without this interface trapping mechanism, i.e., films
which are compositionally uniform and/or continuously graded. Thus, compositional
interfaces appear to promote enhanced material dielectric properties. It is noteworthy to
mention that preliminary device modeling efforts, based on Zeland Software Inc.'s IE3D
full-wave simulator, utilizing a two layer stratified dielectric compositional BST thin film
material design demonstrated an improvement o f 0.08 dB in insertion loss at Ka-band
[158]. This preliminary modeling analysis supports the experimental results o f this study.
We note that in order obtain a reliable comparison o f dielectric properties (dielectric loss,
permittivity, and tunability) for graded/layered and single composition BST, the films
must be fabricated via similar techniques and parameters, as well as be grown on the
same substrate. To our knowledge no reported work has compared the losses and/or
permittivity for graded films to that o f single uniform composition paraelectric thin films
which were prepared by the same method.
Figure 3.6 displays the room temperature tunability results as a function o f applied
electric field for the m ultilayer and uniform paraelectric (BST60/40) composition thin
films. As expected, for both films the tunability increased with increasing electric field.
The tighter tunability curve for the multilayer BST film implies higher tuning at the same
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
applied field with respect to the uniform composition BST film. For example, at 444
kV/cm the tunability is 65.5% for the m ultilayer film and 42% for the uniform
composition BST film. Thus, the tunability o f the multilayer film is elevated by 56% with
respect to that o f the uniform composition BST film. The compositionally heterogeneous
nature and the presence o f internal stresses most likely play a significant role in
improving the dielectric tunability o f the m ultilayered BST film with respect to that o f the
uniform composition BST film. Our room temperature dielectric data suggest that the
m ultilayer BST compositional design holds significant benefits, in terms o f permittivity,
loss and tunability, for tunable device elements as compared to uniform compositional
BST60/40 thin films. This higher tunability at a lower applied field is very important
result, as in a phase shifter circuit, higher tunability allows for fewer tuning elements
which are cascaded to achieve the desired phase shifting [159]. The decrease o f the
amount o f tuning elements directly reduces the net circuit loss. Thus, this higher
tunability combined with the preliminary device modeling results m entioned above (0.8
dB insertion loss improvement) bodes well for utilization o f m ultilayer BST thin films as
enhanced property tunable devices.
70
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Multi-layer BS
«%
\
20 1
\
BST 60/40
*
/
/V '
/'
0
-600
-400
-200
§
200
Electric H eld (kWcm)
400
600
Figure 3.6 The room temperature tunability results as a function of applied electric field for the
multi-layer BST films (open circles) and uniform paraelectric BST60/40 (filled squares) thin
films.
The temperature dependence o f the dielectric response for the multilayer BST
film and homogenous uniform composition paraelectric (BST60/40) BST film measured
at 1 M Hz is shown in Figure 3.7. Figure 3.7(a) demonstrates that the permittivity and
dissipation factor o f the multilayer BST film exhibited minimal dispersion as a function
o f temperature ranging from 90 to -10°C. Lu et al. [65] also reported a flat variation o f
dielectric permittivity for compositionally graded (BST75/25 - BST80/20 - BST90/10)
PLD deposited BST films over a wide temperature range (20-130°C) although two
anomalous peaks were reported at 59°C and 92°C, near the phase transition temperatures
o f BST80/20 (59°C) and BST90/10 (89°C), respectively. In our case no such anomalous
behavior or peaks are observed which would represent the phase transition temperatures
of BST75/25 (~50°C) or BST90/10 (88°C) for the multilayer film. W hen compared to the
71
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uniform composition paraelectric BST60/40 films (Figure 3.7(b)), the m ultilayer film
possesses a broader, more flat, diffuse dielectric response as a function o f temperature.
Specifically, the effective change in TCC with respect to uniform BST is significant; i.e.,
from 20 to 90°C, TCC was lowered by 70% with respect to the uniform composition BST
corresponding to a ~3:1 change. Similarly from 20 to -10°C the TCC value o f the
multilayer BST film was lowered by 15% with respect to the uniform composition BST
film. From Figure 3.7 it is also important to note that the dielectric loss exhibits negligible
dispersion over the measured temperature range. This is important, since in phase shifter
devices the loss must be consistent or predictable to ensure antenna performance
consistency and reliability with respect to variable temperature.
0.030
500
0.020
-
0.015
B.
B
----
- o ------ - e -
-----S'
0.010
-----------’
■4
•
tan<? =0.0125
.
O
o
LL.
C
o
W
Q.
«
W
■ 0.005
> 200
_a----- □--- tEI----- B>.. . ^
o'
>
0.020 g
•"—•—'
Per mitt
Ol
o
0.025
0.015 §
'5
0.010 S.
7i
O
o
-
>>450
■>
E 400
a>
a
350
10.030
250
(b)
(a )
tan J =0.024
£= 176
,
300 £r=360
0.000
-20
0 20 40 60 80 100
Temperature (°C)
50
-20
'
0
0.005 5
J i
l
l
0.000
20 40 60 80 100
Temperature (°C)
Figure 3.7 The temperature dependence o f the dielectric response for (a) the three time annealed
multi-layer BST film and (b) homogenous uniform composition paraelectric (BST60/40) BST
film measured at 1 MHz.
In order to fully recognize the material property enhancements achieved in this
work literature values for both uniform composition BST and compositionally stratified
BST thin films are tabulated in Table 3.1. Specifically, Table 3.1 summarizes literature
72
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derived dielectric properties, evaluated at 20°C, for single uniform composition BST
films fabricated via sputtering [160], PLD [161],
and sol-gel techniques [162], In
addition, reported literature results for proposed temperature stable material designs,
namely compositionally graded BST [65] and BST/M gO layered film structures [162] are
also listed in Table 3.1 along with our experimental results for the multilayer and single
uniform composition BST thin films. TCC was calculated for the literature studies using
the published plots o f Cp (or sr) verses temperature from -10 to 20°C via Eq. (3.1):
TCC= AC/(C0A7)
(3.1)
where AC is the change in capacitance with respect to Co at 20°C and A T is the change in
temperature relative to 20°C. TCC values reported in Table 3.1 show that the magnitude
o f the TCC for homogenous uniform composition BST thin films is quite high which is
indicative o f the large temperature dependence o f capacitance/permittivity for these films.
Specifically, the decrease in the permittivity as the temperature is raised from 20 to 90°C
for paraelectric uniform BST films ranged from 20% [160] to 60% [162], For these same
films, the permittivity increase ranged from 6.2% [160] to 35% [162] as the temperature
was lowered from 20 to -10°C. Thus, the largest change in Cf/er occurred for the high end
o f the temperature spectrum. The uniform composition BST film, fabricated in this study
was found to possess a much lower TCC value than those from the literature [65,160,162],
To our knowledge, our TCC value for uniform composition BST is the lowest reported to
date. While the reason for this low TCC value is not well understood, it is believed that
the film fabrication method, composition, substrate type, electrode material, processing
temperature, defects and microstructure, all play an important role in determining the
temperature stability o f BST thin films. [104]
73
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Table 3.1 A comparison o f the dielectric properties, TCC, and the percent change o f permittivity
with respect to 20°C for heterogeneous and uniform composition BST thin films. Tabulated data
are from the technical literature and from this study.
Composition
Substrate/deposition
method
Bao.5oSro.5oTi03
LSCO/M gO (PLD-210
nm)
Er
tand
T C C 2 0 -9 0
(20°C)
(20°C)
(ppt/°C)
A8,
(20-90
%)
t c c 2(M.
Aer
10)
Ref.
(p p t/° c )
(20-(-10)
%)
410
0.021
-7.32
51 dec
-4.1
12.2 inc
[40]
320
-
-4.0
20 dec
-2.1
6.2 inc
[39]
Bao.5oSro.5oTi03
LAO (Sol-gel-600 nm)
2934
0.01
-8.52
60 dec
-11.52
35 inc
[41]
Bao.6oSr0.4oTi03
PtSi (M O SD -240 nm)
176
0.024
-2.9
20 dec
0.83
3 dec
This
Work
1932
0.005
-6.89
52 dec
-14.3
43 inc
[41]
1650
0.225
-2.16
15 dec
-
-
[13]
475
-
6.66
44.7 inc
2.25
25 inc
[14]
-0.716
2.1 inc
This
Work
Ba)J,24Si'o.76T i03
PtSi (Sputtered-100 nm)
Ba 0.5oSro.5oTi0 3 /M gOlayered
LAO (Sol-gel-600 nm)
UG (75/25-80/20-90/10BT)
LSM O/LAO (PLD-800
nm)
DG (BT-90/10-80/2075/25)
M gO (PLD-450 nm)
UG (60/40-75/25-90/10)
360
0.012
-0.921
6.4 dec
PtSi (M O SD-220 nm)
Note: UG: upper graded; DG: down graded; dec: decrease; inc: increase.
Table 3.1 also displays the TCC results from three heterogeneous material designs;
a thin film m ultilayered BST/M gO heterostructure [162] and two compositional graded
BST thin film material designs, [62,65] that attempt to lower the TCC, i.e., to broaden the
dielectric anomaly over a wide temperature range. Compared to uniform composition
BST, the heterogeneous material designs were quite successful in lowering the TCC for
over the temperature range o f -10 to 90°C, although the best literature value was obtained
74
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for the compositionally up-graded (BST75/25 - BST80/20 - BST90/10) BST thin film
design by Lu et al. [65]. The dielectric response o f such compositionally graded
ferroelectrics as a function o f temperature exhibits characteristics o f a diffuse phase
transformation, which is reflected by a low TCC value, and is inherently linked, with the
distribution o f the phase transformation temperature resulting from the composition
gradient across the ferroelectric [89,144], It is important to note that the TCC results, for
our experimental BST m ultilayer compositional design, was significantly improved over
the three heterogeneous material designs represented in Table 3.1. Specifically, our
heterostructure exhibited a 6.4% decrease in permittivity as the temperature was elevated
from 20 to 90°C and only a 2.1 increase in permittivity as the temperature was lowered
from 20 to -10°C. This very small change in permittivity and low TCC value suggest that
our compositional multilayer BST design is temperature insensitive over the temperature
range o f -10 to 90°C.
The fact that our m ultilayer was improved over that o f Lu et al. [65] and Zhu et al.
[62] is explained by theoretical models based on a thermodynamic analysis o f graded
ferroelectric materials and m ultilayer heterostructures [89,144], Very briefly, this
formalism considers a single-crystal compositionally graded ferroelectric bar. It basically
integrates free energies o f individual layers taking into consideration the energy due to
the polarization (spontaneous and induced), electrostatic coupling between layers due to
the polarization difference, and the elastic interaction between layers that make up the
graded heterostructure. The mechanical interaction arises from the electrostrictive
coupling between the polarization and the self-strain, and consists o f two components:
the biaxial elastic energy due to the variation o f the self-strain along the thickness and the
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energy associated with the bending o f the ferroelectric due to the inhomogeneous elastic
deformation. Based on this approach, the temperature dependence o f average dielectric
response o f compositionally BST with the same nominal composition (BST75/25) can be
calculated using average thermodynamic expansion coefficients and elastic constants
available in the literature [163] as shown in Figure 2.14. In comparison to a sharp peak o f
the dielectric permittivity at Tc for bulk homogenous ferroelectrics, a diffused dielectric
response with the temperature can be expected for compositionally graded ferroelectrics
as a result o f the polarization grading and interlayer interactions. We note that this model
is developed for bulk compositionally graded ferroelectrics and it is possible to extend it
to thin films by incorporating the internal stresses due to thermal strains as well as the
clamping effect o f the substrate [120]. While these factors tend to decrease the overall
dielectric response [115] compared to bulk graded structures, the temperature dependence
o f the dielectric permittivity displays the same trend.
The maximum in the dielectric permittivity is broadened over a wide range o f
temperature depending on the “strength” o f the composition gradient as shown in Figure
2.14. A steeper composition gradient w ill give rise to a broader maximum. Our multilayer
compositional design BST (BST60/40 - BST75/25 - BST90/10) has a steeper
compositional gradient compared to that o f Lu et a l, [65] (BST75/25 - BST80/20 BST90/10) and Zhu et al. [62] (BST90/10 - BST80/20 - BST75/25). Thus, based
qualitatively on these theoretical results one would expect our multilayer film to possess
a flatter/broader dielectric anomaly, hence a lower TCC, with respect to that o f Lu et al.
[65] and Zhu et al. [62].
The temperature dependence o f the dielectric tunability for the multilayer BST
76
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film is shown in Figure 3.8. From Figure 3.8, it is clear that over the temperature range
o f -10 to 90°C, the tunability is not significantly degraded. The bias-tunability trends are
temperature independent; however, the absolute value o f tunability is slightly modified.
Thus, the multilayer BST design will allow the antenna phase shift to be temperature
stable over the ambient temperature range o f -10 to 90°C. This result is significant, as
microwave voltage tunable phase shifter devices are expected to be operated in
environments with different ambient temperatures with excellent reliability and accuracy.
The fact that our multilayer BST material design possesses excellent dielectric properties
and that both tunability and dielectric loss are stable over a broad temperature range
bodes well for its utilization in the next generation temperature stable microwave
telecommunication devices. Future work will focus on further optimization o f dielectric
properties and the development o f predictive modeling capabilities for enhanced property
temperature insensitive BST thin films materials.
77
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70
_ 60
£ 50
JP 40
13 30
i 20
H
10
0
-500
-250
0
250
500
Electric Field (kV/cm)
Figure 3.8 The temperature dependence o f the dielectric tunability for the multilayer BST film
from 90 to -10°C. The symbols on the plot represent the following temperatures: 90°C (open
circles), 80°C (open squares), 60°C (open diamonds), 40°C (crosses), 20°C (filled circles), and 10°C (open triangles).
3.4 Comparison with Theory
An inhomogeneous internal in-plane strain
[ m7( z ) ] ,
arises from thermal stresses
resulting from cooling down from the annealing temperature. This strain can be
determined from the difference between the coefficients o f thermal expansion (CTE) o f
the BST layers and the substrate, such that u T(z) = [ a r (z) - ars,] ■A T , where apiz) and
as are the CTEs o f the layers and the substrate, respectively. A T is the difference between
annealing temperature (750°C) and room temperature (RT=25°C).
78
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Utilizing formalism described in Section 2.3, we were able to calculate the
electric field dependent tunability o f the BST multilayer heterostructure at different
temperatures as a function o f the biasing field. The dielectric stiffness coefficients, elastic
and electrostrictive moduli, and the CTEs o f the layers and the substrate were compiled
from available literature [89,163], These results are shown in Figure 3.9 and there is an
excellent agreement with the theoretical predictions and the experimental results. In the
calculations at -10°C, there is a small deviation between experimental and theoretical
results at fields >300 kV/cm which may be attributed to the ambiguity in the
thermodynamic parameters used in the model at low temperatures.
The experimental results together with theoretical calculations have significant
technological implications. M icrowave voltage-tunable phase shifter devices are expected
to be operated at variable ambient temperatures with excellent reliability and accuracy.
The m ultilayer BST heterostructure discussed in this study possesses excellent dielectric
properties and both tunability and dielectric loss are stable over a broad temperature
range. Combined with analytical theoretical tools to guide the design, such multilayers or
graded heterostructures may be utilized in the next generation temperature insensitive
tunable devices.
79
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60
40
20
90°C
0
60
£
60°C
• pN
p fi
40°C
C
S3
i—
>—
i—
|—
i—
i—
i—
|—
i—
i—
i—
|—
i—
i—
i—
■
i
i
i
i
i
i
i
i
i
i
i
i
i
i
|—
i—
i—
i—
j
H
-10°C
0
100
200
300
T 1 '
400
1 I
500
Electric field (kV/cm)
Figure 3.9 Tunability of the BST multilayer as a function of external electric field at different
temperatures (solid line: calculation results from theory; solid squares: experimental
measurements).
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3.5 PFM M easurement
Large piezoelectric strains can be expected from multilayer or graded FEs with
systematic variations in the polarization due to an internal electrostatic potential that
arises from the polarization gradient and the commensurate built-in strain field. Our
recent theoretical results on the piezoelectric response o f graded FEs [164] indicate that
these heterostructures may be as effective as RAINBOW ™ (Reduced and Internally
Biased Oxide Wafer) [165] and THUNDER ™ (Thin Unimorph Driver) ceramics. [166]
These are essentially bilayers consisting o f a piezoelectric ceramic bonded to a cermet or
a metal layer and the high displacement is the result o f a built-in non-linear stress field
due to the thermal expansion mismatch between the layers. However, unlike these
composites, there exists a built-in potential in polarization graded FEs, which may lead to
the development o f self-biased transducers. We observed a 50% improvement in the
piezoelectric response of m ultilayered BST films fabricated by M etal-Organic Solution
Deposition (MOSD) over homogeneous BST films when measured via Piezoresponse
Force Microscopy (PFM).
As a reference, a uniform single composition BST60/40 thin film with the same
thickness was also fabricated using the same MOSD technique, but only subjected to a
single post annealing.
The experimental setup for the PFM measurements included: (1) MFP-3D™
Stand Alone Atomic Force Microscope; (2) Conductive diamond coated tips with apex
radius o f 50-150nm and force constant o f 30-40N/m; (3) Agilent 33259A 80 MHz
Function W aveform Generator; (4) Stanford Research Systems, M odel 844 RF lock-in
amplifier. PFM is an atomic force microscopy (AFM) related technique, which has been
81
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routinely used to image and characterize piezoelectric thin films at the nanoscale level
[167].
The PFM technique employs a conducting AFM probe, which is in contact with
the surface to locally bias the sample. For piezoelectric materials, this causes detectable
surface displacements due to converse piezoactuation. In a typical experiment setup, the
piezoelectric thin film is m ounted or grown on a conducting substrate that is grounded
during the PFM measurement. A bias is applied to the tip from a signal generator, which
includes a periodic AC signal (V a c oscillating at frequency a>). W ith the AFM probe
acting as the top electrode and the conducting substrate as the back electrode, an AC
electric field is thereby applied across the piezoelectric film. Any resulting surface
displacements beneath the tip are then detected as deflections o f the integrated AFM
cantilever using a lock in amplifier. This transduction is achieved by reflecting a laser or
LED beam o ff the back o f the lever onto a position sensitive photodiode. The output
measured by the lock-in amplifier gives the piezoresponse in terms o f changes in
amplitude with respect to the applied AC field. The amplitude data is then plotted as a
function o f x-y position o f the topography image. At its simplest, the amplitude o f sample
vibration normal to the surface detected during PFM (zv,*raWo„) is proportional to the
piezoelectric coefficient and the applied bias, Vac , given by the equation:
Zvibration~ dZz- VAC
As a result, PFM provided piezoresponse data and images reveal the coupling
between the electromechanical responses o f the sample. In addition, electrostatic forces
acting between the probe and the sample as well as forces distributed along the cantilever
may also be detected [168], though these were minimized in the present measurement. In
82
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particular, earlier works have shown that PFM carried out at AC frequencies
corresponding to contact resonances o f the cantilever (l-2M H z) can result in higher
piezoactuation contrast and resolution, a strategy employed in this work [169-171].
PFM data were obtained for the multilayered and homogenous BST samples by
acquiring multiple 5 pm scan size images at a single location on each sample (256x256
pixels). For these images, the AC voltage applied to the tip was increased incrementally
from 1 to 10 V (peak to peak) in steps o f 0.5V, providing sets o f 19 images o f the same
region per sample. In order to make a meaningful comparison o f the piezoresponse
between the two samples, all measurements for both samples were made during a single
imaging session and PFM scanning conditions such as equipment offsets and sensitivity
as well as the frequency and voltages o f the AC field were kept the same throughout.
A subset o f the AFM images obtained during the measurements for the
homogenous and m ultilayered sample are shown in Figure 3.10 (a) and (b). The surface
topography images show that the homogenous and multilayered films have relatively
smooth surfaces with root mean square roughness values o f 5 and 3 nm, respectively. For
the homogenous sample, PFM amplitude images taken at each voltage step exhibit a
uniform contrast, with the average amplitude steadily increasing with each incremental
step as expected. This is illustrated in Figure 3.10 (a) for PFM images taken at 2V, 6V
and 10V. The overall intensity o f the images increases with bias showing the stronger
piezoresponse as the AC voltage increases. Histogram data obtained from each o f the
PFM images (insets) denote Gaussian distributions with single narrow peaks.
For the m ultilayered films, the PFM image at 2V shows uniform contrast with a
single peak Gaussian distribution, just as observed in the homogenous film. However, as
83
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the AC voltage is increased to intermediate voltages such as 6V, the PFM images begin
to exhibit areas o f two distinct contrast levels. These spatial inhomogeneities are
especially apparent in histogram data from the 6V PFM image (also inset), which
confirms the bimodal distribution o f regions with lower and higher piezoresponse. As the
voltage is increased beyond 7.5V, the piezoresponse becomes uniform again with a
narrowing, single peak, Gaussian distribution.
Topography
PFM Amplitude
Figure 3.10 (a) The AFM topography and PFM amplitude images taken at 2, 6 and 10V for the
homogenous BST film, (b) The same images obtained for the multilayer graded sample.
The average piezoresponse o f each PFM image obtained at distinct AC excitation
amplitudes is plotted for both the homogenous and multilayered samples in Figure 3.11.
For the homogenous sample, the piezoresponse increases linearly with increasing AC
voltage from 1 to 10V as anticipated. For the graded sample, at lower voltages (<2V) the
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piezoresponse is similar for both samples with no obvious enhancement o f the
piezoelectric strain in the multilayered sample. Both the m ultilayer and the homogeneous
film consist o f randomly oriented grains with randomly oriented polarization vectors.
However, in the multilayer heterostructure the magnitude o f the polarization vector
changes from one composition to the other. At small external fields, these random
polarization vectors start to align but the applied potential is not strong enough to pole the
grains. As the external voltage is increased, there is an enhancement in the piezoresponse
for the multilayered sample by as much as 50% compared to the homogenous sample.
While the gradual increase in the piezoelectricity in both samples may indicate a
reorientation o f the polarization vectors or just an increase in the com ponent o f the
polarization vector along the external electric field, we attribute the difference between
the two samples, i.e., the “hump” in Figure 3.11, to the local internal built-in field due to
the polarization gradient in the layered ferroelectric film [89]. This is a surprising finding
considering that the homogeneous BST60/40 should, on average, have a higher intrinsic
piezoelectric effect due to the close proximity o f the temperature o f measurement (25°C)
to the ferroelectric phase transformation at 5°C compared to the multilayer sample that
contains “harder” ferroelectric compositions BST75/25, and BST90/10. These results
suggest that the internal electrostatic and electromechanical potential due to the
systematic
polarization
variation
improves
piezoelectric
response
as
predicted
theoretically [164], At higher voltages (>5.5V), it is observed that the enhanced response
o f the multilayered sample diminishes and at voltages beyond 7.5V, the response o f the
multilayered sample is equivalent to the homogenous sample. This regression can be
explained by considering the induced polarization that depends on the dielectric response.
85
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The induced polarization at the “softer” end o f the m ultilayer ferroelectric (BST60/40) is
larger than the induced polarization at the BST90/10 end since the dielectric response o f
BST60/40 is larger than that o f BST90/10. As such, at high external fields, the
polarization gradient and the commensurate internal potential decrease, resulting in a
relatively smaller piezoresponse than for intermediate fields.
In summary, we have shown that m ultilayered FE films with a systematic
variation in the composition (and thus the polarization) have a higher piezoelectric
response compared to homogeneous samples for certain field magnitudes. This
enhancement is substantial (-50% ) even for polycrystalline thin films, despite the fact
that the microstructure is laterally inhomogeneous. This indicates that ultimately device
properties could be further improved for single-crystal, monodomain, epitaxially graded
heterostructures.
86
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35
s
3
30
25
c
#o
20
CS
=
O
15
C3
O
N 10
4>
• PM
D5
Multilayer Sample
Homogeneous Sample
o
0
2
6
4
8
10
AC voltage (V)
Figure 3.11 The calculated average piezoresponse of PFM images obtained at each voltage step
versus AC voltage for the multilayer and homogeneous sample. Error bars are too small to be
visualized: on average, the 95% confidence of the measurements is less than 3%.
87
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Chapter 4 Conclusion and Future Work
In conclusion, in this study, we developed a thermodynamic model to describe the
dielectric responses and tunabilities o f ferroelectric multilayered heterostructures for high
performance tunable microwave devices.
A comprehensive thermodynamic m odel was developed for describing the
interlayer coupling between ferroelectrics based on classic Landau theory, which takes
into account the theory o f elasticity and the principle o f electrostatics. Utilizing this
formalism, a simple bilayer was first studied. The polarization profile as a function o f
layer fraction reveals that the existence o f the relative critical fraction near which the
polarizations were suppressed due to the internal electric field resulting from the initial
interlayer polarization difference. Based on this finding, gigantic dielectric response and
tunability were predicted in the vicinity o f this relative critical fraction. These findings
offer us great technological implications. The dielectric constant o f a DE/FE/DE stack
can be optimized by tuning the relative layer fraction and the introduction o f DE layer
can largely reduce the device leakage current. A more general form o f this model was
then developed to analyze the ferroelectric multilayered heterostructures. The interface
effect was studied providing the result that in ultra thin heterostructure the interface effect
must be taken into account, and in thick enough film this effect can be neglected.
Based on these findings, multilayered BST samples were fabricated via industrial
standard MOSD method. At room temperature, the heterostructure has a small-signal
dielectric permittivity o f 360 with a dissipation factor o f 0.012 and a dielectric tunability
o f 65% at 444 kV/cm. These properties exhibited minimal dispersion as a function o f
temperature ranging from 90 to -10°C. These results are in good agreement with the
88
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calculation results based on our thermodynamic model. Furthermore, the piezoelectric
properties were m easured using Piezoresponse Force Microscopy. There is approximately
a 50% improvement in the piezoelectric response o f the multilayered heterostructure
compared to the homogeneous sample, with some spatial inhomogeneity. This
enhancement can be attributed to the internal potential that arises from the polarization
gradient and the commensurate built-in strain in the multilayer sample.
Possible future works related to current research are recommended as below:
1. Extend the model to polarization graded ferroelectrics to analyze the dielectric
tunability.
2. Investigate the effect o f the top and bottom electrodes on the dielectric properties
o f the heterostructures.
3. Study the doping effect on the dielectric properties o f the heterostructures.
4. Fabricate and integrate the ferroelectric heterostructure into devices.
89
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