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Deposition and properties of ferroelectric (lead,strontium) titanium trioxide thin films for room temperature tunable microwave devices

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Deposition and Properties of Ferroelectric
(Pb,Sr)Ti03 Thin Films for Room Temperature
Tunable Microwave Devices
A Dissertation
Presented to
the Faculty of the D epartm ent of Physics
University of Houston
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
By
Shiwei Liu
December 2004
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UMI Number: 3156023
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Deposition and Properties of Ferroelectric
(Pb,Sr)Ti03 Thin Films for Room Temperature
Tunable Microwave Devices
7
/ ' h O_____
u t J C'
~*y'
hiwei Liu
a ppro v :
Dr. Chonglm Chen
M.
Dr. Wei-Kan Chu
Dr. Wolfgang Donner
ri m
Dr. Lowell Wood
Dr. Han Lee
D frjohn Miller
A a
&n, College of N atural Sciences
and Mathematics
11
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ACKNOWLEDGEMENTS
I w ould like to express my deepest gratitude to my supervisor, Dr.
Chonglin Chen, for his support, patience and encouragement throughout my
graduate studies. Dr. Chen always spares his time to solve any little problems,
clarify m any confusing points and give me exciting insights in my academic
research.
My great thanks and appreciation go to all the members working or ever
working in our Oxide Thin Film Laboratory, Yuan Lin, Xin Chen, Jennifer
Weaver, Thinh Nguyen, and M ansour Abdulbaki. W ithout their considerable
help, this dissertation w ould not have been finished.
My very special thanks to Dr. Wolfgang Donner for his help in XRD, Mr.
H ang Dong Lee for his help in RBS, Dr. Jiechao Jiang for his help in TEM, and Dr.
A. Bhalla for his help in IDC measurements.
My thanks also go to the members of my committee, Dr. Wei-Kan Chu, Dr.
Wolfgang Donner, Dr. Pei-Herng Hor, Dr. Lowell Wood, Dr. H an Lee, and Dr.
John Miller for giving their time and expertise to better my work.
The friendship of Hongyi Chen is m uch appreciated for his editorial
advice. He read the complete m anuscript as well as the proofs.
iii
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Last, but not least, I w ould like to thank my wife, Lisha, for her
understanding and love during the past few years. Her support and
encouragement are in the end w hat m ade this dissertation possible. My parents
receive my deepest gratitude and love for their dedication . They have
consistently helped me keep perspective on w hat is the m ost im portant in life
and shown me how to deal w ith reality.
iv
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Deposition and Properties of Ferroelectric
(Pb,Sr)Ti03 Thin Films for Room Temperature
Tunable Microwave Devices
An Abstract of a Dissertation
Presented to
the Faculty of the Departm ent of Physics
University of Houston
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
By
Shiwei Liu
December 2004
v
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ABSTRACT
O ur research implements a new candidate (Pb/Sr)Ti03 (PSTO) for tunable
microwave applications at room tem perature. PSTO thin films are deposited on
different substrates such as LaAlOs (LAO), NdGa 0 3 (NGO), and MgO by laser
ablation deposition technique. Their structural properties are studied by X-ray
diffraction (XRD), Transmission Electron Microscopy (TEM), and Rutherford
Backscattering (RBS). The dielectric properties up to 20 GHz are m easured by
interdigital capacitor (IDC) technique. The results indicate that our PSTO films
are highly epitaxially grow th w ith excellent crystallinity. Large dielectric
constant, high tunability and low dielectric loss indicate that our PSTO films are
very promising for applications in room tem perature tunable microwave devices.
Strain effects on the dielectric properties of PSTO films are studied. We
observed
the
anisotropic
dielectric
properties
in PSTO thin
films
on
orthorhombic (110) NGO substrates, which are attributed to the anisotropic
mismatch strains.
We found that the structural and dielectric properties of PSTO films are
also dependent on the post-annealing methods. Their effects are strongly related
to the strains induced by the different cooling processes.
vi
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CONTENTS
1. Introduction
1
1.1
Historical Background and Motivation
1
1.2
Thesis scope and objectives
5
1.3
Thesis outline
6
2. Ferroelectricity: Basic Properties, Definition and Applications
8
2.1
Ferroelectricity and perovskite materials
2.2
Dielectric properties of ferroelectric materials
17
2.3
Applications of ferroelectric films
27
2.3.1 Summary of applications of ferroelectric thin films
27
2.3.2 Ferroelectric tunable m icrowave devices
29
Materials' requirements for tunable microwave devices
31
2.4
2.5 Overview of the PbxSri-xTi0 3 and BaxSn-xTi0 3 systems
3. Epitaxial Grow th of Thin Films by Pulsed Laser Deposition Technique
8
34
39
3.1
Overview of pulsed laser deposition technique
39
3.2
Grow th mechanism of thin films by laser pulsed deposition
44
3.2.1 General description of nucleation and growth of thin film
44
3.2.2 Growth mechanism of thin films by PLD
50
3.3
Optimal grow th conditions for thin film epitaxy
52
3.4
Deposition of PSTO films using PLD technique
58
vii
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4. Characterization of Ferroelectric (Pb,Sr)Ti0 3 Thin Films
4.1
X-ray diffraction (XRD)
4.1.1 XRD studies on the
4.2
63
63
PSTO film on LaAlOg (001) substrate
64
4.1.2 XRD studies on the PSTO film on NdGaOs (110) substrate
69
4.1.3 XRD studies on the
72
PSTO film on MgO (001) substrate
Transmission electron microscopy (TEM)
74
4.2.1 Cross-sectional TEM studies on the PSTO film on LaAlOs (001)
substrate
74
4.2.2 Cross-sectional TEM studies on the PSTO film on NdGa 0 3 (110)
substrate
77
4.3
Rutherford backscattering spectroscopy (RBS)
4.4
Dielectric property m easurements by interdigital capacitor (IDC)
technique
80
82
4.4.1 IDC measurements on the PSTO film on LaAlOs (001) substrate at 1
MHz
84
4.4.2 IDC m easurem ents on the PSTO film on NdGaOs (110) substrate at
1 MHz
85
4.4.3 IDC measurements on the PSTO film on MgO (001) substrate up to
20 GHz
5.
87
Strain effects on the dielectric properties of PSTO thin films
5.1
90
Anisotropic in-plane strain and dielectric properties in PSTO thin films
on the orthorhombic NGO substrates
90
5.2 Effects of post-annealing m ethods on the structural and dielectric
properties PSTO thin films
95
6. Discussion, O pen Questions, and Prospective
viii
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100
7. References
104
ix
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Chapter 1
Introduction
1.1 Historical background and m otivation
Ferroelectric materials have been studied for more than eighty years since
Valasek, a French researcher, discovered that the polarization of Rochelle salt
(NaKC4H406.4H20, sodium potassium tartate tetrahydrate) could be reversed by
the application of an external field in 1920. Flowever, it was not until 1945 that
the first ferroelectric perovskite BaTiCb was reported by Wul and Goldman. The
interest in ferroelectricity was renewed and then some im portant theoretical and
experimental progresses at the atomic level were made due to the simplicity of
the perovskite lattice structure1'2. The discovery of the ferroelectricity in BaTiCb
clued the scientists to expend considerable effort on a search for more
ferroelectrics w ith the same perovskite structure. Some new materials of KNbCb3,
LiNbCb4, PbTiCh5, (Ba,Sr)Ti0 3 , and (Pb,Sr)Ti0 3 etc. have been found to exhibit
similar ferroelectricity. To date, ferroelectric materials have been chosen for a
broad range of the electronic applications from simple capacitors to complicated
microwave devices as well as mechanic and therm al applications from
1
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piezoelectric transducers to IR radiation detectors due to their piezoelectric and
pyroelectric properties.
In m any applications of microwave electronics, it is often necessary to
tune instantly the electrical behaviors of certain parts of the circuitry. Currently,
such tuning is predom inantly achieved by mechanical m eans such as tuning
screws, tuning plungers, sliding conductors, sliding walls, etc. Bulk ferrite
materials have also been employed for magnetically tunable microwave devices
whose electrical response can be tuned by applying a dc magnetic field.
However, the applications of such tunable devices incorporating ferrites are so
far still limited due to their high unit cost, complexity, large size, high insertion
loss, and low tuning speed8. O n the other hand, ferroelectric materials exhibit the
field-dependent dielectric constants in radio and microwave frequency range,
which suggest their potential applications in the tunable microwave devices such
as phase shifter6, oscillators7, microwave filter8, and harmonic generator, etc.
These ferroelectric devices are fast, small, lightweight, and are easy to be
integrated. Studies on these ferroelectric applications can be traced back to the
early 1960s9'10. The research was discontinued because it is difficult to fabricate
high quality ferroelectric film on metal bottom electrode. It is in the 1990s that
the applications began to emerge due to the crystalline compatibility of
ferroelectric film w ith high-tem perature superconductor bottom electrode.
Moreover, the ferroelectric films are also deposited on perovskite insulator w ith
2
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the coplanar configuration to avoid the difficulty of the bottom electrode. The
key components of these devices usually include a layer of high quality
ferroelectric film deposited on oxide substrates. Figure 1.1 shows the principle of
a simple coplanar waveguide (CPW) phase shifter. A layer of ferroelectric thin
film is deposited on the LaAlC>3 substrate. After that, three coplanar electrodes
are fabricated on the top of the film. A bias voltage Vb is applied between the
m iddle electrode and side electrodes to tune the field-dependent dielectric
constant s(Vb) of the ferroelectric film. The phase shift of the output signal
relative to the input signal,
=
2 7t
K
s(Vb)L where X0 and L are the wavelength
and the device's length respectively, can thus be changed substantially by
adjusting the bias voltage.
Electrodes
Ferroelectric
Film
Figure 1.1 scheme of coplanar waveguide (CPW) phase shifter
3
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The field-dependent dielectric properties of some ferroelectric materials
have
been
studied
experimentally
and
theoretically
by
many
researchers11-12'13'14'15'16'17'18'19'20'21'22. By far m ost research efforts were focused on
the ferroelectric (Ba/Sr)Ti03 (BSTO) systems16'23'17'18'19'20'21'22. Remarkable progress
has been achieved in highly epitaxial grow th of ferroelectric BSTO thin films
w ith high dielectric constant, low dielectric loss, large dielectric tunability, and
small leakage current. Various room tem perature tunable microwave devices,
such as microwave phase shifters, have been developed from the highly epitaxial
BSTO thin films. However, the relatively high dielectric insertion loss,
multiphase interaction, and high frequency soften mode have prevented the
practical applications of the ferroelectric thin films in high frequency tunable
wireless communication although m any efforts were made in the past few years
in order to improve the dielectric properties. New materials are necessary to
enhance the dielectric properties. Recent research24'25 revealed that ferroelectric
(Pb,Sr)Ti0 3 (PSTO) ceramics have extremely high dielectric tunability of 70%
under 20 kV /cm at 10 kHz and room tem perature w ith very low dielectric loss
value of 0.001. These excellent dielectric properties suggest that PSTO could have
super-passing properties to ferroelectric BSTO for developing high frequency
ro o m tem perature m icro w a v e elem en ts. In ad d ition , u n lik e th e ferroelectric
BSTO which possesses three phase transitions, PSTO only has one phase
4
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transition from cubic to tetragonal. This can reduce microphase or precipitation
during film growth.
Synthesis of PSTO thin films by sol gel26-27 and RF-sputtering28 techniques
has recently been attem pted to explore the advantages of this material. The
results indicate that the PSTO thin films have very large dielectric tunability but
w ith m uch higher applied bias field and larger dielectric loss value than its bulk
material, probably due to its nonstoichiometry and grow th defects. To fully
understand the physical properties of PSTO thin films and to explore their
advantages for applications in high frequency tunable microwave elements,
highly epitaxial PSTO films w ith excellent crystalline quality is necessary. It is
expected that Pulsed Laser Deposition (PLD) technique is very promising to
achieve high quality PSTO films because of its inherent advantage to deposit
multi-component oxide. O ur research is m otivated by these considerations.
1.2 Thesis scope and objectives
As the title of this thesis indicates, the purpose of our research is to
implement a new candidate (Pb,Sr)Ti0 3
(PSTO) for tunable microwave
ap p lication s at th e room tem perature. PSTO th in film s are d ep o sited o n different
substrates such as LaAlOs (LAO), NdGaOs (NGO), and MgO by laser ablation
deposition technique. Their structural properties are studied by X-ray diffraction
5
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(XRD), Transmission Electron Microscopy (TEM), and Rutherford Backscattering
(RBS). The dielectric properties up to 20 GHz are m easured by interdigital
capacitor (IDC) technique. The results indicate that our PSTO films are highly
epitaxially growth w ith excellent crystallinity. Large dielectric constant, high
tunability and low dielectric loss indicate that our PSTO films are very promising
for applications in room tem perature tunable microwave devices.
Strain effects on the dielectric properties of PSTO films are studied. We
observed
the
anisotropic
dielectric
properties
in PSTO thin films on
orthorhombic (110) NGO substrates, which are attributed to the anisotropic
mismatch strains.
We found that the structural and dielectric properties of PSTO films are
also dependent on the post-annealing methods. Their effects are strongly related
to the strains induced by the different cooling processes.
1.3 Thesis outline
The thesis is presented in six chapters. Following this brief introduction of
Chapter 1, Chapter 2 reviews the basic properties and definition of ferroelectric
materials and their extensive applications in DRAM, nonvolatile memory, and
especially in microwave devices etc. In Chapter 3 and Chapter 4, we deal with
the epitaxial grow th of (Pb,Sr)TiC>3 thin films and their structural and dielectric
6
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characterization by X-ray, TEM, RBS and IDC techniques. In Chapter 5, some
interesting strain effects on the dielectric properties of (Pb,Sr)Ti0 3 thin films are
studied. Finally, conclusions are m ade and open problems and prospective are
discussed in Chapter 6.
7
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Chapter 2
Ferroelectricity: Basic Properties, Definition
and Applications
2.1 Ferroelectricity and perovskite materials
Ferroelectricity is defined as a unity of spontaneous polarization and
polarization reversal. As the atomic configuration in materials is a function of
tem perature the polarization status is also dependent on tem perature, which is
defined as pyroelectricity. Pyroelectricity is inherent in all ferroelectric crystals.
As to ferrelectricity, pyroelectricity is only a necessary condition. Ferroelectric
crystal has the additional property that the spontaneous polarization can exhibit
two or more than two possible orientations and be reoriented by applying a
sufficiently large electrical field. That is, ferroelectricity is only a subset of
pyroelectricity29.
In general, ferroelectric materials do not show single dom ain structure
where the whole crystal exhibits the same spontaneous polarization direction.
The ferroelectric crystal will divide itself into m any small volumes (called
8
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domains) w ith different polarization direction because of the inevitable crystal
surface, inhomogeneity and mechanic confinement. The boundaries separating
domains are referred to as dom ain walls. This m ulti-domain structure has a
lower energy state than a single dom ain structure. Ferroelectric polarization can
vary as the external electric field changes. This response process is schemed as
"Hysteresis Loop" in Figure 2.1(a). Initially poling (shown as a dotted line) is
achieved by applying an electric field. As the electric field increases, the domains
favorably oriented w ith respect to the field direction at the expense of other
domains. For sufficiently large positive fields (point A), all dipoles are aligned
along the electrical field and the material acts as a single domain. Beyond point A
the polarization is approximately linear to the electrical field. The huge electrical
field induces ionic displacement which stretches the unit cell in a reversible and
approximately linear manner. If this linear response is extrapolated to
polarization axis at E=0, the polarization value at the intersection is designated as
the saturation polarization Psat. W hen the electric field approaches back to zero at
point B, the material exhibits a positive remanence polarization Pr. As mentioned
above, the boundary conditions and inhomogeneity may nucleate new reverse
domains. The resulting polarization Pr at E=0 is a little smaller than Psat. Near
point B the relationship between the electrical field and polarization comes back
to linearity. The dom inant mechanism is attributed to the electronic and ionic
polarizations and the reversible m ovem ent of dom ain walls (such as dom ain wall
9
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bending30). As the electrical field is reversed through negative coercive field -Ec,
the polarization begins to switch quickly. Motion of dom ain walls will be
irreversible. This process is often accompanied by a series of steps: nucleation of
new domains, longitudinal growth, transverse expansion and consolidation of
domains31. For sufficiently large negative fields at point C, all dipoles have been
switched and reoriented w ith the same direction of external field again. When
the field is back to zero, the material shows a negative remanence polarization
(point D). The situation at this point is similar to point B. W hen the electric field
is beyond the positive coercive field Ec, a rapid transition w ith 180° domain
switching happens. The polarization state returns to point A. Various
approaches, for instance equivalent-circuit modeling32'33'34'35'36-37'38'39'40'41'42 and
Monte Carto calculations43 and Preisach Models44'45'46, have been proposed to
simulate the hysteresis features of the ferroelectric materials. The interested
reader m ay refer to the related papers.
Crystal ferroelectricity exists only in a tem perature range. As the
tem perature
increases
beyond
a
characteristic
value,
the
spontaneous
polarization disappears and the ferroelectric materials come into paraelectric
state. The transition between the ferroelectric phase and the paraelectric phase is
n am ed as ferroelectric p h a se transition an d the transition tem perature is referred
to as Curie tem perature Tc. As shown in Figure 2.1(b), the dielectric response is
highly nonlinear as the tem perature increases just above Tc. The static dielectric
10
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constant 8 = dP / dE strongly depends on the bias field (E) as indicated in the
inset of Figure 2.1(b). This nonlinear dielectric property is w hat we will
concentrate on in this dissertation. Well above TC/ the polarization responds to
the electric field approximately linearly with a lower slope (Figure 2.1(c)).
Although the dielectric constant decreases very much in this tem perature range
it is still m uch larger than that of the SiC>2 layer in CMOS. Therefore, ferroelectric
material is also a very prom ising candidate to replace the conventional Si0 2 as
will be discussed in section 2.3.1.
Perrovskites from the mineral perovskite CaTi0 3 are the most important
group of the ferroelectric materials w ith general chemistry formula ABO3 . The
formal valence state of AB is A2+B4+ or A1+B5+. Barium titanate (BaTiCh) and lead
titanate (PbTiCb) are two im portant ferroelectric representatives of this group.
Above Tc both materials are cubic as shown in figure 2.2(a) and 2.3(a). The small
B atom occupies the position of body center w ith 6-fold face-centered oxygen
coordination, which forms an oxygen octahedron. The large sized A ions are
located at the eight cubic corners w ith 12-fold oxygen coordination. Both
materials exhibit structure phase transition from cubic to tetragonal at Tc about
130°C and 490°C, respectively. As illustrated in 2.3 (b), below Tc it is energetically
favorable for the O2' ions to be displaced slightly below face centers and for the
Ti4+ ion to be displaced upw ard from the unit cell center besides the corner
cations are stretched into a tetragonal lattice. The relative change in position of
11
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cations (Ti4+, Pb2+, Ba2+) and anion (O2-) produces a spontaneous polarization,
which is the microscopic origin of hysteresis for single-domain perovskite
materials. As schemed in Figure 2.2 (c) and (d) BaTiCh exhibits two further phase
transition from tetragonal to orthorhombic at the tem perature around 0°C and
from orthorhombic to rhom bohedral at the tem perature around -90°C. Their
spontaneous polarizations are along [110] and [111], respectively.
On the other hand, pure SrTiOs (STO) is paraelectric for all temperatures.
STO thin films often exhibit a ferroelectric phase transition a little above 0 K
(Figure 2.4 (c)), probably because of the impurities and inhomogeneity in the
films47. STO undergoes a structural transition from the cubic phase to an unpolar
aniferrodistortive phase involving the tilting of the oxygen octahedral around
105 K (Figure 2.4 (b)). From 105K dow n to about 50K, the tem perature
dependence of the static dielectric constant is Curie-Weiss-like w ith an
extrapolated transition tem perature of about 36 K48. However, this supposed
ferroelectric
phase
transition
is
suppressed
by
the
large
quantum
fluctuation49'50'51'52'53'54. In fact, STO is the so-called incipient ferroelectrics. A
quantum paraelectric transition, where the dielectric constant tends to saturate
dow n to 0 K, occurs around 4 K49.
12
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sat
CL
c
o
CO
N
*L_
ro
o
CL
-Pr,
-P sa .
Field (E)
(a)
CL
c
o
C
O
N
Field (E)
(b)
CL
co
to
N
Field (E)
(C)
Figure 2.1 Static dielectric responses of ferroelectric materials, (a) Typical
hysteresis loop below Tc (b) Nonlinear dielectric response just above Tc (c)
Approximately linear dielectric response well above Tc
13
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130°
PT
a X®
I
11 .
11 Q c
11
x~
fy
o°
\ ®
-so**
/ X X
Lr
x
x
Cubic
Tetragonal
Orthorhombrc
(a)
(b)
(C)
Rhombohectral
Figure 2.2 Structural phase transitions of BaTiCh [55]
xl x
>—
0 — ----
Pb
-t*
q
Pb
5
U
o r -J Ti
490°
"O n
O-
0
LX
£^
Cubic
if ———
o
o
6
Tetragonal
(a)
(b)
Figure 2.3 Ferroelectric phase transition of PbTiOs [55]
m
H§Sr
O
Sr
,kTi .
OK
105 K
45
Q
o-
k *
Cubic
(a)
0
Tetragonal
(b)
o
if—
Tetragonal
(c)
Figure 2.4 Structural phase transitions of SrTiCh
14
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Sr
The displacive ferroelectric transition occurs as a result of a delicate
balance between the long-range Coulomb interaction and short-range repulsive
restoring force (from the overlapping of electron cloud). The Coulomb force
favors the ferroelectric state, whereas the short-range repulsion favors the
nonpolar cubic structure. The relative strength of these interactions is directly
related to bonding nature, ionic charges, and atomic distance or lattice constant.
A variety of ferroelectric behaviors among the ferroelectric perovskites may be at
least partially understood in the atomic level by considering these effects. They
are also im portant for us to understand w hy similar perovskites display very
different ferroelectricity. For example, theoretical and experimental results show
that Pb-O bonding in PbTiCb is more hybridized than Ba-O bonding56'57'58'59. The
Pb-O bonding nature of cubic phase is ionic, whereas that of the tetragonal phase
is covalent. Ba-O bonding in both cubic and tetragonal BaTi0 3 is ionic. The Ti 3d
states are always strongly hybridized w ith O 2p states in both materials. These
results are easily understandable because Ba has lower ionization potentials and
larger electronegativities than those of Pb and Ti (Table 2.1). Since the sensitivity
of the ferroelectricity to microscopic composition, the ferroelectric characteristics
of the perovskites can be tailored substantially by substituting the A or B cations
w ith other elements as discussed in section 2.5.
15
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Table 2.1 Electron configuration (E.C.), electronegativity (EN), ionization
potential (I+) and ionic radius (n) of some elements
I+
EN
Elements
E.C.
Ti
C.N.
(Pauling Scale)60
(kj/m ol)61
(Angstrom)60
502.9 (1st)
Ba
6s2
0.89
12
Ba2+ 1.61
12
Pb2+ 1.49
12
Sr2+ 1.44
965.2 (2nd)
715.6 (1st)
1450.5 (2nd)
Pb
6s26p2
2.33
3081.5 (3rd)
4083 (4th)
549.5 (1st)
Sr
5s2
0.95
1064.5 (2nd)
658.8 (1st)
Ti4+ 0.605
1309.8 (2nd)
Ti
3d24s2
1.54
6
Ti3+ 0.670
2652.5 (3rd)
Ti2+ 0.86
4174.6 (4th)
1313.9 (1st)
3388.3 (2nd)
O
2s22p4
3.44
6
O2- 1.40
5300.5 (3rd)
7469.2 (4th)
The order-disorder ferroelectricity stems from the therm al tunneling
among the potential wells of the localized charges such as protons. These charges
will prefer to occupy part of the potential wells in the ferroelectric state. For a
long time, the ferroelectricity of BaTiCb and PbTiCh has been regarded as only
displacive type. However, the more detailed studies reveal that both materials
show the characteristics of the order-disorder type. The high resolution
16
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structural information of BaTiOs shows that above Tc Ti4+ ions distribute
random ly at the eight mechanical equilibrium sites a little bit far away from body
center along {111} directions whereas below Tc they prefer to occupy four of the
eight sites besides static displacement is induced along [OOl]62'63'64-65. PbTiCb is in
the same situation, where Ti4+ ions distribute random ly at the six equilibrium
sites along {100} above Tc and in the ferroelectric state they prefer one of the six
sites66-67'68.
2.2 Dielectric response of ferroelectrics
Based on the fundam ental Maxwell Equations in electrodynamics, the
electric displacement D is defined as:
D = £0E + P
(2.1)
Dielectric response of the materials is defined by:
D = £(E,co) E=£r(E,®)£oE=k(E,a))£oE= (l+x(E,a)))£oE
(2.2)
In general, the dielectric perm ittivity is a complex number:
(2.3)
£ r= S r '- j S r "
Some im portant param eters are defined for the tunable microwave
capacitor.
17
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Loss tangent:
£
tan 8 = ^ r
(2.4)
Tunability for a tunable capacitor:
T(Vb) =
Cmax(bias = ° ) ~ C m,„(bias = Vb)
c ™Abias = Q)
(2.5)
e{bias = 0) - e{bias = Vb)
s{bias = 0)
Figure of Merit for a tunable capacitor:
FOM =
(2.6)
tan 8
Obviously, the low dielectric loss and high tunablity are desired for higher
FOM. However, as discussed in section 2.4, the high tunability almost always
conflicts w ith low loss tangent so that a tradeoff needs to be considered.
Two types of im portant dielectric systems are referred to describe the
frequency and tem perature dependences of the dielectric permittivity. One is
"rotatable dipole system (Debye Relaxational Model)" (Figure 2.5(a)); the other is
"dam ped harmonic oscillator system" (Figure 2.5(b)). Both models can be
incorporated into a general dielectric relaxation theory in which any dielectric
system can be described by its characteristic decay function. Following this
theory, the "rotatable dipole system" is characterized by the exponent decay
function
S (0) - £ (oo)
a{t) = —---------------- exp(—t / z )
T
whereas
the
dam ped
18
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harmonic
oscillator
system
Y
is
a(t) = coQexp(-“ Ocos(^]0
characterized
by
the
decay
function
*
Many dielectric systems also exhibit complex relaxation behavior which
cannot be described by either a simple exponent function or a dam ped oscillation
function as the decay function. In fact, m ost dielectric systems exhibit several
discrete values or a continuous distribution of Debye relaxation time. In addition,
in the case of the extremely damping, the decay behavior of both Debye
relaxation model and dam ped oscillator model become identical and it is
therefore not easy to determine w hether a system is basically relaxational or
oscillatory69. Table 2.2 sum m arized the principal sources that contribute to the
dielectric perm ittivity of the ferroelectric materials. It is difficult to exactly model
the dielectric properties because of the various dielectric contributions.
Fortunately, for the microwave dielectric behavior of the high-quality
ferroelectric film in the paraelectric state just above Curie tem perature, many
sources may be ignored such as dom ain wall dynamic movement, second phase
inclusion, grain effects, etc. We consider only the ideal crystalline film in the
following analysis. To the objective of this thesis we give some theoretical
models that take the bias effect into consideration for the application in tunable
microwave devices.
19
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E
E
AAAAAAAAAAAAAA
AAAAAAAAAAAAAA
i
4
\\t
i i
I
I I I
»
ii
Sf
i
i
IS
tI \' \'i
II
t I
ii i i
i i i
i i i
Rotatable dipoles under
polarization field
A. V
/ V/ /
Harmonic oscillators under
polarization field
©S’®®®
•**
©® ®®®
\ f ?
4 f
\ i
\ i
? i >*
@ 9
Randomly orientational
dipoles after field is removed
®
9
®
Thermally vibrating oscillators
after field is removed
P olarization
HDecay Function for
Debye relaxation
c
o
ro
N
Decay Function for
Damped oscillators
ro
o
CL
t
(a)
(b)
Figure 2.5 Two typical dielectric response models: (a) rotatable dipoles (b)
dam ped harmonic oscillators
20
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Table 2.2 various dielectric sources for ferroelectric materials
Source
Distortion of electronic cloud
Ionic displacement
Physical m odel
Damped harmonic
oscillator
Damped harmonic
oscillator
Characteristic Frequency
optical frequency
infrared frequency
^ <7
"
CO<
(£ r =
£0
CT
)
Conducting charges
Ohm law
Cooperative dipole interaction
in dipole glass
Debye relaxation
model
RF and Microwave range
Localized charge m ovem ent in
order-disorder ferroelectrics
Debye relaxation
Model
RF and Microwave range
Dipole switching in a
ferroelectric domain
Hysteresis theory
Static
Domain w all translation
Hysteresis theory
Static
Domain w all dynamic
m ovement
Complex relaxation
model
Debye relaxation
model
Equivalent barrier
layer model
RF and Microwave range
Mixture rule
—
Debye relaxation
model
—
Equivalent capacitor
—
Microdomain in DDF
Intergranular space charge
Second phase inclusions in
ceramics matrix
Interfacial Space charge
between electrode and
ceramics
Nonbonding contact capacitor
between electrode and
ceramics
£ q(0
RF and Microwave range
—
21
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Chang20, Canedy21, Li22, et al. presented a phenomenological theory based
on Devonshire70'71'72 free energy of bulk BaTiCb to analyze the dielectric
behaviors of (Ba,Sr)TiC>3 . This theory incorporated both effects of bias and
substrate clamping. Following Devonshire, Chang20 et al. expand the Gibbs free
energy of the active ferroelectric film in the interdigital capacitor w ith coplanar
electrodes as:
where a x, a 2, y and S are the free energy expansion coefficients; x }and X } are
strains and stress respectively; P is in-plane polarizations; c- is the elastic
constant and
Gtj=cikQkj is the stress-polarization-related electrostriction
coefficients (Qy is the strain-polarization-related electrostriction coefficients), a,
is strongly dependent on the tem perature and can be w ritten as:
a . =<*o(T-T0)
(2 .8)
where a 0 is a positive constant and T0 is the stress-free Curie-Weiss tem perature
that is the same as Curie tem perature Tc in the second order phase transition and
a little bit smaller than Tc in the first order phase transition.
T =T
(Second order)
22
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(2.9)
3a2
T = T 0 -\-------—
(First order)
(2.10)
16 a 0r
All macroscopic quantities can be extracted from Gibbs free energy with
the help of thermodynamic equations. The in-plane dielectric constant of a
ferroelectric film in the paraelectric state can be written as22:
M . . ± . cc
a ++3 £- ^ «E 2
dP £u
a
(2.11)
where
a = a l - 2 c x l(Qn +Qu )
= <x0( T - T ' )
T , =T^ + l c x x{Qn +Qn )
a0
(213)
c =cn +cl2 - 2 — ,
cn
(2.14)
P - a 2+4A(Cj, Qy),
(2.15)
Mcj,Q9) = h c xx{Q^ + Qt2)~ — (Qu +Qt2)2+2cI2QnQl2],
2
c,
(2.16)
x, =
a A f ) ~ ao(f)
(2.17)
«„(/)
The zero-bias dielectric constant and tunability are written as:
, (bias = 0) = —
(2.18)
a
23
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(2.19)
Some im portant strain effects can be extracted from the equations above.
The film's Curie tem perature, zero-bias dielectric constant and tunability will
decrease under the compressive in-plane strain ( x, < 0) while they will increase
under the tensile in-plane strain (x, > 0 ) . Also, both of zero-bias dielectric
constant and tunability achieve the maximal values at Curie tem perature. Since
this phenomenological model is based on thermodynamic equilibrium, it should
hold only at static or low frequency. In addition, the dielectric loss is unavailable
in this model.
Bendik11'12'13'14 proposed a dynamic theory of a soft ferroelectric mode. The
out-of-plane dielectric constant of the active ferroelectric film in the sandwich
capacitor is obtained as a function of the bias field E and the tem perature T.
( 2 .20)
( 2 .21 )
(2 .22)
24
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where EN is the normalized field, 0F is the transition tem perature and T0 is
Debye tem perature. If the denominator of equation (2.14) is expanded in series
for £ « ij , we obtain:
s(E,T) = -------^ ----------------------------------
(
This model takes the ferroelectric vibration mode into consideration so it
is applicable to the higher frequency range (106~101:lHz). However, for the orderdisorder ferroelectric materials, or the displacive ferroelectric materials at lower
frequency and even high frequency near Curie tem perature, where the oscillator
is highly dam ped, the dielectric response is similar to Debye Model. The
dielectric spectra are derived as:
i , ' w ^ . W * e,.( 0)' <,,. t ° >
1+ (cor)
(2-24)
C w = £f )),~ e'.(i°0)«»1+ (cor)
(2.25)
The bias field will change the relaxation time. Because the relaxation
mechanism is usually complicated we phenomenologically expand the relaxation
time in series of the bias field.
r = r0 +a£2 +bE4 +...
(2.26)
Substituting equation (2.26) into equation (2.25) and equation (2.24), we
obtain:
25
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All of equation (2.27), equation (2.23) and equation (2.11) indicate that the
bias field dependence of the dielectric constant may be fitted by Lorentz function
without considering the detailed microscopic mechanisms.
26
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2.3 Applications of ferroelectric film s
2.3.1. Summary of applications of ferroelectric thin film s
DRAM
Multilayer C apacitor
AccousticOptic effect
Bectro-Optic'
effect
piezoelectricity
nonlinear
microwave
dielectric /
constant/
F erro electric
Film
bistable
polarization
pyroelectricity
Figure 2.6 Applications of ferroelectric materials
The ferroelectric materials exhibit extensive functional properties in
electrical, mechanical, and thermal areas. Their applications came out even
before the concept of the ferroelectricity was developed. We summarize their
major applications that are show n in Figure 2.6. These applications are
categorized into seven sections.
27
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•
Ferroelectric materials have m uch larger dielectric constants than those
of SiC>2 so that ferroelectric thin films are very promising to replace silicon
dioxide layers of CMOS unit in electronic device such as DRAM as well as act as
the insulator layers in compact m ultilayer capacitors. A recent breakthrough73
provides a guide for fabricating an atomically abrupt crystalline interface
between strontium titanate and silicon, which is the key issue for the applications
in this area.
•
The bistable polarizations in ferroelectric hysterisis loop give us a
possibility to fabricate nonvolatile ferroelectric memory.
•
Piezoelectric and converse piezoelectric properties of the ferroelectric
materials have wide applications in transducers for converting the electrical
signal to mechanical response and vice versa.
•
Temperature sensitivity of electrical polarization (pyroelectric effect) is
employed to detect the infra red radiation.
•
Refractive index along some crystalline direction can be tuned by
applying a bias electrical field (electro-optic effect). The status of light passing
through the ferroelectric film, such as polarization and phase etc., can be
changed by a proper optical beam configuration. This property can be applied to
optical switch and m odulator, etc.
•
The coupling between the optical wave and acoustic wave in the
ferroelectric film is applied to A-O Bragg deflector.
28
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•
The dielectric constant in microwave range strongly depends on the
applied bias. This property can be applied to microwave devices such as filters
and resonator. Actually this effect is an analogue of the electro-optic effect
extended to the microwave frequency range. We will focus on these applications
in the next section.
2.3.2. Ferroelectric tunable m icrowave devices
Examples of the applications in this area include the field-dependent
capacitors, tunable microwave resonator and oscillator, microwave phase shifter,
frequency-agile filters, and variable-power dividers, etc. Some devices are
discussed in detail.
•
Microwave phase shifter
A phase shifter is a device that can provide a tunable phase relationship
between the input signal and output signal w ith low insertion loss. A num ber of
devices have been dem onstrated based on various ferroelectric thin films. For
example, F. W. Van Keuls et al.6 reported that a relative insertion phase shift of
390° was achieved for an eight-element YBCO/STO/LAO CMPS (coupled
m icrostrip lin e p h a se shifter) at Vdc=360 V, 16G H z an d 40 K. R ecently room
tem perature microwave phase shifters have also been dem onstrated from several
groups, such as a 280° phase shift w ith a figure of merit of 43°/ dB and a 250°
29
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phase shifter w ith a figure of m erit of 53°/ dB based on (Ba,Sr)Ti0 3 ferroelectric
thin films.
•
Microwave filters
A microwave filter is a circuit channel which transmits the desired signal
frequency w ith the m inim um attenuation as possible while by which the
undesired frequencies are stopped or substantially suppressed. Filters usually
consist of both lum ped circuit elements (inductor and capacitor) and distributed
elements (microstrip and waveguide). A. T. Findikoglu, Q. X. Jia, et al.8 prepared
a 3-pole half-wave bandpass CPW (coplanar waveguide) filter incorporating
YBCO/STO layers on LAO substrate. The tunability is about 15% change in
center frequency w ith an applied voltage of 125 V.
•
Tunable Microwave oscillators
A microwave dielectric oscillator is a circuit that serves as a frequencylocked local high Q resonance cavity to clean up the broadband phase noise in a
communication channel conveying digital data with phase m odulation on a
carrier signal. The resonance cavity usually consists of a high dielectric constant
ceramics, either in bulk or thin film, for confining the electromagnetic fields to
the dielectric region and its immediate vicinity by reflection at the dielectric-air
interface. Recently, a discriminator-stabilized superconductive/ferroelectric
oscillator developed by the NASA Glenn Research Center exhibits the great
30
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improvements w ith electrical tuning, electronic frequency locking, and a
concomitant reduction in phase noise7.
2.4 Materials' requirem ents for tunable microwave devices
Currently, the major issue for tunable microwave devices is to improve
the dielectric properties of the active ferroelectric films. To achieve a good
performance of the microwave devices, high dielectric constant, low dielectric
loss, high dielectric tunabilities, low leakage current, and low tem perature
coefficient of the dielectric constant are required. However, these requirements
almost always conflict w ith each other. For example, the fabrication conditions
which tend to reduce dielectric loss also tend to reduce the dielectric constant
and tunability. Therefore, a tradeoff among these dielectric properties exists for
special applications.
•
High dielectric constant
Higher dielectric constant may reduce the physical size of the microwave
devices. The larger the dielectric constants of the active ferroelectric materials are,
the smaller the microwave elements are. The dielectric constant of the
ferroelectric m aterial ach iev es th e m axim al v a lu e at the p h a se transition p o in t so
that Curie tem perature of the ferroelectric film should be near the working
tem perature of devices.
31
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•
High tunabilities
The higher dielectric tunability increases the phase shift under a constant
bias field. The higher tunability is, the lower bias voltage is required. As
explained in section 2.2, the tunability is maximized at the phase transition point.
Therefore, it also favors the higher tunability w hen Curie tem perature of the
ferroelectric film is near the working tem perature of devices.
•
Low dielectric loss
A low dielectric loss tangent (0.01 or less) is very desirable to decrease the
insertion loss and hence increase the phase shifting per decibel of loss. Also, the
low dielectric loss is beneficial to expand the operating frequency of the
microwave device. Furthermore, the low dielectric loss may reduce the heat
generated by the devices and thus improve the reliability of the microwave
devices. Since the dielectric loss is usually large below Curie tem perature due to
the formation of the ferroelectric domains and inhomogeneity, the active film
should be in its paraelectric state just above Curie temperature.
•
Small DC leakage current and higher breakdow n field
The leakage current is detrimental to the device's behaviors due to the
generated heat. This property gives way to apply higher bias to improve
tunabilities.
32
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•
Low tem perature coefficient of dielectric properties
The heat is inevitable for any electronic devices running at room
tem perature. In the case of ferroelectric microwave devices, this tem peraturerising of the active ferroelectric film induces the change of the dielectric constant
and thus the drift of the microwave signal. To get a stable performance of the
device, the dielectric properties m ust not strongly depend on the temperature.
However, the bulk ferroelectric crystals exhibit a sharp dielectric peak at Curie
tem perature, which makes the bulk materials im proper for the tunable
microwave applications. Fortunately, the ferroelectric films, especially the
ferroelectric solid solutions, undergo a "diffuse phase transition" with a broad
and flat profile of the dielectric constant versus tem perature, which makes the
ferroelectric applications in microwave devices possible.
In addition to the requirem ents for the dielectric behaviors, other material
properties
such
as
the
sm ooth
surface
morphology,
thermally
stable
film /substrate interface, pure phase w ith dense microstructure, and minimal
defects are required to achieve a good device performance and long-term
reliability74.
33
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2.5 O verview of the PbxSri-xTi 0 3 and BaxSri-xTi 0 3 systems
PbxSri-xTi0 3
and BaxSri-xTi0 3
are the solid solutions of the typical
perovskite materials of PbTiOs or BaTiOs and an incipient ferroelectric SrTiOs.
Both solid solutions exist for the whole concentration range. The "A" sites of
ABO3 formula are random ly occupied by Pb or Ba and Sr ions. These materials
have attracted a lot of interest in recent years because of their technical
importance as well as being a group of im portant carriers of disorder physical
properties.
m
d is o r d e r
i.
s
0
order
0
concentration x
Figure 2.8 Schematic (X, T) phase diagram for typical ferroelectric solid solution
of (Ai-xBx)T i03 [78]
34
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Both materials are often described as dipole glass75'76'77'78, an analogue of
spin glass. The random-site electric dipoles come from the substituting Pb or Ba
ions for Sr ions. Their strange physical properties are generally attributed to the
competition of the long-range order due to the cooperative dipole interactions,
short-range inhomogeneity due to the local compositional variation over the
length scales of lOnm to lOOnm, and the fluctuation of the local field at the unit­
cell level due to the specificity of the dipole-dipole interaction potential77.
Though the site's substitution is random , the orientational order of the dipoles is
possible under certain conditions. Figure 2.778 shows a general phase diagram for
the dipole glass. There is a threshold of the substitution concentration xc over
which a phase transition from glass state w ith zero spontaneous polarization to
the ferroelectric order state occurs. As the tem perature increases, the
orientational system becomes completely disordered. The critical tem perature is
termed freezing tem perature in the case of the disorder-to-glass transition (glass
phase transition) whereas it is term ed Curie tem perature in the case of the
disorder-to-order transition (ferroelectric phase transition). Since some subjects
of the dipole glass are still unclear today, we will not talk about their inherent
physical origin and just present some im portant ferroelectric properties here.
The critical concentrations for BaxSri-xTi0 3
and PbxSri-xTi0 3
were
experimentally found to be xc = 0.035 79 and xc = 0.00280, respectively. The Cuie
tem perature for the ferroelectric phase transition just above the critical
35
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concentration is proportional to (jc-jcc)1/2 w ithin the ranges of 0.035-0.2 for
BaxSri-xTi0 3 7 9 and 0.002-0.05 for PbxSn-xTiCb80. O ut of these ranges the Curie
tem peratures of both BaxSn-xTi03 and PbxSn-xTi0 3 are linear to x. As show n in
Figure 2.8(a)84, the Curie tem perature of PbxSn-xTi0 3 can be tailored from 0 K
(SrTiCb) to 490°C (PbTiCb). In our case, Pbo.3sSro.65Ti03 (Tc=0°C) was selected to
satisfy the requirem ent for room tem perature applications.
In fact, both ferroelectric and glass phase transitions take place over a
wide range of the tem perature range, indicated by the w idened dielectric peak as
a function of tem perature, leading to w hat is commonly term ed "diffuse phase
transition". The Curie law is not satisfied. Even the ferroelectric phase transition
can transform from first order to second order. Generally the tem perature
corresponding to the m axim um static dielectric constant is chosen as Curie
temperature. Due to this property PbxSri-xTi03 and BaxSri-xTi0 3 etc are also
term ed dirty displacive ferroelectrics (DDF)81'82'83 by some authors, whereas the
prototypical displacive BaTiCb, etc. w ith sharp phase transition are termed
normal displacive ferroelectrics (NDF).
The dielectric relaxation phenomena exist widely in the lower microwave
frequency range (~MHz) due to the various complicated relaxation sources
whereas generally the dam ped harmonic oscillator behaviors due to the
displacive component dom inate in the higher microwave frequency (~GHz). It is
36
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expected that the dielectric relaxation and the order-disorder component should
be enhanced by the random substitution in the A sites of ABO3 .
m
w
m
m
m
•m
m
(b)
Figure 2.8 Curie tem perature, lattice constants and tetragonality vs. molar
percentage for (PbxSri-x)TiC>3 solid solution [84]
X-ray diffraction revealed that lattice param eters of the perovskite solid
solution depend on composition. For instance, the lattice constants of PbxSri37
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xTi03 at room tem perature are show n in Figure 2.8(b)84 where tetragonality and
lattice volume derive from these lattice parameters. Over a critical molar
percentage above 40% PbxSri-xTi0 3 comes into the ferroelectric phase with
tetragonal lattice from cubic phase. It is not strange that any notable change of
the lattice volume is not observed in cubic phase as the concentration of lead
increases because of the nearly equal ionic radius of Pb2+ and Sr2+ (Table 2.1).
However, the notable increase of the lattice volume in tetragonal phase is mainly
due to the large ferroelectric self strain85.
The bonding nature in PbxSn-xTi0 3 is largely affected by the atomic
substitution in "A" site. Strontium substituting for lead enhances the ionic nature
in PbxSn-xTi0 3 material, where covalent Pb-O is replaced by ionic Sr-O. In the
case of Strontium substituting for Barium in BaxSri-xTi0 3 no bonding nature is
changed because both Ba-O and Sr-O are ionic. This point is reflected in the
different behaviors of giant splitting of longitudinal and transverse optical
phonons between PbxSri-xTi0 3 and BaxSn-xTi0 3 58.
38
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Chapter 3
Epitaxial Growth of Thin Films by Pulsed
Laser Deposition Technique
3.1 O verview of pulsed laser deposition technique
The first laser was m ade from ruby in 1960 and currently w as widely
applied in industry as well as lab research. The higher coherence rank of laser,
essentially different from conventional light which at most possesses one rank of
coherence, gave us an opportunity to generate the controllable and high-quality
light w ith good monochrome, high pow er density, and small spatial dispersion.
Today the laser, together w ith the computer, are hailed as two of the most
significant inventions of the 20th century. However, the first dem onstration of
PLD in 1965 by Smith and Turner86 did not stimulate m uch interest because their
films were inferior to those obtained via other deposition techniques.
Immediately after the discovery of high tem perature superconductivity in 1986,
Dijkamp and Venkatesan87 et al. successfully deposited the YBCO thin films via
PLD, which were found to be superior in quality to those previously grown
39
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using other deposition methods. A flood of interest is thereby renewed after a
twenty-year dormancy.
K rF
E x c im e r
L aser
Figure 3.1 Scheme of pulsed laser deposition process
In principle the PLD technique is simple. As shown in Figure 3.1 a pulsed
laser beam (typical 20 ns pulse duration, 108 W /cm 2 energy density for excimer
laser) is focused onto the surface of a solid target. Its energy is strongly absorbed
there in a small volume. This absorption leads to a high local tem perature
(typically m uch above the boiling point of the target) and enough to break dow n
an y chem ical b o n d s w ith in the v o lu m e. T hus a sm all am ou n t o f target m aterials
evaporated rapidly into fully ionized plasm a in the vicinity the target surface
(about 5Ojum). This high tem perature and high pressure plasma consists of
40
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electrons, highly excited and ionized species. As a result of the pressure gradient
the plasma then expanded into the vacuum or collides and reacts with
background gas in the chamber. An ablation plume is thus formed, which looks
like a forward jet w ith nearly uniform momenta distribution confined in the
forward direction by background gas. At the same time the plasma itself also
absorbed a large of am ount of energy directly from the incident laser beam by
inverse Bremsstrahlung. This process enhances the plasma state and reduces the
energy of the incident beam. Finally the ablated species condense on the
substrate placed on a heater opposite to the target. The detailed modeling of PLD
may be obtained in the related references88'89'90'91.
The absorption mechanisms in the initial stage of PLD are very
complicated. Some authors92 proposed four possible mechanisms.
•
Direct coupling between lattice vibration and photons (h o « E gap).
•
Metallic interaction between the inherent free or nearly free carriers
and photons (ho < Egap).
•
Induced metallic interaction between photons and excited free carriers
generated by the external laser beam itself (ho > Egap).
•
Electron-hole excitation by light (ho > Egap).
The last three mechanisms require a m ediate mechanism of rapid electronlattice coupling to transfer heat from electrons to lattice. Actually, the interaction
process of PLD is not completely understood. The difficulty concerns why the
41
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pulsed UV excimer laser radiation is m ore efficient than long-wavelength IR
radiation, though some authors give only partial explanation93.
The technique of PLD w as found to have significant advantages over
other deposition methods.
•
It is easy to repeat the stoichiometry of the target to the deposited film
due to the extremely high local tem perature and heating rate, which leads to the
congruent evaporation of the target irrespective of the evaporating point of the
constituent elements or com pounds in the target.
•
Local heating in a small volume on the target surface prevents possible
damage to unheated part of the target materials.
•
Relatively high deposition rates can be achieved w ith pulse-
controllable thickness.
•
Since the high kinetic energy (10-100 eV) of species in the ablation
plume promotes surface mobility on the growing film, PLD dem ands a much
lower substrate tem perature than other film deposition techniques.
•
Extremely clean deposition technique w ith external laser heating
compared to internal filament heating.
•
PLD can produce films w ith quality comparable to MBE (molecular
beam epitaxy) w ith m uch lower cost.
42
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•
The laser is independent of the chamber system. Multilayer films may
be deposited by only rotating various targets into and out of the beam focal
point.
•
PLD is so straightforward that only a few parameters, such as laser
energy density, pulse repetition rate, need to be controlled during film
deposition.
In spite of these unique benefits, industrial applications of PLD are absent.
This technical limitation is due to some inherent drawbacks associated w ith PLD
process.
•
Highly forward-directed plume causes thickness of the deposited film
highly non-uniform. This makes PLD inapplicable to the large scale of thin films.
•
The plume generally contains macroscopic particulates (micro size),
which is obviously detrimental to the film's properties. Two m ost im portant
mechanisms of mechanical shock wave and subsurface boiling are attributed to
the form ation of these particulates.
•
Incomplete understanding of the PLD processes makes the theoretical
m odeling difficult. This difficulty elongates the period for novel materials
deposition.
43
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3.2
Growth m echanism of thin film by p ulsed laser deposition
3.2.1 General description of nucleation and growth of thin film
In microscopic view the thin film is form ed by a series of kinetic processes.
Some typical atomistic processes on an ideal crystal surface are illustrated in
Figure 3.294.
(a) deposit flux R.
(b) surface diffusion of adatoms.
(c) adatom s meet and bind w ith each other.
(d) adatom s attach to existing island.
(e) atoms detach from the island edge.
(f) atoms diffuse along the island edge.
(g) atoms can diffuse and bind on top of island.
(h) atoms deposited on top of island can move dow n to substrate.
(i) some atoms can re-evaporate.
Moreover, if the crystal surface is nonideal some processes such as atomic
attachm ent to defect and step, interdiffusion and interfacial reactions are also
important.
44
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Figure 3.2 atomistic processes on an ideal crystal surface [94]
At the early stages of the thin film growth, it is generally accepted that
there are three possible modes. They are illustrated in Figure 3.3. In the case of
layer-by-layer m ode (Figure 3.3(a)), also nam ed Frank-van der Merwe mode, the
lateral growth of the thin film dominates. It may be realized by the formation of
monolayer or polylayer nuclei in a two-dimensional way95. Moreover, the
process may be m ononuclear or polynuclear95, w ith free energy barrier or
barrier-absent,
incurred
by
surface step
or
screw
dislocation,
and
in
supersaturation or even undersaturation96. The island mode (Volmer-Weber
mode) is in the opposite situation. The norm al grow th of nuclei happens as well
as lateral growth. Some three-dimensional islands are formed on the substrate
surface as show n in figure 3.3(b). The layer plus island growth mode (Stranski45
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Krastanov mode) is an intermediate case (Figure 3.3(c)). Initially the growth
condition favors layer growth. However, this condition is reversed by some
disturbance such as strain due to the lattice mismatch after one or several
monolayers are deposited. Thus the following grow th of the thin film exhibits an
island mode. The three-dimensional islands form on the top of the lower layer.
layer-by-layer mode
island m ode
layer-plus-island mode
'd m
&
i*YV
OUUOJUUCX
(a)
(b)
(c)
Figure 3.3 Growth modes of thin film on crystal surface
Growth mode of the thin film is affected by external supersaturation as
well as in h erent surface en ergy. M arkov and K asch iew 95 d eriv ed a criterion for
the growth modes.
46
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(layer mode)
(3.2)
hki
where a s and u i are the free energy of the substrate surface
and interface
respectively, <Jm is the specific surface energy of the contact plane of the deposit,
and Aju - kTs \ns is related to substrate tem perature Ts and supersaturation
s
R
~R„
The detailed processes of the island grow th mode may be divided into
four stages.
1. Nucleation: small stable nuclei are formed on the substrate.
2. Growth of the nuclei and form ation of large islands.
3. Coalescence of the islands and form ation of a continuous film.
4.
Structure and surface morphology evolution in bulk thin film: re­
crystallization, defect elimination, grain growth, and shadowing take place via
bulk diffusion, surface diffusion and geometry constraint97.
The impinging atoms are absorbed by the substrate surface, which may be
characterized by sticking and therm al accommodation coefficients98. It is
statistically possible that some absorbed atoms collide and bind w ith each other
to form temporal small subnuclei, which is obviously unstable and tend to
dissociate due to the energy barrier incurred by subnuclear surface. However,
47
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under some supersaturation these subnucei have still some chance to climb over
the free energy barrier by thermal tunneling to form the stable supernuclei with
larger size, which are more likely to grow rather than dissociate. Usually these
stable nuclei exhibit more or less crystalline structure and orientation. They
behave like a seed for the following grow th of thin film. As the density of stable
supernuclei increases w ith time up to some maximum value, the coalescence of
nuclei occur via some mass transport mechanism such as Ostwald ripening,
sintering97, and even nuclei migration. In the end of this stage a continuous film
will form, which looks like more or less connected network containing empty
channels98. As the film goes thicker, the bulk behaviors in materials take more
im portant effects. The incorporated atoms in films reach their equilibrium
position in the lattice via bulk diffusive motion. Crystalline defects such as void
are also reduced and crystallinity is improved. The larger grain continues to
grow at the expense of the smaller one w ith the physical mechanism similar to
Ostwald ripening. Columnar grain may also be formed due to the shadowing
phenom enon or diffuse-limited growth. The final microstructure and surface
morphology will depend on the competing of bulk diffusion, surface diffusion,
adsorption, and shadowing, which is described by a structure zone m ode97. This
model is based on the fact that films generally exhibit obviously distinct
microstructures in certain tem perature and deposition rate ranges. According to
nucleation theory some significant results are sum m arized as follows:
48
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t ,T s I => i t => r* ^,G* l , J t
=> fine-grained or even amorphous films, smooth surface
(3.3)
R l , T s t => si= > r* t,G * t , j 4 => I arg e crystallites or even monocrystallinefilms, rough surface
(3.4)
where R is the deposition rate, Ts is substrate tem perature, s is the
supersaturation, r* is the size of critical nucleus, G* is the nucleation barrier, and J
is the nucleation rate. These results usually give us the useful clues to control the
growth processes of the thin film.
Usually, the nucleation phase plays a key role for the further growth, and
it determines the final structure and properties of the thin film. Moreover, this
process is controllable via fostering desired nuclei and suppressing others by
carefully controlled deposition conditions or artificial graphoepitaxy. The mode
of nucleation or growth is also affected by supersaturation as indicated in
equation (3.1) and (3.2). Under high supersaturation (high deposit flux and low
temperature), the island grow th m ode often transits to the low island growth
mode, layer mode, and even continuous m ode (a special case of layer mode)
because in this case the two-dimensional nucleation exhibits a lower energy
barrier whereas the three-dimensional nucleation is not energetically favored.
49
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3.2.2 Growth m echanism of thin film s by PLD
The PLD technique shows some special features that separate itself from
the conventional deposition techniques such as sputtering, evaporation and
MBE.
First of all, the extremely high supersaturation in PLD plume reduces the
nuclei to very small size (practically one atom) or makes two-dimensional
nucleation favored. Based on this consideration, Metev and M eteva" presented a
theoretical investigation of the nucleation and grow th process of PLD. In this
model the first monolayer is formed on the substrate via two-dimensional
nucleation w ith disk-shaped nuclei of monatomic height. After the first layer
reaches enough coverage, the second layer (also of monatomic height) begins to
grow w ith continuous mode on top of the first layer. In this case the atoms are
random ly incorporated into this layer w ithout two-dimensional nucleation. The
third layers are filled w ith the same way after second layer reaches some
coverage. Therefore, the overall growth mode of the film will be dependent on
competition between the lateral growth of the flat cluster and the filling of its top
layers. Some useful results are achieved from this model. As deposit flux
increases and the substrate tem perature decreases, the grow th m ode transits
from high island m ode to low island mode or even continuous mode. The film's
textures will exhibit monocrystalline (high island mode), polycrystalline (low
island mode) or am orphous (continuous m ode)100.
50
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Secondly, in PLD the deposit flux pulse (about 1 ms width) is separated by
a silent duration w ith period of about 100ms w ithout any deposit coming100. The
small nuclei formed during high supersaturated deposit flux will be unstable
and dissociate into mobile species that w ould nucleate new cluster during the
time of no deposit arrival. Thus it is expected that a cyclical nucleation and
dissociation process should happen during the overall deposition process. This
discontinued feature of PLD has also other effects that are related to the
repetition rate of laser pulse. For instance, the high energetic plume incurred by
laser pulse leads to a blast wave in oxygen, leaving behind a rarefied ambient for
the second pulse if the repetition rate is enough high. G upta101 reported the
defect formation caused by this transient decrease in the ambient oxygen
concentration during fabrication of YBCO.
Finally, the high kinetic energy of impinging atoms in the deposit plume
is a big challenge for total thermal accommodation. The adsorbed atoms keep
some excessive energy so that their real tem perature is higher than that of
substrate. The high kinetic energy m ay also cause some defects on the substrate
as crystallization centers. Both factors will give us a benefit that the film may be
fabricated by PLD at lower substrate's tem perature. On the other hand, too high
kinetic energy is detrimental to the film's quality due to the generation of the
micro particles in the plum e as m entioned in section 3.1.
51
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3.3 Optimum growth conditions for thin film heteroepitaxy
Heteroepitaxial films have crucial importance for applications in today's
electronic devices. Usually the realization of new and better devices relies on the
refinement of the epitaxial techniques. It has also continued to be of scientific
interest to investigate the physics underlying epitaxial growth. There are three
types of epitaxial interfaces. If an epitaxial film is only slightly latticemismatched w ith the crystal substrate, grow th generally takes place in a coherent
fashion which leaves the film homogeneously strained and commensurate with
the substrate. As the film thickness reaches a critical value he, it becomes
energetically favorable for misfit dislocation to be introduced at the interface to
accommodate the lattice mismatch and to relax the strained film. This process
usually takes place in a gradual fashion, which may be described by increasing
dislocation density, decreasing spacing between dislocations and partially
relaxed strain. This type of interface shows a configuration of some large areas of
coherent lattice planes that are separated by incoherent local dislocations.
However, w hen the lattice mismatch is very large this configuration actually
does not exist and the interface may be expected to be completely incoherent
w ith no continuity between the lattice planes on the two sides of the interface.
This type of interface exhibits low adherence because of a lack of interfacial
bonding. Actually an atomic displacement may also take place in the interface
that is called "geometrical misfit dislocation"102'103'104. The interface needs to be
52
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described by the concept of "coincident-site lattice" that is often used to describe
the high-angle grain boundary105.
Possibly the most im portant factor which affects the heteroepitaxial
grow th between two materials of similar lattice structure and bonding nature is
the lattice mismatch defined as:
a?( s ) - a ( f )
«<>(/)
where a0(s) and a0( / ) are the unstrained lattice constants of film and substrate
respectively. The definition (3.5) for lattice mismatch is convenient for us to
study the film's strain, but another definition as described in equation (3.6) is
often adopted w hen we concentrate on the interfacial structure.
jr
^
f l o ( / ) - f l „ ( g )
(3 6)
a 0( s )
Many
papers106'107'108'109'110'111-112'113'114'115
studied
the
strained-layer
heterostructure in equilibrium. Van der Merwe106-107 obtained an approximate
expression for the thickness dependence of strain:
x=[(l~*n>
)(n
r ‘bl x(jW
W 1+^
8k ( l -<2l
v ) ( f2 +
f 0) ff0Gf
h
P = [8nG,
l-v
x [(1 + ^ ) ( 2 + /„ )’ G ,]'1
Lrs
<37>
(3.8)
where h is the film's thickness; f 0 is the lattice mismatch defined as equation
(3.5); b is the edge component of the Burgers vector of the dislocation; Gf and Gs
53
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are the shear moduli of the film and substrate respectively;
Gi
is the shear
m odulus of the interface, often taken as being equal to the shear m odulus of the
softer one in the film and the substrate; v is the Poisson's ratio, assum ed to be
the same for the film and the substrate. The critical thickness he is obtained by
letting x = f Q. Some more simplified formulas are also available for a quick
estimate108.
fo
x(d) =
f^ rl
ld+Xr
(d <dJ
(d
>d
c)
^
d,= T 7 r—
\fo\-Xr
(3-10>
xr « 0
(3.11)
where d and d c are the film's thickness and critical thickness in unit of
monolayer, respectively; f 0 is the lattice mismatch as defined in equation (3.5);
xr is the residual strain, often taken as zero. For PSTO films they are often
deposited on perovskite or quasi perovskite substrates such as LaAlC>3 , NdGaCb
and SrTiCb to obtain the compressive stress and cubic MgO substrate to obtain
the tensile stress. The corresponding lattice mismatch and critical thickness are
estimated in the Table 3.1.
54
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Table 3.1 lattice mismatch and critical thickness for PSTO films on different
substrates
ao(f) (nm)
Substrate
ao(s) (nm)
fo
dc (nm)
LaAlOs
0.382
-2.5%
16
MgO
0.4212
7.4%
5
SrTiOs
0.3907
-0.3%
130
NdGaOa
0.386
-1.5%
26
0.392
To get a quantitative feeling about the value of the stress induced by the
misfit strain in the perovskite thin film, we apply Hooke's law to the case of
isotropic in-plane strain in cubic systems.
|V
f cHi
C12
C,2
0
0
0"
C>2
C11
Cn
0
0
0 h x2i
Cm C12 Cu
0
0
0
x3
0
0
0
C44
0
0
0
0
0
0
0
0
0
0
0
C44
0
0
0
0
,0 ,
C44)
where x3 —x 2 = x is in-plane strain, crl —cr2 = cr is in-plane stress, and cr3 = 0
is out-of-plane stress. After simplification we obtain:
55
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a = (cu + c u
(3.13)
~ c n )x
Substituting the typical values of BaTiCh (cu = 2 . 7 5 1 2 x l 0 " A / 7 m 2,
cI2 = 1.7897 x 10" N / m 220) and taking x = 0.3%, we get the in-plane stress as
high as 0.66 GPa, which is large enough to incur some obvious physical
phenomena.
However, for ferroelectric thin films the generation of the lattice
dislocation in the interface is only one of the possible mechanisms for strain
relaxation. The detailed relaxation processes are complex from deposition stage
to cooling stage of the thin film. Speck and Pompe116-117'118 m ade a systematic
study on this topic. Generally, the deposition tem perature (Tg) is higher than
Curie tem perature (Tc) of the thin film so that in the stage of the film growth the
strain is accommodated by only misfit dislocation as discussed above. On cooling
to Tc the further misfit dislocation generation is possible due to the different
thermal expansion coefficients between the film and substrate. During the stage
of the paraelectric to ferroelectric transition, the relaxation processes become
very complicated. Additional self-strain due to this phase transition takes an
effect. The total strain may be relaxed either by further generation of interface
dislocations or by dom ain formation. Fortunately, in our applications Curie
tem perature of the high-quality PSTO films is supposed to be zero degree; that is,
below room tem perature so that the ferroelectric self-strain and dom ain
56
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formation may be ignored though the "diffused phase transition" for
ferroelectric film indicates some micro-domains exist even well above Curie
temperature.
Under the conditions of the layer grow th the preparation of epitaxial films
is generally w ithout problems. The atomic layers try to maximally repeat the
substrate's lattice structure and grow layer by layer. In m any cases epitaxy
occurs as a natural consequence of this grow th mode. However, heteroepitaxy
w ith island growth m ode is m uch m ore complicated. Initially it is possible that
the nuclei w ith different orientation coexist but the disoriented nuclei will
reorient or disappear after further grow th by some kinetic or thermodynamic
mechanisms. For instance, the islands may not only migrate on the substrate
surface but also rotate. This lateral m igration will be complete if the clusters have
reached an epitaxial position by rotation w ith respect to the substrate. Also when
tw o islands w ith different orientation coalesce, the final union often takes the
orientation of the larger island, which favors a single orientation in the final film.
These processes are obviously complex and affected by m any factors such as
lattice mismatch, contamination and surface defect, and chemical factors etc.
Some authors observed a critical tem perature above which the epitaxial growth
takes place. The reasons why the higher tem perature favors epitaxy are
sum m arized below.
•
lower supersaturation.
57
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•
desorption of impurities in high temperature.
•
more energy is available for surface atoms attaining equilibrium sites.
•
enhance re-crystallization and defect elimination by bulk diffusion.
•
facilitate island m igration and rotation to reach epitaxial position.
A further im portant factor for epitaxy is the deposition rate. It was
observed that the following between the critical tem perature and deposition rate
should be satisfied119.
* < /l-ex p (-% 4
(3.14)
k T c
Lower deposition rate provides the enough time for atoms to jump into a
position of equilibrium before it collides w ith another atoms as well as larger
nuclei indicated in section 3.2.1.
3.4 D eposition of PSTO film s u sing PLD technique
Although PLD has the benefit of stoichiometric transfer of the target
composition to the deposited film as m entioned in section 3.1., more efforts are
required for deposition of m any ferroelectric materials (PSTO, LiNbOs and KTN
etc) that contain some volatile constituents such as Pb, Li and K. The correct
stoichiometry may be realized via the special target technique w ith excess
am ount of the volatile constituent as well as carefully controlled deposition
58
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conditions. In our case a target w ith a nominal P b/S r ratio of 35:65 and 20 %
excess of Pb was adopted to compensate the volatilization of Pb during the
epitaxial growth. Moreover, the lead-sufficient target is helpful for stabilizing the
perovskite phase in the PSTO film. Figure 3.4 shows the X-ray 9 ~ 26 scanning
pattern of the high density PSTO com pound target. The full pow der diffraction
peaks for cubic PSTO compound appear, which indicates that the PSTO is in the
cubic phase w ith the lattice constant of 0.3898 nm calculated from the PSTO (002)
reflection . Every time prior to feeding PSTO target into deposition chamber the
target is polished by a 15 micro sand paper to remove nonstoichiometric
composition on its surface caused by the last target ablation.
LAO (001), NGO (110) and MgO (001) substrates were selected to
epitaxially grow the PSTO thin films. To remove the contamination on the
substrate surfaces, both LAO and NGO substrates were cleaned in Acetone and
Alcohol via ultrasonic whereas MgO substrate was just rinsed in Alcohol for one
minute to avoid possible surface damage. The substrates were then clamped on
the heater and pum ped overnight at tem perature 250°C to reduce the surface
adsorption and achieve a base pressure as low as 1 0 7 Torr. A KrF excimer laser
w ith a w avelength of 248 nm was employed for the epitaxial grow th of PSTO
thin films. Before the deposition of the films, the substrates were annealed at
820°C for several minutes in 1 atm pure oxygen ambient and at the same time the
target was also pre-irradiated to remove some possible contamination w hen it
59
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was polished. During the deposition, a pure oxygen pressure was m aintained at
about 200 mTorr. Soon after the deposition, a 1 atm of pure oxygen was
introduced to the deposition chamber and the films were kept at the deposited
tem perature for 20 minutes before the tem perature was slowly cooled dow n to
room temperature.
Though some clues to the conditions of thin film's fabrication are given by
the thermodynamic and kinetic theory, the optim um deposition param eters for
the epitaxial grow th are realized by experimentally trying in the param eter space
especially for multi-component materials. Table 3.2 summarizes the optim um
conditions for the epitaxial growth of PSTO films.
60
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o
CO
c
=5
CM
O
O
CD
CO
c
■4CD
—
>
c
O
o
o
T3
O
CM
CM
CM
20 (degree)
Figure 3.4 X-ray diffraction of the 0 ~ 26 scans from the high density powdered
PSTO com pound target
61
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Table 3.2 O ptim um conditions for epitaxial grow th of PSTO thin film using the
PLD technique
Target
Pb/Sr=35:65 plus 20 at. % excess Pb
Substrates
(001) LAO, (110) NGO and (001) MgO
Laser
KrF 248nm
Temp
820°C
O2 pressure
200 mTorr - 250 mTorr
Energy density
2J/cm 2
Repetition
4 Hz - 5 Hz
Annealling
20 m in in 1 atm O 2
Deposition rate
7.0 n m /m in
62
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Chapter 4
Characterization of Ferroelectric (Pb,Sr)Ti03
Thin Films
4.1 X-ray Diffraction (XRD)
XRD is the most powerful and nondestructive technique for macroscopic
studies of crystallinity, strain and interfacial relationship of thin films. Several
scanning m ethods that are often used by us are summarized.
•
Coplanar symmetric and asymmetric radial scans provide information
about the epitaxial orientation of the thin film on the substrate, the in-plane and
out-of-plane lattice parameters.
•
XRD rocking scans give information about the crystalline quality.
Rocking curve from symmetric 6 scan supplies the tilt distribution of the film's
crystallites whereas the rocking curve from the asymmetric (j) scan gives us the
information about the average distribution of the crystallites' rotation.
•
Pole figure m easurem ent is perform ed to study the texture of thin
films and interfacial relationship on substrate. If the film is polycrystalline, the
63
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poles plotted on the projection will be uniformly distributed. If the film has
preferred orientation, the poles will tend to cluster together in certain areas of the
projection. If the film has good single crystal quality, each cluster should form a
high intensity spot. In this case the interfacial relationship is also easy to be
extracted out from the relative position of poles from both film and substrate.
4.1.1 XRD studies on the PSTO film on LaAlC>3 (001) substrate125
XRD studies were performed on PSTO film on LAO (001) substrates.
Figure 4.1 is a diffraction pattern of the 0 ~ 20 radial scan along the surface
normal from an x-ray diffractometer using Cu-radiation. The figure shows that
only PSTO (OOl)-type reflections together w ith the corresponding reflections from
the LAO substrate appear, indicating that the as-grown film is c-axis aligned. The
high-resolution m easurem ent (A # = 0.006°) of the rocking 0 scan from the
(002) reflection shows that the tilt distribution of the film crystallites is
extraordinarily narrow (the full w idth at half maximum (FWHM) is only 0.054°
as shown in the inset of Figure 4.1), whereas the distribution of the crystallites'
rotation has a w idth of 0.43° from the (311) asymmetric (j) scan as show n in
Figure 4.2. Pole figure studies have been perform ed from the PSTO {111}
reflections (Figure 4.3). The fourfold symmetric reflection peaks from {111}
planes w ith no satellites or broadening are obtained, suggesting that the films
64
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have a high degree of in-plane orientation. From these observations and the
widths of the radial scans, it is evident that the film consists of well aligned, 200
nm long columnar grains w ith an average diameter of 20 nm. This evidence
indicates that PSTO films exhibit excellent epitaxy with very good single crystal
quality. Moreover, the film exhibits a slight tetragonal distortion w ith the c-axis
length of 0.3914(1) nm and the a-axis length of 0.3918(2) nm, respectively. The in­
plane lattice mismatch, defined as equation (3.6), is calculated as 2.5%. There is a
slight difference from the lattice param eters obtained from our PSTO
polycrystalline pow der target which is cubic at room tem perature as mentioned
in section 3.4. The distorted epitaxial film exhibits the tetragonal symmetry
probably resulting from the therm al residual stress due to the different thermal
expansion coefficients of the PSTO film and LAO substrate. We find that both
lattice constants of the a-axis and c-axis are smaller than the lattice constant
calculated from XRD results of the PSTO target in section 3.4, which is attributed
to the unit cell volume expansion because of the oxygen vacancies formed during
film deposition.
65
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w
PSTOfOOS)
St
Iff
2
!
| ft m m
m
|
-ft
e
3
8
o
I
I
Itf
f 2
I ’
o
10 ’
23.2
234
23oe
23,8
ft (d a p )
10°
i if *-s * »■#
f«>v m m m
1 1"
20
I
90
f! f!
I I
40
I
I
I
50
2© [deg]
Figure 4.1 0-20 scan of x-ray diffraction showing that the as-grown PSTO film on
(001) LAO substrate is c-axis oriented. Only (001) reflections appear in the
diffraction pattern. The inset is a rocking curve m easurem ent from the (002)
PSTO reflection.
66
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P S T O (311)
15-
1 i5-
[degj
Figure 4.2 XRD asymmetric (f> scan of the as-grown PSTO film on the (001) LAO
substrate from PSTO (311) planes indicating the distribution of the crystallites'
rotation has a w idth of 0.43°.
67
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P S T O {111}
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 I I | IT I II H I I | I I I I I I I I I | I I I I I
-TO
-TO
-5D
i
SI
"I®
deg]
Figure 4.3 XRD (j) scan from the (111) planes of the as-grown PSTO film on the
(001) LAO substrate showing that only sharp {111} reflection peaks appear in the
pattern.
68
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4.1.2 XRD studies on the PSTO film on NdGaOs (110) substrate120
XRD studies were also performed on PSTO films on NGO (110) substrates.
Figure 4.4 shows the results of the x-ray 6 ~ 20 radial scan. Only the (00/) peaks
of the PSTO thin films appear in the diffraction pattern, suggesting that the asgrown thin films are c-axis oriented. W ith the Lorentz function fitting using the
parameters of peak intensity, peak position, and peak broadening, the out-ofplane lattice param eter can be calculated to be c = 0.39172 nm. The XRD
asymmetric scan from the reflection of PSTO (103) was also perform ed to get the
information of in-plane lattice parameters. The in-plane lattice param eter is
extracted to be a = 0.39269 nm, which is slightly larger than the halves of the in­
plane lattice param eters of 0.772 nm along [ 110] and 0.770 nm along [001]
direction for the NGO substrate. The inset in Figure 4.4 shows the rocking curve
measurement from the reflection of PSTO (002) planes. The full w idth at half
maxima (FWHM) is only 0.018° from the PSTO (001) reflection, indicating that
the as-grown PSTO films have excellent single crystallinity. The excellent
crystallinity and epitaxial behavior are confirmed by the x-ray diffraction pole
figure study as seen in Figure 4.5, which comes from the PSTO {101} reflections.
The high degree of single crystallinity is revealed from the sharp diffraction spots
w ith no satellites or broadening in fourfold symmetric reflection along the {101}
pole. Also, the interface relationship is determ ined to be
and [100]p s t o
/ /
[0 0 1 ]n g o
(0 0 1 )psto
/ / (110)
from the in-plane orientation.
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ngo
o
o
o
CM
O
O
=3
CO
'c/>
c
0
c
11.30
I
20
I
25
11.35
6 (degree)
I------ 1------ 1------ 1
30
35
11.40
I-------1------ 1------ 1------ 1-----40
45
50
20 (degree)
Figure 4.4 X-ray diffraction 0 ~ 26 scan showing that only (00/) reflections of the
PSTO film on the (110) NGO substrate appear in the diffraction pattern
indicating that the film is c-axis oriented. The inset is a rocking curve
m easurement from the (002) PSTO reflection w ith the FWHM value of only
0.018°, suggesting that the as-grown PSTO film has excellent single crystallinity.
70
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90
PST (101) MOO{200)
PST (101)
NGO{020)
270
Figure 4.5 Pole figure of PSTO (101) planes for the as-grown PSTO film on the
(110) NGO substrate showing that only {101} reflections appear in the pattern
indicating the films have excellent single crystal quality.
71
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4.1.3 XRD studies on the PSTO film on MgO (001) substrate
XRD 0 —2 0 radial scan and rocking scan were also performed to study
the epitaxial behavior and crystalline quality of the PSTO film on MgO (001)
substrate. As shown in Figure 4.6 the diffraction pattern of the 0 —20 radial
scan shows that only PSTO (OOl)-type reflections together w ith the corresponding
reflections from the MgO (001) substrate appear, indicating that the as-grown
film is c-axis aligned. The rocking 0 scan from the (002) reflection of PSTO
shows that the tilt distribution of the film crystallites is very narrow (the full
w idth at half maximum (FWHM) is about 0.27° as shown in the inset of Figure
4.6). These results suggest the PSTO film deposited on MgO substrate is highly
epitaxially grown with very good crystallinity.
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CM
O
O
FWHM=0.27°
CM
O)
o
D
05
22.0 22.5 23.0 23.5 24.0 24.5
9 (degree)
cn
c
CD
c
■+-»
20
25
30
35
40
45
50
29 (degree)
Figure 4.6 X-ray diffraction 0 ~ 26 scans showing that only (00Z) reflections of
the PSTO film on the (001) MgO substrate appear in the diffraction pattern
indicating that the films are c-axis oriented. The inset is a rocking curve
m easurem ent from the (002) PSTO reflection w ith the FWHM value of only 0.28°,
suggesting that the as-grown PSTO films have excellent single crystallinity.
73
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4.2 Transm ission Electron Microscopy (TEM)
Transmission Electron Microscopy
resolution
is
considered
to
be
(TEM) with its unique atomic
another
powerful
technique
for
fully
understanding the microstructures and defect nature of thin films. It provides a
means for direct observation of microstructure, crystallinity and interface
structure over scale length from atomic resolution to micron dimensions.
4.2.1 Cross-sectional TEM studies on the PSTO film on LaA103 (001)
substrate125
Cross-sectional TEM studies have been conducted on the epitaxial PSTO
film deposited on (001) LAO. Figure 4.7(a) is a low-magnification, bright field
TEM image showing that the as-grown PSTO film has a sharp interface and good
epitaxial behavior. The antidom ain boundary that formed directly at the
interface between the PSTO film and the LAO substrate can be clearly seen in the
image. This phenom enon is som ewhat similar to the previous observations of
BSTO films on (001) MgO and (001) LaAlOs.
Figures 4.7(b) - (d) show the
selected area electron diffraction (SAED) patterns taken along a [110] direction of
the LAO substrate (b), the [110] direction of the PSTO film (c), and the interface
covering both the substrate and the film (d), respectively. The film has excellent
crystallinity that is evident from the sharp diffraction spots, as show n in Figure
4.7(c). Neither precipitate nor segregation is found in the films. The diffraction
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
pattern at the interface is a simple superposition of the PSTO film and the LAO
substrate. Again, the sharp electron diffraction spots w ith no satellites or
broadening at the interface indicate that the film has excellent single-crystallinity.
The interface relationship has been determ ined to be
(0 0 1 )p s to //(0 0 1 )la o ,
< 1 0 0 > p s to //< 1 0 0 > la o
and
which agrees w ith the XRD studies. From the highly
ordered electron diffraction spots, the lattice mismatch, defined as equation (3.6),
can be estim ated to be 4.0%, which is m uch larger than the value of 2.5%
estimated from XRD and the value calculated from the lattice param eters of both
PSTO and LAO unit cells. This difference could be due to the fact that the strain
in TEM sample is one-dimensional because the TEM sample is very thin along
the interface whereas it is two-dimensional in both x-ray samples and theoretical
calculation. This phenom enon has been observed earlier in other systems18. The
strain is usually relaxed by forming periodical edge dislocations at the interface
between the film and the substrate. The high-resolution cross-sectional TEM
studies have dem onstrated this epitaxial behavior. As shown in Figure 4.7(e) the
film has good epitaxial quality w ith a sharp interface structure. Edge dislocations
were found to form over the entire interface w ith an average separation of about
26 lattice planes along the PSTO [110] direction, which also gives a lattice misfit
in the range of 4.0%, in good agreement w ith results from the electron
diffraction. This confirms that the PSTO film is of excellent single crystallinity.
Neither a precipitate nor any other phase is present in the film or at the interface.
75
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Figure 4.7 Cross-sectional TEM studies show ing the epitaxial behavior of PSTO
films on (001) LAO: (a) a low-magnification, bright field TEM image (b) SAED
from the LAO substrate (c) SAED from the PSTO film (d) SAED from the
interface covering both the PSTO film and LAO substrate (e) high resolution
TEM image
76
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4.2.2 Cross-sectional TEM studies on PSTO film on NdGaOs (110) substrate120
Cross-sectional TEM studies have also been conducted on a PSTO film on
(110) NGO to understand the interface structure and epitaxial behavior. Figure
4.8(a) is a low-magnification, bright field TEM image showing that the as-grown
PSTO film has an excellent crystallinity and good epitaxial behavior. Figures
4.8(b) - (d) show the selected area electron diffraction (SAED) patterns taken
from the NGO substrate (b), the PSTO film (c), and the interface covering both
the substrate and the film (d), respectively. The film has excellent crystallinity
that is evident from the sharp diffraction spots, as shown in Figure 4.8(c). Neither
precipitate nor segregation is found in the film. The diffraction pattern at the
interface is a simple superposition of the PSTO film and the NGO substrate.
Again, the sharp electron diffraction spots w ith no satellites or broadening at the
interface indicate that the film has excellent single-crystallinity. The interface
relationship
has
(0 0 1 )p s to //(H 0 )n g o ,
been
determ ined
to
be
< 1 0 0 > p sto / /< 0 0 1 > n g o
and
which agrees w ith the XRD studies. No visible interface
strain fringes can be seen at the interface, which indicates that the strain is
probably relaxed by forming edge dislocations at the interface between the film
and the substrate. The high-resolution cross-sectional TEM studies have
dem onstrated this epitaxial behavior, as show n in Figure 4.8(e). The film has
good epitaxy quality w ith a sharp interface structure. Rarely edge dislocations, or
very large inter spacing between the edge dislocations, are found along the
77
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interface because of a very small lattice misfit between the substrate and film, as
seen from Figure 4.8(f). Furthermore, it should be pointed out here that neither a
precipitate nor any other phase is present in the film or at the interface.
78
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Figure 4.8 Cross-sectional TEM studies of the PSTO film on (110) NGO: (a) a lowmagnification, bright field TEM image (b) SAED from the NGO substrate, (c)
SAED from the PSTO film (d) SAED from the interface covering both the PSTO
film and NGO substrate (e) high resolution TEM image
79
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4.3 Rutherford backscattering spectroscopy (RBS)121
Rutherford Backscattering Spectroscopy (RBS) is a very popular technique
for thin film characterization. Briefly, RBS uses a very high energy and low mass
ion beam, such as He+ w ith Mev energy, that penetrates up to a depth of microns
into the film and substrate, w ith a subsequent collection of the elastically
scattering ions from the Coulomb repulsion that occurs between the incident ions
and nucleus of thin film and substrate. By analyzing the energy spectrum from
the scattered ions, one can determine the stoichiometry of thin film compositions
w ith accuracies up to ± 1.0% for heavy elements. If the incident high-energy ion
beam is aligned along a particular crystalline channel, the backscattering ion
count will be m uch lower than that from random aligned incidence. Usually, a
yield, defined as the count ratio of the detected backscattering ions from the
channeling and random spectra, is as low as a few percentages for an epitaxial
film with good crystallinity.
Figure 4.9 shows the random and aligned spectra for a PSTO film
deposited on (001) LAO substrate using 1.8 MeV He ions. The RBS signals in the
random spectrum reveal the clear steps corresponding to the Pb, Sr and Ti at
channel num bers at 311, 366 and 409, respectively. All of the RBS signals from
the aligned spectrum appear at small peaks. To be seen clearly, the aligned
spectrum is m ultiplied by a factor of 3. The minimal yield taken behind the Pb
80
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surface peak is about 3.75%, indicating the excellent crystallinity of the PSTO
film.
10-
o
o
o
1.8 MeV He* RBS-Channeling spectra
Pb
Aligned
Ramdom
□□
C 43
O
o
50
X
, =3.75%
^min
100
150
200
250
300
350
400
450
500
Channel
Figure 4.9 1.8 MeV He ion channeling random and aligned spectra taken on the
PSTO film on (001) LAO substrate. The aligned spectrum is m ultiplied by a factor
of 3 to see the small peaks clearly.
81
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4.4 Dielectric property measurements by Interdigital Capacitor (IDC)
Technique
Interdigital
capacitors
provide
a
powerful
m ethod
for
dielectric
measurements w ithout bottom electrodes as well as are widely used as lum ped
elements in microwave devices. This technique is especially useful for perovskite
films because of their incompatibility w ith metal bottom electrode. An
interdigital capacitor has a coplanar electrode configuration as shown in Figure
4.10(a). After the PSTO film is deposited on the insulating substrate such as LAO,
MgO, NGO etc, two finger-like electrodes are fabricated on its top. The finger's
length is generally millimeter order and its w idth and gaps between fingers are
generally micrometer order to get higher capacitance up to several thousand Pico
Farads. Figure 4.10(b) is a "side view". The bias voltage and the small high
frequency signal are applied to the two electrodes. Dielectric constants are
extracted from the capacitance using the conformal m apping-based model
developed by Gevorgian122'123'124. In this model the solutions for dielectric
constants of co-planar configuration are obtained by a complex transformation
from polar coordinates to Cartesian coordinates.
82
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Au
Electrode
FE Film
Side View
(b)
Figure 4.10 Scheme of Interdigital Capacitor Technique
83
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4.4.1 IDC measurements on the PSTO film on LaAlOs (001) substrate at 1
MHz125
3.5
o
——
§
Experimental
Theoretical
3.0
% 2.5
2.0
1.5
Tunability = 48 %
-40
0
-20
20
40
Electric Field (kV/cm)
Figure 4.11 The interdigital dielectric property m easurement at 1 MHz at room
tem perature showing PSTO film on LAO (001) has a very large dielectric
tunability value of 48% and high dielectric constant w ith bias dependence of
Lorentz function.
The dielectric property measurements performed by Interdigital Capacitor
Technique show that the room tem perature dielectric constant and the dielectric
loss tangent for a 200 nm thick PSTO film on LAO (001) substrate are around
84
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3100 and 0.008, respectively, at 1 MHz (Figure 4.11). A large tunability of as
much as 48% at 40 kV /cm (near saturated), or 34% at 20 kV /cm (unsaturated),
has been achieved from the as-grown films. FOM is calculated as 60 at 40 kV/ cm
bias field. Thus, the dielectric properties of the highly epitaxial ferroelectric PSTO
thin films are m uch better than the films prepared by other techniques. Also, this
dielectric tunability value is som ewhat similar to BSTO thin films on LAO
suggesting that the epitaxial quality and the dielectric properties of PSTO thin
films are good for developing high frequency tunable microwave elements
operating at room temperature. As m entioned in section 2.2, the field
dependence of the dielectric constant may be fitted by Lorentz function as shown
in Figure 4.11.
4.4.2 IDC measurements on the PSTO film on NdGaOs (110) substrate at 1
MHz
Figure 4.12 shows the dielectric constant vs. the electric field for the asgrown PSTO film on NGO (110) substrate m easured at 1.0 M Hz and room
tem perature. The room tem perature dielectric constant was determ ined to be
4300 w ith a dielectric loss value of 0.01 at zero electric field. The tunability was
found to be as large as 56 % and FOM is calculated as 56 at 40 kV/ cm bias field.
Again, such a high tunability w ith low dielectric loss implied the great potential
85
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application of PSTO thin films. The Lorentz fitting indicates the bias dependence
of the dielectric constant is a Lorentz function as mentioned in section 2.2.
4500
Experim ental
Theoretical
4000*4—»
c
O
«♦C
—
»
3500-
(/)
c
o
2
3000-
+->
o
0)
0 2500-
Tunability=56%
b
2000
-
1500
-60
-40
0
-20
20
40
60
Electric Fields (kV/cm)
Figure 4.12 The dielectric constant of the PSTO film on NGO (110) at 1.0 MHz at
the room tem perature as a function of applied electric field showing a very large
dielectric tunability and high dielectric constant w ith bias dependence of Lorentz
function.
86
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4.4.3 IDC measurements on the PSTO film on M gO (001) substrate up to 20
GHz
High frequency measurements are perform ed on PSTO film on MgO (001)
substrate as shown in Figure 4.13. The experimental data are well fitted by the
Lorentz function (Figure 4.13(a)). Zero-bias dielectric constants and tunabilities
are extracted from the fitting param eters as shown in Figure 4.13 (b) and (c),
respectively. It is expected that the dielectric constants at zero field decrease from
1865 to 1420 as the m easurem ent frequencies increase from 245 MHz to 20 GHz.
The tunability is as large as 43% at 245 MHz and decreases quickly to about 38%
at about 1 GHz. From 1 GHz to 20 GHz the tunability decreases slowly to about
34%. These excellent data indicate that our PSTO films still work at real
microwave frequency although their dielectric behaviors deteriorate a little at the
higher frequency.
87
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1.95-
0 .2 4 5 GHz
0 .6 9 5 GHz
2 .1 9 5 GHz
4 .9 9 5 GHz
10.04 GHz
14.99 GHz
20 GHz
1.80-
^■ 7
1.65-
Os\ ^
43/ /
■ ///
//
(0
1.50-
v /
tf)
c
o 1.35
O
o
*i—
t5 1.20
©
c/
°/ /*
A/ ,5?
/> '
o
/
©
b
1.05
0 .9 0 -
i
I
-30
-20
——
-10
10
——
20
— I—
30
40
50
B ias (V)
(a)
1.95
o 1.80o
o
X
03 1.65to
c
o
O
o
+■»
c
13
o
Q) 1.50b
1.35
0
10
5
15
20
Frequency (GHz)
(b)
88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.44
0.430.420.41 0.40-
£
0.39-
® 0.380.370.3 6 0.3 5 0.340.33
0
5
10
15
20
Frequency (GHz)
(C)
Figure 4.13 Dielectric m easurements of the PSTO film on MgO (001) at different
frequency at room tem perature by Interdigital capacitor technique, (a) Dielectric
constant vs. bias field showing a very large dielectric tunability and a high
dielectric constant w ith bias dependence of Lorentz function, (b) Zero-bias
dielectric constants of the PSTO film decrease as the measurement frequencies increase,
(c) Frequency-dependence of tunability of the PSTO film.
89
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Chapter 5
Strain effects on the dielectric properties of
PSTO thin films
5.1 Anisotropic in-plane strain and dielectric properties in PSTO thin film s on
the orthorhombic NG O substrate126
As m entioned in section 3.3 the stress in a perovskite oxide due to the
lattice mismatch is often as high as GPa order. This stress has some im portant
effects on the dielectric constant and tunability as discussed theoretically in
section 2.2. Recent experimental studies127'128'129'130'131'132'19'21'22 have shown that
internal stresses strongly affect the dielectric properties of the ferroelectric thin
films on various substrates. Anisotropic in-plane strain can be induced in
(Pb,Sr)Ti0 3 thin film by using orthorhombic NGO (110) as a substrate. The high
resolution x-ray diffraction measurements have been performed to extract the
lattice con stants o f b o th PSTO film and N G O substrate,
( go,
20 ) scans w ere
performed around the (001), (013), and (103) reflections of PSTO. Figure 5.1(a)
shows the scan around the symmetric reflections of PSTO (001) and NGO (110).
90
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The difference
A go in
go
axis between the highest points of PSTO (001) and NGO
(110) is zero, suggesting that the (001) plane of PSTO is parallel to the (110) plane
of the substrate and has no detectable tilt. The narrow FWHM of PSTO (001)
along both
go
axis and 26 axis, which is comparable with that of the substrate, again
confirms the high crystalline quality of the film. The half difference A# in 26 axis
between the film and the substrate is -0.178°, indicating the larger lattice constant of the
film compared to that of the substrate.
The
( go,
26) scan around the asymmetric reflections of PSTO (013) and
NGO (420) was acquired by
a
glancing exit scan as show n in Figure 5.1(b).
A go
and A6 between the film and the substrate are 0.087° and -0.891°, respectively. With the
same measurement setting but
<f)
rotated 90°, the
( go,
26) scan around the asymmetric
reflections of PSTO (103) and NGO (332) was obtained and are shown in Figure
5.1(c).
A go
and A6 between the film and the substrate are -0.022° and -0.711°,
respectively.
The reciprocal space maps (RSM) are plotted from these three
( go,
26) scans
along in-plane directions PSTO [010] and [100] as shown in Figure 5.2. These
scanning results were simulated with the program and the lattice param eters of the
NGO substrate are extracted as a=0.54248 nm, b=0.54981 nm, and c=0.77060 nm
whereas the lattice param eters of the PSTO film are a=0.39176 nm, b=0.39194 nm,
and c=0.39214 nm. The PSTO film exhibits anisotropic orthorhombic distortion,
which may be caused by orthorhombic compressive stress from the substrate.
91
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Since the exact lattice param eters for the unstrained PSTO film are unavailable, it
is more convenient to take Tetragonality, defined as (c-a)/c along [100] or (c-b)/c
along [010], as a scale to measure the in-plane strain relatively. By definition, the
tetragonalities for the PSTO film are calculated as 0.097% along [100] and 0.051%
along [010], respectively.
The dielectric constants of this PSTO film are m easured along PSTO [100]
and PSTO [010] at 1 MHz and room tem perature, respectively. A significant
difference between these tw o orientations is observed (Figure 5.3). Along PSTO
[100], where the compressive strain is larger, the tunability under the bias field of
50 kV /cm is around 33%. O n the other hand, along PSTO [010], where the in­
plane strain is smaller, the tunability reaches 48%. In addition, the dielectric
constant under zero bias along PSTO [010] (£ ,([0 1 0 ]) = 2034) is about 24%
larger than that along [100] (£,.([100]) = 1634). It is believed that the anisotropic
in-plane dielectric behavior comes from the orthorhombic in-plane strain in the
PSTO film. This result is consistent w ith the discussion in section 2.2. The larger
the compressive strain is, the smaller the dielectric constant and the tunability
are.
92
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250-
NGO(110)
0
\
: NGCK420 )
(b)
: NGCK332 )
-500
-250-
o
500
500
(a)
-1000
-1000
2
-1500
CO -500-
<
>
<xN
PST(001 ) -2000
-2000
-2500
-2500
PST 103)
-750-
PST(013)
-3000
-1000-
-3500
-10 0 0 -5 0 0
0
500 1000
-100 0 -5 0 0
0
500 1000
-1000-500
500 1000
co (arcsec)
Figure 5.1 (go, 29) scans around (a) PSTO (001) and NGO (110), (b) PSTO (013)
and NGO (420), and (c) PSTO (103) and NGO (332).
NGO[110] l PST[0Q1]
. /'... NGO(42Q)
NGO[110] APST[001]
PST(103)
NGO(332)
001
Aw= 0.087°
PST(013)
NGO(110)
NGO(110)
PST(001)
PST(001)
?0M
AO=-0.711°
Au>=- 0.022'
PST[010]
NGOfllO]
PST[100]
►
NGO[001]
( 000 )
(b)
(a)
93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 5.2 Schematic of reciprocal space for diffraction nodes of (a) PSTO (001),
NGO (110), PSTO (013), and NGO (420) and (b) PSTO (001), NGO (110), PSTO
(103), and NGO (332).
2500
along PSTO [010]
Tetragonality = 0.051%
Tunability = 48%
e = 2034
2250
^
2000
H
1750
c
TO
O
o
£
/
■
_
1500
®
aA^
AA
■ a A“
■a a
O
0)
i
\
-x
aa
A
“a
\
'
■
Aa
along PSTO [100]
ASg
Tetragonality = 0.097%
‘^
Tunability = 33%
er = 1634
1250
Q
V
aAaAAaAa ^
AAAg*fi
1000
a a ^
■■■
n—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—r-
750
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
Electric Field (kV/cm)
Figure 5.3 Anisotropic in-plane dielectric properties in the as-grown PSTO film
on the (110) NGO substrate m easured at 1 MHz and room tem perature by the
interdigital technique.
94
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5.2 Effects of post-annealing m ethods on the structural and dielectric
properties of PSTO th in film s133
The post-annealing process has a significant effect on the structural and
dielectric properties of the PSTO film. Both PSTO thin films were deposited on
NGO (110) substrate w ith the same thickness under the same conditions,
including tem perature, oxygen pressure, laser energy and repetition rate. The
only difference is the cooling process after the deposition. The slowly cooled (SC)
sample was annealed for 10 minutes at the deposition tem perature before being
slowly cooled dow n at 1 °C /m in to the room tem perature, while the fast cooled
(FC) sample was cooled dow n to the room tem perature by turning off the
heater's power immediately after the film deposition. Figure 5.4 shows the
symmetric scan pattern along the normal of the PSTO films. The PSTO (002) peak
shifts from 46.316° to 46.267°. Lattice param eters are extracted from high
resolution X-ray diffraction as a=0.39184 nm, b=0.39227 nm, c=0.39172 nm for the
SC sample
(( go,
26) scan are shown in Figure 5.1) and a=0.39176 nm, b=0.39194
nm, c=0.39214 nm for the FC sample
(( go,
26) scan are shown in Figure 5.5),
respectively. These results indicate that both samples exhibit the orthorhombic
distortion as discussed in section 5.1.2. The SC sample is distorted w ith the
anisotropic in-plane tensile strain whereas the FC sample is distorted w ith the
anisotropic in-plane compressive strain. The tetragonalities for the former are
calculated as -0.031% along [100] and -0.140% along [010], and for the latter as
95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.097% along [100] and 0.051% along [010]. The different strain behavior between
the SC sample and the FC sample may be attributed to the different strain
relaxation during the cooling process.
The dielectric behaviors of both samples are m easured along PSTO [100]
and PSTO [010] at 1 MHz and room tem perature, respectively (Figure 5.6(a)). The
anisotropic in-plane dielectric properties are observed in both SC and FC
samples. To correlate the strain w ith the dielectric properties, the dielectric
constant at zero field and the tunability at 50 kV/ cm are extracted from Figure
5.6(a) and then plotted in Figure 5.6(b) and 5.6(c). About a 20% difference in
tunability and a 48% difference in dielectric constant under zero field have been
observed in the SC sample between [010] direction (£,([010]) = 4220,
Tunability([0l0]) = 5 9% )
and
[100]
direction
( s r^XL
j / =2200,
Tunability([100]) = 39% ). O n the other hand, the differences in tunability and
dielectric constant under the zero field for FC sample (£ r ([010]) = 2040,
Tunability([0\0]) = 4 8 % , £r ([100]) = 1630, and Tunability([l00]) = 33% ) are
about 15% and 20%, respectively. Figure 5.6(b) and Figure 5.6(c) show the trend
that the larger the compressive strain is, the smaller the tunability and the
dielectric constant under the zero field are, whereas the larger the tensile strain
is, the larger the tunability and the dielectric constant under the zero field are.
These results are consistent w ith the discussion in section 2.2.
96
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slowly cooled sample
fast cooled sample
ZJ
w
O'
a
m
SZ)
a.
22.5
-//
23.0
r
46.0
—
i—
i—
46.5
i—
47.0
20 (degree)
Figure 5.4 XRD 6-20 scan of the slowly cooled (SC) and fast cooled (FC) samples
--------------
■
2 00- a
-------------- 1-------------
0- b
NGO(110)
■%
-500-
0-
t
-200-
0-
\\
I
-1000-
-
PST(OOI)
-600-
i
-fton
-QUO—
-1500 -
-2000 -
.
PST(103)
-2500-
1
-3000-
-10G0-
1 l 1
500 1000
-2000 -
.
-2500-
PST(013)
-3000 -
-3500 -
■..1..r 1
-1000-500 0
NGO(420)
-1000 -
I
-1500-
20 -400-
-500-
jNGO(332)
-3500 -
h" i i 1
-1000-500
"l >"
' 1 '
0
500 1000
-1000-500
0
500 1000
(o (arcsec)
Figure 5.5
( go,
26) scans for the FC sample around (a) PSTO (001) and NGO (110),
(b) PSTO (013) and NGO (420), and (c) PSTO (103) and NGO (332).
97
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4500•
o
■
□
40003500 H
SC
SC
FC
FC
along
along
along
along
[010]
[100]
[010]
[100]
+mt
S
«
c
3000-
o0
u
2500-
13
2000 -
1
(D
Q
1500-
500-
■"“ bbbbb
bbbi
1000.
~l
T ”
-25
-50
i
T "
25
50
Electric Field (kV/cm)
(a)
4500
SC
SC
FC
FC
4000-
C
-2
(/)
3500-
O
3000-
along
along
along
along
[010]
[100]
[010]
[100]
c
o
2500-
2000-
1500
-0.15
-
0.10
0.00
-0.05
0.05
0.10
Tetragonality (%)
0-0
98
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65
Tetragonality (%)
(c)
Figure 5.6 The dielectric properties of slowly cooled (SC) and fast cooled (FC)
samples m easured at 1 MHz and room tem perature
99
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Chapter 6
Discussion, Open Questions, and Prospective
In this dissertation, the high quality (Pb,Sr)TiC>3 films for the tunable
microwave devices are reported. Their microstructure information and dielectric
properties are sum m arized in the following table.
Table 6.1 Microstructure information and dielectric properties of PSTO film at 1
MHz and room tem perature on various substrates
Tilt
FWHM
0.054°
Tetra.
Er
Tuna.
Loss
-0.11%
48%
0.008
0.018°
- 0.25%
3100
4300
56%
0.01
- 0.140%
4220
59%
-
SC [100] PSTO on
(110) NGO
-0.031%
2200
39%
-
FC [010] PSTO on
(110) NGO
0.051%
2040
48%
—
0.097%
1630
33%
--
-
1420
(20 GHz)
34%
(20 GHz)
-
Substrate
PSTO on (001) LAO
PSTO on (110) NGO
SC [010] PSTO on
(110) NGO
-
0.04°
FC [100] PSTO on
(110) NGO
PSTO on (001) MgO
0.27°
100
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As indicated in the table, The PSTO film that was deposited on the NGO
substrate has the best crystalline quality w ith the smallest FWHM of tilt
distribution, whereas the PSTO film that was deposited on MgO substrate has
the worse crystalline quality w ith the largest FWHM of tilt distribution. These
results are understandable because the PSTO film has the smallest value of lattice
mismatch w ith NGO substrate while the PSTO film has the largest value of
lattice mismatch w ith MgO substrate. The maximal zero-bias dielectric constant
is achieved for -0.25% distorted PSTO film deposited on NGO substrate but with
a little larger dielectric loss tangent than that of the PSTO film on LAO substrate.
It is evident that the most im portant microstructure factor that affects the
dielectric properties of PSTO epitaxial films are the strain type and its strength
regardless of the selected substrates and the FWHM of tilt distribution. For
instance, the dielectric constant of FC PSTO film along [100] in-plane direction is
m uch smaller than that of the PSTO film on LAO substrate though both films
have similar FWHM of tilt distribution.
The PSTO film deposited on MgO substrate exhibit zero-field dielectric
permittivity above 1420 at 20 GHz w ith about 34% tunability and the low
dielectric loss similar to (Ba,Sr)Ti0 3 thin films. These outstanding dielectric
properties indicate that the (Pb,Sr)Ti0 3 film is a very prom ising candidate for a
real microwave device working at room tem perature. To achieve a stable
dielectric behavior and a reliable microwave device, the tem perature dependence
101
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of dielectric properties of PSTO film should be checked carefully. A small
tem perature coefficient of the dielectric properties are required as discussed in
section 2.4. The compositionally134 or dopedly135 graded (Pb,Sr)TiC>3 films are
suggested to obtain a broad and flat profile of the dielectric permittivity versus
tem perature w ithout decreasing the dielectric permittivity. Similar to the
(Ba,Sr)Ti0 3 system, another promising technique to im prove the microwave
dielectric properties, such as low loss, large tunability, high breakdow n field and
also small tem perature coefficient, is to introduce some acceptor dopants into the
(Pb,Sr)Ti0 3 films. The m ost common acceptor dopants that were proved to work
in (Ba,Sr)TiC>3 films are those variable valence elements such as Fe, Co, Mn, Ni,
W, and Mg135-136-137-138'139. These acceptors occupy the Ti sites of the (Ba,Sr)Ti03
and can prevent the reduction of Ti4+ to Ti3+ by neutralizing the donor action of
oxygen vacancies as well as broaden Curie tem perature range.
Reliability is an old issue for ferroelectric materials. W hether fatigue,
aging, imprint, and time dependent dielectric breakdow n etc. have a detrimental
effect on the performance of the microwave device is unclear. These basic
phenomena of ferroelectric materials have to be considered in the design of the
complicated microwave devices w ith long-term stable performance.
C urrently,
th e
system atic
research
on
the
fu n d a m en ta l
p h ysical
mechanisms of these dielectric properties is absent because of the coexistence of
the various dielectric sources in the ferroelectric films. Although some
102
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phenomenological theories20-21'22 are available for explaining the strain effects on
dielectric properties, they are obviously not applicable for the dynamic dielectric
behaviors in high frequency and ignore the microscopic mechanism. The
dynamic theory111213-14 based on the soft ferroelectric mode is also im proper for
the ferroelectric solid solution w ith obvious dielectric relaxation. We tried a
phenomenological Taylor expansion of the relaxation time as a function of the
dielectric field to explain the Lorentz dependence of dielectric constant in section
2.2, but further numerical fitting and the inherent microscopic mechanisms for
this expansion are needed.
Finally, the fundam ental physical mechanism for the observed confliction
between the large dielectric tunability and low dielectric loss is unclear. The
research in this direction is very helpful to clue us to achieve a maximal dielectric
tunability and a minimal insertion loss of the microwave devices74.
103
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References
1J. C. Slater, "The lorentz correction in barium titanate," Phys. Rev. 78, 748 (1950).
2 John H. Barrett, "Dielectric constant in perovskite type crystals," Phys. Rev. 86,
118 (1952).
3 B. T. Matthias, "N ew ferroelectric crystals," Phys. Rev. 75,1771 (1949).
4 B. T. Matthias, and J. P. Remeika, "Ferroelectricity in the Ilmenite structure,"
Phys. Rev. 76,1886 (1949).
5 Gen Shirane, Sadao Hoshino, and Kazuo Suzuki, "X-ray study of the phase
transition in Lead Titanate," Phys. Rev. 80,1105 (1950).
6 F. W. Van Keuls, R. R. Romanofsky, D. Y. Bohman, M. D. Winters, F. A.
Miranda, C. H. Mueller, R. E. Treece, T. V. Rivkin, and D. Galt, "(YBa2 Cu 3 0 7 -5 ,
Au)/SrTi 0 3 /L aA I 0 3 thin film conductor/ferroelectric coupled microstripline
phase shifters for phased array applications," Appl. Phys. Lett. 71, 3075 (1997).
7 R. R. Romanofsky, F. W. Van Keuls, and F. A. Miranda, "A cryogenic GaAs
PF1EMT/Ferroelectric Ku-Band Tunable Oscillator," Journal.de Physique IV, 8,
171 (1998).
8 A. T. Findikoglu, Q. X. Jia, and X.D. Wu, "Tunable and adaptive bandpass filter
using a nonlinear dielectric thin film of SrTiOs," Appl. Phys. Lett. 68,1651
(1996).
104
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9 "1964 Microwave ferroelectric phase shifters and switches," US Army Final
Report Contract DA 36-039-AMC-02340(E), US Army Electronics Laboratories,
Fort Monmouth, NJ, USA.
10 Rupprecht, G. and Bell, P. O. "Microwave losses in strontium titanate above
the phase transition," Phys. Rev. 123,1915 (1962).
11 O. G. Bendik, "Model of the ferroelectric mode," Soviet Physics - Solid State 14,
849 (1972).
12 O. G. Vendik, "Dielectric nonlinearity of the displacive ferroelectrics at UHF,"
Ferroelectrics 12, 85 (1976).
13 Orest G. Vendik, "M odeling the dielectric response of incipient ferroelectrics,"
J. Appl. Phys. 82,4475 (1997).
14 Orest G. Vendik, Leon T. Ter-Martirosyan and Svetlana P. Zubko, "Microwave
losses in incipient ferroelectrics as functions of the tem perature and the
biasing field," J. Appl. Phys. 84,993 (1998).
15 H. N. Al-Shareef, D. Dimos, M. V. Raymond and R.W. Schwartz, "Tunability
and calculation of the Dielectric constant of capacitor Structures with
interdigital electrodes," Journal of Electroceramics 1:2,145 (1997).
16 C. L. Chen, H. H. Feng, Z. Zhang, A. Brazdeikis, Z. J. Huang, W. K. Chu, C. W.
Chu, F. A. Miranda, F. W. Van Keuls, R. R. Romanofsky, and Y. Liou,
"Epitaxial ferroelectric Bao.sSro.sTiCb thin films for room-temperature tunable
element applications," Appl. Phys. Lett. 75,412 (1999).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
17 K. R. Carroll, J. M. Pond, D. B. Chrisey, J. S. Horwitz, R. E. Leuchtner, and K. S.
Grabowski, "Microwave m easurem ent of the dielectric constant of
Sro.5Bao.5Ti03 ferroelectric thin films," Appl. Phys. Lett. 62,1845 (1993).
18 Q. X. Jia, J. R. Groves, P. Arendt, Y. Fan, A. T. Findikoglu, S. R. Foltyn, H. Jiang,
and F. A. Miranda, "Integration of nonlinear dielectric barium strontium
titanate w ith polycrystalline yttrium iron garnet," Appl. Phys. Lett. 74,1564
(1999).
19 Z.-G. Ban and S. P. Alpay, "Optimization of the tunability of barium strontium
titanate films via Epitaxial stresses," J. Appl. Phys. 93,504 (2003).
20 Wontae Chang and Charles M. Gilmore, "Influence of strain on microwave
dielectric properties of (Ba, Sr) T1O 3 thin films," J. Appl. Phys, 87, 3044 (2000).
21 C. L. Canedy, Hao Li, and S. P. Alpay, "Dielectric properties in heteroepitaxial
Bao.6Sro.4Ti03 thin films: Effect of internal stresses and dislocation-type
defects," Appl. Phys. Lett. 77,1695 (2000).
22 Flao Li, A. L. Roytburd, and S. P. Alpay, "Dependence of dielectric properties
on internal stresses in epitaxial barium strontium titanate films," Appl. Phys.
Lett. 78,2354 (2001).
28 C. L. Chen, J. Shen, S. Y. Chen, G. P. Luo, C. W. Chu, F. A. Miranda, F. W. Van
Keuls, J. C. Jiang, E. I. Meletis, and H. Y. Chang, "Epitaxial grow th of dielectric
Bao.6Sro.4TiC>3 thin film on MgO for room tem perature microwave phase
shifters," Appl. Phys. Lett. 78, 652 (2001).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
24 Y. Somiya, A. S. Bhalla, and L. E. Cross, "Study of (Sr,Pb)Ti0 3 ceramics on
dielectric and physical properties," The International Journal of Inorganic
Materials 3, 709 (2001).
25 Xianran Xing, Jun Chen, Jinxia Deng, and Guirong Liu, "Solid solution PbixSrxTiC) 3 and its therm al expansion," Journal of Alloys and Compounds 360, 286
(2003).
26 M. Jain, S. B. Majumder, R. Guo, A. S. Bhalla, and R. S. Katiyar, "Synthesis and
characterization of lead strontium titanate thin films by sol-gel technique,"
Materials Letters 56, 692 (2002).
27 M. Jain, N. K. Karan, R. S. Katiyar, A. S. Bhalla, F. A. M iranda, and F. W. Van
Keuls, "Pbo.3 Sro.7 TiC>3 thin films for high-frequency phase shifter applications,"
Appl. Phys. Lett. 85,275 (2004).
28 Tomoaki Karaki, Jing Du, Tadashi Fujii, and Masatoshi Adachi, "Electrical
properties of epitaxial (Pb,Sr)TiC>3 thin films prepared by RF m agnetron
sputtering," Japanese Journal of Applied Physics 41,6761 (2002).
291. S. Zheludev, "Ferroelectricity and symmetry," Solid State Physics 26,429
(1971).
30 R.C. Smith and C.L. Horn, "Domain wall theory for ferroelectric hysteresis,"
Journal of Intelligent Material Systems and Structures 10,195-213 (1999).
31 W. L. Zhong, "Physics of Ferroelectricity (in Chinese)," p. 294 (2000).
107
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32 Radiant Technologies INC., "RT6000HVS system operating manual," p. 21-11,
(1994).
33 Julie K. Raye and Ralph C. Smith, "A tem perature-Dependent hysteresis model
for relaxor ferroelectric compounds," SAMSI Technical Reports, #2004-5 (2004).
34 S. L. Miller, R. D. Nasby, and J. R. Schwank, "Device modeling of ferroelectric
capacitors," J. Appl. Phys. 68, 6463 (1990).
35 S. L. Miller, J. R. Schwank, and R. D. Nasby, "Modeling ferroelectric capacitor
switching with asymmetric nonperiodic input signals and arbitrary initial
conditions," J. Appl. Phys. 70,2849 (1991).
36 Ali Sheikholeslami and P. Glenn Gilak, "A survey of behavioral modeling of
ferroelectric capacitors," IEEE Transactions on Ultrasonics, Ferroelectrics, and
Frequency Control 44, 917 (1997).
37 Ali Sheikholeslami and P. Glenn Gilak, "Transient modeling of ferroelectric
capacitors for nonvolatile memories," IEEE Transactions on Ultrasonics,
Ferroelectrics, and Frequency Control 43,450 (1996).
38 Douglas E. Dunn, "A ferroelectric capacitor macromodel and param eterization
algorithm for spice simulation," IEEE Transactions on Ultrasonics, Ferroelectrics,
and Frequency Control 41, 360 (1994).
39 D. B. A. Rep, and M. W. J. Prins, "Equivalent-circuit m odeling of ferroelectric
switching devices," J. Appl. Phys. 85,7923 (1999).
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40 S. Sivasubramanian, A. Widom, and Y. Srivastava, "Equivalent circuit and
simulations for Landau-Khalatnikov model of ferroelectric hysteresis/' IEEE
Transactions on Ultrasonics, Ferroelectrics and Frequency Control 50, 950 (2003).
41 G. Le G rand de Mercey and O. Kowarik, "Relaxation model for ferroelectric
capacitors," ESSDERC 2001 (2001).
42 C. Kuhn, H. Honigschmid and O. Kowarik, "A new physical model for the
relaxation in ferroelectrics," ESSDERC 2000,164 (2000).
43 L. Pardo, J. Mendiola, and C. Alemany, "Theoretical treatm ent of ferroelectric
composites using Monte Carlo calculations," J. Appl. Phys. 64,5092 (1988).
44 D. Hughes and J. T. Wen, "Preisach m odeling of piezoceramic and shape
memory alloy hysteresis," Smart Materials and Structures 6,287 (1997).
45 F. Preisach, "Uber die magnetische nachwirkung," Zeitschrift fur Physik 94, 277302 (1935).
46 K. Sadeghipour, R. Salomon and S. Neogi, "Development of a novel
electrochemically active membrane and sm art material based vibration
sensor/dam per," Smart Materials and Structures 1,172 (1992).
47 M. J. Lancaster, J. Powell and A. Porch, "Thin-film ferroelectric microwave
devices," Supercond. Sci. Technol. 11,1323 (1998).
48 S. Tinte, M. G. Stachiotti, and S.R. Phillpot, "Ferroelectric properties of BaxSnxTi0 3 solid solutions obtained by molecular dynamics simulation," Journal of
Physics: Condensed Matter 16,3495 (2004).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49 K. A. Muller, and H. Burkard, "SrTi0 3 : An intrinsic quantum paraelectric
below 4 K," Phys. Rev. B 19,3593 (1979).
50 Chen Ang, A. S. Bhalla, and L. E. Cross, "Dielectric behavior of paraelectric
KTaCb, CaTi0 3 ,and (Lm/2 N ai/ 2 )Ti0 3 under a dc electric field," Phys. Rev. B 64,
184104 (2001).
51 R. M artonak and E. Tosatti, "Path-integral monte carlo study of a model twodimensional quantum paraelectric," Phys. Rev. B 49,12596 (1994).
52 T. Schneider, H. Beck, and E. Stoll, "Q uantum effects in an n-component vector
model for structural phase transitions," Phys. Rev. B 13,1123 (1976).
53 W. Zhang and David Vandebilt, "Effect of quantum fluctuations on structural
phase transitions in SrTiCb and BaTiCb," Phys. Rev. B 53, 5047 (1996).
54 R. Roussev and A. J. Millis, "Theory of the quantum paraelectric-ferroelectric
transition," Phys. Rev. B 67, 014105 (2003).
55 Ralph Smith, " Smart materials: model development and control design," (to be
published by SIAM in Jannuary 2005).
56 Ronald E. Cohen, "Origin of ferroelectricity in perovskite oxides," Nature 358,
136 (1992).
57 Yoshihiro Kuroiwa, Shinobu Aoyagi, and Akikatsu Sawada, "Evidence for PbO covalency in tetragonal PbTiOs," Phys. Rev. Lett. 87,217601 (2001).
110
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
58 Shou-Yi Kuo, Chung-Ting Li, and Wen-feng Hsieh, "Decreasing giant splitting
of longitudinal and transverse optical phonons in PbxSri-xTiQ? due to Pb
covalency," Appl. Phys. Lett. 81,3019 (2002).
59 W. Zhong, R. D. King-Smith, and David Vanderbilt, "Giant LO-TO splittings in
perovskite ferroelectric," Phys. Rev. Lett. 72,3618 (1994).
60 B. K. Vainshtein, V. M. Fridkin and V. L. Indenbom, "Structure of Crystals
(Modern Crystallography 2)," Springer-Verlag (1995).
61 h t t p : / / ww w.fact-index.com /p / pe/periodic_table
standard_.htm l
62 R. Comes, M. Lambert, and A. Guinier, "The chain structure of BaTiCb and
KNbCb," Solid State Communications 6, 715 (1968).
63 K. H. Ehses, H. Bock, and K. Fischer, "The tem perature dependence of the
Debye-Waller-factor in barium titanate," Ferroelectrics 37,507 (1981).
64 K. Itoh, L. Z. Zeng, E. Nakam ura, and N. Mishima, "Crystal structure of
BaTiCb in the cubic phase," Ferroelectrics 63, 29 (1985).
65 Chen Jun, Fan Chan-gao, Li Qi, and Feng Duan, "Transmission electron
microscope studies of para-ferroelectric phase transitions in BaTiC>3 and
KNbCb," Journal of Physics C: Solid State Phys. 21, 2255 (1988).
66 R. J. Nelmes, R. O. Piltz, W. F. Kuhs, Z. Tun, and R. Restori, "Oder-disorder
behavior in the transition of PbTiCh," Ferroelectrics 108,165 (1990).
67 N. Sicron, B. Ravel, Y. Yacoby, E. A. Atern, F. Dogan, and J. J. Rehr, "N ature of
the ferroelectric phase transition in PbTiCb," Phys. Rev. B 50,13168 (1994).
Ill
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
68 M. D. Fontana, H. Idriss, G. E. Kugel, and K. Wojcik, "Raman spectrum in
PbTiOs re-examined: dynamics of the soft phonon and the central peak,"
Journal of Physics: Condensed Matter 3, 8695 (1991).
69 M. E. Lines, and A. M. Glass, "Principles and applications offerroelectrics and
related materials," Oxford University Press (1977).
70 A. F. Devonshire, "Theory of Barium Titanate-Part I," Phil. Mag. 40,1040
(1949).
71 A. F. Devonshire, "Theory of Barium Titanate-Part II," Phil. Mag. 42,1065
(1951).
72 A. F. Devonshire, "Theory of ferroelectrics," Advances in Physics 3,85 (1954).
73 Clemens J. Forst, Christopher R. Ashman, Karlheinz Schwarz and Peter E.
Blochi, "The interface between silicon and a high-K oxide," Nature 427, 53
(2004).
74 Xinhua Zhu, Jianmin Zhu, Shunhua Zhou, Zhiguo Liu, Naiben Ming,
Shengguo Lu, Helen Lai-wah Chan and Chung-loong Choy, "Recent progress
of (Ba,Sr)Ti0 3 thin films for tunable m icrowave devices," Journal of Electronic
Materials 32,1125 (2003).
75 S. F. Edwards and P. W. Anderson, "Theory of spin glasses," Journal of Physics
F: Metal Physics 5, 965 (1975).
76 K. Binder and A. P. Young, "Spin glasses: Experimental facts, theoretical
concepts, and open questions," Reviews of Modern Physics 58,801 (1986).
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77 B. E. Vugmeister and M. D. Glinchuk, "Dipole glass and ferroelectricity in
random-site electric dipole system s/' Reviews of Modem Physics 62, 993 (1990).
78 U. T. Hochli, K. Knorr and A. Loidl, "Orientational glasses," Advances in
Physics 39,405 (1990).
79 V. V. Lemanov, E. P. Smirnova, P. P. Symikov and E. A. Tarakanov, "Phase
transitions and glasslike behavior in Sri-xBaxTi0 3 ," Phys. Rev. B 54, 3151 (1996).
80 V. V. Lemanov, E. P. Smirnova and E. A. Tarakanov, "Ferroelectric properties
of SrTi0 3 -PbTi0 3 solid solutions," Phys. Solid State 39,628 (1997).
81 Gerald Burns and B.A. Scott, "'D irty' Displacive Ferroelectrics," Solid State
Communications 13,417 (1973).
82 Gerald Burns and B.A. Scott, "Index of refraction 'Dirty' displacive
ferroelectrics," Solid State Communications 13,423 (1973).
83 Gerald Burns, "Dirty displacive ferroelectrics," Phys. Rev. B 13, 215 (1975).
84 Landolt-Bornstein, " Numerical Data and Functional Relationships in Science and
Technology," Vol. 16(a), edited by K.-H. Hellwege and A. M. Hellwege, p.418
(1981).
85 Shoichiro Nomura, and Shozo Sawada, “Dielectric properties of Lead-Strontium
Titanate,” Journal of the Physical Society of Japan 10, 108 (1955).
86 H ow ard M. Smith, and A. F. Turner, "Vacuum deposited thin films using a
ruby laser," Appl. Opt. 4,147 (1965).
113
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87 D. Dijkamp, T. Venkatesan, X. D. Wu, S. A. Shaheen, N. Jisrawi, Y. H. Min-Lee,
W. L. Mclean, M. Croft, "Preparation of Y-Ba-Cu oxide superconductor thin
films using pulsed laser evaporation from high Tc bulk material," Appl. Phys.
Lett. 51,619 (1987).
88 Rajiv K. Singh and J. Narayan, "Pulsed-laser evaporation technique for
deposition of thin films: Physics and theoretical model," Phys. Rev. B 41, 8843
(1990).
89 R. F. Wood, and G. E. Giles, "Macroscopic theory of pulsed-laser annealing. I.
Thermal transport and melting," Phys. Rev. B 23, 2923 (1980).
90 M. Aden, E. W. Kreutz and A. Voss, "Laser-induced plasma formation during
pulsed laser deposition," Journal of Physics D: Applied Physics 26,1545 (1993).
91 M artin Von Allmen, " Laser-beam interactions with materials-Physical principles and
applications," Springer-Verlag (1987).
92 A. A. Grinberg, R. F. Mckhtiev, S. M. Ryvkin, V. M. Salmanov, and I. D.
Yaroshetskii, "Absorption of laser radiation and damage in semiconductors,"
Soviet Physics - Solid State 9,1085 (1967)
93 J. Hermann, A. L. Thomann, C. Boulmer-Leborgne, and B. Dubreuil etc.,
"Plasma diagnostics in pulsed laser TiN layer deposition," J. Appl. Phys. 77,
2928 (1994).
94 C. Ratsch and J. A. Venables, "Nucleation theory and the early stages of thin
film growth," Journal of Vacuum Science and Technology 21, S96 (2003).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
951. Markov and R. Kaischew, "Influence of supersaturation on the mode of
crystallization on crystalline substrate," Thin Solid Films 32,163 (1976).
96 K. Reichelt, "Nucleation and grow th of thin films," Vacuum 38,1083 (1988).
97 Milton Ohring, " Materials science of thin films-Deposition and Structure,"
Academic Press, second edition (2002).
98 Ludmila Eckertova, "Physics of thin films," Plenum Press, second revised
edition (1986).
99 S. Metev and K. Meteva, "Nucleation and growth of laser-plasma deposited
thin films," Applied Surface Science 43, 402 (1989).
100 Douglas B. Chrisey and Graham K. Hubler, " Pulsed laser deposition of thin
films," John Wiley & Sons Inc. (1994).
101 A. Gupta, B. W. Hussey, A. Kussmaul and A. Segmuller, "Defect formation
caused by a transient decrease in the ambient oxygen concentration during
growth of YBa2 Cu 3 0 7 - 5 films," Appl. Phys. Lett. 57,2365 (1990).
102 R. W. Vook, "Structure and grow th of thin films," International Metals Reviews
TJ, 209 (1982).
103 Y. Ikuhara, P. Pirouz, A. H. Heuer, S. Yadavalli, and C. P. Flynn, "Structure of
V -A I2O 3
interfaces grow n by molecular beam epitaxy," Phil. Mag. A 70, 75
(1994).
104 A. Tram pert and K. H. Ploog, "Heteroepitaxy of large-misfit systems: Role of
coincidence lattice," Cryst. Res. Technol. 35, 793 (2000).
115
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105 D. Hull and D. J. Bacon, " Introduction to dislocations," Pergam on Press, third
edition (1984)
106 J. H. Van der Merwe, "Crystal interfaces. Part I. Semi-Infinite Crystals," J.
Appl. Phys. 34,117 (1963).
107 J. H. Van der Merwe, "Crystal interfaces. Part II. Finite Overgrowths," J. Appl.
Phys. 34,123 (1963).
108 D. J. Dunstan, S. Young and R. H. Dixon, "Geometrical theory of critical
thickness and relaxation in strained-layer growth," J. Appl. Phys. 70, 3038
(1991).
109 J. W. Matthews, "Defects associated w ith the accommodation of misfit
between crystals," Journal of Vacuum Science and Technology 12,126 (1975).
110 F. C. Frank and J. H. van der Merwe, "One-dimensional disclocations. I. Static
theory," Proc. Roy. Soc. A. 198,205 (1949).
111 F. C. Frank and J. H. van der Merwe, "One-dimensional disclocations. II.
Misfitting monolayers and oriented overgrowth," Proc. Roy. Soc. A. 198,216
(1949).
112 J. W. M atthews and A. E. Bkakeslee, "Defects in epitaxial multilayers I. Misfit
dislocations," Journal of Crystal Growth 27,118 (1974).
113 R. People and J. C. Bean, "Calculation of critical layer thickness versus lattice
mismatch for GexSii-x/S i strained-layer heterostructures," Appl. Phys. Lett. 47,
322 (1985).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114 J. R. Willis and Suresh C. Jain, "The energy of an array of dislocations:
implications for strain relaxation in semiconductor heterostructures/' Phil.
Mag. A 62,115 (1990).
115 J. W. Matthews, S. Mader, and T. B. Light, "Accommodation of misfit across
the interface between crystals of semiconducting elements or compounds," /.
Appl. Phys. 41,3800 (1970).
116 J. S. Speck and W. Pompe, "Domain configurations due to m ultiple misfit
relaxation mechanisms in epitaxial ferroelectric thin films. I. Theory," /. Appl.
Phys. 76,466 (1994).
117 J. S. Speck, A. Seifert, W. Pompe and R. Ramesh, "Domain configurations due
to multiple misfit relaxation mechanisms in epitaxial ferroelectric thin films. II.
Experimental verification and implications," }. Appl. Phys. 76,477 (1994).
118 J. S. Speck, A. C. Daykin, A. Seifert, A. E. Romanov and W. Pompe, "Domain
configurations due to multiple misfit relaxation mechanisms in epitaxial
ferroelectric thin films. III. Interfacial defects and dom ain misorientations," /.
Appl. Phys. 78,1696 (1995).
119 Billy W. Sloope and Calvin O. Tiller, "Formation conditions and structure of
Ge films deposited on polished (111) CaF2 substrates in an ultrahigh-vacuum
system," J. Appl. Phys. 36,3174 (1965).
120 X. Chen, Y. Lin, S. W. Liu, C. L. Chen, J. C. Jiang, E. I. Meletis, Q. X. Jia, and A.
Bhalla, "Ferroelectric (Pb,Sr)TiC>3 thin films w ith extra large dielectric
117
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tunability: a good candidate for room tem perature tunable microwave
elements," (submitted).
121 S. W. Liu, Y. Lin, J. Weaver, W. Donner, X. Chen, C. L. Chen, H. D. Lee, W. K.
Chu, J. C. Jiang, E. I. Meletis, and A. Bhalla, "H igh dielectric tunability
ferroelectric (Pb,Sr)Ti0 3 thin films for room tem perature tunable microwave
devices," Proceedings of 106thAnnual Meeting and Explosion of the American
Ceramic Society (in press).
122 S. S. Gevorgian, D. I. Kaparkov and O. G. Vendik, "Electrically controlled
HTSC/ferroelectric coplanar waveguide," IEE. Proc. - Microw. Antennas
Propag. 141,501 (1994).
123 S. Gevorgian, E. Carlsson, S. Rudner, L. D. W ernlund, X. Wang and U.
Helmersson, "Modelling of thin-film H TS/ ferroelectric Inter digital
capacitors," IEE. Proc.-Microw. Antennas Propag. 143,397 (1996).
124 Spartak S. Gevorgian, Peter L. J. Linner and Erik Ludvig Kollberg, "CAD
Models for M ultilayered substrate Interdigital capacitors," IEEE Transactions
on Microwave Theory and Techniques 44, 896 (1996).
125 S. W. Liu, Y. Lin, J. Weaver, W. Donner, X. Chen, C. L. Chen, J. C. Jiang, E. I.
Meletis, and A. Bhalla, "High-dielectric-tunability of ferroelectric (Pb,Sr)Ti0 3
thin films," Appl. Phys. Lett. 85,3202 (2004).
118
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
126 Y. Lin, X. Chen, S. W. Liu, C. L. Chen, Jang-Sik Lee, Y. Li, Q. X. Jia, and A.
Bhalla, "Anisotropic in-plane strains and dielectric properties in (Pb.Sr)Ti0 3
thin films on NdGaCb substrates," Appl. Phys. Lett. 84,577 (2004).
127 A. R. James, and X. X. Xi, "Effects of buffer layer thickness and strain on the
dielectric properties of epitaxial SrTiCb thin films," J. Appl. Phys. 92, 6149
(2002).
128 Wontae Chang, Steven W. Kirchoefer, Jeffrey M. Pond, James S. Horwitz, and
Louise Sengupia, "Strain-relieved Bao.6Sro.4Ti03 thin films for tunable
microwave applications," J. Appl. Phys. 92,1528 (2002).
129 G-F.
Huang, and S. Berger, "Combined effect of thickness and stress on
ferroelectric behavior of thin BaTiC>3 films," ]. Appl. Phys. 93, 2855 (2003).
130 S. Hyun, and K. Char, "Effects of strain on the dielectric properties of tunable
dielectric SrTiCb thin films," Appl. Phys. Lett. 79, 254 (2001).
131C. M. Carlson, T. V. Rivkin, P. A. Parilla, J. D. Perkins, D. S. Ginley, A. B.
Kozyrev, V. N. Oshadchy, and A. S. Pavlov, "Large dielectric constant
(G/Go>6000) Bao.4 Sro.6 Ti0 3 thin films," Appl. Phys. Lett. 76,1920 (2000).
132 George A. Rossttti, Jr. and L. Eric Cross, and Keiko Kushida, "Stress induced
shift of the Curie point in epitaxial PbTiCb thin films," Appl. Phys. Lett. 59, 2524
(1991).
119
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
133 Y. Lin, X. Chen, S. W. Liu, C. L. Chen, Jang-Sik Lee, Y. Li, and Q. X. Jia,
"Epitaxial nature and dielectric properties of (Pb,Sr)Ti0 3 thin films on
NaGaCh substrates," (submitted)
134 Xinhua Zhu, Nui Chong, Helen Lai-Wah Chan, Chung-Loong Choy, KinH ung Wong, Zhiguo Liu, and Naiben Ming, "Epitaxial grow th and planar
dielectric properties of compositionally graded (Bai-xSrx)Ti0 3 thin films
prepared by pulsed-laser deposition," Appl. Phys. Lett. 80,3376 (2003).
135 M. Jain, S. B. Majumder, R. S. Katiyar, F. A. Miranda, and F. W. Van Keuls,
"Im provem ent in electrical characteristics of graded manganese doped barium
strontium titanate thin films," Appl. Phys. Lett. 82,1911 (2003).
136 Wontae Chang, Louise Sengupta, "MgO-mixed Bao.6 Sro.4 Ti0 3 bulk ceramics
and thin filmsfor tunable microwaveapplications," ]. Appl. Phys. 92, 3941
(2002).
137 Kun Ho Ahn and Sunggi Baik, Sang Sub Kim, "Significant suppression of
leakage current in (Ba, Sr) TiCb thin films by Ni or Mn doping," J. Appl. Phys.
92,2651 (2002).
138 P. C. Joshi and M. W. Cole, "M g-doped Bao.6Sro.4 Ti0 3 thin films for tunable
microwave applications," Appl. Phys. Lett. 77, 289 (2000).
139 M. W. Cole, W. D. Nothwang, C. Hubbard, E. Ngo, and M. Ervin, "Low
dielectric loss and enhanced tunability of Bao.6 Sro.4 Ti0 3 based thin films via
120
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
material compositional design and optimized film processing m ethods," J.
Appl. Phys. 93, 9218 (2003).
121
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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