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Dielectric functions and electronic band structure
of lead zirconate titanate thin lms
Hosun Lee
Virginia Commonwealth University
Youn Seon Kang
Virginia Commonwealth University
Sang-Jun Cho
Virginia Commonwealth University
See next page for additional authors
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Dielectric functions and electronic band structure of lead zirconate titanate
thin films
Hosun Lee,
a兲
Youn Seon Kang, Sang-Jun Cho, Bo Xiao, and Hadis Morkoç
Department of Electrical Engineering, Virginia Commonwealth University, 601 W. Main Street, Richmond,
Virginia 23284
Tae Dong Kang and Ghil Soo Lee
Department of Physics, Kyung Hee University, Suwon 449-701, South Korea
Jingbo Li and Su-Huai Wei
National Renewable Energy Laboratory, Golden, Colorado 80401
P. G. Snyder
Department of Electrical Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588
J. T. Evans
Radiant Technology Inc., 2021 Girard Blvd, SE3. Albuquerque, New Mexico 87106
共Received 2 June 2005; accepted 3 October 2005; published online 9 November 2005兲
We measure pseudodielectric functions in the visible-deep ultraviolet spectral range of
Pb共Zr
x
Ti
1−x
兲O
3
共x =0.2,0.56,0.82兲共PZT兲,Pb
0.98
Nb
0.04
共Zr
0.2
Ti
0.8
兲
0.96
O
3
,Pb
0.91
La
0.09
共Zr
0.65
Ti
0.35
兲
0.98
O
3
, and Pb
0.85
La
0.15
Ti
0.96
O
3
films grown on platinized silicon substrates using a
sol-gel method and on 共0001兲 sapphire using a radio-frequency sputtering method. Using a
parametric optical constant model, we estimate the dielectric functions 共
⑀
兲 of the perovskite oxide
thin films. Taking the second derivative of the fitted layer dielectric functions and using the standard
critical-point model, we determine the parameters of the critical points. In the second derivative
spectra, the lowest band-gap energy peak near 4 eV is fitted as a double peak for annealed PZTs due
to the perovskite phase. As-grown PZTs have mainly pyrochlore phase and the lowest band-gap
peak is fitted as a single peak. We also examine the effect of dopants La and Nb, which substitute
at Pb and Zr 共Ti兲 sites, respectively. We found three band gaps E
a
共⬃3.9 eV兲, E
b
共⬃4.5 eV兲, and
E
c
共⬃6.5 eV兲 in the order of increasing energy. The E
a
and E
b
band-gap energies were not sensitive
to Zr composition. We discuss the change of critical-point parameters for PZTs in comparison to the
band-structure calculations based on local-density approximation. The near constancy of the lowest
band-gap energy independent of Zr composition is consistent with the band-structure
calculations. © 2005 American Institute of Physics. 关DOI: 10.1063/1.2128043兴
I. INTRODUCTION
Perovskite oxide materials have very wide applications:
various sensors, nonvolatile and dynamic random access
memories, tunable capacitors for high-frequency microwave
applications, electro-optic modulators, infrared detectors,
and microelectromechanical systems.
1,2
Hybridized semicon-
ductors including perovskite oxide materials are being inves-
tigated intensively.
3
Among various perovskite oxide materi-
als, Pb共Zr
x
Ti
1−x
兲O
3
共PZT兲 is the most widely
commercialized due to its excellent ferroelectric and piezo-
electric material properties notwithstanding fatigue.
4
The in-
terface degradation between PZT layer and metal electrodes
is known to be the main cause for fatigue of PZT.
5
Other
lead-free perovskite oxide materials such as Ba
1−x
Sr
x
TiO
3
,
SrBi
2
Ta
2
O
9
, and Bi
3.25
La
0.75
Ti
3
O
12
are being investigated as
alternatives because of health and environmental concerns as
well as fatigue-free properties.
Electrical properties of PZTs have been investigated
intensively.
5
However, optical properties of PZT are rela-
tively less investigated.
6,7
Spectroscopic ellipsometry can
measure dielectric functions 共
⑀
兲 of ferroelectric thin films
and subsequently can provide electronic band-structure infor-
mation as well as thickness and microstructure. Several el-
lipsometric investigations have been reported.
7,8
However,
their spectral range was limited to the region below and near
the lowest band-gap region, that is, between 1.5 and 5 eV.
7,8
Ellipsometric studies have not been done which cover the
near-infrared 共NIR兲 to deep ultraviolet 共DUV兲 spectral re-
gion.
PZT-based devices show excellent ferroelectric proper-
ties such as high remanent polarization and low coercive
electric field. Semiconducting properties of PZT perovskite
oxides have also been reported by using current-voltage
measurements by Pintile et al.
9
and Boerasu et al.
10
They
noted that a large concentration of defects can act as trapping
centers and that Schottky barriers can be present at contacts
instead.
In order to obtain superior ferroelectric and piezoelectric
properties, perovskite oxides 共ABO
3
兲 must be annealed after
deposition to increase the perovskite phase. However, the
a兲
Permanent address: Department of Physics, Kyung Hee University, Suwon
449-701, South Korea, on sabbatical leave; electronic mail:
hlee@khu.ac.kr
JOURNAL OF APPLIED PHYSICS 98, 094108 共2005兲
0021-8979/2005/98共9兲/094108/10/$22.50 © 2005 American Institute of Physics98, 094108-1
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perovskite phase may not result because of the incomplete
transformation from pyrochlore phase 共A
2
B
2
O
7
兲, which lacks
ferro- and piezoelectric properties.
11
The properties of PZT films can be modified optically
and electrically by the addition of foreign ions, for example,
La and Nb, substituting for host atoms 关Pb, Zr 共Ti兲兴. The
addition of donor dopants reduces the concentration of in-
trinsic oxygen vacancies caused by PbO evaporation during
the growth and annealing of PZT thin films. Electrons from
donors compensate holes from acceptor impurities originat-
ing from Pb vacancies. The transparent
Pb
1−x
La
x
共Zr
y
Ti
1−y
兲
1−0.25x
O
3
共PLZT兲 films have distinguished
electro-optic effects and excellent relaxor properties, and
have improved various material characteristics: dielectric,
ferroelectric, piezoelectric, electro-optic, and pyroelectric
behaviors.
12
In general, relaxor behavior is characterized by
a broad maximum in the temperature dependence of dielec-
tric property, and a strong frequency dispersion of the per-
mittivity at temperatures around and below the transition
temperature. Nb dopant increases the electrical resistance of
Pb
1−0.5x
Nb
x
共Zr
y
Ti
1−y
兲
1−x
O
3
共PNZT兲 thin films and produces
polarization hysterisis loops with low coercive fields and
large remanent polarizations.
13
Pb
1−x
La
x
Ti
1−x/4
O
3
共PLT兲 also
has interesting properties of dielectric, ferroelectric, pyro-
electric, piezoelectric, and nonlinear electro-optic properties.
Particularly, relaxor behavior is observed.
14
In this work, we measured the pseudodielectric functions
of PZTs, PLT, and doped PZTs. Using a parametric optical
constant 共POC兲 model, we estimated the dielectric functions
of PZT layers and determined the critical-point 共CP兲 param-
eters by performing a standard critical-point 共SCP兲 model
analysis. The determined band-gap values are consistent with
literature values. The lowest band gaps are fitted as a double
peak 共E
a
and E
b
兲, and the band-gap energies are almost con-
stant, independent of Zr composition. We also compared the
experimentally determined band-gap values with those of
band-structure calculations of local-density approximation
共LDA兲. The calculated results showed that PZT has a direct
band gap at the X point and that the band-gap energy is
almost constant as a function of Zr composition.
II. EXPERIMENTS
We grew Pb共Zr
x
Ti
1−x
兲O
3
共x=0.56 and 0.82兲共abbreviated
as PZT56 and PZT82兲 samples on sapphire 共Al
2
O
3
兲 using rf
magnetron sputtering methods. We also grew
Pb共Zr
0.2
Ti
0.8
兲O
3
共abbreviated as PZT20兲,
Pb
0.98
Nb
0.04
共Zr
0.2
Ti
0.8
兲
0.96
O
3
共abbreviated as PNZT兲,
Pb
0.91
La
0.09
共Zr
0.65
Ti
0.35
兲
0.98
O
3
共abbreviated as PLZT兲, and
Pb
0.85
La
0.15
Ti
0.96
O
3
共abbreviated as PLT兲 thin films using sol-
gel methods on platinized silicon 共Pt/TiO
2
/SiO
2
/Si兲 at Ra-
diant Technologies.
We used rf sputtering to grow PZT56 and PZT82 on
sapphire. The growth temperature was measured to be
410 °C, and rf power was 200 W. The argon and oxygen gas
flow rates were 40 and 19 SCCM 共standard cubic centimeter
per minute兲, respectively. We used a nominal
Pb
1.2
共Zr
0.5
Ti
0.5
兲O
3
target of 20% excess Pb, adopted a rotat-
ing substrate holder, and used additional Zr and Ti pellets to
control stoichiometry. The PZT samples were annealed at
800 °C in air to obtain the perovskite phase.
PZT, PLT, PNZT, and PLZT thin films with 270 nm
thickness were grown using sol-gel process on platinized
silicon wafer. The structure of the platinized silicon was
Pt共150 nm兲/TiO
2
共40 nm兲/SiO
2
共500 nm兲/共100兲 silicon sub-
strate. The Pt and TiO
2
layers were deposited by e-beam
deposition. PZT layers were crystallized by annealing in
oxygen ambient at a temperature of 650 °C. Ferroelectric
capacitors were fabricated from PZT, PLT, PNZT, and PLZT
samples and tested using ferroelectric testers at Radiant
Technologies. They showed excellent ferroelectric hysteresis
behavior in terms of low coercive bias voltage and large
remanent polarization. For example, the PNZT layer had a
coercive bias voltage of 2 V and remanent polarization of
18
C/cm
2
.
Microstructure and crystal orientation were determined
using a conventional x-ray diffractometer 共MacScience
Model M18XHF, maximum power 18 kW兲. The composi-
tions were determined by using energy-dispersive x-ray
spectrometry 共EDS兲. We estimated surface roughness with
atomic force microscopy 共AutoProbe CP Research System,
Thermo Microscope Inc.兲. Surface morphology of the
samples was diagnosed with scanning electron microscopy.
The x-ray and atomic force microscopy 共AFM兲 results are
summarized in Table I.
Spectroscopic ellipsometric measurements were per-
formed using variable angle spectroscopic ellipsometry and
vacuum ultraviolet spectroscopic ellipsometry 共J. A. Wool-
lam Co.兲 at incidence angles of 60°, 65°, 70°, and 75° using
an autoretarder. Multiangle capability increases the accuracy
of layer modeling.
III. RESULTS
A. X ray and microstructure
Figures 1共a兲–1共h兲 show the x-ray data of the PZT, PLT,
and doped PZT thin films. PZT56 and PZT82 which were
sputter grown on sapphire and annealed showed higher crys-
tallinity than PZT20, PLT, PNZT, and PLZT samples sol-gel
grown on platinized silicon substrates because the x-ray in-
tensity from the perovskite phase was much higher for the
sputter-grown and annealed samples. As-grown PZTs using
sputter deposition have mainly the pyrochlore phase with a
small proportion of the perovskite phase as shown in Figs.
1共a兲 and 1共c兲.
15
Table I lists the main x-ray peaks from the
perovskite phase of annealed PZTs and those of the pyro-
chlore phase from as-grown PZTs. PZTs grown on platinized
silicon wafer using the sol-gel method have mainly 共001兲
perovskite phase, whereas PZTs grown using the sputtering
method have mainly the 共111兲 phase for PZT56 and mainly
the 共110兲 phase for PZT82. Sample microstructure and crys-
tal orientation can be affected by Zr composition, buffer and
substrate effects, annealing condition, and growth methods.
A morphotropic phase boundary of tetragonal to rhombohe-
dral phase transition occurs at Zr=0.53 for bulk PZT
094108-2 Lee et al. J. Appl. Phys. 98, 094108 共2005兲
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crystals.
16
Note that annealed PZT56 shows a small amount
of
␣
-PbO phase, which formed during annealing, as shown
in Fig. 1共b兲.
17
B. Spectroscopic ellipsometry
We modeled the sample structures as surface roughness
layer, main layer, and substrate. To model the surface rough-
ness layer, we used an effective-medium approximation with
a mixture of the main layer and voids. The effective dielec-
tric function was calculated by the Bruggeman effective-
medium approximation 共EMA兲,
18
f
pzt
⑀
pzt
−
⑀
eff
⑀
pzt
+2
⑀
eff
+ f
void
⑀
void
−
⑀
eff
⑀
void
+
⑀
eff
=0, 共1兲
where the effective dielectric function of the rms roughness
layer was denoted by
⑀
eff
, and dielectric functions 共volume
fractions兲 of PZT phase and voids are denoted, respectively,
as
⑀
pzt
共f
pzt
兲 and
⑀
void
共f
void
兲. Details are shown in Table II.
The dielectric function of the main PZT layer was fitted
using the POC model, in which the dielectric function is
written as the summation of m energy-bounded, Gaussian-
broadened polynomials and P poles accounting for the index
effects due to absorption outside the model region.
19
The
advantage of the POC model is that we can determine simul-
taneously both the band-gap parameters and the dielectric
function from the pseudodielectric function. The POC model
equation is Kramers-Kronig consistent, and is given by
⑀
共
兲 =
⑀
1
共
兲 + i
⑀
2
共
兲 =1
+ i
兺
j=1
m
冕
Emin
Emax
W
j
共E兲⌽共ប
,E,
j
兲dE
+
兺
j=m+1
m+P+1
A
j
共ប
兲
2
− E
j
2
, 共2兲
where
⌽共ប
,E,
兲 =
冕
0
⬁
e
i共ប
−E+i2
2
s兲s
ds −
冕
0
⬁
e
i共ប
+E+i2
2
s兲s
ds
=
冑
8
2
关e
−y
1
2
+ e
−y
1
2
erf共iy
1
兲
− e
−y
2
2
− e
−y
2
2
erf共iy
2
兲兴, 共3a兲
y
1
=
ប
− E
2
冑
2
, y
2
=
ប
+ E
2
冑
2
, 共3b兲
W
j
共E兲 =
兺
k=0
N
P
j,k
E
k
u共E − a
j
兲u共b
j
− E兲, 共4兲
where u共x兲 the unit step function. Here E
j
,
j
, and A
j
are the
energy threshold, broadening, and amplitude, respectively,
for the jth band-gap structure.
The SCP model assumes simple parabolic dispersion re-
lations for the valence and conduction bands and was devel-
oped by Cardona
20
and Aspnes.
21
This model provides accu-
rate CP parameters such as energy threshold, broadening,
amplitude, and excitonic phase angle. The SCP line-shape
equation is given by
22
⑀
共ប
兲 = C − Ae
i⌽
共ប
− E + i⌫兲
n
, 共5兲
where the CP is described by the amplitude A, threshold
energy E, broadening ⌫, and the excitonic phase angle ⌽.
The exponent n takes the values of −1/2 for one-dimensional
共1D兲,0关logarithmic, i.e., ln共ប
−E +i⌫兲兴 for two-
dimensional 共2D兲, and 1/2 for three-dimensional 共3D兲 CP’s.
Discrete excitons are represented by n =−1. Here the exci-
tonic phase angle ⌽ represents a coupling between the dis-
crete exciton states and continuum band states. To remove
the background contribution, we fit the second derivative of
the dielectric function with respect to energy 关d
2
⑀
/d共ប
兲
2
兴
using the SCP model.
Figure 2 shows the pseudodielectric functions of 共a兲
PZTs and 共b兲 PLT and doped PZTs. The three band-gap
peaks are identified as E
a
, E
b
, and E
c
, respectively. The band-
TABLE I. Thickness and volume fraction of void in surface roughness layer. The thickness of the main layer
was determined by ellipsometry. AFM-measured roughness and the main x-ray peaks are listed with crystal
phase 共Pv: perovskite, Pr: pyrochlore兲, substrate, and growth method.
Main
layer
thickness
共nm兲
Roughness
layer
thickness
共nm兲, void
fraction
共%兲
AFM rms
roughness
共nm兲
Main
x-ray
peak
Substrate, growth
method
Pb共Zr
0.2
Ti
0.8
兲O
3
204.0 9.1, 29.8 2.05 Pv 共100兲 Platinized Si, sol gel
Pb共Zr
0.56
Ti
0.44
兲O
3
, as grown 367.9 6.2, 22.1 Pr 共400兲 Al
2
O
3
, sputter
Pb共Zr
0.56
Ti
0.44
兲O
3
339.9 16.7, 28.8 5.27 Pv共111兲 Al
2
O
3
, sputter
Pb共Zr
0.82
Ti
0.18
兲O
3
, as grown 188.8 9.9, 19.5 Pr 共222兲 Al
2
O
3
, sputter
Pb共Zr
0.82
Ti
0.18
兲O
3
177.2 13.5, 25.2 11.43 Pv 共110兲 Al
2
O
3
, sputter
Pb
0.98
Nb
0.04
共Zr
0.2
Ti
0.8
兲
0.96
O
3
177.2 11.4, 23.3 2.57 Pv 共100兲 Platinized Si, sol gel
Pb
0.91
La
0.09
共Zr
0.65
Ti
0.35
兲
0.98
O
3
291.0 10.0, 12 1.07 Pv 共100兲 Platinized Si, sol gel
Pb
0.85
La
0.15
Ti
0.96
O
3
308.2 0.0, 0.0 5.11 Pv共100兲 Platinized Si, sol gel
094108-3 Lee et al. J. Appl. Phys. 98, 094108 共2005兲
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