Defects on Ferroelectric and Dielectric Properties
of Thin-Film BariumStrontium Titanates
Davor B
ALZAR
1
,2,
, Padmanabhan A. R
AMAKRISHNAN
3
, Priscila S
PAGNOL
4
,
Sugantha M
ANI
1
,2
, Allen M. H
ERMANN
3
and Mohammad A. M
ATIN
5
1
Department of Physics & Astronomy, University of Denver, Denver, CO 80208, U.S.A.
2
National Institute of Standards and Technology, Boulder, CO 80305, U.S.A.
3
Department of Physics, University of Colorado, Boulder, CO 80309, U.S.A.
4
Chemistry Institute, UNESP, CEP 14801-970 Araraquara-SP, Brazil
5
Department of Engineering, University of Denver, Denver, CO 80208, U.S.A.
(Received May 29, 2002; accepted for publication August 8, 2002)
Pristine, W and Mn 1% doped Ba
0
.6
Sr
0
.4
TiO
3
epitaxial thin lms grown on the LaAlO
3
substrate were deposited by pulsed
laser deposition (PLD). Dielectric and ferroelectric properties were determined by the capacitance measurements and X-ray
diffraction was used to determine both residual elastic strains and defect-related inhomogeneous strains by analyzing diffraction
line shifts and line broadening, respectively. We found that both elastic and inhomogeneous strains are affected by doping. This
strain correlates with the change in Curie-Weiss temperature and can qualitatively explain changes in dielectric loss. To explain
the experimental ndings, we model the dielectric and ferroelectric properties of interest in the framework of the Landau-
Ginzburg-Devonshire thermodynamic theory. As expected, an elastic-strain contribution due to the epilayer-substrate mist
has an important inuence on the free-energy. However, additional terms that correspond to the defect-related inhomogeneous
strain had to be introduced to fully explain the measurements.
[DOI: 10.1143/JJAP.41.6628]
KEYWORDS: ferroelectric thin lms, strain, defects, Curie-Weiss temperature, bariumstrontium titanate
1.
Introduction
Thin lm ferroelectric (FE) materials have received con-
siderable attention because of their growing use in electronic,
electro-optical, optical and acoustic devices. Potential appli-
cations include integrated, nonvolatile, and dynamic random
access memories, pyroelectric detectors, and acoustic trans-
ducers.
1)
These materials also exhibit nonlinear dielectric
properties under an external electric eld, which is exploited
in tunable microwave devices, such as microstrip line phase
shifters, high-Q resonators, and tunable lters.
2)
For these ap-
plications, it is imperative that the lms exhibit a high dielec-
tric constant and tunability, and low dielectric loss. While rea-
sonable success has been achieved with tunability, the major
challenge has been lowering the dielectric loss and in particu-
lar understanding its mechanism. It was elucidated that losses
depend on substrate and post annealing treatments
3)
and the
lm thickness,
4)
in that the free-standing lms generally have
low losses
5)
and that crystalline SrRuO
3
, YBCO
6)
and amor-
phous
7)
buffer layers decrease losses. This indicates that min-
imizing lattice mist between the lm and substrate is of ut-
most importance. Indeed, dielectric losses depend on resid-
ual stresses of both intrinsic (caused by optical-phonon in-
teraction with the applied electric eld) and extrinsic (caused
by lattice defects) nature. The latter is an especially impor-
tant and complicated process because many possible defects
can be involved, such as ferroelectric domains, grain bound-
aries, stacking faults, dislocations, vacancies, and vacancy
complexes. Of the various ferroelectric materials, perovskite
oxide thin lms are considered as potential candidates for tun-
able microwave devices because of their high dielectric con-
stant. Materials investigated widely are based on solid solu-
tions of Ba
x
Sr
1
x
TiO
3
(BSTO), which exhibit high tunability
and easily controlled Curie temperature by varying chemical E-mail address: balzar@du.edu
composition. Losses can be controlled by doping very small
percentages (
< 4%) of ions such as Mn, W, Ca, Mg, and Zr.
8)
Our previous studies on doped BSTO lms
9)
indicate that
the ferroelectric transition temperature and the extrinsic di-
electric losses depend on the internal stresses and defects.
Thus it is evident that lattice strain plays a crucial role in
inuencing the dielectric and ferroelectric properties. To un-
derstand this further, we attempted to investigate the effect
of doping on the ferroelectric properties. Here, we report on
the correlation between Curie-Weiss temperature and residual
elastic strain (stress) and defect concentration.
2.
Theory
A comprehensive treatment of the inuence of homoge-
neous strain, due to the mist in lattice parameter and ther-
mal expansion coefcients, on the ferroelectric transition tem-
perature and electrical permittivity, was reported by Pertsev
et al.
10)
They start with the expression for the Gibbs free en-
ergy, close to the transition temperature and appearance of
polarization P:
G
= a
1
(P
2
1
+ P
2
2
+ P
2
3
) + a
11
(P
4
1
+ P
4
2
+ P
4
3
)
+ a
12
(P
2
1
P
2
2
+ P
2
1
P
2
3
+ P
2
2
P
2
3
) + a
111
(P
6
1
+ P
6
2
+ P
6
3
)
+ a
112
[P
4
1
(P
2
2
+ P
2
3
) + P
4
3
(P
2
1
+ P
2
2
) + P
4
2
(P
2
1
+ P
2
3
)]
+ a
123
P
2
1
P
2
2
P
2
3
Q
11
(
1
P
2
1
+
2
P
2
2
)
Q
12
[
1
(P
2
2
+ P
2
3
) +
2
(P
2
1
+ P
2
3
)] Q
44
P
1
P
2 6
1/2<i>s
11
(
2
1
+
2
2
) s
12 1 2
1/2<i>s
44 2
6
.
Here, a
i,j,k
are dielectric stiffness coefcients, s
ij
is the elas-
tic compliance tensor, Q
ij
the electrostrictive tensor, and i
is
the mechanical stress tensor, all in the Voigt condensed tensor
notation.
In the approximation of the single-domain two-dimensional
6628 Jpn. J. Appl. Phys. Vol. 41 (2002) Pt. 1, No. 11B
D. B
ALZAR
et al.
6629
thin lm constrained by the substrate, one can write the addi-
tional term to the Gibbs free energy due to elastic-strain e
i
contribution as:
10)
G
= G +
i
e
i i
.
This expression considers only elastic strains. However, crys-
talline defects (oxygen vacancies, for instance) will affect the
polarization of a ferroelectric.
11)
We proposed
12)
that the in-
ternal crystalline defects induce similar changes of the Gibbs
free energy,
G
= G +
i i i
,
through the inhomogeneous strain i
(so-called strain of the
III kind that inuences the diffraction line width, for instance)
and the stress of the III kind i
.
On the assumption that the spontaneous polarization axis
is perpendicular to the lm surface and isotropy of inhomo-
geneous strain, we have:
12)
G
= a
3
P
2
3
+ a
33
P
4
3
+ a
111
P
6
3
+
e
2
m
s
11
+ s
12
+ 32
2
m
s
11
+ 2<i>s
12
(1)
where the renormalized coefcients a were given else-
where.
12)
Similarly, the Curie-Weiss temperature is renormal-
ized:
12)
T
C-W
= max 2<i>C
0
2<i>Q
12
s
11
+ s
12
e
m
+ Q
11
+ 2<i>Q
12
s
11
+ 2<i>s
12 m
, 2<i>C
0
Q
11
+ Q
12
s
11
+ s
12
e
m
+ Q
11
+ 2<i>Q
12
s
11
+ 2<i>s
12 m
.
(2)
Here, C and 0
are the Curie-Weiss constant and the permit-
tivity of the vacuum, respectively. The second term in eq. (2)
is given by the inhomogeneous strain. Note that its contribu-
tion is always positive unlike that of the elastic-strain term
that can be either positive or negative, depending on whether
the lm is in tension or compression parallel to its surface.
3.
Experimental
The pristine BSTO and Mn, W-doped and co-doped
Ba
0
.6
Sr
0
.4
Ti
0
.99
M
0
.01
O
3
(M
= Mn, W) thin lms were
deposited on (001) LaAlO
3
(LAO) substrate using a KrF
eximer laser (248 nm) at 700 C at oxygen partial pressures of
300 mTorr. During deposition, the stoichiometric BSTO tar-
gets with densities of 98% were used. The energy density was
about 1.52 J/cm
2
. The lms were post-annealed in owing
oxygen at 950 C for 6 h.
Dielectric measurements were carried out on these lms
using a 4-capacitor shadow mask design with interdigitated
capacitors. The mask has 6 terminal pads for contact, with
nger widths of 125
µm and nger separation of 75 µm. The
interdigitated capacitor congurations were obtained by ther-
mal evaporation of silver to a thickness of 150 nm. Fine-gauge
copper leads were then attached to each capacitor using silver
paste. The whole assembly was then annealed at 300 C in Ar
to ensure good electrical contact and to decompose the or-
ganic matter present in the silver paste.
The capacitance and dielectric loss (tan
) were measured
using a HP 4192A LCR meter
13)
at a constant frequency of
1 MHz. For temperature variation a closed cycle He refrigera-
tor was used. Automated data acquisition was achieved by the
LABVIEW
13)
program. A standard 2 pF capacitor was used
to calibrate the instrument which gave
< 1% error in the fre-
quency range studied.
The optical properties were measured with a dual mode au-
tomatic ellipsometer model L116A
13)
at room temperature.
The ellipsometer measurements can be used for determining
the lm thickness and refractive index of optically transpar-
ent and absorbing layers, in the range between a few
A and
a few
µm. The lm thickness was relatively nonuniform due
to the deposition technique used and varied in the range of
10003500
A.
X-ray diffraction (XRD) data were collected using com-
mercial four-circle and two-circle double-axis diffractome-
ters with Cu K
radiation excited at 45 kV and 40 mA. To
thoroughly study the mist relationship at the lm-substrate
interface, we recorded reciprocal space maps for all lms.
Reciprocal space maps discern differences between different
types of defects in epilayers, in particular mosaicity paral-
lel to the lm surface and strain variations perpendicular to
the lm surface. Reciprocal space maps of asymmetric reec-
tions (013) were used to obtain both parallel and perpendic-
ular (to the lm surface) latti