Lallart M. Ferroelectrics: Characterization and Modeling
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Changes of Crystal Structure and Electrical Properties with Film Thickness and
Zr/(Zr+Ti) Ratio for Epitaxial Pb(Zr,Ti)O
3
films Grown on (100)
c
SrRuO
3
//(100)SrTiO
3
Substrates…
239
On the other hand, the 50 nm thick PZT film show a relatively low leakage current level
oscillating between 10
-7
and 10
-5
A/cm² at an electric field of 100 kV/cm, independently
from the Zr/(Zr+Ti) ratio. These results are coherent with reported data (Shiosaki, 1995;
Oikawa et al., 2002). Indeed, it has been shown that PZT films with low Zr/(Zr+Ti) ratio
present typically larger leakage current density compared to that of films with large Zr/(Zr+Ti)
ratio (Shiosaki, 1995). While it has been revealed (Oikawa et al., 2002) that Sr and/or Ru
diffusion into PZT might create a conductive path, which is in good agreement with our results
because a longer deposition time could induce a large amount of Sr and/or Ru diffusion into
the bottom electrode.
Fig. 10 summarizes the polarization - electric field (P - E) relationships for films with various
Zr/(Zr+Ti) ratio and film thickness.
-120
-80
-40
0
40
80
120
-120
-80
-40
0
40
80
120
Polarization (µC/cm
2
)
-120
-80
-40
0
40
80
120
-400 -200 0 200 400
-120
-80
-40
0
40
80
120
Electric field (kV/cm)
-120
-80
-40
0
40
80
120
-120
-80
-40
0
40
80
120
Polarization (µC/cm
2
)
-120
-80
-40
0
40
80
120
-400 -200 0 200 400
-120
-80
-40
0
40
80
120
Electric field (kV/cm)
Zr/(Zr+Ti) ; 0.13
0.30
0.54
0.67
0.35
0.53
0.63
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Thickness : 50nm
Thickness : 250nm
Fig. 10 Polarization - electric field (P - E) relationships for films with various Zr/(Zr+Ti)
ratio and film thickness. from 50 nm thick films [(a)-(d)] and 250 nm thick films [(e) - (h)].
Ferroelectrics - Characterization and Modeling
240
0
40
80
120
P
r
(µC/cm
2
)
Zr/(Zr+Ti) ;
0.13
0.30
0.54
0.67
0 100 200 300 400
0
50
100
150
200
Electric field (kV/cm)
E
c
(kV/cm)
Zr/(Zr+Ti) ;
0.13
0.30
0.54
0.67
0
40
80
120
P
r
(µC/cm
2
)
Zr/(Zr+Ti) ;
0.35
0.53
0.63
0 100 200 300 400
0
50
100
150
200
Electric field (kV/cm)
E
c
(kV/cm)
Zr/(Zr+tI) ;
0.35
0.53
0.63
(a)
(b)
(c)
(d)
Thickness : 50nm
Thickness : 250nm
Fig. 11. Saturation properties of P
r
and E
c
values against the maximum applied electric filed
for 50 nm [(a), (b)] and 250nm [(c), (d)] PZT films having various Zr/(Zr+Ti) ratio content.
Notice that the 250 nm thick film with Zr/(Zr+Ti)=0.19 showed high leakage current level
that cannot display P - E hysterisis loops from the PZT films [Fig. 9(a)]. However, others
showed P - E hysteresis loops originated to the ferroelectricity. Good saturation properties
of Pr and the coercive field (Ec) against the maximum electric filed are confirmed for both of
50 nm and 250 nm thick films.
We notice on these figures that fully polar axis oriented [(001)-oriented] films with 50 nm in
thickness exhibit larger P
r
values than 250 nm PZT films with the coexistence of (100) and
(001) orientations. This result is coherent if we consider the difference in the relative volume
fraction of the c-domain in the latter samples. However, the differences in domain structure
between the two thickness of the present samples remains and issue to fix for a good
comparative analysis.
To get insight into this issue, we calculated the spontaneous polarization (P
sat
) from P
r
/V
c
,
calibrated P
r
value by the c-domain volume fraction, V
c
, assuming that the 90° a-domain do
not switch under an external electric field. The results are summarized in Fig. 12.
On this figure, P
r
values extracted from 50 nm-thick films are presented with closed diamonds,
while open diamonds represents P
r
values of 250 nm-thick films. By way of comparison, we
included on Fig. 12, reported data for the 100% c-axis-oriented Pb(Zr
0.5
Ti
0.5
)O
3
film by Ishida et
al. (square plot) (Ishida et al., 2002) and also theoretical calculated data of P
sat
against the
Zr/(Zr+Ti) ratio reported by Haun et al. (dashed line) (Haune et al., 1989).
We notice that the estimated P
sat
value in the present study is larger than reported data.
However, our results have the same trend as predicted by theoretical calculations.
A good explanation of this latter result might be given by getting insight into the
relationship linking tetragonality (c/a) to spontaneous polarization (P
sat
).
Changes of Crystal Structure and Electrical Properties with Film Thickness and
Zr/(Zr+Ti) Ratio for Epitaxial Pb(Zr,Ti)O
3
films Grown on (100)
c
SrRuO
3
//(100)SrTiO
3
Substrates…
241
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
20
40
60
80
100
120
Zr/(Zr+Ti) ratio
P
sat
(µC/cm
2
)
Haun et al.
Ishida et al.
50nm
250nm
Fig. 12. Estimated P
sat
as a function of Zr/(Zr+Ti) ratio in films.
1.00 1.01 1.02 1.03 1.04 1.05 1.06
0
20
40
60
80
100
120
c/a ratio
P
sat
(µC/cm
2
)
Fig. 13. Relationship between P
sat
and the c/a ratio of PZT films.
Ferroelectrics - Characterization and Modeling
242
Indeed, the unit cell distortion inducing P
sat
might be related to cell parameters by the
following equation (Joan & Shirane, 1992):
2
1
sat
c
QP
a
⋅=−
(1)
where, Q represents the apparent electrostrictive coefficient.
To highlight this relationship, we gathered data presented on Figures 7(b) and (e) and
Fig. 12 on the same chart, as shown in Fig. 13:
Our data seem to be in agreement with the quadratic form presented in equation (1) linking
P
sat
to unit cell tetragonality, c/a ratio. In a previous article we could emphasis that our
estimated electrostrictive coefficient, Q, is Q = 0.049 m
4
/C
2
We also characterized the relative dielectric constant (ε
r
) versus Zr/(Zr+Ti) ratio as well as
thickness dependency. These results are presented on Fig. 14. On this figure, we notice that
both thicknesses considered in this study respect the same ε
r
tendency with regards to Zr
content. Indeed, ε
r
increases with increasing Zr/(Zr+Ti) ratio.
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
200
400
600
800
Zr/(Zr+Ti) ratio
Relative dielectric constant ,
ε
r
50 nm
250 nm
Fig. 14. Evolution of ε
r
measured at 1 kHz as function of Zr/(Zr+Ti) ratio for 50 nm (
) and
250 nm (
) thick films.
On the other hand, we noticed that squareness in P - E hysteresis loops defined by the
P
r
/P
sat
ratio, is also influenced by the Zr/(Zr+Ti) ratio of the films regardless of V
c
in the
film. [see Fig. 15 (a)]. Indeed, as it can be observed on this figure, both 50 nm and 250 nm
thick films present the same decreasing trend when Zr/(Zr+Ti) ratio increases. This result is
in a good agreement with results presented on Fig. 14 since ε
r
can be extracted from the
saturated branch of P - E hysteresis loops.
Changes of Crystal Structure and Electrical Properties with Film Thickness and
Zr/(Zr+Ti) Ratio for Epitaxial Pb(Zr,Ti)O
3
films Grown on (100)
c
SrRuO
3
//(100)SrTiO
3
Substrates…
243
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.5
0.6
0.7
0.8
0.9
1.0
Zr/(Zr+Ti) ratio
P
r
/P
sat
ratio
1.00 1.01 1.02 1.03 1.04 1.05 1.06
0.5
0.6
0.7
0.8
0.9
1.0
c/a ratio
P
r
/P
sat
ratio
(a)
(b)
50nm
250nm
Fig. 15. Evolution of P
r
/P
sat
ratio as function of Zr/(Zr+Ti) ratio (a) and c/a ratio (b)
4. Summary
Epitaxial PZT thin films were grown at 540°C on SrRuO
3
-coated (001) SrTiO
3
substrates by
pulsed MOCVD. To characterize the impacts of the Zr/(Zr+Ti) ratio and the film thickness
on the volume fraction of c-domain, 50 nm and 250 nm thick films have been grown with
different Zr/(Zr+Ti) ratio ranging from 0.1 to 0.7.
Ferroelectrics - Characterization and Modeling
244
HRXRD characterization showed that 50 nm thick films present a fully polar-axis oriented
tetragonal films regardless of Zr/(Zr+Ti) up to 0.54, while 250 nm thick films are tetragonal
single phase for the films with the Zr/(Zr+Ti) ratio smaller than 0.45, then, coexistence of
tetragonal and rhombohedral phase from Zr/(Zr+Ti)=0.45 to 0.6. Appearing of two
symmetry coexistence is related to the stress relaxation process occurring at relatively thick
film.
Concerning electrical properties, 50-nm-thick PZT films with fully polar-axis orientation
present larger P
r
and P
sat
values than thicker films. On the other hand, we investigated the
impact of Zr/(Zr+Ti) ratio on the ferroelectricity of PZT films, showing the linear
relationship between P
sat
2
and the c/a ratio of the films.
5. Acknowledgement
This work was partially supported by Grants-in-Aid from the Ministry of Education,
Culture, Sports, Science and Technology, Japan for the Elements Science and Technology
Project (21360316 and 20047004)”
6. References
K. Nagashima, M. Aratani, and H. Funakubo, J. Appl. Phys. 89, 4517 (2001).
N. Okuda, K. Saito, and H. Funakubo, Jpn. J. Appl. Phys., Part 1 39, 572 (2000).
K. Saito, T. Kurosawa, T. Akai, T. Oikawa, and H. Funakubo, J. Appl. Phys. 93, 545 (2003).
G. Shirane and K. Suzuki, J. Phys. Soc. Jpn. 7, 333 (1952).
H. Morioka, S. Yokoyama, T. Oikawa, K. Saito and H. Funakubo. Mat. Res. Soc. Symp. Proc.
784, C6.2.1 (2004)
H. Morioka, S. Yokoyama, T. Oikawa and H. Funakubo Appl. Phys. Lett. 85, 3516 (2004).
K. Saito, T. Kurosawa, T. Akai, S. Yokoyama, H. Morioka, T. Oikawa, and H. Funakubo,
Mater. Res. Soc. Symp. Proc. 748, U13.4 (2003).
H. Morioka, G. Asano, T. Oikawa, H. Funakubo, and K. Saito, Appl. Phys. Lett. 82, 4761
(2003).
H. Morioka, K. Saito, S. Yokoyama, T. Oikawa, T. Kurosawa, and H. Funakubo, J. Mater. Sci.
44, 5318 (2009)
T. Shiosaki, Science Forum, Japan (1995)
T. Oikawa, K. Takahashi, J. Ishida, Y. Ichikawa, T. Ochiai, K. Saito, A. Sawabe and H.
Funakubo, Int. Ferro. 46, 55 (2002)
J. Ishida, T. Yamada, A. Sawabe, K. Okuwada, and K. Saito, Appl. Phys. Lett. 80, 467 (2002)
M. J. Haun, Z. Q. Zhuang, E. Furman, S. J. Jang, and L. E. Cross, J. Am. Ceram. Soc. 72, 1140
(1989)
F. Jona and G. Shirane, Ferroelectric Crystal, 145, Dover, New York, (1992).
13
Double Hysteresis Loop in
BaTiO
3
-Based Ferroelectric Ceramics
Sining Yun
School of Material Science and Engineering,
Xi’an University of Architecture and Technology, Xi’an, Shaanxi,
China
1. Introduction
In 1951, the notion of anti-ferroelectricity based on the phenomenological theory was firstly
proposed by C. Kittel (Kittel, 1951), and who predicted exist of the anti-ferroelectric
materials and its some intrinsic characteristics. Subsequently, a double hysteresis (P–E) loop
and a ferroelectric-antiferroelectric (FE-AFE) phase transition were observed in PbZrO
3
(Shirane et al., 1951, 1952) and Pb(Zr, Ti)O
3
(Sawaguchi, 1953) ceramics with a perovskite
structure. Since then, the double hysteresis loop, one important macroscopic effect, has been
regarded as a typical characteristic of antiferroelectric materials. This kinds of
antiferroelectric behavior is also observed in Pb(Zr, Sn, Ti)O
3
and Pb(La, Zr, Sn, Ti)O
3
ceramics (Berlincourt, 1963, 1964; Biggers & Schulze, 1974; Gttrttritja et al., 1980; Shebanov et
al., 1994).
Interestingly, the double hysteresis loops have been observed in BaTiO
3
(Merz, 1953),
BaTiO
3
-based (Ren, 2004; Zhang & Ren, 2005, 2006; Liu et al., 2006), (Na
0.5
Bi
0.5
)TiO
3
-based
(Takenaka, 1991; Sakata & Masuda, 1974; Tu et al., 1994; Sakata et al., 1992), (Ba, Sr)TiO
3
(Zhang et al., 2004), KNbO
3
(Feng & Ren, 2007, 2008), BiFeO
3
(Yuen et al., 2007) and other
lead-based perovskite ceramics such as Pb(Yb
0.5
Ta
0.5
)O
3
(Yasuda & Konda, 1993)
,
Pb(Fe
2/3
W
1/3
)O
3
-Pb(Co
1/2
W
1/2
)O
3
(Uchino & Nomura, 1978), Pb(Sc
0.5
Ta
0.5
)O
3
(Chu et al.,
1993) and Pb(Co
1/2
W
1/2
)O
3
(Hachiga et al., 1985) over the past decades. However, the
observed double hysteresis loops have different physical origins.
For the physical origins of the double P-E loops observation in the perovskite structure
materials, they can be generally classified into several groups below: (1) the double P-E
loops result from antiferroelectric components. i.e., the observed double P-E loops in
PbZrO
3
and
Pb(Zr, Ti)O
3
ceramics. (2) the double P-E loops result from an electric field-
induced antiferroelectric-to-ferroelectric phase transition as shown observed in Pb(La, Zr,
Sn, Ti)O
3
ceramics. (3) two successive paraelectric-antiferroelectric-ferroelectric (PE-AFE-
FE) phase transitions is often observed in highly ordered perovskite lead-based and lead-
free complex compounds, and the double P-E loops are expected to accompany this phase
transition. Such case often occur in Pb(Yb
0.5
Ta
0.5
)O
3,
Pb(Fe
2/3
W
1/3
)O
3
-Pb(Co
1/2
W
1/2
)O
3
,
Pb(Sc
0.5
Ta
0.5
)O
3
and Pb(Co
1/2
W
1/2
)O
3
and (Na
0.5
Bi
0.5
)TiO
3
-based ceramics. (4) an aging
effect far below Curie temperature ( T
c
) can induce the double P-E loops observation in
many kind different compositional ceramics such as acctor-doped BaTiO
3
ceramics, Mn-
Ferroelectrics - Characterization and Modeling
246
doped (Ba, Sr)TiO
3
ceramics, KNbO
3
-based ceramics and BiFeO
3
ceramics. The aging-
induced double P-E loops has been the highlights based on the high-quality publications
and their cited times. (5) for the observed double P-E loops in BaTiO
3
crystals at the Curie
point, its origin can not attributed to any one group mentioned above. The BaTiO
3
crystals
go from a paraelectric to a ferroelectric state, while (Pb, Ba)ZrO
3
ceramics go from an
antiferroelectric to a ferroelectric state when an electric field is applied. It is generally
believed that the Curie point of the BaTiO
3
crystal shifts to higher temperature when a dc
bias field is applied. The more detailed discussion about the origin of the double P-E
loops in the BaTiO
3
crystal can consult the previous literatures titled “A theory of double
hysteresis for ferroelectric crystals” (Srivastava, 2006).
After a brief review of the physical origin of double hysteresis loops in different
perovskite structure (A
+
B
5+
O
3
, A
2+
B
4+
O
3
, AA’BO
3
, ABB’O
3
, etc) ceramic materials, this
chapter begins with aging effect, namely a gradual change in physical properties with
time. This is followed by discussions of the aging-induced double hysteresis loops in Bi
doped (Ba, Ca)TiO
3
and Bi doped (Ba, Sr, Ca)TiO
3
ferroelectric ceramics. Some emphasis
will be on the roles of acceptor-doping and donor-doping in understanding the physics of
these materials.
2. Experimental procedures
2.1 Ceramics synthesis
A conventional solid reaction route was employed to synthesize ceramics samples. Reagent
grade BaCO
3
(99.8%), Bi
2
O
3
(99.8%), SrCO
3
(99.8%), CaCO
3
(99.8%) and TiO
2
(98%) as the
raw materials were weighed according to the compositions (Ba
1-x
Ca
x
)
1-1.5y
Bi
y
TiO
3
(Bi-BCT, x
=0.10, 0.20 and 0.30, y=0.05) and (Ba
1-x
Ca
x/2
Sr
x/2
)
1-1.5y
Bi
y
TiO
3
(Bi-BCST, x=0.10, 0.20 and 0.40,
y=0 and 0.05). (Ba
0.925
Bi
0.05
)(Ti
0.90
Ca
0.10
)O
3
(designated hereafter Bi-BTC) was prepared to
compare the effect of Ca substitution at the Ti sites of Bi-BCT. After ball-milled in alcohol for
6 h using agate balls in a planetary mill, the slurry was dried, and then calcined at 1100
o
C
for 4-5h. The calcined powder was ball milled and dried again to obtain homogeneous
powder. Pellets of 10 mm in diameter and ~1 mm thick were pressed using 5 % PVA binder.
Slow heating at 500
o
C for 3-4h burned out the binder. The samples were sintered at 1240
o
C
-1300
o
C in air for 3 h, with heating rates of 200
o
C/h. The samples were cooled with the
furnace.
2.2 Characterizations
The phase structures of the ceramics at different temperature were checked by the X-ray
powder diffraction (XRD, D/Max2200 RZGAKV: Rigaku Inc.D, Japan) on an automated
Rigaku D/max 2400 X-ray diffractometer with rotating anode using CuK
α
radiation. The
microstructures were examined by a scanning electron microscopy (SEM, Quanta 200 FEG
System: FEI Co., USA) with X-ray energy dispersive spectroscopy (EDS) for chemical
analysis. Raman scattering investigation was performed at room temperature by using an
ALMEGA dispersive Raman spectrometer (ALMEGA, Therm Nicolet, Madison,WI).
2.3 Property measurements
After polishing, the dimensions were measured before silver electrodes were deposited on
the pellets, then the specimens were fired at 810
o
C for 10 mins. Dielectric properties at
Double Hysteresis Loop in BaTiO
3
-Based Ferroelectric Ceramics
247
frequencies ranging from 0.1kHz to 100 kHz were measured with an Agilent 4284A LCR
meter, as samples were heated at a rate of 2
o
C/min from negative 80 to positive 200
o
C.
Hysteresis loops were measured in a wide temperature range using a computer-controlled,
modified Sawyer-Tower circuit at frequency of 1 Hz. Current-field relation was measured
on an automatic ferroelectric test system of aixACT TF-ANALY2ER2000. Applied electric
field signal is triangular, and a period time is a second.
3. Results and discussion
3.1 Structural analysis
It has been reported that the solubility limit of Bi is around 5 at. % in BaTiO
3
(Zhou et al.,
1999), and around 10 at. % in (Ba
0.2
Sr
0.8
)TiO
3
(Zhou et al., 2000), respectively. Moreover, 5 at.
% of Bi doping can be fully incorporated into the perovskite lattice of Ba
1-x
Sr
x
TiO
3
(x < 0.80)
(Zhou et al., 2001). It is then possible to assume that 5 at. % of Bi doping can be fully
incorporated into the perovskite lattice of (Ba
1-x
Ca
x
)TiO
3
(Bi-BCT, x=0.10, 0.20 and 0.30) and
(Ba
1-x
Ca
x/2
Sr
x/2
)TiO
3
(Bi-BSCT, x=0.10, 0.20 and 0.40). XRD analysis confirmed this
assumption. Fig. 1 show the XRD patterns of 5 at. % of Bi doped (Ba
1-x
Ca
x
)TiO
3
ceramics.
The XRD patterns of all the compositions showed mainly a single perovskite phase.
The structural evolution of Bi-doped BCST ceramics samples from x=0.10 to 0.40 is shown in
Fig. 2. The XRD results of 5 at. % Bi-doped BCST are consistent with those of (Ba
1-x
Sr
x
)
1-
1.5y
Bi
y
TiO
3
(Zhou et al., 2001) and Bi-BCT, showing that they are a single phase. The
crystalline symmetry of Bi-doped BCST ceramics is a rhombohedral for x=0.40. However, it
tends appreciably towards the tetragonal for x=0.20. The rhombohedral phase is illustrated
by the increased splitting between the (021) and (003) peaks in two-theta near 39
o
while the
tetragonal phase is illustrated by the increased splitting between the (002) and (200) peaks in
two-theta near 45
o
. There are splits in the peaks observed at two-theta of about 39
o
and 45
o
,
respectively, as shown in Fig.3, indicating the coexistence of the tetragonal and
rhombohedral phases of Bi-BCST for x=0.10 and that of Bi-BCT for x=0.10 and 0.20.
25 30 35 40 45 50 55 60 65
(220)
(211)
(210)
(200)
(111)
(110)
(100)
Intensity (arb.unit)
x=0.30
x=0.20
x=0.10
Two-Theta [Deg.]
Fig. 1. XRD patterns of Bi-BCT ceramics with different compositions (x=0.10, 0.20 and 0.30,
y=0.05).
Ferroelectrics - Characterization and Modeling
248
25 30 35 40 45 50 55 60 65
(100)
(202)
(003)/(021)
x=0.10
x=0.20
x=0.40
Intensity (arb.unit)
(220)
(113)/(211)
(210)
(002)/(200)
(111)
(110)
Two-theta [Deg.]
Fig. 2. XRD patterns of Bi-BSCT ceramics with different compositions (x=0.10, 0.20 and 0.40,
y=0.05).
38 40 44 46
38 44 46
(003)/(021)
(202)
x=0.10
x=0.20
x=0.40
(002)/(200)
(111)
Two-theta [Deg.]
Bi-BSCT
(021)
(003)
x=0.10
x=0.20
x=0.30
Intensity (arb.unit)
(002)/(200)
(111)
Bi-BCT
Fig. 3. Enlarged XRD patterns of Bi-BCT and Bi-BSCT( y=0.05) ceramics with different
compositions with two-theta value ranging from 37.5
o
to 46.5
o
.