Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications
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Handbook of dielectric, piezoelectric and ferroelectric materials660
is poled almost completely in the direction determined by this field. It is
clear that the main volume of the sample being in the ferroelectric state will
demonstrate the usual switching behavior. The influence of non-polar inclusions
are essential only in the regions close to the interfaces (boundaries of non-
polar inclusions). The backswitching (switching in negative field) takes place
in these regions under the action of E
dep
(produced by bound charges at the
boundaries of non-polar inclusions), which stimulates the switching to the
multidomain state in the bulk. This first switching stage is characterized by
the averaged value of the local coercive field E
m1
. The transition from the
multidomain state to the single domain one in the regions close to interfaces
is hindered by increasing of E
dep
. Thus, the final switching stage is characterized
by averaged value of the local coercive field E
m2
. It is clear that the single
domain state existing in high applied field is unstable and will be destroyed
by E
dep
after external field switch-off. Thus, the splitting 0.5 (E
m2
– E
m1
) is
determined by the value of E
dep
:
E
dep
= 0.5 (E
m2
– E
m1
) 21.8
The critical temperature dependence of E
dep
(Fig. 21.25b) allows us to define
the temperature T
f
, which characterizes transition to the unstable field-induced
state caused by the appearance of non-polar inclusions. For PLZT 8/65/35 T
f
= 38°C has been obtained.
21.8.2 Switching by rectangular pulses
It is well known that recording of the switching current under application of
the rectangular pulses is the most effective for quantitative characterization
of the domain kinetics (Merz, 1956). The analysis of the switching current
data based on the Kolmogorov–Avrami (K-A) approach (Kolmogorov, 1937;
Avrami, 1939) to the description of the phase growth during phase
transformation was proposed by Ishibashi and Takagi (1971). The modification
of the K-A approach for polarization reversal in finite media (Shur et al.,
1998) allows us to find out the domain growth dimensionality. As a result, it
is possible to distinguish between two main variants of nucleation processes
and to reveal the geometry of the domain structure without direct visualization
(Shur et al., 1998).
The switching current data (Fig. 21.26) recorded under the action of
rectangular pulses for the relaxor phase (T > T
fd
) have been fitted using the
following formula:
j(t) = j
c
(t) + j
s
(t) 21.9
where j
c
(t) = j
0
exp(–t/τ
c
) is due to charging of ferroelectric capacitor, τ
c
depends on the parameters of the external circuit, j
s
is the proper switching
current caused by polarization reversal in ferroelectric regions.
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Nano- and micro-domain engineering 661
The switching current component j
s
has been fitted by K-A formula modified
for switching in finite media, which accounts for existence of the heterophase
structure of relaxors (Fig. 21.26) (Shur et al., 1998, 1999a):
j
s
(t) = 2P
s
dq(t)/dt 21.10
where q(t) = exp[ – (t/t
0
)
n
(1 – t/t
m
)], t
0
and t
m
are time constants, t
m
accounts
for the impingement of the growing domains on the switched volume boundary.
Exponent n is so-called growth dimensionality.
Two limiting situations of the nucleation process are usually considered
following Kolmogorov classification. The first, α model, when the nuclei
are arising through the whole process with nucleation probability α(t), and
the second, β model, when all nuclei have arisen at the very beginning of the
process with the density β (Shur et al., 1998). n = d + 1 for α model, and n
= d for β model, where d is the topological dimensionality. In our approach
the meaning of d is changed and it is interpreted as the growth dimensionality
equal to 1, 2, or 3. d = 3 for growth of new domains in the bulk, d = 2 for
sideways growth of cylinder domains, and d = 1 for parallel shift of the walls
of domains organized in the maze-like structure (Ishibashi and Tagaki, 1971;
Shur et al., 1998).
It has been found out by analysis of the switching current data measured
in PLZT ceramics in all experimental conditions that the best-fit value of the
growth dimensionality is equal to 2 and can be classified as α(1D) process.
It means that the parallel shift of the domain walls is the predominant
mechanism of the domain kinetics. Thus, the polarization reversal in relaxor
ceramics is the result of the evolution of the maze domain structure, which
is in accordance with interpretation of the hysteresis loop data.
Current, a.u.
20
15
10
5
0
01020304050
Time, ms
21.26
Switching current under application of rectangular pulses for
PLZT 7/65/35. Experimental points are fitted by Equations [21.9] and
[21.10]. Short dashes –
j
c
(
t
), charging of ferroelectric capacitor; long
dashes –
j
s
(
t
), switching current caused by polarization reversal in
ferroelectric regions.
E
= 7.6kV/cm.
T
= 89°C.
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Handbook of dielectric, piezoelectric and ferroelectric materials662
21.8.3 Visualization of the nano-domain structure
The nanoscale domain structure has been visualized with good contrast by
PFM (Fig. 21.27b). The typical domain pattern of PLZT ceramics after zero-
field-cooling represents the quasi-regular nanoscale maze (‘fingerprint’ pattern).
Light and dark areas correspond to domains with different polarization
directions. It has been shown that the fractions of the areas occupied by
different domains are almost equal.
The PFM images contain the piezoelectric response of the domain structure
integrated over the volume, the depth of which depends on the applied
voltage. Thus, the observed diffused boundaries between neighboring domains
are caused by randomly oriented charged domain walls. It is an evidence of
the existence of 3D maze structure, predicted by our interpretations of the
switching data. The similarity of the structures in grains with different
orientations is the additional argument in favor of 3D maze geometry (Fig.
21.27a).
The main characteristics of the maze domain structure have been extracted
by statistical analysis of the PFM images. It has been found that the average
value of the maze segment width (‘period’) is essentially dependent on the
La concentration. For x = 9.75% the maze period is 170 ∼ 220nm, while for
x = 7% the period is 30 ∼ 40nm.
A fractal analysis was carried out by so-called ‘island method’ of PFM
images considered as the section of 3D domain structure (Feder, 1988). The
obtained value of fractal dimension is equal to 2.5±0.1. Such a result allows
us to suppose that the formation of the nanoscale domain structure during
zero-field cooling is the random spatially non-correlated process (Feder,
1988).
21.27
(a) Nanoscale structure in different grains and (b) maze domain
structure visualized by PFM in PLZT 9.75/65/35 ceramics.
(a)
2µm
(b)
0.5µm
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Nano- and micro-domain engineering 663
21.9 Conclusions and future trends
In this chapter, we have formulated the unified approach to the domain
kinetics based on the nucleation mechanism of the polarization reversal and
demonstrated its validity for understanding the variety of experimentally
observed domain evolution scenarios in LN and LT single crystals. It has
been proved that the kinetics of the ferroelectric domain structure essentially
depends upon the effectiveness of the screening processes. Original scenarios
of the domain structure evolution were revealed experimentally and discussed
within unified approach accounting for the decisive role of the retardation of
the screening process. It has been shown that the predetermined nucleation
effect plays the key role in the growth of the polygon domains in LN and LT.
It has been demonstrated that the degree of screening effectiveness determines
the formation of the whole variety of the shapes of isolated domains
experimentally observed in LN and LT from regular hexagons to three-ray
stars. The role of merging in formation of super-fast X domain walls was
revealed experimentally and by computer simulation. We have demonstrated
that the evolution of a domain structure in LN and LT under the highly non-
equilibrium switching conditions proceeds through the formation of the self-
assembled nanoscale structures.
The results of the fundamental investigations were used as a physical
basis of ‘domain engineering’. The proposed and realized new techniques
allow the production of the short-pitch regular domain patterns with record
periods in LN and LT single crystals. The modern tricks in nanoscale domain
engineering (formation of nanoscale quasi-regular domain structures) have
been reviewed. The elements with tailored domain structures demonstrate
nonlinear optical properties required for modern coherent light frequency
conversion devices with upgraded characteristics. The application of the
proposed approach to the analysis of the hysteresis loops and switching
current data in relaxor PLZT ceramics enables us to reveal the key role of
nanoscale non-polar inclusions in polarization reversal in relaxor state.
The recent achievements in studying the domain kinetics with nanoscale
resolution allow predicting that the future of the domain engineering lies in
the production of the tailored nano-domain structure and the structures
possessing the nanoscale period accuracy. Several approaches to creation of
the regular nanoscale structures can be singled out. The precise periodic
structures can be produced as a result of the local switching of the single-
domain using application of the inhomogeneous electric field by the nanoscale
electrode pattern, conductive tip of SPM or electron beam. According to the
experimental results discussed above the periodic nanoscale heterogeneous
modification of the surface layer by various alternative methods looks very
promising. The most interesting and effective methods are those that
are based on formation of self-assembled structures. Some examples of
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Handbook of dielectric, piezoelectric and ferroelectric materials664
quasi-regular self-assembled structures and ways to produce them were
discussed in this chapter.
It is clear that the future development of nanoscale engineering requires
deep investigations of the polarization kinetics in normal and relaxor
ferroelectrics using modern sophisticated experimental methods with nanoscale
resolution including elaborate modes of SPM, scanning electron and ion
microscopy, and focused ion beam (FIB). The development of a reliable
technology for domain engineering at the submicrometer scale would be a
major breakthrough, leading to a brand new generation of photonic devices.
In this chapter I have attempted to show how these two aims are interconnected.
The occurrence of nano-domain chains destroying the duty cycle and that of
nano-domain ensembles occur under the same highly non-equilibrium
conditions.
21.10 Acknowledgments
The research was made possible in part by INTAS (Grant 03-51-6562); by
Federal Agency of Science and Innovation (Contract 02.513.11.3128); by
Program ‘Development of the Scientific Potential of High Education’ of the
Federal Agency of Education (Grant RNP 2.1.1.8272); by RFBR-CNRS
(Grant 05-02-19648), and by RFBR (Grants 06-02-08149-ofr and 07-02-96033-
r_ural). It is a pleasure to acknowledge the many helpful stimulating discussions
with A. Alexandrovski, A. Bratkovski, R.L. Byer, L.E. Cross, M.M. Fejer, J.
Fousek, V.M. Fridkin, K. Kitamura, A.L. Korzhenevskii, A.P. Levanyuk,
A.L. Roytbourd, E.L. Rumyantsev, J.F. Scott and L.A. Shuvalov in the course
of preparation of this publication.
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