Local polarization dynamics in ferroelectric materials

Rep. Prog. Phys. 73 (2010) 056502
S V Kalinin et al
High Low
ττ τ
2
1
Amplitude
(a)
Time
(b)
Vac
δτ
τ 3
V
tip
= V
dc
+ V
ac
sinωt
−
V c
−
R 0
Response
+
R s
−
R
R init
−
V c
Bias
(c)
−
R s
(d)
−
R 0
+
V c
Figure 37. (a) Switching and (b) probing waveforms in SS-PFM. (c) Data acquisition sequence. (d) Schematics of well-saturated
electromechanical hysteresis loop in the PFM experiment. Forward and reverse coercive voltages, V + and V − , nucleation voltages, V
c
+ and
Vc −,
forward and reverse saturation and remanent responses, R+ 0 , R− 0 , R+ s and R− s , are shown. Also shown is the initial response, R init. The
work of switching A s is defined as the area within the loop. The imprint bias and maximum switchable polarization are defined as
Im = V
0 + − V −
0
and R m = R
s + − R− s
correspondingly. Adapted with permission from [328]. Copyright 2006, American Institute of Physics.
hysteresis loops. This approach was later used by
several groups to probe crystallographic orientation and
microstructure effects on switching behavior [157, 162, 324–
327]. Recently, PFM spectroscopy has been extended to
an imaging mode using an algorithm for fast (30–100 ms)
hysteresis loop measurements developed by Jesse et al [328].
In the switching spectroscopy PFM (SS-PFM), hysteresis
loops are acquired at each point of the image and analyzed
to yield 2D maps of imprint, coercive bias and work of
switching, providing a comprehensive description of the
switching behavior of the material at each point.
Below, we summarize the technical aspects of voltage and
time spectroscopy in PFM, discuss relevant theoretical aspects
and summarize recent experimental advances.
4.1. Experimental apparatus for PFS and SS-PFM
During the acquisition of a hysteresis loop piezoresponse force
spectroscopy (PFS), the tip is fixed at a given location on
the surface and the waveform V tip = V probe (t) + V ac cos ωt
is applied to the tip. V ac is the amplitude of the PFM driving
signal. The probing signal, V probe (t), is shown in figure 37 and
is composed of a sequence of pulses with amplitude, V i , and
length, τ 1 (HIGH state) separated by intervals of zero bias lasting
for τ 2 (LOW state). The measured responses yield on-field and
off-field hysteresis loops.
To generate SS-PFM maps, the hysteresis loops are
acquired over M × M point mesh with spacing, l, between
points. The hysteresis curves are collected at each point and
stored in a 3D data array for subsequent analysis. Parameters
describing the switching process such as positive and negative
coercive bias, imprint voltage and saturation response can
be extracted from the data sets and plotted as 2D maps;
alternatively, hysteresis loops from selected point(s) can be
extracted and analyzed.
An ideal hysteresis loop for electromechanical measurements
is shown in figure 37(d). Acquired at each point is
a hysteresis loop containing the forward, R + (V ), and reverse,
R − (V ), branches. The zero of R + (V ) defines positive coercive
bias, V + , and the zero of R − (V ) defines negative coercive bias,
V − . The imprint is defined as Im = (V + + V − )/2. The values
of R
0 + = R+ (0) and R − 0
= R− (0) define positive and negative
remanent responses, while R 0 = R
0 + − R− 0
is the remanent
switchable response. Finally, R + (+∞) = R − (+∞) = R s
+
and R + (−∞) = R − (−∞) = Rs
− are the saturation responses
and R s = R s + − R− s is the maximal switchable response. In
some cases, contributions of electrostatic signals (tip electrode)
or bimorph-like substrate bending (macroscopic capacitors)
necessitate the introduction of vertical offset to symmetrize
the loop. Finally, the forward and reverse domain nucleation
voltages, V c
+ and Vc − , corresponding to the cross-over
between constant and rapidly changing regions of the loop,
are attributable to domain nucleation below the tip. Additionally,
the effective work of switching is defined as the area within
a hysteresis loop,
A s =
∫ +∞
−∞
(
R + (V ) − R − (V ) ) dV. (4.1)
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