Local polarization dynamics in ferroelectric materials

Rep. Prog. Phys. 73 (2010) 056502
S V Kalinin et al
Response, a.u.
1.0
0.5
0.0
-0.5
-1.0
(a)
-10 -5 0 5 10
Bias, V dc
Work of switching, a.u. V
(b)
15
10
5
0
0 2 4 6 8 10
Modulation voltage, V ac
1.5
1.0
0.5
0.0
Switchable response, a.u.
Figure 38. The driving bias effect on the hysteresis loop shape. (a) Hysteresis loops for PZT thin film for ( ) 1.5 V pp ,() 4V pp ,()6V pp
and (•) 8V pp driving amplitudes. (b) Driving bias dependence of effective work of switching and saturation response. Reprinted
from [329]. Copyright 2006, American Institute of Physics.
These parameters provide a measure of the switching
properties of the material.
4.1.1. Effect of imaging conditions on hysteresis loops. As
in any spectroscopic method, PFS and SS-PFM are highly
susceptible to a large number of external and internal factors
that affect the veracity of spectroscopic data acquisition. The
detailed analysis of instrumental factors is reported in [329].
Below, we discuss the effect of measurement parameters
on PFS.
4.1.2.1. Probing bias and the bias window. One important
consideration in PFM and SS-PFM is the choice of driving
voltage, V ac , and bias window of measurements, V dc ∈
(V min ,V max ). Ideally the measurements are performed in the
low signal limit, V ac ≪ (V + + V − ). However, practical
considerations such as maximizing the signal strength often
necessitate the use of high driving voltages, in particular for
materials with relatively low piezoelectric coupling. The effect
of a finite probing bias on the loop shape strongly depends
on the fundamental hysteresis loop formation mechanism and
bias frequency, and cannot be explained by a simple model.
Here, we summarize the experimental studies of the driving
bias effect.
Shown in figure 37(a) are experimentally observed
hysteresis loops obtained on a pulsed-laser deposition grown
PZT thin film (70 nm) for different probing biases. The loops
are normalized by bias amplitude to ensure similar units. Note
that for V ac below the coercive bias, the loop shape remains
largely unchanged—the loops slightly narrow indicating the
onset of switching, but the variation in relevant parameters
is relatively small (figure 37(b)). Conversely, modulation
amplitudes greater than the coercive bias effectively result
in a collapse of the loop to a straight line. The changes in
the effective work of switching and switchable response as a
function of V ac are shown in figure 38(b). The small variation
in relevant characteristics for small biases is presumably due
to a relatively larger noise level. Note that the behavior in
figure 38 is reproducible and the shape is regained when small
biases are used demonstrating that the collapse in the loop
shape cannot be attributed to the damage to the conductive tip
coating or the surface. Thus, for certain materials, voltages at
∼2/3 of the coercive bias level can be used to yield high-quality
loops. At the same time, for materials with small coercive bias,
e.g. ferroelectric nanodots, ultrathin films, etc, imaged at large
modulation voltages, the absence of hysteresis loops can be
erroneously interpreted as evidence for non-ferroelectric state.
The dependence of the loop parameters on the bias window
is illustrated in figure 39. The hysteresis loops become
saturated when the bias windows exceed 20 V (figure 49(a)).
The origins of the slight downward trend are unclear but can
possibly be attributed to reverse switching induced by charge
injection at the surface [304]. The bias window dependence of
switchable polarization is illustrated in figure 39(b). Note the
good agreement between the values obtained from fitting and
those measured directly from the loop. Figure 39(c) illustrates
the dependence of the positive and negative nucleation biases
on the bias window. Despite the relatively large error in the
determination of nucleation bias, the values are nearly biaswindow
independent, suggesting that the loop formation is
controlled by the nucleation process. Finally, figure 39(d)
illustrates the bias window dependence of the effective work of
switching as determined from functional fitting and the direct
integration of the area below the curve. The values obtained
are in good agreement and also illustrate that the leveling-off
of hysteresis parameters at large voltages are indicative of loop
saturation.
4.1.2.2. Ambient effects. One of the well-known factors
affecting SPM measurements under ambient conditions is the
presence of wetting water layers and associated capillary tip–
surface forces as described in section 3.2.5. Here, we present
experimental evidence illustrating the possible role of ambient
conditions on hysteresis measurements by PFM.
Shown in figure 40(a) is the PFM hysteresis loop obtained
on a freshly prepared (buffered HF etch followed by O 2
annealing) atomically flat STO (1 0 0) surface. Shown are
the average values and error bars corresponding to standard
deviations determined from 64 hysteresis loops acquired on
an 8×8 mesh of points separated by 100 nm. Note that
clear hysteretic behavior can be seen despite the fact that
the surface is (nominally) non-ferroelectric. We attribute
39