Local polarization dynamics in ferroelectric materials

Rep. Prog. Phys. 73 (2010) 056502
S V Kalinin et al
Loop II
1.5
Loop I
(8.4 V, 2.2)
PFM Signal, a.u.
(d)
3
2
1
0
-1
-2
-3
Loop I
Loop III
-10 -5 0 5 10
Bias, V
Signal, a.u.
(e)
1.0
0.5
0.0
(-6.6 V, 0.5)
(-9 V, 0.3)
(-5.0 V, 1.2)
(-3.6 V, 0.7)
(1.4 V, 0.3)
-10 -5 0 5 10
Bias, V
Figure 54. (a) Topography, (b) 2D map of negative nucleation bias. (c) Integral fine structure map for the forward branch of the hysteresis
loop. (d) Loops from locations marked in (a) and (e) hysteresis loop fine structure in loop I. Reproduced from [319]. Copyright 2008,
American Institute of Physics.
asymmetric. This observation suggests that the amplitude
of the pulse-induced polarization varies significantly from
point to point, while the kinetics of the observed logarithmic
relaxation is more uniform.
4.6. Switching in ferroelectric capacitors
Switching in ferroelectric capacitors was extensively studied
by the Gruverman [241, 341], Stolichnov [373–376] and Noh
[377] groups in the context of applications to FeRAM. It is well
recognized that polarization switching in capacitors is initiated
at a relatively small number of defect sizes, and the switching
process proceeds though domain wall motion. PFM can be
employed to study capacitor switching in the stroboscopic
mode, in which domain pattern changes as a function of voltage
pulse length and amplitude are measured [93–95, 241, 378]
This step-by-step switching [342, 343, 368] approach can
be used to measure the domain kinetics (nucleation and
growth) during polarization reversal and the results can be
compared with experimental macroscopic results and with
theory [81, 377, 379–383]. As discussed in section 2.3.3.5,
this approach is limited by the resolution of PFM on capacitor
structures, which is determined by the structure thickness
rather than tip–surface contact area.
Despite this limitation, this approach was extensively
used to study imprint and flexoelectric effects in capacitors
[241], variability of switching behavior in capacitor structures
[341, 378], interplay between nucleation and domain wall
motion [368] and nucleation probability distribution in capacitors
[377]. Noteworthy is that similar studies can be performed
dynamically (using real-time resolution) using focused x-rays
[369]. However, since the top electrode covers the surface of
the ferroelectric, it is not possible to correlate the surface structure
with the nucleation sites, nor is it possible to rule out the
influence of the metal–ferroelectric interface roughness.
The second approach for probing polarization dynamics
in capacitors is based on SS-PFM, as reported recently [384].
It has been shown that in polycrystalline materials, switching
often proceeds through the formation of correlated clusters
containing 10 2 –10 3 grains, presumably stabilized by elastic
interactions active on the length scale of film thickness.
Finally, studies of in-plane capacitor switching using
a combination of in-plane electric field and PFM imaging
(i.e. capacitor cross-section studies) merit separate discussion.
This approach was introduced by Lu et al [385] and Gysel
et al [386] using beveled and cross-sectioned planar capacitors,
and further developed by Balke et al using specially fabricated
structures [387]. These measurements allow the nucleation
and lateral wall growth stages to be visualized directly and
to establish the relationship between these processes and the
field history of the sample. Ultimately, these studies can be
performed in the electron microscopy geometry, potentially
providing insight into domain nucleation and wall motion
mechanisms on the sub-10 nanometer and atomic levels.
5. Phase-field simulations of local ferroelectric
switching mechanism
Polarization switching under PFM is a temporal and spatial
evolution process driven by a highly inhomogeneous external
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