Local polarization dynamics in ferroelectric materials

Rep. Prog. Phys. 73 (2010) 056502
S V Kalinin et al
Activation energy (eV)
Nucleus radius (nm) Nucleus length (nm)
10 5
10 4
10 3
10 2
(a)
Critical radius (nm) Critical length (nm) Critical voltage (V)
10
1
-1 -0.5 0. 0.5 1 -1 -0.5 0. 0.5 1
10 4 10 4
10 3 (b)
(e)
10 3
10 2
10 2
10
10
1
1
-1 -0.5 0. 0.5 1. -1 -0.5 0. 0.5 1.
60
20 (c)
(f)
40
10
20
0
0
-1 -0.5 0. 0.5 1. -1 -0.5 0. 0.5 1.
σ S (P S units)
σ S (P S units)
10 4
10 3
10 2
10
(d)
Figure 33. (a) Activation energy (eV) at U cr and nucleus sizes (b), (c); (d) critical voltage U cr (V), critical domain sizes (nm): length l(U cr )
(e) and radius r(U cr ) (f ) versus surface charge density σ S (in P S units). Solid curves correspond to EPCM model of the tip; dotted ones
correspond to the exact series for the sphere–tip interaction energy, dashed curves represent the capacitance approximation. Material
parameters are given in caption to figure 31. Reproduced from [317].
3.3.3. Surface screening effects. Theoretical descriptions
of nanodomain formation in the field of a local probe under
ambient conditions should take into consideration the layer
of adsorbed water located below the tip apex [277], and,
more generally, the dynamic and static surface charging and
screening phenomena.
The relevance of the specific screening mechanism on
polarization switching dynamics depends on the relationship
between the corresponding relaxation time, τ S , and voltage
pulse time, τ U (i.e. the recording time of the domain). ‘Fast’
screening mechanisms with τ S τ U significantly affect the
switching process, whereas the ‘slow’ ones with τ S ≫ τ U
can be ignored. However, these slow mechanisms can
significantly affect the domain stability after switching by
providing additional channels for minimizing depolarization
energy.
The role of environmental effects and screening
mechanisms on switching can be illustrated as follows. Shown
in figure 33 are the activation energies for nucleation (a)
and nucleus sizes (b), (c), critical voltage (d) and sizes
(e), (f ) calculated in the framework of the sphere–plane
model, the modified point charge model and the capacitance
approximation under different screening conditions on the
surface, i.e. σ S values. It is clear from the figure that all
critical parameters rapidly increase under the charge density σ S
increase from −P S to +P S . In particular, the activation barrier
for nucleation at the onset of domain stability (see figure 33(a))
is minimal for complete screening at σ S = −P S (10 eV)
and increases up to 10 5 eV for σ S → +P S . However, the
barrier height strongly decreases with further voltage increase
U>U cr at all σ S values. Note that the barrier calculated in the
inhomogeneous electric field of the tip is 3–5 orders lower than
the one calculated by Landauer for the homogeneous electric
field. The values obtained at σ S > −P S are still too high for
thermal fluctuations to cause the domain nucleation at U ≈
U cr . Thus the observed domains could either originate at higher
voltages in the perfect ferroelectric sample, or nucleation must
be defect-related.
This analysis suggests that environmental effects and
surface states will critically influence polarization switching
processes in PFM. In particular, the dependence of critical
voltage U cr values over ambient conditions (if any) could
clarify the surface screening influence. As a recent example,
Terabe et al [318] have demonstrated that values of U cr on
+Z and −Z cuts of LNO or LTO crystals differ by a factor
of 2, illustrating the effect of the surface state on the switching
mechanism.
3.3.4. Switching in the presence of defects. In the
mesoscopic models considered above, the defect can affect the
34