Local polarization dynamics in ferroelectric materials

Rep. Prog. Phys. 73 (2010) 056502
2. Principles and instrumental aspects of PFM
S V Kalinin et al
2.1. Basic principles of PFM
The PFM approach for probing piezo- and ferroelectric properties
at the nanoscale is based on the strong coupling between
polarization and electromechanical behavior. Correspondingly,
these behaviors can be addressed by applying a highly
localized electric field to the material and probing the resultant
minute surface displacements with ∼picometer precision.
Atomic force microscopy (AFM) [112] provides an ideal platform
for these studies due to intrinsically high vertical resolutions,
and high localization of electric fields at the junction
between the metalized tip and the surface. Hence, PFM is a
contact-mode AFM technique in which an electrically biased
conductive AFM tip is used as a probe of local electromechanical
coupling via the converse piezoelectric effect. Remarkably,
the basic image formation mechanism in PFM is complementary
to force-based AFM methods (force is applied and the tip
deflection is measured) and scanning tunneling microscopy
(STM) [113] (bias is applied, and a current is measured).
This unique mechanism defines all aspects of PFM operation,
including resolution, quantitativeness and the potential for the
use of resonance enhancement, as discussed below.
Following the invention of STM (1982) and AFM
(1986) [112–114], the first instances of measuring biasinduced
sample deformation in piezoelectric materials by a
scanning probe came in 1991 when piezoelectric response, or
piezoresponse (PR), was measured using scanning acoustic
microscopy [115] and STM [116]. Shortly thereafter, the first
papers on piezoelectric measurements [117] and ferroelectric
domain visualization [118, 119] by AFM were reported.
Papers by Takata et al [120, 121] (using strain imaging via
tunneling acoustic microscopy), Franke et al [122], Kolosov
et al [123], Gruverman et al [124–128] and Hidaka et al
[129] followed. The work of Gruverman et al is particularly
notable for demonstrating imaging and switching in inorganic
ferroelectrics and coining the terms ‘Piezoresponse’ and
‘PFM’ which have now become standard. In the past decade
and a half, PFM has become the premier tool for studying static
and dynamic properties of ferroelectric materials, as evidenced
by a number of recent books and reviews [106–111]. PFM
has been extended beyond ferroelectric thin films, ceramics
and crystals to ferroelectric polymers [130–137], piezoelectric
semiconductors (GaN [138, 139] AlN [140, 141] and ZnO
[142–144]) and piezoelectric biopolymers, including collagen
[145–152] and chitin [153, 154].
2.1.1. Elementary theory of PFM. In PFM, a voltage is
applied to a conductive tip
V tip = V dc + V ac cos (ωt) (2.1)
in contact with a piezoelectric material. Here V dc is the dc bias
(switching bias), V ac is the ac bias (probing bias) and ω is the
ac bias frequency (driving frequency).
As the sample expands and contracts due to the converse
piezoelectric effect, the tip deflection is monitored using a
lock-in amplifier so that the tip oscillation
A = A 0 + A 1ω cos (ωt + ϕ) , (2.2)
Figure 3. The sample deformation can be detected via a tip
deflection caused by the (a) expansion or contraction of the
piezoelectric material or via a tip torsion caused by the (b) shear
deformation of the material. The deflection and torsion signals
represent vector components of the polarization and can be
combined to determine the real space polarization orientation via (c)
vector PFM (BiFeO 3 (BFO) film, topography inset). Reprinted
from [111]. Copyright 2008, Cambridge University Press.
and hence the sample deformation at the driving frequency
of the ac voltage, A 1ω , is recorded simultaneously with
topography. Here A 0 is the static surface displacement and ϕ is
the phase shift between the driving voltage V ac and the voltageinduced
deformation, A 1ω . The PFM amplitude provides
information on the magnitude of the local electromechanical
coupling, while the PFM phase image provides information
on the ferroelectric domain orientation. Typically the imaging
resolution of PFM is less than ∼10–30 nm as determined from
half of the width of a domain wall in the mixed PFM signal,
PR = A 1ω · cos (ϕ) . (2.3)
The resolution is ultimately limited by the tip–sample
contact area (nominally determined by the radius of the tip
apex), though additional mechanisms for broadening such as
electrostatic interactions and the formation of a liquid neck
in the tip–surface junction are possible. Note that PFM can
also be used to visualize the domain structure through a metal
electrode. In this case, the field is applied uniformly across
the ferroelectric capacitor, and the resolution is limited by the
thicknesses of the top electrode and ferroelectric layer [155].
In addition to the time-dependent flexural vibration
signals, the torsional oscillation of the cantilever can be
monitored in order to measure piezoelectric shear deformations
via the frictional force resulting from any in-plane component
of polarization. This in-plane PFM, commonly called lateral
PFM (LPFM) in contrast to out-of-plane PFM or vertical PFM
(VPFM), was first demonstrated by Eng et al [156, 157] and
has been applied to a number of materials systems including
films, crystals, nanostructures and capacitors [158–163]. The
in- and out-of-plane polarization information can be combined
to reconstruct the real space polarization via vector PFM [164]
(figure 3).
2.1.2. PFM versus other SPMs. The fundamental factors
underpinning the contrast formation mechanism in any
5