Piezoresponse Force Microscopy (PFM)

 Basic Principle

Piezoresponse force microscopy (PFM) is based on the mechanical deformation of a sample due to the converse piezoelectric effect: The application of an electric field leads to thickness changes and / or to shearing of the material, depending on the direction of the electric field together with the piezoelectric tensor elements.

For PFM a scanning force microscope is operated in contact mode with a voltage (typically ~ 10 V) applied to the tip. The electric field causing the piezoelectric deformations is thus applied only locally between the sharp tip and a back-electrode underneath the sample, resulting in a local deformation of the sample in a restricted volume of few cubic µm at its very surface. The amplitude of the deformations being extremely small, of the order of few pm only, the voltage applied to the tip is frequency modulated (typically some 10 kHz) and readout is performed with a Lock-In amplifier (LIA).

Figure 1
Electronic setup for PFM-operation.
Topography and piezoresponse can be read-out independentyl and simultaneously

In-plane and out-of-plane signals

PFM has become a very versatile tool for the investigation of ferroelectric domain patterns. This is due to the fact that ferroelectricity etails piezoelectricity, and consequently a ferroelectric domain pattern can be recorded by PFM. A material where ferroelectric domains are of major interest for non-linear optical applications is lithium niobate (LiNbO₃). An example of a domain pattern imaged by PFM can be seen in the figure shown opposite. In (a) the out-of-plane signal (deflection) and the in-plane signal (buckling a the top edge) can be seen, both showing up in the vertical PFM output chanel. In (b) all edges show an in-plane signal (torsion) as measured by lateral PFM output chanel. The out-of-plane signal can be attributed to a thickess change of the sample, The in-plane signals are, in the case of LiNbO₃, most probably a combination of a deformation at the domain boundary and the electric field at the sample surface.

Vertical (a) and lateral (b) output chanels recorded simultanesouly with two independent lock-in amplifiers and the respective scan-lines in (c). In (d) the domain configuration is shown and (e) schematically depicts the possible movemets of the tip. Deflection is caused by an out-of-plane driving force and buckling and torsion are caused by an in-plane driving force. Obviously the vertical out-put channel records a combination of deflection and buckling.

PFM on all crystallographic faces

In some cases it is of interrest to map the ferroelectric domain patterns irrespective of the crystallographic faces. In order to understand the contrast mechanism which leads to a PFM signal is it most approprite to investigate a crystal with a known crystallographic cut and a known domain pattern. We used a LiNbO₃ crystal which was periodically poled in two directions. Utilizing the knowledge gained from the simple situation described above, it becomed possible to explain the origin of the PFM contrast observed on all faces of such a sample.

Figure 3
Images (a,b), (c,d) and (e,f) display the vertical and lateral read-out channels, respectively. The image paires were recorded simultanesously. Obviously on all faces, the domain pattern can be detected by PFM. Note that in Figs. (b) and (f) only the domain boundaries are visible, in (c) and (d) only the domain faces are displayed, and in (a) both, boudaries and faces are seen.

Determination of the orientation
of an arbitrarily oriented particle

Samples with LiNbO₃ particles of different orientations embedded in a non-ferroelectroic matrix were fabricated in a sol-gel process. In order to determine the orientation of the individual particles the first necessity is to unambiguously separate between out-of-plane and in-plane signal (which both show up in the same read-out chanel, see above). This can be performed by rotating the sample by 90° and 180° and subsequently recording the very same area. We therefore used a high-precision computer controlled rotation stage built on purpose. The next step consists of the adequate addition/subtraction of the obtained images. The result is shown in the figure opposed. Obtaining from such images the direction of polarization of every particle is a very cumbersome task and needs a quantitative analysis of the PFM contrasts. A task which needs, most probably, finite element simulation.

Figure 4
Measured (a and d) and deduced (b and c) PFM images of arbitrarily oriented ferroelectric particles.

Quantitative PFM measurements

The smalless of the piezoresponse, typically of the order of 10 pm/V only, makes PFM imaging very sensitive to any environmental noise. In particular mechanical resonances of the experimental setup, also if they are only of few pm amplitude, prevent from quantitative measurements. The opposed figure shows an example for a PFM signal comprising the piezoelectric response of the sample and the frequency dependent background owing to the mechanical resonances of the SPM head (a). Background subtraction in PFM imaging is therefore of major interest. The result can be seen in (b), where a frequency-independent PFM signal is shown.

Figure 5
PFM signal on a LiNbO₃ sample before (a) and after (b) the subtration of the background. Please note the x10-zoomed vertical scale of the background-free signal.

Lateral resolution in PFM

Same than in every scanning probe technique, the lateral resolution of the measurements is of major interest. In the case of PFM, the witdth a (atomically sharp) domain wall is seen reflects the lateral resolution. The contrast in PFM is due to the local mechanical deformation of the sample surface. This limits by nature the possible lateral resolution due to clamping effects: when scanning across a domain boundary, one side expands whereas the other side contracts.

Figure 6
(a) Model used for calculating the expected deformation: volumes I and II cancel out each-other, the deformation of volume II will govern the PFM signal. (b) Comparison of the experimental data with the result obtained from the model. (c) lateral resolution masured with tips of different radii using a t = 500 nm thick sample. The line represents the result from the model.