Piezoresponse force microscopy

This is achieved by bringing a sharp conductive probe into contact with a ferroelectric surface (or piezoelectric material) and applying an alternating current (AC) bias to the probe tip in order to excite deformation of the sample through the converse piezoelectric effect (CPE).

The resulting deflection of the probe cantilever is detected through standard split photodiode detector methods and then demodulated by use of a lock-in amplifier (LiA).

Piezoresponse force microscopy is a technique which since its inception and first implementation by Güthner and Dransfeld [1] has steadily attracted more and more interest.

This is due in large part to the many benefits and few drawbacks that PFM offers researchers in varying fields from ferroelectrics, semiconductors and even biology.

[2] In its most common format PFM allows for identification of domains from relatively large scale e.g. 100×100 μm2 scans right down to the nanoscale with the added advantage of simultaneous imaging of sample surface topography.

Indeed what started as a user modified AFM has now attracted the attention of the major SPM manufacturers so much so that in fact many now supply ‘ready-made’ systems specifically for PFM each with novel features for research.

Consider that a static or DC voltage applied to a piezoelectric surface will produce a displacement but as applied fields are quite low and the piezoelectric tensor coefficients are relatively small then the physical displacement will also be small such that it is below the level of possible detection of the system.

In order to separate this low level signal from random noise a lock-in technique is used wherein a modulated voltage reference signal, of frequency ω and amplitude Vac is applied to the tip giving rise to an oscillatory deformation of the sample surface, from the equilibrium position d0 with amplitude D, and an associated phase difference φ.

A lock-in-amplifier (LiA) is then able to retrieve the amplitude and phase of the CPE induced surface deformation by the process outlined below.

The converse piezoelectric effect (CPE) describes how an applied electric field will create a resultant strain which in turn leads to a physical deformation of the material.

If the piezoelectric tensor is considered to be that of the tetragonal crystal system (that of BaTiO3) then it is such that the equation will lead to the strain components for an applied field.

If the field is applied exclusively in one direction i.e. E3 for example, then the resulting strain components are: d31E3, d32E3, d33E3 Thus for an electric field applied along the c-axis of BaTiO3 i.e. E3, then the resulting deformation of the crystal will be an elongation along the c-axis and an axially symmetric contraction along the other orthogonal directions.

This is generally required in order to provide a means of applying a bias to the sample, and can be achieved through manufacturing standard silicon probes and coating them in a conductive material.

However, phase and amplitude of the input signal can also be calculated and made output from the LiA if desired, so that the full amount of information is available.

[5] The separation of these components is possible through the use of a split photodiode detector, standard to all optical detection AFM systems.

Similarly a lateral deflection is defined as {(B+D)-(A+C)}/(ABCD) to describe positive and negative torsional movements of the cantilever.

So VPFM will utilise the vertical deflection signal from the photodiode detector so will only be sensitive to out-of-plane polar components and LPFM will utilise the lateral deflection signal from the photodiode and will only be sensitive to in-plane polar components.

In this way it is possible to determine the orientation of the vertical components of polarisation from analysis of the phase information, φ, contained in the input signal, readily available after demodulation in the LiA, when using the VPFM mode.

In a similar sense the orientations of in-plane polar components can also be determined from the phase difference when using the LPFM mode.

PFM has been successfully applied to a range of biological materials such as teeth,[6] bone, lung,[7] and single collagen fibrils.

Several additions have been made to PFM that substantially increase the flexibility of the technique to probe nanoscale features.

[10] Typically this contact resonance is in the kilo- to mega-hertz range which is several times higher in frequency than the first free harmonic in air of the cantilever used.

It is then possible to adapt the AC bias driving frequency correspondingly in order to maintain the signal boost that results from the contact resonance.

In this technique the area underneath the PFM tip is switched with simultaneous acquisition of a hysteresis loop that can be analysed to obtain information about the sample properties.

[11] A series of hysteresis loops are acquired across the sample surface in order to map the switching characteristics as a function of position.

The Band Excitation (BE) technique for scanning probe microscopy uses a precisely determined waveform that contains specific frequencies to excite the cantilever or sample in an atomic force microscope to extract more information, and more reliable information from a sample.

This software enables users of atomic force microscopes to easily: build complex band-excitation waveforms, set up the microscope scanning conditions, configure the input and output electronics to generate the waveform as a voltage signal and capture the response of the system, perform analysis on the captured response, and display the results of the measurement.

Contact mode is not suitable for samples with features susceptible to damage or displacement by the tip's drag.

Piezoresponse Force Microscopy image of BaTiO3 domains
PFM of BaTiO 3 single crystal showing simultaneously acquired topography (top) and domain structure (bottom). The scale bar is 10 μm
Diagram showing cantilever movements from mechanical deformation of piezoelectric domains
Top line shows an in-phase piezoresponse to the driving voltage and the bottom line shows a 180° out-of-phase piezoresponse to driving voltage. Alignment of electric field and polarisation orientation (top right) results in an expansion of the domain, giving a positive deflection as measured by the photodiode. When the bias is negative the domain contracts giving a negative deflection as measured by the photodiode meaning that the piezoresponse will always be in-phase with the driving voltage. For anti-alignment of electric field and polarisation orientation (bottom right) a positive bias results in a contraction of the domain and so gives a negative deflection as measured by the photodiode therefore the piezoresponse is 180° out-of-phase with the driving voltage. In this way the orientation of polarisation within a domain can be observed.
Scanning electron microscope images of increasing magnification of a conductive coated scanning probe
Scanning electron microscopy images of a PtIr 5 coated scanning probe. From left to right shows images of increasing magnification where the scale bar in the first image is 50 μm and in the third is 200 nm. The first image shows the substrate, cantilever and the tip whereas the second image shows the tip geometry whilst the last image shows the tip apex and demonstrates the fine point that is achieved e.g. radius of curvature of less than 40 nm.
Diagram showing cantilever dynamics and the optical detection through AFM split photodiode detector
Diagrams showing the effect of cantilever movement with the photodetector represented by the square with quadrants labelled A, B, C and D. Torsional bending of the cantilever (left) leads to a change in lateral deflection and (right) vertical displacement of the cantilever leads to a change in vertical deflection
180° ferroelectric domains as imaged by PFM
180° ferroelectric domains in KTP as imaged by PFM. Below are the associated line profiles across the domains
Typical atomic force microscopy set-up
Typical atomic force microscopy set-up