26 Atomic Force Microscopy and Piezo Response Microscopy

Introduction

Ferroelectric materials form a sub-class of piezoelectric materials which undergo deformation when some voltage is applied or vice versa. These materials have wide range of properties which includes switchable electric polarization, high non-linear optical activity, strong piezoelectricity etc. These characteristics have applications in various electronic devices (IR detectors, microwave filters, non-volatile memories etc.). The synthesis and fabrication of ferroelectric materials on micro- and nano-scale demands the detailed study and of these materials at nanoscale level. These materials exhibit a distinct size effect which significantly deviates the properties from bulk to their low dimensional structure. Thus, ferroelectrics are analogous to magnetic where long-range dipole interactions can be extensively modified in lower geometries which is also dependent on whether a ferroelectric is restricted in one, two, or three dimensions. To deeply understand the structures and functionalities of these types of materials Atomic Force Microscopy (AFM) in extension with Piezoresponse Microscopy (PFM) are popular instruments used. Atomic force Microscopy (AFM) and Piezoresponse Force Microscopy (PFM) have led to a great development in this area.

Working principles of AFM

AFM works on a principle similar to the working principle of a stylus profilometer where a cantilever tip, on interaction with the sample surface, senses the local forces generated between the molecules of the tip and the sample surface as shown in Figure 1. The word “microscope” here refers to the capability of the tool to measure microscopic features of materials . In AFM the images are taken by touching the sample surface without the use of any light source. By using this method, the topography of the sample along with high resolution can be recorded. It also enables to study the characteristics and the strength of interaction between sample surface and cantilever tip as shown in Figure 1. Since no light source is being used in the AFM, it is possible to attain high resolution in diffraction limit. Its resolution only depends on the radius of the tip and the spring constant of the cantilever. Following are the main constituents of the AFM instruments:

• Probe is a pointed tip which is mounted on a soft moving cantilever
• Feedback loop monitors and allows the instrument to measure the interaction forces between the molecules on the tip and the sample surface
• Optical lever measures the deflections of cantilever
• Piezoelectric scanner is responsible for moving the cantilever tip with respect to the surface of sample in 3 dimensions
• Conversion system acquires the raw data and converts it into a display image.

Operating principle

The heart of the AFM lies with the cantilever/tip assembly that interacts with the substrate; this assembly is also commonly referred to as the probe. The tip interacts with the substrate through a raster scanning motion. The up/down and side to side motion of the tip as it scans along the surface is monitored through the “beam deflection method”. The beam deflection method consists of a laser that is reflected off the back end of the cantilever and directed towards a position sensitive detector that tracks the vertical and lateral motion of the probe. The deflection sensitivity of these detectors has to be calibrated in terms of how many nanometers of motion corresponds to a unit of voltage measured on the detector. Nanosurf instruments provide a straightforward procedure for calibration of this sensitivity and this procedure is described below in the calibration section.

The probe can also be mounted into a holder with a shaker piezo. The shaker piezo provides the ability to oscillate the probe at a wide range of frequencies (typically 100 Hz to 2 MHz) enabling dynamic modes of operation in the AFM. The dynamic modes of operation can be performed either in resonant modes (where operation is at or near the resonance frequency of the cantilever) or non-resonant modes (where operation is at a frequency usually far below the cantilever’s resonance frequency).

Different modes in AFM

1. Static mode

Static mode (also known as contact mode) is the simplest mode in operation of an AFM, in which the probe is in constant contact with the surface of the sample along with the rastering of probe onto the sample surface. This mode is useful for studying simple imaging of robust samples which can handle heavy loads and torsional forces exerted in this mode while operation.

Static mode works in the deflection feedback mode or constant force configuration in which the deflection of cantilever is mainly the feedback parameter. The deflection of cantilever is set which is related to tip pressure onto the surface of sample resulting in control of tender or aggressive pressure while interaction of the probe with the sample.

Constant height mode is a form of static mode in which the probe is made to maintain a fixed height over the surface of the sample. In this mode, no feedback force is used. Constant height mode is generally emplyed in atomic resolution AFM.

The commonly used mode in which AFM is operated is constant force mode. Moreover, the topographical image can be improved by adding a deflection signal to the sample surface morphology which is also known as the error signal because the deflection is a feedback parameter. Structures or morphology appearing in the contact force mode are because of the “error” occurring in the feedback loop.

In constant force mode, two images are observed as output: (i) height (along z-direction topography) and (ii) deflection signal.

2. Lateral force mode

Lateral force mode which is also commonly known as frictional force mode is another form of static mode. The imaging process is just same as that in the static mode with exception in the scanning motion of the cantilever where the cantilever motion is carried out in the axis perpendicular to it. Figure 2 shows the schematic of the lateral force mode scanning configuration.

In this configuration, as the probe raster scans along the sample surface, it is used for determining the friction of the surface as the side to side twisting of the cantilever via torque. These types of measurements are converted to frictional force by calibrating the constant of torsional spring of the cantilever tip.

While using this mode it is important to know about the topography of the surface of sample because the surface could also incur torsion onto a cantilever as well. To avoid this repeatedly, lateral force images are recorded by moving the cantilever and tracing the images in both the forward and reverse scan directions and then subtracting from each another.

3. Dynamic mode (amplitude modulation)

Dynamic mode (also known as amplitude modulation mode (AM-AFM)) consists of the cantilever tip oscillating at a high frequency or at close to resonance. In AM-AFM mode, the amplitude of oscillation is the feedback parameter. Other dynamic modes have frequency (frequency modulation) or phase (phase modulation) as different parameters for feedback. AM-AFM is also commonly known as tapping or contact mode.

AM-AFM has several advantages over the other modes as the cantilever oscillates at resonance and interacts with the surface of sample by tapping over it. In this mode the sharpness of the tip can be preserved as there is gentle interaction of cantilever with the sample surface as compared to static mode. The tapping of cantilever over the surface of sample also reduces the torsional forces. Thus, this mode is preferred for studying the surface morphology of soft materials such as polymers or nanostructures etc. where dynamic modes are less destructive. Finally, fine-tune interaction between cantilever and sample surface is possible by using the oscillation amplitude of the cantilever as the feedback parameter.

The cantilever is oscillated at the excitation frequency by using a Piezo shaker. The frequency of the cantilever tip is swept across a particular range, and a peak in the frequency spectrum is observed. This peak corresponds to the resonance frequency of the cantilever as shown in Figure 3.

The cantilever is then moves over the sample surface with a sinusoidal motion where its behaviour is similar to a damped spring or to a single harmonic oscillator. The amplitude of the cantilever oscillations reduces as it scans over the sample surface as shown in Figure 4.

The reduction in amplitude is the source of the feedback and one can set the amplitude according to the kind of interaction with the sample.

Piezoresponse Force Microscopy

Piezoresponse force microscopy (PFM) is based on the principle of piezoelectric effect where the mechanical deformation in the sample are observed when some field is applied. On applying an electric field, the thickness changes or the material undergoes shearing, depending upon the direction of the electric field along with the piezoelectric tensor elements. PFM is thus employed for studying the primary mechanisms underlying in the functionalities of the ferroelectric materials. The prompt advancement of scanning probe microscopy and, particularly, PFM has led to great innovations.

Working Principle

In PFM, a conductive AFM tip is made to contact the surface of the ferroelectric or piezoelectric materials. A certain voltage is applied between the sample surface and the tip which creates an external electric field contained in the sample. Because of the “inversed piezoelectric effect” observed within the ferroelectric/piezoelectric materials, the sample would either expand or contract accordingly. If suppose, the initial domain polarization is parallel to the applied electric field, then when the tip comes in contact with the sample surface, domain expansion would lead to bending of the cantilever tip in the upward direction which results in a greater deflection as compared to the position of the cantilever tip before applying the electric field as shown in Figure 5. The opposite effect occurs if the initial domain polarization was in the direction opposite to the applied electric field. The amount of change in the cantilever deflection is directly proportional to the applied electric field.

If a small AC component is present in the applied voltage, the inversed piezoelectric response from the sample results in the oscillation of the sample surface with the frequency same as the applied AC voltage. If the sample is an ideal piezoelectric crystal, its polarization would be related to applied mechanical stress according to the following equation:

Here, dijk is the rank-3 piezoelectric tensor corresponding to the material. For materials having tetragonal crystal structures, this piezoelectric tensor can be reduced to the following form:

If the applied AC modulation voltage is V=V0 cos(ωt), then the sample surface vibration will be ΔZ=ΔZ0 cos(ωt+φ), with the amplitude of vibration ΔZ0=d33V0, and phase φ=0 (if the domain polarization in the sample is oriented parallel to the applied electric field) and out of phase i.e. φ=180° (if it is anti-parallel to the applied electric field) as shown in Figure 6.

Figure 7 shows the phase contrast which is generated in PFM imaging and reflects the polarity of domains in different sample locations, It can be observed from Figure 7 the circled portion is in 180° phase contrast in two adjacent domains in the PFM phase image.

Vector PFM with one vertical and two lateral channels can provide more complete information for a more complex sample domain orientation that contains not only components perpendicular to the surface in contact with the AFM tip, but also components along different directions within the plane of the surface. For example, for obtaining the d15 component of the piezoelectric tensor in tetragonal piezoelectric crystals, lateral components of AFM tip vibration are need to be studied which are proportional to the in-plane displacement of the sample surface (Figure 8). This takes the form ΔL=ΔL0 cos(ωt+φ), with the amplitude of vibration ΔL0=d15V0. It is important to note that if a DC bias is applied between the tip and the sample in combination with the AC voltage, both the in-plane and out-of-plane electromechanical response of the sample are also functions of this DC voltage.

Most common applications of PFM are the characterization of electromechanical properties of materials, including detailed domain mapping and investigation of domain switching properties in ferroelectric and piezoelectric materials. The applications also include the study of their reliability issues such as electromechanical imprint, fatigue and dielectric break-down and studying other material properties of novel polymers and bio-engineered materials which are based on detailed nanoscale structural and electrical characterization of such materials.

Summary:

1. Studied about the need of AFM and PFM
2. Working principle of AFM and PFM
3. Different modes of operations of AFM
4. Details about imaging process in PFM

References:

1. Atomic force microscopy in cell biology,L Wilson, PT Matsudaira, BP Jena, JKH Horber
2. Scanning Probe Microscopy of Functional Materials, Sergei V. Kalinin, Alexei Gruverman
3. Advanced Characterization of Multiferroic Materials by Scanning Probe Methods and Scanning Electron Microscopy, Michael R. Koblischka Anjela Koblischka‐Veneva