Piezo-response Force Microscopy (PFM)

Piezo Response Force Microscopy (PFM)

The word “piezo” is derived from the Greek word piezein, meaning “to press tightly”. Piezoelectricity is the ability of a material to convert mechanical energy (pressing) into electric energy (polarization) and vice versa. The direct piezoelectric effect is the generation of electric polarization in response to an applied stress. The directionality and the magnitude of polarization is proportional to the stress applied, and the polarization can have components in the parallel and perpendicular directions. The opposite phenomenon, the inverse piezoelectric effect, is the generation of a mechanical deformation in response to an applied electrical field.

Piezoelectric materials are prevalent in our everyday lives. For example, ferroelectric materials are a subset of piezoelectric material that possess an inherent spontaneous polarization and can be found in capacitors, nonvolatile memory, ultrasound imaging, data storage, thermistors, oscillators, filters, light deflectors, modulators, and monitors, to name a few. In fact, atomic force microscopes (AFM) rely on the inverse piezoelectric effect in their scanner design. As components continue to miniaturize in the electronics industry, piezoelectric thin films have also become a significant area of interest (e.g. functionally coated flexible glass). Thin films exhibit piezoelectric behavior in distinct regions (often called domains) in the sub-nanometer regime. Understanding the domain size as well as their response under an applied electric field enables dynamic measurements of domain switching and local hysteretic behavior. These material properties allow researchers to understand structure function relationships for material design.

AFM can measure the local inverse piezoelectric response with high fidelity and provide high resolution piezoelectric information with correlative surface topography. This mode of operation of AFM is often termed as Piezo response Force Microscopy (PFM). PFM can measure deformations in the sub-nanometer regime and map ferroelectric domains with a lateral resolution of a few nanometers.

How does it work?

AFM is a surface characterization technique that rasters a fine needle at the free end of a cantilever across the sample surface. Light is reflected off the back of the cantilever onto a position sensitive photodiode that registers the motion of the cantilever.

In PFM mode, AFM is operated in contact mode where the cantilever is continuously in contact with the sample at a constant force. To apply an electrical field over the sample, a sample is mounted on a conductive substrate and a conductive cantilever is used as the second electrode. Either electrode can be used to apply the voltage, though the first generally performs better. Figure 1 shows a schematic PFM setup.

Figure 1: Schematic of a Piezo-response Force Microscopy experiment. Voltage is applied to a conductive tip in contact with sample and mechanical deformation of the sample is measured by the deflection of the laser.
Figure 1: Schematic of a Piezo-response Force Microscopy experiment. Voltage is applied to a conductive tip in contact with sample and mechanical deformation of the sample is measured by the deflection of the laser.

To measure the piezo response, an AC voltage is applied between the tip and the substrate causing a periodic expansion and/or contraction of the sample. With the tip constantly in contact with the sample, the oscillatory movement of the sample surface induces a periodic cantilever bending that is analyzed by the AFM controller’s lock-in amplifier.

During PFM imaging, the amplitude and phase response of the cantilever are recorded. Phase contrast in PFM provides information about the direction of the electrical polarization relative to electrical field. The amplitude shows the magnitude of the piezo response and can often be used to discern features such as the position of domain walls.

The electrical polarization can have components both parallel/antiparallel as well as perpendicular to the applied field, the AC field will result in out-of-plane and in-plane oscillations of the sample surface, thus causing vertical and lateral bending of the cantilever, as denoted in Figure 2.

If the response observed is purely parallel/antiparallel to the field (Figure 2a,b), the out-of-plane amplitude and phase of the vertical cantilever bending provides direct information about the magnitude and polarization (parallel vs. anti-parallel) of the sample deformation. If the polarization and electric field are perpendicular to one another (Figure c,d), inplane movement of the sample results.

Figure 2: Schematics of (a-b) vertical and (c-d) lateral PFM mode. The applied electric field (E) and polarization (P) direc-tions are denoted with arrows. Vector PFM is performed by combining data with a 0° and 90° rotation of the sample to obtain 3D vector information of the response.
Figure 2: Schematics of (a-b) vertical and (c-d) lateral PFM mode. The applied electric field (E) and polarization (P) directions are denoted with arrows. Vector PFM is performed by combining data with a 0° and 90° rotation of the sample to obtain 3D vector information of the response.

With a purely out-of-plane response, the effective piezoelectric coefficient, d33, can be calculated from the measured amplitude (A) of the oscillation and the applied voltage over the sample (VAC):

𝑑33=𝐴/𝑉𝐴𝐶

Below the resonance frequency of the cantilever, the amplitude A can be expressed in pm (by converting voltage to distance using the cantilever deflection sensitivity) and the effective piezoelectric coefficient can be measured quantitatively. However, it is not straightforward to compare d33 measurements obtained by AFM with other bulk techniques. It is well known that material properties can vary significantly on the nanoscale compared to the bulk, and the piezoelectric effect is no exception.

In practice, materials can exhibit a mechanical response in three dimensions. Movement both in-plane and out-of-plane relative to the sample surface can occur in response to the applied voltage. To capture this, vector PFM is used to monitor both vertical and lateral deflection of the cantilever. Additionally, a sample area is measured at two rotational orientations with respect to the cantilever. The data can be mathematically reconstructed to combine both the in-plane and out-of-plane vector components to provide a 3D map of the piezo response.

Beyond imaging, AFM can also provide a means to spectroscopy, locally induce polarization at the tip to understand material hysteresis or write domains using lithography. These topics will be covered in more detail below.

Experimental setup

As illustrated in Figure 1, PFM requires an AFM that can perform electrical measurements with conductive cantilevers. To measure both the out-of-plane and in-plane responses, two independent internal lock-in amplifiers are required to measure the amplitude and phase of each component.

An additional, essential part for many samples is a camera view that allows to view the sample from above to find areas of interest, as illustrated in Figure 3. Particularly for 2D materials, the flakes of interest must be located and positioned under the cantilever.

Figure 3: A top view camera image is essential for most PFM samples. This image shows flakes of 2D material on a gold substrate. Flakes of different thickness appear as different colors in the image.
Figure 3: A top view camera image is essential for most PFM samples. This image shows flakes of 2D material on a gold substrate. Flakes of different thickness appear as different colors in the image.

Several practical aspects of PFM are worth mentioning, including sample preparation and cantilever choice. While flat samples are generally suitable for performing PFM as is, some rougher samples such as ceramics may require polishing prior to imaging. Care must be taken to work with contamination-free surfaces. A thick insulating layer between conductive substrate and sample should generally be prevented, as this will reduce the field strength over the sample and hence the piezo response.

Conductive cantilevers for PFM have a wide range of force constants varying from <0.1 N/m to =40 N/m with a resonance frequency range between 10-400 kHz. Stiffer cantilevers minimize the contribution of electrostatic interaction with samples, whereas softer probes are less prone to tip wear and sample damage during scanning. While Pt/Ir coated probes can be used for performing PFM measurements, studies have shown that conductive diamond or PtSi coated tips have shown improved stability of the PFM signal. Another important parameter for measurements is the optical sensitivity, which is inversely proportional to the probe length. Therefore, the shorter cantilevers provide better signal.

Specialized PFM measurements such as high-voltage PFM (HV-PFM) and dual frequency response tracking (DFRT) require additional instrumentation. For HV-PFM, an additional high-voltage amplifier is connected to a user output of the AFM controller and directly controlled from the AFM software. The user channel is calibrated so that the user can directly set the output voltage of the HV-amplifier. DFRT-PFM will be explained in more detail later. For this mode, Nanosurf equipment can be combined with an external lock-in amplifier from Zurich Instruments and signals can be imported via user input channels. Zurich Instruments' lock-in amplifiers are powerful tools, not only for PFM, but other advanced AFM modes such as frequency modulated, heterodyne Kelvin Probe Force Microscopy (KPFM), and other multi-frequency applications.

Traditional PFM Applications

Lithium niobate (LiNbO3) is versatile ferroelectric material and widely used in applications ranging from waveguides to piezoelectric sensors. A PFM measurement is shown in Figure 4. This sample is periodically poled and shows a pure out-of-plane response with alternating domains parallel and antiparallel to the applied field. At ambient conditions, the piezo response is stable over a large voltage range of the applied electric field. The topography and magnitude (amplitude signal) of the piezo response are not affected by the polarization, but phase changes by 180° indicating that the electrical polarization is switching in the out-of-plane direction. The amplitude does not change significantly between the oppositely poled domains.

Figure 4.: Vertical PFM images of periodically poled lithium niobate. (a) Representative topography with phase information color overlaid for a 20x20 µm<sup>2</sup> area showing, (b) horizontal profile of the amplitude and (c) phase, showing little influence of amplitude with polarity and the 180° phase shift as expected. Data courtesy: Brian Odermatt, EPFL/Nanosurf.
Figure 4: Vertical PFM images of periodically poled lithium niobate. (a) Representative topography with phase information color overlaid for a 20x20 µm2 area showing, (b) horizontal profile of the amplitude and (c) phase, showing little influence of amplitude with polarity and the 180° phase shift as expected. Data courtesy: Brian Odermatt, EPFL/Nanosurf.

Ferroelectric 2D materials and thin films are growing in interest with potential applications in energy, electronics and optoelectronics. PFM of CuInP2S6 flakes on a silicon substrate are shown in Figure 5. The PFM measurement provides the magnitude of the vertical deformation (amplitude image, Figure 5a) and the corresponding polarization direction (phase image, Figure 5b). To more easily distinguish the polarization direction of an amplitude, the amplitude and phase information can be combined by using an amplitude projection (Figure 5c). By multiplying the amplitude with the cosine of the phase, which is 0° or 180° the sign is consistent to the polarization direction, and distinct domains can be more readily observed (Figure 5c, arrow heads).

Ferroelectric thin films are easily characterized using PFM. Figure 6 shows the piezoelectric characterization of a piezoelectric and high magnetostrictive thin film that was grown using a sol-gel process on a flexible glass substrate. The surface topography reveals "protrusions" with a dome-like morphology that are microns across (Figure 6a). The amplitude projections of the out-of-plane response (Figure 6b) and the in-plane response (Figure 6c) clearly show the differences in domain size and structure within individual dome-like protrusions on the sample.

Dual frequency resonance tracking (DFRT) PFM

In a traditional PFM measurement, the probe is oscillated at frequencies well below the resonance frequency of the cantilever (Figure 7a). A main advantage of working at these frequencies is that the deflection can be readily converted into picometers, using the deflection sensitivity of the cantilever. However, signals are often small and can be challenging to measure, particularly for thin samples. The piezo response can be enhanced by working at a resonance frequency of the cantilever. Since PFM is performed in contact mode, the first available resonance frequency is the contact resonance, where the cantilever makes a buckling movement with both the tip and the base of the cantilever fixed. The sample is used as a “shaker piezo”, to oscillate the cantilever in its (contact) resonance, which is about 4-5 times higher than the fundamental resonance frequency of the cantilever that is only fixed at one side.

Working at the contact resonace is susceptible to crosstalk between the PFM response and other tip sample interactions, because the contact resonance depends on the local stiffness of the sample. To avoid this crosstalk, the DFRT mode was introduced. In DFRT mode, an AC voltage is applied at two frequencies on either side of the contact resonance peak with equal amplitude (Figure 7b). When the contact resonance shifts, the amplitudes also undergoes a shift (Figure 7c) and a feedback algorithm in the lock-in amplifier nullifies the difference by modulation of the excitation frequencies. The difference Δf between the two excitation frequencies is kept fixed in feedback (Figure 7d). By applying this method, changes in the contact resonance frequency are largely decoupled from the PFM response.

Contact frequency enhanced PFM can be used to study the piezo-ceramic material - lead zirconate titanate (PZT). Improvement of fatigue and retention of PZT can be made by adding small amounts of donor dopant like ions of La3+. With signal enhancement at the contact resonance frequency, grain and domain morphology of such samples can be successfully examined with PFM, as illustrated in Figure 8.

Figure 5: Vertical PFM imaging of 2D ferroelectric CuInP<sub>2</sub>S<sub>6</sub> on Silicon substrate. (a) amplitude (b) phase and (c) amplitude projection, all represented as a color overlay on the topography.  
Image size: 5x5 µm<sup>2</sup> (color scales do not include illumination effects from the topography visualization).
Figure 5: Vertical PFM imaging of 2D ferroelectric CuInP2S6 on Silicon substrate. (a) amplitude (b) phase and (c) amplitude projection, all represented as a color overlay on the topography. Image size: 5x5 µm2 (color scales do not include illumination effects from the topography visualization).
Figure 6: Out-of-plane and in-plane PFM response recorded on a 800 nm PZT thin film, grown by sol-gel method on Pt(111)/Ti/Flexible glass. (a) Topography, (b) out-of-plane amplitude projection, (c) in-plane amplitude projection. Image size: 9x9 µm<sup>2</sup> (color scales do not include illumination effects from the topography visualization). Data courtesy: Dr. Itamar Neckel, Brazilian Center for Research in Energy and Materials – CNPEM, Brazilian Synchrotron Light Laboratory LNLS.
Figure 6: Out-of-plane and in-plane PFM response recorded on a 800 nm PZT thin film, grown by sol-gel method on Pt(111)/Ti/Flexible glass. (a) Topography, (b) out-of-plane amplitude projection, (c) in-plane amplitude projection. Image size: 9x9 µm2 (color scale do not include illumination effects from the topography visualization). Data courtesy: Dr. Itamar Neckel, Brazilian Center for Research in Energy and Materials – CNPEM, Brazilian Synchrotron Light Laboratory LNLS.
Figure 7: Schematics showing (a) traditional PFM measurement in off resonance mode and dual frequency resonance enhanced PFM mode. (b-d) DFRT amplitude response upon a change in contact resonance frequency.
Figure 8: PFM measurement at contact resonance frequency (a) amplitude (arbritrary units), (b) phase (c) profile In the phase, showing domain widths ~100 nm range. Excitation: VAC= 5 V at f=304 kHz, Cantilever: Pt-coated Si with nominal spring constant k=1.5 N/m. Image size: 3x3 µm<sup>2</sup>. Sample courtesy: Prof. A. Kholkin, University of Aveiro, Portugal, data courtesy: Sergei Magonov, SPM labs, AZ
Figure 8: PFM measurement at contact resonance frequency (a) amplitude (arbitrary units), (b) phase (c) profile In the phase, showing domain widths ~100 nm range. Excitation: VAC= 5 V at f=304 kHz, Cantilever: Pt-coated Si with nominal spring constant k=1.5 N/m. Image size: 3x3 µm2. Sample courtesy: Prof. A. Kholkin, University of Aveiro, Portugal, data courtesy: Sergei Magonov, SPM labs, AZ

As a demonstration of DFRT, the PFM phase signal of a thin film of CuInP2S6 is shown in Figure 9. Despite a modualtion amplitude of less than 1V, the amplification by the contact resonance gives improved contrast and makes the borders between oppositely polarized domains clearer for visualization.

Figure 9: Piezo phase response from a thin film CuInP2S6 grown on a silicon surface imaged with DFRT PFM showing oppositely polarized domains while applying <1 V of AC modulation.
Figure 9: Piezo phase response from a thin film CuInP2S6 grown on a silicon surface imaged with DFRT PFM showing oppositely polarized domains while applying <1 V of AC modulation.

Spectroscopy and high-voltage PFM

To look beyond imaging, AFM can also be used for spectroscopy and to locally "write" domains by applying a DC bias to the sample. In spectroscopy, the amplitude and phase of the piezo response are measured as a function of an applied bias voltage over the sample. One of the main applications for spectroscopy is to determine the voltage needed for domain reversal. In ferroelectric materials, the external voltage required to reverse a polarization is called the coercive field. To reach the coercive filed may require bias voltages exceeding ±10 V. In such cases a high-voltage amplifier is connected to a user output and voltages up to ±200 V can be applied. AC voltages can also be applied via the high-voltage (HV) amplifier to improve the signal to noise ratio of weak piezoelectric properties. To perform HV-PFM, the sample must be stable under high voltage and to prevent physical harm to the user or damage to electronic equipment, care must be taken that no electronics are exposed when high voltages are applied.

However, increasing bias voltage offset increases the contribution of electrostatic forces on the cantilever. This electrostatic contribution may even exceed the PFM response, obscuring domain reversal. Switching spectroscopy PFM (SS-PFM) is a spectroscopy method to reduce the effect of electrostatics. Rather than ramping the voltage linearly, a train of voltage pulses is applied, switching off the voltage difference in between. During this switching, the AC voltage is continuously applied to record the PFM response both in the on and off states of the voltage. This is schematically depicted in Figure 10. The “on” and “off” states refer to the status of the DC bias voltage. While the DC voltage is used to modify the polarization, the AC voltage is used to measure the piezoelectric signal at the same time.

To demonstrate SS-PFM, amplitude and phase behavior of a P(VDF-TrFE) thin film is shown in Figure 11. The data were recorded during the off phase of an SS-PFM experiment. Pulses between -40V and +40V were applied using a HV amplifier. As the voltage pulses were ramped upward, at +16 V the polarization switching was observed. This is indicated by the amplitude dropping to zero and the 180° phase shift. As the voltage was ramped down, the polarization switches back at -25 V, returning to the starting point.

Polarization and lithography

Once the required voltage to overcome the coercive field is known, for example from an SS-PFM experiment, the tip can be used to locally polarize the sample. Lithography can be used to to write single domains, domain arrays, and complex patterns without changing the surface topography.

Figure 10: Schematic diagram of SS-PFM measurement depicting a train of DC bias pulses on top of an AC modulation.
Figure 10: Schematic diagram of SS-PFM measurement depicting a train of DC bias pulses on top of an AC modulation.
Figure 11: Piezo response hysteresis loop of P(VDF-TrFE) thin film (a) amplitude vs applied voltage and (b) phase vs applied volt-age obtained by SS-PFM.
Sample courtesy: Joanneum Research Forschungsgesellschaft mbH, Austria.
Figure 11: Piezo response hysteresis loop of P(VDF-TrFE) thin film (a) amplitude vs applied voltage and (b) phase vs applied volt-age obtained by SS-PFM. Sample courtesy: Joanneum Research Forschungsgesellschaft mbH, Austria.
PFM high-voltage lithography on a P(VDF-TrFE) thin film is demonstrated in Figure 12. The tip was biased and scanned in square regions to intentionally polarize regions and reverse the polarity of a smaller region. First, a 3x3 µm2 area was imaged while applying a bias voltage of +40 V to the sample substrate. The polarization was subsequently reversed by scanning areas of 2x2 µm2, and 1x1 µm2 and applying -40 V and +40 V, respectively. Figure 12 shows a 4x4 µm2 image of the PFM amplitude projection (amplitude multiplied with the cosine of the phase) on the P(VDF-TrFE) film after these manipulation steps. Outside the largest area, the thin film is not polarized, and the amplitude is consequently small. After polarization with a positive substrate voltage, the sample shows zero phase and high amplitude, denoted by the magenta color. The 500 nm green region shows polarization reversal, with similar amplitude, but opposite sign, due to the 180° phase difference. In the magenta inner square represents a 1x1 µm2 region where the polarization was reversed a second time. Interestingly, the shape of the domain borders between the oppositely polarized regions extend into the adjacent regions, indicating collective switching of domains outside the tip-sample contact area.
Figure 12: PFM amplitude projection of P(VDF-TrFE) thin film after applying DC sample bias of 40 V, -40 V, and 40 V during consecutive scanning of 3x3 µm<sup>2</sup>, 2x2 µm<sup>2</sup>, and 1x1 µm<sup>2</sup> areas respectively. The AC amplitude amounted to 5 V. Sample courtesy: Joanneum Resear Forschungsgesellschaft mbH, Austria.
Figure 12: PFM amplitude projection of P(VDF-TrFE) thin film after applying DC sample bias of 40 V, -40 V, and 40 V during consecutive scanning of 3x3 µm2, 2x2 µm2, and 1x1 µm2 areas respectively. The AC amplitude amounted to 5 V. Sample courtesy: Joanneum Research Forschungsgesellschaft mbH, Austria.

Conclusion

Understanding the piezo-responsive behavior of materials will continue to be critical for the advancement of a wide range of technologies. Characterization on the nanometer scale has emerged, as the miniaturization of electronics continues. PFM uniquely enables researchers to study the electromechanical properties of materials with nanometer spatial resolution and picometers of sensitivity. Nanosurf PFM capabilities extend beyond traditional PFM imaging to improve signal to noise, measure switching dynamics, perform lithography, and apply high voltages according to your experiment needs.

Notes:

  1. PFM is available on CoreAFM, FlexAFM and DriveAFM from Nanosurf.
  2. AFM and PFM images were processed with MountainsSPIP 9.

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