Dual Frequency Resonance Tracking: Stabilizing the Piezoresponse

Ferroelectrics found extensive uses in industrial applications because of their unparalleled electromechanical and electrical characteristics, for example, as actuators, sensors and capacitors [1], [2].

The suitability of ferroelectrics for modern communication technology is currently investigated by researchers, including 5G [3] and as active layers in photovoltaics [4, 5] among other applications [6].

Ferroelectricity is the consequence of an alteration in crystal symmetry during a phase transition. A sudden electrical polarization is introduced by an off-centering of the center ion or tilting of ionic groups. The crystal forms domains of parallelly aligned polarization in order to reduce the electrostatic energy.

Without an external electric field, these domains are randomly oriented so that the macroscopic electrical polarization of the crystal stays fixed at zero (Figure 1a).

Yet, electric fields can permanently switch the domain orientation, which facilitates the customization of domain patterns for distinctive applications (Figure 1b) [7].

Characterizing the resulting domain patterns demands an electromechanical imaging method that visualizes domains locally with greater spatial resolution to respond to ever-decreasing device sizes.

A contact mode Atomic Force Microscopy (AFM) technique, known as Piezoelectric Force Microscopy (PFM), is perfectly suited here [8], [9]. In PFM, an AC voltage between the tip and a back electrode is applied below the sample, while a conductive tip attached to a cantilever scans the surface of a ferroelectric sample.

Since all ferroelectric materials are piezoelectric, the AC voltage applied initiates a periodic deformation of the sample, called piezoresponse (Figure 1c).

For domains with a polarization perpendicular to the sample surface and depending on the polarization orientation in the domains below the tip, the piezoresponse is either in phase or 180° out of phase with the applied AC voltage (Figure 1d).

The PFM phase transports information across the domain orientation. Between adjacent domains of opposite polarization orientation at the position of boundaries, so called domain walls, the piezoresponse simultaneously cancels out and the PFM amplitude achieves a minimum. The position of domain walls is visualized by the PFM amplitude [8].

a) Schematic of ferroelectric domains with parallel electric polarization (small blue arrows). The random formation of + and –domains cancels out a macroscopic polarization. b) The application of a local electric field selectively switches the orientation of a –domain to a +domain. c) PFM work principle: an AC voltage applied between tip and a conductive back electrode below the sample introduces an oscillating piezoresponse (red double arrow) in the ferroelectric. The cantilever detects the oscillating piezoresponse via the optical beam deflection method. d) Depending on the domain orientation below the tip the material either expands or contracts, leading to 180° phase shift between oppositely oriented out of plane domains.

Figure 1. a) Schematic of ferroelectric domains with parallel electric polarization (small blue arrows). The random formation of + and –domains cancels out a macroscopic polarization. b) The application of a local electric field selectively switches the orientation of a –domain to a +domain. c) PFM work principle: an AC voltage applied between tip and a conductive back electrode below the sample introduces an oscillating piezoresponse (red double arrow) in the ferroelectric. The cantilever detects the oscillating piezoresponse via the optical beam deflection method. d) Depending on the domain orientation below the tip the material either expands or contracts, leading to 180° phase shift between oppositely oriented out of plane domains. Image Credit: Park Systems

PFM implements low frequency AC voltages in its conventional configuration, far from the contact resonance of the cantilever. Known as single frequency off resonance PFM, this methodology has an inherently lower sensitivity for topographic crosstalk due to contact mechanics between surface and tip on the PFM signal.

Depending on the samples, off resonance PFM may necessitate greater amplitudes of the AC voltages to accomplish an appropriate signal to noise ratio in the piezoresponse.

The signal-to-noise ratio can be improved by applying an AC voltage close or at the contact resonance of the cantilever, which is approximately three to five times the free resonance for materials with poor piezoresponses, like thin films or materials sensitive to high drive voltages [8].

The piezoresponse detected becomes exposed to crosstalk in this single frequency resonance enhanced PFM technique, for example, from sample mechanics and topography.

It is hard to acquire a stable and unchanged tip sample contact while scanning, especially on rough surfaces, but the frequency of the contact resonance is heavily reliant on it.

Additional changes in the contact resonance are further introduced by heterogeneities in the sample mechanics [10].

Here, it is demonstrated how stabilization of the resonance enhanced piezoresponse is achieved.

This is done by utilizing an additional feedback that monitors the contact resonance during the PFM scan in a technique called Dual Frequency Resonance Tracking (DFRT) on a Park Systems NX10 AFM with a Zurich Instruments HF2 Lock In Amplifier (LIA).

For DFRT, the HF2 produces two sidebands left and right of the contact resonance at frequencies determined by the bandwidth at half the maximum of the contact resonance.

The feedback constantly compares the amplitudes of both sidebands and adjusts the frequency of the AC voltage to maintain a constant amplitude ratio during the PFM scan [10].

Due to the number of demodulators and feedbacks available, the HF2 enables synchronous monitoring of the vertical contact resonance (CR1) and the lateral resonance (CR2), as displayed in Figure 2.

Frequency spectrum of cantilever in contact showing the vertical contact resonance CR1 and lateral contact resonance CR2. The sidebands used for the resonance tracking are generated at frequencies fm (grey bars) from the contact resonances, given by the bandwidth of the respective resonance. A feedback monitors the amplitude ratio of both sidebands (A2 and A3 for the vertical resonance and A5 and A6 for the lateral resonance) and readjusts the frequency of the AC voltage to keep the ratio constant

Figure 2. Frequency spectrum of cantilever in contact showing the vertical contact resonance CR1 and lateral contact resonance CR2. The sidebands used for the resonance tracking are generated at frequencies fm (grey bars) from the contact resonances, given by the bandwidth of the respective resonance. A feedback monitors the amplitude ratio of both sidebands (A2 and A3 for the vertical resonance and A5 and A6 for the lateral resonance) and readjusts the frequency of the AC voltage to keep the ratio constant. Image Credit: Park Systems

Simple synchronization of the AFM and the LIA enables access to the vertical and lateral measurement signals as well as the potential to apply an external tip bias directly to the cantilever on the Park Systems NX series.

The PFM signals can be inserted into the NX AFM controller through the five auxiliary inputs available and then measured and displayed by Park Systems’ SmartScan™ software or by the data acquisition module of Zurich Instruments’ LabOne® software.

In this application note, imaging of the piezoresponse was conducted on a Bismuth Ferrite (BFO) film via DFRT and the results compared to a single frequency resonance enhanced PFM measurement.

It was determined that a considerable reduction of topographic crosstalk for DFRT in both PFM amplitude and PFM phase led to a clear visualization of domain walls and oppositely oriented domains.

Simultaneous vertical and lateral DFRT PFM measurements were conducted, demonstrating the versatility of the technique and the possibility for reliable and precision domain imaging on ferroelectric materials.

Experimental

For the DFRT PFM measurement on the ferroelectric BFO, a Park Systems NX10 was used coupled with a Zurich Instruments HF2 LIA. All measurements were carried out with free resonance of 75 kHz conductive, and a PtIr coated PPP EFM cantilever with a nominal spring constant of 2.8 N/m.

With a free resonance of 75 kHz, a vertical contact resonance in the range of 250 400 kHz and a lateral contact resonance in the range of 550 750 kHz was anticipated. A setpoint of ~30 nN for all scans was selected. The scan rate was 0.2 Hz; the scan size 2×2 µm;  and the resolution 512×512 px.

To generate the vertical DFRT and single frequency resonance-enhanced PFM measurements, the vertical cantilever displacement from the signal access module was set to the first input of the HF2.

While the tip bias was applied via the HF2 output 1 straight to the cantilever via a conductive clip type probehand, the PFM signals were fed from the HF2 to the AFM controller via the four auxiliary outputs in the HF2 and four auxiliary inputs on the NX AFM controller.

Thus, the necessary PFM signals could be shown and registered via SmartScan™ by selecting the internal contact or PFM mode and adding the relevant auxiliary inputs to the measurement channels.

If it was necessary to collect additional signals, synchronization of the AFM scan and data collection was ready to go by way of connecting the end-of-line trigger from the AFM controller to the DOI of the HF2, thus enabling the data acquisition via LabOne®.

The vertical cantilever displacement to input 1 and the lateral cantilever displacement to input 2 of the HF2 was performed for the capture of simultaneous lateral and vertical DFRT PFM measurements. By adding the lateral drive from output 2 to the vertical AC drive, both the vertical and the lateral AC voltage frequency could be applied to the cantilever via output 1.

Results and Discussion

To demonstrate DFRT PFM on a Park Systems NX10 AFM with a Zurich Instruments HF2 LIA, the ferroelectric domains of a BFO sample were imaged. In advance of the first measurement of the vertical piezoresponse of BFO, the frequency feedback was set by recording the frequency spectrum of the AC voltage (1 V) while conducting tip-sample contact.

It was observed the vertical contact resonance was at 353 kHz. With bandwidth at half maximum of 4.4 kHz, the sidebands formed at ±2.2 kHz from the resonance, at 350.8 and 355.2 kHz, respectively (Figure 3).

Frequency spectrum of the AC voltage between tip and sample in contact, with AC amplitudes of 1 V on the carrier signal and both sidebands. The vertical contact resonance (CR1) was positioned at 353 kHz, both sidebands (SB) were generated in 2.2 kHz from the contact resonance

Figure 3. Frequency spectrum of the AC voltage between tip and sample in contact, with AC amplitudes of 1 V on the carrier signal and both sidebands. The vertical contact resonance (CR1) was positioned at 353 kHz, both sidebands (SB) were generated in 2.2 kHz from the contact resonance. Image Credit: Park Systems

Typically, a symmetrical shape of the contact resonance guarantees a steady function of the DFRT feedback; deviations were found from a symmetric resonance at higher voltages. This was potentially due to electrostatic interactions.

However, the feedback advisor in Zurich Instruments’ LabOne® software discovered the appropriate gain settings for the measurement with the suitable frequencies for the center and sideband frequencies, as well as the pixel dwell time for the scan.

Figure 4 outlines the results of vertical DFRT PFM measurement. The BFO sample imaged had a root mean square roughness of 3.4 nm with marked holes, up to 20 nm in depth (Figure 4a).

These topographical features were imperceptible in the PFM signals (Figure 4b and c), signifying well-functioning DFRT feedback, which counterbalances any topographic crosstalk as a result of fluctuations in the tip sample contact mechanics. The frequency signal of the DFRT feedback (Figure 4d) captured frequency shifts at positions relative to the holes in the height channel.

Results of vertical DFRT PFM measurement on a BFO sample. a) Sample topography in the height channel with line profile extracted along the red line. Exemplary hole outlined by blue box in image and profile. b), c) PFM amplitude and phase measured on the second sideband (SB) at f1+f1m with an amplitude of 1 V, resolving the position of the domain walls and the domain orientation, respectively. The line profiles extracted along the red line show amplitude minima at the domain walls and a full 180° phase contrast, as well as minimal topographic crosstalk (blue box). d) Frequency signal of the DFRT feedback imaged the compensated frequency shifts introduced by holes in the topography (blue box)

Figure 4. Results of vertical DFRT PFM measurement on a BFO sample. a) Sample topography in the height channel with line profile extracted along the red line. Exemplary hole outlined by blue box in image and profile. b), c) PFM amplitude and phase measured on the second sideband (SB) at f1+f1m with an amplitude of 1 V, resolving the position of the domain walls and the domain orientation, respectively. The line profiles extracted along the red line show amplitude minima at the domain walls and a full 180° phase contrast, as well as minimal topographic crosstalk (blue box). d) Frequency signal of the DFRT feedback imaged the compensated frequency shifts introduced by holes in the topography (blue box). Image Credit: Park Systems

Extraction of the line profiles along the red line for each of the signals was conducted to better illustrate the minimized topographic crosstalk in the PFM signals.

The profiles determined that the hole in the height channel, emphasized by the blue boxes in the images and the line profiles, had limited influence on the PFM amplitude and no bearing on the PFM phase.

Instead, it was observed that there was a clear domain wall and domain orientation contrast in PFM amplitude and PFM phase, respectively. The minima in the PFM amplitude corresponded to the outlines of the domains in the PFM phase, which caught the full 180° contrast, symptomatic of oppositely oriented out of plane domains.

Another measurement was taken at the same sample location with the same measurement parameters, but without DFRT feedback, to compare the DFRT measurement to a single frequency resonance enhanced PFM measurement (Figure 5).

Here,  the PFM signals at a frequency near to the contact resonance with 1 V AC excitation were measured. The height channel in Figure 5a resolved the same holes as the previous scan - one flawless hole highlighted in the blue box.

However, in this measurement, crosstalk caused by the holes was clearly observed in the PFM amplitude as well as the PFM phase (Figure 5b and c).

Besides the domain walls, the PFM amplitude now included the holes in the topography as amplitude minima.

Thus, a determination of topographic crosstalk and a true PFM signal is difficult to achieve without previous knowledge of the domain structure. Similarly, the PFM phase exhibited phase extrema at the position of the holes in the topography in addition to a ~180° domain contrast.

The phase contrast as a result of the topographic crosstalk was up to 120° and could likely cause errors in the data interpretation.

Moreover, three frequency spectra were recorded with the same cantilever, 1 V AC amplitude and an equal loading force (~30 nN) at three separate locations in the measurement area (Figure 5d).

Vertical single frequency resonance-enhanced PFM measurement on the same BFO sample location as the previous DFRT PFM measurement, with the sample height in a), the PFM amplitude in b) and the PFM phase in c). The measurement was conducted with 1 V AC amplitude at 356 kHz for a contact resonance of 357 kHz. The PFM amplitude and PFM phase resolved the position of domain walls as amplitude minima and the domain orientation with a full 180° phase contrast, respectively. Both PFM signals displayed a strong topographic crosstalk (blue boxes). d) Three consecutive frequency spectra with 1 V AC amplitude at three different locations in the measurement area showing a 9 kHz shift in the vertical contact resonance (CR1).

Figure 5. Vertical single frequency resonance-enhanced PFM measurement on the same BFO sample location as the previous DFRT PFM measurement, with the sample height in a), the PFM amplitude in b) and the PFM phase in c). The measurement was conducted with 1 V AC amplitude at 356 kHz for a contact resonance of 357 kHz. The PFM amplitude and PFM phase resolved the position of domain walls as amplitude minima and the domain orientation with a full 180° phase contrast, respectively. Both PFM signals displayed a strong topographic crosstalk (blue boxes). d) Three consecutive frequency spectra with 1 V AC amplitude at three different locations in the measurement area showing a 9 kHz shift in the vertical contact resonance (CR1). Image Credit: Park Systems

A considerable shift occurred in the vertical contact resonance for the second of the recorded spectra by almost 10 kHz. Therefore, the importance of tracking the resonance frequency for resonance enhanced PFM is perfectly illustrated by this shift in the contact resonance between three consecutive spectra.

Finally, the capabilities for simultaneous vertical and lateral DFRT PFM were tested. Utilizing the two inputs on the HF2, the vertical and the lateral cantilever displacement were fed from the NX10 AFM into the LIA, providing the AC excitation voltage at the vertical while the lateral resonance was applied directly to the cantilever.

Illustrated in Figures 6a and b, the frequency spectra of the vertical contact resonance at 350 kHz (1 V AC amplitude) and the lateral contact resonance at 690 kHz (1 V AC amplitude) are seen.

Frequency spectra of the AC voltage between tip and sample in contact, with AC amplitudes of 1 V on the carrier signal and both sidebands. a) The vertical contact resonance (CR1) was at 350 kHz, both sidebands (SB) were generated in 2 kHz from the CR1. b) The lateral contact resonance (CR2) was at 690 kHz, both SB were generated in 1.5 kHz from CR2

Figure 6. Frequency spectra of the AC voltage between tip and sample in contact, with AC amplitudes of 1 V on the carrier signal and both sidebands. a) The vertical contact resonance (CR1) was at 350 kHz, both sidebands (SB) were generated in 2 kHz from the CR1. b) The lateral contact resonance (CR2) was at 690 kHz, both SB were generated in 1.5 kHz from CR2. Image Credit: Park Systems

Analog to the first DFRT measurement, the frequencies of the two sidebands relative to the bandwidth at half maximum of both resonances were determined. For the lateral signal, the sidebands were at ±1.5 kHz from the contact resonance. For the vertical signal, the sidebands were at ±2 kHz from the contact resonance.

To independently monitor both resonance frequencies during the scan, two frequency feedbacks to track the vertical were utilized as well as the lateral resonance. To determine suitable feedback gains, the advisor function in the LabOne® software was employed.

Figure 7a demonstrates the sample topography on the same sample location as both previous measurements (Figure 4 and 5), leading to the resolution of a corresponding surface structure with distinct holes. The vertical PFM amplitude closely resembled the signal in Figure 4, with an obvious domain wall contrast, observable as amplitude minima (Figure 7b).

It was found that minimal crosstalk with the topography indicated a well-functioning DFRT feedback in accordance with the previous DFRT PFM measurement (Figure 4).

On the contrary, the lateral PFM amplitude in Figure 7c demonstrated a noticeably different structure than the vertical PFM amplitude. Here, occasional amplitude contrast resolved in plane ferroelastic twin domains of BFO, indicating the success of lateral DFRT PFM measurement [11].

Results of a simultaneous vertical and lateral DFRT PFM measurement on a BFO sample. a) Sample topography in the height channel. b), c) Vertical and lateral PFM amplitude, respectively. Both were measured on the second sideband (SB) at f1+f1m and f2+f2m with an amplitude of 1 V. The vertical PFM amplitude resembled previous results by imaging the position of the domain walls with minimal topographic crosstalk. The lateral PFM amplitude resolved characteristic periodic ferroelastic domains

Figure 7. Results of a simultaneous vertical and lateral DFRT PFM measurement on a BFO sample. a) Sample topography in the height channel. b), c) Vertical and lateral PFM amplitude, respectively. Both were measured on the second sideband (SB) at f1+f1m and f2+f2m with an amplitude of 1 V. The vertical PFM amplitude resembled previous results by imaging the position of the domain walls with minimal topographic crosstalk. The lateral PFM amplitude resolved characteristic periodic ferroelastic domains. Image Credit: Park Systems

Conclusion

In this study, successful imaging of ferroelectric domains of a Bismuth Ferrite (BFO) film with resonance enhanced Piezoelectric Force Microscopy (PFM) was conducted on a Park Systems NX10 Atomic Force Microscope (AFM) with a Zurich Instruments HF2 Lock In Amplifier (LIA).

It was determined that the additional frequency feedback in Dual Frequency Resonance Tracking (DFRT) considerably limits the topographic crosstalk in contrast to single frequency resonance enhanced PFM.

DFRT PFM, therefore, produces more precise and trustworthy PFM data when characterizing ferroelectric domain patterns, necessary for the industrial application of ferroelectrics, as well as academic research.

DFRT compensates for alterations in the contact resonance introduced by changes in the tip sample contact mechanics, especially where rough samples are concerned. It was also demonstrated that the capacity of simultaneous vertical and lateral DFRT PFM measurements highlights the versatility and potential in material characterization methodologies.

The accessible measurement signals on AFMs from Park Systems enable easy integration and synchronization of the AFM and Zurich Instruments’ HF2 LIA for DFRT PFM.

Acknowledgment

Thanks to Dr. Akash Bhatnagar, Centre for Innovation Competence SiLi-nano® Germany, for providing the BFO sample.

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This information has been sourced, reviewed and adapted from materials provided by Park Systems.

For more information on this source, please visit Park Systems.

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