Stabilizing the Piezoresponse for Ferroelectric Domain Characterization

Ferroelectrics found widespread industrial applications because of their unique electromechanical and electrical properties, for example as sensors, actuators, and capacitors1, 2.

Today, researchers assess the suitability of ferroelectrics for modern communication technology like 5G3, as active layers in photovoltaics4, 5, and a number of other applications6.

Ferroelectricity is due to an alteration in crystal symmetry during a phase transition. In this instance, an off-centering of the center ion or tilting of ionic groups brings about a spontaneous electrical polarization. The crystal forms domains of parallelly aligned polarization in order to lower the electrostatic energy.

These domains are oriented randomly without an external electric field, so the macroscopic electrical polarization of the crystal remains zero (Figure 1a). Yet, electric fields are able to switch the domain orientation permanently, which enables the customization of domain patterns for specific applications (Figure 1b).7

An electromechanical imaging technique that locally visualizes domains with the high spatial resolution is needed for the characterization of the resulting domain patterns, in order to respond to ever-decreasing device sizes. Here, a contact mode Atomic Force Microscopy (AFM) technique, Piezoelectric Force Microscopy (PFM), is ideally suited8, 9.

In PFM, the surface of a ferroelectric sample is scanned with a conductive tip attached to a cantilever, while applying an AC voltage between the tip and a back electrode below the sample. As all ferroelectric materials are piezoelectric, the applied AC voltage introduces a periodic deformation of the sample, known as piezoresponse (Figure 1c).

The piezoresponse is either in-phase or 180 ° out of phase with the applied AC voltage for domains with a polarization perpendicular to the sample surface, depending on the polarization orientation in the domains below the tip (Figure 1d). So, the PFM phase carries information on the domain orientation.

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 the 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 a 180° phase shift between oppositely oriented out of plane domains.

At the same time, at the position of boundaries between adjacent domains of opposite polarization orientation, so-called domain walls, the piezoresponse cancels out and the PFM amplitude reaches a minimum. So, the PFM amplitude visualizes the position of domain walls8.

PFM applies low-frequency AC voltages in its standard configuration, far from the contact resonance of the cantilever.

This method, known as single frequency off-resonance PFM, has an intrinsically low sensitivity for topographic crosstalk due to contact mechanics between tip and surface on the PFM signal. Off resonance PFM may require high amplitudes of the AC voltages to achieve a sufficient signal to noise ratio in the piezoresponse, depending on the samples.

For materials sensitive to high drive voltages, or materials which possess weak piezoresponses, such as thin films, the signal-to-noise ratio can be heightened by applying an AC voltage close or at the contact resonance of the cantilever, which is around three to five times the free resonance8.

Yet, the detected piezoresponse becomes prone to crosstalk, e.g. from topography and sample mechanics, in this single frequency resonance-enhanced PFM technique.

The frequency of the contact resonance is strongly dependent on an unchanged and stable tip-sample contact, which is challenging to acquire during scanning, especially on rough surfaces. Additionally, heterogeneities in the sample mechanics bring about further changes in the contact resonance10.

Here, using additional feedback that tracks the contact resonance during the PFM scan, it is demonstrated how to stabilize the resonance-enhanced piezoresponse. This is 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 either side of the contact resonance at frequencies supplied by the bandwidth at half the maximum of the contact resonance. The feedback continuously compares the amplitudes of both sidebands throughout the PFM scan and readjusts the frequency of the AC voltage to keep the amplitude ratio constant10.

Due to the number of demodulators and feedbacks available, the HF2 enables simultaneous tracking of the vertical contact resonance (CR1) and the lateral resonance (CR2) as shown 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. The frequency spectrum of the 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. 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.

The simple access to the lateral and vertical measurement signals, in addition to the possibility to apply an external tip bias directly to the cantilever on the Park Systems NX series, permits a straight forward synchronization of the AFM and the LIA.

The PFM signals may be fed into the NX AFM controller via the five available auxiliary inputs and displayed and recorded by Park Systems’ SmartScan™ software or by the data acquisition module of Zurich Instruments’ LabOne® software.

In this article, the piezoresponse is imaged on a Bismuth Ferrite (BFO) film using DFRT and the results are compared to a single frequency resonance-enhanced PFM measurement.

A significant reduction of topographic crosstalk for DFRT was exhibited in both PFM amplitude and PFM phase, resulting in clear visualization of domain walls and oppositely oriented domains, respectively.

Furthermore, simultaneous vertical and lateral DFRT PFM measurements were performed, demonstrating the method’s versatility and potential for accurate and reliable domain imaging on ferroelectric materials.

Experimental

A Park Systems NX10 coupled with a Zurich Instruments HF2 LIA was used for the DFRT PFM measurement on the ferroelectric BFO. All measurements were performed using a conductive PtIr coated PPP EFM cantilever with a nominal spring constant of 2.8 N/m and 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 expected with a free resonance of 75 kHz. A setpoint of ~30 nN was selected for all scans. The resolution was 512×512 px, the scan rate was 0.2 Hz, and the scan size was 2×2 µm.

The vertical cantilever displacement from the signal access module was given to the first input of the HF2 for the vertical DFRT and single frequency resonance-enhanced PFM measurements, while applying the tip bias via the HF2 output 1 directly to the cantilever using 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. So, the PFM signals required could be shown and recorded via SmartScan™ by selecting the internal contact or PFM mode and adding the according to auxiliary inputs to the measurement channels.

If the collection of additional signals was needed, it was possible to readily synchronize the AFM scan and data collection by connecting the end of line trigger from the AFM controller to the DOI of the HF2 and permitting the data acquisition via LabOne®.

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

Results and Discussion

The ferroelectric domains of a BFO sample were imaged for the demonstration of DFRT PFM on a Park Systems NX10 AFM with a Zurich Instruments HF2 LIA. Before the first measurement of the vertical piezoresponse of BFO, the frequency feedback was set up by recording the frequency spectrum of the AC voltage (1 V) during tip-sample contact.

The vertical contact resonance was observed at 353 kHz. The sidebands were generated at ±2.2 kHz from the resonance with bandwidth at half maximum of 4.4 kHz, 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.

Typically, a symmetric shape of the contact resonance ensures stable operation of the DFRT feedback; deviations from a symmetric resonance at higher voltages were found, which could be due to electrostatic interactions.

With the appropriate frequencies for sideband and center frequencies, in addition to the pixel dwell time for the scan, the feedback advisor in Zurich Instruments’ LabOne® software found gain settings which were suitable for the measurement.

The results of vertical DFRT PFM measurement are shown in Figure 4. The imaged BFO sample had a root mean square roughness of 3.4 nm with distinct holes, up to 20 nm in-depth, as seen in Figure 4a.

These topographical features were barely visible in the PFM signals (Figure 4b and c), demonstrating a well functioning DFRT feedback, which compensates for topographic crosstalk caused by alterations in the tip-sample contact mechanics.

Indeed, the frequency signal of the DFRT feedback (Figure 4d) displayed frequency shifts at positions that corresponded to the holes in the height channel. Line profiles were extracted along the red line for each of the signals in order to further illustrate the minimized topographic crosstalk in the PFM signals.

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 the 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 with 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) The frequency signal of the DFRT feedback imaged the compensated frequency shifts introduced by holes in the topography (blue box).

The profiles exhibited that the hole in the height channel, which is shown by the blue boxes in the images and the line profiles, had little effect on the PFM amplitude and no effect on the PFM phase.

Instead, a clear domain wall is seen, and a domain orientation contrast in PFM amplitude and PFM phase, respectively. The minima in the PFM amplitude correlated to the outlines of the domains in the PFM phase, which captured the complete 180 ° contrast, suggesting oppositely oriented out of plane domains.

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

In this instance, the PFM signals were measured at a frequency close to the contact resonance with 1 V AC excitation. The height channel in Figure 5a resolved the same holes as the previous scan – one exemplary hole outlined by the blue box.

Yet, in this measurement crosstalk as a result of the holes in the PFM amplitude as well as the PFM phase (Figures 5b and c) could be clearly observed. In addition to the domain walls, the PFM amplitude now featured the holes in the topography as amplitude minima.

A distinction of topographic crosstalk and a true PFM signal is difficult 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 caused by the topographic crosstalk was up to 120 ° and could easily result in errors in the data interpretation. Furthermore, three frequency spectra were recorded with the same cantilever, 1 V AC amplitude, and the same loading force (~30 nN) at three different places in the measurement area (Figure 5d).

A significant shift in the vertical contact resonance was found for the second of the recorded spectra of almost 10 kHz. This shift in the contact resonance between three consecutive spectra perfectly shows how crucial tracking the resonance frequency is for resonance enhanced PFM.

Lastly, the capabilities for simultaneous vertical and lateral DFRT PFM were assessed. The two inputs on the HF2 were utilized to feed the vertical and the lateral cantilever displacement from the NX10 AFM into the LIA and gave the AC excitation voltage at the vertical and the lateral resonance directly to the cantilever.

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 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).

Figures 6a and b show 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).

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

In order to track both resonance frequencies independently during the scan, two frequency feedbacks were utilized to track the vertical as well as the lateral resonance. To find the appropriate feedback gains, the advisor function in the LabOne® software was used.

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 was generated in 1.5 kHz from CR2.

Figure 7a exhibits the sample topography on the same sample location as both previous measurements (Figures 4 and 5), resolving a comparable surface structure with distinct holes.

The vertical PFM amplitude strongly resembled the signal in Figure 4, with a clear domain wall contrast, visible as amplitude minima (Figure 7b). Minimal crosstalk was observed with the topography, demonstrating a well functioning DFRT feedback in agreement with the DFRT PFM measurement taken previously (Figure 4).

On the other hand, the lateral PFM amplitude in Figure 7c, exhibited a much different structure than the vertical PFM amplitude. In this case, a periodic amplitude contrast is resolved in-plane ferroelastic twin domains of BFO, indicating a successful lateral DFRT PFM measurement11.

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.

Conclusion

In this assessment, ferroelectric domains of a Bismuth Ferrite (BFO) film with resonance-enhanced Piezoelectric Force Microscopy (PFM) were imaged successfully on a Park Systems NX10 Atomic Force Microscope (AFM) with a Zurich Instruments HF2 Lock-In Amplifier (LIA).

It was demonstrated that the additional frequency feedback in Dual Frequency Resonance Tracking (DFRT) reduces topographic crosstalk significantly, compared to single-frequency resonance-enhanced PFM.

So, DFRT PFM produces more accurate and reliable PFM data for the characterization of ferroelectric domain patterns, needed for the industrial application of ferroelectrics, in addition to academic research. DFRT compensates for shifts in the contact resonance introduced by changes in the tip-sample contact mechanics, particularly on rough samples.

Additionally, the capability of simultaneous vertical and lateral DFRT PFM measurements is shown, highlighting the method’s versatility and potential in material characterization.

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

Acknowledgments

Produced from materials originally authored by Ilka M. Hermes from Park Systems Europe GmbH and Romain Stomp from Zurich Instruments AG.

References and Further Reading

  1. D. Damjanovic, P. Muralt, and N. Setter, “Ferroelectric sensors,” IEEE Sens. J., vol. 1, no. 3, pp. 191–206, 2001.
  2. P. Muralt, “Ferroelectric thin films for micro-sensors and actuators: a review,” J. Micromech. Microeng., vol. 10, no. 2, pp. 136–146, 2000.
  3. N. M. Dawley et al., “Targeted chemical pressure yields tuneable millimetre-wave dielectric,” Nat. Mater., vol. 19, no. 2, pp. 176–181, 2020.
  4. A. Bhatnagar, A. Roy Chaudhuri, Y. Heon Kim, D. Hesse, and M. Alexe, “Role of domain walls in the abnormal photovoltaic effect in BiFeO3,” Nat. Commun., vol. 4, no. 1, p. 2835, 2013.
  5. K. T. Butler, J. M. Frost, and A. Walsh, “Ferroelectric materials for solar energy conversion: photoferroics revisited,” Energy Environ. Sci., vol. 8, no. 3, pp. 838–848, 2015.
  6. J. F. Scott, “Applications of Modern Ferroelectrics,” Science, vol. 315, no. 5814, pp. 954–959, Feb. 2007.
  7. A. K. Tagantsev, L. E. Cross, and J. Fousek, Domains in ferroic crystals and thin films, vol. 13. Springer, 2010.
  8. E. Soergel, “Piezoresponse force microscopy (PFM),” J. Phys. D Appl. Phys., vol. 44, no. 46, p. 464003, 2011.
  9. P. Güthner and K. Dransfeld, “Local poling of ferroelectric polymers by scanning force microscopy,” Appl. Phys. Lett., vol. 61, no. 9, pp. 1137–1139, 1992.
  10. B. J. Rodriguez, C. Callahan, S. V Kalinin, and R. Proksch, “Dual-frequency resonance-tracking atomic force microscopy,” Nanotechnology, vol. 18, no. 47, p. 475504, 2007.
  11. A. Alsubaie, P. Sharma, J. H. Lee, J. Y. Kim, C.-H. Yang, and J. Seidel, “Uniaxial Strain-Controlled Ferroelastic Domain Evolution in BiFeO3,” ACS Appl. Mater. Interfaces, vol. 10, no. 14, pp. 11768–11775, 2018.

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

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

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