Electromechanical coupling is one of the fundamental mechanisms underlying the functionality of many materials. These include inorganic macro-molecular materials, such as piezo- and ferroelectrics, as well as many biological systems. This application note discusses problems and solutions to piezoresponse force microscopy (PFM) measurements using the MFP-3D™ AFM and Cypher™ AFM from Asylum Research.
Limitations of Conventional PFM Methodologies
High Voltage Limitations
Traditionally, the use of 1-10Vpp driving amplitude on materials with strong electromechanical responses (e.g. d33 ≈ 100pm/V for PZT, 10pm/V for LiNbO3) allowed direct imaging and spectroscopy of ferroelectric materials sufficient for applications corresponding to a detection limit of 50pm at ~100kHz. Measurements of lower sensitivity materials require the use of higher voltages or the use of contact resonance.
Imaging at Contact Resonance
For some samples, using a higher drive voltage is undesirable. High drive voltages will result in polarization switching or even damage to the sample. Recent advances in theoretical understanding of the PFM imaging mechanism illustrate that the primary limitation of previous commercial and home built SPMs is their inability to effectively use resonance enhancement.
Probe polarization dynamics in commercial low voltage ferroelectric capacitors is optimal for driving amplitudes of 30-100mV (to avoid bias-induced changes in domain structures), which is 1-2X below the magnitude of standard, low-frequency PFM capabilities. Finally, the use of PFM as an electrophysiological tool necessitates operation in the mV regime, as required to prevent damage to biological systems, as well as stray electrochemical reactions.
The resonant frequencies are determined only by the weakly voltage-dependent mechanical properties of the system and are independent of the relative contributions of the electrostatic and electromechanical interactions. As shown by Sader in the vicinity of a resonance for small damping (Q > 10), the amplitude and phase frequency response can be described using the harmonic oscillator model as
where, Amax is the amplitude at the resonance ω0, and Q and is the quality factor that describes energy losses in the system. Resonance is a phenomenon used in many SPM techniques. The cantilever response at resonance is essentially multiplied by the so-called "quality factor" (Q) of the cantilever
Typical Q values in air for PFM cantilevers range from 10-100x. This implies that one can amplify a weak PFM signal by a factor of 10-100x by simply driving the tip voltage at the contact resonant frequency.
Figure 1 shows a representative cantilever in contact with a surface. The potential of the cantilever is being oscillated, which in turn induces a piezo response in the sample surface (Atip-samp, Φtip-samp). The cantilever in contact with the surface has a resonance defined by the mechanical properties of the cantilever and the stiffness of the tip-sample contact. This resonance can have a high quality factor (Q) for typical PFM samples that effectively amplifies the piezo signal by a factor of ~Q near the resonance. For samples with small piezo coefficients, this is potentially a very important effect and could mean the difference between only noise or a measurable signal. Unfortunately, because the cantilever resonance frequency depends on the tip-sample contact stiffness, the resonance frequency is very unstable. As the tip scans over the sample topography, the stiffness of the mechanical contact (ktip-samp) will typically change significantly. This, in turn, affects the resonance frequency.
Figure 1. In PFM, the cantilever voltage is modulated, usually at some fixed frequency. This causes the sample to distort at some amplitude and phase. Mediated by the contact mechanics, this drives the tip which, in turn, is monitored by the AFM sensor.
To understand how resonance is affected in PFM, we first describe an "ideal" situation as illustrated in Figure 2. This shows a numerical simulation of the cantilever response using realistic cantilever parameters (Olympus AC240 cantilever with a 320kHz contact resonant frequency, 2N/m spring constant) and sample parameters (d33 ≈ 100pm/V). The noise visible in the PFM amplitude and phase curves were calculated to be the ideal thermal (Brownian motion) noise of a cantilever at typical room temperature, 300 Kelvin. Here, the domain structure is shown in the middle of the image with purely vertical polarization vectors. The sample is treated as perfectly smooth, meaning that the contact stiffness remains constant as a function of position. The simulation reproduces many of the features present in a real scan where the measured phase reproduces a map of the domain structure, and the amplitude goes to zero at the domain boundaries. This occurs as the tip is being driven by two oppositely oriented domains, each canceling the other since they are 180° out of phase. As discussed below, real-world samples have behaviors that make extracting unambiguous domain maps much more complicated.
Figure 2. This figure shows the ideal and measured PFM response of an idealized tip (green) scanning over a smooth surface (black line below the "tip"). The domain structure of the ferroelectric sample is shown below the surface where the arrows correspond to the sample polarization direction. The gray hatched regions between the domains are representative of the domain walls. The "ideal phase" (blue, thin curve) and "ideal amp" (red thin curve) show the idealized response of a probe that measures the piezoelectric response over the domains. The measured PFM amplitude (red, thick curve) and phase (blue, thick curve) channels appear above the scanning tip. Because these measurements are made below the resonant frequency where there is no resonance enhancement of the PFM signal, the signal to noise is relatively small for the measured signal. Click here to watch the movie.
The gain in the signal from the Q-factor when operating near resonance improves the SNR for the PFM amplitude and the phase. This is illustrated in Figure 3 which shows the same sample as in Figure 2 but now imaged with the cantilever voltage being modulated at the cantilever resonance. This should not come as a surprise; as with many other types of dynamic SPM, oscillating at the cantilever resonance greatly benefits the SNR. However, the experimental conditions shown in Figure 2 are very rare. Usually, the sample will have some roughness. This roughness will lead to position-dependent changes in the contact resonant frequency. The effects of this resonant frequency variation on PFM contrast can easily completely mask the desired PFM signal. Figures 4, 5, and 6 illustrate this.
Figure 3. This figure shows the same situation as described in Figure 2, except that here we are using resonance enhancement to boost the small PFM signal. The inset frequency tune in the upper right corner shows the drive frequency. In this case, since the Q-value of the resonance is 100, the SNR of the measured PFM amplitude (red, thick curve) and phase (blue, thick curve) has dramatically improved. Click here to watch the movie.
Figure 4. This figure shows a practical limitation of using the contact resonance as the drive frequency. In conventional PFM systems, the contact resonance can change by 10-30kHz over the course of imaging a rough sample. Typical cantilevers have a full-width half max of 4-10kHz meaning the phase shift due to the changing contact resonances will easily be near 180° over the scan. The PFM phase shift will be added to the phase of the cantilever contact resonance, yielding a convolution that makes practical interpretation of domain structures very difficult. This is clear in comparing the PFM phase signal to the sample domain structure. In contrast to the off-resonance smooth sample, it is quite difficult to correlate the domain structure with the PFM phase. Click here to watch the movie.
Figure 5. (top): PFM phase channel on a polished PZT sample. The cantilever was driven near the contact resonance to enhance the SNR. There is significant crosstalk between the sample topography and the PFM signal. Red arrows indicate "roughness" where the contact stiffness modulates the phase. In addition to the surface roughness changing the contact resonance and therefore the measured phase, changes in the tip can also cause large phase shifts. The yellow arrows indicate a sudden tip change caused a change in the contact resonance. 4µm scan (top), 2µm scan (bottom).
Figure 6. (right). PZT showing crosstalk, 14µm scan.
If we return to our idealized sample and add roughness to the surface, we can see that it modulates the contact resonance. For example, if the tip is on a tall part of the sample, it is in contact with a relatively compliant part of the sample. Sharp points are, after all, relatively easy to blunt. Because the contact stiffness is small, the contact resonance frequency will drop. If the cantilever is being driven at a fixed frequency, the phase will increase as the resonance moves to lower values. Conversely, if the tip is in a valley, the contact stiffness will be increased, raising the resonant frequency and the phase measured at a fixed frequency will drop. Phase shifts associated with changes in the contact resonance sum with phase shifts due to domain structures of the piezo material. As a consequence, interpretation of the domain structure becomes much more difficult and in many cases, impossible. Figure 4 shows a case where the domains are completely masked by the large phase shifts originating with the moving contact resonance.
Another source of phase shifts can come from irreversible changes to the cantilever itself. PFM is a contact mode technique and therefore can exert large forces on the tip. If the tip fractures or picks up a contaminant, the contact resonance can experience a sudden jump, usually positive, since tip wear tends to blunt the tip. The resonance jumps are typically of the order of a few kHz. This causes large, discontinuous changes in the measured phase. Figures 5 and 6 show PFM data taken on a rough PZT surface. A number of successive tip changes caused the contact resonance to change, resulting in an irreversible change in the overall measured phase. Note that in addition to these jumps, there is significant "roughness" in the phase signals that probably originates with topographic contact resonance crosstalk.
By avoiding the resonance, the topographic crosstalk on rough samples can be reduced, as shown in Figure 7. When the cantilever is driven well below resonance, the domain structure is reproduced quite accurately. However, this comes at the high price of a poor SNR. In practice, the reduced SNR (see in particular the PFM phase trace) may obviate imaging of a large number of weak piezo materials with conventional PFM.
Figure 7. Driving below contact resonance with conventional PFM. Here, the cantilever is driven well below the contact resonant frequency. The effects of surface roughness are minimized, though still visible in the measured PFM amplitude. However, this reduction in crosstalk comes at the high price of severely reduced sensitivity. Thus, for weak piezo materials, this operational mode is undesirable. The improved topographic crosstalk rejection results in an immeasurably small signal with conventional PFM. Click here to watch the movie.
Summary of Limitations of Conventional PFM Methodologies
To summarize the discussion in this section, with conventional PFM imaging and the contact resonance, we are left with the situation where we need to choose between two sub-optimal alternatives:
- Operate on resonance to benefit from the boosted signal but have complicated artifacts that do not allow unambiguous determination of the sample domain structure, or
- Avoid resonance to minimize topographic crosstalk, but suffer from the small signals inherent in piezo materials.
Solutions to Limits of Conventional PFM with Asylum's PFM and SPM Capabilities
Increasing the Drive Voltage
Perhaps the most obvious option for improving the response of PFM is to simply increase the drive amplitude. The signal is usually proportional to the drive voltage, so increasing the drive voltage by 10x will result in a 10x improvement in the SNR. A more powerful drive amplifier also enables operation at higher frequencies.
Asylum's Piezoresponse Force Module is currently the only commercially-available AFM that enables high voltage PFM measurements. A programmable bias of up to +220V for the MFP-3D and up to +150V for the Cypher AFM is applied to the AFM tip using a proprietary high voltage amplifier, cantilever and sample holder. The amplitude of the response measures the local electromechanical activity of the surface while the phase yields information on the polarization direction. High probing voltages can characterize even the weakest piezoelectric sample and insure that you have the ability to switch the polarization of high-coercivity materials. The fully integrated system allows both PFM imaging modes and spectroscopy modes. All PFM imaging and spectroscopy modes are fully integrated with the AFM system software and Piezoresponse Force Module hardware. An easy-to-use PFM menu panel (Figure 8) provides users with point-and-click navigation to the operation they wish to perform. For advanced users, custom panels can by created within the flexible IGOR Pro environment.
Figure 8. MFP-3D Piezo Force Module software menu allows easy point and click navigation.
Using Contact Resonance as a PFM Amplifier
Sometimes increasing the SNR by simply increasing the drive voltage is not an option. In some ferroelectric samples, the polarization might be reversed by too large a PFM drive voltage. On others, the sample might actually breakdown, leading to large current flow, sample damage or even destruction. Another effective way to increase the SNR in PFM imaging and other measurements is to make use of the contact resonance. Resonance enhances the signal by the natural gain of the cantilever - by roughly the factor Q (quality factor) of the cantilever.
As noted above, driving near the contact resonance at a fixed frequency can sometimes lead to enormous topographic cross-coupling. To avoid this, and to maintain the advantages of resonance, requires that we continually adjust the drive frequency to keep it at the contact resonance. If one can remain on resonance despite changes in the contact resonance frequency, then the artifacts present in the above examples would not be present, while still reaping the Q-factor signal boost.
The most common kind of resonance-tracking feedback loop is called a phase-locked loop (PLL). It utilizes the phase sensitive signal of a lock-in amplifier to maintain the system at a specific phase value, typically 90°. The PLL is generally limited to techniques where the phase and amplitude of the driving force is constant (e.g. the mechanical excitation of a cantilever resonance using an external actuator). This is manifestly not the case in PFM, where the relationship between the phase of the excitation force and driving voltage strongly depends on material properties. The amplitude and phase of the local response are a convolution of material response to the external field and cantilever response to the material-dependent local force, which cannot be separated unambiguously. Figure 9 is an example where, for antiparallel domains, a conventional PLL will actually drive a PFM away from resonance.
Figure 9. For domains with an antiparallel (180° ) orientation, conventional PLLs drive the PFM frequency away from resonance. (Top) Amplitude, red, and phase, blue, cantilever response over antiparallel domains. In the measurement, phase is offset by 180° over anti-parallel domains (see curves on the right). (Bottom) PFM phase signal driving the cantilever off resonance. Note the increased noise in the phase signal away from the resonant frequency. This increased noise would be apparent in an image as well, similar to the PZT image in Figures 5 and 6.
Dual AC Resonance Tracking (DART)
This patent pending dual-excitation method allows the cantilever to be operated at or near resonance for techniques where conventional PLLs are not stable. Figure 10 shows how DART works. The potential of the conductive cantilever is the sum of two oscillating voltages with frequencies at or near the same resonance. The resulting cantilever deflection is digitized and then sent to two separate lock-in amplifiers, each referenced to one of the drive signals. By measuring the amplitudes at these two frequencies, it is possible to measure changes in the resonance behavior and furthermore, to track the resonant frequency. Specifically, by driving at one frequency below resonance (A1), and another above (A2), A2-A1 gives an error signal that the ARC2™ controller uses to track the resonance frequency changes.
Figure 10. Schematic diagram of Asylum Research's new DART showing a drive phase independent feedback signal.
DART-PFM studies of polarization switching are illustrated in Figure 11, where the resonant frequency(A), amplitude(B) and phase(C) images of a lithium niobate surface are shown Figure 11A. The PFM amplitude and phase images show a macroscopic 180° domain wall and two inversion domains which are typical for this material. Higher resolution DART-PFM images of pre-existing domains(D-F) illustrate strong frequency contrast, and nearly constant PFM amplitudes within and outside the domain. In comparison, Figures 11(G-I) are DART-PFM images of domains switched by the application of three 176V magnitude pulses for ~10 seconds in three adjacent locations. Note the significant change of resonant frequency and the strong amplitude depression in the newly fabricated domain.
Figure 11."(A), (D), (G) Resonance frequency, (B), (E), (H) piezoresponse amplitude and (C), (F), (I) piezoresponse phase images of antiparallel domains in lithium niobate. Shown are images of the (A)-(C) native domain structure, (D)-(F) an intrinsic domain and (G)-(I) domains switched by ±176 V (locations marked in (E)). The images are obtained at wf = 4 kHz and Vac = 66 V. The frequency images have been flattened to account for minute changes of contact radius from line to line.
Additional DART images of ferroelectric materials are shown in Figures 12 and 13. Figure 12 shows a series of images of PFM on multiferroic BiFeO3 nanofibers. Figure 13 shows a short relaxation study on a sol-gel sample. Regions of the sol-gel PZT were reversed by applying a 15 volt bias to the tip. These regions gradually relaxed over a 1.5 hour period. DART allowed stable, reproducible imaging over an extended period of time.
Figure 12. PFM of multiferroic BiFeO3 nanofibers, 1µm scan. Collaboration with Shuhong Xie, Xiangtan University, China and JiangYu Li, University of Washington.
Figure 13. Stable imaging using DART allows relaxation studies. This series of images shows the relaxation of sol-gel taken at different intervals for approximately 1.5 hours. 3.5µm scan.
Band Excitation (BE)
Band Excitation is a new option that can be utilized with PFM. The technology is exclusively available with Asylum Research SPMs under license from Oak Ridge National Laboratory and has received the R&D 100 award for 2008. The Band Excitation controller and software extend the capabilities of Asylum's MFP-3D and Cypher AFMs to probe local amplitude frequency curves and transfer functions and map local energy dissipation on the nanoscale.
The applicability of SPM for mapping energy transformations and dissipation has previously been limited by the fundamental operation mechanism employed in nearly all conventional SPMs; i.e., the response was measured at a single frequency. Determining dissipation with a single frequency measurement required time-consuming multiple measurements. Simply put, there were more uncertainties than there were measured quantities. Band Excitation surmounts this difficulty by detecting responses at all frequencies simultaneously. Band Excitation introduces a synthesized digital signal that spans a continuous band of frequencies, and monitors the response within the same frequency band. This allows ~100x improvement in data acquisition speed compared to other commercially-available technologies.
The immediate benefit of this approach is that a full response spectrum can be collected (with insignificant [30-50%] decrease in signal to noise ratio) in the amount of time required for obtaining a single pixel in conventional single-frequency SPM. Band Excitation allows quantitative mapping of local energy dissipation in materials on the nanoscale. Figure 14 shows an example image of an amyloid fibril (bovine insulin) on mica imaged in water using the BE-PFM technique. The image size 250nm x 250nm.
Figure 14. Amyloid fibril (bovine insulin) on mica imaged in water using BE-PFM technique, 250nm x 250nm. Image courtesy of G. L. Thompson, V. V. Reukov, A. A. Vertegel, M. P. Nikiforov, Clemson University, Dept. Bioengineering, and S. Jesse, S. V. Kalinin, Oak Ridge National Lab.
In summary, both DART and BE modes have numerous advantages for PFM measurements:
- SNR is increased by a factor of 100, eliminating crosstalk issues by using, rather than avoiding, resonance.
- Eliminates the problems with PLL stability.
- For BE, data acquisition is improved by ~100x compared to other commercially-available swept frequency technologies.
- Imaging modes and hardware are fully integrated.
This information has been sourced, reviewed and adapted from materials provided by Asylum Research - An Oxford Instruments Company.
For more information on this source, please visit Asylum Research - An Oxford Instruments Company.