About Park Systems
Basic Principles of PFM
Optimization of PFM Signal
About Park Systems
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This application note presents the basics, instrumentation and potential applications of the piezoelectric force microscopy (PFM), a new scanning probe microscopy mode that utilizes the piezoelectric effect of materials to generate contrast. Various topics involved in improving image quality and resolution, eliminating artifacts and extracting information from the generated image are discussed. Also, we have included a brief introduction of the spectroscopy mode which allows quantitatively analyses of the piezoelectric response of materials under applied voltage.
Basic Principles of PFM
From the first day scanning probe microscopy is introduced to the contemporary research frontier, new modes and applications have emerged with unprecedented speed, allowing this versatile tool to look into ever-increasing aspects of local material properties at nanometer scale. Piezoelectric Force Microscopy (PFM) is one of such novel modes which has gained increasing recognition though recent years for the unique information it can offer on the electromechanical coupling characteristics of various ferroelectric, piezoelectric, polymer and biological materials.
In PFM operation, a conductive AFM tip is brought into contact with the surface of the studied ferroelectric or piezoelectric materials, and a pre-set voltage is applied between the sample surface and the AFM tip, establishing an external electric field within the sample. Due to the electrostriction, or "inversed piezoelectric" effects of such ferroelectric or piezoelectric materials, the sample would locally expand or contract according to the electric field. For example, if the initial polarization of the electrical domain of the measured sample is perpendicular to the sample surface, and parallel to the applied electric field, the domains would experience a vertical expansion. Since the AFM tip is in contact with the sample surface, such domain expansion would bend the AFM cantilever upwards, and result in an increased deflection compared to the status before applying the electric field. Conversely, if the initial domain polarization is anti-parallel to the applied electric field, the domain would contract and in turn result in a decreased cantilever deflection (Figure 1). The amount of cantilever deflection change, in such situation, is directly related to the amount of expansion or contraction of the sample electric domains, and hence proportional to the applied electric field.
Figure 1. Cantilever deflection change
If the applied voltage contains a small AC component, the inversed piezoelectric response from the sample would result in sample surface oscillation in the same frequency as the applied AC voltage. In the case that the sample is an ideal piezoelectric crystal, its polarization would be related to applied mechanical stress by the following equation:
Pi = dijksjk
in which dijk is the rank-3 peizoelectric tensor of the material. For such materials with tetragonal crystal structures, this piezoelectric tensor can be reduced to the following form:
in which case, under the applied AC modulation voltage V = V0cos(ωt), sample surface vibration would take the form ΔZ = ΔZ0cos(ωt + φ), with the vibration amplitude ΔZ0 = d33V0, and phase f = 0 if the sample domain polarization is oriented parallel to the applied electric field, and out of φ = 180° if it is oriented anti-parallel to the applied electric field (Figure 2). Such oscillation would be directly reflected in the amplitude and phase signal of the AFM probe contacting the surface, and can be read out using a lock-in amplifier.
Figure 2. Vibration amplitude for parallel and anti-parallel orientation of polarization
In typical PFM imaging, the applied AC voltage is set to be much lower than the coercive bias for sample domain switching, to avoid alternation of the local domain structure of the studied sample. If such criterion is met, the phase contrast generated in PFM imaging would reflect the domain polarity in different sample locations, while from the magnitude of the amplitude signal local piezoelectric coefficient of the sample can be extracted, as discussed in the former paragraph. Figure 3 shows such an example of such PFM amplitude and phase images obtained on PZT-5H sample. As can be observed in the circled portion 180°, phase contrast is evident in two adjacent domains in PFM phase image, and the domain wall between them can be observed with reduced amplitude in PFM amplitude image. Also can be noticed is that the both the upward and downward oriented domains has induced PFM amplitude signal with similar magnitude, indicating the material property is relatively homogenous in the studied sample.
Figure 3. PFM amplitude and phase images obtained on PZT-5H sample
For more complicated sample domain orientation containing not only components perpendicular to the surface in contact with the AFM tip, but also components along different directions within the surface plane, vector PFM with one vertical and two lateral channels can provide more complete information. For example, to obtain the d15 component of the piezoelectric tensor in tetragonal piezoelectric crystals, we need to measure lateral components of AFM tip vibration proportional to the in-plane sample surface displacement (Figure 4), which would take the form would take the form ΔL = ΔL0cos(ωt + φ), with the vibration amplitude ΔL0 = d15V0 Notice if a DC bias is applied between the tip and the sample in conjunction with the AC voltage, both the in-plane and out-of-plane electromechanical response of the sample are also functions of this applied DC voltage.
Figure 4. Vertical and lateral PFM amplitude and phase images
In most of the real cases, the studied sample contains random-oriented polycrystalline grain structure, often with non-zero lateral components in its piezoelectric tensor. In this case, the detected vertical PFM signal is no longer only proportional to d33, but also dependent on the d31 and d15 components. E.g., the vertical PFM amplitude would no longer be ΔZ0 = d33V0 instead, it would take the form
ΔZ0 = dZZV0 = [(d31 + d15)sin2θcosθ + d33cos2θ]V0
in which θ is part of the local orientation map (θ, φ, ψ) between the lab coordinate system and the crystal coordinate system of the sample. Nevertheless, if both the vertical and two lateral components of PFM signal are obtained on the sample location, either the intrinsic sample piezoelectric constants dij or the local orientation map (θ, φ, ψ) can be extracted from such data. In a word, 3D PFM has opened the possibility of a complete 3D reconstruction of the polarization vector of the studied sample at nanometer scale.
Common application of PFM includes local characterization of electromechanical properties of materials, including detailed domain mapping and study of domain switching dynamics; testing of micro- and nano-electromechanical devices (e.g., piezoelectric actuators, transducers, and MEMS), electro-optical devices and nonvolatile memory components (i.e., FERAM devices), addressing their reliability issues such as electromechanical imprint, fatigue and dielectric break-down; exploring the local and global relationship between polarity and other material properties on novel polymer and bio-engineered materials based on detailed nanoscale structural and electrical characterization of such materials, etc.
Optimization of PFM Signal
In the real world, measured PFM signal often contains additional contributions from both local and distributed electrostatic force in addition to the local electromechanical response from the sample, i.e., A = Aem + Aes + Anl.Aem, the electromechanical response from the sample, is the real term that reflects the local domain structure of the sample, while Aes, the local electrostatic force operating at the tip-surface junction and Anl, the electrostatic response of the cantilever resulted from the field between the cantilever itself and the sample surface, as seen in Figure 5, are distractive terms which needs to be minimized to avoid imaging artifacts.
Figure 5. Local Piezoresponse Contrast
However, by carefully choosing cantilever for samples with different magnitude of electromechanical response, the contribution of the electrostatic terms can be minimized. Since the total PFM signal Z = (deff + Lwe0ΔV / 48kh2)VAC in which deff is the effective piezoelectric constant along the direction of the measurement, L , w and k are the length, width and spring constant of the cantilever used for the measurement, h is the height of the AFM tip, ε0 and ΔV are the dielectric constant of the air and the average voltage applied between the tip and the sample, respectively, to increase the percentage of the real electromechanical contribution to this signal, we should choose a cantilever that is stiff enough keff >> k = Lwe0ΔV / 48deffh2) to decrease the second term in the equation above.
Since PFM is a contact-based imaging technique, using very stiff cantilevers could induce irreversible sample damage in on softer materials, or samples that are not firmly attached to the substrate surface, such as ZnO nanowire samples loosely scattered on Si wafer surface. In such situations, choosing a cantilever with short and narrow geometry could also help to reduce the contribution from the electrostatic term. In addition, obtaining PFM image at zero DC bias would greatly reduce contribution of the electrostatic term, both local and non-local.
Finally, electrostatic components that contribute to the PFM signal would decrease with increased frequency of the applied AC voltage, and the non-local components decreases especially fast. Also, imaging at higher frequencies would generally result in cantilever stiffening, which improves the contact between tip and sample surface. Hence, PFM images obtained at higher frequency generally contains less contribution from the electrostatic terms, and exhibits a better signal to noise ratio. Optimum vertical PFM signal can be obtained in frequencies around MHz order, while lateral PFM signal is usually optimal at frequencies between 10 and 100 kHz, depending on both the AFM probe used and the sample imaged. However, continue increase of the frequency for the applied AC voltage would eventually hit the upper limit set by the bandwidth of the photodetector and the lock-in amplifier. At extremely high frequencies, no signal would be transuded due to the drastically increased stiffness of the cantilever.
When an appropriate cantilever is chosen for the studied sample, contact resonance effect can be utilized to increase the contribution from the eletromechanical component, Aem, and improve the quality of PFM imaging. In practice, after bringing the AFM tip in contact with the sample surface to be studied in PFM mode, a frequency sweep could be performed for the AC voltage applied between the tip and the sample, and the amplitude/phase vs. frequency behavior can be recorded (Figure 6). The resonant peak shown in the amplitude vs. frequency chart is defined by the mechanical properties of the cantilever, the intrinsic electromchanical properties of the sample, and the stiffness of the tip-sample contact. If the AC voltage applied to the tip is operated in the vicinity of such resonant frequency, the high quality factor of the resonant peak would greatly increase the signal-to-noise ratio in observed PFM amplitude and phase signal (Figure 7: away from resonance, 17kHz, low signal vs. near resonance, 377kHz, high signal).
Figure 6. Resonant peak in amplitude vs. frequency chart
Figure 7. Signal-to-noise ratio in observed PFM amplitude and phase signal
Extra cautions do need to be taken to avoid the strong cross-talk between topographical and electromechanical signals when using resonance enhancement to increase PFM image quality, since the frequency of such contact resonance is affected by the tip-sample contact stiffness, which is in turn affected by the contact area between the tip and the sample (Figure 8). For example, when the tip is in contact with a concaved area of sample surface, the tip-sample contact stiffness would increase comparing to the case when the tip is in contact with a flat area of sample surface. This would in turn raise the contact resonant frequency. If the AC voltage applied to the tip is fixed at the exact contact resonant frequency measured when the tip is in contact with the flat area, a large drop in the observed PFM amplitude would occur since the new contact resonance no longer occurs at this specific frequency.
Figure 8. Resonance affected by the contact area between the tip and the sample
To minimize this instability and largely eliminate the cross-talk between topographical and PFM channels of signal, the frequency of the AC driving signal is best chosen in the vicinity of the resonance, but not exactly at the resonant peak (Figure 9).
Figure 9. Resonant: 360kHz, cross-talk of topo-PFM signal in amplitude imaging; near resonance: 377kHz, good signal quality and almost no cross-talk
When attempting to use contact resonance for PFM signal enhancement, due to the electrostatic effect, softer cantilevers may show multiple peaks in the frequency sweep chart (Figure 10), and not all peaks would generate stable PFM signal. If such soft cantilever is needed for the specific sample to be studied (e.g., ZnO wire scattered on Si substrate may be scratched or even detached with scanned in PFM mode using very stiff cantilevers), each of the presented peaks may be tested individually until the one that provides clear, stable PFM signal is found. In most cases, repeat the frequency sweep a couple of times may help stabilize the spectra and eliminate any non-intrinsic peaks.
Figure 10. Peaks in the frequency sweep chart
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