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J. Korean Ceram. Soc. > Volume 56(4); 2019 > Article
Yang and Kim: Nanoscale Probing of Ferroelectric Domain Switching Using Piezoresponse Force Microscopy


In ferroelectric materials, piezoresponse force microscopy (PFM) has been widely used to explore ferroelectric domain switching. In this article, we review the fundamentals of nanoscale probing of ferroelectric domain switching using PFM, including the basic principles of PFM and a variety of PFM studies on local domain switching. We also introduce advanced PFM techniques for exploring switching behavior. Finally, we discuss several issues and perspectives in nanoscale probing of ferroelectric domain switching using PFM. PFM has played an important role in exploring switching behavior in ferroelectric materials, and it could be further developed to probe more detailed switching information.

1. Introduction

Ferroelectric materials possess spontaneous polarization, which can be switched by the application of an electric field. There have been extensive efforts to utilize these materials as the key element for the next-generation information storage devices, such as ferroelectric random-access memories and ferroelectric field-effect transistors. For their practical applications, understanding the switching behavior of spontaneous polarization is essential because each direction of the polarization can be used as a single bit in information technologies. While macroscopic electrical measurements based on the detection of a switching current provide overall polarization switching behavior over a capacitor area, they do not provide local switching behavior inside the capacitor, i.e., how domains with opposite polarization nucleate and subsequently grow. However, as the size of devices decreases, it becomes more important to explore local switching behavior because local defects can hinder domain wall motion, and as a result, can significantly affect the overall switching behavior.1-3) To probe local switching behavior in ferroelectric materials, piezoresponse force microscopy (PFM), one of the modes of atomic force microscopy (AFM), has been widely used for the last two decades.4-7) It is now an indispensable tool to investigate ferroelectric domain switching at the nanometer level.
In this article, we review the fundamentals of nanoscale probing of ferroelectric domain switching using PFM. We first describe the basic principles of PFM and then cover a variety of PFM studies on local domain switching performed in bare ferroelectric surfaces and in capacitor structures. Finally, we introduce advanced PFM techniques for exploring switching behavior.

2. Principles of Piezoresponse Force Microscopy

PFM is based on the detection of bias-induced sample deformation, i.e., electromechanical response. All ferroelectric materials should have piezoelectric and converse piezoelectric effects. Therefore, if an electric field is applied to a conductive AFM tip in contact with a ferroelectric sample, a mechanical displacement will be induced. PFM detects the periodic converse piezoelectric response from the first harmonic component of the tip deflection, A = Acos(ωt + φ), generated by the application of the AC bias, Vtip = V0 cos(ωt). Here, the deflection amplitude A and phase difference φ between the tip deflection and the AC bias are directly related to the local piezoresponse magnitude (consequently, polarization magnitude) and the local polarization orientation (e.g., for upward domains, φ = 0°, and for downward domains, φ = 180°), respectively. By using a lock-in amplifier, both A0 and φ signals can be measured with a relatively high signal-to-noise ratio. More details of conventional PFM have been published elsewhere.4,6,8,9)
It should be noted that the principles of PFM are clear but the reliable acquisition of PFM data is not easy. In general cases, other artifacts besides piezoresponse can be added to the measured tip deflection amplitude A, such as capacitive cantilever-surface interaction and electrostatic contribution between the tip and the surface.4,7,8,10-13) These electrostatic artifacts can be reduced by using sufficiently stiff cantilevers, i.e., with high spring constants (e.g., above 40 N/m).4,14) In addition, hysteretic surface charging15,16) or ionic motion11,17-21) can generate PFM-like responses even in non-ferroelectric samples. Therefore, one should be careful when interpreting PFM data. Other complementary methods can be useful to check the reliability of obtained PFM signals, such as polarization-electric field hysteresis loop measurements or other scanning probe microscopy-based techniques like contact-Kelvin probe force microscopy.15,16,22)

3. Domain Switching in Bare Ferroelectric Surfaces

Since domain switching in ferroelectric materials underpins the operational mechanisms of multiple practical applications, such as storage and information technologies, it is necessary to understand switching behavior as a function of voltage pulse conditions. When a voltage or an electric field is applied to the electrode, domain switching in a metal-ferroelectric-metal (MFM) structure typically occurs via domain nucleation and subsequent domain growth, as presented schematically in the upper part of Fig. 1(a). Similar to the MFM structure, when a voltage is applied through the AFM tip, the domain switching proceeds as follows (see the lower part of Fig. 1(b)): (i) initially, the ferroelectric film is polarized as the upward domain; (ii) when the voltage is applied, the upper part of the upward domain underneath the AFM tip is initially switched to the opposite direction, so called nucleation; (iii) with increasing duration or magnitude of the applied voltage, the nucleation grows along the thickness direction, so called forward growth; (iv) once the nucleation reaches the bottom electrode, the domain starts to grow sideways, so called sideways growth. As a result, the domain switching procedure, i.e., domain nucleation and subsequent domain growth, is dependent on the pulse width and pulse voltage of the applied voltage.23-26) As shown in Fig. 1(b), the domain size in a poly(vinylidene fluoride-co-trifluoroethylene) [P(VDF-TrFE)] thin film increases with increasing pulse width and pulse voltage.23) The domain size is logarithmically proportional to the pulse width, as shown in Fig. 1(c), and is linearly proportional to the pulse voltage. 8) However, if the ferroelectric materials are polycrystalline, the sideways domain growth can be hindered by grain boundaries.24) In such a case, the correlation between the domain size and pulse conditions can be somewhat different from the usual case.
In addition to the application of the electric field, environmental conditions can induce domain switching27-29) because the surface state of ferroelectric materials is sensitive to environmental conditions. Among them, an oxygen atmosphere induces chemical switching inside ferroelectric thin films29) because its chemical potential produces an electric field across the film. In a similar manner, the oxidation of ferroelectric surfaces can switch the polarization direction. 27) In Fig. 2(a)(i), the as-prepared domain structures in the BiFeO3 (BFO) thin film show a downward matrix domain with upward needle-like domains. However, after 10 min of oxygen plasma treatment, the downward area was significantly increased compared to that of the as-prepared state, as shown in Fig. 2(a)(ii). The area of the upward domains gradually increased as the duration of the treatment was increased, as shown in Fig. 2(b). The relative humidity is also able to affect domain switching25,28,30) due to screening depolarization charges.25) As shown in Fig. 2(c), the domain size in P(VDF-TrFE) thin films was increased as the relative humidity was increased. A similar trend was also observed for the opposite domains, as shown in Fig. 2(d). These results clearly show that domain switching is closely related to the environmental conditions.

4. Switching Dynamics in Capacitor Structures

4.1. Operational mechanism of stroboscopic and domain tracing PFM

PFM is a powerful tool to measure ferroelectric domains with a high spatial resolution of less than 10 nm. However, it has a low time resolution. As with all AFM-based techniques, the scanning time for one PFM image is typically several minutes. Even in high-speed PFM, the image acquisition time for a single frame is several seconds.31) This indicates that we cannot observe the whole domain switching process, including domain nucleation (normally occurs within 1 ns) and subsequent domain growth (from nanoseconds to microseconds or longer depending on the experimental conditions), in real-time using PFM.
To improve the time resolution of PFM imaging, several methods have been proposed. The main idea behind these methods is to observe step-by-step domain switching by using pulse trains, leading to PFM imaging of domain switching in pseudo real-time. Two major methods are illustrated in Fig. 3(a) and (b), which are called the stroboscopic method and the domain tracing method, respectively. The stroboscopic method applies a series of short switching pulses with fixed amplitude and incrementally increasing duration (i.e., t1 < t2),34) as shown in Fig. 3(a). After each switching pulse, PFM imaging is carried out. At the beginning of each cycle, the ferroelectric capacitor is poled to make a single domain state. The stroboscopic approach is based on the assumption that the domain switching behaviors are almost identical from cycle to cycle. Indeed, in most ferroelectric capacitors, domain nucleation occurs in particular sites presumably due to local defects.33) Based on this inhomogeneous nucleation, the stroboscopic method has been applicable to many ferroelectric capacitors.33,35-37)
The domain tracing method is the approach used to focus on the acquisition of PFM images for a single switching process. Even if inhomogeneous nucleation occurs, the nucleation process still has a stochastic nature, i.e., nucleation probability is not 100%. In the stroboscopic method, a poling pulse resets the capacitor at the beginning of each cycle. Consequently, if the same switching pulses are used, the PFM images can be slightly different; several domains appear in some images, but they are absent in others. To reduce this drawback and obtain the information for a single switching process, the domain tracing method uses only one poling pulse, as shown in Fig. 3(b).32) Then, a series of switching pulses (usually of the same pulse duration) are applied with PFM imaging between the switching pulses. In the domain tracing method, it is assumed that the PFM image obtained after the ith pulse is almost the same as that obtained after a single pulse of t = τ1 + τ2 + ··· + τi. Aa a result, all PFM images obtained before the (i + 1)th pulse show the domain switching behavior during a single pulse of t. This method allows us to trace a particular domain and investigate its dynamics. Several remarkable PFM studies on ferroelectric domain dynamics in capacitors have been done using the domain tracing method.38-41)
It should be noted that both of the aforementioned methods have reliability issues in terms of the obtained PFM images. One should check whether polarization relaxation, imprint, and other events related to domain stability issues occur or not during PFM imaging. In this respect, comparisons between the volume fraction of switched domains in local PFM images and the switched polarization fraction obtained by the separate switching current measurements are required to validate the stroboscopic and domain tracing methods. For example, as shown in Fig. 3(c), the excellent agreement between PFM data and switching current measurement data indicates that the step-by-step PFM method used is valid. However, in the case of the 45-nm-thick Pb(Zr, Ti)O3 (PZT) film in Fig. 3(d), good agreement is not shown, and one cannot use these step-by-step PFM methods in those samples.

4.2. Switching dynamics in micron-scale capacitors

In this section, we introduce several PFM studies that have investigated nucleation and domain wall motion in micron-scale capacitors using the stroboscopic and domain tracing methods described in the previous section. As described in the upper part of Fig. 1(a), PFM imaging of the capacitor geometry allows us to observe nucleation processes occurring at multiple sites related to intrinsic local defects and domain wall motion under a uniform electric field. In addition, the effect of the tip on PFM imaging and related electrostatic effects can be reduced. However, the spatial resolution is slightly lower than direct imaging of the bare ferroelectric surface. The resolution in the capacitor imaging case is expected to be about 0.2dtop, where dtop is the thickness of the top electrode.42)
First, we discuss the PFM results of domain switching dynamics in micron-scale capacitors with relatively large area, top electrodes, such as tens of micrometers or larger. In such capacitors, it is somewhat difficult to apply a reliable and sufficient electric field via a nanosized AFM tip. This is because the tip keeps moving continuously along the top electrode for imaging, and the contact between the tip and top electrode is not stable. To resolve this problem and improve PFM imaging of capacitor geometry, the modified-PFM setup illustrated in Fig. 4(a) was developed.33) The main modification of this setup is to adopt a separate probe needle that applies an external electric field to the top electrode. Consequently, for imaging, a nonconductive AFM tip can be used in the modified-PFM setup, since PFM detects electromechanical displacement; and thus, additional electrostatic artifact can be removed.
Using the modified-PFM setup, inhomogeneous nucleation (i.e., nucleation that occurs at a particular sites) was clearly demonstrated.33) Fig. 4(b) shows the spatial probability distribution of nucleation sites in 170-nm-thick PZT capacitors obtained by summing 30 PFM phase images. Darker spots indicate the sites where nucleation occurred more frequently, and the background white region implies that no nucleation occurred in that region during 30 repetitions. As shown in Fig. 4(c), most nucleation sites have a nucleation probability above 90%, suggesting that the energy barrier for nucleation is reduced at particular sites, presumably due to local defects. Of course, it should be noted that the stochastic nature of the nucleation process is also observed in this experiment, as shown by the several sites with nucleation probabilities below 30%.
Modified PFM is also a powerful tool to investigate domain wall motion in micron-scale capacitors when combined with the domain tracing method. Fig. 5(a) shows ferroelectric domain nucleation and wall motion in 100-nm-thick epitaxial PZT capacitors with a 100-μm-diameter top electrode depending on the magnitude and time of the applied electric field.32) While the nucleation process is more dominant under high voltages, domain wall motion is more dominant under low voltages. In addition, from successive PFM images, the domain wall velocity of a particular domain was estimated, and therefore, the creep nature of ferroelectric domain walls was also studied.32, 38) Fig. 5(b) and (c) show a PFM study that investigated the origin of ferroelectric fatigue in epitaxial PZT capacitors.41) As shown in Fig. 5(b), domain switching in the virgin capacitor is coincident with the conventional picture of ferroelectric domain switching, i.e., nucleation, growth, and finally coalescence of domains. However, in the fatigued state shown in Fig. 5(c), the reversed domains are nanosized spot-like and most regions are frozen, i.e., domain wall pinning. This example shows that PFM can be a powerful tool to resolve long-standing issues in the ferroelectric community, such as polarization fatigue. There are several review articles on PFM studies on micron-scale capacitors that stress the role of local defects in ferroelectric domain dynamics.5,43)

4.3. Switching dynamics in nanoscale capacitors

When the capacitor size goes down into the nanoscale regime, the switching behavior can be somewhat different from that in the microscale regime.3,44-46) Fig. 6(a) presents the domain switching behavior as a function of pulse width in 70-nm-diameter PZT nanocapacitors.44) As the pulse width increased, nucleation occurred at the capacitor boundary, and then it grew sideways. Eventually, the entire nanocapacitor was switched to the opposite direction. Based on these PFM images, the switching dynamics seems to follow conventional switching behavior, i.e., domain nucleation and subsequent domain growth, as discussed in Section 3. However, as shown in Fig. 6(b), the switching dynamics in the nanocapacitors show a slightly different trend compared to the classical one, which is usually explained by the Kolmogorov-Avrami-Ishibashi (KAI) model, as shown in Fig. 4(b).47,48) Because the size of the nuclei is relatively large compared to the area of the nanocapacitors, the switching dynamics in the nanocapacitor might not be explained by the classical model, which assumes that the area of the nuclei is negligible. Interestingly, in some cases, domain wall pinning during the switching procedure was observed, as shown in Fig. 6(c) and (d).3) This might be related to the local point defect at the center of the nanocapacitor.1) In addition, when a much longer or higher voltage pulse, compared to typical switching pulse conditions, was applied to the nanocapacitor, the domain wall started to propagate into the neighboring nanocapacitors, generating significant cross-talk.46)

5. Advanced PFM Techniques for Probing Switching Behavior

5.1. Band excitation PFM

As described in Section 2, since PFM utilizes an AC bias with a particular frequency ω for imaging, the choice of ω is very important for reliable measurements. As there are many AFM modes, one has to avoid or reduce topographic cross-talk, which distorts the PFM response. The mechanism of topographic cross-talk can be understood as follows. Here, we only address indirect topographic cross-talk, which is more critical in PFM.49-51) The measured PFM signal is a product of the intrinsic piezoresponse of the sample and cantilever transfer function.49,50) The latter part, the cantilever transfer function, is determined by the mechanical property of the tip-surface junction. This indicates that, even on piezoelectrically uniform surfaces, most real materials have topographically rough surfaces, giving rise to a shift of the cantilever transfer function and consequently a distortion of the PFM signals. To avoid this indirect topographic cross-talk, so-called conventional single-frequency PFM uses a low frequency of tens of kHz, well below the contact resonance frequency ωr, which is typically hundreds of kHz. In such a low frequency regime, the cantilever transfer function is almost flat, and therefore, PFM imaging is not significantly affected by a shift of the cantilever transfer function.
However, low-frequency PFM does not have a big advantage in terms of signal amplification when using ωr. Recently, the range of PFM applications keeps increasing from conventional ferroelectrics to not-well-established ferroelectric materials, ultrathin films, and even biological systems. To enhance the signal-to-noise ratio significantly and minimize topographic cross-talk, advanced PFM techniques have been developed, such as band excitation (BE)50,52) and dual resonance AC resonance tracking (DART).53) The main advancement of these methods is to use multiple frequencies, allowing us to trace the local ωr continuously during scanning. The DART method uses two frequencies around ωr, while BE uses a band of frequencies that can cover the shift of the local ωr during scanning. The BE technique is more powerful, as it captures all responses within a particular frequency band. Consequently, the BE method can obtain all the information of the cantilever transfer function, such as ωr and quality factor, as well as PFM amplitude and phase. More details of the BE techniques 50,52) and the BE-PFM results54) on ferroelectric domain switching and other functional imaging have been published elsewhere.

5.2. Spectroscopy based PFM

In addition to BE-PFM, there are several advanced PFM spectroscopy techniques for exploring switching behavior. 2,55-57) Switching spectroscopy PFM (SS-PFM) allows the exploration of spatially varied switching behavior over a certain area based on grid point measurements.1) In SS-PFM, a local hysteresis loop is collected at each grid point on a N × M mesh, as shown in Fig. 7(a)(i). In each hysteresis loop measurement, the piezoresponse is acquired during the off-field state within the triangle voltage waveform of Fig. 7(a)(ii). Based on the measurements at each grid point, a PFM hysteresis loop can be obtained, as presented in Fig. 7(a)(iii). Once the PFM hysteresis loop is collected at each grid point, switching parameters, such as coercive voltage VC and work of switching, i.e., the area under the loop, can be extracted, as shown in Fig. 7(a)(iii). Fig. 7(b) and (c) show the PFM amplitude in the BFO nanocapacitor and the corresponding spatial map of work of switching obtained by SS-PFM, respectively.2)
When the voltage waveform is modified, it can be used to explore more complicated switching behavior beyond the simple hysteresis loop. As shown in Fig. 7(d), a first-order reversal curve (FORC) type waveform can be used to explore the switching field distribution and switching behavior.2,58) Fig. 7(e) and (f) are the FORC results obtained at two different points of Fig. 7(g). As shown in Fig. 7(e-g), the local switching behavior can be different for each nanocapacitor, and furthermore, it can even be different inside a single nanocapacitor. Moreover, when a voltage waveform is generated in a similar manner to that in Fig. 3(a) at each grid point, it is possible to explore local switching dynamics both along the thickness direction and over the area of the capacitor. This method is referred to as switching dynamics spectroscopy PFM (SDS-PFM).57) Fig. 7(h) and (i) present spatial maps of the characteristic switching time coefficient and activation field, respectively, obtained by SDS-PFM. These results indicate that the entire switching dynamics, beyond a simple ferroelectric hysteresis loop, can be accessed by the PFM spectroscopy techniques.

6. Summary

PFM provides us with unique opportunities to investigate ferroelectric domain switching behavior at the nanometer level. Due to advancements of step-by-step PFM imaging methods, the time resolution problem has been overcome, and this allows PFM imaging of domain switching in pseudo real-time. Thus, many problems of ferroelectric domain switching have been revealed, such as inhomogeneous nucleation and ferroelectric domain wall motion. In addition, due to the high resolution of AFM measurements, nanoscale switching behavior can be explored in nanocapacitors. In terms of PFM techniques, there have been many technological advances. Beyond conventional single-frequency PFM, to enhance the signal-to-noise ratio and to minimize topographic cross-talk, novel PFM techniques based on the use of multiple frequencies, such as BE and DART, have been developed. FORC-type SS-PFM and SDS-PFM allow us to investigate more complicated switching behavior at the nanoscale. These PFM techniques allow us to explore ferroelectric switching behavior in ferroelectric materials, and could be further developed to probe more detailed switching information.


This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) (No. NRF-2017R1C1B2010258) (S.M.Y.) This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2019R1A6A1A03033215) (Y.K.).

Fig. 1
(a) Domain switching behavior for (upper) metal-ferroelectric-metal and (lower) AFM tip-ferroelectric-metal structures. (b) PFM phase image of dot-patterned domains formed by negative voltage pulses to the bottom electrode in 90-nm-thick P(VDF-TrFE) thin films. (c) Domain size dependence on the pulse conditions at negative positive voltage pulses. Figures (b) and (c) were reprinted with permission from Ref.23) Copyright 2010 American Institute of Physics.
Fig. 2
(a) PFM phase images of (i) as-prepared and (ii) oxygen plasma treated states for 10 min in 30-nm-thick BFO thin films. The scale bar corresponds to 400 nm. (b) Dependence of the area of the upward domains on the duration of the oxygen plasma treatment. Figures (a) and (b) were reprinted with permission from Ref.27) Copyright 2010 American Institute of Physics. (c) PFM phase images of the downward domains at different relative humidity conditions in the P(VDT-TrFE) thin film. Pulse amplitude and width were +15 V and 500 ms, +16 V and 50 ms, and +17 V and 100 ms from the first row of the images, respectively. The scale bar is 500 nm. (d) Dependence of the perimeter of the downward (solid) and upward domains (hollow) on the relative humidity conditions. Figures (c) and (d) were reprinted with permission from Ref.28) Copyright 2014 IOP Publishing.
Fig. 3
Schematic of pulse sequences used (a) to employ the stroboscopic PFM method and (b) the domain tracing method. Figures (a) and (b) were reprinted from Ref.32). Copyright 2008 American Institute of Physics. (c) Dependence of switching behaviors on the switching pulse width tsw. The sample is an epitaxial SrRuO3/Pb(Zr, Ti)O3/SrRuO3 capacitor. The lines indicate the switched polarization fraction Δp obtained by the electrical switching current measurements, and the symbols indicate the volume fraction q of the reversed domains estimated from the PFM measurements. The inset shows a typical polarization-electric field hysteresis loop of the sample. Figure (c) was reprinted from Ref..33) Copyright 2007 American Institute of Physics. (d) Values of Δp-q for 45-nm-thick and 100-nm-thick epitaxial Pb(Zr, Ti)O3 films, which did and did not have relaxation problems, respectively. Figure (d) was reprinted from Ref..32) Copyright 2008 American Institute of Physics.
Fig. 4
(a) Schematic diagram of the modified-PFM setup. (b) The spatial probability distribution of nucleation sites in a 6 μm × 6 μm scan area in an epitaxial PZT capacitor. (c) The numerical distribution of nucleation sites in terms of the probability obtained from (b). Figures (a)-(c) were reprinted from Ref..33) Copyright 2007 American Institute of Physics.
Fig. 5
(a) Visualization of successive domain evolution images at various pulse widths at Vapp = −3, −6, and −8 V. The scan area was 5 μm × 5 μm. Contrast indicates the amount of reversed polarization. The time indicates the total width of the applied switching pulses t, as described in Section 4.1. Figure (a) was reprinted from Ref..32) Copyright 2008 American Institute of Physics. Time-dependent PFM phase and amplitude images of domain evolution under −150 kV cm−1 for (b) the virgin state and (c) the fatigued state (after 104 cycles). The scan area was 3 μm × 3 μm. Here, the time also indicates the total width of the applied switching pulses t, as described in Section 4.1. All images were measured at the same sample position. Figures (b) and (c) were reprinted with permission from Ref..41) Copyright 2012 Publisher Wiley-VCH Verlag GmbH & Co. KGaA.
Fig. 6
(a) (i) PFM phase and (ii) PFM amplitude images, and (iii) schematic cross-sectional domain structures of instantaneous domain configurations developing at different pulse widths under an applied voltage of +2.0 V. (b) Pulse width dependence of the normalized switched area for +1.0 V (blue triangle) and +2.0 V (black square) when there is no domain wall pinning. Figures (a) and (b) were reprinted with permission from Ref.44) Copyright 2010 American Chemical Society. (c) (top) PFM phase images and (bottom) their schematic domain structures of instantaneous domain configurations developing at different pulse widths under applied biases of +2.0 V for the as-prepared mono-downward capacitors. The blue solid and dashed lines indicate defects and capacitor boundaries, respectively. (d) Pulse width dependence of the normalized switched area on the pulse amplitudes of +1.5 V (red circle), +2.0 V (black square), and +2.5 V (green inverse-triangle), when there is domain wall pinning. The blue (red) arrows indicate the pinning (de-pinning) points. Figures (c) and (d) were reprinted by permission from Springer Customer Service Centre GmbH, Ref.3) Copyright 2014.
Fig. 7
(a) (i) In SS-PFM, a local hysteresis loop is collected at each grid point on a N × M mesh. (ii) The voltage waveform for a single point probing in SS-PFM and data acquisition sequence. (iii) A PFM hysteresis loop is collected at each grid point. Forward and reverse coercive voltages. Figure (a) was reprinted by permission from Springer Customer Service Centre GmbH: Springer Nature, Ref.1) Copyright 2008. (b) PFM phase and (c) spatial map of work of switching of BFO nanocapacitors. (d) Voltage waveform for FORC-type SS-PFM. (e, f) FORC was measured at the (e) blue and (f) black filled circles of Fig. (g), which is the sum of the piezoresponse. Figures (b)-(g) were reprinted with permission from Ref.2) Copyright 2011 American Chemical Society. (h, i) Spatial maps of (h) characteristic switching time coefficient log(τ0) and (i) activation electric field Ea obtained by SDS-PFM. Figures (h) and (i) were reprinted with permission from Ref.55) Copyright 2013 Publisher Wiley-VCH Verlag GmbH & Co. KGaA. The scale bar is 100 nm.


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