Piezoresponse Force Microscopy

Piezoresponse force microscopy (PFM) is a commercially available function of atomic force microscopy (AFM). Before introducing the basic principle for PFM, it is worthy to mention the basic function of AFM and the underlying mechanism. AFM is mainly used to map the surface morphology of samples, which is achieved by scanning a tip over the sample surface and modifying the tip-surface distance using a feedback loop.

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The topography image can be done by either contact or non-contact (AC) mode. In AC mode, generally the cantilever is mechanically oscillated by a piezoelectric actuator located on the cantilever holder (Note that the excitation source is not restricted to piezoelectric materials). Then the signal generator sweeps a wide range of frequencies and locates one near the resonance of the cantilever. When the tip approaches the surface, the tip-surface force (repulsive or attractive) modifies the resonance peak, and the topography is mapped by the feedback loop (Figure 2-9). Mapping the local physical and chemical properties, such as surface potential and current are also available because these properties can generate a force interaction between the tip and sample. Among these wide applications, PFM is a useful technique to image the local domain structures and dipole switching behaviour.

Figure 2-9 A shift in resonance frequency as the tip-surface interaction changes. The black line is the resonance frequency for the free oscillation. The blue and red lines

denote the peak shift induced by repulsive and attractive force, respectively. The PFM technique is based on the detection of bias-induced surface deformation. Therefore, it works in the contact mode, measuring the topography and piezoresponse of samples at the same time. By applying an ac voltage on the tip, the tip deflection for the vertical PFM (VPFM) is: d=d0+d33Vaccos(ωt+φ) where the d33 is the local piezoelectric

coefficient. In Figure 2-10a and b, the polarization vectors with the same d33 lie in parallel

and antiparallel to the E-field, respectively. They show the same amplitude but the polarization direction, which is decided by the phase difference, φ, between the tip bias

Attractive Repulsive Amplitude (m V) Phase ( °) Frequency (kHz)

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and surface oscillation, is 180° different. Obviously, the phase contrast is very evident but the amplitude, d33Vac, of these local piezoresponse signals are usually very weak.

Applying high drive voltages will induce other problems such as polarization reversal and damage to the samples. Therefore, the contact resonance is proposed to act as an amplifier to improve the piezoresponse signals. In this way, the quality factor, Q (~100 in air), is gained for enhancing the amplitudes, i.e., A= d33QVac. As the contact resonant frequency

depends on the tip-sample stiffness, so it is every sensitive to the surface and tip conditions. Generally, a rough surface is not allowed for PFM measurement because it induces strong crosstalk between the piezoresponse and topography. Even though, the contact resonant frequency will not remain constant during the scanning, and the resonance frequency is required to be tracked so the excitation signals can change accordingly to keep Q factor constant. With the development of the instruments, the most effective resonance tracking methods are the Dual AC Resonance Tracking (DART) and band excitation (BE).16, 17 _{The DART method uses two separate oscillating voltages with}

the frequencies near the same resonance while BE synthesized signal contains a continuous band of frequencies to excite the sample and monitoring the response spectra. The details of these two technologies are not included in this thesis.

Figure 2-10 The deformation of the ferroelectric materials under a biased tip. E-field is parallel (a) or antiparallel (b) to the spontaneous polarization. (c), (d) Shear deformation

when the E-field is perpendicular to the spontaneous polarization. (Reproduced from Balke et.al.18₎

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In addition to mapping the local domain structure, PFM is capable of investigating the local domain, or polarization switching behaviour by the built-in spectroscopic mode, i.e., switching spectroscopic PFM (SS-PFM). The waveform used for SS-PFM is a triangular pulse wave superimposed with an AC signal (Figure 2-11a). Between each dc voltage step, the offset is zero and the applied ac signal is used to detect the piezoresponse, which equals Acosφ, where A is the amplitude and φ is the phase. Generally, pulse-off states provide reliable hysteretic behaviour because a strong electro-static force is involved in the pulse-on states. The results of SS-PFM, PR hysteresis loop (Figure 2-11b) are very similar to the macroscopic P-E hysteresis loop but it only probes the domain switching at a single location under a sharp tip.18 _{Figure 2-11c illustrates the domain}

evolution under the biased tip and both nucleation (1 and 4) and growth (2 and 3) processes are involved. Obviously, the surface domain can be aligned by the biased tip. In this project, the local poling process is achieved by scanning a region with a relatively strong dc bias.

In this thesis, the topography, PFM image, SS-PFM and local poling processes were conducted was a commercial AFM instrument (Cypher, Asylum Research) with Olympus AC240TM _{(spring constant k ~ 2 N/m and resonance frequency f ~ 70 kHz) and Asylum01}

(k ~ 2 N/m and f ~ 70 kHz) probes. In order to avoid the impact of the surface topography, all the ceramic pellets were polished to the roughness ~ 10 nm. The high voltage cantilever holder (up to 100 V) was adopted for SS-PFM and local poling experiments.

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waveform and (b) experimental piezoresponse hysteresis loop. (c) The domain evolution process at the different point of PR hysteresis loop. (Reproduced from Jesse

et.al.19₎