Contact-resonance scanning probe techniques are frequently used for characterizing the mechanical sample properties via atomic force acoustic/ultrasonic microscopy as well as for detecting sample displacement via piezoresponse force microscopy (PFM) and via electrochemical strain microscopy (ESM). For a better understanding of the measurement principle and for a quantification of the signals, a theoretical description of the cantilever motion is necessary. Here, we present a comprehensive model from which the cantilever motion can be calculated numerically. Compared to previous models, our model takes into account a sample tilt and a position-dependent electrostatic load acting on the cantilever. We demonstrate a phase calibration technique for PFM and ESM measurements, which allows us to determine the absolute excitation phase of the signal with an uncertainty of only 2° for an amplification factor of 100.

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