Challenges for the determination of piezoelectric constants with piezoresponse force microscopy

At first sight, piezoresponse force microscopy (PFM) seems an ideal technique for the determination of piezoelectric coefficients, thus making use of its ultrahigh vertical resolution (<0.1pm∕V). In general, however, only qualitative PFM imaging is performed and in the few publications containing quantitative data, the obtained values vary considerably with respect to macroscopic measurements. In this contribution, we present a reliable calibration procedure for PFM followed by a careful analysis of the encounted difficulties using PFM for determining piezoelectric coefficients. We point out different approaches for their solution and expose why those difficulties cannot be circumvented without an extensive effort.