Limitations 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 (PCs), thus making use of its ultra-high vertical resolution (<0.1 pm/V). Christman et al. \cite{Chr98} first used PFM for this purpose. Their measurements, however, yielded only reasonable results of unsatisfactory accuracy, amongst others caused by an incorrect calibration of the setup. In this contribution a reliable calibration procedure is given followed by a careful analysis of the encounted difficulties determining PCs with PFM. We point out different approaches for their solution and expose why, without an extensive effort, those difficulties can not be circumvented.