A coupled analysis of the piezoresponse force microscopy signals

We present a coupled theory on the piezoresponse force microscopy (PFM) responses by solving the electromechanical equations for transversally isotropic piezoelectric materials. The effective piezoelectric coefficients calculated from the coupled, the decoupled, and the indentation theories are then compared with the true piezoelectric coefficient d33. An approximately linear relationship between the effective piezoelectric coefficient from the coupled PFM analysis and d33 is obtained. Finally, the coupled analysis is extended to the piezoelectric film/substrate system. The obtained results are believed to be useful in quantitatively interpreting the PFM signals.