Substrate effects on piezoresponse force microscopy electromechanical responses of piezoelectric thin films

To explore substrate influences on piezoresponse force microscopy (PFM) responses, the coupled theory is extended to investigate the electromechanical responses of PFM on piezoelectric films bonded to rigid and dielectric, rigid and insulating, elastic and conducting and elastic and dielectric substrates. It is found that all responses transit to the half space results when the normalized thickness (film thickness to tip curvature radius t/R0) is larger than about 0.08 for PZT4, and degenerate to the dielectric half space solutions as expected for rigid and dielectric substrate case, when the normalized thickness approaches zero verifying the calculations. PFM responses are greatly reduced by substrate dielectric permittivity thus a conducting substrate is recommended to eliminate the dielectric constant influences and the dielectric “dead layer” should be avoided or carefully dealt with. For elastic substrates, the tip induced surface displacement for a relatively thick film, image charge and image charge distance are slightly affected by the change of the substrate Young's modulus and Poisson's ratio. And the effective piezoelectric coefficient is remarkably decreased when t/R0 < 0.001. However as t/R0 > 0.001 in which region a practical PFM experiment would fall, so long as the substrate is matched or harder, the substrate could be deemed as a rigid one and the investigation of PFM responses would be greatly facilitated. Then effective piezoelectric coefficients from the decoupled and coupled theories of films on elastically matched, conducting or dielectric substrates are compared indicating that the decoupled theory tends to overestimate effective piezoelectric coefficient for thin films, the same as that for half space case. The obtained influences of substrate properties may serve as a primary experimental guidance for the choosing a proper substrate and supply useful information for the quantitative interpretation of the PFM signals.