Sample Geometry Effects on Electric-Field-Induced Displacements in Piezoelectric Thin Films Measured by Atomic Force Microscopy

Abstract

ABSTRACTElectric-field-induced displacements of PZT film capacitor Pt/PZT(5μm)/Pt/SiO2/Si(100) were calculated by finite element method with various parameters of sample geometry: the diameter of top electrode φ TE ranging from 0.2 μ m to 1000 μ m and whether PZT film was continuous or side-etched. If φ TE was larger than 40μ m, surface longitudinal displacement (corresponding to AFM-measured strain) was not equal to net longitudinal displacement of PZT film, including a contribution of the bending motion of substrate. In contrast, if φ TE was smaller than 4μ m and PZT film was continuous, effective d33 evaluated from net longitudinal displacement was smaller than intrinsic d33, because the side PZT film clamped the edge of the capacitor disk and prevented the whole disk from elongating longitudinally. It was also revealed that d33 value calculated from net longitudinal displacement of PZT film depended on the Poisson's ratio of PZT and was not equal to intrinsic d33, excluding the case that φ TE was smaller than 4μ m and PZT film was side-etched. In conclusion, it is suggested that smaller φ TE (< 4μ m, in our case) and side-etch treatment permit a precision measurement of d33; however this condition is difficult to be satisfied experimentally.