Nonlinear Electric Field Dependence of the Transverse Piezoelectric Response in a Ferroelectric Film

A non-linearly decreasing piezoelectric coefficient with an external electric field is an intrinsic property of a fully poled ferroelectric film, which has been observed in the measured longitudinal piezoelectric responses. However, for transverse piezoelectric responses, the observed converse piezoelectric coefficients (e31,f) have displayed a different trend. Here we show that this disagreement can be rationally resolved by utilizing a small field e31,f test under a sweeping direct current bias voltage, in which the field-dependent transverse piezoelectric response is analyzed in a stepwise manner. Understanding of this nonlinear field-dependence will help improve the design of transverse piezoelectric devices.