Electrode size and boundary condition independent measurement of the effective piezoelectric coefficient of thin films

Abstract

The determination of the piezoelectric coefficient of thin films using interferometry is hindered by bending contributions. Using finite element analysis (FEA) simulations, we show that the Lefki and Dormans approximations using either single or double-beam measurements cannot be used with finite top electrode sizes. We introduce a novel method for characterising piezoelectric thin films which uses a differential measurement over the discontinuity at the electrode edge as an internal reference, thereby eliminating bending contributions. This step height is shown to be electrode size and boundary condition independent. An analytical expression is derived which gives good agreement with FEA predictions of the step height.