Finite element formulation for piezoelectric semiconductor plates

Abstract

Piezoelectric semiconductor plates with both semiconducting and piezoelectric properties are widely used in micro-electromechanical systems. However, it is difficult to obtain theoretical solutions due to the complexity of the mathematics required to describe these systems. In this paper, finite element formulation is present for numerical analysis of piezoelectric semiconductor plate. A plate model using a first-order Mindlin series expansion was employed. Standard Galerkin weak form was derived and discretization equations were obtained. The proposed method was verified by a custom partial-differential-equation module of COMSOL Multiphysics. Numerical analysis revealed that the deflection, electric potential, and current density of the piezoelectric semiconductor were sensitive to the initial carrier concentration within a certain range, and that the initial carrier concentration influenced the dimensionless electric displacement intensity factor of the crack tip. By allowing bending analysis of piezoelectric semiconductor plates, our numerical approach will be valuable for guiding the design of piezoelectric semiconductor structures.