Piezoelectric semiconductor materials have attracted great attention due to their both piezoelectric and semiconducting properties and application prospect in multi-functional devices. In this study, analytical solutions for thick piezoelectric semiconductor plates with periodic boundary conditions are obtained and electromechanical coupling effects are investigated. After the drift-diffusion equations for both electrons and holes are linearized for small carrier concentration perturbations, the governing equations are solved by the extended Stroh formalism whose purposes are solving eigenvalues and eigenvectors. The analytical solution in the form of series is acquired, and its coefficients are determined by the boundary conditions that also are expanded to Fourier series, whatever they are generalized displacement, generalized stress or mixed. The distributions of electromechanical fields and concentrations of electrons and holes are calculated under three different boundary conditions. In the first example, a uniformly distributed load model is established to verify the correctness of the analytical solution. In the second example, the boundary periods at different scales are considered, which affect the attenuation of physical fields from the boundary to the center. In the last example, the physical field distributions in the plate in the bending state is discussed. The results provide theoretical methods for piezoelectric semiconductor materials research, are instructive to piezoelectric semiconductor devices design.

Theoretical analysis of thick piezoelectric semiconductor plates with periodic boundary conditions

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