Theoretical Analysis of Piezoelectric Semiconductor Thick Plates with Periodic Boundary Conditions

Piezoelectric semiconductors, being materials with both piezoelectric and semiconducting properties, are of particular interest for use in multi-functional devices and naturally result in multi-physics analysis. This study provides analytical solutions for thick piezoelectric semiconductor plates with periodic boundary conditions and includes an investigation of electromechanical coupling effects. Using the linearization of the drift-diffusion equations for both electrons and holes for small carrier concentration perturbations, the governing equations are solved by the extended Stroh formalism, which is a method for solving the eigenvalues and eigenvectors of a problem. The solution, obtained in the form of a series expansion with an unknown coefficient, is solved by matching Fourier series expansions of the boundary conditions. The distributions of electromechanical fields and the concentrations of electrons and holes under four-point bending and three-point bending loads are calculated theoretically. The effects of changing the period length and steady-state carrier concentrations are covered in the discussion, which also reflects the extent of coupling in multi-physics interactions. The results provide a theoretical method for understanding and designing with piezoelectric semiconductor materials.