Exact solutions for plane stress problems of piezoelectric semiconductors: Tuning free-carrier motions by various mechanical loadings

Certain crystalline solids can be used for semiconducting devices, while mechanical forces have a great impact on their electrical behaviors. Especially, piezoelectric semiconductors (PSs) are one of the deformation-sensitive crystals. Mechanical forces can be utilized to tune the electronic transports in PSs. To illustrate these effects quantitatively, this paper provides exact solutions for free-carrier motions in different deformation modes of PSs. Two-dimensional (2D) governing equations for a rectangular domain are first presented based on the three-dimensional (3D) phenomenological theory. Then, exact solutions for plane stress problems with the c-axis along two perpendicular directions are formulated. By applying the analytical solutions, we study the distributions of free carriers when mechanical forces are applied. Four main deformation modes are investigated including extension, bending, thickness-shear, and thickness-stretch. Numerical results reveal that the poling direction of PSs can effectively change the coupling mechanism between the electric and mechanical fields. The electrons redistribute themselves to shield the piezoelectric polarization, resulting in a reduction of the electric potential. These findings shed light on the impact of mechanical loadings on charge redistribution and can serve as benchmarks for designing piezotronic devices.