Transient analysis on surface heated piezoelectric semiconductor plate lying on rigid substrate

Based on the thermo-electro-elastic coupling theory, the mathematical model for a surface heated piezoelectric semiconductor (PS) plate is developed in the time domain. Applying the direct and inverse Laplace transformations to the established model, the mechanical and electrical responses are investigated. The comparison between the analytical solution and the finite element method (FEM) is conducted, which illustrates the validity of the derivation. The calculated results show that the maximum values of the mechanical and electrical fields appear at the heating surface. Importantly, the perturbation carriers tend to concentrate in the zone near the heating surface under the given boundary conditions. It can also be observed that the heating induced elastic wave leads to jumps for the electric potential and perturbation carrier density at the wavefront. When the thermal relaxation time is introduced, all the field quantities become smaller because of the thermal lagging effect. Meanwhile, it can be found that the thermal relaxation time can describe the smooth variation at the jump position. Besides, for a plate with P-N junction, the effect of the interface position on the electrical response is studied. The effects of the initial carrier density on the electrical properties are discussed in detail. The conclusions in this article can be the guidance for the design of PS devices serving in thermal environment.