The effect of the surface recombination velocity on 2D thermoelastic semiconductor solid sphere problem

Abstract

This work presents a general mathematical model for thermo-electro-mechanical wave propagation in a two-dimensional spherical semiconductor medium subjected to an axisymmetric thermal shock and attraction-free surface. Two distinct boundary conditions governing carrier diffusion are considered to evaluate their influence on the system's physical response. In the first application, a Dirichlet boundary condition is imposed on the current carrier, prescribing a given carrier concentration at the surface. In the second, a Robin-type boundary condition is applied, allowing the incorporation of surface recombination velocity to capture the dynamic interaction between the surface and the carrier diffusion process. The generalized mathematical model encompasses several previously established formulations as special cases, enabling a unified theoretical framework and direct comparison with earlier results. The governing equations are solved analytically in the Laplace domain, and the numerical inversion is performed using a Fourier series-based approach to retrieve the solutions in the physical domain. A comprehensive set of physical fields—including temperature, stress components, displacement, and carrier density—is evaluated for the proposed boundary conditions. The numerical results are illustrated graphically, and discussed through 2D plots, meridional contours, and 3D animations generated by MATLAB.