Thermal-Diffusive Processes of an Electron-Hole Non-Local Semiconductor Model with Variable Thermal Conductivity and Hall Current Effect

Abstract

In this work, a novel model is presented that describes thermal diffusion processes through non-local semiconductor materials. The material under study is subjected to the influence of a strong magnetic field, which creates a Hall current. Interference between the excited electrons and the excited holes of a non-local semiconductor that had been exposed to temperature was present, and thermal conductivity depending on changes in graduated temperature were accounted for. The governing equations are written in a dimensionless form in one dimension (1D) where the thermal conductivity is taken as a function of temperature through electronic and elastic deformation (ED and ED) processes. Laplace transforms in one dimension with initial conditions were used to convert partial differential equations to arrive at exact formulas of solutions. To obtain the exact linear solutions, some boundary conditions taken on the free surface of the non-local semiconductor were used. Using numerical methods of inverse Laplace transforms, the complete solutions of the physical quantities under study were obtained. To further understand how various variables (thermal memory, variable thermal conductivity, and Hall current) affect the non-local semiconductor, numerical physical fields were simulated, and are graphically depicted, and discussed herein.