Laser short-pulse impact on magneto-photo-thermo-diffusion waves in excited semiconductor medium with fractional heat equation

In this work, magneto-thermodiffusion waves in an excited semiconductor medium are investigated under the impact of laser short-pulse heating. The Caputo fractional derivative is applied on the main heat equation according to the photo-thermoelasticity theory. The governing equations describe the effect of holes and electrons interactions inside the medium under the influence of external magnetic field. The main equations are considered one-dimensional (1D) during an electronic deformation and a thermoelastic deformation. The Laplace transform with some initial conditions applied is used to obtain the analytical solutions of the main physical fields in dimensionless form. Some boundary conditions taken on the semiconductor surface are applied to determine the values of some undefined parameters. The complete numerical solutions are obtained according to the inversion method with Riemann-sum approximation of the Laplace transforms. The input physical parameters of silicon semiconductor material are used to make the simulations and comparisons. The numerical simulations are presented graphically and discussed according to the different values of time-fractional derivative, magnetic field, and thermal relaxation time.