Fractional Order GN Model on Photo-Thermal Interaction in a Semiconductor Plane

Abstract

A mathematical model of Green–Naghdi photothermal theory based on fractional-order of heat transfer is given to study the wave propagation in a two-dimensional semiconductor material. Closed-form analytical solutions to obtain the physical quantities subjected to a heat flux with a pulse that decays exponentially in the surface of semiconductor half-space are presented. Through the use of Laplace and Fourier transforms with the methodology of eigenvalues techniques, the analytical solutions of all physical quantities are obtained. A semiconductor medium such as silicon is studied. The derived method is evaluated with numerical results which are applied to the semiconductor medium in simplified geometry. The significant influence of time-fractional derivative parameters are discussed for all physical quantities. Suitable discussions and conclusions are presented.