Fractional Photo-Thermoelastic Semiconductor with Hall Current: A Boundary Value Analysis

Abstract

This study deals with a boundary value problem for a generalized fractional-order photo-thermoelastic semiconductor medium in the presence of Hall current and rotational effects. The formulation is developed within the framework of the Moore-Gibson-Thompson (MGT) heat conduction theory, extended to fractional-order derivatives in time in order to incorporate memory and nonlocal behavior in heat transfer processes. The model accounts for the coupled effects of thermal relaxation, thermal displacement, plasma generation, and electromagnetic interactions, including the Hall current and Lorentz force. The governing equations consist of the fractional-order heat conduction equation, equation of motion, constitutive relations, plasma diffusion equation, and generalized Ohm's law. These equations are formulated as a boundary value problem for a one-dimensional cylindrical semiconductor medium subjected to external laser pulse heating. Appropriate initial and boundary conditions are imposed to ensure the physical relevance of the model. The analytical solution of the problem is obtained using the Laplace transform technique, leading to closed-form expressions in the transform domain. The inversion of the Laplace transform is carried out numerically to obtain the physical distributions of temperature, displacement, carrier density, and stress. Numerical computations are performed for silicon material to examine the influence of key parameters such as fractional order, Hall parameter, rotation, and thermal relaxation time. The results indicate that the fractional-order parameter significantly affects thermal wave propagation and introduces memory-dependent behavior. Moreover, the Hall current and rotational effects are found to have a considerable impact on the thermo-mechanical and electromagnetic responses. The present boundary value formulation provides a comprehensive framework for analyzing coupled thermo-plasma-elastic phenomena in semiconductor materials, with potential applications in modern electronic and photothermal devices.