Characterization of the Photothermal Interaction of a Semiconducting Solid Sphere Due to the Fractional Deformation, Relaxation Time, and Various Reference Temperature under L-S Theory

Abstract

In the present paper, we constructed a new mathematical model of a thermoelastic semiconducting solid sphere based on the L-S model to study the photothermal interaction. Among this work, we considered the fractional-order strain, which has been introduced by Youssef. The bounding surface of the sphere has been thermally loaded by a thermal shock. Laplace transform has been applied, and its inversions have been obtained numerically. For silicon (Si) material, the numerical results of the temperature increment, carrier density increment, strain, displacement, stress, and stress-strain energy have been represented in figures with various values of the fractional-order parameter, relaxation time parameter, and reference temperature. The relaxation time parameter and reference temperature have significant effects on all the studied functions. The fractional-order parameter has limited effects on the temperature increment and carrier density increment, while it has significant effects on the strain, displacement, stress, and stress-strain energy.