A hyperbolic two-temperature photo-thermal interactions in a semiconductor material
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ORIGINAL PAPER
A hyperbolic two-temperature photo-thermal interactions in a semiconductor material T Saeed1 and I Abbas1,2* 1
Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia 2
Department of Mathematics, Faculty of Science, Sohag University, Sohaˆg, Egypt Received: 11 January 2020 / Accepted: 10 April 2020
Abstract: This work is concerned with the study of the thermodynamic temperature, conductive temperature, the carrier density, displacement and stress in a semi-infinite semiconductor medium during the photo-thermal process. The medium is considered to be a semiconducting media with an isotropic and homogeneous. Also, the thermal and elastic properties have been considered without neglecting the coupling between the thermoelastic and the plasma waves. The techniques of Laplace transforms are used to get the analytical solutions of the problem in the transformed domain by the eigenvalues method and the inversions of Laplace transformations have been carried numerically. The results are graphically represented to show the effects of the two-temperature parameter. Keywords: Photo-thermal theory; Two-temperatures model; Eigenvalue approach; Laplace transforms
1. Introduction The thermoelasticity model with classical two-temperatures are presented by Gurtin and Williams [1], Chen et al. [2] and Chen and Gurtin [3], wherein by using another one depending on the classical two-temperature (thermodynamically temperature T and conductivity temperature / ), the classical Clausius–Duhem inequality has been substituted. The first is due to the thermal processes and the second is due to the inherent mechanical processes between the particles and the elastic material layers. Youssef and El-bary [4] have studied the generalized thermoelastic interactions under the hyperbolic two-temperature model. Only in the last decade was observed, developed in many works the theory of thermoelasticity under two temperatures, and found applications mainly in problems in which the discontinuities of restrictions have no physical interpretations. Ezzat and Youssef [5] have studied the twotemperatures model in three-dimensional problem for thermoelastic plane due to ramp type heating. Ezzat et al. [6] have investigated the effects of fractional order and
*Corresponding author, E-mail: [email protected]
two-temperatures theory in magneto-thermoelasticity under dual-phase-lag heat transfer. During the last 25 years, great efforts have been made to study the structures of semiconductors and microelectronics through photo-thermal (PT) and photoacoustic (PA) technology. Recently, [7, 8] are considered both the PT and PA technology as insignia modes that quite sensible to photoexcited carrier dynamics. The change in the propagation of thermal, elastic and plasma wave go back to the linear coupling through the heat and the mass transport (i.e., thermal-diffusive) have included. In the science of material, the variables heating conductivity that depen
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