Eur. Phys. J. Plus (2022) 137: 105
https://doi.org/10.1140/epjp/s13360-021-02298-8

Regular Article

Thermo-optical-mechanical excited waves of functionally graded semiconductor material with hyperbolic two-temperature

¹ Department of Mathematics, College of Science, Taif University, P. O. Box 11099, 21944, Taif, Saudi Arabia
² Mathematics Department, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt
³ Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt
⁴ Department of Mathematics, Faculty of Science, Taibah University, Madinah, Saudi Arabia
⁵ National Mathematics Committee, Academy of Scientific Research and Technology, P.O. Box 11516, Cairo, Egypt
⁶ Council of Futuristic Studies and Risk Management, Academy of Scientific Research and Technology, P.O. Box 11516, Cairo, Egypt

^b khlotfy_1@yahoo.com

Received: 20 September 2021
Accepted: 17 December 2021
Published online: 11 January 2022

Abstract

A novel theoretical model during a photo-thermoelasticity theory is used to investigate a one-dimensional (1D) problem for the non-homogenous (Functionally Graded (FG)) semiconductor material. This phenomenon is studied in the context of hyperbolic two-temperature theory with a new parameter. The coupled between the thermal-plasma-elastic distributions is investigated theoretically. The basic thermal-elastic and optical physical constants are considered as a function of the horizontal distance during the photothermal transport processes under the impact of both some thermal–mechanical-plasma forces. The Laplace transformation method is applied for the main equations to obtain the analytical solutions of some physical field as well as the thermal, carrier density, temperature, displacement and mechanical distributions during the semiconductor medium. To get the basic variables in Laplace domain analytically, some thermal, mechanical loads and plasma conditions can be applied at the surface of the medium. The inverse of the Laplace transformation is used with numerical technique to obtain the complete solutions of the main physical quantities in space–time domain. The main physical field is displayed graphically and discussed theoretically under the influences of some parameters.