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 twotemperature 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.