This article introduces a new mathematical, theoretical physics model for discussing the interaction between the electrons and holes in the semiconductor medium. The model has been studied in the context of the generalized elasto-thermodiffusion (ETD) theory of the photothermal (PT) transport processes. The governing equations give a detailed account of a one-dimensional (1D) deformation. The wave distribution inside the medium propagates without dispersion or attenuation. The basic equations are obtained in a non-dimensionalized case. The hole charge carrier, displacement, thermal, and plasma waves are coupled due to thermal variations. The Laplace transform method has been applied to solve the coupled governing equations. Some boundary conditions are applied to the interface adjacent to the vacuum to obtain the main physical quantities analytically in the Laplace domain. The inversion of the Laplace transform is applied with a numerical method to obtain the complete solutions in the time domain for the basic physical fields in this phenomenon. The consequences of thermoelasticity, the phase lag (relaxation time) of the temperature gradient, and the phase lag of the heat flux are graphically derived and explained in comparison to silicon and germanium semiconductor materials.