\In this work, the effect of hydrostatic initial stress is studied with the exited semiconductor material. Electrons are exited at the free surface of the elastic semiconductor medium using the photo-thermal-elastic theory during the transport (diffusion) process. The thermal memories are due to the dual-phase-lag (DPL) relaxation times of the heat conduction equation with a novel model. In this model, the thermal conductivity is chosen as a linear dependent function of the thermal temperature impact which is variable. The effect of gravitational field is taken into account during the two-dimensional (2D) elastic deformation under the impact of an internal heat source. The Kirchhoff transformation mapping is used. The harmonic wave (normal mode) method is applied for the 2D governing equations to obtain the main physical fields analytically. Some thermal and mechanical forces are applied with other elastic-plasma conditions at the free surface of the semiconductor material to get the complete solutions. Some comparisons used a novel parameters which depend on the DPL model and the differences in the thermal conductivity parameters and they are illustrated graphically and discussed.