The primary objective of this study is to investigate the stochastic plasma-mechanical-elastic wave propagation at the boundary of an elastic half-space in a semiconductor material using photo-thermoelasticity theory. The novelty of this work lies in the combination of stochastic simulation with temperature-dependent electrical conductivity and variable thermal conductivity, applied to a two-dimensional (2D) electromagnetic problem based on the electron-hole interaction model. Unlike previous studies, this work incorporates white noise as the randomness factor, providing a more realistic representation of random processes in semiconductor materials. The normal mode analysis technique is used to derive both deterministic and stochastic wave behaviors, focusing on short-time dynamics. The results, which are numerically analyzed and graphically represented, provide new insights into the differential behavior of stochastic versus deterministic distributions in magneto-photo-thermoelastic wave propagation, contributing to a more comprehensive understanding of semiconductor behavior under random influences.