A spectral stochastic framework for hygro-photo-thermoacoustic-elastic semiconductors under coloured boundary excitation

This work presents a stochastic analysis of a coupled hygro-photo-thermoelastic semiconductor within the framework of classical thermoelasticity (CTE), including acoustic and moisture effects. The boundary excitation is modeled using spectrally constructed colored noise to represent realistic fluctuations in laser intensity and environmental conditions. The stochastic disturbance is characterized by a power-law spectral density S(Ω)∝1/Ωβ, enabling the study of different regimes such as white (β=0), pink (β=1), and Brownian noise (β=2). The model describes the coupled behavior of temperature, carrier density, displacement, stress, acoustic pressure, and moisture concentration in a semiconductor half-space under harmonic optical excitation. The stochastic response is obtained via convolution with the deterministic Green’s function, allowing evaluation of mean and variance. While the mean response remains unchanged due to the zero-mean excitation, the variance is strongly influenced by β. Numerical results (for silicon) show that increasing β enlarges the probabilistic response envelope, with Brownian noise leading to significant variance amplification, especially in stress and moisture fields. These results highlight the important role of temporally correlated noise in affecting thermoelastic waves, carrier dynamics, acoustic response, and moisture transport, and provide a unified framework for analyzing such systems under realistic stochastic boundary conditions.