A memory-dependent stochastic framework for photoacoustic interactions in poro-semiconductor media under extended Green–Naghdi and spatiotemporal nonlocal effects

Abstract

This study presents a stochastic framework for analyzing coupled photoacoustic thermo-hydro-mechanical interactions in a porous semiconductor medium, extending beyond conventional deterministic models by explicitly incorporating randomness, memory effects, and spatiotemporal nonlocality. Unlike classical approaches that assume idealized and noise-free conditions, the proposed formulation integrates stochastic boundary excitation through a Wiener process, enabling a more realistic representation of laser-induced thermal fluctuations. The constitutive relations are modeled using a Klein–Gordon-type nonlocal operator, incorporating intrinsic length- and time-scale parameters, while heat conduction is described within an extended Modified Green–Naghdi (MGN) framework that accounts for finite-speed propagation. Closed-form analytical solutions are obtained using normal-mode analysis, and numerical simulations are performed for poro-silicon to evaluate the impact of stochasticity on thermophysical fields. The results reveal that stochastic effects significantly amplify the near-surface thermal response, where the variance of temperature, Vθ(x,z,t), is observed to be approximately 70%–100% higher than the corresponding deterministic solution, indicating that stochasticity can nearly double the effective thermal fluctuations at the boundary. This discrepancy gradually diminishes with increasing depth, leading to convergence between stochastic and deterministic profiles. Additionally, acoustic pressure exhibits pronounced boundary-layer fluctuations before stabilizing within the medium. These findings demonstrate that incorporating stochastic effects is essential for accurately capturing boundary-dominated photoacoustic phenomena in semiconductor materials. The proposed model provides a unified and physically consistent framework that enhances predictive capability and is applicable to advanced technologies such as MEMS devices, photothermal imaging, laser-based material processing, and nanoscale semiconductor systems.