Quantum-Enhanced Photo-Thermoelastic Multi-Temperature Heat Transfer and Wave Propagation in Laser-Excited Semiconductors

This study develops a novel theoretical framework for analyzing wave propagation in semiconductor media based on a generalized multi-temperature quantum photo-thermoelastic model. The formulation extends classical photo-thermoelastic semiconductor theory by incorporating nonequilibrium heat transport through a multi-temperature approach, in which conductive and thermodynamic temperatures interact via coupling parameters. Quantum carrier transport is introduced using a density-gradient model, leading to a higher-order diffusion term that captures nonlocal effects at micro- and nano-scales. The resulting system describes the fully coupled interaction among elastic deformation, multi-temperature heat conduction, and photogenerated carrier dynamics under laser excitation. A normal-mode analysis is employed to derive the governing dispersion relations and obtain analytical expressions for the physical fields. Numerical simulations, performed for silicon as a representative semiconductor, are used to examine the influence of multi-temperature parameters on temperature distribution, displacement, carrier density, and stress components. The results demonstrate that the multi-temperature formulation significantly modifies thermal wave behavior, enhances energy redistribution, and reduces stress concentration compared with classical single-temperature models. Moreover, the interplay between quantum diffusion and multi-temperature effects leads to smoother field profiles and increased attenuation. The proposed model provides new insights for the design of advanced optoelectronic and nano-scale semiconductor devices operating under ultrafast thermal loading.