Fractional-order modeling of photo-thermoelastic waves in double-porosity semiconductor structures with decaying heat flux

This work develops a theoretical model for photo-thermoelastic wave propagation in a two-dimensional double-porosity semiconductor medium, incorporating fractional-order heat conduction and a spatially decaying heat source. The classical Lord–Shulman generalized thermoelasticity model is extended by employing a Caputo-type fractional time derivative to better capture memory-dependent and nonlocal heat transport phenomena commonly observed in micro- and nano-structured materials. The coupled system considers mechanical deformation, heat conduction, and diffusion of photogenerated carriers. Using the normal mode method, analytical solutions are derived, and numerical results for silicon are presented. The analysis is conducted in a 2D elastic half-space, with spatial and temporal field variables governed by harmonic wave assumptions. The findings indicate that increasing the fractional order enhances thermal memory, resulting in delayed diffusion and stronger stress responses, whereas higher decay parameters intensify thermal gradients and localize wave effects. These findings demonstrate the critical role of memory-dependent heat conduction and porosity architecture in controlling wave propagation characteristics, with potential applications in the design and optimization of semiconductor-based optoelectronic devices, thermal sensors, and energy harvesters.