Multi-temperature photoacoustic dynamics in a semiconductor medium with fractional order heat and variable thermal conductivity

Abstract

This paper presents a novel fractional-order photoacoustic model for semiconductor media subjected to laser excitation, formulated within the framework of multi-temperature thermoelasticity and variable thermal conductivity. The proposed model addresses key limitations of classical heat conduction theories by incorporating Caputo fractional time derivatives. Additionally, spatially variable thermal conductivity allows for modeling heterogeneous material properties and realistic thermal gradients. The governing equations couple thermoelastic displacement, thermodynamic and conductive temperature fields, and carrier concentration, capturing the dynamic interactions among thermal, mechanical, and electronic subsystems. Using the normal mode analysis technique allows for analytical and numerical exploration of wave propagation characteristics. Silicon is used as the reference medium in simulations, and results are presented for varying fractional orders and thermal conductivity profiles. The proposed formulation provides a more comprehensive description of memory-dependent thermal transport and coupled thermoelastic–carrier wave propagation in semiconductor materials, offering potential applications in optoelectronic devices, laser-based material diagnostics, and micro-scale thermal management technologies. These findings demonstrate the improved physical accuracy and predictive capabilities of the proposed model, making it highly applicable to modern semiconductor technologies.