Study of the behavior of photothermal and mechanical stresses in semiconductor nanostructures using a photoelastic heat transfer model that incorporates non-singular fractional derivative operators

Abstract

This study presents a novel nonlocal mathematical model for thermo-photo-elasticity, addressing the limitations of classical theories in understanding the interactions between thermal, mechanical, and photoelastic deformations in semiconductors, such as silicon and germanium. The model incorporates nonlocal elasticity, modified heat conduction, and non-singular fractional derivatives, which capture memory effects and nonlocal thermal conduction, offering a more accurate representation of heat propagation. By extending classical elasticity to include long-range spatial and temporal interactions, the model is particularly suited for materials where microscale effects impact macroscopic mechanical behavior. Additionally, it introduces the modified Moore–Gibson–Thompson (MGT) heat conduction model, accounting for finite-speed heat propagation and time delays, thus replacing the classical Fourier approach with a more comprehensive framework that integrates plasma waves and thermomechanical effects.