Memory-driven heat and carrier transport in a damaged triple porous semiconductor media under extended Lord-Shulman model and KG nonlocal effect

Purpose The present study aims to develop a comprehensive multi-physics model to analyze heat transfer and coupled thermo–mechanical–carrier behavior in a mechanically damaged semiconductor medium with triple porosity, incorporating memory-dependent heat conduction and Klein–Gordon (KG)-type nonlocal effects. Design/methodology/approach A unified theoretical framework is formulated by integrating memory-dependent modified Lord–Shulman (MDMLS) heat conduction models with nonlocal elasticity and carrier transport in a triple-porous semiconductor medium. The governing coupled partial differential equations are reduced using normal-mode analysis, leading to a system of algebraic equations. The characteristic equation is solved analytically to obtain the displacement, temperature, carrier concentration, void volume fraction and stress fields. Numerical simulations based on silicon material parameters are performed to study the effects of memory, nonlocality and mechanical damage. Findings The results reveal that thermo-mechanical and transport responses are strongly localized within a near-surface interaction zone governed by decaying eigenmodes. Memory-dependent heat conduction significantly alters the amplitude and attenuation of field variables. Research limitations/implications The analysis is restricted to a linearized, two-dimensional half-space configuration and assumes idealized boundary conditions. Experimental validation and extension to nonlinear, transient or three-dimensional configurations are not considered and may be addressed in future work. Practical implications The proposed model provides insights into heat transfer and wave propagation in semiconductor materials with complex microstructures. The findings are relevant for the design of micro/nano-electronic devices, thermal management systems, porous coatings and semiconductor components subjected to coupled thermal and mechanical loading. Originality/value This work presents the first unified formulation combining triple porosity, mechanical damage, memory-dependent heat conduction and KG-type nonlocality in semiconductor media. The study offers new physical insights into boundary-dominated multiphysics interactions and provides a novel analytical–numerical framework for advanced heat transfer modeling in complex porous materials.