Nonlocal Bi-Fractional DPL Multi-Temperature Photo-Thermoelastic Waves in Semiconductors with Variable Thermal Conductivity under Ramp-Type Loading

This study presents a generalized theoretical framework for analyzing wave propagation in a semiconductor medium within the context of nonlocal photo-thermoelasticity. The model incorporates bi-fractional dual-phase-lag (DPL) heat conduction, a multi-temperature formulation distinguishing between thermodynamic and conductive temperatures, and temperature-dependent thermal conductivity under ramp-type thermal loading. Nonlocal elasticity is introduced to account for size-dependent mechanical behavior, which becomes significant in micro- and nanoscale semiconductor structures. The governing equations, describing the coupled interactions among displacement, temperature fields, and carrier concentration, are formulated in a two-dimensional setting and reduced using the normal mode method to obtain a characteristic equation governing wave propagation. The influence of the nonlocal parameter, fractional orders, and phase-lag times on the attenuation and dispersion characteristics of thermoelastic waves is examined. The results reveal that nonlocality significantly smooths stress distributions and reduces wave amplitudes, while the bi-fractional DPL model introduces pronounced memory effects that delay thermal responses and modify phase behavior. Furthermore, ramp-type thermal loading leads to more gradual stress development compared with instantaneous heating. The proposed model provides a comprehensive framework for understanding coupled wave phenomena in semiconductor media and offers new insights into the role of size effects and thermal memory in advanced solid-state systems.