Fractional photo-thermoelastic waves of hydrodynamic semiconductors with Hall currents and variable thermal conductivity

This study presents a novel investigation of fractional photo-thermoelastic wave propagation in hydrodynamic semiconductor media, incorporating the combined influences of Hall currents and spatially variable thermal conductivity under laser-pulsed excitation. The model builds upon the generalized photo-thermoelasticity framework, extending it with fractional-order heat conduction to account for memory effects and non-Fourier behavior at the nanoscale. By introducing a temperature-dependent thermal conductivity function, the heat transfer equation reflects realistic diffusion patterns found in poro-semiconductor materials under dynamic thermal loading. The Hall current effect introduces additional electromagnetic-mechanical coupling, modifying carrier transport and wave dynamics. A system of coupled field equations is formulated, incorporating fractional heat conduction, charge carrier motion, and excess pore pressure in a poro-hydrodynamic semiconductor environment. The normal mode analysis technique is employed to derive analytical expressions for the physical variables, and the influence of thermal conductivity variation is examined in detail. Results illustrate the significant impact of non-uniform thermal conduction and Hall currents on the physical fields. The findings contribute to the optimization of semiconductor device design, with implications for advanced photothermal technologies, optoelectronic systems, and energy harvesting applications.