Atangana-Baleanu Fractional Approach to Photothermal Wave Propagation in Semiconductor Materials under the Influence of a Moving Heat Source

The present article indicates a pioneering investigation into the photo-thermal transport processes within semiconductor materials influenced by a mobile heat source. This study addresses critical research gaps by employing an advanced heat transfer theory grounded in fractional derivatives, as formulated by Atangana-Baleanu. This innovative approach incorporates non-singular kernel functions, enabling the derivation of accurate solutions for complex thermal mechanisms. The research makes a significant contribution to the field by providing analytical solutions in the frequency domain through the application of the Laplace transform algorithm and the eigenvalue methodology. Key findings reveal intricate relationships between various field quantities, including temperature, displacement, carrier density, and thermal stress, which are illustrated through the graphical results. These results are analyzed across diverse parameters such as material depth, fractional parameters, the lifetime of photo-generated carriers, as well as the velocity and intensity of the moving heat source. Notably, the inclusion of fractional quantities elucidates the precise and finite nature of photo-thermal waves, distinguishing this work from traditional hyperbolic thermoelasticity theories. The implications of these findings extend to a deeper understanding and optimization of semiconductor materials in practical applications, while also suggesting new avenues for future research in the field of thermal transport.