MGT Photothermal Model Incorporating a Generalized Caputo Fractional Derivative with a Tempering Parameter: Application to an Unbounded Semiconductor Medium

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This work introduces a novel approach to modeling the photothermal behavior of semiconducting materials by developing a Moore-Gibson-Thompson (MGT) fractional photothermal model that incorporates a generalized Caputo fractional derivative with a tempering parameter. This advanced model is specifically designed to analyze elastic plasmonic wave systems in photothermal environments, offering deeper insights into the interactions between thermal, mechanical, and electromagnetic fields in semiconductors. By including the two-parameter tempered-Caputo fractional derivative, the model accounts for memory effects inherent in the thermal and mechanical behavior of materials exposed to high-energy processes. The model is applied to an infinite semiconducting medium with a drag-free spherical cavity subjected to a dynamically changing thermal field. This setup is highly relevant to semiconductor technology applications, where precise control over thermal and mechanical responses is crucial. The findings of this study could have significant implications for the design and analysis of semiconductor devices, particularly those operating under extreme thermal or electromagnetic conditions.