Fractional Order GN Model on Photo-Thermal Interaction in a Semiconductor Plane

Abstract

A mathematical model of Green–Naghdi photothermal theory based on fractional-order of heat transfer is given to study the wave propagation in a two-dimensional semiconductor material. Closed-form analytical solutions to obtain the physical quantities subjected to a heat flux with a pulse that decays exponentially in the surface of semiconductor half-space are presented. Through the use of Laplace and Fourier transforms with the methodology of eigenvalues techniques, the analytical solutions of all physical quantities are obtained. A semiconductor medium such as silicon is studied. The derived method is evaluated with numerical results which are applied to the semiconductor medium in simplified geometry. The significant influence of time-fractional derivative parameters are discussed for all physical quantities. Suitable discussions and conclusions are presented.

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Acknowledgments

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No (KEP-24-130-38). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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Correspondence to Aatef Hobiny.

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Hobiny, A., Abbas, I. Fractional Order GN Model on Photo-Thermal Interaction in a Semiconductor Plane. Silicon 12, 1957–1964 (2020). https://doi.org/10.1007/s12633-019-00292-5

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Keywords

  • Laplace-Fourier transforms
  • Fractional GN model
  • Photo-thermal waves
  • Eigenvalues approach