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Laser short-pulse impact on magneto-photo-thermo-diffusion waves in excited semiconductor medium with fractional heat equation

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Abstract

In this work, magneto-thermodiffusion waves in an excited semiconductor medium are investigated under the impact of laser short-pulse heating. The Caputo fractional derivative is applied on the main heat equation according to the photo-thermoelasticity theory. The governing equations describe the effect of holes and electrons interactions inside the medium under the influence of external magnetic field. The main equations are considered one-dimensional (1D) during an electronic deformation and a thermoelastic deformation. The Laplace transform with some initial conditions applied is used to obtain the analytical solutions of the main physical fields in dimensionless form. Some boundary conditions taken on the semiconductor surface are applied to determine the values of some undefined parameters. The complete numerical solutions are obtained according to the inversion method with Riemann-sum approximation of the Laplace transforms. The input physical parameters of silicon semiconductor material are used to make the simulations and comparisons. The numerical simulations are presented graphically and discussed according to the different values of time-fractional derivative, magnetic field, and thermal relaxation time.

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The information applied in this research is ready from the authors at request.

Abbreviations

\(\lambda ,\,\,\mu \quad \quad \;\) :

Lamé’s parameters

\(n_{0}\) :

Electrons concentration at equilibrium

\(h_{0}\) :

Holes concentration at equilibrium

\(T_{0} \;\) :

Absolute temperature

\(\gamma = (3\lambda + 2\mu )\alpha_{t}\) :

The volume coefficient of thermal expansion

\(\sigma_{{{\text{ij}}}}\) :

Stress tensor

\({\uprho }\quad \quad\) :

Medium density

\(\alpha_{t}\) :

The coefficient of linear thermal expansion

\(e = \frac{\partial u}{{\partial x}}\) :

Cubical dilatation

\(\tau_{q}\) and \(\tau_{\theta }\) :

The thermal relaxation times (phase lag)

\(C_{e}\) :

Specific heat at constant strain of the medium

\(K\) :

The thermal conductivity of the medium

\(\tau^{*}\) :

The photogenerated carrier lifetime

\(E_{g}\) :

The energy gap of the medium of semiconductor

\(\delta_{n} = (2\mu + 3\lambda )d_{n}\) :

The electrons elastodiffusive parameter

\(\delta_{h} = (2\mu + 3\lambda )d_{h}\) :

The holes elastodiffusive parameter

\(d_{n}\) :

The coefficients of electronic deformation

\(d_{h}\) :

The coefficients of hole deformation

\(p\) :

The power intensity

\(\delta\) :

The absorption coefficient

\(\Omega\) :

The pulse parameter

\(\mu_{0}\) :

The magnetic permeability

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Acknowledgements

The authors extend their appreciation to Princess Nourah bint Abdulrahman University for funding this research under Researchers Supporting Project number (PNURSP2022R154) Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia

    Shreen El-Sapa

  2. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    Kh. Lotfy

  3. Department of Mathematics, Faculty of Science, Taibah University, Madinah, Saudi Arabia

    Kh. Lotfy

  4. Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt

    A. El-Bary

  5. Council of Futuristic Studies and Risk Management, Academy of Scientific Research and Technology, Cairo, Egypt

    A. El-Bary

  6. National Committee for Mathematics, Academy of Scientific Research and Technology, Cairo, Egypt

    A. El-Bary

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  1. Shreen El-Sapa
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Contributions

K. L Conceptualization, Methodology, Software, Data curation, E-S Writing- Original draft preparation. A. E-B Supervision, Visualization, Investigation, Software, Validation. All authors: Writing- Reviewing and Editing.

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Correspondence to Kh. Lotfy.

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El-Sapa, S., Lotfy, K. & El-Bary, A. Laser short-pulse impact on magneto-photo-thermo-diffusion waves in excited semiconductor medium with fractional heat equation. Acta Mech 233, 3893–3907 (2022). https://doi.org/10.1007/s00707-022-03291-7

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