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Laser short-pulse effect on magneto-photo-elasto-thermodiffusion waves of fractional heat equation for non-local excited semiconductor

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Abstract

The impact of the laser pulse is used to investigate the magneto-thermodiffusion waves in the context of photo-thermoelasticity theory. The governing mathematical equations of the non-local excited semiconductor material are used according to the Caputo fractional derivative of the heat equation. The main equations are studied under the influence of slowly magnetic field when the interactions between holes and electrons have occurred. According to the electronic and thermoelastic deformations, the one-dimensional (1D), dimensionless main equations are used to describe the non-local case. In the closed form, the Laplace transform is used with initial conditions to formulate the main ordinary differential equations. The analytical solutions are obtained when some surface non-local semiconductor conditions are applied at the boundary to observe the physical fields. The inverse of the Laplace transform with Riemann-sum approximation is applied numerically to obtain the complete solutions. The simulation of wave propagation of the main fields with some comparisons is obtained graphically and discussed when the physical constants of semiconductor silicon (Si) material are used.

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Data Availability

The authors are willing to provide the data used in this study upon request.

Abbreviations

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

Lame’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

\({\uprho }\) :

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

\(K\) :

The thermal conductivity

\(\tau^{*}\) :

The lifetime

\(E_{g}\) :

The energy gap

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

The parameter of electrons elastodiffusive

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

The parameter of holes elastodiffusive

\(d_{n}\) :

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 fund this research under Researchers Supporting Project number (PNURSP2022R229) 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

    Weaam Alhejaili

  2. School of Engineering, College of Engineering and Physical Science, University of Guelph, Guelph, ON, Canada

    Mohamad Abou El Nasr

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

    Kh. Lotfy

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

    Kh. Lotfy

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

    A. El-Bary

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

    A. El-Bary

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  1. Weaam Alhejaili
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  2. Mohamad Abou El Nasr
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  3. Kh. Lotfy
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  4. A. El-Bary
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Contributions

Kh.L: Conceptualization, Methodology, Software, Data curation, WA: Writing—Original draft preparation. AE-B and MAEN: Supervision, Visualization, Investigation, Software, Validation. All authors: Writing- Reviewing and Editing.

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Correspondence to Kh. Lotfy.

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Alhejaili, W., Nasr, M.A.E., Lotfy, K. et al. Laser short-pulse effect on magneto-photo-elasto-thermodiffusion waves of fractional heat equation for non-local excited semiconductor. Opt Quant Electron 54, 833 (2022). https://doi.org/10.1007/s11082-022-04247-w

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