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Photo-Elasto-Thermodiffusion Waves of Fractional Heat Order Excited with Laser Short-Pulse Impact for Semiconductor Medium

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Abstract

In this investigation, laser short-pulse heating is studied in an elastic-thermodiffusion (ETD) model. A fractional-order of the heat equation for strain photo-thermoelasticity theory is considered when the interactions inside the semiconductor elastic medium between the holes and electrons occur. The decaying period for the photo-generated processes is obtained via the generalized thermoelasticity theory. The solutions of the governing equations are obtained during thermoelastic (TD) and electronic (ED) deformation in one-dimensional (1D) space and under the Laplace domains. Afterward, the complete dimensionless quantities of physical fields with a complex inversion formula of the Laplace transform are obtained numerically according to the Fourier expansion under initial and boundary conditions. Comparisons are presented according to different parameters; time-fractional order, thermal memories, and the pulse intensity. Such parameters are illustrated for the main physical fields. Finally, silicon material is used to describe the wave propagations simulation inside the medium and is discussed in detail.

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Data Availability

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

Abbreviations

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

Counterparts of Lame’s parameters,

\(n_{0}\) :

Equilibrium carrier concentration (electrons concentration)

\(h_{0}\) :

Equilibrium holes concentration

\(T_{0} \;\) :

Absolute temperature,

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

The volume coefficient of thermal expansion,

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

Components of the stress tensor,

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

Density of the medium,

\(\alpha_{t}\) :

The coefficient of linear thermal expansion

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

Cubical dilatation,

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

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,

\(\Omega\) :

Pulse parameter

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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 (PNURSP2022R154 ) Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors are thankful to Taif University and Taif University researchers supporting project number (TURSP-2020/160), Taif University, Taif, 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, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia

    Mohamed S. Mohamed & A. M. S. Mahdy

  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

Authors
  1. Shreen El-Sapa
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  2. Mohamed S. Mohamed
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  3. Kh. Lotfy
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  4. A. M. S. Mahdy
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  5. A. El-Bary
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Contributions

KL: Conceptualization, Methodology, AE: Software, Data curation, MM: Writing- Original draft preparation. SE: Supervision, Visualization, Investigation, Software, Validation. AM: Writing- Reviewing and Editing.

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Correspondence to Kh. Lotfy.

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El-Sapa, S., Mohamed, M.S., Lotfy, K. et al. Photo-Elasto-Thermodiffusion Waves of Fractional Heat Order Excited with Laser Short-Pulse Impact for Semiconductor Medium. J Low Temp Phys 209, 124–143 (2022). https://doi.org/10.1007/s10909-022-02781-1

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