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Effect of an excited non-local microelongated semiconductor with variable thermal conductivity on the propagation of photo-thermoelastic waves

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Abstract

An innovative concept of a microelongated non-local semiconductor material is developed. According to photothermal transport processes, the material is stimulated. When the thermal conductivity of the non-local medium is changed, the photo-thermoelasticity theories are used. The microelongation instance and the interference between the photothermoelastic propagation waves in the non-local medium are both described by the effective framework. When electronic and thermoelastic deformation processes are taking place, thermal conductivity may be thought of as a linear function of temperature. The dimensionless main fields are extracted using a maps converter in two dimensions (2D). The fundamental equations have been transformed into higher-order ordinary differential equations using the harmonic wave approach in accordance with the normal mode analysis. Applying a few conditions chosen from the non-local semiconductor surface yields complete solutions. With graphics, the numerical simulation results for silicon (Si) are shown. For the considered physical variables during the changing thermal conductivity and microelongation, comparisons are performed and explained.

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

Abbreviations

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

Lame’s elastic parameters

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

Deformation potential difference

\(T_{0} \;\) :

Reference temperature

\(\hat{\gamma } = (3\lambda + 2\mu )\alpha_{{t_{1} }}\) :

Volume thermal expansion

\(\sigma_{ij}\) :

Microelongational stress tensor

\(\rho \quad \quad\) :

The density

\(\alpha_{{t_{1} }}\) :

Coefficients of linear thermal expansion

\(e\) :

Strain

\(C_{e}\) :

Specific heat

\(K\) :

The thermal conductivity

\(D_{E}\) :

The carrier diffusion coefficient

\(\tau\) :

The photogenerated carrier lifetime

\(E_{g}\) :

The energy gap

\(e_{ij}\) :

Components of strain tensor

\(\Pi ,\Psi\) :

Two scalar functions

\(j_{0}\) :

The microinertia of microelement

\(a_{0} ,\,\alpha_{0} ,\lambda_{0} ,\lambda_{1}\) :

Microelongational material parameters

\(\tau_{0} ,\nu_{0}\) :

Relaxation times

\(\varphi\) :

The scalar microelongational function.

\(m_{k}\) :

Components of the microstretch vector

\(s = s_{kk}\) :

Stress tensor component

\(\delta_{ik}\) :

Kronecker delta

\(d_{n}\) :

The electronic deformation coefficient

\(\xi\) :

The length-related elastic nonlocal parameter

\(l\) :

The external characteristic length scale

\(a\) :

The internal characteristic length

\(e_{0}\) :

Non-dimensional material property

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Funding

The authors extend their appreciation to Princess Nourah bint Abdulrahman University for fund this research under Researchers Supporting Project number (PNURSP2023R154) 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. Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt

    Alaa A. El-Bary

  3. Council of Future Studies and Risk Management, Academy of Scientific Research and Technology, Cairo, Egypt

    Alaa A. El-Bary

  4. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box44519, Zagazig, Egypt

    Khaled Lotfy

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

    Khaled Lotfy

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  1. Shreen El-Sapa
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Contributions

KL: Conceptualization, Methodology, Software, Writing- Original draft preparation. SES: Supervision, Visualization, Investigation, Software, Validation. AEB: Writing- Reviewing and Editing, Data curation.

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Correspondence to Khaled Lotfy.

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El-Sapa, S., El-Bary, A.A. & Lotfy, K. Effect of an excited non-local microelongated semiconductor with variable thermal conductivity on the propagation of photo-thermoelastic waves. Opt Quant Electron 55, 569 (2023). https://doi.org/10.1007/s11082-023-04836-3

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