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Response of excited microelongated non-local semiconductor layer thermomechanical waves to photothermal transport processes

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Abstract

The governing equations for microelongated semiconductors are presented in a novel mathematical–physical way. The model is examined in line with the photogenerated transport processes when the microelongated elastic non-local semiconductor medium is powered. The primary governing equations reveal the interplay between elastic, thermal, and plasma waves when microelongation is taken into account. In this regard, the generalized photothermoelasticity theory is taken into consideration. The dimensionless analytical formulations for temperature, carrier density, displacement, stresses, and microelongation distributions have been obtained using the harmonic wave technique. During the electronic and thermoelastic deformation processes in two dimensions, the general solutions of the principal distributions are determined (2D). To get the full answers, several criteria are taken into account at the non-local medium's free surface. The numerical results were obtained using computer programming. These data were represented graphically for the work of the simulation and comparison with the experimental results under the influence of some of the variables under study.

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Abbreviations

\(\lambda ,\,\,\mu\) :

Lame’s elastic semiconductor parameters

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

The deformation potential difference

\(T\) :

The thermodynamic (temperature) heat

\(T_{0} \;\) :

Reference temperature in its natural state

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

The volume thermal expansion

\(\sigma_{ij}\) :

The microelongational stress tensor

\(\rho \quad \quad\) :

The density of the non-local medium

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

Coefficients of linear thermal expansion

\(C_{{\text{E}}}\) :

Specific heat of the microelongated material at constant strain

\(k\) :

The thermal conductivity

\(D_{{\text{E}}}\) :

The carrier diffusion coefficient

\(\tau\) :

The carrier lifetime

\(E_{{\text{g}}}\) :

The energy gap

\(d_{n}\) :

The coefficients of electronic deformation

\(\Pi ,\Psi\) :

The scalar and vector functions, respectively

\(j_{0}\) :

The microinertia of microelement

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

Microelongational material parameters

\(\xi_{1}\) :

The non-local scale parameter

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

Thermal relaxation times

\(\varphi\) :

The scalar microelongational function

\(m_{k}\) :

Components of the microstretch vector

\(s = s_{kk}\) :

Stress tensor component

\(\delta_{ik}\) :

Kronecker delta

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Acknowledgements

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number RI-44-0334.

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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 & Weaam Alhejaili

  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

    Alaa A. El-Bary

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

    Alaa A. El-Bary

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

    Alaa A. El-Bary

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  1. Shreen El-Sapa
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El-Sapa, S., Alhejaili, W., Lotfy, K. et al. Response of excited microelongated non-local semiconductor layer thermomechanical waves to photothermal transport processes. Acta Mech 234, 2373–2388 (2023). https://doi.org/10.1007/s00707-023-03504-7

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