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Pulsed excitation heating of semiconductor material and its thermomagnetic response on the basis of fourth-order MGT photothermal model

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Abstract

When designing mechanical equipment, it’s important to consider the photothermal impacts in addition to mechanical ones. This is because photothermal effects can have a significant influence on equipment performance. In this paper, a new theory of thermo-photoelasticity is presented that explains the processes of photoelectron carriers and heat transport in homogeneous and isotropic viscoelastic semiconductor materials. The proposed model combines fourth-order Moore–Gibson–Thompson (MGT) thermoelasticity with the coupled plasma equation. We also include the viscoelastic linear Kelvin–Voigt model, which represents the viscous nature of matter, as part of the model derivation process. We study the problem of a thermoelastic semiconductor medium with stable elastic properties and its traction-free surface exposed to heat flux in the form of laser pulses. To provide analytical solutions for all the variables studied, we use the normal mode approach as the methodology. Furthermore, we estimate the effects of laser pulse rise time, viscosity, and thermal parameters on all fields studied with the help of some comparisons displayed in different illustrations.

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Abbreviations

\(\lambda_{{\text{e}}} ,{ }\mu_{{\text{e}}}\) :

Elastic constants

\(\alpha_{{\text{t}}}\) :

Coefficient of thermal expansion

\(\alpha_{1} ,{ }\alpha_{2}\) :

Viscoelastic relaxation times

\({\upgamma } = \left( {3\lambda + 2\mu } \right)\alpha_{{\text{t}}}\) :

Thermal coupling coefficient

\(T_{0}\) :

Initial temperature

\(\theta = T - T_{0}\) :

Temperature increment

\(T\) :

Absolute temperature

\(C_{e}\) :

Specific heat

\(e = {\text{div}}\;{\mathbf{u}}\) :

Cubical dilatation

\(\sigma_{ij}\) :

Stress tensor

\(e_{ij}\) :

Strain tensor

\(N\) :

Carrier density

\(\overrightarrow {H}\) :

Heat flow vector

\({\varvec{u}}\) :

Displacement vector

\(\overrightarrow {X}\) :

Position vector

\(\overrightarrow {F}\) :

External force vector

\(\mu_{0}\) :

Magnetic permeability

\(K\) :

Thermal conductivity

\(\rho\) :

Material density

\(Q\) :

Heat source

\(K^{*}\) :

Ate of thermal conductivity

\(\delta_{ij}\) :

Kronecker′s delta function

\(\nabla^{2}\) :

Laplacian operator

\(\tau_{q}\) :

Phase lag of heat flow

\(\tau_{\theta }\) :

Phase lag of temperature gradient

\(d_{n}\) :

Electronic deformation coefficient

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

Semiconductor gap energy

\(\kappa\) :

Thermal activation coupling parameter

\(\gamma_{n} = \left( {3\lambda + 2\mu } \right)d_{n}\,\tau_{B}\) :

Bulk-free carrier lifetime

\(\vartheta ,\left( {\dot{\vartheta } = \theta } \right)\) :

Thermal displacement

\(D_{E}\) :

Ambipolar diffusion parameter

\(\overrightarrow {J}\) :

Current density

\(\varepsilon_{0}\) :

Electric permeability

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Acknowledgements

H.M. Sedighi is grateful to the Research Council of Shahid Chamran University of Ahvaz for its financial support (Grant no. SCU.EM1401.98). The first three authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education, Saudi Arabia, for funding this research work through the project number (IFKSURG-1232).

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Authors and Affiliations

  1. Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    S. S. Askar & A. Foul

  2. Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat, 77455, Saudi Arabia

    Ahmed E. Abouelregal

  3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Ahmed E. Abouelregal

  4. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

  5. Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

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  1. S. S. Askar
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  2. Ahmed E. Abouelregal
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  3. A. Foul
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  4. Hamid M. Sedighi
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All authors discussed the results, and the final text was reviewed through the contribution of all authors.

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Correspondence to Ahmed E. Abouelregal or Hamid M. Sedighi.

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Askar, S.S., Abouelregal, A.E., Foul, A. et al. Pulsed excitation heating of semiconductor material and its thermomagnetic response on the basis of fourth-order MGT photothermal model. Acta Mech 234, 4977–4995 (2023). https://doi.org/10.1007/s00707-023-03639-7

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