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Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature

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Abstract

In this work, a novel generalized model of photothermal theory with two-temperature thermoelasticity theory based on memory-dependent derivative (MDD) theory is performed. A one-dimensional problem for an elastic semiconductor material with isotropic and homogeneous properties has been considered. The problem is solved with a new model (MDD) under the influence of a mechanical force with a photothermal excitation. The Laplace transform technique is used to remove the time-dependent terms in the governing equations. Moreover, the general solutions of some physical fields are obtained. The surface taken into consideration is free of traction and subjected to a time-dependent thermal shock. The numerical Laplace inversion is used to obtain the numerical results of the physical quantities of the problem. Finally, the obtained results are presented and discussed graphically.

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Abbreviations

\(\lambda, \mu\) :

Counterparts of Lame’s parameters

\(N_{0}\) :

Equilibrium carrier concentration at temperature \(T\)

\(\delta_{n}\) :

The difference of deformation potential of conduction and valence band, \(\theta = T - T_{0}\) Thermodynamic temperature deviation

\(\phi = \phi - T_{0}\) :

Conductive temperature deviation

\(a\) :

Two-temperature parameter

\(T\) :

Absolute temperature

\(T_{0}\) :

Temperature of the medium in its natural state assumed to be \(|\frac{\theta}{T_{0}} |\ll 1\)

\(\phi\) :

Conductive absolute temperature

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

The volume thermal expansion

\(\sigma_{ij}\) :

Components of the stress tensor

\(\rho\) :

Density of the medium

\(\alpha_{T}\) :

The coefficient of linear thermal expansion

\(e\) :

Cubical dilatation

\(\tau_{0}\) :

Thermal relaxation time

\(C_{e}\) :

Specific heat at constant strain of the solid plate

\(k\) :

The thermal conductivity of the sample

\(D_{E}\) :

The carrier diffusion coefficient

\(\tau\) :

The photogenerated carrier lifetime

\(E_{g}\) :

The energy gap of the semiconductor

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Authors and Affiliations

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

    K. Lotfy

  2. Department of Applied Mathematics, University of Caclcutta, Kolkata, 700009, India

    N. Sarkar

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  1. K. Lotfy
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  2. N. Sarkar
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Correspondence to K. Lotfy.

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Lotfy, K., Sarkar, N. Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature. Mech Time-Depend Mater 21, 519–534 (2017). https://doi.org/10.1007/s11043-017-9340-5

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