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A Study of Influence of Hall Effect in Semiconducting Spherical Shell with Moore-Gibson-Thompson-Photo-Thermoelastic Model

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

This research aims to study the photo-thermoelastic interactions in an infinite semiconducting spherical shell in the context of the Moore-Gibson-Thompson-Photo-Thermo elasticity theory. The spherical shell is influenced by a high magnetic field acting along its axis. The inner and outer boundary surface of the spherical shell is traction free and subjected to time-dependent heating. The numerical expressions for the components of displacement, temperature field, carrier density, and thermal stresses are obtained in the Laplace transform domain. The numerical inversion technique is used to obtain the solution in the physical domain. The impact of Hall current on the displacement, temperature, thermal stresses, and carrier density are represented graphically for silicon material using MATLAB software.

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Data availability

For the numerical results, silicon material has been taken from Abouelregal and Atta (2022).

Abbreviations

\({\delta }_{ij}\) :

Kronecker delta

\({\beta }_{ij}\) :

Thermal elastic coupling tensor

\(T\) :

Thermodynamic temperature

\({T}_{0}\) :

Reference temperature s.t. \(\left|T/{T}_{0}\right|<<1,\)

\({N}_{0}\) :

Carrier concentration at equilibrium position

\({\sigma }_{ij}\) :

Stress tensors (Nm−2)

\({\tau }_{0}\) :

Thermal relaxation parameter

\({\omega }_{e}\) :

Electron frequency

\({D}_{E}\) :

Carrier diffusion coefficients

\({H}_{i}\) :

Intensity tensor of the magnetic field

\({\alpha }_{t}\) :

Linear thermal expansion coefficient

\({\delta }_{n}\) :

Electronic deformation coefficient

\({K}_{ij}\) :

Coefficient of Thermal conductivity

\({d}_{n}\) :

Coefficient of electronic deformation

\({\epsilon }_{ijk}\) :

Permutation symbol

H(t):

Heaviside function

\({\sigma }_{0}\) :

Electrical conductivity

\({T}_{1},{T}_{2}\) :

Constant coefficients

\({K}_{n}\)():

Modified Bessel functions of 2nd kind of order n

\({\mu }_{0}\) :

Magnetic permeability

\({n}_{e}\) :

Electron number density

\(\lambda ,\mu\) :

Lame’s elastic constants

\(M\) :

Hartmann number

\({m}_{e}\) :

Electron mass

\(\tau\) :

Photo-generated carrier lifetime

\(N\) :

Carrier density,

\(\rho\) :

Medium density (Kgm−3)

\({e}_{kk}\) :

Cubical dilatation

\({J}_{i}\) :

Conduction current density tensor

\({E}_{g}\) :

Energy gap of the semiconductor parameter,

\(t\) :

Time

\(\Omega\) :

Angular frequency

\({F}_{i}\) :

The body force

\({K}_{ij}^{*}\) :

Materialistic constant

\(m\) :

Hall effect parameter

\({e}_{ij}\) :

Strain tensors (mm−1)

\(\kappa\) :

Coupling parameter for thermal activation

\({{\varvec{H}}}_{0}\) :

Magnetic field

\({u}_{i}\) :

Components of displacement (m)

\({s}_{v}\) :

Surface recombination velocity

\({c}_{e}\) :

Electron charge

\({t}_{e}\) :

Electron collision time,

\({E}_{i}\) :

Intensity tensor of the electric field,

\({C}_{E}\) :

Specific heat at constant strain

\({s}_{v}\) :

Surface recombination velocity

\({F}_{r}\) :

Radial component of Lorentz force

\({I}_{n}()\) :

Modified Bessel functions of 1st kind of order n

H(t):

Heaviside function

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Acknowledgements

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No fund /grant/scholarship has been taken for the research work.

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Authors and Affiliations

  1. Department of Mathematics, Government College for Girls Palwal, Kurukshetra, Haryana, India

    Iqbal Kaur

  2. UIET, Kurukshetra University, Kurukshetra, Haryana, India

    Kulvinder Singh

Authors
  1. Iqbal Kaur
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  2. Kulvinder Singh
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Contributions

IK: Idea formulation, Conceptualization, Formulated strategies for mathematical modelling, methodology refinement, Formal analysis, Validation, Writing- review & editing. KS: Conceptualization, Effective literature review, Experiments and Simulation, Investigation, Methodology, Software, Supervision, Validation, Visualization, Writing—original draft. Both authors read, and approved the final manuscript.

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Correspondence to Iqbal Kaur.

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Kaur, I., Singh, K. A Study of Influence of Hall Effect in Semiconducting Spherical Shell with Moore-Gibson-Thompson-Photo-Thermoelastic Model. Iran J Sci Technol Trans Mech Eng 47, 661–671 (2023). https://doi.org/10.1007/s40997-022-00532-x

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  • DOI: https://doi.org/10.1007/s40997-022-00532-x

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