Skip to main content
SpringerLink
Log in

Modeling photoexcited carrier interactions in a solid sphere of a semiconductor material based on the photothermal Moore–Gibson–Thompson model

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

Semiconductor materials, which are the aim of this study, are among the most recent advanced materials in the infrared and microwave domains. The reason for focusing on semiconducting elastic materials stems from their abundance in nature and also their numerous benefits in mechanical engineering and cotemporary physics. This work intends to provide a theoretical framework by considering the effects of thermal and electronic elastic deformation in a semiconductor medium during the exciting thermo-photovoltaic process. To this end, a modified photothermal model, in which the heat conduction is represented by the Moore–Gibson–Thompson (MGT) equation, is established by incorporating a relaxation parameter into the Green–Naghdi type III concept. The proposed model is used to investigate the interactions between plasma, thermal and elastic processes through a solid sphere of semiconductor material subject to a thermal shock in conjunction with an external magnetic field. The influence of thermal and carrier lifetime parameters on different physical properties of silicon material is graphically illustrated using theoretical simulated results by employing the Laplace technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Abbreviations

σij :

denote the components of stress field

\(\varrho\) :

is material’s density

u i :

are the displacement components

F i :

are the components of body forces and i, j, k = 1, 2, 3

eij :

represent the components of the strain tensor

ekk = e:

is the cubical dilatation

dnij = dni δij :

are difference in deformation potential of the conduction and valence bands

Cijkl :

stand for the elastic constants

βij = βiδij :

symbolize the stress-temperature coefficients. In addition

θ = T − T 0 :

denotes the thermodynamical temperature

T 0 :

is the reference temperature

N :

shows the carrier density

D Eij :

are the diffusion coefficients

k :

marks the thermal activation coupling parameter

\(\tau\) :

stands for the lifetime of photo-generated electron–hole pairs

G :

is the carrier photogeneration “source” term

K ij :

refers to the thermal conductivity tensor

C E :

denotes the specific heat at constant volume

Q :

is the heat source

References

  1. M.J. Adams, G.F. Kirkbright, Thermal diffusivity and thickness measurements for solid samples utilising the optoacoustic effect. Analyst 102(1218), 678–682 (1977)

    Article  ADS  Google Scholar 

  2. H. Vargas, L.C.M. Miranda, Photoacoustic and Re1ated phototherma1 technique. Phys. Rep. 161(2), 43–101 (1988)

    Article  ADS  Google Scholar 

  3. S.O. Ferreira, A.C. Ying, I.N. Bandeira, L.C.M. Miranda, H. Vargas, Photoacoustic measurement of the thermal diffusivity of Pb1−xSnxTe alloys. Phys. Rev. B 39(11), 7967–7970 (1989)

    Article  ADS  Google Scholar 

  4. M.I.A. Othman, E.E.M. Eraki, Effect of gravity on generalized thermoelastic diffusion due to laser pulse using dual-phase-lag model. Multidiscip. Model. Mater. Struct. 14(3), 457–481 (2018)

    Article  Google Scholar 

  5. R.G. Stearns, G.S. Kino, Effect of electronic strain on photoacoustic generation in silicon. Appl. Phys. Lett. 47(10), 1048–1050 (1985)

    Article  ADS  Google Scholar 

  6. J.P. Gordon, R.C.C. Leite, R.S. Moore et al., Long- transient effects in lasers with inserted liquid samples. Bull Am Phys Soc. 119, 501 (1964)

    Google Scholar 

  7. D.M. Todorovic, P.M. Nikolic, A.I. Bojicic, Photoacoustic frequency transmission technique: electronic deformation mechanism in semiconductors. J. Appl. Phys. 85, 7716 (1999)

    Article  ADS  Google Scholar 

  8. Y.Q. Song, D.M. Todorovic, B. Cretin, P. Vairac, Study on the generalized thermoelastic vibration of the optically excited semiconducting microcantilevers. Int. J. Solids Struct. 2010, 47 (1871)

    MATH  Google Scholar 

  9. A.E. Abouelregal, Magnetophotothermal interaction in a rotating solid cylinder of semiconductor silicone material with time dependent heat flow. Appl. Math. Mech.-Engl. Ed. 42, 39–52 (2021)

    Article  MathSciNet  Google Scholar 

  10. A.E. Abouelregal, H.M. Sedighi, A.H. Shirazi, The effect of excess carrier on a semiconducting semi-infinite medium subject to a normal force by means of Green and Naghdi approach. SILICON (2021). https://doi.org/10.1007/s12633-021-01289-9

    Article  Google Scholar 

  11. A.E. Abouelregal, H. Ahmad, S.K. Elagan, N.A. Alshehri, Modified Moore–Gibson–Thompson photo-thermoelastic model for a rotating semiconductor half-space subjected to a magnetic field. Int. J. Mod. Phys. C (2021). https://doi.org/10.1142/S0129183121501631

    Article  Google Scholar 

  12. K. Zakaria, M.A. Sirwah, A.E. Abouelregal, A.F. Rashid, Photo-Thermoelastic model with time-fractional of higher order and phase lags for a semiconductor rotating materials. SILICON 13, 573–585 (2021)

    Article  Google Scholar 

  13. H.W. Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)

    Article  ADS  Google Scholar 

  14. A.E. Green, K.A. Lindsay, Thermoelasticity. J. Elast. 2(1), 1–7 (1972)

    Article  Google Scholar 

  15. D.Y. Tzou, Experimental support for the lagging behaviour in heat propagation. J. Thermophys. Heat Transf. 9(4), 686–693 (1995)

    Article  Google Scholar 

  16. D.Y. Tzou, A unified approach for heat conduction from macro to microscale. J. Heat Transf. 117, 8–16 (1995)

    Article  Google Scholar 

  17. A.E. Abouelregal et al., Temperature-dependent physical characteristics of the rotating nonlocal nanobeams subject to a varying heat source and a dynamic load. Facta Univ. Series: Mech. Eng. (2021). https://doi.org/10.22190/FUME201222024A

    Article  Google Scholar 

  18. A.E. Abouelregal, W.W. Mohammed, H. Mohammad-Sedighi, Vibration analysis of functionally graded microbeam under initial stress via a generalized thermoelastic model with dual-phase lags. Arch. Appl. Mech. 91(5), 2127–2142 (2021)

    Article  ADS  Google Scholar 

  19. A.E. Abouelregal, H.M. Sedighi, A new insight into the interaction of thermoelasticity with mass diffusion for a half-space in the context of Moore–Gibson–Thompson thermodiffusion theory. Appl. Phys. A 127(8), 1–14 (2021)

    Article  Google Scholar 

  20. R. Balokhonov et al., Computational microstructure-based analysis of residual stress evolution in metal-matrix composite materials during thermomechanical loading. Facta Univ. Series: Mech. Eng. 19(2), 241–252 (2021)

    Article  Google Scholar 

  21. A.E. Abouelregal, On green and naghdi thermoelasticity model without energy dissipation with higher order time differential and phase-lags. J. Appl. Comput. Mech. 6(3), 445–456 (2020)

    Google Scholar 

  22. A.E. Green, P.M. Naghdi, A re-examination of the basic postulates of thermomechanics. Proc. Royal Soc. A Math. Phys. Eng. Sci. 432, 171–194 (1991)

    ADS  MathSciNet  MATH  Google Scholar 

  23. A.E. Green, P.M. Naghdi, On undamped heat waves in an elastic solid. J. Therm. Stresses 15(2), 253–264 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  24. A.E. Green, P.M. Naghdi, Thermoelasticity without energy dissipation. J. Elast. 31(3), 189–208 (1993)

    Article  MathSciNet  Google Scholar 

  25. I. Lasiecka, X. Wang, Moore–gibson–thompson equation with memory, part II: general decay of energy. J. Diff. Eqns. 259, 7610–7635 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  26. R. Quintanilla, Moore-Gibson-Thompson thermoelasticity. Math. Mech. Solids 24, 4020–4031 (2019)

    Article  MathSciNet  Google Scholar 

  27. R. Quintanilla, Moore-Gibson-Thompson thermoelasticity with two temperatures. Appl. Eng. Sci. 1, 100006 (2020)

    Google Scholar 

  28. A.E. Abouelregal, I.-E. Ahmed, M.E. Nasr, K.M. Khalil, A. Zakria, F.A. Mohammed, Thermoelastic processes by a continuous heat source line in an infinite solid via Moore–Gibson–Thompson thermoelasticity. Materials 13(19), 4463 (2020)

    Article  ADS  Google Scholar 

  29. A.E. Abouelregal, H. Ahmad, T.A. Nofal, H. Abu-Zinadah, Moore–Gibson–Thompson thermoelasticity model with temperature-dependent properties for thermo-viscoelastic orthotropic solid cylinder of infinite length under a temperature pulse. Phys. Scr. (2021). https://doi.org/10.1088/1402-4896/abfd63

    Article  Google Scholar 

  30. A.E. Aboueregal, H.M. Sedighi, The effect of variable properties and rotation in a visco-thermoelastic orthotropic annular cylinder under the Moore Gibson Thompson heat conduction model. Proc. Inst. Mech. Eng. Part L. J. Mater. Design Appl. 235(5), 1004–1020 (2021)

    Google Scholar 

  31. A.E. Aboueregal, H.M. Sedighi, A.H. Shirazi, M. Malikan, V.A. Eremeyev, Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach. Continuum Mech. Thermodyn. (2021). https://doi.org/10.1007/s00161-021-00998-1

    Article  Google Scholar 

  32. A.E. Abouelregal, H. Ersoy, Ö. Civalek, Solution of Moore–Gibson–Thompson equation of an unbounded medium with a cylindrical hole. Mathematics 9(13), 1536 (2021)

    Article  Google Scholar 

  33. B. Kaltenbacher, I. Lasiecka, R. Marchand, Wellposedness and exponential decay rates for the Moore–Gibson–Thompson equation arising in high intensity ultrasound. Control Cybernet 40, 971–988 (2011)

    MathSciNet  MATH  Google Scholar 

  34. N. Bazarra, J.R. Fernández, R. Quintanilla, Analysis of a Moore-Gibson-Thompson thermoelastic problem. J. Comput. Appl. Math. 382(15), 113058 (2020)

    MathSciNet  MATH  Google Scholar 

  35. Y.Q. Song, J.T. Bai, Z.Y. Ren, Study on the reflection of photothermal waves in a semiconducting medium under generalized thermoelastic theory. Acta Mech. 223, 1545–1557 (2012)

    Article  MathSciNet  Google Scholar 

  36. D.M. Todorovic, Plasma, thermal, and elastic waves in semiconductors. Rev. Sci. Instrum. 74, 582 (2003)

    Article  ADS  Google Scholar 

  37. A.N. Vasilev, V.B. Sandomirskii, Photoacoustic effects in finite semiconductors. Sov. Phys. Semicond. 18, 1095 (1984)

    Google Scholar 

  38. C. Cattaneo, A form of heat-conduction equations which eliminates the paradox of instantaneous propagation. Compt. Rend 247, 431–433 (1958)

    MATH  Google Scholar 

  39. P. Vernotte, Some possible complications in the phenomena of thermal conduction. Compt. Rend 252, 2190–2191 (1961)

    Google Scholar 

  40. A.E. Abouelregal, A novel generalized thermoelasticity with higher-order time-derivatives and three-phase lags. Multidiscip. Model. Mater. Struct. 16(4), 689–711 (2019)

    Article  Google Scholar 

  41. A.E. Abouelregal, Two-temperature thermoelastic model without energy dissipation including higher order time-derivatives and two phase-lags. Mater. Res. Express 16, 116535 (2019)

    Article  ADS  Google Scholar 

  42. G. Honig, U. Hirdes, A method for the numerical inversion of Laplace transform. J. Comp. Appl. Math. 10, 113–132 (1984)

    Article  MathSciNet  Google Scholar 

  43. D.Y. Tzou, Macro-to Micro-Scale Heat Transfer: The Lagging Behavior (Taylor & Francis, Abingdon, UK, 1997)

    Google Scholar 

  44. A. Soleiman, A.E. Abouelregal, H. Ahmad, P. Thounthong, Generalized thermoviscoelastic model with memory dependent derivatives and multi-phase delay for an excited spherical cavity. Phys. Scripta 95(11), 115708 (2020)

    Article  ADS  Google Scholar 

  45. D. Trajkovski, R. Čukić, A coupled problem of thermoelastic vibrations of a circular plate with exact boundary conditions. Mech. Res. Commun. 26(2), 217–224 (1999)

    Article  Google Scholar 

Download references

Funding

The authors received no funding for the research, authorship and publication of this article.

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayat, Saudi Arabia

    Ahmed E. Abouelregal

  2. Basic Sciences Research Unit, Jouf University, Al-Qurayat, 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, 61357-43337, Ahvaz, Iran

    Hamid M. Sedighi

  5. Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, 61357-43337, Ahvaz, Iran

    Hamid M. Sedighi

  6. Civil Engineering Department, Faculty of Engineering, Suleyman Demirel University, 32260, Isparta, Turkey

    Abdullah H. Sofiyev

Authors
  1. Ahmed E. Abouelregal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamid M. Sedighi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdullah H. Sofiyev
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors discussed the results, reviewed and approved the final version of the manuscript.

Corresponding author

Correspondence to Hamid M. Sedighi.

Ethics declarations

Conflict of Interest

The authors declared no potential conflicts of interest with respect to the research, authorship and publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abouelregal, A.E., Sedighi, H.M. & Sofiyev, A.H. Modeling photoexcited carrier interactions in a solid sphere of a semiconductor material based on the photothermal Moore–Gibson–Thompson model. Appl. Phys. A 127, 845 (2021). https://doi.org/10.1007/s00339-021-04971-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-021-04971-2

Keywords

Search

Navigation