Skip to main content
SpringerLink
Log in

A Dual-Phase-Lag Model of Photothermoelastic Waves in a Two-Dimensional Semiconducting Medium

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

In this article, the generalized model for photothermal wave under dual-phase-lag model is utilized to compute the increment of temperature, the components of displacement, the carrier density and the stress components in a two-dimension semiconducting media. By using Fourier and Laplace transformations with the eigenvalue techniques methodology, the exact solutions of all physical quantities are obtained. A semiconductor media such as silicon has been studied. Finally, the outcomes are represented graphically to display the difference among the models of classical dynamical coupled, the Lord and Shulman and the dual phase lag.

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

REFERENCES

  1. McDonald, F.A. and Wetsel, G.C., Generalized Theory of the Photoacoustic Effect, J. Appl. Phys., 1978, vol. 49, no. 4, pp. 2313–2322.

  2. Jackson, W. and Amer, N.M., Piezoelectric Photoacoustic Detection: Theory and Experiment, J. Appl. Phys., 1980, vol. 51, no. 6, pp. 3343–3353.

  3. Stearns, R. and Kino, G., Effect of Electronic Strain on Photoacoustic Generation in Silicon, Appl. Phys. Lett., 1985, vol. 47, no. 10, pp. 1048–1050.

  4. Todorović, D., Photothermal and Electronic Elastic Effects in Microelectromechanical Structures, Rev. Sci. Instruments, 2003, vol. 74, no. 1, pp. 578–581.

  5. Todorović, D., Plasma, Thermal, and Elastic Waves in Semiconductors, Rev. Sci. Instruments, 2003, vol. 74, no. 1, pp. 582–585.

  6. Todorović, D., Plasmaelastic and Thermoelastic Waves in Semiconductors, J. Phys. IV (Proc.) EDP Sci., 2005, vol. 125, pp. 551–555.

  7. Rosencwaig, A., Opsal, J., and Willenborg, D.L., Thin-Film Thickness Measurements with Thermal Waves, Appl. Phys. Lett., 1983, vol. 43, no. 2, pp. 166–168.

  8. Opsal, J. and Rosencwaig, A., Thermal and Plasma Wave Depth Profiling in Silicon, Appl. Phys. Lett., 1985, vol. 47, no. 5, pp. 498–500.

  9. Abbas, I.A., Aly, K., and Alzahrani, F.S., A Two-Temperature Photothermal Interaction in a Semiconducting Material, J. Adv. Phys., 2017, vol. 6, no. 3, pp. 402–407.

  10. Abbas, I.A. and Aly, K., A Generalized Model on Plasma, Thermal and Elastic Waves in a Semiconductor Medium, J. Adv. Phys., 2017, vol. 6, no. 3, pp. 317–325.

  11. Hobiny, A.D. and Abbas, I.A., A Study on Photothermal Waves in an Unbounded Semiconductor Medium with Cylindrical Cavity,Mech. Time-Depend. Mater., 2017, vol. 21, no. 1, pp. 61–72.

  12. Biot, M.A., Thermoelasticity and Irreversible Thermodynamics,J. Appl. Phys., 1956, vol. 27, no. 3, pp. 240–253.

  13. Lord, H.W. and Shulman, Y., A Generalized Dynamical Theory of Thermoelasticity, J. Mech. Phys. Solids, 1967, vol. 15, no. 5, pp. 299–309.

  14. Tzou, D.Y., Unified Field Approach for Heat Conduction from Macro- to Micro-Scales, J. Heat Transfer, 1995, vol. 117, no. 1, pp. 8–16.

  15. Tzou, D.Y., Experimental Support for the Lagging Behavior in Heat Propagation, J. Thermophys. Heat Transfer, 1995, vol. 9, no. 4, pp. 686–693.

  16. Abbas, I.A. and Zenkour, A.M., Dual-Phase-Lag Model on Thermoelastic Interactions in a Semi-Infinite Medium Subjected to a Ramp-Type Heating, J. Comput. Theor. Nanosci., 2014, vol. 11, no. 3, pp. 642–645.

  17. Song, Y., Todorovic, D.M., Cretin, B., and Vairac, P., Study on the Generalized Thermoelastic Vibration of the Optically Excited Semiconducting Microcantilevers, Int. J. Solids Struct., 2014, vol. 47, no. 14, pp. 1871–1875.

  18. Song, Y., Bai, J., and Ren, Z., Reflection of Plane Waves in a Semiconducting Medium under Photothermal Theory, Int. J. Thermophys., 2012, vol. 33, no. 7, pp. 1270–1287.

  19. Song, Y., Bai, J., and Ren, Z., Study on the Reflection of Photothermal Waves in a Semiconducting Medium under Generalized Thermoelastic Theory, Acta Mech., 2012, vol. 223, no. 7, pp. 1545–1557.

  20. Abbas, I.A., Eigenvalue Approach to Fractional Order Generalized Magneto-Thermoelastic Medium Subjected to Moving Heat Source, J. Magnet. Magnetic Mater., 2015, vol. 377, no. 452–459.

  21. Abbas, I.A., Generalized Thermoelastic Interaction in Functional Graded Material with Fractional Order Three-Phase Lag Heat Transfer, J. Cent. South Univer., 2015, vol. 22, no. 5, pp. 1606–1613.

  22. Abbas, I.A., A Problem on Functional Graded Material under Fractional Order Theory of Thermoelasticity, Theor. Appl. Fract. Mech., 2014, vol. 74, no. 1, pp. 18–22.

  23. Abbas, I.A., Eigenvalue Approach on Fractional Order Theory of Thermoelastic Diffusion Problem for an Infinite Elastic Medium with a Spherical Cavity, Appl. Math. Modell., 2015, vol. 39.20, pp. 6196–6206.

  24. Ezzat, M.A., El-Karamany, A.S., and Fayik, M.A., Fractional Ultrafast Laser-Induced Thermoelastic Behavior in Metal Films,J. Therm. Stress, 2012, vol. 35, no. 7, pp. 637–651.

  25. Song, Y., Cretin, B., Todorovic, D.M., and Vairac, P., Study of Photothermal Vibrations of Semiconductor Cantilevers Near the Resonant Frequency, J. Phys. D. Appl. Phys., 2008, vol. 41, no. 15, pp. 155106.

  26. Mandelis, A., Nestoros, M., and Christofides, C., Thermoelectronic-Wave Coupling in Laser Photothermal Theory of Semiconductors at Elevated Temperatures, Opt. Eng., 1997, vol. 36, no. 2, pp. 459–468.

  27. Das, N.C., Lahiri, A., and Giri, R.R., Eigenvalue Approach to Generalized Thermoelasticity, Indian J. Pure Appl. Math., 1997, vol. 28, no. 12, pp. 1573–1594.

  28. Abbas, I.A., Eigenvalue Approach in a Three-Dimensional Generalized Thermoelastic Interactions with Temperature-Dependent Material Properties, Comp. Math. Appl., 2014, vol. 68, no. 12, pp. 2036–2056.

  29. Abbas, I.A., Eigenvalue Approach for an Unbounded Medium with a Spherical Cavity Based upon Two-Temperature Generalized Thermoelastic Theory, J. Mech. Sci. Tech., 2014, vol. 28, no. 10, pp. 4193–4198.

  30. Abbas, I.A., A Dual Phase Lag Model on Thermoelastic Interaction in an Infinite Fiber-Reinforced Anisotropic Medium with a Circular Hole, Mech. Based Design Struct. Mach., 2015, vol. 43, no. 4, pp. 501–513.

  31. Abbas, I.A., The Effects of Relaxation Times and a Moving Heat Source on a Two-Temperature Generalized Thermoelastic Thin Slim Strip,Canadian J. Phys., 2015, vol. 93, no. 5, pp. 585–590.

  32. Stehfest, H., Algorithm 368: Numerical Inversion of Laplace Transforms [D5], Commun. ACM, 1970, vol. 13, no. 1, pp. 47–49.

  33. Song, Y., Todorovic, D.M., Cretin, B., and Vairac, P., Bending of Semiconducting Cantilevers under Photothermal Excitation,Int. J. Thermophys., 2014, vol. 35, no. 2, pp. 305–319.

Download references

Funding

This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No (D-196-130-1439). The authors gratefully acknowledge the DSR technical and financial support.

Author information

Authors and Affiliations

  1. Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, King Abdulaziz University , 21589, Jeddah, Saudi Arabia

    A. D. Hobiny & I. A. Abbas

  2. Department of Mathematics, Faculty of Science, Sohag University, 82524, Sohag, Egypt

    I. A. Abbas

Authors
  1. A. D. Hobiny
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. A. Abbas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. A. Abbas.

Additional information

Russian Text © The Author(s), 2019, published in Fizicheskaya Mezomekhanika, 2019, Vol. 22, No. 2, pp. 105–112.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hobiny, A.D., Abbas, I.A. A Dual-Phase-Lag Model of Photothermoelastic Waves in a Two-Dimensional Semiconducting Medium. Phys Mesomech 23, 167–175 (2020). https://doi.org/10.1134/S1029959920020083

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959920020083

Keywords

Search

Navigation