Skip to main content
SpringerLink
Log in

Thermomechanical Response Model on a Reflection Photothermal Diffusion Waves (RPTD) for Semiconductor Medium

  • Original Paper
  • Published:
Silicon Aims and scope Submit manuscript

Abstract

The generalized model for plasma, thermal and elastic waves under thermo mechanical response model of a reflection-photo-thermal-diffusion (RPTD) for semiconductor material has been applied to determine the carrier density, the displacement, the temperature, diffusion and the stresses in a semiconductor elastic medium. The reflection coefficient ratios of incident wave (CI) were analytical obtained by using the method of harmonic wave. For a semiconducting elastic material like silicon, variations of the amplitude of reflection coefficient ratios with the angle of incidence are graphical shown. Numerical results show the influence of thermoenergy coupling parameter, the thermoelectric coupling parameter and the complex circular frequency with variations of thermal relaxation times on reflection coefficient ratios.

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

Similar content being viewed by others

References

  1. Biot MA (1956) Thermoclasticity and irreversible thermodynamics. J. Appl. Phys. 27:240–253

    Article  Google Scholar 

  2. Green AE, Lindsay KA (1972). Thermoelasticity J Elasticity 2:1–7

    Article  Google Scholar 

  3. Dhaliwal RS, Sherief HH (1980) Generalized thermoelasticity for anisotropic media. Q. Appl. Math. 38:1–8

    Article  Google Scholar 

  4. Kumar R, Singh B (1998) Reflection and refraction of micro-polar elastic waves at a loosely bonded interface between viscoelastic solid and micro-polar elastic solid. Int. J. Eng. Sci. 36:101–117

    Article  Google Scholar 

  5. Gordon JP, Leite RCC, Moore RS, Porto SPS, Whinnery JR (1964) Long-transient effects in lasers with inserted liquid samples. Bull. Am. Phys. Soc. 119:501

    Google Scholar 

  6. Kreuzer LB (1971) Ultralow gas concentration infrared absorption spectroscopy. J. Appl. Phys. 42:29–34

    Article  Google Scholar 

  7. Lotfy K (2017) Photothermal waves for two temperature with a semiconducting medium under using a dual-phase-lag model and hydrostatic initial stress. Waves Random Complex Media 27(3):482–501

    Article  Google Scholar 

  8. Sing MC, Chakraborty N (2013) Reflection and refraction of P.SV and thermal waves.at an initially stressed solid-liquid interface in generalized thermo-elasticity. Appl. Math. Model. 37:463–475

    Article  Google Scholar 

  9. Singh B (2002) Reflection of thermo-viscoelastic waves from free surface in the presence of magnetic field. Proc Nat Acad Sci India 72(A) (II)):109–120

    Google Scholar 

  10. Singh B (2000) Reflection of plane sound wave form a micro-polar generalized solid half-space. J. Sound Vib. 235:685–696

    Article  Google Scholar 

  11. Othman MIA, Song Y (2008) Reflection of magneto-thermo-elastic waves with two relaxation times and temperature dependent elastic moduli. Appl. Math. Model. 32:483–500

    Article  Google Scholar 

  12. Song YQ, Bai JT, Ren ZY (2012) Study on the reflection of photothermal waves in a semiconducting medium under generalized thermoelastic theory. Acta Mech. 223:1545–1557

    Article  Google Scholar 

  13. Song YQ, Todorovic DM, Cretin B, Vairac P (2010) Study on the generalized thermoelastic vibration of the optically excited semiconducting microcantilevers. Int. J. Solids Struct. 47:1871

    Article  Google Scholar 

  14. Abo-Dahab SM, Lotfy K (2017) Two-temperature plane strain problem in a semiconducting medium under photothermal theory. Waves Random Complex Media 27:67–91

    Article  Google Scholar 

  15. Chen PJ, Gurtin ME (1968) On a theory of heat conduction involving two temperatures. Zamp. 19:614–627

    Google Scholar 

  16. Youssef HM (2006) Theory of two-temperature-generalized thermoelasticity. IMA J. Appl. Math. 71:383–390

    Article  Google Scholar 

  17. Youssef HM, Al-Lehaibi EA (2007) State-space approach of two-temperature Generalized thermoelasticity of one-dimensional problem. Int. J. Solids Struct. 44:1550–1562

    Article  Google Scholar 

  18. Misra JC, Kar SB, Samanta SC (1987) The effects of mechanical and thermal relaxations in a heated viscoelastic medium containing a cylindrical hole were studied. Trans CSME 11:151

    Google Scholar 

  19. Chandrasekharaiah DS, Srinath KS (1998) Thermoelastic interactions without energy dissipation due to a point heat source. J. Elast. 50:97–108

    Article  Google Scholar 

  20. Chandrasekharaiah DS, Murthy HN (1991) Temperature-rate-dependent thermo-elastic interactions due to a line heat source. Acta Mech. 89:1–12

    Article  Google Scholar 

  21. Hobiny A, Abbas IA (2016) A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity, Mech. Time-Depend. Mater. 6:1–12

    Google Scholar 

  22. Hobiny A, Abbas IA (2018) Analytical solutions of photo-thermo-elastic waves in a non-homogenous semiconducting material. Results in Physics 10:385–390

    Article  Google Scholar 

  23. Lotfy K (2017) A novel solution of fractional order heat equation for photothermal waves in a semiconductor medium with a spherical cavity. Chaos, Solitons Fractals 99:233–242

    Article  Google Scholar 

  24. Lotfy K, Gabr ME (2017) Response of a semiconducting infinite medium under two temperature theory with photothermal excitation due to laser pulses. Opt. Laser Technol. 97:198–208

    Article  CAS  Google Scholar 

  25. Lotfy K (2018) A novel model of photothermal diffusion (PTD) for polymer nano-composite semiconducting of thin circular plate. Phys. B Condens. Matter 537:320–328

    Article  CAS  Google Scholar 

  26. Song P, Liu J, Xu H, Wang Y (2018) Carrier Transport Parameter Imaging in a Multi-crystalline Silicon Solar Cell by Laser-Induced Photocarrier Radiometry. Int. J. Thermophys. 39:119

    Article  Google Scholar 

  27. Vyrko E, Volkov DS, Proskurnin MA (2018) Numerical Simulation of Photothermal Lens Spectrometry Models Relevant for Analytical Chemistry. Int. J. Thermophys. 39:117

    Article  Google Scholar 

  28. Tam AC (1983) Ultrasensitive Laser Spectroscopy. Academic Press, New York, pp 1–108

    Book  Google Scholar 

  29. Tam AC (1986) Applications of photoacoustic sensing techniques. Rev. Mod. Phys. 58:381–390

    Article  CAS  Google Scholar 

  30. Tam AC (1989) Photothermal Investigations in Solids and Fluids. Academic Press, Boston, pp 1–33

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Kh. Lotfy, R. Tantawy & N. Anwar

  2. Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt

    S. M. Abo-Dahab

  3. Department of Mathematics, Faculty of Science, Taif University, P.O. Box: 888, Taif, Saudi Arabia

    S. M. Abo-Dahab

Authors
  1. Kh. Lotfy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. M. Abo-Dahab
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Tantawy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. N. Anwar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kh. Lotfy.

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

Lotfy, K., Abo-Dahab, S.M., Tantawy, R. et al. Thermomechanical Response Model on a Reflection Photothermal Diffusion Waves (RPTD) for Semiconductor Medium. Silicon 12, 199–209 (2020). https://doi.org/10.1007/s12633-019-00116-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12633-019-00116-6

Keywords

Search

Navigation