pp 1–12 | Cite as

Response of Semiconductor Medium of Variable Thermal Conductivity Due to Laser Pulses with Two-Temperature through Photothermal Process

  • Kh. LotfyEmail author
  • R. S. Tantawi
  • N. Anwer
Original Paper


A novel model of variable thermal conductivity of semiconductor medium in two-temperature theory is studied. The Photothermal excitation due to laser pulses is investigated. The governing equations have been studied under three theories in generalized thermoelasticity during Photothermal transport process. Taken into consideration the linearity of thermal conductivity, in which depend on temperature. The normal mode method is used to obtain the exact expressions of some physical fields analytically, in the context of the recombination between thermal-elastic-plasma waves. The silicon (Si) material is used to the numerical simulation. Some comparisons between the results are made as the influence of thermoelectric coupling parameter, variable thermal conductivity and two-temperature parameter of physical fields. The numerical calculations have been discussed and illustrated graphically.


Photothermal L-S theory Thermoelasticity Laser pulse Variable thermal conductivity Two-temperature 


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Conflict of Interest

No potential conflict of interest was reported by the author.


  1. 1.
    Biot MA (1956) Thermoelasticity and irreversible thermodynamics. J Appl Phys 27:240–253CrossRefGoogle Scholar
  2. 2.
    Lord H, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15:299–309CrossRefGoogle Scholar
  3. 3.
    Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2:1–7CrossRefGoogle Scholar
  4. 4.
    Chandrasekharaiah DS (1986) Thermoelasticity with second sound: a review. Appl Mech Rev 39:355–376CrossRefGoogle Scholar
  5. 5.
    Chandrasekharaiah DS (1998) Hyperbolic thermoelasticity: a review of recent literature. Appl Mech Rev 51:705–729CrossRefGoogle Scholar
  6. 6.
    Sharma JN, Kumar V, Dayal C (2003) Reflection of generalized thermoelastic waves from the boundary of a half-space. J Therm Stresses 26:925–942CrossRefGoogle Scholar
  7. 7.
    Joseph DD, Preziosi L (1989) Heat waves. Rev Mod Phys 61:41–73CrossRefGoogle Scholar
  8. 8.
    Joseph DD (1990) Luigi Preziosi. Heat waves Reviews of Modern Physics 62:375–391CrossRefGoogle Scholar
  9. 9.
    Gordon JP, Leite RCC, Moore RS, Porto SPS, Whinnery JR (1965) Long-transient effects in lasers with inserted liquid samples. J Appl Phys 36:3–8CrossRefGoogle Scholar
  10. 10.
    Kreuzer LB (1971) Ultralow gas concentration infrared absorption spectroscopy. J Appl Phys 42:2934–2943CrossRefGoogle Scholar
  11. 11.
    Tam AC. Ultrasensitive laser spectroscopy. New York (NY): Academic Press; 1983. p. 1–108Google Scholar
  12. 12.
    Tam AC (1986) Applications of photoacoustic sensing techniques. Rev Mod Phys 58:381–431CrossRefGoogle Scholar
  13. 13.
    Tam AC. Photothermal investigations in solids and fluids (1989) Boston. Academic Press, MA, pp 1–33Google Scholar
  14. 14.
    Todorović DM, Nikolić PM, Bojičić AI (1999) Photoacoustic frequency transmission technique: electronic deformation mechanism in semiconductors. J Appl Phys 85:7716–7726CrossRefGoogle Scholar
  15. 15.
    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 47:1871–1875CrossRefGoogle Scholar
  16. 16.
    Chen PJ, Gurtin ME, Williams WO (1968) A note on non-simple heat conduction. Zamp 19:969–970Google Scholar
  17. 17.
    Chen PJ, Gurtin ME, Williams WO (1969) On the thermodynamics of non- simple elastic materials with two temperatures. Zamp 20:107–112Google Scholar
  18. 18.
    Chen JK, Beraun JE, Tham CL (2004) Ultrafast thermoelasticity for short- pulse laser heating. Int J Eng Sci 42:793–807CrossRefGoogle Scholar
  19. 19.
    Quintanilla TQ, Tien CL (1993) Heat transfer mechanism during short-pulse laser heating of metals. ASME J Heat Transfer 115:835–841CrossRefGoogle Scholar
  20. 20.
    Youssef HM (2006) Theory of two-temperature-generalized thermoelasticity. IMA J Appl Math 71:383–390CrossRefGoogle Scholar
  21. 21.
    Youssef HM, Al-Lehaibi EA (2007) State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem. Int J Solids Struct 44:1550–1562CrossRefGoogle Scholar
  22. 22.
    Youssef HM, El-Bary AA (2006) Mathematical model for thermal shock problem of a generalized thermoelastic layered composite material with variable thermal conductivity. Com, Meth Sci Tech 12:165–171CrossRefGoogle Scholar
  23. 23.
    Othman MIA, Lotfy K (2010) On the plane waves of generalized thermo-microstretch elastic half-space under three theories. Int Comm Heat Mass Transfer 37:192–201CrossRefGoogle Scholar
  24. 24.
    Othman MIA, Abo-dahab S, Lotfy K (2014) Gravitational effect and initial stress on generalized magneto-thermo-microstretch elastic solid for different theories. Appl Math Comput 230:597–608Google Scholar
  25. 25.
    Lotfy K (2014) Two temperature generalized magneto-thermoelastic interactions in an elastic medium under three theories. Appl Math Comput 227:871–888Google Scholar
  26. 26.
    Kh L, Hassan W (2014) Normal mode method for two-temperature generalized Thermoelasticity under thermal shock problem. J Thermal Stresses 37:545–560CrossRefGoogle Scholar
  27. 27.
    Abo-Dahb S, Lotfy K (2017) Two-temperature plane strain problem in a semiconducting medium under photothermal theory. Waves Random Complex Media 27(1):67–91CrossRefGoogle Scholar
  28. 28.
    Abo-Dahb SM, Lotfy Kh, Gohaly A. Rotation and magnetic field effect on surface waves propagation in an elastic layer lying over a generalized thermoelastic diffusive half-space with imperfect boundary. Math Probl Eng. 2015. Article ID 671783.
  29. 29.
    Kh L, Kumar R, Hassan W, Gabr M (2018) Thermomagnetic effect with microtemperature in a semiconducting Photothermal excitation medium. Appl Math Mech Engl Ed 39(6):783–796CrossRefGoogle Scholar
  30. 30.
    Kh L, Gabr M (2017) Response of a semiconducting infinite medium under two temperature theory with photothermal excitation due to laser pulses. Opt Laser Technol 97:198–208CrossRefGoogle Scholar
  31. 31.
    Al-Qahtani H, Datta SK (2008) Laser generalized thermoelastic waves in an anisotropic plate, Exact Analysis. J Therm Stresses 31:569–583CrossRefGoogle Scholar
  32. 32.
    Mandelis A, Nestoros M, Christofides C (1997) Thermoelectronic-wave coupling in laser photothermal theory of semiconductors at elevated temperatures. Opt Eng 36:459–468CrossRefGoogle Scholar
  33. 33.
    Todorović DM (2003) Plasma, thermal, and elastic waves in semiconductors. Rev Sci Instrum 74:582–585CrossRefGoogle Scholar
  34. 34.
    Lotfy K (2018) A novel model of Photothermal diffusion (PTD) fo polymer Nano- composite semiconducting of thin circular plate. Physica B- Condenced Matter 537:320–328CrossRefGoogle Scholar
  35. 35.
    Christofides C, Othonos A, Loizidou E (2002) Influence of temperature and modulation frequency on the thermal activation coupling term in laser photothermal theory. J Appl Phys 92:1280–1285CrossRefGoogle Scholar
  36. 36.
    Lotfy K (2016) The elastic wave motions for a photothermal medium of a dual-phase-lag model with an internal heat source and gravitational field. Can J Phys 94:400–409CrossRefGoogle Scholar
  37. 37.
    Youssef H, El-Bary A (2010) Two-temperature generalized Thermoelasticity with variable thermal conductivity. J Therm Stresses 33:187–201CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceZagazig UniversityZagazigEgypt

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