Skip to main content
SpringerLink
Log in

Fractional Order GN Model on Photo-Thermal Interaction in a Semiconductor Plane

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

Abstract

A mathematical model of Green–Naghdi photothermal theory based on fractional-order of heat transfer is given to study the wave propagation in a two-dimensional semiconductor material. Closed-form analytical solutions to obtain the physical quantities subjected to a heat flux with a pulse that decays exponentially in the surface of semiconductor half-space are presented. Through the use of Laplace and Fourier transforms with the methodology of eigenvalues techniques, the analytical solutions of all physical quantities are obtained. A semiconductor medium such as silicon is studied. The derived method is evaluated with numerical results which are applied to the semiconductor medium in simplified geometry. The significant influence of time-fractional derivative parameters are discussed for all physical quantities. Suitable discussions and conclusions are presented.

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. McDonald FA, Wetsel Jr GC (1978) Generalized theory of the photoacoustic effect. J Appl Phys 49(4):2313–2322

    Article  CAS  Google Scholar 

  2. Jackson W, Amer NM (1980) Piezoelectric photoacoustic detection: theory and experiment. J Appl Phys 51(6):3343–3353

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  4. Todorović D (2003) Photothermal and electronic elastic effects in microelectromechanical structures. Rev Sci Instrum 74(1):578–581

    Article  Google Scholar 

  5. Todorović D (2003) Plasma, thermal, and elastic waves in semiconductors. Rev Sci Instrum 74(1):582–585

    Article  Google Scholar 

  6. Song Y et al (2008) Study of photothermal vibrations of semiconductor cantilevers near the resonant frequency. J Phys D Appl Phys 41(15):155106

    Article  Google Scholar 

  7. Rosencwaig A, Opsal J, Willenborg DL (1983) Thin-film thickness measurements with thermal waves. Appl Phys Lett 43(2):166–168

    Article  Google Scholar 

  8. Green AE, Naghdi PM (1993) Thermoelasticity without energy dissipation. J Elast 31(3):189–208

    Article  Google Scholar 

  9. Green A, Naghdi P (1991) A re-examination of the basic postulates of thermomechanics. Proc R Soc Lond A Math Phys Sci 432(1885):171–194

    Google Scholar 

  10. Othman MI, Marin M (2017) Effect of thermal loading due to laser pulse on thermoelastic porous medium under GN theory. Res Phys 7:3863–3872

    Google Scholar 

  11. Abbas IA, Youssef HM (2013) Two-temperature generalized thermoelasticity under ramp-type heating by finite element method. Meccanica 48(2):331–339

    Article  Google Scholar 

  12. Abbas IA, Youssef HM (2012) A nonlinear generalized Thermoelasticity model of temperature-dependent materials using finite element method. Int J Thermophys 33(7):1302–1313

    Article  CAS  Google Scholar 

  13. Kumar R, Abbas IA (2013) Deformation due to thermal source in micropolar thermoelastic media with thermal and conductive temperatures. J Comput Theor Nanosci 10(9):2241–2247

    Article  CAS  Google Scholar 

  14. Abbas IA, Youssef HM (2009) Finite element analysis of two-temperature generalized magneto-thermoelasticity. Arch Appl Mech 79(10):917–925

    Article  Google Scholar 

  15. Abbas IA (2007) Finite element analysis of the thermoelastic interactions in an unbounded body with a cavity. Forsch Ingenieurwes 71(3–4):215–222

    Article  Google Scholar 

  16. Abbas IA, Abo-Dahab S (2014) On the numerical solution of thermal shock problem for generalized magneto-thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity. J Comput Theor Nanosci 11(3):607–618

    Article  CAS  Google Scholar 

  17. Abbas IA (2009) Generalized magneto-thermoelasticity in a nonhomogeneous isotropic hollow cylinder using the finite element method. Arch Appl Mech 79(1):41–50

    Article  Google Scholar 

  18. Abbas IA (2014) A problem on functional graded material under fractional order theory of thermoelasticity. Theor Appl Fract Mech 74:18–22

    Article  Google Scholar 

  19. Hobiny A, Abbas IA (2018) The influence of thermal and conductive temperatures in a nanoscale resonator. Res Phys 9:705–711

    Google Scholar 

  20. Marin M, Öchsner A (2017) The effect of a dipolar structure on the Hölder stability in Green–Naghdi thermoelasticity. Contin Mech Thermodyn 29(6):1365–1374

    Article  Google Scholar 

  21. El-Karamany AS, Ezzat MA (2011) On the two-temperature Green–Naghdi thermoelasticity theories. J Therm Stresses 34(12):1207–1226

    Article  Google Scholar 

  22. Ezzat MA, El-Karamany AS, El-Bary AA (2018) Two-temperature theory in Green–Naghdi thermoelasticity with fractional phase-lag heat transfer. Microsyst Technol 24(2):951–961

    Article  CAS  Google Scholar 

  23. Abbas IA (2014) Fractional order GN model on thermoelastic interaction in an infinite fibre-reinforced anisotropic plate containing a circular hole. J Comput Theor Nanosci 11(2):380–384

    Article  CAS  Google Scholar 

  24. Song Y et al (2010) Study on the generalized thermoelastic vibration of the optically excited semiconducting microcantilevers. Int J Solids Struct 47(14–15):1871–1875

    Article  Google Scholar 

  25. Song Y, Bai J, Ren Z (2012) Reflection of plane waves in a semiconducting medium under Photothermal theory. Int J Thermophys 33(7):1270–1287

    Article  CAS  Google Scholar 

  26. Song Y, Bai J, Ren Z (2012) Study on the reflection of photothermal waves in a semiconducting medium under generalized thermoelastic theory. Acta Mech 223(7):1545–1557

    Article  Google Scholar 

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

    Google Scholar 

  28. Abbas IA, Aly K, Dahshan A (2018) Analytical solutions of plasma and Thermoelastic waves Photogenerated by a focused laser beam in a semiconductor material. Silicon 10(6):2609–2616

    Article  CAS  Google Scholar 

  29. Lotfy K (2018) Effect of variable thermal conductivity during the photothermal diffusion process of semiconductor medium. Silicon 11:1–11

    CAS  Google Scholar 

  30. Lotfy K (2019) Analytical solutions of photo-thermal-elastic waves in a semiconductor material due to pulse heat flux with thermal memory. Silicon:1–11

  31. Lotfy K et al (2019) Thermomechanical Response Model on a Reflection Photothermal Diffusion Waves (RPTD) for semiconductor medium. Silicon:1–11

  32. Lotfy K, Tantawi R, Anwer N (2019) Response of semiconductor medium of variable thermal conductivity due to laser pulses with two-temperature through photothermal process. Silicon:1–12

  33. Lotfy K, Tantawi R (2019) Photo-Thermal-Elastic Interaction in a Functionally Graded Material (FGM) and magnetic field. Silicon:1–9

  34. Zenkour AM (2019) Effect of thermal activation and diffusion on a photothermal semiconducting half-space. J Phys Chem Solids 132:56–67

    Article  CAS  Google Scholar 

  35. Zenkour AM (2019) Refined multi-phase-lags theory for photothermal waves of a gravitated semiconducting half-space. Compos Struct 212:346–364

    Article  Google Scholar 

  36. Todorović D (2005) Plasmaelastic and thermoelastic waves in semiconductors. J Phys IV (Proceedings) 125:551. EDP sciences

    Article  Google Scholar 

  37. Lord HW, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15(5):299–309

    Article  Google Scholar 

  38. Mandelis A, Nestoros M, Christofides C (1997) Thermoelectronic-wave coupling in laser photothermal theory of semiconductors at elevated temperatures. Opt Eng 36(2):459–468

    Article  CAS  Google Scholar 

  39. Debnath L, Bhatta D (2014) Integral transforms and their applications. Chapman and Hall/CRC, Boca Raton

    Book  Google Scholar 

  40. Das NC, Lahiri A, Giri RR (1997) Eigenvalue approach to generalized thermoelasticity. Indian J Pure Appl Math 28(12):1573–1594

    Google Scholar 

  41. Abbas IA (2015) A dual phase lag model on thermoelastic interaction in an infinite fiber-reinforced anisotropic medium with a circular hole. Mech Based Des Struct Mach 43(4):501–513

    Article  Google Scholar 

  42. Stehfest H (1970) Algorithm 368: numerical inversion of Laplace transforms [D5]. Commun ACM 13(1):47–49

    Article  Google Scholar 

  43. Song Y et al (2014) Bending of semiconducting cantilevers under photothermal excitation. Int J Thermophys 35(2):305–319

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No (KEP-24-130-38). The authors, therefore, acknowledge with thanks DSR technical and financial support.

Author information

Authors and Affiliations

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

    Aatef Hobiny & Ibrahim Abbas

  2. Department of mathematics, Faculty of Science, Sohag University, Sohag, Egypt

    Ibrahim Abbas

Authors
  1. Aatef Hobiny
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ibrahim Abbas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aatef Hobiny.

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

Hobiny, A., Abbas, I. Fractional Order GN Model on Photo-Thermal Interaction in a Semiconductor Plane. Silicon 12, 1957–1964 (2020). https://doi.org/10.1007/s12633-019-00292-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12633-019-00292-5

Keywords

Search

Navigation