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Photothermal Excitation Process in Semiconductor Materials under the Effect Moisture Diffusivity

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Abstract

A novel technique is used to study the moisture diffusivity influence in the free surface of an elastic semiconductor medium according to a one-dimensional (1D) deformation. The problem is formulated to study the coupled between the plasma, thermo-elastic waves, and moisture diffusivity. The investigation is conducted during a photothermal transport process with the effects of moisture diffusivity. The governing equations of the elastic waves, carrier density, heat conduction equation, moisture equation, and constitutive relationships are obtained for the thermo-elastic medium using the Laplace transform method. The mechanical stress, thermal, and plasma boundary conditions are applied to obtain the basic physical quantities in the Laplace domain. The inversion of the Laplace transform with the numerical method is applied to obtain the complete solutions in the time domain for the main physical fields under investigation. The effects of thermoelectric, thermoelastic, and reference moisture parameters of the applied force on the displacement component, moisture concentration, carrier density, force stress, and temperature distribution have been discussed graphically.

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Data Availability

The information applied in this research is ready from the authors at request.

This study and all procedures performed involving human participants were in accordance with the ethical standards.

References

  1. Szekeres A (2000) Analogy between heat and moisture thermohygro-mechanical tailoring of composites by taking into account the second sound phenomenon. Comput Struct 76:145–152

    Article  Google Scholar 

  2. Szekeres A (2012) Cross-coupled heat and moisture transport: part 1 theory. J Therm Stresses 35:248–268

    Article  Google Scholar 

  3. Gasch T, Malm R, Ansell A (2016) Coupled hygro-thermomechanical model for concrete subjected to variable environmental conditions. Int J Solids Struct 91:143–156

    Article  Google Scholar 

  4. Szekeres A, Engelbrecht J (2000) Coupling of generalized heat and moisture transfer, periodica polytechnica series. Mech Eng 44(1):161–170

    Google Scholar 

  5. Biot M (1956) Thermoelasticity and irreversible thermodynamics. J Appl Phys 27:240–253

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Chandrasekharaiah DS (1986) Thermoelasticity with second sound: a review. Appl Mech Rev 39:355–376

    Article  Google Scholar 

  9. Kreuzer LB (1971) Ultralow gas concentration infrared absorption spectroscopy. J Appl Phys 42:2934

    Article  CAS  Google Scholar 

  10. Tam AC (1983) Ultrasensitive laser spectroscopy, pp. 1–108. Academic Press, New York

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

    Article  CAS  Google Scholar 

  12. Tam AC (1989) Photothermal investigations in solids and fluids, pp. 1–33. Academic Press, Boston

  13. Todorovic DM, Nikolic PM, Bojicic AI (1999) Photoacoustic frequency transmission technique: electronic deformation mechanism in semiconductors. J Appl Phys 85:7716

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  15. Abo-dahab S, Lotfy Kh (2017) Two-temperature plane strain problem in a semiconducting medium under photothermal theory. Waves Ran Comp Med 27(1):67–91

    Article  Google Scholar 

  16. Lotfy K, Sarkar N (2017) Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two- temperature. Mech Time- Depend Mater 21:519–534

    Article  Google Scholar 

  17. Lotfy K, Elidy ES, Tantawi RS (2021) Photothermal excitation process during hyperbolic two-temperature theory for magneto-thermo-elastic semiconducting medium. SILICON 13:2275–2288

    Article  CAS  Google Scholar 

  18. Hosseini S, Sladek J, Sladek V (2013) Application of meshless local integral equations to two dimensional analysis of coupled non-Fick diffusion-elasticity. Eng Anal Boundary Elem 37(3):603–615

    Article  Google Scholar 

  19. Honig G, Hirdes U (1984) A method for the numerical inversion of laplace transforms., Comp Appl Math 10(1):113–132

  20. Lotfy Kh, Elidy E, Tantawi R (2021) Piezo-photo-thermoelasticity transport process for hyperbolic two-temperature theory of semiconductor material. Int J Mod Phys C 32(07):2150088

    Article  CAS  Google Scholar 

  21. Green A (1972) A note on linear thermoelasticity. Mathematica 19:69–75

    Google Scholar 

  22. Ackerman C, Bentman B, Fairbank H, Guyer R (1966) Second sound in helium. Phys Rev Lett 16:789–791

    Article  CAS  Google Scholar 

  23. Lotfy Kh, Elidy E, Tantawi R (2021) Photothermal excitation process during hyperbolic two-temperature theory for magneto-thermo-elastic semiconducting medium. Silicon 13, 2275–2288

  24. Ezzat M (2022) Hyperbolic thermal-plasma wave propagation in semiconductor of organic material. Waves Rand Comp media 32(1):334–358

    Article  Google Scholar 

  25. Ezzat M (2021) A novel model of fractional thermal and plasma transfer within a non-metallic plate. Smart Stru Syst 27(1):73–87

    Google Scholar 

Download references

Acknowledgements

The authors extend their appreciation to Princess Nourah bint Abdulrahman University for fund this research under Researchers Supporting Project number (PNURSP2023R154) Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Funding

The authors extend their appreciation to Princess Nourah bint Abdulrahman University for fund this research under Researchers Supporting Project number (PNURSP2023R154) Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia

    Shreen El-Sapa

  2. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box44519, Zagazig, Egypt

    Kh. Lotfy, E. S. Elidy & Ramdan S. Tantawi

  3. Department of Mathematics, Faculty of Science, Taibah University, Madinah, Saudi Arabia

    Kh. Lotfy

  4. Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt

    A. El-Bary

  5. Council of Futuristic Studies and Risk Management, Academy of Scientific Research and Technology, Cairo, Egypt

    A. El-Bary

Authors
  1. Shreen El-Sapa
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  2. Kh. Lotfy
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  3. E. S. Elidy
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  4. A. El-Bary
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  5. Ramdan S. Tantawi
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Contributions

Kh. Lotfy: Conceptualization, Methodology, Software, Data curation. E. Elidy: Writing- Original draft preparation, Visualization. Ramdan. S. Tantawi: Visualization, Investigation, Software, Validation. A. El-Bary: Writing- Reviewing and Editing. S. El-Sapa: Supervision, Investigation, Software, Validation.

Corresponding author

Correspondence to E. S. Elidy.

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El-Sapa, S., Lotfy, K., Elidy, E.S. et al. Photothermal Excitation Process in Semiconductor Materials under the Effect Moisture Diffusivity. Silicon 15, 4171–4182 (2023). https://doi.org/10.1007/s12633-023-02311-y

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  • DOI: https://doi.org/10.1007/s12633-023-02311-y

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