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Moisture Diffusivity and Photothermal Excitation in Non-Local Semiconductor Materials with Laser Pulses

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Abstract

The impact of moisture diffusivity on the free surface of an elastic non-local semiconductor medium for a one-dimensional (1D) deformation is examined using a novel model. The problem is designed to investigate how moisture diffusivity processes and plasma, thermo-elastic waves interact when laser pulses are present. The study is carried out while a photo-thermoelasticity transport process with moisture diffusivity is in existence. The governing equations for elastic waves, carrier density, heat conduction equation, moisture equation, and constitutive relationships for the photo-thermo-elastic media are determined using the Laplace transform technique. The fundamental physical quantities in the Laplace domain are obtained by applying mechanical stresses, temperature, and plasma boundary conditions. For the primary physical domains under study, the inversion of the Laplace transform using a numerical approach is used to find full solutions in the time domain. Graphical discussions have been made of the effects of thermal memory, laser pulses, and reference moisture parameters on the displacement component, moisture concentration, carrier density, force stress, and temperature distribution.

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Data Availability

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

Abbreviations

\(\lambda ,\mu\) :

Lame’s elastic semiconductor parameters

\({\delta }_{n}=\left(3\lambda +2\mu \right){d}_{n}\) :

The deformation potential difference

\({T}_{0}\) :

Reference temperature in its natural state

\({\gamma }_{t}=\left(3\lambda +2\mu \right){\alpha }_{T}\) :

The volume thermal expansion

\({N}_{0}\) :

The equilibrium carrier concentration

\(\rho\) :

The density of the non-local medium

\({\alpha }_{T}\) :

Coefficients of linear thermal expansion

\({C}_{e}\) :

Specific heat of the microelongated material at constant strain

\(k\) :

The thermal conductivity

\({D}_{E}\) :

The carrier diffusion coefficient

\(\tau\) :

The carrier lifetime

\({E}_{g}\) :

The energy gap

\({d}_{n}\) :

The coefficients of electronic deformation

\({\beta }_{ij}\), \({\beta }_{ij}^{m}\) :

The isothermal and elastic coupling coefficients of moisture

\({\varepsilon }_{kl}\) :

The strain tensor

\({C}_{\text{ijkl}}\) :

The isothermal parameters tensor

\({\tau }_{0},{\nu }_{0}\) :

Thermal relaxation times

\({D}_{T}\) :

The temperature diffusivity

\({D}_{m}\) :

The diffusion coefficient of moisture

\({\sigma }_{ij}\) :

The stress tensor

\({\delta }_{ik}\) :

Kronecker delta

\({D}_{T}^{m}\), \({D}_{m}^{T}\) :

The coupled diffusivities

\({m}_{0}\) :

The reference moisture

\({k}_{m}\) :

The moisture diffusivity

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. 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 42:2934

    Article  CAS  Google Scholar 

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

    Book  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Google Scholar 

  10. 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 

  11. 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 

  12. 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 

  13. 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 

  14. Lotfy Kh (2017) Photothermal waves for two temperature with a semiconducting medium under using a dual-phase-lag model and hydrostatic initial stress. Waves Ran Comp Med 27(3):482–501

    Article  Google Scholar 

  15. Lotfy Kh (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 94:400–409

    Article  CAS  Google Scholar 

  16. Lotfy Kh (2018) A novel model of photothermal diffusion (PTD) fo polymer nano- composite semiconducting of thin circular plate. Physica B-Condenced Matter 537:320–328

    Article  CAS  Google Scholar 

  17. Lotfy Kh, Kumar R, Hassan W, Gabr M (2018) Thermomagnetic effect with microtemperature in a semiconducting Photothermal excitation medium Appl. Math Mech Engl Ed 39(6):783–796

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Lotfy Kh (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 

  20. Lotfy Kh (2019) A novel model for Photothermal excitation of variable thermal conductivity semiconductor elastic medium subjected to mechanical ramp type with two-temperature theory and magnetic field. Sci Rep 9:3319

    Article  PubMed  PubMed Central  Google Scholar 

  21. Hasselman D, Heller R (1980) Thermal stresses in severe environments. Plenum Press, New York

    Book  Google Scholar 

  22. Youssef H (2005) State-space approach on generalized thermoelasticity for an infinite material with a spherical cavity and variable thermal conductivity subjected to ramp type heating. Can Appl Math Q 13(4):369–390

    Google Scholar 

  23. Youssef H, El-Bary A (2006) Thermal shock problem of a generalized thermoelastic layered composite material with variable thermal conductivity. Math Problems Eng 87940

  24. Youssef H, Abbas I (2007) Thermal shock problem of generalized thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity. Comput Methods Sci Technol 13(2):95–100

    Article  Google Scholar 

  25. Marin M, Vlase S, Paun M (2015) Considerations on double porosity structure for micropolar bodies. AIP Adv 5(3):037113

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. Hosseini SM, 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 

  31. Eringen A (1972) Nonlocal polar elastic continua. Int J Eng Sci 10:1–16

    Article  Google Scholar 

  32. Eringen A, Edelen D (1972) On nonlocal elastic. Int J Eng Sci 10:233–248

    Article  Google Scholar 

  33. Alhashash A, Elidy E, El-Bary A, Tantawi R, Lotfy Kh (2022) Two-temperature semiconductor model photomechanical and thermal wave responses with moisture diffusivity process. Crystals 12:1770

    Article  CAS  Google Scholar 

  34. Mahdy A, Lotfy Kh, El-Bary A, Sarhan H (2021) Effect of rotation and magnetic field on a numerical-refined heat conduction in a semiconductor medium during photo-excitation processes. Eur Phys J Plus 136(5):1–17

    Article  Google Scholar 

  35. 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

    Article  CAS  Google Scholar 

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

    Google Scholar 

  37. Brancik L (1999) Programs for fast numerical inversion of Laplace transforms in MATLAB language environment. Proc. 7th Conf. MATLAB’99, pp 27–39

  38. Lotfy K, Elidy ES, Tantawi RS (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 

  39. Marin M (2010) Harmonic vibrations in thermoelasticity of microstretch materials. J Vibration Acoustics Trans ASME 132(4):044501

    Article  Google Scholar 

  40. Mondal S, Sur A (2021) Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responses. Waves Random Complex Media 31(6):1835–1858

    Article  Google Scholar 

  41. Ezzat M (2020) Hyperbolic thermal-plasma wave propagation in semiconductor of organic material. Waves Rand Comp Media. https://doi.org/10.1080/17455030.2020.1772524

    Article  Google Scholar 

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

    Google Scholar 

  43. Liu J, Han M, Wang R, Xu S, Wang X (2022) Photothermal phenomenon: Extended ideas for thermophysical properties characterization. J Appl Phys 131:065107. https://doi.org/10.1063/5.0082014

    Article  CAS  Google Scholar 

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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.

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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. Box 44519, Zagazig, Egypt

    Khaled Lotfy & M. H. Ahmed

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

    Khaled Lotfy & M. H. Ahmed

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

    Alaa A. El-Bary

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

    Alaa A. El-Bary

Authors
  1. Shreen El-Sapa
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  2. Khaled Lotfy
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  3. Alaa A. El-Bary
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  4. M. H. Ahmed
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Contributions

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

Corresponding author

Correspondence to Khaled Lotfy.

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El-Sapa, S., Lotfy, K., El-Bary, A.A. et al. Moisture Diffusivity and Photothermal Excitation in Non-Local Semiconductor Materials with Laser Pulses. Silicon 15, 4489–4500 (2023). https://doi.org/10.1007/s12633-023-02333-6

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  • DOI: https://doi.org/10.1007/s12633-023-02333-6

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