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The Effect of Excess Carrier on a Semiconducting Semi-Infinite Medium Subject to a Normal Force by Means of Green and Naghdi Approach

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Abstract

For engineers and physicists, it is important to investigate the excitement of thermoelastic vibrations by photothermal effects since they are used in many fields. For this purpose, the photo-thermoelastic waves throughout the photothermal process for a semiconducting half-space have been investigated in this work. In contrast to many scientists who ignore the coupling effects between plasma and thermoelasticity, the influences of thermoelastic, carrier recombination and electronic elastic deformations on the semiconductor solids have been studied here. One of the thermoelastic theories which is appropriate for the limited speeds of heat waves has been considered. To solve the non-dimensional system resulting from generalized thermal elasticity theory without dissipating energy, coupled plasma, elastic wave and thermal wave equations, the normal mode technique has been applied. The amplitude expression for the field variables have been derived and graphically displayed. The numerical results have been verified and the influence of various factors has been also studied. In addition, several special cases of interest have been deduced. The analysis showed that the effective parameters have important effects on the physical fields by applying the presented model.

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References

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. A. E. Green and K.A. Lindsay, Thermoelasticity, J. Elast, 2, 1–7,

  4. Green AE, Naghdi PM (1993) Thermoelasticity without energy dissipation. J Elast 31:189–209

    Article  Google Scholar 

  5. Tzou DY (1996) Macro-to-microscale heat transfer: the lagging behavior. DC, Taylor & Francis, Washington

  6. Tzou DY (1995) A unified approach for heat conduction fromMacro-toMicro-scales. J Heat Transf 117:8–16

    Article  Google Scholar 

  7. Tzou DY (1995) Experimental support for the lagging behavior in heat propagation. J Thermophys Heat Transf 9:686–693

    Article  CAS  Google Scholar 

  8. Chandrasekharaiah DS (1986) Thermoelasticity with second sound: a review, applied mechanics. Appl Mech Rev Mar vol 39(3):355–376

    Article  Google Scholar 

  9. Todorović DM, Nikolić PM, Bojičić AI (1999) Photoacoustic fre-quency transmission technique: electronic deformation mechanismin semiconductors. J Appl Phys 85:7716–7726

    Article  Google Scholar 

  10. Song Y, Todorović DM, Cretin B, Vairac P (2010) Study on the generalized thermoelastic vibration of theoptically excited semiconducting microcantilevers. Int J Solids Struct 47:1871–1875

    Article  Google Scholar 

  11. Song Y, Todorovic DM, Cretin B, Vairac P, Xu J, Bai J (2014) Bending of semiconducting cantilevers under photothermal excitation. Int J Thermophys 35(2):305–319

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  14. Hobiny A, Abbas I (2019) A GN model on photothermal interactions in a two-dimensions semiconductor half space. Results Phys 15:102588

    Article  Google Scholar 

  15. Alzahrani FS, Abbas IA (2020) Photo-thermal interactions in a semiconducting media with a spherical cavity under hyperbolic two-temperature model. Mathematics 8:585

    Article  Google Scholar 

  16. Alzahrani F, Abbas I (2020) The effect of a hyperbolic two-temperature model with and without energy dissipation in a semiconductor material. Mathematics 8:1711

    Article  Google Scholar 

  17. Othman MIA, Tantawi RS, Eraki EEM (2016) Propagation of the photothermal waves in a semiconducting medium under L-S theory. J Therm Stresses 39(11):1419–1427

    Article  Google Scholar 

  18. Abo-Dahab SM (2020) P-waves reflection in a semiconducting photothermal diffusion medium with initial stress and magnetic field. Mechanics Based Design of Structures and Machines:1–21. https://doi.org/10.1080/15397734.2020.1801462

  19. Abouelregal AE (2020) Magneto-photothermal interaction in a rotating solid cylinder of semiconductor silicone material with time dependent heat flow. Appl Math Mech-Engl Ed 42:39–52. https://doi.org/10.1007/s10483-021-2682-6

    Article  Google Scholar 

  20. Abouelregal AE (2020) Modified fractional photo-Thermoelastic model for a rotating semiconductor half-space subjected to a magnetic field. Silicon 12:2837–2850

    Article  CAS  Google Scholar 

  21. Abouelregal, A. E., Modified fractional thermoelasticity model with multi-relaxation times of higher order: Application to spherical cavity exposed to a harmonic varying heat. Waves in Random and Complex Media, 1–21. doi:https://doi.org/10.1080/17455030.2019.1628320 (2019)

  22. Abouelregal AE (2019) Two-temperature thermoelastic model without energy dissipation including higher order time-derivatives and two phase-lags. Materials Research Express 6(11):116535

    Article  CAS  Google Scholar 

  23. Abouelregal AE (2020) On Green and Naghdi thermoelasticity model without energy dissipation with higher order time differential and phase-lags. Journal of Applied and Computational Mechanics 6(3):445–456

    Google Scholar 

  24. Abouelregal AE (2019) A novel generalized thermoelasticity with higher-order time-derivatives and three-phase lags. Multidiscip Model Mater Struct 16(4):689–711

    Article  Google Scholar 

  25. Abouelregal AE (2020) Three-phase-lag thermoelastic heat conduction model with higher-order time-fractional derivatives. Indian J Phys 94:1949–1963

    Article  CAS  Google Scholar 

  26. Abouelregal, A.E., Elhagary, M.A., Soleiman, A., Khalil, Generalized thermoelastic-diffusion model with higher-order fractional time-derivatives and four-phase-lags, Mechanics Based Design of Structures and Machines, (2020) https://doi.org/10.1080/15397734.2020.1730189, 1, 18

  27. Amin, M.M., Abdel Allah Nasr, A.M., El-Bary, A.A., Abo-Dahab, S.M., Propagation of surface waves in generalized thermoelastic media under influence of magnetic field and rotation and its applications in engineering and geophysics, Mechanics Based Design of Structures and Machines, (2020) https://doi.org/10.1080/15397734.2020.1804934

  28. Sharma DK, Thakur PC, Sarkar N (2020) Effect of dual-phase-lag model on free vibrations of isotropic homogenous nonlocal thermoelastic hollow sphere with voids. Mechanics Based Design of Structures and Machines:1–17. https://doi.org/10.1080/15397734.2020.1824792

  29. Todorovic DM (2003) Plasma, thermal, and elastic waves in semiconductors. Rev Sci Instrum 74(582):1980

    Google Scholar 

  30. Sedighi HM (2014) Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory. Acta Astronautica 95:111–123

    Article  Google Scholar 

  31. Brlić T, Rešković S, Jurković Z, Janeš G (2020) Mathematical modeling of the influence parameters during formation and propagation of the Lüders bands. Facta Universitatis, Series: Mechanical Engineering 18(4):595–610

    Article  Google Scholar 

  32. Shariati A, Mohammad-Sedighi H, Żur KK, Habibi M, Safa M (2020) On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams. Materials 13(7):1707

    Article  CAS  Google Scholar 

  33. Pavlović IR, Pavlović R, Janevski G, Despenić N, Pajković V (2020) Dynamic behavior of two elastically connected nanobeams under a white noise process. Facta Universitatis, Series: Mechanical Engineering 18(2):219–227

    Article  Google Scholar 

  34. Sedighi HM, Shirazi KH (2015) Dynamic pull-in instability of double-sided actuated nano-torsional switches. Acta Mechanica Solida Sinica 28(1):91–101

    Article  Google Scholar 

  35. Qie N, Houa W-F, He J-H (2021) The fastest insight into the large amplitude vibration of a string. Reports in Mechanical Engineering 2(1):1–5

    Article  Google Scholar 

  36. Ouakad HM, Sedighi HM (2016) Rippling effect on the structural response of electrostatically actuated single-walled carbon nanotube based NEMS actuators. International Journal of Non-Linear Mechanics 87:97–108

    Article  Google Scholar 

  37. Ding W, Li Y, Dong W, Wei AL (2021) Constrainted least squares solution of Sylvester equation [J]. Mathematical Modelling and Control 1(2):112–120. https://doi.org/10.3934/mmc.2021009

    Article  Google Scholar 

  38. Sedighi HM, Malikan M (2020) Stress-driven nonlocal elasticity for nonlinear vibration characteristics of carbon/boron-nitride hetero-nanotube subject to magneto-thermal environment. Phys Scr 95(5):055218

    Article  CAS  Google Scholar 

  39. Sedighi HM, Daneshmand F (2014) Static and dynamic pull-in instability of multi-walled carbon nanotube probes by He’s iteration perturbation method. J Mech Sci Technol 28(9):3459–3469

    Article  Google Scholar 

  40. Shariati A, Mohammad-Sedighi H, Żur KK, Habibi M, Safa M (2020) On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams. Materials 13(7):1707

    Article  CAS  Google Scholar 

  41. Samaniego E, Anitescu C, Goswami S, Nguyen-Thanh VM, Guo H, Hamdia K, Rabczuk T (2020) An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications. Comput Methods Appl Mech Eng 362:112790

    Article  Google Scholar 

  42. Rabczuk T, Ren H, Zhuang X (2019) A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem, CMC-computers. Materials & Continua 59(1):31–55

    Article  Google Scholar 

  43. Cosmin Anitescu, Elena Atroshchenko, Naif Alajlan, Timon Rabczuk, Artificial Neural Network Methods for the Solution of Second Order Boundary Value Problems, CMC-Computers, Materials & Continua, Vol.59, No.1, pp. 345–359

  44. Cheng JC, Zhang SY (2000) Normal mode expansion method for lasergenerated ultrasonic lamb waves in orthotropic thin plates. Appl Phys B Lasers Opt 70:57–63

    Article  CAS  Google Scholar 

  45. Ghasemi H, Brighenti R, Zhuang X, Muthu J, Rabczuk T (2015) Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach. Struct. Multidiscip. O. 51(1):99–112

    Article  Google Scholar 

  46. Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T (2016) A software framework for probabilistic sensitivity analysis for computationally expensive models. Adv Eng Softw 100:19–31

    Article  Google Scholar 

  47. Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T (2015) Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Comp Part B: Eng 68:446–464

    Article  CAS  Google Scholar 

  48. Oliver Brand, Isabelle Dufour, Stephen M. Heinrich, and Fabien Josse, editors. Resonant MEMS. Advanced Micro and Nanosystems. Wiley-VCH, Weinheim, Germany, 2015

  49. Li C, Gao S, Niu S, Liu H (2016) Study of intrinsic dissipation due to thermoelastic coupling in gyroscope resonators. Sensors 16(9):1445

    Article  Google Scholar 

  50. Wang YZ, Liu D, Wang Q, Zhou JZ (2016) Thermoelastic behavior of elastic media with temperature-dependent properties under transient thermal shock. J Therm Stresses 39(4):460–473

    Article  Google Scholar 

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Dara Availability

All data will be available upon the request of readers and/or the reviewers.

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All code data will be available upon the request of readers and/or the reviewers.

Funding

H. M. Sedighi is grateful to the Research Council of Shahid Chamran University of Ahvaz for its financial support (Grant No. SCU.EM99.98).

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat, Saudi Arabia

    Ahmed E. Abouelregal

  2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Ahmed E. Abouelregal

  3. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, 61357-43337, Iran

    Hamid M. Sedighi & Ali H. Shirazi

  4. Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

Authors
  1. Ahmed E. Abouelregal
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  2. Hamid M. Sedighi
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  3. Ali H. Shirazi
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Contributions

Author 1 planned the scheme and initiated the project and wrote the manuscript; Author 2 and Author 3 developed the mathematical modeling and examined the theory validation. The manuscript was written through the contribution of all authors. All authors discussed the results, reviewed, and approved the final version of the manuscript.

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Correspondence to Hamid M. Sedighi.

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Abouelregal, A.E., Sedighi, H.M. & Shirazi, A.H. The Effect of Excess Carrier on a Semiconducting Semi-Infinite Medium Subject to a Normal Force by Means of Green and Naghdi Approach. Silicon 14, 4955–4967 (2022). https://doi.org/10.1007/s12633-021-01289-9

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  • DOI: https://doi.org/10.1007/s12633-021-01289-9

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