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Stress effects on electric currents in antiplane problems of piezoelectric semiconductors over a rectangular domain

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Abstract

We study stress-induced electric potential and mobile charge distributions in antiplane deformations of piezoelectric semiconductors. The macroscopic theory of piezoelectric semiconductors is used. A double trigonometric series solution is obtained for the linearized problem over a rectangular domain, showing the formation of electric potential barriers or wells under local mechanical loads. A nonlinear numerical analysis is performed using COMSOL to obtain the current–voltage relation and the current density distribution. Results show that the stress-induced potential barriers/wells affect the electric current distributions and current–voltage relation. Thus, mechanical loads affect the semiconduction in the body, which is the foundation of piezotronic devices made from piezoelectric semiconductors. The effects of various physical and geometric parameters are examined.

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References

  1. Wang, Z.L.: Nanobelts, Nanowires, and nanodiskettes of semiconducting oxides—from materials to nanodevices. Adv. Mater. 15, 432–436 (2003)

    Article  MathSciNet  Google Scholar 

  2. Wen, X.N., Wu, W.Z., Ding, Y., Wang, Z.L.: Piezotronic effect in flexible thin-film based devices. Adv. Mater. 25, 3371–3379 (2013)

    Article  Google Scholar 

  3. Kim, K.K., Kim, H.S., Hwang, D.K., Lim, J.H., Park, S.J.: Realization of p-type ZnO thin films via phosphorus doping and thermal activation of the dopant. Appl. Phys. Lett. 83(1), 63–65 (2003)

    Article  Google Scholar 

  4. Wang, Z.L., Wu, W.Z., Falconi, C.: Piezotronics and piezophototronics with third generation semiconductors. MRS Bull. 43(12), 922 (2018)

    Article  Google Scholar 

  5. Hu, W.G., Kalantar-Zadeh, K., Gupta, K., Liu, C.P.: Piezotronic materials and large-scale piezotronics array devices. MRS Bull. 43, 936–940 (2018)

    Article  Google Scholar 

  6. Voon, L.C.L.Y., Willatzen, M.: Electromechanical phenomena in semiconductor nanostructures. J. Appl. Phys. 109, 031101 (2011)

    Article  Google Scholar 

  7. Kumar, B., Kim, S.W.: Recent advances in power generation through piezoelectric nano-generators. J. Mater. Chem. 21, 18946–18958 (2011)

    Article  Google Scholar 

  8. Gao, P.X., Song, J.H., Liu, J., Wang, Z.L.: Nanowire piezoelectric nanogenerators on plastic substrates as flexible power sources for nanodevices. Adv. Mater. 19, 67–72 (2007)

    Article  Google Scholar 

  9. Wang, X.D., Zhou, J., Song, J.H., Liu, J., Xu, N.S., Wang, Z.L.: Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire. Nano Lett. 6, 2768–2772 (2006)

    Article  Google Scholar 

  10. Yu, J., Ippolito, S.J., Wlodarski, W., Strano, M., Kalantar-Zadeh, K.: Nanorod based shottky contact gas sensors in reversed bias condition. Nanotechnology 21, 265502 (2010)

    Article  Google Scholar 

  11. Wang, Z.L.: Piezopotential gated nanowire devices: Piezotronics and piezo-phototronics. Nano Today 5, 540–552 (2010)

    Article  Google Scholar 

  12. Wang, Z.L.: Piezotronics and Piezo-Phototronics. Springer-Verlag, Berlin, Heidelberg (2012)

    Book  Google Scholar 

  13. Gokhale, V., Rais-Zadeh, M.: Phonon-electron interactions in piezoelectric semiconductor bulk acoustic wave resonators. Sci. Rep. 4, 5617 (2014)

    Article  Google Scholar 

  14. Sharma, J.N., Sharma, K.K., Kumar, A.: Surface waves in a piezoelectric–semiconductor composite structure. Int. J. Solids Struct. 47(6), 816–826 (2010)

    Article  Google Scholar 

  15. Jiao, F.Y., Wei, P.J., Zhou, Y.H., Zhou, X.L.: The dispersion and attenuation of the multi-physical fields coupled waves in a piezoelectric semiconductor. Ultrasonics 92, 68–78 (2019)

    Article  Google Scholar 

  16. Othmani, C., Takali, F., Njeh, A.: Theoretical study on the dispersion curves of Lamb waves in piezoelectric-semiconductor sandwich plates GaAs-FGPM-AlAs: Legendre polynomial series expansion. Superlatt. Microstruct. 106, 86–101 (2017)

    Article  Google Scholar 

  17. Tian, R., Liu, J.X., Pan, E., Wang, Y.S., Soh, A.K.: Some characteristics of elastic waves in a piezoelectric semiconductor plate. J. Appl. Phys. 126, 12 (2019)

    Google Scholar 

  18. Cao, X., Hu, S., Liu, J., Shi, J.: Generalized rayleigh surface waves in a piezoelectric semiconductor half space. Meccanica 54, 271–281 (2019)

    Article  MathSciNet  Google Scholar 

  19. Sladek, J., Sladek, V., Pan, E., Young, D.L.: Dynamic anti-plane crack analysis in functional graded piezoelectric semiconductor crystals. CMES 99(4), 273–296 (2014)

    MathSciNet  MATH  Google Scholar 

  20. Fan, C., Yan, Y., Xu, G.T., Zhao, M.H.: Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method. Eng. Fract. Mech. 165, 183–196 (2016)

    Article  Google Scholar 

  21. Qin, G.S., Lu, C.S., Zhang, X., Zhao, M.H.: Electric current dependent fracture in GaN piezo-electric semiconductor ceramics. Materials 11, 10 (2018)

    Google Scholar 

  22. Yang, J.S.: Analaysis of Piezoelectric Semiconductor Structures. Springer Nature, Switzerland (2020)

    Book  Google Scholar 

  23. Afraneo, R., Lovat, G., Burghignoli, P., Falconi, C.: Piezo-semiconductive quasi-1D nano-devices with or without anti-symmetry. Adv. Mater. 24(34), 4719–4724 (2012)

    Article  Google Scholar 

  24. Zhang, C.L., Wang, X.Y., Chen, W.Q., Yang, J.S.: An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force. Smart Mater. Struct. 26, 025030 (2017)

    Article  Google Scholar 

  25. Guo, M.K., Li, Y., Qin, G.S., Zhao, M.H.: Nonlinear solutions of PN junctions of piezoelectric semiconductors. Acta Mech. 230, 1825–1841 (2019)

    Article  MathSciNet  Google Scholar 

  26. Gao, Y.F., Wang, Z.L.: Equilibrium potential of free charge carriers in a bent piezoelectric semiconductive nanowire. Nano Lett. 9, 1103–1110 (2009)

    Article  Google Scholar 

  27. Fan, S.Q., Liang, Y.X., Xie, J.M., Hu, Y.T.: Exact solutions to the electromechanical quantities inside a statically-bent circular ZnO nanowire by taking into account both the piezoelectric property and the semiconducting performance: Part I-Linearized analysis. Nano Energy 40, 82–87 (2017)

    Article  Google Scholar 

  28. Zhang, C.L., Wang, X.Y., Chen, W.Q., Yang, J.S.: Bending of a cantilever piezoelectric semiconductor fiber under an end force. In: Altenbach, H., et al. (eds.) Generalized Models and Non-Classical Approaches in Complex Materials, pp. 261–278. Springer Cham, Switzerland (2018)

    Chapter  Google Scholar 

  29. Liu, Y., Wahyudin, E.T.N., He, J., Zhai, J.: Piezotronics and piezophototronics in two-dimensional materials. MRS Bull. 43, 959–964 (2018)

    Article  Google Scholar 

  30. Karel-Alexander, N.D., Mitchell, T., Ong, E.J.R.: Intrinsic piezoelectricity in two-dimensional materials. J. Phys. Chem. Lett. 3, 2871–2876 (2012)

    Article  Google Scholar 

  31. Li, X., Zhu, H.: Two-dimensional MoS2: Properties, preparation, and applications. J. Mater. 1, 33–44 (2015)

    Google Scholar 

  32. Zhou, Y.L., Liu, W., Huang, X., Zhang, A.H., Zhang, Y., Wang, Z.L.: Theoretical study on two-dimensional MoS2 piezoelectric nanogenerators. Nano Res. 9, 800–807 (2016)

    Article  Google Scholar 

  33. Li, N., Qian, Z.H., Yang, J.S.: Effects of edge and interior stresses on electrical behaviors of piezoelectric semiconductor films. Ferroelectrics 571, 96–108 (2021)

    Article  Google Scholar 

  34. Qu, Y., Jin, F., Yang, J.: Stress-induced electric potential barriers in thickness-stretch deformations of a piezoelectric semiconductor plate. Acta Mechanica 232(11), 4533–4543 (2021)

    Article  MathSciNet  Google Scholar 

  35. Luo, Y.X., Cheng, R.R., Zhang, C.L., Chen, W.Q., Yang, J.S.: Electromechanical fields near a circular PN junction between two piezoelectric semiconductors. Acta Mech. Solida Sin. 31(2), 127–140 (2018)

    Article  Google Scholar 

  36. Pierret, R.F.: Semiconductor Device Fundamentals. Addison-Wesley, Reading, Massachusetts (1996)

    Google Scholar 

  37. Auld, B.A.: Acoustic Fields and Waves in Solids, vol. I. John Wiley and Sons, New York (1973)

    Google Scholar 

  38. Sze, S.M.: Physics of Semiconductor Devices, 3rd edn. John Wiley and sons, New York (2006)

    Book  Google Scholar 

  39. Lanczos, C.: Discourse on Fourier Series. Hafner, New York (2016)

    Book  Google Scholar 

  40. Vattré, E., Pan, E.: Thermoelasticity of multilayered plates with imperfect interfaces. Int. J. Eng. Sci. 158, 103409 (2021)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 12072167 and 11972199), the special research funding from the Marine Biotechnology and Marine Engineering Discipline Group in Ningbo University, the Zhejiang Provincial Natural Science Foundation of China (Nos.LR12A02001 and LGG19A020001) and the K. C. Wong Magana Fund through Ningbo University.

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Correspondence to Jianke Du or Jiashi Yang.

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He, J., Du, J. & Yang, J. Stress effects on electric currents in antiplane problems of piezoelectric semiconductors over a rectangular domain. Acta Mech 233, 1173–1185 (2022). https://doi.org/10.1007/s00707-022-03148-z

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  • DOI: https://doi.org/10.1007/s00707-022-03148-z

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