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Nonlinear solutions of PN junctions of piezoelectric semiconductors

  • MingKai Guo
  • Yuan Li
  • GuoShuai Qin
  • MingHao ZhaoEmail author
Original Paper
  • 13 Downloads

Abstract

A PN junction between two types of piezoelectric semiconductors (PSCs) is analyzed based on the fully coupled nonlinear equations of PSCs without any assumptions. A perturbation theory is employed to obtain the analytical solution of the considered nonlinear problem. A general solution to one-dimensional problems for PSCs is represented by a sum of a series of perturbation solutions. Typical properties including the electromechanical fields, built-in potential and the current–voltage characteristics of the piezoelectric PN junction are investigated for conditions of mechanical loading combined with a bias. The results reveal that the simplified linear (i.e., first-order perturbation) solution reported in the literature fails to describe the nonlinear characteristics, such as current–voltage characteristics of the piezoelectric PN junction, although it can give the electromechanical fields as well as concentrations of the electrons and holes near the interface of the PN junction for small carrier concentration perturbations. The presented nonlinear solution is valid and corresponds closely with the numerical solutions based on the commercial software COMSOL.

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Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 11702252 and 11572289).

References

  1. 1.
    Hutson, A.R.: Piezoelectricity and conductivity in ZnO and CdS. Phys. Rev. Lett. 4, 505–507 (1960)CrossRefGoogle Scholar
  2. 2.
    Zhao, M.H., Wang, Z.L., Mao, S.X.: Piezoelectric characterization of individual zinc oxide nanobelt probed by piezoresponse force microscope. Nano. Lett. 4, 587–590 (2004)CrossRefGoogle Scholar
  3. 3.
    Yang, J.S., Zhou, H.G.: Acoustoelectric amplification of piezoelectric surface waves. Acta. Mech. 172, 113–122 (2004)CrossRefGoogle Scholar
  4. 4.
    Wang, Z.L.: Nanopiezotronics. Adv. Mater. 19, 889–892 (2007)CrossRefGoogle Scholar
  5. 5.
    Qin, G.S., Ma, S.J., Lu, C., Wang, G., Zhao, M.H.: Influence of electric field and current on the strength of depoled GaN piezoelectric semiconductive ceramics. Ceram. Int. 44, 4169–4175 (2018)CrossRefGoogle Scholar
  6. 6.
    Zhao, M.H., Ma, S.J., Lu, C.S., Fan, C.Y., Qin, G.S.: Influence of polarization on the electromechanical properties of GaN piezoelectric semiconductive ceramics. Ceram. Int. 44, 12648–12654 (2018)CrossRefGoogle Scholar
  7. 7.
    Zhang, Y., Liu, Y., Wang, Z.L.: Fundamental theory of piezotronics. Adv. Mater. 23, 3004–3013 (2011)CrossRefGoogle Scholar
  8. 8.
    Liu, Y., Zhang, Y., Yang, Q., Niu, S.M., Wang, Z.L.: Fundamental theories of piezotronics and piezo-phototronics. Nano Energy 14, 257–275 (2015)CrossRefGoogle Scholar
  9. 9.
    Wang, Z.L.: Nanobelts, nanowires, and nanodiskettes of semiconducting oxides—from materials to nanodevices. Adv. Mater. 15, 432–436 (2003)CrossRefGoogle Scholar
  10. 10.
    Kumar, B., Kim, S.W.: Recent advances in power generation through piezoelectric nanogenerators. J. Mater. Chem. 21, 18946–18958 (2011)CrossRefGoogle Scholar
  11. 11.
    Lee, K.Y., Bae, J., Kim, S., Lee, J.H., Yoon, G.C., Gupta, M.K., Kim, S., Kim, H., Park, J., Kim, S.W.: Depletion width engineering via surface modification for high performance semiconducting piezoelectric nanogenerators. Nano Energy 8, 165–173 (2014)CrossRefGoogle Scholar
  12. 12.
    Wauer, J., Suherman, S.: Thickness vibrations of a piezo-semiconducting plate layer. Int. J. Eng. Sci. 35, 1387–1404 (1997)CrossRefGoogle Scholar
  13. 13.
    Li, P., Jin, F., Yang, J.S.: Effects of semiconduction on electromechanical energy conversion in piezoelectrics. Smart Mater. Struct. 24, 025021 (2015)CrossRefGoogle Scholar
  14. 14.
    Yang, J.S., Yang, X.M., Turner, J.A.: Amplification of acoustic waves in laminated piezoelectric semiconductor plates. Arch. Appl. Mech. 74, 288–298 (2004)CrossRefGoogle Scholar
  15. 15.
    Yang, J.S., Zhou, H.G.: Wave propagation in a piezoelectric ceramic plate sandwiched between two semiconductor layers. Int. J. Appl. Electromagn. 22, 97–109 (2005)CrossRefGoogle Scholar
  16. 16.
    Yang, J.S., Yang, X.M., Turner, J.A.: Amplification of acoustic waves in piezoelectric semiconductor shells. J. Intell. Mater. Syst. Struct. 16, 613–621 (2005)CrossRefGoogle Scholar
  17. 17.
    Yang, J.S., Zhou, H.G.: Propagation and amplification of gap waves between a piezoelectric half-space and a semiconductor film. Acta. Mech. 176, 83–93 (2005)CrossRefGoogle Scholar
  18. 18.
    Hu, Y.T., Zeng, Y., Yang, J.S.: A mode III crack in a piezoelectric semiconductor of crystals with 6 mm symmetry. Int. J. Solids Struct. 44, 3928–3938 (2007)CrossRefGoogle Scholar
  19. 19.
    Zhao, M.H., Li, Y., Yan, Y., Fan, C.Y.: Singularity analysis of planar cracks in three-dimensional piezoelectric semiconductors via extended displacement discontinuity boundary integral equation method. Eng. Anal. Bound. Elem. 67, 115–125 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Fan, C.Y., 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)CrossRefGoogle Scholar
  21. 21.
    Zhao, M.H., Pan, Y.B., Fan, C.Y., Xu, G.T.: Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors. Int. J. Solids. Struct. 94–95, 50–59 (2016)CrossRefGoogle Scholar
  22. 22.
    Zhang, Q.Y., Fan, C.Y., Xu, G.T., Zhao, M.H.: Iterative boundary element method for crack analysis of two-dimensional piezoelectric semiconductor. Eng. Anal. Bound. Elem. 83, 87–95 (2017)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhao, Y.F., Zhou, C.G., Zhao, M.H., Pan, E.N., Fan, C.Y.: Penny-shaped cracks in three-dimensional piezoelectric semiconductors via Green’s functions of extended displacement discontinuity. J. Intell. Mater. Syst. Struct. 28, 1775–1788 (2017)CrossRefGoogle Scholar
  24. 24.
    Yang, J.S.: A semi-infinite anti-plane crack in a piezoelectric semiconductor. Int. J. Fract. 130, L169–L174 (2004)CrossRefGoogle Scholar
  25. 25.
    Zhang, C.L., Wang, X.Y., Chen, W.Q., Yang, J.S.: Carrier distribution and electromechanical fields in a free piezoelectric semiconductor rod. J. Zhejiang Univ. Sci. A 17, 37–44 (2016)CrossRefGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    Yang, G.Y., Du, J.K., Wang, J., Yang, J.S.: Electromechanical fields in a nonuniform piezoelectric semiconductor rod. J. Mech. Mater. Struct. 13, 103–120 (2018)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Dai, X.Y., Zhu, F., Qian, Z.H., Yang, J.S.: Electric potential and carrier distribution in a piezoelectric semiconductor nanowire in time-harmonic bending vibration. Nano Energy 43, 22–28 (2018)CrossRefGoogle Scholar
  29. 29.
    Aspitarte, L., McCulley, D.R., Minot, E.D.: A nanoscale pn junction in series with tunable Schottky barriers. J. Appl. Phys. 122, 134304 (2017)CrossRefGoogle Scholar
  30. 30.
    Chung, S.Y., Kim, S., Lee, J.H., Kim, K., Kim, S.W., Kang, C.Y., Yoon, S.J., Kim, Y.S.: All-solution-processed flexible thin film piezoelectric nanogenerator. Adv. Mater. 24, 6022 (2012)CrossRefGoogle Scholar
  31. 31.
    Pierret, R.F., Neudeck, G.W.: Advanced Semiconductor Fundamentals. Addison-Wesley, Reading (1987)Google Scholar
  32. 32.
    Van Zeghbroeck, B.: Principles of Semiconductor Devices, vol. 34. Colorado University, Boulder (2004)Google Scholar
  33. 33.
    Yang, J.S.: An anti-plane crack in a piezoelectric semiconductor. Int. J. Fract. 136, L27–L32 (2005)CrossRefGoogle Scholar
  34. 34.
    Luo, Y.X., Zhang, C.L., Chen, W.Q., Yang, J.S.: An analysis of PN junctions in piezoelectric semiconductors. J. Appl. Phys. 122, 204502 (2017)CrossRefGoogle Scholar
  35. 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, 127–140 (2018)CrossRefGoogle Scholar
  36. 36.
    Fan, S.Q., Yang, W.L., Hu, Y.T.: Adjustment and control on the fundamental characteristics of a piezoelectric PN junction by mechanical-loading. Nano Energy 52, 416–421 (2018)CrossRefGoogle Scholar
  37. 37.
    Yang, G.Y., Du, J.K., Wang, J., Yang, J.S.: Extension of a piezoelectric semiconductor fiber with consideration of electrical nonlinearity. Acta. Mech. 229, 4663–4676 (2018)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Holzapfel, G.A.: Nonlinear solid mechanics: a continuum approach for engineering science. Meccanica 37, 489–490 (2002)CrossRefGoogle Scholar
  39. 39.
    Sze, S.M., Ng, K.K.: Physics of Semiconductor Devices. Wiley, Hoboken (2006)CrossRefGoogle Scholar
  40. 40.
    Bykhovski, A., Kaminski, V., Shur, M., Chen, Q., Khan, M.A.: Piezoresistive effect in wurtzite n-type GaN. Appl. Phys. Lett. 68, 818–819 (1996)CrossRefGoogle Scholar
  41. 41.
    Ancona, M., Binari, S., Meyer, D.: Fully coupled thermoelectromechanical analysis of GaN high electron mobility transistor degradation. J. Appl. Phys. 111, 074504 (2012)CrossRefGoogle Scholar
  42. 42.
    Qin, G., Zhang, X., Ma, S., Zhang, Q., Fan, C., Zhao, M.: An accurate computational method for analysis of electromechanical properties of structures with metal-GaN piezoelectric semiconductor contact. Comput. Mater. Sci. 152, 70–77 (2018)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanics and Engineering ScienceZhengzhou UniversityZhengzhouPeople’s Republic of China
  2. 2.School of Mechanical EngineeringZhengzhou UniversityZhengzhouPeople’s Republic of China
  3. 3.Henan Key Engineering Laboratory for Anti-fatigue Manufacturing TechnologyZhengzhou UniversityZhengzhouPeople’s Republic of China

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