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Transient Bending Vibration of a Piezoelectric Semiconductor Nanofiber Under a Suddenly Applied Shear Force

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Abstract

We study transient bending vibration of a ZnO piezoelectric semiconductor nanofiber fixed at one end with a suddenly applied shear force at the other end. A one-dimensional model based on the phenomenological theory of piezoelectric semiconductors consisting of the equations of piezoelectricity coupled to the continuity equation of electrons is used. An approximate theoretical analysis is performed, accompanied by a finite element analysis using COMSOL. The evolutions of deflection, electric potential and electron distribution are calculated and examined. It is found that when the fiber reaches its largest deflection, the distributions of the electromechanical fields are qualitatively similar to those in the case of static loading under the same shear force, but the amplitudes of the fields are about twice as large roughly.

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References

  1. Hickernell FS. The piezoelectric semiconductor and acoustoelectronic device development in the sixties. IEEE Trans Ultrason Ferroelectr Freq Control. 2005;52(5):737–45.

    Google Scholar 

  2. Wang ZL. Nanobelts, nanowires, and nanodiskettes of semiconducting oxides-from materials to nanodevices. Adv Mater. 2003;15(5):432–6.

    Google Scholar 

  3. Wen XN, Wu WZ, Ding Y, Wang ZL. Piezotronic Effect in Flexible Thin-film Based Devices. Adv Mater. 2013;25(24):3371–9.

    Google Scholar 

  4. Lee KY, Kumar B, Seo JS, Kim KH, Sohn JI, Cha SN, Choi D, Wang ZL, Kim SW. P-type polymer-hybridized high-performance piezoelectric nanogenerators. Nano Lett. 2012;12(4):1959–64.

    Google Scholar 

  5. Gao PX, Song JH, Liu J, Wang ZL. Nanowire piezoelectric nanogenerators on plastic substrates as flexible power sources for nanodevices. Adv Mater. 2007;19(1):67–72.

    Google Scholar 

  6. Choi MY, Choi D, Jin MJ, Kim I, Kim SH, Choi JY, Lee SY, Kim JM, Kim SW. Mechanically powered transparent flexible charge-generating nanodevices with piezoelectric ZnO nanorods. Adv Mater. 2009;21(21):2185–9.

    Google Scholar 

  7. Romano G, Mantini G, Garlo AD, D’Amico A, Falconi C, Wang ZL. Piezoelectric potential in vertically aligned nanowires for high output nanogenerators. Nanotechnology. 2011;22(46):465401.

    Google Scholar 

  8. Wang XD, Zhou J, Song JH, Liu J, Xu NS, Wang ZL. Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire. Nano Lett. 2006;6(12):2768–72.

    Google Scholar 

  9. Wang ZL. Piezopotential gated nanowire devices: piezotronics and piezo-phototronics. Nano Today. 2010;5(6):540–52.

    Google Scholar 

  10. Buyukkose S, Hern’andez-M’ınguez A, Vratzov B, Somaschini C, Geelhaar L, Riechert H, Wilfred W, Santos P. High-frequency acoustic charge transport in GaAs nanowires. Nanotechnology. 2014;25(13):135204.

    Google Scholar 

  11. Yu J, Ippolito SJ, Wlodarski W, Strano M, Kalantar-Zadeh K. Nanorod based Schottky contact gas sensors in reversed bias condition. Nanotechnology. 2010;21(26):265502.

    Google Scholar 

  12. Lew Yan Voon LC, Willatzen M. Electromechanical phenomena in semiconductor nanostructures. J Appl Phys. 2011;109(3):3.

    Google Scholar 

  13. Liu Y, Zhang Y, Yang Q, Niu SM, Wang ZL. Fundamental theories of piezotronics and piezo-phototronics. Nano Energy. 2015;14:257–75.

    Google Scholar 

  14. Wang ZL, Wu WZ. Piezotronics and piezo-phototronics: fundamentals and applications. Natl Sci Rev. 2013;1(1):62–90.

    MathSciNet  Google Scholar 

  15. Pierret RF. Semiconductor fundamentals. Reading: Addison-Wesley; 1988.

    Google Scholar 

  16. Zhang CL, Wang XY, Chen WQ, Yang JS. An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force. Smart Mater Struct. 2017;26(2):025030.

    Google Scholar 

  17. Zhang CL, Luo YX, Cheng RR, Wang XY. Electromechanical fields in piezoelectric semiconductor nanofibers under an axial force. MRS Adv. 2017;2(56):3421–6.

    Google Scholar 

  18. Araneo R, Lovat G, Burghignoli P, Falconi C. Piezo-semiconductive quasi-1D nanodevices with or without anti-symmetry. Adv Mater. 2012;24(34):4719–24.

    Google Scholar 

  19. Gao YF, Wang ZL. Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics. Nano Lett. 2007;7(8):2499–505.

    Google Scholar 

  20. Gao YF, Wang ZL. Equilibrium potential of free charge carriers in a bent piezoelectric semiconductive nanowire. Nano Lett. 2009;9(3):1103–10.

    Google Scholar 

  21. Fan SQ, Liang YX, Xie JM, Hu YT. Exact solutions to the electromechanical quantities inside a staticallybent circular ZnO nanowire by taking into account both the piezoelectric property and the semiconducting performance: part I-Linearized analysis. Nano Energy. 2017;40:82–7.

    Google Scholar 

  22. Zhang CL, Wang XY, Chen WQ, Yang JS. Bending of a cantilever piezoelectric semiconductor fiber under an end force. In: Generalized models and non-classical approaches in complex materials 2. Cham: Springer; 2018. p. 261–78.

    Google Scholar 

  23. Liang YX, Fan SQ, Chen XD, Hu YT. Nonlinear effect of carrier drift on the performance of an n-type ZnO nanowire nanogenerator by coupling piezoelectric effect and semiconduction. Beilstein J Nanotechnol. 2018;9(1):1917–25.

    Google Scholar 

  24. Wang KF, Wang BL. Electrostatic potential in a bent piezoelectric nanowire with consideration of size-dependent piezoelectricity and semiconducting characterization. Nanotechnology. 2018;29(25):255405.

    Google Scholar 

  25. Zhang CL, Wang XY, Chen WQ, Yang JS. Propagation of extensional waves in a piezoelectric semiconductor rod. AIP Adv. 2016;6(4):045301.

    Google Scholar 

  26. Dai XY, Zhu F, Qian ZH, Yang JS. Electric potential and carrier distribution in a piezoelectric semiconductor nanowire in time-harmonic bending vibration. Nano Energy. 2018;43:22–8.

    Google Scholar 

  27. Jin LS, Yan XH, Wang XF, Hu WJ, Zhang Y, Li LJ. Dynamic model for piezotronic and piezo-phototronic devices under low and high frequency external compressive stresses. J Appl Phys. 2018;123(2):025709.

    Google Scholar 

  28. Wang GL, Liu JX, Liu XL, Feng WJ, Yang JS. Extensional vibration characteristics and screening of polarization charges in a ZnO piezoelectric semiconductor nanofiber. J Appl Phys. 2018;124(9):094502.

    Google Scholar 

  29. Yang WL, Hu YT, Yang JS. Transient extensional vibration in a ZnO piezoelectric semiconductor nanofiber under a suddenly applied end force. Mater Res Exp. 2018;6(2):025902.

    Google Scholar 

  30. Auld BA. Acoustic fields and waves in solids, vol. I. New York: Wiley; 1973.

    Google Scholar 

  31. Wauer J, Suherman S. Thickness vibrations of a piezo-semiconducting plate layer. Int J Eng Sci. 1997;35(15):1387–404.

    MATH  Google Scholar 

  32. Li P, Jin F, Yang JS. Effects of semiconduction on electromechanical energy conversion in piezoelectrics. Smart Mater Struct. 2015;24(2):025021.

    Google Scholar 

  33. Gokhale VJ, Rais-Zadeh M. Phonon-electron interactions in piezoelectric semiconductor bulk acoustic wave resonators. Sci Rep. 2014;4:5617.

    Google Scholar 

  34. Collet B. Acoustic wave propagation in cubic piezoelectric semiconductor plates. J Acoust Soc Am. 2008;123(5):3694.

    Google Scholar 

  35. Gu CL, Jin F. Shear-horizontal surface waves in a half-space of piezoelectric semiconductors. Philos Mag Lett. 2015;95(2):92–100.

    MathSciNet  Google Scholar 

  36. Sharma JN, Sharma KK, Kumar A. Surface waves in a piezoelectric-semiconductor composite structure. Int J Solids Struct. 2010;47(6):816–26.

    MATH  Google Scholar 

  37. Yang JS. An anti-plane crack in a piezoelectric semiconductor. Int J Fract. 2005;136(1):27–32.

    Google Scholar 

  38. Hu YT, Zeng Y, Yang JS. A mode III crack in a piezoelectric semiconductor of crystals with 6 mm symmetry. Int J Solids Struct. 2007;44(11–12):3928–38.

    MATH  Google Scholar 

  39. Sladek J, Sladek V, Pan E, Young DL. Dynamic anti-plane crack analysis in functional graded piezoelectric semiconductor crystals. CMES. 2014;99(4):273–96.

    MathSciNet  MATH  Google Scholar 

  40. Sladek J, Sladek V, Pan E, Münsche M. Fracture analysis in piezoelectric semiconductors under a thermal load. Eng Fract Mech. 2014;126:27–39.

    Google Scholar 

  41. Zhao MH, Pan YB, Fan CY, Xu CT. Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors. Int J Solids Struct. 2017;94–95(5):50–9.

    Google Scholar 

  42. Fan CY, Yan Y, Xu GT, Zhao MH. Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method. Eng Fract Mech. 2016;165:183–96.

    Google Scholar 

  43. Yang JS, Song YC, Soh AK. Analysis of a circular piezoelectric semiconductor embedded in a piezoelectric semiconductor substrate. Arch Appl Mech. 2006;76(7–8):381–90.

    MATH  Google Scholar 

  44. Luo YX, Zhang CL, Chen WQ, Yang JS. An analysis of PN junctions in piezoelectric semiconductors. J Appl Phys. 2017;122(20):204502.

    Google Scholar 

  45. Yang GY, Du JK, Wang J, Yang JS. Electromechanical fields in a nonuniform piezoelectric semiconductor rod. J Mech Mater Struct. 2018;13(1):103–20.

    MathSciNet  Google Scholar 

  46. Fan SQ, Yang WL, Hu YT. Adjustment and control on the fundamental characteristics of a piezoelectric PN junction by mechanical-loading. Nano Energy. 2018;52:416–21.

    Google Scholar 

  47. Luo YX, Cheng RR, Zhang CL, Chen WQ, Yang JS. Electromechanical fields near a circular PN junction between two piezoelectric semiconductors. Acta Mech Solida Sin. 2018;31(2):127–40.

    Google Scholar 

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Correspondence to Jiashi Yang.

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Liang, Y., Yang, W. & Yang, J. Transient Bending Vibration of a Piezoelectric Semiconductor Nanofiber Under a Suddenly Applied Shear Force. Acta Mech. Solida Sin. 32, 688–697 (2019). https://doi.org/10.1007/s10338-019-00109-3

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  • DOI: https://doi.org/10.1007/s10338-019-00109-3

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