Applied Mathematics and Mechanics

, Volume 40, Issue 5, pp 591–600 | Cite as

Stress-induced potential barriers and charge distributions in a piezoelectric semiconductor nanofiber

  • Shuaiqi Fan
  • Yuantai HuEmail author
  • Jiashi Yang


The performance of a piecewise-stressed ZnO piezoelectric semiconductor nanofiber is studied with the multi-field coupling theory. The fields produced by equal and opposite forces as well as sinusoidally distributed forces are examined. Specific distributions of potential barriers, wells, and regions with effective polarization charges are found. The results are fundamental for the mechanical tuning on piezoelectric semiconductor devices and piezotronics.

Key words

ZnO nanofiber mechanical tuning multi-field coupling theory potential barrier potential well 

Chinese Library Classification


2010 Mathematics Subject Classification



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  1. [1]
    HUTSON, A. R. and WHITE, D. L. Elastic wave propagation in piezoelectric semiconductors. Journal of Applied Physics, 33, 40–47 (1962)CrossRefGoogle Scholar
  2. [2]
    WHITE, D. L. Amplification of ultrasonic waves in piezoelectric semiconductors. Journal of Applied Physics, 33, 2547–2554 (1962)CrossRefzbMATHGoogle Scholar
  3. [3]
    COLLINS, J. H., LAKIN, K. M., QUATE, C. F., and SHAW, H. J. Amplification of acoustic surface waves with adjacent semiconductor and piezoelectric crystals. Applied Physics Letters, 13, 314–316 (1968)CrossRefGoogle Scholar
  4. [4]
    WANG, Z. L. Nanobelts, nanowires, and nanodiskettes of semiconducting oxides—from materials to nanodevices. Advanced Materials, 15, 432–436 (2010)CrossRefGoogle Scholar
  5. [5]
    WEN, X. N., WU, W. Z., DING, Y., and WANG, Z. L. Piezotronic effect in flexible thin-film based devices. Advanced Materials, 25, 3371–3379 (2013)CrossRefGoogle Scholar
  6. [6]
    LEE, K. Y., KUMAR, B., SEO, J. S., KIM, K. H., SOHN, J. I., CHA, S. N., CHOI, D., WANG, Z. L., and KIM, S. W. P-type polymer-hybridized high-performance piezoelectric nanogenerators. Nano Letters, 12, 1959–1964 (2012)CrossRefGoogle Scholar
  7. [7]
    GAO, Y. F. and WANG, Z. L. Electrostatic potential in a bent piezoelectric nanowire: the fun-damental theory of nanogenerator and nanopiezotronics. Nano Letters, 7, 2499–2505 (2007)CrossRefGoogle Scholar
  8. [8]
    LU, M. P., SONG, J. H., LU, M. Y., CHEN, M. T., GAO, Y. F., CHEN, L. J., and WANG, Z. L. Piezoelectric nanogenerator using p-type ZnO nanowire arrays. Nano Letters, 9, 1223–1227 (2009)CrossRefGoogle Scholar
  9. [9]
    YANG, Q., LIU, Y., PAN, C. F., CHEN, J., WEN, X. N., and WANG, Z. L. Largely enhanced ef-ficiency in ZnO nanowire/p-polymer hybridized inorganic/organic ultraviolet light-emitting diode by piezo-phototronic effect. Nano Letters, 13, 607–613 (2013)CrossRefGoogle Scholar
  10. [10]
    WANG, X. D., ZHOU, J., SONG, J. H., LIU, J., XU, N. S., and WANG, Z. L. Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire. Nano Letters, 6, 2768–2772 (2006)CrossRefGoogle Scholar
  11. [11]
    LAO, C. S., PARK, M. C., KUANG, Q., DENG, Y. L., SOOD, A. K., POLLA, D. L., and WANG, Z. L. Giant enhancement in UV response of ZnO nanobelts by polymer surface-functionalization. Journal of the American Chemical Society, 129, 12096–12097 (2007)CrossRefGoogle Scholar
  12. [12]
    LI, P., JIN, F., and MA, J. X. One-dimensional dynamic equations of a piezoelectric semicon-ductor beam with a rectangular cross section and their application in static and dynamic char-acteristic analysis. Applied Mathematics and Mechanics (English Edition), 39(5), 685–702 (2018) Scholar
  13. [13]
    LEW-YAN-VOON, L. C. and WILLATZEN, M. Electromechanical phenomena in semiconductor nanostructures. Journal of Applied Physics, 109, 031101 (2011)CrossRefGoogle Scholar
  14. [14]
    PAN, E. Elastic and piezoelectric fields around a quantum dot: fully coupledor semicoupled model? Journal of Applied Physics, 91, 3785–3796 (2002)CrossRefGoogle Scholar
  15. [15]
    PAN, E. Elastic and piezoelectric fields in substrates GaAs (001) and GaAs (111) due to a buried quantum dot. Journal of Applied Physics, 91, 6379–6387 (2002)CrossRefGoogle Scholar
  16. [16]
    JOGAI, B., ALBRECHT, J. D., and PAN, E. Effect of electromechanical coupling on the strain in AlGaN/GaN heterojunction field effect transistors. Journal of Applied Physics, 94, 3984–3985 (2003)CrossRefGoogle Scholar
  17. [17]
    JOGAI, B., ALBRECHT, J. D., and PAN, E. Electromechanical coupling in free-standing Al-GaN/GaN planar structures. Journal of Applied Physics, 94, 6566–6573 (2003)CrossRefGoogle Scholar
  18. [18]
    LIU, Y., ZHANG, Y., YANG, Q., NIU, S. M., and WANG, Z. L. Fundamental theories of piezotronics and piezo-phototronics. Nano Energy, 14, 257–275 (2015)CrossRefGoogle Scholar
  19. [19]
    WANG, Z. L. and WU, W. Z. Piezotronics and piezo-phototronics: fundamentals and applications. National Science Review, 1, 62–90 (2014)CrossRefGoogle Scholar
  20. [20]
    GAO, Y. F. and WANG, Z. L. Electrostatic potential in a bent piezoelectric nanowire: the fun-damental theory of nanogenerator and nanopiezotronics. Nano Letters, 7, 2499–2505 (2007)CrossRefGoogle Scholar
  21. [21]
    GAO, Y. F. and WANG, Z. L. Equilibrium potential of free charge carriers in a bent piezoelectric semiconductive nanowire. Nano Letters, 9, 1103–1110 (2009)CrossRefGoogle Scholar
  22. [22]
    FAN, S. Q., LIANG, Y. X., XIE, J. M., and HU, Y. T. Exact solutions to the electromechanical quantities inside a statically-bent circular ZnO nanowire by taking into account both the piezo-electric property and the semiconducting performance: part I, linearized analysis. Nano Energy, 40, 82–87 (2017)CrossRefGoogle Scholar
  23. [23]
    LIANG, Y. X., FAN, S. Q., CHEN, X. D., and HU, Y. T. Nonlinear effect of carrier drift on the performance of an n-type ZnO nanowire nanogenerator by coupling piezoelectric effect and semiconduction. Beilstein Journal of Nanotechnology, 9, 1917–1925 (2018)CrossRefGoogle Scholar
  24. [24]
    DAI, X. Y., ZHU, F., QIAN, Z. H., and YANG, J. S. Electric potential and carrier distribution in a piezoelectric semiconductor nanowire in time-harmonic bending vibration. Nano Energy, 43, 22–28 (2017)CrossRefGoogle Scholar
  25. [25]
    ZHANG, C. L., WANG, X. Y., CHEN, W. Q., and YANG, J. S. An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force. Smart Material Structures, 26, 025030 (2016)CrossRefGoogle Scholar
  26. [26]
    ZHANG, C. L., LUO, Y. X., CHENG, R. R., and WANG, X. Y. Electromechanical fields in piezoelectric semiconductor nanofibers under an axial force. MRS Advances, 2, 3421–3426 (2017)CrossRefGoogle Scholar
  27. [27]
    CHENG, R. R., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. Piezotronic effects in the extension of a composite fiber of piezoelectric dielectrics and nonpiezoelectric semiconductors. Journal of Applied Physics, 124, 064506 (2018)CrossRefGoogle Scholar
  28. [28]
    WANG, G. L., LIU, J. X., LIU, X. L., FENG, W. J., and YANG, J. S. Extensional vibration char-acteristics and screening of polarization charges in a ZnO piezoelectric semiconductor nanofiber. Journal of Applied Physics, 124, 094502 (2018)CrossRefGoogle Scholar
  29. [29]
    YANG, W. L., HU, Y. T., and YANG, J. S. Transient extensional vibration in a ZnO piezoelec-tric semiconductor nanofiber under a suddenly applied end force. Materials Research Express, 6, 025902 (2018)CrossRefGoogle Scholar
  30. [30]
    FAN, S. Q., YANG, W. L., and HU, Y. T. Adjustment and control on the fundamental charac-teristics of a piezoelectric PN junction by mechanical-loading. Nano Energy, 52, 416–421 (2018)CrossRefGoogle Scholar
  31. [31]
    JIN, L. S., YAN, X. H., WANG, X. F., HU, W. J., ZHANG, Y., and LI, L. J. Dynamical model for piezotronic and piezo-phototronic devices under low and high frequency external compressive stresses. Journal of Applied Physics, 123, 025709 (2018)CrossRefGoogle Scholar
  32. [32]
    AULD, B. A. Acoustic Fields and Waves in Solids, John Wiley and Sons, New York (1973)Google Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanics, Hubei Key Laboratory of Engineering Structural Analysis and Safety AssessmentHuazhong University of Science and TechnologyWuhanChina
  2. 2.Department of Mechanical and Materials EngineeringUniversity of Nebraska-LincolnLincoln, NebraskaU.S.A.

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