Skip to main content
SpringerLink
Log in

Effects of mechanical loadings on the performance of a piezoelectric hetero-junction

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A fully-coupled model for a piezoelectric hetero-junction subjected to a pair of stresses is proposed by discarding the depletion layer approximation. The effect of mechanical loadings on PN junction performance is discussed in detail. Numerical examples are carried out for a p-Si/ZnO-n hetero-junction under a pair of stresses acting on the n-type ZnO portion near the PN interface, where ZnO has the piezoelectric property while Si is not. It is found that the bottom of conduction band is lowered/raised near the two loading points due to the decrease/increase in the electron potential energy there induced by a tensile-stress mode via sucking in majority-carriers from two outside regions, which implies appearance of a potential barrier and a potential well near two loading points. Furthermore, the barrier height and well depth gradually become large with increasing tensile stress such that more and more electrons/holes are inhaled in loading region from the n-/p-zone, respectively. Conversely, rising/dropping of conduction band bottom is brought out near the two loading points by a compressive-stress mode due to the increase/decrease in the potential energy of electrons by pumping out the majority-carriers from the loading region to the two outside regions. Therefore, a potential well and a potential barrier are induced near the two loading points, such that more and more electrons/holes are driven away from the loading region to the n-zone/p-zone, respectively, with the increasing compressive stress. These effects are important to tune the carrier recombination rate near the PN interface. Thus, the present study possesses great referential significance to piezotronic devices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. WANG, Z. L. Piezotronics and Piezo-phototronics, The Science Publishing Company, Beijing (2014)

    Google Scholar 

  2. ZHU, G., YANG, R. S., WANG, S. H., and WANG Z. L. Flexible high-output nanogenerator based on lateral ZnO nanowire array. Nano Letters, 10, 3151–3155 (2010)

    Article  Google Scholar 

  3. WANG, L. F. and WANG, Z. L. Advances in piezotronic transistors and piezotronics. Nano Today, 37, 101108 (2021)

    Article  Google Scholar 

  4. GAO, Y. F. and WANG, Z. L. Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotrionics. Nano Letters, 7, 2499–2505 (2007)

    Article  Google Scholar 

  5. FALCONI, C. Piezoelectric nanotransducers. Nano Energy, 59, 730–744 (2019)

    Article  Google Scholar 

  6. ZHANG, Y., LIU, Y., and WANG, Z. L. Fundamental theory of piezotronics. Advanced Materials, 23, 3004–3013 (2011)

    Article  Google Scholar 

  7. PENG, Y. Y., QUE, M. L., LEE, H. E., BAO, R. R., WANG, X. D., LU, J. F., YUAN, Z. Q., LI, X. Y., TAO, J., SUN, J. L., ZHAI, J. Y., LEE, K. J., and PAN, C. F. Achieving high-resolution pressure mapping via flexible GaN/ZnO nanowire LEDs array by piezo-phototronic effect. Nano Energy, 58, 633–640 (2019)

    Article  Google Scholar 

  8. JIANG, C. Y., JING, L., HUANG, X., LIU, M. M., DU, C. H., LIU, T., PU, X., HU, W. G., and WANG, Z. L. Enhanced solar cell conversion efficiency of InGaN/GaN multiple quantum wells by piezo-phototronic effect. ACS Nano, 11, 9405–9412 (2017)

    Article  Google Scholar 

  9. ZHANG, Y., YANG, Y., and WANG, Z. L. Piezo-phototronics effect on nano/microwire solar cells. Energy and Environmental Science, 5, 6850–6856 (2012)

    Article  Google Scholar 

  10. WU, W. Z. and WANG, Z. L. Piezotronic nanowire-based resistive switches as programmable electromechanical memories. Nano Letters, 11, 2779–2785, (2011)

    Article  Google Scholar 

  11. PIERRET, R. F. Semiconductor Fundamentals, Addison-Wesley, New Jersey (1988)

    Google Scholar 

  12. SU, Z., LI, H. P., CHEN, P., HU, S. Y., and YAN, Y. W. Novel heterostructured InN/TiO2 submicron fibers designed for high performance visible-light-driven photocatalysis. Catalysis Science and Technology, 7, 5105 (2017)

    Article  Google Scholar 

  13. ZHANG, Y. M., HU, G. W., ZHANG, Y., LUCY, L., MORTENN, W., and WANG, Z. L. High performance piezotronic devices based on non-uniform strain. Nano Energy, 60, 649–655 (2019)

    Article  Google Scholar 

  14. FENG, X. Y., ZHANG, Y., and WANG, Z. L. Theoretical study of piezotronic heterojunction. Science China Technological Sciences, 56, 2615–2621 (2013)

    Article  Google Scholar 

  15. LAN, F. F., CHEN, Y. D., ZHU, J. Q., LU, Q. X., JIANG, C., HAO, S. F., CAO, X., WANG, N., and WANG, Z. L. Piezotronically enhanced detection of protein kinases at ZnO micro/nanowire heterojunctions. Nano Energy, 69, 104330 (2020)

    Article  Google Scholar 

  16. ZHU, L. P. and WANG, Z. L. Piezotronic effect on Rashba spin-orbit coupling based on MAPbI3/ZnO heterostructures. Applied Physics Letters, 117, 071601 (2020)

    Article  Google Scholar 

  17. CHEN, L., WANG, B. Y., DONG, J. Q., GAO, F. L., ZHENG, H. W., HE, M., and WANG, X. F. Insights into the pyro-phototronic effect in p-Si/n-ZnO nanowires heterojunction toward high-performance near-infrared photosensing. Nano Energy, 78, 105260 (2020)

    Article  Google Scholar 

  18. WANG, Q. Y., QIU, Y., YANG, D. C., LI, B., ZHANG, X. T., TANG, Y., and ZHANG, H. Q. Improvement in piezoelectric performance of a ZnO nanogenerator by modulating interface engineering of CuO-ZnO heterojunction. Applied Physics Letters, 113, 053901 (2018)

    Article  Google Scholar 

  19. HUANG, K. and HAN, R. Q. The Physical Basis of Semiconductors, The Science Publishing Company, Beijing (2015)

    Google Scholar 

  20. YANG, W. L., LIU, J. X., XU, Y. L., and HU, Y. T. A full-coupling model of PN junctions based on the global-domain carrier motions with inclusion of the two metal/semiconductor contacts at endpoints. Applied Mathematics and Mechanics (English Edtion), 41(6), 845–858 (2020) https://doi.org/10.1007/s10483-020-2617-9

    Article  MathSciNet  Google Scholar 

  21. YANG, W. L., LIU, J. X., and HU, Y. T. Mechanical tuning methodology on the barrier configuration near a piezoelectric PN interface and the regulation mechanism on I — V characteristics of the junction. Nano Energy, 81, 105581 (2021)

    Article  Google Scholar 

  22. LUO, Y. X., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. An analysis of PN junctions in piezoelectric semiconductors. Journal of Applied Physics, 122, 204502 (2017)

    Article  Google Scholar 

  23. GUO, M. K., LU, C. S., QIN, G. S., and ZHAO, M. H. Temperature gradient-dominated electrical behaviours in a piezoelectric PN junction. Journal of Electronic Materials, 50, 947–953 (2021)

    Article  Google Scholar 

  24. GUO, M. K., LI, Y., QIN, G. S., and ZHAO, M. H. Nonlinear solutions of PN junctions of piezoelectric semiconductors. Acta Mechanica, 230, 1825–1841 (2019)

    Article  MathSciNet  Google Scholar 

  25. CHENG, R. R., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. Temperature effects on PN junctions in piezoelectric semiconductor fibers with thermoelastic and pyroelectric couplings. Journal of Electronic Materials, 49, 3140–3148 (2020)

    Article  Google Scholar 

  26. REN, C., WANG, K. F., and WANG, B. L. Analysis of piezoelectric PN homojunction and heterojunction considering flexoelectric effect and strain gradient. Journal of Physics D: Applied Physics, 54, 495102 (2021)

    Article  Google Scholar 

  27. FANG, K., LI, P., and QIAN, Z. H. Static and dynamic analysis of a piezoelectric semiconductor cantilever under consideration of flexoelectricity and strain gradient elasticity. Acta Mechanica Solida Sinica, 34, 673–686 (2021)

    Article  Google Scholar 

  28. ZHAO, M. H., LIU, X., FAN, C. Y., LU, C. S., and WANG, B. B. Theoretical analysis on the extension of a piezoelectric semi-conductor nanowire: effects of flexoelectricity and strain gradient. Journal of Applied Physics, 127, 085707 (2020)

    Article  Google Scholar 

  29. QU, Y. L., JIN, F., and YANG, J. S. Effects of mechanical fields on mobile charges in a composite beam of flexoelectric dielectrics and semiconductors. Journal of Applied Physics, 127, 194502 (2020)

    Article  Google Scholar 

  30. QU, Y. L., JIN, F., and YANG, J. S. Bending of a flexoelectric semiconductors plate. Acta Mechanica Solida Sinica (2022) https://doi.org/10.1007/s10338-021-00296-y

  31. SUN, L., ZHU, L. F., ZHANG, C. L., CHEN, W. Q., and WANG, Z. L. Mechanical manipulation of silicon-based schottky diodes via flexoelectricity. Nano Energy, 83, 105855 (2021)

    Article  Google Scholar 

  32. WANG, L. F., LIU, S. H., FENG, X. L., ZHANG, C. L., ZHU, L. P., ZHAI, J. Y., QIN, Y., and WANG, Z. L. Flexoelectronics of centrosymmetric semiconductors. Nature Nanotechnology, 15, 661–667 (2020)

    Article  Google Scholar 

  33. ZHANG, J. Small-scale effects on the piezopotential properties of tapered gallium nitride nanowires: the synergy between surface and flexoelectric effects. Nano Energy, 79, 105489 (2021)

    Article  Google Scholar 

  34. LEE, K. Y., BAE, J., KIM, S. M., LEE, J. H., YOON, G. C., GUPTA, M. K., KIM, S. J., KIM, H., PARK, J. J., and KIM, S. W. Depletion width engineering via surface modification for high performance semiconducting piezoelectric nanogenerators. Nano Energy, 8, 165–173 (2014)

    Article  Google Scholar 

  35. 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)

    Article  Google Scholar 

  36. YANG, W. L., HU, Y. T., and PAN, E. Tuning electronic energy band in a piezoelectric semiconductor rod via mechanical loading. Nano Energy, 66, 104147 (2019)

    Article  Google Scholar 

  37. ZHANG, C. L., LUO, Y. X., CHENG, R. R., and YANG, J. S. Electromechanical fields in piezoelectric semiconductor nanofibers under an axial force. MRS Advances, 2, 3421–3426 (2017)

    Article  Google Scholar 

  38. LIU, E. K., ZHU, B. S., and LUO, J. S. The Physics of Semiconductors, Publishing House of Electronics Industry, Beijing (2014)

    Google Scholar 

  39. SZE, S. M. and KWOK, K. N. Physics of Semiconductor Devices, John Wiley & Sons, New Jersey (2007)

    Google Scholar 

  40. OHTOMOA, A. and KAWASAKI, M. Structure and optical properties of ZnO/Mg0.2Zn0.8O superlattices. Applied Physics Letters, 75, 980–982 (1999)

    Article  Google Scholar 

  41. FANG, Y. J., SHA, J., WANG, Z. L., WAN, Y. T., XIA, W. W., and WANG, Y. W. Behind the change of the photoluminescence property of metal-coated ZnO nanowire arrays. Applied Physics Letters, 98, 033103 (2011)

    Article  Google Scholar 

Download references

Funding

Project supported by the National Natural Science Foundation of China (Nos. 11972164 and 12102141)

Author information

Authors and Affiliations

  1. Department of Mechanics, School of Aerospace Engineering, Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Huazhong University of Science and Technology, Wuhan, 430074, China

    Wanli Yang, Renzhong Hong & Yuantai Hu

  2. Department of Microelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yunbo Wang

Authors
  1. Wanli Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Renzhong Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yunbo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuantai Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yunbo Wang or Yuantai Hu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, W., Hong, R., Wang, Y. et al. Effects of mechanical loadings on the performance of a piezoelectric hetero-junction. Appl. Math. Mech.-Engl. Ed. 43, 615–626 (2022). https://doi.org/10.1007/s10483-022-2848-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-022-2848-7

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation