SpringerLink
Log in

Surface Elastic Effects on Electromechanical Responses of a Piezoelectric Semiconducting Nanobeam

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

Piezoelectric semiconductors (PSCs) find extensive applications in modern smart electronic devices because of their dual properties of being piezoelectric and semiconductive. With the increasing demand for miniaturization of these devices, the performance of their components needs to be carefully designed and optimized, especially when reduced to nanosize. It has been shown that surface elastic properties play a substantial role in the mechanical performance of nanoscale materials and structures. Building on this understanding, the surface elastic effects, encompassing surface residual stress, surface membrane stiffness, and surface bending stiffness, are comprehensively taken into account to explore the electromechanical responses of a PSC nanobeam. Additionally, the flexoelectric effect on their responses is also systematically studied. The results of this work reveal that surface elastic properties predominantly influence mechanical performance, while the flexoelectric effect plays a more dominant role in electric-related quantities at the nanoscale. Notably, the significance of surface bending rigidity, which was often underestimated in the earlier literature, is demonstrated. Furthermore, owing to the flexoelectric effect, the linear distribution of electric potential and charge carriers along the length transforms into a nonlinear pattern. The distributions of electric potential and charge carriers across the cross section are also evidently impacted. Moreover, the size-dependent responses are evaluated. Our findings may provide valuable insights for optimizing electronic devices based on nanoscale PSCs.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Wang ZL. Progress in piezotronics and piezo-photonics. Adv Mater. 2012;24:4632–46.

    Article  CAS  PubMed  Google Scholar 

  2. Yang JS. Analysis of piezotronics semiconductor structures. Berlin: Springer Nature Switzerland AG; 2020.

    Book  Google Scholar 

  3. Song JH, Zhou J, Wang ZL. Piezoelectric and semiconducting coupled power generating process of a single ZnO belt/wire: a technology for harvesting electricity from the environment. Nano Lett. 2006;6(8):1656–62.

    Article  ADS  CAS  PubMed  Google Scholar 

  4. Kumar B, Kim SW. Energy harvesting based on semiconducting piezoelectric ZnO nanostructures. Nano Energy. 2012;1:342–55.

    Article  CAS  Google Scholar 

  5. Auld BA. Acoustic fields and waves in solids, vol. 1. New York: Wiley; 1973.

    Google Scholar 

  6. Yang WL, Hu YT, Yang JS. Transient extensional vibration in a ZnO piezoelectric semiconductor nanofiber under a suddenly applied end force. Mater Res Express. 2019;6:025902.

    Article  ADS  Google Scholar 

  7. Yang JS, Zhou HG. Amplification of acoustic waves in piezoelectric semiconductor plates. Int J Solids Struct. 2005;42:3171–83.

    Article  Google Scholar 

  8. Wang ZL. Piezotronics and piezo-phototronics. Berlin: Springer; 2012.

    Book  Google Scholar 

  9. Zhou XF, Shen B, Lyubartsev A, Zhai JW, Hedin N. Semiconducting piezoelectric heterostructures for piezo- and piezophotocatalysis. Nano Energy. 2022;96:107141.

    Article  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Fan SQ, Liang YX, **e JM, Hu YT. 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. 2017;40:82–7.

    Article  CAS  Google Scholar 

  13. Cheng RR, Zhang CL, Chen WQ, Yang JS. Piezotronic effects in the extension of a composite fiber of piezoelectric dielectrics and nonpiezoelectric semiconductors. J Appl Phys. 2018;124:064506.

    Article  ADS  Google Scholar 

  14. Ma LL, Chen WJ, Zheng Y. Flexoelectric effect at the nanoscale. In: Schmauder S, Chen CS, Chawla K, Chawla N, Chen W, Kagawa Y, editors. Handbook of mechanics of materials. Singapore: Springer; 2018. p. 1–42.

    Google Scholar 

  15. Liu C, Wu HP, Wang J. Giant piezoelectric response in piezoelectric/dielectric superlattices due to flexoelectric effect. Appl Phys Lett. 2016;109:192901.

    Article  ADS  Google Scholar 

  16. Majdoub MS, Sharma P, Cagin T. Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect. Phys Rev B. 2008;77:125424.

    Article  ADS  Google Scholar 

  17. Zhou ZD, Yang CP, Su YX, Huang R, Lin XL. Electromechanical coupling in piezoelectric nanobeams due to the flexoelectric effect. Smart Mater Struct. 2017;26:095025.

    Article  ADS  Google Scholar 

  18. Qu YL, ** F, Yang JS. Effects of mechanical fields on mobile charges in a composite beam of flexoelectric dielectrics and semiconductors. J Appl Phys. 2020;127:194502.

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  20. Zhao MH, Liu X, Fan CY, Lu CS, Wang BB. Theoretical analysis on the extension of a piezoelectric semi-conductor nanowire: effects of flexoelectricity and strain gradient. J Appl Phys. 2020;127: 085707.

    Article  ADS  CAS  Google Scholar 

  21. Zhao MH, Niu JN, Lu CS, Wang BB, Fan CY. Effects of flexoelectricity and strain gradient on bending vibration characteristics of piezoelectric semiconductor nanowires. J Appl Phys. 2021;129: 164301.

    Article  ADS  CAS  Google Scholar 

  22. Sun L, Zhang ZC, Gao CF, Zhang CL. Effect of flexoelectricity on piezotronic responses of a piezoelectric semiconductor bilayer. J Appl Phys. 2021;129:244102.

    Article  ADS  CAS  Google Scholar 

  23. Qu YL, ** F, Yang JS. Bending of a flexoelectric semiconductor plate. Acta Mech Solida Sin. 2022;35(3):434–45.

    Article  Google Scholar 

  24. Guo JY, Nie GQ, Liu JX, Zhang LL. Free vibration of a piezoelectric semiconductor plate. Eur J Mech/A Solids.2022;95:104647.

    Article  MathSciNet  Google Scholar 

  25. Gurtin ME, Murdoch AI. A continuum theory of elastic material surfaces. Arch Ration Mech Anal. 1975;57:291–323.

    Article  MathSciNet  Google Scholar 

  26. Gurtin ME, Murdoch AI. Surface stress in solids. Int J Solids Struct. 1978;14:431–40.

    Article  Google Scholar 

  27. Duan HL, Wang J, Karihaloo BL, Huang ZP. Nanoporous materials can be made stiffer than non-porous counterparts by surface modification. Acta Mater. 2006;54(11):2983–90.

    Article  ADS  CAS  Google Scholar 

  28. Ansari R, Sahmani S. Surface stress effects on the free vibration behavior of nanoplates. Int J Eng Sci. 2011;49(11):1204–15.

    Article  MathSciNet  CAS  Google Scholar 

  29. Yan Z, Jiang LY. Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-planie constraint. Proc Royal Soc A. 2012;468:3458–75.

    Article  ADS  Google Scholar 

  30. Huang DW. Size-dependent response of ultra-thin films with surface effects. Int J Solids Struct. 2008;45:568–79.

    Article  CAS  Google Scholar 

  31. Steigmann DJ, Ogden RW. Plane deformations of elastic solids with intrinsic boundary elasticity. Proc Royal Soc London A Math Phys Eng Sci. 1959;453:853–77.

    Article  MathSciNet  Google Scholar 

  32. Chhapadia P, Mohammadi P, Sharma P. Curvature-dependent surface energy and implications for nanostructures. J Mech Phys Solids. 2011;59:2103–15.

    Article  ADS  MathSciNet  Google Scholar 

  33. Mohammadi P, Sharma P. Atomistic elucidation of the effect of surface roughness on curvature-dependent surface energy, surface stress, and elasticity. Appl Phys Lett. 2012;100:133110–4.

    Article  ADS  Google Scholar 

  34. Neffati D, Kulkarni Y. Homogenization of surface energy and elasticity for highly rough surfaces. J Appl Mech. 2022;89:041004.

    Article  CAS  Google Scholar 

  35. Ban YX, Mi CW. Analytical solutions of a spherical nanoinhomogeneity under far-field unidirectional loading based on Steigmann-Ogden surface model. Math Mech Solids. 2020;25:1904–23.

    Article  MathSciNet  Google Scholar 

  36. Li XB, Mi CW. Effects of surface tension and steigmann-ogden surface elasticity on hertzian contact properties. Int J Eng Sci. 2019;145:103165.

    Article  Google Scholar 

  37. Shen SP, Hu SL. A theory of flexoelectricity with surface effect for elastic dielectrics. J Mech Phys Solids. 2010;58:665–77.

    Article  ADS  MathSciNet  CAS  Google Scholar 

  38. Liang X, Hu SL, Shen SP. Effects of surface and flexoelectricity on a piezoelectric nanobeam. Smart Mater Struct. 2014;23:035020.

    Article  ADS  CAS  Google Scholar 

  39. Xu XJ, Deng ZC, Wang B. Closed solutions for the electromechanical bending and vibration of thick piezoelectric nanobeams with surface effects. J Phys D Appl Phys. 2013;46:405302–11.

    Article  CAS  Google Scholar 

  40. Wang KF, Wang BL. Effects of surface and interface energies on the bending behavior of nanoscale multilayered beams. Physica E. 2013;54:197–201.

    Article  ADS  CAS  Google Scholar 

  41. Zhu CS, Fang XQ, Liu JX, Li HY. Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells. Eur J Mech A/Solids. 2017;66:423–32.

    Article  MathSciNet  Google Scholar 

  42. Yan Z, Jiang LY. Size-dependent bending and vibration behavior of piezoelectric nanobeams due to flexoelectricity. J Phys D Appl Phys. 2013;46:355502.

    Article  Google Scholar 

  43. Shingare KB, Kundalwal SI. Flexoelectric and surface effects on the electromechanical behavior of graphene-based nanobeams. Appl Math Model. 2020;81:70–91.

    Article  MathSciNet  Google Scholar 

  44. Mizzi CA, Marks LD. The role of surfaces in flexoelectricity. J Appl Phys. 2021;129:224102.

    Article  ADS  CAS  Google Scholar 

  45. Zhang ZC, Liang C, Wang Y, Xu RQ, Gao CF, Zhang CL. Static bending and vibration analysis of piezoelectric semiconductor beams considering surface effects. J Vibr Eng Technol. 2021;9:1789–800.

    Article  Google Scholar 

Download references

Acknowledgements

We wish to acknowledge the support of the National Natural Science Foundation of China [Grant number: 11702076], and the Natural Science Foundation of Anhui Province [Grant numbers: 2208085MA17 and 2208085ME129].

Author information

Authors and Affiliations

  1. School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China

    Aowen Bao, **aobao Li, Yuxue Pu & Chunxiao Zhan

Authors
  1. Aowen Bao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **aobao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuxue Pu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chunxiao Zhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to **aobao Li or Yuxue Pu.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bao, A., Li, X., Pu, Y. et al. Surface Elastic Effects on Electromechanical Responses of a Piezoelectric Semiconducting Nanobeam. Acta Mech. Solida Sin. (2024). https://doi.org/10.1007/s10338-023-00459-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10338-023-00459-z

Keywords

Search

Navigation