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Electromechanical field analysis of PN junctions in bent composite piezoelectric semiconductor beams under shear forces

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Abstract

In piezotronics, PN junctions usually possess both piezoelectricity and semiconductor properties. This allows them to be manipulated mechanically by external forces through the coupling between deformation and free carriers. For a conventional non-piezoelectric PN junction, however, the mechanical manipulation seems difficult to achieve. In this paper, we theoretically demonstrate that this problem may be addressed via structural design. A composite beam model consisting of a piezoelectric dielectric layer and two non-piezoelectric PN junction layers is proposed. Then its electromechanical response under three different types of shear loads is examined based on a one-dimensional phenomenological theory. Results show as expected that the electrical behaviors of the junction can be tuned mechanically when the external force is applied on the interface, which provides a new idea for the design of piezotronic devices. Further, the effects of the doping level, thickness ratio, and material combination are also investigated, providing a comprehensive understanding of the proposed composite model.

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References

  1. Hickernell, F.S.: The piezoelectric semiconductor and acoustoelectronic device development in the sixties. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 737–745 (2005)

    Article  PubMed  Google Scholar 

  2. Gao, P.X., Song, J.H., Liu, J., Wang, Z.L.: Nanowire piezoelectric nanogenerators on plastic substrates as flexible power sources for nanodevices. Adv. Mater. 19(1), 67–72 (2007)

    Article  CAS  Google Scholar 

  3. Choi, M.Y., Choi, D., Jin, M.J., Kim, I., Kim, S.H., Choi, J.Y., Lee, S.Y., Kim, J.M., Kim, S.W.: Mechanically powered transparent flexible charge-generating nanodevices with piezoelectric ZnO nanorods. Adv. Mater. 21(21), 2185–2189 (2009)

    Article  CAS  Google Scholar 

  4. Romano, G., Mantini, G., di Carlo, A., D’Amico, A., Falconi, C., Wang, Z.L.: Piezoelectric potential in vertically aligned nanowires for high output nanogenerators. Nanotechnology 22(46), 465401 (2011)

    Article  PubMed  Google Scholar 

  5. Wang, Z.L.: Nanobelts, nanowires, and nanodiskettes of semiconducting oxides—from materials to nanodevices. Adv. Mater. 15(5), 432–436 (2003)

    Article  Google Scholar 

  6. Wang, X., Zhou, J., Song, J., Liu, J., Xu, N., Wang, Z.L.: Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire. Nano Lett. 6(12), 2768–2772 (2006)

    Article  ADS  CAS  PubMed  Google Scholar 

  7. Wang, Z.L.: Piezopotential gated nanowire devices: piezotronics and piezo-phototronics. Nano Today 5(6), 540–552 (2010)

    Article  Google Scholar 

  8. Büyükköse, S., Hernandez-Minguez, A., Vratzov, B., Somaschini, C., Geelhaar, L., Riechert, H., Van Der Wiel, W., Santos, P.: High-frequency acoustic charge transport in GaAs nanowires. Nanotechnology 25(13), 135204 (2014)

    Article  ADS  PubMed  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  10. Wen, X.N., Wu, W.Z., Ding, Y., Wang, Z.L.: Piezotronic effect in flexible thin-film based devices. Adv. Mater. 25(24), 3371–3379 (2013)

    Article  CAS  PubMed  Google Scholar 

  11. Lee, K.Y., Kumar, B., Seo, J.S., Kim, K.H., Sohn, J.I., Cha, S.N., Choi, D., Wang, Z.L., Kim, S.W.: p-Type polymer-hybridized high-performance piezoelectric nanogenerators. Nano Lett. 12(4), 1959–1964 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  12. 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)

    Article  CAS  Google Scholar 

  13. Wang, Z.L., Wu, W.Z.: Piezotronics and piezo-phototronics: fundamentals and applications. Natl. Sci. Rev. 1(1), 62–90 (2014)

    Article  MathSciNet  CAS  Google Scholar 

  14. Wang, Z.L.: Piezotronics and piezo-phototronics. Springer, Berlin (2012)

    Book  Google Scholar 

  15. Auld, B.A.: Acoustic fields and waves in solids. Pипoл Клaccик (1973)

  16. Pierret, R.F., Neudeck, G.W.: Advanced semiconductor fundamentals. Addison-Wesley, Reading (1987)

    Google Scholar 

  17. Wauer, J., Suherman, S.: Thickness vibrations of a piezo-semiconducting plate layer. Int. J. Eng. Sci. 35(15), 1387–1404 (1997)

    Article  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. 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(11–12), 3928–3938 (2007)

    Article  CAS  Google Scholar 

  21. Sladek, J., Sladek, V., Pan, E., Young, D.L.: Dynamic anti-plane crack analysis in functional graded piezoelectric semiconductor crystals. Cmes-Comput Model Eng Sci 99(4), 273–296 (2014)

    MathSciNet  Google Scholar 

  22. Sladek, J., Sladek, V., Pan, E., Wunsche, M.: Fracture analysis in piezoelectric semiconductors under a thermal load. Eng. Fract. Mech. 126, 27–39 (2014)

    Article  Google Scholar 

  23. 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)

    Article  Google Scholar 

  24. 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)

    Article  Google Scholar 

  25. 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)

    Article  MathSciNet  Google Scholar 

  26. 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(1), 37–44 (2016)

    Article  CAS  Google Scholar 

  27. Zhang, C.L., Wang, X.Y., Chen, W.Q., Yang, J.S.: Propagation of extensional waves in a piezoelectric semiconductor rod. AIP Adv. 6(4), 045301 (2016)

    Article  ADS  Google Scholar 

  28. 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(2), 025030 (2017)

    Article  ADS  Google Scholar 

  29. Cheng, R.R., Zhang, C.L., Chen, W.Q., Yang, J.S.: Piezotronic effects in the extension of a composite fiber of piezoelectric dielectrics and nonpiezoelectric semiconductors. J. Appl. Phys. 124(6), 064506 (2018)

    Article  ADS  Google Scholar 

  30. Zhang, C., Luo, Y., Cheng, R., Wang, X.: Electromechanical fields in piezoelectric semiconductor nanofibers under an axial force. MRS Advances 2(56), 3421–3426 (2017)

    Article  CAS  Google Scholar 

  31. Gao, Y., Wang, Z.L.: Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics. Nano Lett. 7(8), 2499–2505 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  32. Luo, Y.X., Zhang, C.L., Chen, W.Q., Yang, J.S.: Piezopotential in a bended composite fiber made of a semiconductive core and of two piezoelectric layers with opposite polarities. Nano Energy 54, 341–348 (2018)

    Article  CAS  Google Scholar 

  33. Fang, K., Qian, Z.H., Yang, J.S.: Piezopotential in a composite cantilever of piezoelectric dielectrics and nonpiezoelectric semiconductors produced by shear force through e(15). Mater. Res. Express 6(11), 115917 (2019)

    Article  ADS  Google Scholar 

  34. Yang, G.Y., Yang, L., Du, J.K., Wang, J., Yang, J.S.: PN junctions with coupling to bending deformation in composite piezoelectric semiconductor fibers. Int. J. Mech. Sci. 173, 105421 (2020)

    Article  Google Scholar 

  35. Luo, Y.X., Zhang, C.L., Chen, W.Q., Yang, J.S.: An analysis of PN junctions in piezoelectric semiconductors. J. Appl. Phys. 122(20), 204502 (2017)

    Article  ADS  Google Scholar 

  36. Yang, G.Y., Du, J.K., Wang, J., Yang, J.S.: Electromechanical Fields in a Nonuniform Piezoelectric Semiconductor Rod. J. Mech. Mater. Struct. 13(1), 103–120 (2018)

    Article  MathSciNet  Google Scholar 

  37. Fang, K., Qian, Z., Yang, J.: Piezopotential in a composite cantilever of piezoelectric dielectrics and nonpiezoelectric semiconductors produced by shear force through e15. Mater. Res. Express 6(11), 115917 (2019)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (12061131013, 11972276, 12172171, and 12211530064), the State Key Laboratory of Mechanics and Control of Mechanical Structures at NUAA (No. MCMS-I-0522G01), the Fundamental Research Funds for the Central Universities (NS2022011 and NE2020002), National Natural Science Foundation of Jiangsu Province (BK20211176), Local Science and Technology Development Fund Projects Guided by the Central Government (2021Szvup061), Jiangsu High-Level Innovative and Entrepreneurial Talents Introduction Plan (Shuangchuang Doctor Program, JSSCBS20210166), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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Correspondence to Zhenghua Qian.

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Appendix

Appendix

In Fig. 

Fig. 12
figure 12

Comparison of the linear analytical and nonlinear numerical results

12, it can be seen that the difference between the linearization theory derived in this paper and the nonlinear solution of COMSOL is relatively small, which can verify the correctness of the theory in this paper.

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Liu, D., Fang, K., Li, P. et al. Electromechanical field analysis of PN junctions in bent composite piezoelectric semiconductor beams under shear forces. Acta Mech 235, 1067–1082 (2024). https://doi.org/10.1007/s00707-023-03790-1

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  • DOI: https://doi.org/10.1007/s00707-023-03790-1

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