Applied Mathematics and Mechanics >
Exact multi-field coupling modeling and analysis of piezoelectric semiconductor plates
Received date: 2025-01-15
Revised date: 2025-05-20
Online published: 2025-06-30
Supported by
Project supported by the National Natural Science Foundation of China (Nos. U21A20430 and 12472155), the Science Research Project of Hebei Education Department of China (No. BJK2022055), the “333 Talents Project” of Hebei Province of China (No. C20231111), the Natural Science Foundation of Hebei Province of China (Nos. A2024210002 and A2023210064), and the S&T Program of Hebei Province of China (No. 225676162GH)
Copyright
This study aims to present exact multi-field coupling modeling and analysis of a simply-supported rectangular piezoelectric semiconductor (PSC) plate. Under the linear assumption of drift-diffusion current for a small electron concentration perturbation, the governing equations are solved by extending the classical Stroh formalism to involve all the physical fields of PSCs. The general solutions are obtained and then utilized to analyze three-dimensional (3D) problems of static deformation and free vibration of the PSC plate. To investigate the multi-physics interactions along the plate thickness, the distribution forms of electromechanical fields and electron concentration perturbation are given exactly, which are helpful for the development of the PSC plate theory. The differences between the PSC and purely piezoelectric as well as purely elastic counterparts are emphasized, in the context of evaluating the material performances with changing initial electron concentration. The results demonstrate that the PSC coupling exists only within a specific range of the initial electron concentration, where it exhibits a transition from the piezoelectric characteristics to the elastic ones. In addition, the dependence of coupling behaviors on the plate thickness is clarified. These results can not only be benchmarks in the development of PSC plate theories or other numerical methods, but also be guidance for the design of plate-based PSC devices.
Lele ZHANG , Zheng ZHAO , Xiaofan HU , Guoquan NIE , Jinxi LIU . Exact multi-field coupling modeling and analysis of piezoelectric semiconductor plates[J]. Applied Mathematics and Mechanics, 2025 , 46(7) : 1331 -1346 . DOI: 10.1007/s10483-025-3272-7
| [1] | HUTSON, A. R. Piezoelectricity and conductivity in ZnO and CdS. Physical Review Letters, 4, 505–507 (1960) |
| [2] | FAN, J. C., SREEKANTH, K. M., XIE, Z., CHANG, S. L., and RAO, K. V. p-type ZnO materials: theory, growth, properties and devices. Progress in Materials Science, 58(6), 874–985 (2013) |
| [3] | TEO, K. H., ZHANG, Y. H., CHOWDHURY, N., RAKHEJA, S., MA, R., XIE, Q. Y., YAGYU, E., YAMANAKA, K., LI, K. X., and PALACIOS, T. Emerging GaN technologies for power, RF, digital, and quantum computing applications: recent advances and prospects. Journal of Applied Physics, 130(16), 160902 (2021) |
| [4] | YANG, Q., WANG, W. H., XU, S., and WANG, Z. L. Enhancing light emission of ZnO microwire-based diodes by piezo-phototronic effect. Nano Letters, 11(9), 4012–4017 (2011) |
| [5] | ZHOU, J., GU, Y. D., FEI, P., MAI, W. J., GAO, Y. F., YANG, R. S., BAO, G., and WANG, Z. L. Flexible piezotronic strain sensor. Nano Letters, 8(9), 3035–3040 (2008) |
| [6] | HICKERNELL, F. S. The piezoelectric semiconductor and acoustoelectronic device development in the sixties. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 52(5), 737–745 (2005) |
| [7] | HE, F., LI, W. Q., LIU, B. B., ZHONG, Y., JIN, Q. F., and QIN, X. J. Progress of piezoelectric semiconductor nanomaterials in sonodynamic cancer therapy. ACS Biomaterials Science & Engineering, 10(1), 298–312 (2023) |
| [8] | WANG, L. F. and WANG, Z. L. Advances in piezotronic transistors and piezotronics. Nano Today, 37, 101108 (2021) |
| [9] | ROZAS, G., PASCUAL WINTER, M. F., FAINSTEIN, A., JUSSERAND, B., VACCARO, P. O., SARAVANAN, S., and SAITO, N. Piezoelectric semiconductor acoustic cavities. Physical Review B, 72(3), 035331 (2005) |
| [10] | VOON, L. C. L. Y. and WILLATZEN, M. Electromechanical phenomena in semiconductor nanostructures. Journal of Applied Physics, 109(3), 031101 (2011) |
| [11] | YANG, J. S. Analysis of Piezoelectric Semiconductor Structures, Springer Nature, Switzerland (2020) |
| [12] | WANG, Z. L. and WU, W. Z. Piezotronics and piezo-phototronics: fundamentals and applications. National Science Review, 1(1), 62–90 (2014) |
| [13] | WANG, Z. L., ZHANG, Y., and HU, W. G. Piezotronics and Piezo-phototronics, Springer, Berlin (2012) |
| [14] | LI, P., JIN, F., and MA, J. X. One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis. Applied Mathematics and Mechanics (English Edition), 39(5), 685–702 (2018) https://doi.org/10.1007/s10483-018-2325-6 |
| [15] | ZHANG, C. L., WANG, X. Y., CHEN, W. Q., and YANG, J. S. Bending of a cantilever piezoelectric semiconductor fiber under an end force. Generalized Models and Non-classical Approaches in Complex Materials, Springer, 261–278 (2018) |
| [16] | LIANG, Y. X., YANG, W. L., and YANG, J. S. Transient bending vibration of a piezoelectric semiconductor nanofiber under a suddenly applied shear force. Acta Mechanica Solida Sinica, 32, 688–697 (2019) |
| [17] | LUO, Y. X., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. Piezotronic effect of a thin film with elastic and piezoelectric semiconductor layers under a static flexural loading. Journal of Applied Mechanics, 86(5), 051003 (2019) |
| [18] | QU, Y. L., JIN, F., and YANG, J. S. Stress-induced electric potential barriers in thickness-stretch deformations of a piezoelectric semiconductor plate. Acta Mechanica, 232, 4533–4543 (2021) |
| [19] | CAO, Y., GUO, Z. W., and QU, Y. L. Static bending and forced vibration analyses of a piezoelectric semiconductor cylindrical shell within first-order shear deformation theory. Applied Mathematical Modelling, 126, 625–645 (2024) |
| [20] | WANG, T. Y., ZHU, F., LI, P., XU, Z. L., MA, T. F., KUZNETSOVA, I., and QIAN, Z. H. Analysis and modeling of two-dimensional piezoelectric semiconductor shell theory. European Journal of Mechanics-A/Solids, 106, 105331 (2024) |
| [21] | GUO, Z. W., CHEN, J. B., ZHANG, G. Y., MI, C. W., and QU, Y. L. Exact solutions for plane stress problems of piezoelectric semiconductors: tuning free-carrier motions by various mechanical loadings. European Journal of Mechanics-A/Solids, 101, 105073 (2023) |
| [22] | ZHU, J. Y., NEGAHBAN, M., XU, J., XIA, R. Y., and LI, Z. Theoretical analysis of piezoelectric semiconductor thick plates with periodic boundary conditions. Micromachines, 14(12), 2174 (2023) |
| [23] | PAN, E. N. and CHEN, W. Q. Static Green's Functions in Anisotropic Media, Cambridge University Press, New York (2015) |
| [24] | KUO, H. Y., SHIH, C. L., and PAN, E. N. Enhancing magnetoelectric effect in magneto-electro-elastic laminated composites via interface modulus and stress. International Journal of Solids and Structures, 195, 66–73 (2020) |
| [25] | TIAN, R., LIU, J. X., PAN, E. N., WANG, Y. S., and SOH, A. K. Some characteristics of elastic waves in a piezoelectric semiconductor plate. Journal of Applied Physics, 126(12), 125701 (2019) |
| [26] | HUTSON, A. R. and WHITE, D. L. Elastic wave propagation in piezoelectric semiconductors. Journal of Applied Physics, 33, 40–47 (1962) |
| [27] | WHITE, D. L. Amplification of ultrasonic waves in piezoelectric semiconductors. Journal of Applied Physics, 33, 2547–2554 (1962) |
| [28] | TING, T. C. T. Anisotropic Elasticity, Oxford University Press, New York (1996) |
| [29] | PAN, E. Exact solution for simply supported and multilayered magneto-electro-elastic plates. Journal of Applied Mechanics, 68(4), 608–618 (2001) |
| [30] | PAN, E. and HEYLIGER, P. R. Free vibrations of simply supported and multilayered magneto-electro-elastic plates. Journal of Sound and Vibration, 252(3), 429–442 (2002) |
| [31] | VATTRé, A. and PAN, E. Dislocation singularities in layered magneto-electro-elastic plates. International Journal of Engineering Science, 181, 103765 (2022) |
| [32] | KUO, H. Y. and CHUNG, C. Y. Multiferroic laminated composites with interfacial imperfections and the nonlocal effect. Composite Structures, 287, 115235 (2022) |
| [33] | STROH, A. N. Dislocations and cracks in anisotropic elasticity. Philosophical Magazine, 3(30), 625–646 (1958) |
| [34] | HUANG, H. Y., ZHU, F., ZHU, J. Q., WANG, B., and QIAN, Z. H. A general approach for dispersion relations in multilayered structures with an arbitrary number of piezoelectric layers and elastic layers. Acta Mechanica, 231, 489–502 (2020) |
| [35] | PAN, E. and HEYLIGER, P. R. Exact solutions for magneto-electro-elastic laminates in cylindrical bending. International Journal of Solids and Structures, 40(24), 6859–6876 (2003) |
| [36] | HE, Q. L., ZHU, C. S., HAN, B. H., FANG, X. Q., and LIU, J. X. Size-dependent free vibration of piezoelectric semiconductor plate. Acta Mechanica, 234(10), 4821–4836 (2023) |
| [37] | ZHANG, Q. Y., LI, M. E., and ZHAO, M. H. Dynamic analysis of a piezoelectric semiconductor nanoplate with surface effect. Materials Today Communications, 33, 104406 (2022) |
| [38] | LI, M. G., ZHANG, Q. Y., WANG, B. B., and ZHAO, M. H. Analysis of flexural vibrations of a piezoelectric semiconductor nanoplate driven by a time-harmonic force. Materials, 14(14), 3926 (2021) |
| [39] | FANG, X. Q., HE, Q. L., MA, H. W., and ZHU, C. S. Multi-field coupling and free vibration of a sandwiched functionally-graded piezoelectric semiconductor plate. Applied Mathematics and Mechanics (English Edition), 44(8), 1351–1366 (2023) https://doi.org/10.1007/s10483-023-3017-6 |
| [40] | QU, Y. L., JIN, F., and YANG, J. S. Buckling of a Reissner-Mindlin plate of piezoelectric semiconductors. Meccanica, 57(11), 2797–2807 (2022) |
| [41] | HEYLIGER, P. R., RAMIREZ, F., and PAN, E. Two-dimensional static fields in magnetoelectroelastic laminates. Journal of Intelligent Material Systems and Structures, 15, 689–709 (2004) |
| [42] | GUO, J. Y., NIE, G. Q., LIU, J. X., and ZHANG, L. L. Free vibration of a piezoelectric semiconductor plate. European Journal of Mechanics-A/Solids, 95, 104647 (2022) |
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