Applied Mathematics and Mechanics >
Lamb waves in multilayered piezoelectric semiconductor plates
Received date: 2025-04-02
Revised date: 2025-06-28
Online published: 2025-07-28
Supported by
Project supported by the National Natural Science Foundation of China (Nos. U21A20430 and 12302202), the Hebei Natural Science Foundation of China (No. A2023210040), the Science and Technology Project of Hebei Education Department of China (No. BJ2025005), and the Hebei Provincial Department of Human Resources and Social Security of China (No. C20220324)
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In this paper, we theoretically study the Lamb wave in a multilayered piezoelectric semiconductor (PSC) plate, where each layer is an n-type PSC with the symmetry of transverse isotropy. Based on the extended Stroh formalism and dual-variable and position (DVP) method, the general solution of the coupled fields for the Lamb wave is derived, and then the dispersion equation is obtained by the application of the boundary conditions. First, the influence of semiconducting properties on the dispersion behavior of the Lamb wave in a single-layer PSC plate is analyzed. Then, the propagation characteristics of the Lamb wave in a sandwich plate are investigated in detail. The numerical results show that the wave speed and attenuation depend on the stacking sequence, layer thickness, and initial carrier density, the Lamb wave can propagate without a cut-off frequency in both the homogeneous and multilayer PSC plates due to the semiconducting properties, and the Lamb wave without attenuation can be achieved by carefully selecting the semiconductor property in the upper and lower layers. These new features could be very helpful as theoretical guidance for the design and performance optimization of PSC devices.
Ru TIAN , Lisha YI , Guoquan NIE , Jinxi LIU , Ernian PAN , Yuesheng WANG . Lamb waves in multilayered piezoelectric semiconductor plates[J]. Applied Mathematics and Mechanics, 2025 , 46(8) : 1493 -1510 . DOI: 10.1007/s10483-025-3287-6
| [1] | HUTSON, A. R. Piezoelectricity and conductivity in ZnO and CdS. Physical Review Letters, 4(10), 505–507 (1960) |
| [2] | LUO, J. T., LUO, P. X., XIE, M., DU, K., ZHAO, B. X., PAN, F., FAN, P., ZENG, F., ZHANG, D. P., ZHENG, Z. H., and LIANG, G. X. A new type of glucose biosensor based on surface acoustic wave resonator using Mn-doped ZnO multilayer structure. Biosensors and Bioelectronics, 49, 512–518 (2013) |
| [3] | FORTUNATO, E. M. C., BARQUINHA, P. M. C., PIMENTEL, A. C. M. B. G., GON?ALVES, A. M. F., MARQUES, A. J. S., PEREIRA, L. M. N., and MARTINS, R. F. P. Fully transparent ZnO thin-film transistor produced at room temperature. Advanced Materials, 17(5), 590–594 (2005) |
| [4] | ZHANG, C. L., WANG, X. Y., CHEN, W. Q., and YANG, J. S. Carrier distribution and electromechanical fields in a free piezoelectric semiconductor rod. Journal of Zhejiang University-SCIENCE A, 17(1), 37–44 (2016) |
| [5] | WANG, Z. L. Nanobelts, nanowires, and nanodiskettes of semiconducting oxides — from materials to nanodevices. Advanced Materials, 15(5), 432–436 (2003) |
| [6] | OLSON, D. C., PIRIS, J., COLLINS, R. T., SHAHEEN, S. E., and GINLEY, D. S. Hybrid photovoltaic devices of polymer and ZnO nanofiber composites. Thin Solid Films, 496(1), 26–29 (2006) |
| [7] | DURAISAMY, N., KWON, K. R., JO, J., and CHOI, K. H. Development of nanostructured ZnO thin film via electrohydrodynamic atomization technique and its photoconductivity characteristics. Journal of Nanoscience and Nanotechnology, 14(8), 5849–5855 (2014) |
| [8] | WANG, Z. L. Nanopiezotronics. Advanced Materials, 19(6), 889–892 (2007) |
| [9] | WANG, Z. L. Piezopotential gated nanowire devices: piezotronics and piezo-phototronics. Nano Today, 5(6), 540–552 (2010) |
| [10] | 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 Materials and Structures, 26(2), 025030 (2017) |
| [11] | HUTSON, A. R. and WHITE, D. L. Elastic wave propagation in piezoelectric semiconductors. Journal of Applied Physics, 33(1), 40–47 (1962) |
| [12] | WHITE, D. L. Amplification of ultrasonic waves in piezoelectric semiconductors. Journal of Applied Physics, 33(8), 2547–2554 (1962) |
| [13] | YANG, J. S. and ZHOU, H. G. Amplification of acoustic waves in piezoelectric semiconductor plates. International Journal of Solids and Structures, 42(11-12), 3171–3183 (2005) |
| [14] | LIANG, Y. X. and HU, Y. T. Effect of interaction among the three time scales on the propagation characteristics of coupled waves in a piezoelectric semiconductor rod. Nano Energy, 68, 104345 (2020) |
| [15] | YANG, W. L., GUO, L. Y., ZHANG, S. L., and HU, Y. T. On elastic wave propagation in piezoelectric semiconductors with coupled piezoelectric and semiconductor properties. International Journal of Engineering Science, 205, 104160 (2024) |
| [16] | LI, D. Z., ZHANG, C. L., ZHANG, S. F., WANG, H. M., CHEN, W. Q., and ZHANG, C. Z. Propagation of terahertz elastic longitudinal waves in piezoelectric semiconductor rods. Ultrasonics, 132, 106964 (2023) |
| [17] | WEI, Z. B., WEI, P. J., XU, C. Y., and GUO, X. Dispersion and bandgap feature of coupled Bloch waves in one-dimensional piezoelectric semiconductor phononic crystal with PN junction. Acta Mechanica, 235, 7405–7417 (2024) |
| [18] | GUO, X., WEI, P. J., XU, M. X., and LAN, M. Dispersion relations of anti-plane elastic waves in micro-scale one dimensional piezoelectric semiconductor phononic crystals with the consideration of interface effect. Mechanics of Materials, 161, 104000 (2021) |
| [19] | GUO, X. and WEI, P. J. Dispersion relations of in-plane elastic waves in nano-scale one dimensional piezoelectric semiconductor/piezoelectric dielectric phononic crystal with the consideration of interface effect. Applied Mathematical Modelling, 96, 189–214 (2021) |
| [20] | LI, D. Z., LI, S. P., MA, N. N., WANG, H. M., ZHANG, C. L., and CHEN, W. Q. Propagation characteristics of elastic longitudinal wave in a piezoelectric semiconductor metamaterial rod and its tuning. International Journal of Mechanical Sciences, 266, 108977 (2024) |
| [21] | ZHU, F., JI, S. H., ZHU, J. Q., QIAN, Z. H., and YANG, J. S. Study on the influence of semiconductive property for the improvement of nanogenerator by wave mode approach. Nano Energy, 52, 474–484 (2018) |
| [22] | 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, 125701 (2019) |
| [23] | TIAN, R., LIU, J. X., PAN, E. N., and WANG, Y. S. SH waves in multilayered piezoelectric semiconductor plates with imperfect interfaces. European Journal of Mechanics-A/Solids, 81, 103961 (2020) |
| [24] | LI, D. Z., LI, S. P., ZHANG, C. L., and CHEN, W. Q. Propagation characteristics of shear horizontal waves in piezoelectric semiconductor nanoplates incorporating surface effect. International Journal of Mechanical Sciences, 247, 108201 (2023) |
| [25] | XIAO, Z. G., SUN, L., CHEN, W. Q., and ZHANG, C. L. Nonlinear multi-field coupling modeling of multilayer-stacked piezoelectric semiconductor structures. International Journal of Mechanical Sciences, 288, 110025 (2025) |
| [26] | GU, C. L. and JIN, F. Shear-horizontal surface waves in a half-space of piezoelectric semiconductors. Philosophical Magazine Letters, 95(2), 92–100 (2015) |
| [27] | CAO, X. S., HU, S. M., LIU, J. J., and SHI, J. P. Generalized Rayleigh surface waves in a piezoelectric semiconductor half space. Meccanica, 54, 271–281 (2019) |
| [28] | XU, C. Y., WEI, P. J., WEI, Z. B., and GUO, X. Shear horizontal wave in a piezoelectric semiconductor substrate covered with a metal layer with consideration of Schottky junction effects. Applied Mathematical Modelling, 109, 509–518 (2022) |
| [29] | XU, C. Y., WEI, P. J., WEI, Z. B., and GUO, X. Effects of corrugated boundaries on Rayleigh waves in a piezoelectric semiconductor substrate covered with a metal layer. Applied Mathematical Modelling, 125, 110–124 (2024) |
| [30] | XIA, Q. G., ZOU, Y. Y., LOU, J., ZHANG, M. H., and DU, J. K. Effect of initial stresses on propagation of leaky surface acoustic wave in a piezoelectric semiconductor composite structure. Applied Mathematical Modelling, 141, 115908 (2025) |
| [31] | LIU, J. S. and HE, S. T. Theoretical analysis on Love waves in a layered structure with a piezoelectric substrate and multiple elastic layers. Journal of Applied Physics, 107, 073511 (2010) |
| [32] | ZHANG, Z. W., WEN, Z. Y., and WANG, C. M. Investigation of surface acoustic waves propagating in ZnO-SiO2-Si multilayer structure. Ultrasonics, 53(2), 363–368 (2013) |
| [33] | GAO, Q. and ZHANG, Y. H. An accurate method for guided wave propagation in multilayered anisotropic piezoelectric structures. Acta Mechanica, 231, 1783–1804 (2020) |
| [34] | YANG, J. S. Analysis of Piezoelectric Semiconductor Structures, Springer Cham, Switzerland (2020) |
| [35] | CHEN, J. Y., GUO, J. H., and PAN, E. Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect. Journal of Sound and Vibration, 400, 550–563 (2017) |
| [36] | LIU, H. and PAN, E. Indentation of a flat-ended cylinder over a transversely isotropic and layered half-space with imperfect interfaces. Mechanics of Materials, 118, 62–73 (2018) |
| [37] | QIN, L. F., CHEN, Q. M., CHENG, H. B., CHEN, Q., LI, J. F., and WANG, Q. M. Viscosity sensor using ZnO and AlN thin film bulk acoustic resonators with tilted polar c-axis orientations. Journal of Applied Physics, 110, 094511 (2011) |
| [38] | PAN, E. N. and CHEN, W. Q. Static Green's Functions in Anisotropic Media, Combridge University Press, New York (2015) |
| [39] | ZHAO, M. H., YANG, C. H., FAN, C. Y., and XU, G. T. Extended displacement discontinuity method for analysis of penny-shaped cracks in three-dimensional thermal piezoelectric semiconductors. European Journal of Mechanics-A/Solids, 70, 23–36 (2018) |
| [40] | ACHENBACH, J. Wave Propagation in Elastic Solids, Elsevier, North Holland (2012) |
| [41] | CORTES, D. H., DATTA, S. K., and MUKDADI, O. M. Dispersion of elastic guided waves in piezoelectric infinite plates with inversion layers. International Journal of Solids and Structures, 45, 5088–5102 (2008) |
| [42] | TAKALI, F., OTHMANI, C., and LV, C. F. Influence of gold electrode layers on the SH waves propagation in sandwich structures based on Au/PMN-0.33PT/Au and Au/PZT-5H/Au: numerical implementation. Materials Science and Engineering: B, 272, 115383 (2021) |
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