Applied Mathematics and Mechanics (English Edition) ›› 2025, Vol. 46 ›› Issue (8): 1571-1590.doi: https://doi.org/10.1007/s10483-025-3284-7
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Dejuan KONG1, Zhuangzhuang HE2, Chengbin LIU3, Chunli ZHANG2,†(
)
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RSSReceived:2025-04-04
Revised:2025-06-22
Published:2025-07-28
Contact:
Chunli ZHANG, E-mail: zhangcl01@zju.edu.cnSupported by:2010 MSC Number:
Dejuan KONG, Zhuangzhuang HE, Chengbin LIU, Chunli ZHANG. Analysis of multi-field coupling behaviors of sandwich piezoelectric semiconductor beams under thermal loadings. Applied Mathematics and Mechanics (English Edition), 2025, 46(8): 1571-1590.
Fig. 1
Sketch of an S-TPS beam under a uniform temperature change (color online)"
Fig. 2
Comparisons between the analytical solutions and COMSOL simulations of the multi-field coupling mechanical responses of the S-TPS beam with n0=1020 m-3 and r=1 subjected to different gradient temperature changes (θ(0)=0.1 K, 0.2 K, and 0.3 K): (a) w, (b) S33, (c) E3, and (d) n(0) (color online)"
Fig. 3
The multi-field coupling mechanical responses of the S-TPS beam with θ(0)=0.1 K and r=1 for different initial electron concentrations (n0=1020 m-3, 1021 m-3, and 1022 m-3): (a) w, (b) S33, (c) E3, and (d) n(0) (color online)"
Fig. 4
The multi-field coupling mechanical responses of the S-TPS beam with n0=1020/m3 and θ(0)=0.1 K for different thickness ratios (r=0.5, 1, and 1.5): (a) w, (b) S33, (c) E3, (d) n(0) (color online)"
Fig. 5
The axial compressive force (Nθ) induced by temperature change of the S-TPS beam with θ(0)=0.1 K: (a) the curves of Nθ versus n(0) for r=0.5, 1, and 1.5; (b) the curves of Nθ versus r for n0=1019 m-3, 1020 m-3, and 1021 m-3 (color online)"
Fig. 6
Comparisons between the analytical solutions and COMSOL simulations of the multi-field coupling mechanical responses of the S-TPS beam with n0=1020 m-3 and r=1 subjected to different gradient temperature changes (θ(1)=1 000 K/m, 2 000 K/m, 3 000 K/m): (a) v, (b) φ(1), (c) D3(1), and (d) n(1) (color online)"
Fig. 7
The multi-field coupling mechanical responses of the S-TPS beam with r=1 and θ(1)=3 000 K/m for n0=1020 m-3, 1021 m-3, and 1022 m-3: (a) v, (b) φ(1), (c) D3(1), and (d) n(1) (color online)"
Fig. 8
The multi-field coupling mechanical responses of the S-TPS beam with θ(1)=1 000/m and n0=1020 m-3 for r=0.5, 1, and 1.5: (a) v, (b) φ(1), (c) D3(1), and (d) n(1) (color online)"
Fig. 9
The critical buckling mechanical (Ncr) and thermal (θcr) loadings of the considered S-TPS beam: (a) the curve of Ncr versus n0, (b) the curve of θcr versus n0, (c) the curve of Ncr versus r, and (d) the curve of θcr versus r (color online)"
| [65] | FRERICH, T., BRAUNER, C., JENDRNY, J., and HERMANN, A. S. Modeling the influence of interleaf layers in composite materials on elastic properties, thermal expansion, and chemical shrinkage. Journal of Composite Materials, 53, 2415–2428 (2019) |
| [66] | REN, C., WANG, K. F., and WANG, B. L., Electromechanical analysis of a piezoelectric semiconductor bilayer system with imperfect interface. European Journal of Mechanics-A/Solids, 103, 105173 (2024) |
| [1] | WANG, Z. L. Nanobelts, nanowires, and nanodiskettes of semiconducting oxides: from materials to nanodevices. Advanced Materials, 15(5), 432–436 (2003) |
| [2] | ÖZGÜR, Ü., ALIVOV, Y. I., LIU, C., TEKE, A., RESHCHIKOV, M. A., DOĞAN, S., AVRUTIN, V., CHO, S. J., and MORKOÇ, H. A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98, 041301 (2005) |
| [3] | DJURIŠIĆ, A. B., CHEN, X. Y., LEUNG, Y. H., and NG, A. M. C. ZnO nanostructures: growth, properties and applications. Journal of Materials Chemistry, 22, 6526–6535 (2012) |
| [4] | WANG, Z. L. Piezopotential gated nanowire devices: piezotronics and piezo-phototronics. Nano Today, 5, 540–552 (2010) |
| [5] | WANG, Z. L. and WU, W. Z. Piezotronics and piezo-phototronics: fundamentals and applications. National Science Review, 1, 62–69 (2014) |
| [6] | WANG, Z. L. Nanopiezotronics. Advanced Materials, 19(6), 889–892 (2007) |
| [7] | YANG, Q., GUO, X., WANG, W. H., ZHANG, Y., XU, S., LIEN, D. H., and WANG, Z. L. Enhancing sensitivity of a single ZnO micro-/nano-wire photodetector by piezo-phototronic effect. ACS Nano, 4, 6285–6291 (2010) |
| [8] | ZHU, L. P., WANG, L. F., PAN, C. F., CHEN, L. B., XUE, F., CHEN, B. D., YANG, L. J., SU, L., and WANG, Z. L. Enhancing the efficiency of silicon-based solar cells by the piezo-phototronic effect. ACS Nano, 11, 1894–1900 (2017) |
| [9] | KAZMI, J., ABBAS, A., YOUNG, D. J., SHAH, J. H., AHMAD, W., AHMAD SHAH, S. S., ALI RAZA, S. R., MOHAMED, M. A., GOVOROV, A. O., and WANG, Z. M. ZnO nanowire UV photodetectors: at the intersection of flexibility, biocompatibility, and visible blindness. Materials Today, 82, 139–180 (2025) |
| [10] | WU, W. Z. and WANG, Z. L. Piezotronics and piezo-phototronics for adaptive electronics and optoelectronics. Nature Reviews Materials, 1, 16031 (2016) |
| [11] | YANG, R. S., LIU, C. P., FRÖEMLING, T., HAO, J. H., RAO, J. V. S., and ZHAO, Y. Q. Piezotronic and piezo-phototronic sensors. MRS Bulletin, 50, 123–129 (2025) |
| [12] | FAN, S., LIANG, Y., XIE, J., and HU, Y. 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, 40, 82–87 (2017) |
| [13] | HUANG, H., QIAN, Z., and YANG, J. I-V characteristics of a piezoelectric semiconductor nanofiber under local tensile/compressive stress. Journal of Applied Physics, 126, 164902 (2019) |
| [14] | 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, 025030 (2017) |
| [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. Advanced Structures and Materials, 90, 261–278 (2018) |
| [16] | FANG, K., LI, N., LI, P., QIAN, Z. H., KOLESOV, V., and KUZNETSOVA, I. Effects of an attached functionally graded layer on the electromechanical behaviors of piezoelectric semiconductor fibers. Applied Mathematics and Mechanics (English Edition), 43(9), 1367–1380 (2022) https://doi.org/10.1007/s10483-022-2900-5 |
| [17] | ZHANG, Q. Y., XU, J. H., WANG, B. B., ZHAO, M. H., and LU, C. S. Bending characteristics of a one-dimensional piezoelectric semiconductor curved beam. Archive of Applied Mechanics, 94, 2807–2818 (2024) |
| [18] | REN, C., LIU, C., WANG, K. F., and WANG, B. L. Electro-mechanical-carrier coupling model of single piezoelectric semiconductor fiber pull-out. Mechanics of Materials, 200, 105188 (2025) |
| [19] | YANG, L., DU, J. K., and YANG, J. S. Interaction between bending and mobile charges in a piezoelectric semiconductor bimorph. Applied Mathematics and Mechanics (English Edition), 43(8), 1171–1186 (2022) https://doi.org/10.1007/s10483-022-2889-7 |
| [20] | DAI, X., ZHU, F., QIAN, Z., and YANG, J. Electric potential and carrier distribution in a piezoelectric semiconductor nanowire in time-harmonic bending vibration. Nano Energy, 43, 22–28 (2018) |
| [21] | WANG, G., LIU, J., LIU, X., FENG, W., and YANG, J. Extensional vibration characteristics and screening of polarization charges in a ZnO piezoelectric semiconductor nanofiber. Journal of Applied Physics, 124, 094502 (2018) |
| [22] | YANG, W., HU, Y., and YANG, J. Transient extensional vibration in a ZnO piezoelectric semiconductor nanofiber under a suddenly applied end force. Materials Research Express, 6, 025902 (2018) |
| [23] | FANG, X. Q., DUAN, J. Q., ZHU, C. S., and LIU, J. X. Vibration analysis of piezoelectric semiconductor beams with size-dependent damping characteristic. Materials Today Communications, 36, 106929 (2023) |
| [24] | ZHU, C. S., FANG, X. Q., and LIU, J. X. Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model. Applied Mathematics and Mechanics (English Edition), 44(10), 1761–1776 (2023) https://doi.org/10.1007/s10483-023-3039-7 |
| [25] | ZHANG, M. and GUO, J. H. Bending, free vibration and buckling of layered piezoelectric semiconductor nanoplates based on modified couple stress theory. Acta Mechanica, 236, 519–540 (2025) |
| [26] | LIANG, C., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. Static buckling of piezoelectric semiconductor fibers. Materials Research Express, 6, 125919 (2019) |
| [27] | QU, Y., JIN, F., and YANG, J. S. Buckling of a Reissner-Mindlin plate of piezoelectric semiconductors. Meccanica, 57, 2797–2807 (2022) |
| [28] | ZHANG, Z. C., LIANG, C., KONG, D. J., XIAO, Z. G., ZHANG, C. L., and CHEN, W. Q. Dynamic buckling and free bending vibration of axially compressed piezoelectric semiconductor rod with surface effect. International Journal of Mechanical Sciences, 238, 107823 (2023) |
| [29] | ZHANG, M. and GUO, J. H. Bending, free vibration and buckling of layered piezoelectric semiconductor nanoplates based on modified couple stress theory. Acta Mechanica, 236, 519–540 (2025) |
| [30] | GU, C. and JIN, F. Shear-horizontal surface waves in a half-space of piezoelectric semiconductors. Philosophical Magazine Letters, 95, 92–100 (2015) |
| [31] | JIAO, F., WEI, P., ZHOU, X., and ZHOU, Y. The dispersion and attenuation of the multi-physical fields coupled waves in a piezoelectric semiconductor. Ultrasonics, 92, 68–78 (2019) |
| [32] | TIAN, R., LIU, J., PAN, E., WANG, Y., and SOH, A. K. Some characteristics of elastic waves in a piezoelectric semiconductor plate. Journal of Applied Physics, 126, 125701 (2019) |
| [33] | 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) |
| [34] | LI, D. Z., ZHANG, C. L., ZHANG, S. F., WANG, H. M., and CHEN, W. Q. Propagation of terahertz elastic longitudinal waves in piezoelectric semiconductor rods, Ultrasonics, 132, 106964 (2023) |
| [35] | LI, D. Z., LI, S. P., MA, N. N., WANG, H. M., ZHANG, C. L., and CHEN, W. Q. Propagation characteristics of elastic wave in a piezoelectric semiconductor metamaterial rod and its tuning. International Journal of Mechanical Sciences, 266, 108977 (2024) |
| [36] | 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) |
| [37] | YANG, W. L., LIU, J. X., YANG, Y. Z., and HU, Y. T. The mechanism to reform dynamic performance of an elastic wave-front in a piezoelectric semiconductor by the wave-carrier interaction induced from static biasing fields. Applied Mathematics and Mechanics (English Edition), 44(3), 381–396 (2023) https://doi.org/10.1007/s10483-023-2968-7 |
| [38] | ZHANG, L. L., GUO, H. C., LIU, J. X., and HU, Y. T. SH surface waves in piezoelectric semiconductors loaded with a finite viscous liquid layer. Acta Mechanica, 236, 903–914 (2024) |
| [39] | XU, J., ZHANG, Y. Q., ZHU, J. Y., NEGAHBAN, M., and LI, Z. Flexural wave characteristics in piezoelectric semiconductor beams. Mechanics of Advanced Materials and Structures (2024) https://doi.org/10.1080/15376494.2024.2446714 |
| [40] | SLADEK, J., SLADEK, V., PAN, E., and YOUNG, D. L. Dynamic anti-plane crack analysis in functional graded piezoelectric semiconductor crystals. Computer Modeling in Engineering and Sciences, 99, 273–296 (2014) |
| [41] | ZHAO, M., PAN, Y., FAN, C., and XU, G. Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors. International Journal of Solids and Structures, 94-95, 50–59 (2016) |
| [42] | ZHAO, Y., ZHOU, C., ZHAO, M., PAN, E., and FAN, C. Penny-shaped cracks in three-dimensional piezoelectric semiconductors via Green's functions of extended displacement discontinuity. Journal of Intelligent Material Systems and Structures, 28, 1775–1788 (2017) |
| [43] | LI, Y., YAN, S. J., ZHAO, M. H., and REN, J. L. Fracture analysis of planar cracks in 3D thermal piezoelectric semiconductors. International Journal of Mechanical Sciences, 273, 109212 (2024) |
| [44] | GAO, S. J., ZHANG, L. L., LIU, J. X., NIE, G. Q., and CHEN, W. Q. Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter. Applied Mathematics and Mechanics (English Edition), 45(4), 645–662 (2024) https://doi.org/10.1007/s10483-024-3107-5 |
| [45] | 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) |
| [46] | YANG, Y. Z. and HU, Y. T. Energy transfer, conversion and mechanical regulation in graded piezoelectric semiconductor bipolar junction transistor. International Journal of Heat and Mass Transfer, 232, 129546 (2024) |
| [47] | 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) |
| [48] | 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) |
| [49] | SUN, L., ZHANG, Z. C., GAO, C. F., and ZHANG, C. L. Effect of flexoelectricity on piezotronic responses of a piezoelectric semiconductor bilayer. Journal of Applied Physics, 129, 244102 (2021) |
| [50] | 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) |
| [51] | WANG, K. F. and WANG, B. L. Electrostatic potential in a bent piezoelectric nanowire with consideration of size-dependent piezoelectricity and semiconducting characterization. Nanotechnology, 29, 255405 (2018) |
| [52] | CHENG, R. R., ZHANG, C. L., and YANG, J. S. Thermally induced carrier distribution in a piezoelectric semiconductor fiber. Journal of Electronic Materials, 48(8), 4939–4946 (2019) |
| [53] | LI, S. P., CHENG, R. R., MA, N. N., and ZHANG, C. L. Analysis of piezoelectric semiconductor fibers under gradient temperature changes. Applied Mathematics and Mechanics (English Edition), 45(2), 311–320 (2024) https://doi.org/10.1007/s10483-024-3085-8 |
| [54] | ZHAO, L. K., GU, S., SONG, Y. Q., and JIN, F. Transient analysis on surface heated piezoelectric semiconductor plate lying on rigid substrate. Applied Mathematics and Mechanics (English Edition), 43(12), 1841–1856 (2022) https://doi.org/10.1007/s10483-022-2927-6 |
| [55] | YAN, Y. X., ZHU, C. S., FANG, X. Q., and SHI, L. Free vibration of functionally-graded piezoelectric semiconductor rectangular beam under thermal load. Physica B: Condensed Matter, 690, 416265 (2024) |
| [56] | 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 |
| [57] | ZHAO, L. K., JIN, F., SHAO, Z. S., and WANG, W. J. Nonlinear analysis on electrical properties in a bended composite piezoelectric semiconductor beam. Applied Mathematics and Mechanics (English Edition), 44(12), 2039–2056 (2023) https://doi.org/10.1007/s10483-023-3064-9 |
| [58] | CHENG, R. R., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. Piezotronic effects in the extension of a composite fiber of piezoelectric dielectrics and nonpiezoelectric semiconductors. Journal of Applied Physics, 124, 064506 (2018) |
| [59] | 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-Transactions of the ASME, 86, 051003 (2019) |
| [60] | LI, Y. S., FENG, W. J., and WEN, L. Free vibration of piezoelectric semiconductor composite structure with fractional viscoelastic layer. Applied Mathematics and Mechanics (English Edition), 46(4), 683–698 (2025) https://doi.org/10.1007/s10483-025-3237-8 |
| [61] | YANG, Z., ZHANG, Z. C., LIU, C. B., GAO, C. F., CHEN, W. Q., and ZHANG, C. L. Analysis of a hollow piezoelectric semiconductor composite cylinder under a thermal loading. Mechanics of Advanced Materials and Structures, 30, 2037–2046 (2023) |
| [62] | ZHANG, Q. Y., XU, J. H., SONG, Z. C., and TAN, N. Temperature effects on GaN/AlN heterojunction in a piezomagnetic and piezoelectric semiconductor composite fiber. Physica Status Solid (a), 221, 2400186 (2024) |
| [63] | AULD, B. A. Acoustic Fields and Waves in Solids, John Wiley and Sons, New York (1973) |
| [64] | ALBERTSSON, J., ABRAHAMS, S. C., and KVICK, A. Atomic displacement, anharmonic thermal vibration, expansivity and pyroelectric coefficient thermal dependences in ZnO. Acta Crystallographica Section B, 45, 34–40 (1989) |
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