Interaction between bending and mobile charges in a piezoelectric semiconductor bimorph

doi:10.1007/s10483-022-2889-7

Abstract

Abstract: We study the bending of a two-layer piezoelectric semiconductor plate (bimorph). The macroscopic theory of piezoelectric semiconductors is employed. A set of two-dimensional plate equations is derived from the three-dimensional equations. The plate equations exhibit direct couplings among bending, electric polarization along the plate thickness, and mobile charges. In the case of pure bending, a combination of physical and geometric parameters is identified which characterizes the strength of the interaction between the mechanical load and the distribution of mobile charges. In the bending of a rectangular plate under a distributed transverse mechanical load, it is shown that mobile charge distributions and potential barriers/wells develop in the plate. When the mechanical load is local and self-balanced, the induced carrier distributions and potential barriers/wells are also localized near the loading area. The results are fundamentally useful for mechanically manipulating mobile charges in piezoelectric semiconductor devices.

Key words: piezoelectric, plate, bimorph, bending, piezotronic

2010 MSC Number:

74K20
82D37

Lei YANG, Jianke DU, J. S. YANG. Interaction between bending and mobile charges in a piezoelectric semiconductor bimorph. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1171-1186.

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References

[1] WANG, Z. L. Nanobelts, nanowires, and nanodiskettes of semiconducting oxides-from materials to nanodevices. Advanced Materials, 15, 432-436(2003)
[2] KIM, K. K., KIM, H. S., HWANG, D. K., LIM, J. H., and PARK, S. J. Realization of p-type ZnO thin films via phosphorus doping and ther mal activation of the dopant. Applied Physics Letters, 83(1), 63-65(2003)
[3] JEONG, S. H., JEONG, Y. M., and MOON, J. H. Solution-processed zinc tin oxide semiconductor for thin-film transistors. Journal of Physical Chemistry C, 112, 11082-11085(2008)
[4] WANG, Z. L. Piezotronics and Piezo-phototronics, Springer, Berlin (2012)
[5] LIN, P., PAN, C. F., and WANG, Z. L. Two-dimensional nanomaterials for novel piezotronics and piezophototronics. Materials Today Nano, 4, 17-31(2018)
[6] WANG, Z. L., WU, W. Z., and FALCONI, C. Piezotronics and piezo-phototronics with thirdgeneration semiconductors. MRS Bulletin, 43(12), 922-927(2018)
[7] LIU, Y. D., WAHYUDIN, E. T. N., HE, J. H., and ZHAI, J. Y. Piezotronics and piezophototronics in two-dimensional materials. MRS Bulletin, 43(12), 959-964(2018)
[8] JIAO, F. Y., WEI, P. J., ZHOU, Y. H., and ZHOU, X. L. Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces. European Journal of Mechanics A/Solids, 75(5), 70-81(2019)
[9] JIAO, F. Y., WEI, P. J., ZHOU, Y. H., and ZHOU, X. L. The dispersion and attenuation of the multi-physical fields coupled waves in a piezoelectric semiconductor. Ultrasonics, 92, 68-78(2019)
[10] 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)
[11] WAUER, J. and SUHERMAN, S. Thickness vibrations of a piezo-semiconducting plate layer. International Journal of Engineering Science, 35, 1387-1404(1997)
[12] WANG, G. L., LIU, J. X., LIU, X. L., FENG, W. J., and YANG, J. S. Extensional vibration characteristics and screening of polarization charges in a ZnO piezoelectric semiconductor nanofiber. Journal of Applied Physics, 124, 094502(2018)
[13] 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(4), 273-296(2014)
[14] SLADEK, J., SLADEK, V., PAN, E., and MÜNSCHE, M. Fracture analysis in piezoelectric semiconductors under a thermal load. Engineering Fracture Mechanics, 126, 27-39(2014)
[15] ZHAO, M. H., PAN, Y. B., FAN, C. Y., and XU, G. T. Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors. International Journal of Solids and Structures, 94, 50-59(2016)
[16] QIN, G. S., LU, C. S., ZHANG, X., and ZHAO, M. H. Electric current dependent fracture in GaN piezoelectric semiconductor ceramics. Materials, 11(10), 2000(2018)
[17] 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)
[18] 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)
[19] 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(25), 255405(2018)
[20] REN, C., WANG, K. F., and WANG, B. L. Adjusting the electromechanical coupling behaviors of piezoelectric semiconductor nanowires via strain gradient and flexoelectric effects. Journal of Applied Physics, 128(21), 215701(2020)
[21] ZHAO, M. H., LIU, X., FAN, C. Y., LU, C. S., and WANG, B. B. Theoretical analysis on the extension of a piezoelectric semi-conductor nanowire:effects of flexoelectricity and strain gradient. Journal of Applied Physics, 127(8), 085707(2020)
[22] AFRANEO, R., LOVAT, G., BURGHIGNOLI, P., and FALCONI, C. Piezo-semiconductive quasi-1D nanodevices with or without anti-symmetry. Advanced Materials, 24, 4719-4724(2012)
[23] 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)
[24] GAO, Y. F. and WANG, Z. L. Equilibrium potential of free charge carriers in a bent piezoelectric semiconductive nanowire. Nano Letters, 9, 1103-1110(2009)
[25] FAN, S. Q., LIANG, Y. X., XIE, J. M., and HU, Y. T. 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)
[26] LIANG, Y. X., FAN, S. Q., CHEN, X. D., and HU, Y. T. Nonlinear effect of carrier drift on the performance of an n-type ZnO nanowire nanogenerator by coupling piezoelectric effect and semiconduction. Nanotechnology, 9, 1917-1925(2018)
[27] YANG, J. S. Analaysis of Piezoelectric Semiconductor Structures, Springer Nature, Switzerland (2020)
[28] YANG, J. S. and ZHOU, H. G. Amplification of acoustic waves in piezoelectric semiconductor plates. International Journal of Solids and Structures, 42, 3171-3183(2005)
[29] YANG, J. S., YANG, X. M., and TURNER, J. A. Amplification of acoustic waves in laminated piezoelectric semiconductor plates. Archive of Applied Mechanics, 74, 288-298(2004)
[30] 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. ASME Journal of Applied Mechanics, 86, 051003(2019)
[31] QU, Y. L., JIN, F., and YANG, J. S. Temperature effects on mobile charges in thermopiezoelectric semiconductor plates. International Journal of Applied Mechanics, 13(3), 2150037(2021)
[32] 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)
[33] QU, Y. L., JIN, F., and YANG, J. S. Bending of a flexoelectric semiconductor plate. Acta Mechanica Solida Sinica, 35, 434-445(2022)
[34] DONG, S. X., BOUCHILLOUX, P., DU, X. H., and UCHINO, K. Ring type uni/bimorph piezoelectric actuators. Journal of Intelligent Material Systems and Structures, 12(9), 613-616(2002)
[35] SMITS, J. G., DALKE, S. I., and COONEY, T. K. The constituent equations of piezoelectric bimorphs. Sensors and Actuators A:Physical, 28(1), 41-61(1991)
[36] HA, S. K. Admittance matrix of asymmetric piezoelectric bimorph with two separate electrical ports under general distributed load. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 48, 976-984(2001)
[37] BENASCIUTTI, D., MORO, L., ZELENIKA, S., and BRUSA, E. Vibration energy scavenging via piezoelectric bimorphs of optimized shapes. Microsystem Technologies, 16, 657-668(2010)
[38] VEL, S. S. and BATRA, R. C. Analysis of piezoelectric bimorphs and plates with segmented actuators. Thin-Walled Structures, 39(1), 23-44(2001)
[39] CUI, J., DU, J. K., WANG, J., and YANG, J. S. A piezoelectric gyroscope based on thickness-shear modes of an AlN bimorph with inclined C axes. Philosophical Magazine Letters, 94(7), 447-454(2014)
[40] MICHELE, P. Magnetic plucking of piezoelectric bimorphs for a wearable energy harvester. Smart Materials and Structures, 25(4), 045008(2016)
[41] YANG, J. S. Mechanics of Piezoelectric Structures, World Scientific, Singapore (2020)
[42] AULD, B. A. Acoustic Fields and Waves in Solids, Wiley, New York (1973)
[43] PIERRET, R. F. Semiconductor Device Fundamentals, Pearson, Uttar Pradesh (1996)
[44] MINDLIN, R. D. High frequency vibrations of piezoelectric crystal plates. International Journal of Solids and Structures, 8(7), 895-906(1972)
[45] TSUBOUCHI, K., SUGAI, K., and MIKOSHIBA, N. AlN material constants evaluation and SAW properties on AlN/Al₂O₃ and AlN/Si. Proceedings of the IEEE Ultrasonics Symposium, 375-380(1981)
[46] SZE, S. M. Physics of Semiconductor Devices, John Wiley and Sons, New York (2006)