## Application of the homotopy analysis method to nonlinear characteristics of a piezoelectric semiconductor fiber. (Application of the homopoty analysis method to nonlinear characteristics of a piezoelectric semiconductor fiber.)(English)Zbl 1480.74075

Summary: Based on the nonlinear constitutive equation, a piezoelectric semiconductor (PSC) fiber under axial loads and Ohmic contact boundary conditions is investigated. The analytical solutions of electromechanical fields are derived by the homopoty analysis method (HAM), indicating that the HAM is efficient for the nonlinear analysis of PSC fibers, along with a rapid rate of convergence. Furthermore, the nonlinear characteristics of electromechanical fields are discussed through numerical results. It is shown that the asymmetrical distribution of electromechanical fields is obvious under a symmetrical load, and the piezoelectric effect is weakened by an applied electric field. With the increase in the initial carrier concentration, the electric potential decreases, and owing to the screening effect of electrons, the distribution of electromechanical fields tends to be symmetrical.

### MSC:

 74F15 Electromagnetic effects in solid mechanics 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics 78A55 Technical applications of optics and electromagnetic theory
Full Text:

### References:

 [1] 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) [2] Qin, Y.; Wang, X. D.; Wang, Z. L., Microfibre-nanowire hybrid structure for energy scavenging, nature, 451, 7180, 809-813 (2008) [3] Liu, Y.; Yang, Q.; Zhang, Y.; Yang, Y. Z.; Wang, Z. L., Nanowire piezo-phototronic photodetector: theory and experimental design, Advance Materials, 24, 11, 1410-1417 (2012) [4] Wang, Z. L., Strain-gated piezotronic transistors based on vertical zinc oxide nanowires, ACS Nano, 6, 5, 3760-3766 (2012) [5] Wang, Z. L., Piezopotential gated nanowire devices: piezotronics and piezo-phototronics, Nano Today, 5, 6, 540-552 (2010) [6] Hutson, A. R.; White, D. L., Elastic wave propagation in piezoelectric semiconductors, Journal of Applied Physics, 33, 1, 40-47 (1962) [7] Gavini, A.; Cardona, M., Modulated piezoreflectance in semiconductor, Physical Review B, 1, 2, 672-682 (1970) [8] Chattopadhyay, D., Piezoelectric and deformation potential acoustic scattering mobility of a two-dimensional electron gas in quantum wells, Physica Status Solidi (B), 135, 1, 409-413 (2010) [9] Zhang, X. B.; Taliercio, T.; Kolliakos, S.; Lefebvre, P., Influence of electron-phonon interaction on the optical properties of III nitride semiconductors, Journal of Physics: Condensed Matter, 13, 32, 7053-7074 (2001) [10] Sakai, K.; Fukuyama, A.; Toyoda, T.; Ikari, T., Piezoelectric photothermal spectra of Co doped ZnO semiconductor, Japanese Journal of Applied Physics, 41, 5, 3371-3373 (2002) [11] He, J. H.; Hsin, C. L.; Liu, J.; Chen, L. J.; Wang, Z. L., Piezoelectric gated diode of a single ZnO nanowire, Advanced Materials, 19, 6, 781-784 (2007) [12] Zhou, J.; Gu, Y. D.; Hu, Y. F.; Mai, W. J.; Yeh, P. H.; Bao, G.; Sood, A. K.; Polla, D. L.; Wang, Z. L., Gigantic enhancement in response and reset time of ZnO UV nanosensor by utilizing Schottky contact and surface functionalization, Applied Physics Letters, 94, 19, 191103 (2009) [13] Ko, S. H.; Lee, D.; Kang, H. W.; Nam, K. H.; Yeo, J. Y.; Hong, S. J.; Grigoropoulos, C. P.; Sung, H. J., Nanoforest of hydrothermally grown hierarchical ZnO nanowires for a high efficiency dye-sensitized solar cell, Nano Letters, 11, 2, 666-671 (2011) [14] Yang, J. S., An anti-plane crack in a piezoelectric semiconductor, International Journal of Fracture, 136, 1-4, L27-L32 (2005) · Zbl 1197.74145 [15] Hu, Y. T.; Zeng, Y.; Yang, J. S., A mode III crack in a piezoelectric semiconductor of crystals with 6 mm symmetry, International Journal of Solids and Structures, 44, 3928-3938 (2007) · Zbl 1124.74043 [16] Sladek, J.; Sladek, V.; Pan, E.; Wunsche, M., Fracture analysis in piezoelectric semiconductor under a thermal load, Engineering Fracture Mechanics, 126, 27-39 (2014) [17] Zhao, M. H.; Pan, Y. B.; Fan, C. Y.; Xu, G. T., Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors, International Journal of Solids and Structures, 94-95, 50-59 (2016) [18] 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, Engineering Fracture Mechanics, 165, 183-196 (2016) [19] Zhang, Q. Y.; Fan, C. Y.; Xu, G. T.; Zhao, M. H., Iterative boundary element method for crack analysis of two-dimensional piezoelectric semiconductor, Engineering Analysis with Boundary Elements, 83, 87-95 (2017) · Zbl 1403.74264 [20] 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 Materials and Structures, 26, 2, 025030 (2017) [21] Luo, Y. X.; Zhang, C. L.; Chen, W. Q.; Yang, J. S., An analysis of PN junctions in piezoelectric semiconductors, Journal of Applied Physics, 122, 20, 204502 (2017) [22] Yang, W. L.; Hu, Y. T.; Yang, J. S., Transient extensional vibration in a ZnO piezoelectric semiconductor nanofiber under a suddenly applied end force, Materials Research Express, 6, 2, 025902 (2019) [23] 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) [24] Wang, G. L.; Liu, J. X.; Liu, X. L., Extensional vibration characteristics and screening of polarization charges in a ZnO piezoelectric semiconductor nanofiber, Journal of Applied Physics, 124, 9, 095402 (2018) [25] Dai, X. Y.; Zhu, F.; Qian, Z. H.; Yang, J. S., Electric potential and carrier distribution in a piezoelectric semiconductor nanowire in time-harmonic bending vibration, Nano Energy, 43, 22-28 (2018) [26] Jin, Z. H.; Yang, J. S., Analysis of a sandwiched piezoelectric semiconducting thermoelectric structure, Mechanics Research Communications, 98, 31-36 (2019) [27] Cheng, R. R.; Zhang, C. L.; Chen, W. Q.; Yang, J. S., Temperature effects on PN junctions in piezoelectric semiconductor fibers with thermoelastic and pyroelectric couplings, Journal of Electronic Materials, 49, 5, 3140-3148 (2020) [28] Zhao, M. H.; Yang, C. H.; Fan, C. Y.; Zhang, Q. Y., A shooting method for nonlinear boundary value problems in a thermal piezoelectric semiconductor plate, Zeitschrift für Angewandte Mathematik und Mechanik, 100, 12, e201900302 (2020) [29] Tian, R.; Liu, J. X.; Pan, E.; Wang, Y. S., SH waves in multilayered piezoelectric semiconductor plates with imperfect interfaces, European Journal of Mechanics-A/Solids, 81, 103961 (2020) · Zbl 1475.74072 [30] Zhao, M. H.; Zhang, Q. Y.; Fan, C. Y., An efficient iteration approach for nonlinear boundary value problems in 2D piezoelectric semiconductor, Applied Mathematical Modelling, 74, 170-183 (2019) · Zbl 1481.74194 [31] Yang, G. Y.; Du, J. K.; Wang, J.; Yang, J. S., Extension of piezoelectric semiconductor fiber with consideration of electrical nonlinearity, Acta Mechanica, 229, 11, 4663-4676 (2018) · Zbl 1430.82013 [32] Guo, M. K.; Li, Y.; Qin, G. S.; Zhao, M. H., Nonlinear solutions of PN junctions of piezoelectric semiconductors, Acta Mechanica, 230, 1825-1841 (2019) · Zbl 1428.74079 [33] Liao, S. J., Beyond Perturbation: Introduction to the Homotopy Analysis Method (2004), Boca Raton: CRC Press, Boca Raton · Zbl 1051.76001 [34] Dmmairry, G.; Fazeli, M., Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Communications in Nonlinear Science and Numerical Simulation, 14, 2, 489-499 (2009) [35] Gao, L. M.; Wang, J.; Zhong, Z.; Du, J. K., An analysis of surface acoustic wave propagation in functionally graded plates with homotopy analysis method, Acta Mechanica, 208, 249-258 (2009) · Zbl 1190.74014 [36] Wu, R. X.; Wang, J.; Du, J. K.; Huang, D. J.; Yan, W.; Hu, Y. T., An analysis of nonlinear vibrations of coupled thickness-shear and flexural modes of quartz crystal plates with the homotopy analysis method, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 59, 1, 30-39 (2012) [37] Wu, R. X.; Wang, J.; Du, J. K.; Hu, Y. T.; Hu, H. P., Solutions of nonlinear thickness-shear vibrations of an infinite isotropic plate with the homotopy analysis method, Numerical Algorithms, 59, 213-226 (2012) · Zbl 1396.74063 [38] Lin, X.; Huang, Y.; Zhao, Y.; Wang, T. S., Large deformation analysis of a cantilever beam made of axially functionally graded material by homotopy analysis method, Applied Mathematics and Mechanics (English Edition), 40, 10, 1375-1386 (2019) · Zbl 1431.74067
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.