Nonlinear analysis of deformation-polarization-carrier coupling fields in controllable heterogeneous PN junction nanodevices incorporating surface effect

doi:10.1007/s10483-026-3428-6

Abstract

Abstract:

In this paper, a nonlinear magneto-thermo-mechanical coupling theoretical model related to the coupled extensional and flexural deformation working modes of controllable heterogeneous PN junction devices is established, and the screening effect caused by the doping levels of the initial mobile carrier concentrations, the surface effect and critical thickness of the average electric field, and the active manipulation mechanism and evolution law for the deformation-polarization-carrier coupling fields are investigated. The results show that a relatively moderate doping level can effectively improve the transport behaviors and distribution characteristics of the electrons and holes in the PN junction. When the thickness of the PN junction device is reduced to a critical value, the size-dependent behavior caused by the surface effect owing to the average electric field difference is obvious. The working performance of the controllable giant magnetostrictive Terfenol-D based heterogeneous PN junction device can be improved evidently when the Terfenol-D layers of the laminated nanoplate devive are subjected to the changing operating temperature, applied external magnetic field, or pre-stress stimuli. These findings can provide effective guidance for the explanation of the nonlinear magneto-mechanical-thermo coupling active manipulation mechanism for induced deformation-polarization-carrier coupling fields, as well as the experimental design of Terfenol-D based heterogeneous PN junction nanodevices.

Key words: heterogeneous PN junction device, magneto-electro-semiconductor coupling nanoplate, nonlinear theoretical model, deformation-polarization-carrier coupling field, surface effect, active manipulation

2010 MSC Number:

O343.5

Wenjun WANG, Miaomiao LI, Luke ZHAO, Feng JIN, Tao HOU, Tingting ZHAO, Tianhu HE, Yongbin MA. Nonlinear analysis of deformation-polarization-carrier coupling fields in controllable heterogeneous PN junction nanodevices incorporating surface effect. Applied Mathematics and Mechanics (English Edition), 2026, 47(9): 2021-2042.

TrendMD

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-026-3428-6

https://www.amm.shu.edu.cn/EN/Y2026/V47/I9/2021

Figures/Tables 8

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

[1]	WANG, L., SHEN, H. M., and WANG, Y. X. Generalized semi-analytical modeling of three-dimensional contact responses in piezoelectric semiconductors with conductive indenters. Applied Mathematics and Mechanics (English Edition), 47(3), 555–572 (2026) https://doi.org/10.1007/s10483-026-3358-8
[2]	REN, C., WANG, K. F., and WANG, B. L. Electro-mechanical-carrier coupling model in fractured piezoelectric semiconductor strip with vertical cracks. Applied Mathematics and Mechanics (English Edition), 47(2), 347–368 (2026) https://doi.org/10.1007/s10483-026-3343-6
[3]	NIE, G. Q., WU, Z. W., and LIU, J. X. Static and dynamic responses of a piezoelectric semiconductor beam under different boundary conditions. Applied Mathematics and Mechanics (English Edition), 47(2), 303–324 (2026) https://doi.org/10.1007/s10483-026-3345-8
[4]	WANG, T. Q., ZHU, F., LI, P., XU, Z. L., MA, T. F., KUZNETSOVA, I., and QIAN, Z. H. Analysis of the electromechanical coupling characteristics of piezoelectric semiconductor PN junction shell structures. Applied Mathematics and Mechanics (English Edition), 46(6), 1167–1186 (2025) https://doi.org/10.1007/s10483-025-3259-6
[5]	CAO, Y., GUO, Z. W., and QU, Y. L. Mechanically induced electric potential and charge redistribution in laminated composite piezoelectric semiconductor circular cylindrical thin shells. Thin-Walled Structures, 195, 111372 (2024)
[6]	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)
[7]	WANG, Z. L. Nanopiezotronics. Advanced Materials, 19, 889–892 (2007)
[8]	FANG, K., LI, P., LI, N., LIU, D. Z., QIAN, Z. H., KOLESOV, V., and KUZNETSOVA, I. Model and performance analysis of non-uniform piezoelectric semiconductor nanofibers. Applied Mathematical Modelling, 104, 628–643 (2022)
[9]	FANG, K., LI, P., LI, N., LIU, D. Z., QIAN, Z. H., KOLESOV, V., and KUZNETSOVA, I. Impact of PN junction inhomogeneity on the piezoelectric fields of acoustic waves in piezo-semiconductive fibers. Ultrasonics, 120, 106660 (2022)
[10]	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)
[11]	REN, C., LIU, C., WANG, K. F., and WANG, B. L. Electro-mechanical-carrier coupling behaviors of piezoelectric semiconductor fibers with p-n junctions under pull-out loading. Journal of Applied Physics, 137, 085701 (2025)
[12]	REN, C., WANG, K. F., and WANG, B. L. Electromechanical fields of PN junctions in composite piezoelectric semiconductor beam with electro-mechanical imperfect interface. Thin-Walled Structures, 218, 114115 (2026)
[13]	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)
[14]	YANG, G. Y., YANG, L., DU, J. K., WANG, J., and YANG, J. S. PN junctions with coupling to bending deformation in composite piezoelectric semiconductor fibers. International Journal of Mechanical Sciences, 173, 105421 (2020)
[15]	QU, Y. L., PAN, E., ZHU, F., and DENG, Q. A thermodynamically consistent theory for flexoelectronics: interaction between strain gradient and electric current in flexoelectric semiconductors. International Journal of Engineering Science, 208, 104165 (2025)
[16]	LIU, Y., ZHANG, Y., YANG, Q., NIU, S. M., and WANG, Z. L. Fundamental theories of piezotronics and piezo-phototronics. Nano Energy, 14, 257–275 (2015)
[17]	FAN, S. Q., HU, Y. T., and YANG, J. S. Stress-induced potential barriers and charge distributions in a piezoelectric semiconductor nanofiber. Applied Mathematics and Mechanics (English Edition), 40(5), 591–600 (2019) https://doi.org/10.1007/s10483-019-2481-6
[18]	CHENG, R. R., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. Electrical behaviors of a piezoelectric semiconductor fiber under a local temperature change. Nano Energy, 66, 104081 (2019)
[19]	WANG, J., YU, Y. L., ZHAO, X., SUN, J. Q., WANG, Y. X., and ZHU, H. J. A review on the size-dependent bulking, vibration and, wave propagation of nanostructures. Journal of Physics: Condensed Matter, 35, 293001 (2023)
[20]	WANG, B., GU, Y. J., ZHANG, S. J., and CHEN, L. Q. Flexoelectricity in solids: progress, challenges, and perspectives. Progress in Materials Science, 106, 100570 (2019)
[21]	WANG, L. Y., CHONG, N., LEI, D. X., and OU, Z. Y. Nonlinear vibration analysis of nonlocal fractional viscoelastic piezoelectric nanobeams incorporating surface effects. European Journal of Mechanics-A/Solids, 115, 105840 (2026)
[22]	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)
[23]	ZHOU, F. Q., WANG, X. Q., CHU, L. L., and ZHAO, K. Y. Structure-dependent electro-elastic analysis of flexoelectric semiconductor curved nanoshells based on the modified couple stress theory in orthogonal curvilinear coordinates. Acta Mechanica, 236, 2481–2507 (2025)
[24]	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, 215701 (2020)
[25]	QU, Y. L., ZHU, F., PAN, E., JIN, F., and HIRAKATA, H. Analysis of wave-particle drag effect in flexoelectric semiconductor plates via Mindlin method. Applied Mathematical Modelling, 118, 541–555 (2023)
[26]	THAI, T. Q., ZHUANG, X. Y., and RABCZUK, T. Curved flexoelectric and piezoelectric micro-beams for nonlinear vibration analysis of energy harvesting. International Journal of Solids and Structures, 264, 112096 (2023)
[27]	ZHAO, L. K., LI, P., and JIN, F. Non-homogeneous cross section variation enhanced flexoelectric coupling in semiconductor beams and its application in charge carrier redistribution. Journal of Applied Physics, 131, 065701 (2022)
[28]	FANG, X., WANG, L. Y., LOU, J., FAN, H., and DU, J. K. Flexoelectricity and size effects on SH surface waves in a nanoscale piezoelectric semiconductor layered medium. Applied Mathematical Modelling, 141, 115928 (2025)
[29]	WANG, L. Y., ZHANG, A. B., ZHANG, C. Z., DU, J. K., XIAO, Z. M., and LOU, J. Rayleigh wave propagation in an elastic half-space with an attached piezoelectric semiconductor layer considering flexoelectricity and size-effects. Applied Mathematics and Mechanics (English Edition), 46(6), 1069–1088 (2025) https://doi.org/10.1007/s10483-025-3265-8
[30]	GUO, Z. W., ZHANG, G. Y., MI, C. W., and QU, Y. L. Flexoelectronics of a centrosymmetric semiconductor cylindrical nanoshell. Applied Mathematical Modelling, 137, 115725 (2025)
[31]	SHEN, S. P. and HU, S. L. A theory of flexoelectricity with surface effect for elastic dielectrics. Journal of the Mechanics and Physics of Solids, 58, 665–677 (2010)
[32]	WANG, W. J., LI, P., and JIN, F. Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications. Smart Materials and Structures, 25, 095026 (2016)
[33]	WANG, W. J., LI, P., and JIN, F. An analytical model of a broadband magnetic energy nanoharvester array with consideration of flexoelectricity and surface effect. Journal of Physics D: Applied Physics, 51, 155304 (2018)
[34]	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)
[35]	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)
[36]	YANG, W. L., LIU, Q. Y., and HU, Y. T. A new size-dependent nonlinear model for piezoelectric semiconductor nanofibers by considering the effects of strain gradient and flexoelectricity. European Journal of Mechanics-A/Solids, 106, 105279 (2024)
[37]	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)
[38]	YANG, W. J., LIANG, X., DENG, Q., and SHEN, S. P. Rayleigh wave propagation in a homogeneous centrosymmetric flexoelectric half-space. Ultrasonics, 103, 106105 (2020)
[39]	YANG, L., DU, J. K., WANG, J., and YANG, J. S. An analysis of piezomagnetic-piezoelectric semiconductor unimorphs in coupled bending and extension under a transverse magnetic field. Acta Mechanica Solida Sinica, 34, 743–753 (2021)
[40]	ZHANG, G. Y., GUO, Z. W., QU, Y. L., and MI, C. W. Global and local flexotronic effects induced by external magnetic fields in warping of a semiconducting composite fiber. Composite Structures, 295, 115711 (2022)
[41]	KONG, D. J., CHENG, R. R., ZHANG, C. L., and ZHANG, C. Z. Dynamic manipulation of piezotronic behaviors of composite multiferroic semiconductors through time-dependent magnetic field. Journal of Applied Physics, 128, 064503 (2020)
[42]	WANG, W. J., LI, P., and JIN, F. Magneto-mechanical coupling characteristic analysis of a magnetic energy nanoharvester with surface effect. Applied Mathematical Modelling, 77, 1762–1779 (2020)
[43]	WANG, W. J., JIN, F., HE, T. H., and MA, Y. B. Size-dependent and nonlinear magneto-mechanical coupling characteristics analysis for extensional vibration of composite multiferroic piezoelectric semiconductor nanoharvester with surface effect. European Journal of Mechanics-A/Solids, 96, 104708 (2022)
[44]	WANG, W. J., JIN, F., HE, T. H., and MA, Y. B. Nonlinear magneto-mechanical-thermo coupling characteristic analysis for transport behaviors of carriers in composite multiferroic piezoelectric semiconductor nanoplates with surface effect. Applied Mathematics and Mechanics (English Edition), 43(9), 1323–1338 (2022) https://doi.org/10.1007/s10483-022-2894-9
[45]	WANG, W. J., LI, M. M., JIN, F., HE, T. H., and MA, Y. B. Nonlinear magnetic-mechanical-thermo-electric coupling characteristic analysis on the coupled extensional and flexural vibration of flexoelectric energy nanoharvester with surface effect. Composite Structures, 308, 116687 (2023)
[46]	ZHENG, X. J. and SUN, L. A nonlinear constitutive model of magneto-thermo-mechanical coupling for giant magnetostrictive materials. Journal of Applied Physics, 100, 063906 (2006)
[47]	WANG, W. J., LI, P., JIN, F., and WANG, J. Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects. Composite Structures, 140, 758–775 (2016)
[48]	ZHANG, Q. Y., LI, M. G., and ZHAO, M. H. Dynamic analysis of a piezoelectric semiconductor nanoplate with surface effect. Materials Today Communications, 33, 104406 (2022)
[49]	HE, H. Y., ZHANG, M. J., WANG, W. J., LI, X. D., LI, M. M., and ZHAO, L. K. Two-dimensional linear elasticity equations of thermo-piezoelectric semiconductor thin-film devices and their application in static characteristic analysis. Applied Sciences, 14, 6509 (2024)
[50]	WANG, W. J., LI, M. M., ZHAO, L. K., JIN, F., HE, T. H., MA, Y. B., and HOU, T. Mechanical manipulation of electromechanical fields in multi-tunnel piezoelectric semiconductor thin film devices by creating localized transverse mechanical field excitations. Acta Mechanica, 236, 1151–1177 (2025)
[51]	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)
[52]	WANG, W. J., LI, M. M., ZHAO, L. K., JIN, F., HOU, T., ZHAO, T. T., HE, T. H., and MA, Y. B. Surface effect-dependent active manipulation investigation on nonlinear deformation-polarization-carrier coupling fields in a multiferroic flexoelectric piezoelectric semiconductor device considering coupled extension and bending. Thin-Walled Structures, 228, 115067 (2026)