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The adjustment of electro-elastic properties in non-uniform flexoelectric semiconductor nanofibers

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Abstract

To explore the method of adjusting electro-elastic coupling properties in flexoelectric semiconductor nanofibers, the theoretical model is established, and the non-uniform fibers which can adjust the electro-elastic properties are designed. In order to solve the differential equations with variable coefficients in the established model, the differential quadrature method is adopted to approximate the real solutions. Before analysis, the convergence and correctness of the adopted method are investigated systematically. Considering a fiber with linear profile, it is found that the distributions of all field quantities can be adjusted by manipulating the shape of the cross section. The maximum values of all field quantities appear at the narrow end where the stiffness is the minimum in the entire fiber. By investigating the effects of the cross section parameter, flexoelectric coefficient and initial carrier density on the electro-elastic field quantities, it can be observed that the field quantities are sensitive to the variation of these parameters. Besides, studying the charge production indicates that the total charge in the flexoelectric semiconductor is dominated by the polarization charge. In symmetric non-uniform fibers, the potential barriers and wells which are produced by axial tensile load or piecewise loads are studied, respectively. It is revealed that the height of the potential barrier and the depth of the potential well can be adjusted by designing the non-uniform cross section. Furthermore, it is found that the perturbation carrier in a PN junction tends to concentrate in the zone near the narrow position. The studies in this paper could be the guidance for the applications of flexoelectric semiconductor fibers.

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Acknowledgements

This research is funded by the National Natural Science Foundation of China (Grant No. 12072253).

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  1. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Luke Zhao & Feng Jin

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Appendix 1

Appendix 1

In this appendix, the exact solution based on nonlinear theory is introduced briefly. According to the relevant literature works [54], the nonlinear equations for p-type semiconductor are expressed by

$$\begin{aligned}& {}[c_{33} A(x_{3} )u_{3,3} - c_{33} l_{0}^{2} A(x_{3} )u_{3,333} - f_{3333} A(x_{3} )\varphi_{,33} ]_{,3} = 0, \hfill \\ &[ - \varepsilon_{33} A(x_{3} )\varphi_{,3} + f_{3333} A(x_{3} )u_{3,33} ]_{,3} = qA(x_{3} )(p - N_{A}^{ - } ), \hfill \\ \end{aligned}$$
(26)

where \(p = p_{0} \exp ( - \frac{q}{{k_{B} T}}\varphi )\) can be obtained when the boundaries are electrically isolated, i.e., \(J_{3}^{p} (0) = J_{3}^{p} (L) = 0\). Besides, \(p_{0} = N_{A}^{ - }\) is assumed. Solving the governing equations under the given boundary conditions (Eq. (11)) by using COMSOL Multiphysics software, the nonlinear results will be obtained.

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Zhao, L., Jin, F. The adjustment of electro-elastic properties in non-uniform flexoelectric semiconductor nanofibers. Acta Mech 234, 975–990 (2023). https://doi.org/10.1007/s00707-022-03418-w

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