Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

doi:10.1007/s10483-020-2619-7

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (6): 833-844.doi: https://doi.org/10.1007/s10483-020-2619-7

• 论文 • 下一篇

Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

Wanli YANG¹, Yuantai HU¹, E. N. PAN²

1. Department of Mechanics, Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Computer Modeling and Simulation Group, College of Engineering, University of Akron, Akron, Ohio 44325, U. S. A.

收稿日期:2020-01-15 修回日期:2020-03-14 发布日期:2020-06-08
通讯作者: Yuantai HU, E. N. PAN E-mail:hudeng@263.net;pan2@uakron.edu
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11972164, 11672113, and 11472182) and the Key Laboratory Project of Hubei Province of China (No. 2016CFA073)

Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

Wanli YANG¹, Yuantai HU¹, E. N. PAN²

1. Department of Mechanics, Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Computer Modeling and Simulation Group, College of Engineering, University of Akron, Akron, Ohio 44325, U. S. A.

Received:2020-01-15 Revised:2020-03-14 Published:2020-06-08
Contact: Yuantai HU, E. N. PAN E-mail:hudeng@263.net;pan2@uakron.edu
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11972164, 11672113, and 11472182) and the Key Laboratory Project of Hubei Province of China (No. 2016CFA073)

摘要/Abstract

摘要： The electric band energy variation in a bent piezoelectric semiconductor (PSC) nanowire of circular cross-section induced by the mechanical force is analyzed based on a six-band k·p method. The electric-mechanical fields are first obtained analytically in a cantilever bent PSC nanowire by solving the fully-coupled electro-mechanical equations. Then, the band energy is acquired numerically via the six-band Hamiltonian. By considering further the nonlinear coupling between the piezoelectric and semiconducting quantities, the contribution of the redistribution carriers to the electric field is analyzed from the Gauss's law. Numerical examples are carried out for an n-type ZnO nanowire in different locations induced by an applied concentrated end force. They include the electric potential, heavy hole (HH), light hole (LH), spin-orbit split-off (SO), and conduction band (CB) edges along the axial and thickness directions. Our results show that the applied force has a significant effect on the band energies. For instance, on the bottom surface along the axial direction, the bandgaps near the fixed end are greater than those near the loading end, and this trend is reversed on the top surface. Moreover, at a fixed axial location, the energy level of the lower side can be enhanced by applying a bending force at the end. The present results could be of significant guidance to the electronic devices and piezotronics.

关键词: piezoelectric semiconductor (PSC), mechanical bending, energy band, ZnO

Abstract: The electric band energy variation in a bent piezoelectric semiconductor (PSC) nanowire of circular cross-section induced by the mechanical force is analyzed based on a six-band k·p method. The electric-mechanical fields are first obtained analytically in a cantilever bent PSC nanowire by solving the fully-coupled electro-mechanical equations. Then, the band energy is acquired numerically via the six-band Hamiltonian. By considering further the nonlinear coupling between the piezoelectric and semiconducting quantities, the contribution of the redistribution carriers to the electric field is analyzed from the Gauss's law. Numerical examples are carried out for an n-type ZnO nanowire in different locations induced by an applied concentrated end force. They include the electric potential, heavy hole (HH), light hole (LH), spin-orbit split-off (SO), and conduction band (CB) edges along the axial and thickness directions. Our results show that the applied force has a significant effect on the band energies. For instance, on the bottom surface along the axial direction, the bandgaps near the fixed end are greater than those near the loading end, and this trend is reversed on the top surface. Moreover, at a fixed axial location, the energy level of the lower side can be enhanced by applying a bending force at the end. The present results could be of significant guidance to the electronic devices and piezotronics.

Key words: piezoelectric semiconductor (PSC), mechanical bending, energy band, ZnO

中图分类号:

82D37

Wanli YANG, Yuantai HU, E. N. PAN. Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(6): 833-844.

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Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

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