考虑表面效应的压电半导体梁的静态屈曲行为研究

詹春晓; 李孝宝; 王美芹

doi:10.21656/1000-0887.450200

考虑表面效应的压电半导体梁的静态屈曲行为研究

doi: 10.21656/1000-0887.450200

合肥工业大学土木与水利工程学院，合肥 230009

基金项目:

安徽省自然科学基金 2208085MA17

详细信息

作者简介:
詹春晓(1970—)，男，副教授，博士(E-mail: zhanchunxiao@hfut.edu.cn)

通讯作者:
李孝宝(1985—)，男，研究员，博士(通讯作者. E-mail: xiaobaoli@hfut.edu.cn)

中图分类号: O34
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- 文章访问数: 131
- HTML全文浏览量: 37
- PDF下载量: 36
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-09
- 修回日期: 2024-09-15
- 刊出日期: 2024-10-01

Static Buckling Behaviors of Piezoelectric Semiconductor Beams With Steigmann-Ogden Surface Effects

School of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China

摘要

摘要: 鉴于表面效应和挠曲电效应对纳米材料或结构的力学行为具有显著影响，以纳米尺度压电半导体(PS)梁为研究对象，根据Hamilton变分原理，推导建立了考虑Steigmann-Ogden表面弹性效应和挠曲电效应的Euler-Bernoulli梁理论模型和相应的边界条件. 结合电荷守恒方程和线性漂移扩散方程，研究了该梁结构的静态屈曲行为，得到了短路和开路条件下梁结构的等效弹性常数和屈曲临界压力的解析解. 详细分析了表面效应、尺寸效应、挠曲电效应以及载流子屏蔽效应等因素对梁结构的等效弹性常数的影响规律和作用机制. 该文的研究结果对基于纳米压电半导体梁结构电子器件的设计和应用具有指导作用.
- 压电半导体梁 /
- 屈曲 /
- 表面效应 /
- 挠曲电效应
Abstract: The surface elastic and flexoelectric effects significantly influence the mechanical behaviors of nanoscale materials and structures. The static buckling behaviors of piezoelectric semiconductor (PS) beams were studied through the establishment of an Euler-Bernoulli beam theoretical model in view of the Steigmann-Ogden surface elasticity and flexoelectricity. The governing equations and associated boundary conditions were derived under the Hamiltonian variational principle. In combination with the conservation equations for electrostatics and linear drift-diffusion equations, the analytical solutions of the effective elastic constants and critical buckling loads were obtained under both short and open circuit conditions. Numerical calculations were carried out to explore the effective elastic behaviors of the nanoscale PS beam under the effects of flexoelectricity, surface elasticity and shielding of charge carriers. This work provides a valuable guidance for designing high-performance electronic devices with piezoelectric semiconductor beams.
- piezoelectric semiconductor beam /
- buckling /
- surface effect /
- flexoelectric effect

HTML全文

图 1 n型压电半导体梁结构示意图

Figure 1. The sketch of an n-type piezoelectric semiconductor beam

下载: 全尺寸图片幻灯片

图 2 等效弹性常数对表面弹性常数c₁₁^s的依赖规律

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. The dimensionless effective elastic constants vs. GM surface elastic constant c₁₁^s

下载: 全尺寸图片幻灯片

图 3 等效弹性常数随矩形截面梁高度h的变化

Figure 3. The dimensionless effective elastic constants vs. height h

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图 4 Γ₁和Γ₂随n₀和h的变化

Figure 4. Dependences of Γ₁ and Γ₂ on n₀ and h

下载: 全尺寸图片幻灯片

表 1 短路条件下屈曲临界应力(σ_cr/MPa)

Table 1. Critical buckling stresses (σ_cr/MPa), for the short circuit condition

h/nm	c₁₁^s/(N/m)	l/h
h/nm	c₁₁^s/(N/m)	10	20	50	100
10	-81.97	1 304.3	326.08	52.173	13.043
10	81.97	2 154.2	538.56	86.169	21.542
50	-81.97	1 641.7	410.43	65.669	16.417
50	81.97	1 805.4	451.35	72.217	18.054

下载: 导出CSV

表 2 开路条件下屈曲临界应力(σ_cr/MPa)

Table 2. Critical buckling stresses (σ_cr/MPa), for the open circuit condition

h/nm	c₁₁^s/(N/m)	l/h
h/nm	c₁₁^s/(N/m)	10	20	50	100
10	-81.97	1 316.1	329.02	52.643	13.161
10	81.97	2 166.0	541.49	86.639	21.660
50	-81.97	1 641.9	410.48	65.677	16.419
50	81.97	1 805.6	451.41	72.225	18.056

下载: 导出CSV

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