Quantifying the size-dependent effect of the residual surface stress on the resonant frequencies of silicon nanowires if finite deformation kinematics are considered
Quantifying the size-dependent effect of the residual surface stress on the resonant frequencies of silicon nanowires if finite deformation kinematics are considered
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DOI：
10.1088/0957-4484/20/11/115701
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发表时间：
2009-03
期刊：
影响因子：
3.5
通讯作者：
Harold S. Park
中科院分区：
文献类型：
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作者：
Harold S. Park
本研究有两个主要目标。第一个目标是证明，与线性表面弹性理论的预测相反，当考虑非线性、有限变形运动学时，残余表面应力确实会影响硅纳米线的共振频率。本研究的第二个目标是根据纳米线尺寸，描绘表面应力的残余（与应变无关）部分和表面弹性（与应变有关）部分对纳米线共振频率的相对贡献。这两个目标都是通过使用最近开发的表面柯西 - 玻恩模型实现的，该模型通过一个非线性、有限变形连续介质力学模型考虑纳米尺度的表面应力，从而解决纳米线共振频率的标准有限元特征值问题。除了证明残余表面应力确实会影响硅纳米线的共振频率外，我们还进一步表明其影响具有很强的尺寸依赖性；特别是，我们发现仅考虑残余表面应力会导致纳米线共振频率预测出现重大误差，且误差随着纳米线尺寸的减小而增大。相应地，发现表面应力的应变相关部分随着纳米线尺寸的减小对纳米线共振频率的影响越来越重要。
There are two major objectives to the present work. The first objective is to demonstrate that, in contrast to predictions from linear surface elastic theory, when nonlinear, finite deformation kinematics are considered, the residual surface stress does impact the resonant frequencies of silicon nanowires. The second objective of this work is to delineate, as a function of nanowire size, the relative contributions of both the residual (strain-independent) and the surface elastic (strain-dependent) parts of the surface stress to the nanowire resonant frequencies. Both goals are accomplished by using the recently developed surface Cauchy–Born model, which accounts for nanoscale surface stresses through a nonlinear, finite deformation continuum mechanics model that leads to the solution of a standard finite element eigenvalue problem for the nanowire resonant frequencies. In addition to demonstrating that the residual surface stress does impact the resonant frequencies of silicon nanowires, we further show that there is a strong size dependence to its effect; in particular, we find that consideration of the residual surface stress alone leads to significant errors in predictions of the nanowire resonant frequency, with an increase in error with decreasing nanowire size. Correspondingly, the strain-dependent part of the surface stress is found to have an increasingly important effect on the resonant frequencies of the nanowires with decreasing nanowire size.