An approach to calculate surface effects of polyhedron nanocrystals and its application in silicon nanowires

Abstract

A stretch-release strategy is proposed to analyze the problem of surface energy-induced stress fields in nanocrystals, which is resolved into a stretch sub-problem and a release sub-problem using the superposition principle. The surface effect of silicon nanowires with hexagonal cross-sections is analyzed by the proposed method. The severe stress concentration near the triple junctions of the wire surfaces and the large shear stress on the plane {111} is quantified, which provides a solid mechanical explanation for the kink phenomena in growth transition from direction 〈111〉 to 〈112〉 observed in experiments. Different from the conventional view of negligible surface effect for bulk material, we found that there exists a size-independent part of the surface effect on the stress in the order of tens or hundreds of mega Pascal, which corresponds to the stretch-induced biaxial stress in the surface layer and the shape influence of the geometry of nanocrystals. This size-independent part could well explain the size-independent kinking phenomenon during the growth of silicon nanowires.

摘要

本文提出一种“拉伸-释放”策略, 将表面能在纳米晶体内引起应力场的问题分解为拉伸子问题和释放子问题. 基于该策略和有限元方法分析了表面能在硅纳米线表面角点附近的应力集中和{111}面上的切应力, 为实验中观察到的硅纳米线生长方向由〈111〉转向〈112〉的扭结现象提供了坚实的力学解释. 与传统的块状材料表面效应可忽略的观点不同, 研究发现, 由于表面层拉伸引起的双轴应力和纳米晶体几何形状的影响, 表面能引起的应力存在与尺寸无关的部分, 其值可达数十至数百兆帕. 这一尺寸无关的表面效应很好地解释了硅纳米线生长扭结与纳米线粗细无关的实验现象.