New development and evaluation of stress analysis in nano-scale domain considering surface stresses

2002-2003年间，我们完成了《考虑表面应力的纳米尺度应力分析的新进展与评价》研究。在考虑表面应力的情况下，我们对表面现象进行了一些基本的分析。最后，我们可以得到以下结果：1.我们可以推导出各向异性材料中表面应力以阶跃方式变化的应力和位移的简单表达式。利用这个表达式，当As、Ge等覆盖在Si表面时，Si表面的键长发生变化，从而可以估算出键长的变化。用第一性原理计算了粘接长度的变化。2.利用弹性理论对粘接接触进行了分析。考虑表面应力的边界条件，表面应力来源于表面能。压头和衬底的表面均采用该方法。此外，还假设粘附区的表面应力与…不同比非粘附区的应力大得多，并从原始表面应力中降低。将抛物面压头压入基板，并在压头和基板的两个表面之间发生粘结。由于表面应力的变化，压头与衬底粘结区的表面向内变形。这意味着为了保持区域之间的接触而在粘合区之间产生吸引力，并且需要压头从衬底的拉出力。测试了压头与基板之间的接触压力分布、粘附区的表面轮廓和粘附力。分析结果与赫兹理论的结果进行了比较。根据赫兹理论，压头与基板之间的总力约为无因次接触载荷的0.04~0.06。3.利用弹性力学理论推导了考虑表面应力的表面格林函数。此外，还推导了表面偶极格林函数，并与分子动力学理论得到的表面原子位移进行了比较。考虑表面应力的理论在纳米尺度领域是有用的。较少

We performed the study titled of 'New development and evaluation of stress analysis in nano-scale domain considering surface stresses' from 2002 to 2003. We performed several fundamental analyses on surface phenomena considering surface stresses. Finally, we could get the following results.1.We could derive simple expressions for stresses and displacements in anisotropic materials where surface stresses vary in a step manner. Using this expressions, when As,Ge and so on cover the surface on Si, the bond length at Si surface varies, and then the variation of bond length could be evaluated. The variation of bond length was evaluated using the first principle calculation.2.The adhesion contact analysis using the theory of elasticity was performed. The boundary condition considering the surface stresses, which are originated from surface energy. was employed for the surfaces of indenter and substrate. Furthermore, it was supposed the surface stresses in an adhesion region are different fro … More m that in a non-adhesion region and are reduced from the original surface stresses. A paraboloidal indenter is pressed into the substrate and adhesion occurs between two surfaces of the indenter and the substrate. The surfaces at the adhesion regions of the indenter and the substrate deformed inward due to the variation of the surface stresses. This means that the attractive force between the adhesion region occurs for maintaining the contact of the regions and the pull-off force of the indenter from the substrate is needed. The distribution of contact pressure, the surface profile of adhesion region and adhesive force between the indenter and the substrate were precisely examined. The results in the analysis were compared with those in the Hertz theory. The total force between the indenter and the substrate was about the value of 0.04 to 0.06 reduced from the dimensionless contact load based on Hertz theory.3.Surface Green function considering surface stresses is derived using the theory of elasticity. Furthermore, a surface dipole Green function was derived, and the displacements at the surface atoms deduced from the theory were compared with those from MD. The theory considering surface stresses is useful in a nano scale domain. Less