薄膜表面的吸附与扩散课件.pptVIP

As with virtually all mass-transport-related reliability problems, damage is thermally activated. For pure Al conductors n is typically 2, and Ee, the activation energy for electromigration failure, ranges from 0.5 to 0.8 eV depending on grain size. In contrast, an energy of 1.4 eV is associated with lattice diffusion. Therefore, low-temperature electromigration damage in films is clearly dominated by GB transport. The constant K is dependent on film structure and processing. In order to improve the life of Al metallizations more electromigration-resistant alloys have been developed over the years. In this regard, Al alloyed with a few percent Cu can extend conductor life by perhaps an order of magnitude relative to pure Al. The reasons for this are not completely understood, but it appears that Cu reduces the GB migration of the solvent Al * 增原子的结合能作为位置的函数, 可以表示为z=f(x,y)的曲面. 如图是Brocks(Phys.Rev.Lett.,66, 1729(1991))等用第一原理总能计算方法得到的Si(001)-(2?1)再构表面元胞上增原子结合能的透视图(上)和能量轮廓图(下). 它的X轴通过二聚体(两个靠近的黑原子), 二聚体在Y方向形成链. H点是链内亚稳的势能谷, M点是二聚体链外侧沟内的最稳定的能量最低的势能谷(M点外围第一轮廓线的能量升高0.1eV, 再外面的轮廓线的能量间隔是0.2eV). 它比H势能谷低0.25eV, 鞍点D和B的能量比M点分别高0.6eV和1.0eV. H位置的增原子要经过一个势垒才能到达M位置. 热激活提供的能量可以使增原子跳到相邻的最稳定位置, 但也可以使H位置的原子经过D点跳到相邻的H位置, 此时需要的激活能小于0.6eV, 是一个快速的扩散通路. 而从M点经过H点跳到二聚体链另一侧的M位置需要的激活能为0.8eV. 这就是增原子的扩散过程的各向异性. Mo等得到Si(001)的Ed为0.67eV. * 可用对势模型来估算表面缺陷的形成能和迁移能 so adding (or subtracting) an atom from a kink site is equivalent to condensing (or subliming) an atom from the bulk. This last result may seem surprising, but it arises because moving a kink around on the surface leaves the number of T, L and K atoms, and the energy of the surface, unchanged. * 扩散的驱动力是化学势差，化学势与熵相关，所以需要考虑熵的变化 * 扩散系数的差别主要在于扩散激活能 * * 步长大的替换所需能量大很多 估算并比较Cu（100）表面沿沟扩散和越沟扩散过程的能量变化及其对比 估算Cu（100）表面替代过程的能量变化 在无再构的密排面上, 由于衬底原子和增原子的互作用强、增原子之间的互作用弱, 二聚体中的单原子分别迁移并且不离开另一原子, 其激活能仅比单原子分别迁移大约0.1eV, 附加的这个能量主要用来提供迁移过程中增原子键长被拉长之需. 在非密排表面或再构的表面上, 由于增原子之间的互作用强, 二聚体将一起迁移或替换. 表中包括了铱二聚体的扩散数据(最后两行), 迁移激活能比替换激活能低0.13eV. 和单个增原子在(110)-(1?1)表面上迁移激活能比替换