Cu台阶面多层弛豫的第一性原理研究

First-principles study of the multilayer relaxation of Cu stepped surfaces

采用基于密度泛函理论的第一性原理赝势平面波方法对Cu(311),(511),(331)和(221)四个高指数台阶表面的弛豫结构和弛豫后表面各层的电子特性进行了系统研究.发现四个台阶面的层间弛豫规律依次为-+-…,--+-…,--+-…和---+-…,与其平台-阶梯n(hkl)×(uvw)的表示法2(100)×(111),3(100)×(111),3(111)×(111)和4(111)×(111)中的原子排数n相关,即对有(100)或(111)平台的台阶面,弛豫后最外的n-1个层间距都减小,第n个层间距增大,而随后的第n+1个层间距又减小,并且对有相同平台和阶梯的台阶面,n越大即平台越宽,弛豫后与真空接触的平台面垂直于表面的距离(第一层到第n层的层间距)Δd1,n缩短得越多.Cu(511)和(331)面并不会出现有些文献提到的反常弛豫行为.对所有台阶面,台阶棱上的原子(第一层)的电子态密度在费米能级以下的高能区明显有一个最大的峰值,而在低能区没有峰值,即有更多的电子处于高占据态.这也是台阶棱上的原子最不稳定、在外界的作用下最容易被驱使和剥离的原因.对有相同的平台和阶梯的台阶面,位于台阶棱上的原子、台阶角处的原子、平台中间紧挨着角处的原子及紧挨棱和角处的下层原子的电子态密度曲线分别具有相似的形状.

Using the pseudopotential plane wave（PPPW） method,we performed first principles calculation for the multilayer relaxations and the electron properties of the high-Miller-index stepped Cu（311）,（511）,（331） and（221） surfaces,which are expressed by 2（100）×（111）,3（100）×（111）,3（111）×（111） and 4（111）×（111）,respectively,in the terrace-step notation,i.e.n（hkl）×（uvw）.The interlayer relaxations of them are-＋-…,-＋-…,-＋-… and-＋-…,respectively,which follow the atom-row trend：for stepped Cu surface which has n atom rows in the（100） or（111） terrace,the outermost n-1 interlayer spaces contract,then the n interlayer space expands,and the following n ＋ 1 interlayer space contracts again.For the stepped surfaces with the same（hkl） ×（uvw）,the larger the number of atom rows n in the terrace,the greater the contraction magnitude for Δd1,n.We did not find any indication of anomalous relaxation behavior for Cu（511） and（331） as mentioned in some references.Below Fermi energy level,the density of states of the first layer atom at stepped edge has the largest peak value in higher energy regions and has no peak in lower energy regions,so the first layer atom is most unstable and can be dislodged and peeled off more easily than other surface atoms.For the stepped surfaces with the same（hkl）×（uvw）,the curves of the density of states have similar shapes for the atoms at the step edge,at the corner,at the terrace and near the corner,and the atoms under the step edge and near the corner.