A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories
A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories
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使用经典轨迹计算 Si 在 Si(111) 上的扩散系数的唯象方法
DOI：
10.1063/1.448429
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发表时间：
1985
影响因子：
4.4
通讯作者：
D. Thompson
中科院分区：
文献类型：
--
作者：
I. Noorbatcha;L. Raff;D. Thompson
本文提出了一种由吸附原子从一个吸附点到另一个吸附点的跳跃频率计算表面扩散系数的上界和下界的一般方法。该方法已用于Si在Si（111）表面的扩散。Keating势已被用于Si（111）晶格。吸附原子和晶格之间的相互作用势是涉及晶体的第一层和第二层中的Si原子的60个莫尔斯势的成对和。该势公式预测了Si（111）表面上存在两种不同类型的吸附位。从这些吸附位点的跳跃频率已被计算的经典轨迹方法。使用这些跳跃频率，通过求解一组描述相邻吸附位点之间的吸附原子跳跃的耦合唯象动力学方程来计算扩散系数的下限。在800、1000、1200和1500 K下的结果得出扩散系数D的下限>（8.53±1.11）×exp{−（2430±270）/RT} cm 2/s。在1500 K时，计算的均方位移和速度自相关函数分别给出7.11×10−4和8.69×10−4 cm 2/s的扩散系数，这比1500 K时计算的下限高出约2倍。这表明Si在Si（111）上的扩散涉及高度相关的运动。通过从耦合动力学方程组中去除所有涉及吸附原子运动的项，从而获得扩散系数的上限估计。在1500 K时，以这种方式计算的上限为1.41×10−3 cm 2/s，比计算的扩散系数大2倍。表面扩散活化能的计算（2.43 kcal/mol）表明，从超高真空中Si在Si（111）上的直接沉积获得的该量的实验值最准确地代表了Si（111）上真正的零覆盖极限。无扭结和台阶的晶体.计算跳跃的表面扩散系数的下限和估计上限的一般方法吸附原子从一个吸收位置到另一个吸收位置的频率已被公式化。该方法已用于Si在Si（111）表面的扩散。Keating势已被用于Si（111）晶格。吸附原子和晶格之间的相互作用势是涉及晶体的第一层和第二层中的Si原子的60个莫尔斯势的成对和。该势公式预测了Si（111）表面上存在两种不同类型的吸附位。从这些吸附位点的跳跃频率已被计算的经典轨迹方法。使用这些跳跃频率，通过求解一组描述相邻吸附位点之间的吸附原子跳跃的耦合唯象动力学方程来计算扩散系数的下限。在800，1000，1200，和1500 K的结果产生一个下限的差异。
A general method to calculate a lower bound and an estimated upper bound for the surface diffusion coefficient from jump frequencies of an adatom from one absorption site to another has been formulated. This method has been applied to the surface diffusion of Si on Si(111). Keating’s potential has been used for the Si(111) lattice. The interaction potential between the adatom and the lattice is a pairwise sum of 60 Morse potentials involving the Si atoms in the first and second layers of the crystal. This potential formulation predicts the existence of two different types of adsorption sites on the Si(111) surface. The jump frequencies from these adsorption sites have been calculated by classical trajectory methods. Using these jump frequencies, a lower bound for the diffusion coefficient is calculated by solving a set of coupled phenomenological kinetic equations describing the jumping of adatoms between adjacent adsorption sites. The results at 800, 1000, 1200, and 1500 K yield a lower bound for the diffusion coefficient of D>(8.53±1.11)×exp{−(2430±270)/RT} cm2/s. At 1500 K, the computed mean‐square displacement and velocity autocorrelation function give diffusion coefficients of 7.11×10−4 and 8.69×10−4 cm2/s, respectively, which is in excess of the calculated lower bound at 1500 K by about a factor of 2. This suggests that diffusion of Si on Si(111) involves highly correlated motion. An estimate for the upper bound for the diffusion coefficient is obtained by removing from the set of coupled kinetic equations all terms involving adatom motion which leads back toward the original adsorption site. The upper bound calculated in this manner at 1500 K is 1.41×10−3 cm2/s, which is a factor of 2 greater than the computed diffusion coefficient. The calculated activation energy for surface diffusion (2.43 kcal/mol) suggests that the experimental value for this quantity obtained from the direct deposition of Si on Si(111) in ultra high vacuum most accurately represents the true zero‐coverage limit on a Si(111) crystal free of kinks and steps.A general method to calculate a lower bound and an estimated upper bound for the surface diffusion coefficient from jump frequencies of an adatom from one absorption site to another has been formulated. This method has been applied to the surface diffusion of Si on Si(111). Keating’s potential has been used for the Si(111) lattice. The interaction potential between the adatom and the lattice is a pairwise sum of 60 Morse potentials involving the Si atoms in the first and second layers of the crystal. This potential formulation predicts the existence of two different types of adsorption sites on the Si(111) surface. The jump frequencies from these adsorption sites have been calculated by classical trajectory methods. Using these jump frequencies, a lower bound for the diffusion coefficient is calculated by solving a set of coupled phenomenological kinetic equations describing the jumping of adatoms between adjacent adsorption sites. The results at 800, 1000, 1200, and 1500 K yield a lower bound for the dif...