Institute of Physics, Academy of Sciences of the Czech Republic, v.v.i., Na Slovance 2, 182 21 Prague 8, Czech Republic.
J Phys Condens Matter. 2013 Jul 3;25(26):265003. doi: 10.1088/0953-8984/25/26/265003. Epub 2013 Jun 3.
During deposition on a stepped surface the growth mode depends on the conditions such as temperature T, deposition rate F and width of the terraces w. In this work we studied the influence of all the above mentioned characteristics using the kinetic Monte Carlo (kMC) technique. We concentrated on the conditions on the terrace at the moment of the first nucleation. The critical density of monomers for nucleation ηm decreases with the width of the terrace and the nucleation starts at surprisingly low densities of monomers. We tested several definitions of the critical width for nucleation wc used in various articles in the past and we compared our results with results of the analytical steady-state mean-field model (Ranguelov and Altman 2007 Phys. Rev. B 75 245419). To check how the simplified assumption about the steady-state regime during deposition influences the resulting dependence of wc =/~ (D/F)(κ), we set and also solved a time-dependent analytical model. This analytical model as well as kMC predict that wc =/~ (D/F)(1/5). kMC simulation also shows that the Ehrlich-Schwöbel barrier has only limited influence on the nucleation on the stepped surface at conditions close to the nucleation regime. For all widths of terraces there is a critical value of the Ehrlich-Schwöbel barrier ΔE(c)(ES)/k(B)T ~ 7.3 (ΔE(c)(ES) ~0.11 eV at T = 175 K), and only below this critical value does the Ehrlich-Schwöbel barrier affect the final value of the density of nuclei. The results of the kMC are summarized in a semi-empirical analytical formula which describes the dependence of the step-flow growth and nucleation on the terrace width w, diffusion coefficient D and deposition rate F. In our simulations we tested two models of the stepped surface with different thicknesses of the step, both with an Ehrlich-Schwöbel barrier on the edge of the terrace.
在阶跃表面上沉积时，生长模式取决于温度 T、沉积速率 F 和平台宽度 w 等条件。在这项工作中，我们使用动力学蒙特卡罗（kMC）技术研究了所有上述特征的影响。我们集中研究了在第一个成核瞬间平台上的条件。成核的单体临界密度 ηm 随平台宽度减小，并且单体密度低得令人惊讶时就开始成核。我们测试了过去在各种文章中使用的几个不同的临界成核宽度 wc 的定义，并将我们的结果与解析稳态平均场模型（Ranguelov 和 Altman，2007 年，Phys. Rev. B 75，245419）的结果进行了比较。为了检查在沉积过程中简化稳态假设如何影响 wc =/~ (D/F)(κ) 的结果依赖性，我们设定并求解了一个时间相关的解析模型。这个解析模型以及 kMC 预测 wc =/~ (D/F)(1/5)。kMC 模拟还表明，在接近成核条件下，Ehrlich-Schwöbel 势垒对台阶表面上的成核只有有限的影响。对于所有平台宽度，都存在一个临界的 Ehrlich-Schwöbel 势垒ΔE(c)(ES)/k(B)T ~ 7.3（ΔE(c)(ES) ~0.11 eV，T = 175 K），只有低于这个临界值，Ehrlich-Schwöbel 势垒才会影响核密度的最终值。kMC 的结果总结在一个半经验的解析公式中，该公式描述了台阶流生长和成核对平台宽度 w、扩散系数 D 和沉积速率 F 的依赖性。在我们的模拟中，我们测试了两种具有不同台阶厚度的台阶表面模型，都在平台边缘有一个 Ehrlich-Schwöbel 势垒。
