再论随机沉积中的表面扩散
Revisiting Surface Diffusion in Random Deposition
摘要：
本文用解析方法和推理方法研究了随机沉积模型中表面扩散的影响。对于任何给定的站点，颗粒可以扩散的程度由该站点紧邻的形态决定。从第一性原理出发，推导出了一个解析表达式，用于计算粒子在任意位置扩散到给定长度的概率。使用该方法，不同的扩散长度的概率计算和它们的依赖系统的大小和沉积层的数量进行了研究。对具有不同扩散程度的随机沉积模型中的表面扩散进行了数值模拟，并根据解析计算对模拟结果进行了解释。从而对扩散过程和扩散长度对表面粗糙度的影响有了更清楚的认识。具有表面扩散的系统表现出几乎随机的沉积样行为高达单层沉积。在对数图中，它们的界面宽度最初是线性的，就像随机沉积一样。随着层数的增加，相邻列之间的相关效应变得占主导地位。界面偏离其初始的线性增长，并最终变得饱和。这种行为的解释进行了讨论，并从线性形式的出发点估计分析。
英文摘要：
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate neighbourhood of the site. An analytical expression is derived to calculate the probability of a particle at any chosen site to diffuse to a given length, from first principles. Using the method, the probabilities for different diffusion lengths are calculated and their dependence on system size and the number of deposited layers is studied. Numerical simulation of surface diffusion in random deposition model with varying extents of diffusion are performed and their results are interpreted in the light of the analytical calculations. Thus, a clearer understanding of the diffusion process and the effect of diffusion length on surface roughness is obtained. Systems with surface diffusion show nearly random deposition-like behaviour upto monolayer deposition. Their interface widths, in a logarithmic plot, are initially linear, as in random deposition. With increase in the number of layers, correlation effects between neighbouring columns become dominant. The interface deviates from its initial linear growth and eventually becomes saturated. An explanation for this behaviour is discussed and the point of departure from the linear form is estimated analytically.
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