Ograin Christopher, Lowengrub John
University of California, Santa Barbara, California 93106, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061606. doi: 10.1103/PhysRevE.84.061606. Epub 2011 Dec 20.
The morphology of the solid-vapor interface of a nanoscale thin crystalline film is influenced by many factors including surface diffusion, attachment-detachment, deposition, and interface kinetics. Using a high-order accurate and efficient numerical method, we investigate the dynamics of two dimensional thin films when all of these effects are considered. The observed morphologies consist of facets of constant slope separated by narrow transition intervals: kinks (valleys) and antikinks (hills). The number of kinks and antikinks decreases as the system coarsens in time. Our numerical results confirm that when deposition is present, the only possible coarsening event is the kink-ternary where two kinks meet and annihilate an antikink. We characterize the total amount of coarsening, the time over which the coarsening occurs and the associated coarsening scaling laws when all effects are considered. As found in previous work that considered only attachment-detachment, or surface diffusion, there are three distinct coarsening regimes associated with increasing magnitudes of the deposition flux-fast coarsening, a regime in which periodic structures form with little or no subsequent coarsening, and a regime in which the film surface evolves chaotically. We find that the inclusion of attachment-detachment leads to additional coarsening compared to the dynamics that result from driven surface diffusion alone. When deposition and interface kinetics are both considered, the slowdown of evolution caused by the kinetic effects necessitates a decrease in the deposition flux in order to produce a nonchaotic coarsening regime. Together, these provide testable predictions for experiments of thin-film dynamics.
纳米级薄晶体薄膜的固-气界面形态受许多因素影响，包括表面扩散、附着-脱离、沉积和界面动力学。我们使用一种高阶精确且高效的数值方法，研究当考虑所有这些效应时二维薄膜的动力学。观察到的形态由具有恒定斜率的小面组成，这些小面由狭窄的过渡区间分隔：扭折（谷）和反扭折（山）。随着系统随时间粗化，扭折和反扭折的数量会减少。我们的数值结果证实，当存在沉积时，唯一可能的粗化事件是扭折-三元事件，即两个扭折相遇并湮灭一个反扭折。我们表征了在考虑所有效应时粗化的总量、粗化发生的时间以及相关的粗化标度律。正如在之前仅考虑附着-脱离或表面扩散的工作中所发现的那样，存在三种与沉积通量大小增加相关的不同粗化 regime——快速粗化，一种形成周期性结构且随后几乎没有或没有粗化的 regime，以及一种薄膜表面混沌演化的 regime。我们发现，与仅由驱动表面扩散导致的动力学相比，包含附着-脱离会导致额外的粗化。当同时考虑沉积和界面动力学时，由动力学效应引起的演化减慢需要降低沉积通量，以产生非混沌的粗化 regime。这些共同为薄膜动力学实验提供了可测试的预测。
