Papac Joe, Margetis Dionisios, Gibou Frederic, Ratsch Christian
Department of Mathematics, University of California, Los Angeles, California 90095, USA.
Department of Mathematics, and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):022404. doi: 10.1103/PhysRevE.90.022404. Epub 2014 Aug 14.
We formulate and implement a generalized island-dynamics model of epitaxial growth based on the level-set technique to include the effect of an additional energy barrier for the attachment and detachment of atoms at step edges. For this purpose, we invoke a mixed, Robin-type, boundary condition for the flux of adsorbed atoms (adatoms) at each step edge. In addition, we provide an analytic expression for the requisite equilibrium adatom concentration at the island boundary. The only inputs are atomistic kinetic rates. We present a numerical scheme for solving the adatom diffusion equation with such a mixed boundary condition. Our simulation results demonstrate that mounds form when the step-edge barrier is included, and that these mounds steepen as the step-edge barrier increases.
我们基于水平集技术制定并实施了一种外延生长的广义岛动力学模型，以纳入原子在台阶边缘附着和脱离时额外能量势垒的影响。为此，我们对每个台阶边缘吸附原子（吸附原子）的通量引入了一种混合的罗宾型边界条件。此外，我们给出了岛边界处所需平衡吸附原子浓度的解析表达式。唯一的输入是原子动力学速率。我们提出了一种用于求解具有这种混合边界条件的吸附原子扩散方程的数值方案。我们的模拟结果表明，当包含台阶边缘势垒时会形成丘状结构，并且随着台阶边缘势垒的增加，这些丘状结构会变陡。
