The Blackett Laboratory, Imperial College London, London SW7 2BZ, United Kingdom.
Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, London WC1E 6BT, United Kingdom.
J Chem Phys. 2018 Nov 21;149(19):194107. doi: 10.1063/1.5049548.
We present a procedure for simulating epitaxial growth based on the phase-field method. We consider a basic model in which growth is initiated by a flux of atoms onto a heated surface. The deposited atoms diffuse in the presence of this flux and eventually collide to form islands which grow and decay by the attachment and detachment of migrating atoms at their edges. Our implementation of the phase-field method for this model includes uniform deposition, isotropic surface diffusion, and stochastic nucleation (in both space and time), which creates islands whose boundaries evolve as the surface atoms "condense" into and "evaporate" from the islands. Computations using this model in the submonolayer regime, prior to any appreciable coalescence of islands, agree with the results of kinetic Monte Carlo (KMC) simulations for the coverage-dependence of adatom and island densities and island-size distributions, for both reversible and irreversible growth. The scaling of the island density, as obtained from homogeneous rate equations, agrees with KMC simulations for irreversible growth and for reversible growth for varying deposition flux at constant temperature. For reversible growth with varying temperature but constant flux, agreement relies on an estimate of the formation energy of the critical cluster. Taken together, our results provide a comprehensive analysis of the phase-field method in the submonolayer regime of epitaxial growth, including the verification of the main scaling laws for adatoms and island densities and the scaling functions for island-size distributions, and point to the areas where the method can be extended and improved.
我们提出了一种基于相场法模拟外延生长的方法。我们考虑了一个基本模型，其中生长是由原子通量在加热表面上引发的。在这种通量的存在下，沉积的原子会扩散，最终碰撞形成岛屿，这些岛屿通过边缘迁移原子的附着和脱离而生长和衰减。我们为这个模型实现的相场方法包括均匀沉积、各向同性表面扩散和随机成核（在空间和时间上），这会创建出其边界随着表面原子“凝聚”和“蒸发”而演变的岛屿。在亚单层区域中使用这个模型进行的计算，在任何明显的岛屿聚结之前，与动力学蒙特卡罗（KMC）模拟的结果一致，这些结果涉及到在吸附原子和岛屿密度以及岛屿尺寸分布方面对覆盖率的依赖性，适用于可逆和不可逆生长。从均匀速率方程中得到的岛屿密度的标度与 KMC 模拟的不可逆生长以及在恒定温度下随沉积通量变化的可逆生长的结果一致。对于随温度变化但通量恒定的可逆生长，一致性依赖于对临界团簇形成能的估计。总的来说，我们的结果提供了外延生长亚单层区域中相场方法的全面分析，包括对吸附原子和岛屿密度的主要标度律以及岛屿尺寸分布的标度函数的验证，并指出了可以扩展和改进该方法的领域。
