CFN Colloquium

First-principles studies often rely on the assumption of equilibrium, which can be a poor approximation, e.g., for epitaxial growth. Here, we propose a general effective chemical potential (μ ¯) approach for non-equilibrium systems. It incorporates growth kinetics into the chemical potential, while maintaining its correct equilibrium limits. In studying molecular beam epitaxy (MBE), we divide the process into three stages: pre-nucleation, nucleation, island growth, and focus our efforts on the first two. For the pre-nucleation stage, we solve the rate equations for small clusters on the surface, which serve as the feedstock for the growth, and find that μ ¯ is determined by the most probable, rather than by the lowest-energy, clusters. While this finding contradicts the equilibrium theory (which is in favor of the lowest-energy state), it reinforces the fundamental principle of statistic mechanics. In the case of Bi2Se3, μ ¯ is found to be highly supersaturated. As μ ¯ determines the nucleation barrier for the nucleation stage, this supersaturation leads to a high nucleus concentration and small-sized islands, in qualitative agreement with experiment.