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First-principles studies often rely on the assumption of equilibrium, whichcan be a poor approximation, e.g., for growth. Here, an effective chemicalpotential method for non-equilibrium systems is developed. A salient feature ofthe theory is that it maintains the equilibrium limits as the correct limit. Inapplication to molecular beam epitaxy, rate equations are solved for theconcentrations of small clusters, which serve as feedstock for growth. We findthat the effective chemical potential is determined by the most probable,rather than by the lowest-energy, cluster. In the case of Bi2Se3, the chemicalpotential is found to be highly supersaturated, leading to a high nucleusconcentration in agreement with experiment.

Effective chemical potential for non-equilibrium systems and its application to molecular beam epitaxy of Bi2Se3