Augmentation of the electron counting rule with Ising model.

The stability of a mixture of two different surface reconstructions is investigated focusing on GaN(0001) surface mixed with Ga a d (2 × 2) and 3Ga-H(2 × 2) domains using the density functional theory calculations. Since the number of candidate structures is enormous, the structures sampled by Bayesian optimization are analyzed. As a result, the local electron counting (EC) rule alone was found to be insufficient to explain such stability. Then, augmenting the EC rule, a data-driven Ising model is proposed. The model allows the evaluation of the whole enormous number of candidate structures. The approach is expected to be useful for theoretical studies of such mixtures on various semiconductor surfaces. [ABSTRACT FROM AUTHOR]