Surface energy and the common dangling bond rule for semiconductors

Equilibrium shape and surface energies are among the most basic properties of finite crystals. Yet, an effective approach for accurately calculating individual energy for polar semiconductor surfaces is still lacking, and there is not a general rule regarding surface energies of different orientations. Here, we suggest a wedge-shaped geometry for calculating individual surface energies by direct, first-principles methods. Applications to prototypical semiconductors, Ge, GaAs, and ZnSe, establish a surprisingly simple common dangling bond rule relating surface energies to local chemical similarities.