Structure and formation energy of steps on the GaAs(001)-2 × 4 surface

The energies of various steps on the As-terminated GaAs(001)-2 × 4 surface are evaluated using a novel, approximate method of “linear combination of structural motifs”. It is based on the observation that previous total energy minimizations of semiconductor surfaces produced invariably equilibrium structures made of the same recurring local structural motifs, e.g. tetrahedral fourfold Ga, pyramidal threefold As, etc. Furthermore, such surface structures were found to obey consistently the octet rules as applied to the local motifs. We thus express the total energy of a given semiconductor surface as a sum of (i) the energies _M of the local structural motifs appearing in the surface under consideration and (ii) an electrostatic term representing the Madelung energy of point charges resulting from application of the octet rule. The motif energies are derived from a set of pseudopotential total energy calculations for flat GaAs(001) surfaces and for point defects in bulk GaAs. This set of parameters suffices to reproduce the energies of other (001) surfaces, calculated using the same pseudopotential total energy approach. Application to GaAs(001)-2 × 4 surfaces with steps reveals the following. (i) “Primitive steps”, defined solely according to their geometries (i.e. step heights, widths and orientations) are often unstable. (ii) Additional, non-geometric factors beyond step geometries such as addition of surface adatoms, creation of vacancies and atomic rebonding at step edges are important to lower step energies. So is step-step interaction. (iii) The formation of steps is generally endothermic. (iv) The formation of steps with edges parallel to the direction of surface As dimers (A steps) is energetically favored over the formation of steps whose edges are perpendicular to the As dimers (B steps).