Method of linear combination of structural motifs for surface and step energy calculations: Application to GaAs(001).

Abstract

First-principles calculations of the atomic structure and formation energies of semiconductor surfaces and surface steps are often complicated by the existence of complex structural patterns. We suggest here a simpler, algebraic (not differential) approach that is based on two observations distilled from previous first-principles calculations. First, a relatively large collection of equilibrium structures of surfaces and bulk point defects can be built from a limited number of recurring local ``structural motifs,'' including for GaAs tetrahedrally bonded Ga and As and miscoordinated atoms such as threefold-coordinated pyramidal As. Second, the structure is such that band-gap levels are emptied, resulting in charged miscoordinated atoms. These charges compensate each other. We thus express the total energy of a given surface as a sum of the energies of the motifs, and an electrostatic term representing the Madelung energy of point charges. The motif energies are derived by fitting them to a set of pseudopotential total-energy calculations for flat GaAs(001) surfaces and for point defects in bulk GaAs. This set of parameters is shown to suffice to reproduce the energies of other (001) surfaces, calculated using the same pseudopotential approach. Application of the ``linear combination of structural motif'' (LCSM) method to flat GaAs(001) surfaces reveals the following: (i) The observed h(2\ifmmode\times\else\texttimes\fi{}3) surface may be a disordered c(8\ifmmode\times\else\texttimes\fi{}6) surface. (ii) The observed (2\ifmmode\times\else\texttimes\fi{}6) surface is a metastable surface, only 0.03 eV/(1\ifmmode\times\else\texttimes\fi{}1) higher than the \ensuremath{\alpha}(2\ifmmode\times\else\texttimes\fi{}4) surface having the same surface coverage. (iii) We confirm the recent suggestion by Hashizume et al. that the observed \ensuremath{\gamma}(2\ifmmode\times\else\texttimes\fi{}4) phase of the (2\ifmmode\times\else\texttimes\fi{}4) surface is a mixture of the \ensuremath{\beta}2(2\ifmmode\times\else\texttimes\fi{}4) and c(4\ifmmode\times\else\texttimes\fi{}4) surfaces. In particular, we examined an 8\ifmmode\times\else\texttimes\fi{}7 surface structure which has a lower energy than the earlier proposed \ensuremath{\gamma}(2\ifmmode\times\else\texttimes\fi{}4) structure. Application of the LCSM method to prototype steps on the GaAs(001)-(2\ifmmode\times\else\texttimes\fi{}4) surface is illustrated, comparing the LCSM results directly to pseudopotential results. \textcopyright{} 1996 The American Physical Society.