METHOD OF LINEAR COMBINATION OF STRUCTURAL MOTIFS FOR SURFACE AND STEP ENERGY CALCULATIONS - APPLICATION TO GAAS(001)

First-principles calculations of the atomic structure and formation en ergies of semiconductor surfaces and surface steps are often complicat ed by the existence of complex structural patterns. We suggest here a simpler, algebraic (not differential) approach that is based on two ob servations distilled from previous first-principles calculations. Firs t, a relatively large collection of equilibrium structures of surfaces and bulk point defects can be built from a limited number of recurrin g local ''structural motifs,'' including for GaAs tetrahedrally bonded Ga and As and miscoordinated atoms such as threefold-coordinated pyra midal As. Second, the structure is such that band-gap levels are empti ed, resulting in charged miscoordinated atoms. These charges compensat e 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 represen ting the Madelung energy of point charges. The motif energies are deri ved by fitting them to a set of pseudopotential total-energy calculati ons for flat GaAs(001) surfaces and for point defects in bulk GaAs. Th is set of parameters is shown to suffice to reproduce the energies of other (001) surfaces, calculated using the same pseudopotential approa ch. Application of the ''linear combination of structural motif'' (LCS M) method to Bat GaAs(001) surfaces reveals the following: (i) The obs erved h(2x3) surface may be a disordered c(8x6) surface. (ii) The obse rved (2x6) surface is a metastable surface, only 0.03 eV/(1x1) higher than the alpha(2x4) surface having the same surface coverage. (iii) We confirm the recent suggestion by Hashizume et al, that the observed g amma(2x3) phase of the (2x4) surface is a mixture of the beta 2(2x4) a nd c(4x4) surfaces. In particular, we examined an 8x7 surface structur e which has a lower energy than the earlier proposed gamma(12x4) struc ture. Application of the LCSM method to prototype steps on the GaAs(00 1)-(2x4) surface is illustrated, comparing the LCSM results directly t o pseudopotential results.