D. J. Chadi

We present sets of special points in the Brillouin zone from which the average over the Brillouin zone of a periodic function of wave vector (e.g., energy, charge density, dipole matrix elements, etc.) can be determined in a simple and accurate way once the values of the function at these points are specified. We discuss a method for generating the special-point sets and apply it to the case of crystals with cubic and hexagonal Bravais lattices.

The efficiency of two different methods for obtaining "special" points useful for Brillouin-zone integrations of periodic functions is compared. We find that for some Bravais lattices (such as body-centered cubic and hexagonal), the method suggested by Monkhorst and Pack leads to different and sometimes less efficient point sets than those previously obtained by Chadi and Cohen. For a two-dimensional oblique lattice, special points twice as efficient as those suggested by Cunningham are given.

New structural models for 2\ifmmode\times\else\texttimes\fi{}1 and 4\ifmmode\times\else\texttimes\fi{}2 reconstructed (100) surfaces of Si determined from energy-minimization claculations are presented. The optimal 2\ifmmode\times\else\texttimes\fi{}1 and 4\ifmmode\times\else\texttimes\fi{}2 structures are found to correspond to asymmetric dimer geometries with partially ionic bonds between surface atoms, resulting in semiconducting surface electronic bands. The atomic and electronic structures for the 2\ifmmode\times\else\texttimes\fi{}1 and 4\ifmmode\times\else\texttimes\fi{}2 reconstructed surfaces are discussed.

The formation energies of single- and double-layer steps on Si(001) surfaces were calculated. For each case, two configurations with surface dimerization axes normal or parallel to the step edge were examined. Single-layer steps are found to have the lowest formation energy. Bilayer steps become energetically more favorable on surfaces misoriented towards [110] or [1\ifmmode\bar\else\textasciimacron\fi{}10] axes where low- and high-energy single-layer steps are forced to alternate with each other.

We have carried out ab initio total-energy density-functional calculations to study the reconstructions of GaAs(100) surfaces as a function of Ga and As surface coverage. Equilibrium atomic geometries and energies for Ga- and As-stabilized 1\ifmmode\times\else\texttimes\fi{}1, 2\ifmmode\times\else\texttimes\fi{}1, 1\ifmmode\times\else\texttimes\fi{}2, and 2\ifmmode\times\else\texttimes\fi{}2 surfaces consisting of various combinations of dimers and vacancies were determined. Dimerization of Ga (As) surface atoms is calculated to lower the energy by 1.7 eV (0.7 eV) per dimer and to lead to the most stable atomic configurations. For half-monolayer coverages, relaxation energies are very large, and nondimerized structures are only slightly (0.03--0.05 eV per 1\ifmmode\times\else\texttimes\fi{}1 cell) higher in energy. Asymmetric dimers were tested for As surfaces and found to be higher in energy than symmetric dimers. The stability of surfaces in equilibrium with Ga and As sources is considered and it is shown that the chemical potentials are restricted within limits set by the free energies of the elemental bulk phases of Ga and As. Ab initio calculations of these bulk energies at T=0 K determine the limiting chemical potentials and also the heat of formation, which we find to be 0.73 eV per GaAs pair, compared with the experimental value of 0.74 eV. Our calculations indicate that with excess bulk As available, a full monolayer coverage of As is energetically more favorable than a half-monolayer coverage, whereas with excess Ga available, the surface energy of full and half-monolayer coverages are nearly the same. To examine the effects of larger unit-cell dimensions on total energies, we rely on results from tight-binding calculations. For half-monolayer coverages, 2\ifmmode\times\else\texttimes\fi{}4 unit cells are found to have a significantly lower energy than 2\ifmmode\times\else\texttimes\fi{}2 cells not because of a greater lattice relaxation but because of orbital rehybridization effects which are not possible in a smaller cell. The results of the ab initio and tight-binding calculations indicate that the optimal surface coverage for Ga- and As-terminated surfaces is less than a full monolayer.