Relative stability of Si surfaces: A first-principles study

Surface energies of Si(0 0 1), (1 1 0), (1 1 1), and (1 1 3) surfaces with different reconstructions are calculated systematically using first-principles total-energy method. In order to quantitatively compare their relative stability, the surface energies of different surface orientations and their respective theoretical bulk atom energies are determined simultaneously by linear fitting slab supercell total energy as a function of the atom number in the slab. Equivalent computational parameters and convergence criteria are used for all calculations. Without considering entropy contribution, the relative stability of these Si surfaces with given reconstructions is shown, in decreasing order, from (1 1 1) to (0 0 1) and (1 1 3) at low temperature, and from (0 0 1), (1 1 3), (1 1 0), to (1 1 1) at high temperature.