Study of silicon crystal surface formation based on molecular dynamics simulation results

The equilibrium shape of 〈110〉-oriented single crystal silicon nanowire, 8 nm in cross-section, was found from molecular dynamics simulations using LAMMPS molecular dynamics package. The calculated shape agrees well to the shape predicted from experimental observations of nanocavities in silicon crystals. By parametrization of the shape and scaling to a known value of {111} surface energy, Wulff form for solid-vapor interface was obtained. The Wulff form for solid-liquid interface was constructed using the same model of the shape as for the solid-vapor interface. The parameters describing solid-liquid interface shape were found using values of surface energies in low-index directions known from published molecular dynamics simulations. Using an experimental value of the liquid-vapor interface energy for silicon and graphical solution of Herring's equation, we constructed angular diagram showing relative equilibrium orientation of solid-liquid, liquid-vapor and solid-vapor interfaces at the triple phase line. The diagram gives quantitative predictions about growth angles for different growth directions and formation of facets on the solid-liquid and solid-vapor interfaces. The diagram can be used to describe growth ridges appearing on the crystal surface grown from a melt. Qualitative comparison to the ridges of a Float zone silicon crystal cone is given.