Radius selection and droplet unpinning in vapor-liquid-solid-grown nanowires

Abstract

The requirements for steady nanowire growth under near-equilibrium conditions in the vapor-liquid-solid (VLS) method is examined with particular emphasis on the configuration of the liquid droplet. It is found that the final radius of a cylindrical wire is selected by the fixed volume of liquid VL and the surface-energy ratio γsl/γlv but is independent of the solid-vapor energy γsv. Existing models for growth, based on a balance of configurational forces at the triple junction, are shown to be consistent with the principle of maximal release of free energy. Gibbs’s results on allowable contact angles at a sharp corner predict conditions on γsl/γlv and γsv/γlv for the existence of straight-wire growth. For parameter values that violate these conditions the droplet atop the wire is expected to unpin. A range of alternative configurations for the liquid exist and their relative energies are compared. In particular, it is found that for a certain region in parameter space—not extraordinary in VLS growth—a spherical cap of liquid is not in equilibrium and an annulus of liquid surrounding the wire is energetically preferred. This is suggestive of a possible instability during growth.