Atomistic modeling of the Au droplet–GaAs interface for size-selective nanowire growth

Abstract

Density functional theory calculations within both the local density approximation and the generalized gradient approximation are used to study Au-catalyzed growth under near-equilibrium conditions. We discuss both the chemical equilibrium of a GaAs nanowire with an As${}_{2}$ gas atmosphere and the mechanical equilibrium between the capillary forces at the nanowire tip. For the latter goal, the interface between the gold nanoparticle and the nanowire is modeled atomically within a slab approach, and the interface energies are evaluated from the total energies of the model systems. We discuss three growth regimes, one catalyzed by an (almost) pure Au particle, an intermediate alloy-catalyzed growth regime, and a Ga-catalyzed growth regime. Using the interface energies calculated from the atomic models, as well as the surface energies of the nanoparticle and the nanowire sidewalls, we determine the optimized geometry of the nanoparticle-capped nanowire by minimizing the free energy of a continuum model. Under typical experimental conditions of 10${}^{\ensuremath{-}4}$ Pa As${}_{2}$ and 700 K, our results in the local density approximation are insensitive to the Ga concentration in the nanoparticle. In these growth conditions, the energetically most favored interface has an interface energy of around 45 meV/\AA{}${}^{2}$, and the correspondingly optimized droplet on top of a GaAs nanowire is somewhat larger than a hemisphere and forms a contact angle around 130${}^{\ensuremath{\circ}}$ for both pure Au and Au-Ga alloy nanoparticles.