Predictive modeling of self-catalyzed III-V nanowire growth

We develop a quantitative model of the self-catalyzed vapor-liquid-solid growth of GaAs nanowires, that depends on only a few a priori unknown physical parameters. The model is based on the sole consideration of the As species and incorporates all relevant mechanisms of exchange of As between the vapor, liquid, and solid phases, namely direct impingement of molecules on the droplet, their re-emission by the neighboring surfaces, evaporation from the droplet, and nucleation at the solid-liquid interface. It reproduces quantitatively all salient features of our experimental study, namely the variations of nanowire growth rate with As flux, temperature, and nanowire radius. From these optimized fits, we extract a complete set of model parameters, in particular the nucleus edge energy. We also determine quantities so far inaccessible to experiment, such as the As concentration in the droplet (about 1%), supersaturation of the liquid, and nucleation barrier, for individual nanowires. The model can then be used to predict the growth rate (and all quantities of interest) for an arbitrary GaAs nanowire of given geometry in arbitrary growth conditions, including conditions not yet explored experimentally, provided the fraction of the As flux re-emitted by its environment is known. Although largely ignoring group III elements, our model captures most of the physics of self-catalyzed nanowire growth.