Self-regulated pulsed nucleation in catalyzed nanowire growth

We present a theoretical analysis of catalyzed nanowire growth based on the material balance in a droplet within one monolayer growth cycle. Pulsed supersaturation and nucleation probability density are shown to originate from the material balance under rather general assumptions. We calculate explicitly the time-dependent nucleation probability as a function of nanowire radius and growth conditions. For small nanowire radii, the timescale hierarchy of different growth steps is demonstrated, leading to a temporal anticorrelation of nucleation events. Numerical analysis is performed in the case of Au-catalyzed GaAs nanowires, where the nucleation probabilities are mapped out as functions of nanowire radius at different conditions. The transition from deltalike to Poissonian temporal distribution of nucleation events is discussed depending on relevant parameters. We speculate that the self-regulated narrowing of nucleation probabilities suppresses random broadening of nanowire length distributions. This focusing effect is specific for nucleation in nanovolumes and might be used for tailoring the size spectra of different nano-objects.