Modeling the nucleation statistics in vapor–liquid–solid nanowires

• We proposed theoretical model of nucleation during the VLS growth of nanowires in the mononuclear regime.
• The model accounts for desorption from the droplet and allows one to describe the nucleation statistics and the nanowire length distribution.
• It was shown that the relative dispersion of nanowire length increases with the NW radius and at a higher desorption from the droplet.

The statistics of nucleation events in nanowires growing via the vapor–liquid–solid mechanism in the mononuclear regime is studied theoretically. A semi-analytical model is developed which is capable of describing the distributions of time intervals between the successive nucleation events and some other useful characteristics of nucleation statistics. Our model accounts for desorption from the droplet, which was not included in the previous studies of nucleation statistics. It is shown that the relative dispersion of nucleation distributions increases with the nanowire radius and at a higher desorption rate from the droplet, leading to the corresponding broadening of the length distribution. Using the model is also shown to fit well experimental data available on nucleation statistics in the Au-catalyzed Si and III–V nanowires.