Kinetic Analysis of the VLS Growth of Semiconducting Nanowires

Vapour-Liquid-Solid (VLS) growth mechanism is a popular method for the growth of inorganic semiconducting nanowires (NWs) in the diameter range of sub-100 nm. A kinetic model is presented for the growth of elemental (Si) and binary $(SiO_{\mathrm{x}})$ NWs by incorporating all the atomistic parameters. Importantly, the model connects the macroscopic experimental parameters such as temperature, pressure and catalyst particle with atomistic aspects such as supersaturation, energy barriers and interface diffusivity. The thermodynamic driving force for the NWs growth is estimated by balancing various injection-ejection processes occurring at the catalyst droplet. Using the kinetic framework, the steady state Si concentration in the Au-Si droplet is estimated for the catalyst diameter in the range of 10-100nm. The calculated NWs growth rates were observed to be within an order of magnitude in comparision with the experimentally measured values.