Steady growth of nanowires via the vapor-liquid-solid method

Understanding the dynamics of the growth of nanowires by the vapor-liquid-solid (VLS) process is essential in order to relate the properties of the wire to their processing conditions. A theory for VLS growth is developed that incorporates the surface energy of the solid-liquid, liquid-vapor, and solid-vapor interfaces, allows for supersaturation of growth material in the droplet, and employs contact-line conditions. We predict the profile of catalyst concentration in the droplet, the degree of supersaturation, and the modification to the shape of the solid-liquid interface due to growth, as functions of the material properties and process parameters. Under typical experimental conditions the interface deflection due to growth is predicted to be practically zero. We also find that the growth rate of the wire inherits the same dependence on diameter as the flux of growth material at the liquid-vapor interface; thus, if we assume that the flux is independent of radius, we obtain a growth rate that is also independent of radius. To make a prediction about the actual variation with diameter requires a detailed knowledge of the decomposition kinetics at the liquid-vapor interface. (c) 2007 American Institute of Physics.