Theoretical analysis of the radius of semiconductor nanowires grown by the catalytic vapour–liquid–solid mechanism

We present a theoretical analysis of the radius, r C * , of semiconductor nanowires (SNWs) grown by the catalytic vapour–liquid–solid (VLS) mechanism. Two types of the catalytic metal were examined, namely case I: thin film, and case II: colloids or cluster. In case I, the number density along with the inter-distance between two neighbouring nucleus, D , and the critical radius of the catalytic metal nucleus, R C * , were correlated and determined by either the thermodynamic relationship (determination of R C * followed by D ) or structural instability (determination of D followed by R C * ). In case II, the linearly scaling behaviour of r C * with the observed radius of the SNWs was explained by comparing with experimental data obtained from the literature. Commonly in both cases, it was shown that r C * is thermodynamically determined, assuming the kinetic effect due to the initial diffusion length of the gaseous semiconductor precursor in the early stages of the growth of the SNWs, and that r C * mirrors R C * only when r C * is greater than R C * . We also found that the theoretical analysis of r C * is matched well with experimental data in the literature.