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

Abstract

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 is greater than R-C*. We also found that the theoretical analysis of C-r* is matched well with experimental data in the literature.