The length distribution function of semiconductor filamentary nanocrystals

Abstract

The length distribution function of semiconductor filamentary nanocrystals is analyzed based on the adsorption–diffusion growth model. It is demonstrated that the asymptotic distribution has a Gaussian shape. If the diffusion flux to the apex comes from the entire lateral surface, the average length increases exponentially with time, and the mean-square deviation is proportional to the average length (exponential growth regime). If the diffusion collection of adatoms is limited to the top of the crystal, the average length increases linearly and the mean-square deviation equals the square root of average length (linear Poisson growth regime). In real-world systems, transition from exponential to Poisson growth occurs at lengths of the order of the diffusion length of adatoms. The dispersion of the distribution is actually defined at the exponential stage. The general classification of length distributions of various crystals is given. It is demonstrated that self-induced GaN- and Ga-catalytic III–V filamentary nanocrystals should be more homogeneous than Au-catalytic ones.