Insights into the kinetics of semiconductor nanocrystal nucleation and growth

A model is presented for the colloidal synthesis of semiconductor nanocrystals capturing the reactions underlying nucleation and growth processes. The model combines an activation mechanism for precursor conversion to monomers, discrete rate equations for formation of small-sized clusters, and continuous Fokker-Planck equation for growth of large-sized clusters. The model allows us to track the temporal evolution of the entire cluster size distribution and compute several experimental observables including mean size and size distribution. The model predicts five distinct regions: generation of monomers, small cluster formation, size distribution focusing due to precursor depletion, pseudo steady state region, and size distribution broadening, with the latter three explicitly reproducing available experimental data at larger cluster sizes. Furthermore, we identify two nondimensional parameter combinations and discuss how these can be used to guide experiments to yield a more rational approach to synthesis modification. Contrary to the common hypothesis that diffusion is essential for size distribution focusing, the model shows that focusing can be achieved under pure reaction control. In addition, the model yields new insights into the synthesis of small nanocrystals with narrow size distributions either by modulation of temperature over the duration of nanocrystal synthesis or by introduction of small quantities of additives that enhance the rate of precursor conversion to monomers. We show that for a given set of reaction parameters, there is an optimum in the duration of high temperature and additive concentration minimizing polydispersity.