Combined Theoretical-Experimental Approach to the Growth Kinetics of Colloidal Semiconductor Nanocrystals

A new theoretical analytical model is proposed in order to provide a quantitative description of the growth kinetics of colloidal semiconductor nanocrystals. The temporal evolution of the mean size of the nanocrystal ensemble in solution was determined by monitoring the variation of the absorption and photoluminescence spectra in the course of the chemical synthesis and then submitting the resulting optical data to a calculation procedure that generated the corresponding time-evolving particle size distribution. Two main problems were addressed and properly correlated: the size-dependence of the bandgap transition for a single semiconductor nanocrystal, which was treated within the framework of the finite-depth square-well effective mass approximation, and the inhomogeneous broadening of the optical spectra due to the distribution of nanocrystal sizes and hence the distribution of bandgaps. By application of the reported methodology to CdTe nanocrystals synthesized through a one-pot aqueous chemical route, growth curves (mean particle size as a function of time) were calculated for syntheses performed under various initial experimental conditions. Such kinetic results were interpreted in the sense of the well-established classical crystallization theories based on homogeneous nucleation and growth of spherical particles in solution, including a detailed study on the Ostwald ripening process. Specific growth modes were identified along with numerical estimates for their characteristic rate constants. The presented calculation method is easy to implement, and it can be used to access the size evolution of solution-grown nanocrystals of many other semiconductor materials, regardless of the adopted preparation procedure.