The kinetics of growth of semiconductor nanocrystals in a hot amphiphile matrix.

ABSTRACT

The first comprehensive study on the kinetics of nanocrystal growth in a hot amphiphile medium is presented. An example is given with CdSe semiconductor nanocrystals grown after the injection of precursor (a mixture of Cd- and Se-reagents) in concentrated tri-octylphosphine oxide matrix (heated to more than 300 degrees C). The particle size distribution is reconstructed as a function of time from the absorption and photoluminescence spectra collected during the synthesis process. For this purpose a new expression is used relating the exciton energy due to quantum confinement with the nanocrystal radius. The growth kinetics is considered as a two-stage process in order to describe the time variation of nanoparticle size. During the first stage, called reaction-limited growth, the size of initial nucleus rapidly increases due to a sort of surface reaction exhausting the precursor in the nanoparticle vicinity. The growth in such conditions favors also a remarkable narrowing of the size distribution. The nanocrystal develops further on account of a slow precursor transfer from a distant space driven by the concentration gradient--classical diffusion-limited growth. The width of size distribution also increases proportional to the average particle size. Any growth will stop after the precursor concentration reaches a minimum value defining the limit for the final nanocrystal size in a batch. Solving the kinetic equations for the growth rate in each case of kinetics derives analytical expressions for the mean radius and variance of size distribution. Then the respective expressions are matched in a uniform solution valid during the entire synthesis. The theoretical model is in a good quantitative agreement with the experimental data for independent syntheses. Important characteristic scales of the processes (time-constant and length) and microscopic parameters of the reacting system (interfacial energy and reaction rate constant) are estimated from the data. It turns out that the fast reaction-limited growth is important to obtain well-defined nanocrystals of high optical quality by using less energy, time and consumable. However, to make them reproducibly uniform one should control also the ultra-fast nucleation process preceding the nanocrystal growth, which is still unknown. Nevertheless, our current findings allow the conceptual design of a new continuos-flow reactor for the manufacturing of a large amount of uniform nanocrystals.