Modeling of kinetically limited growth rate for solution-synthesized germanium nanocrystals

Abstract

Solution synthesis is a common method for preparing semiconductor nanocrystals (NCs). For such solution synthesis, many investigations have considered diffusion-limited growth, in which the diffusion of reactants through the boundary layer (BL) limits the NC growth rate. These studies often model the growth rate with a diffusion BL thickness much larger than the NC size and with unphysically low diffusion constants on the order of 10−12 cm2 s−1. In this work, we have examined the growth of Ge NCs synthesized by injecting Ge amide precursors into a solution of 1-octadecene, oleylamine, and hexadecylamine. We have previously established this low-temperature, low-pressure synthesis route. The resulting Ge growth rate compares well with our model, in which we consider both BL diffusion and surface kinetics of Ge precursors and organic ligand adsorbates. Our modeling results suggest that the NC growth is limited not by diffusion, but by the surface adsorption and desorption kinetics. The BL thickness in the stirred reaction vessel is calculated to be on the same order of magnitude as the crystal radius; therefore, the surface kinetics cannot be ignored. Furthermore, the synthesis temperature is near 300 °C, where the Ge monomer diffusion coefficient within the growth solution is substantially increased and estimated to be on the order of 10−5 cm2 s−1. These considerations agree well with our experimentally measured growth rate and strongly suggest that the NC size evolution is controlled primarily by the surface kinetics.