Insights into the Kinetics of Semiconductor Nanocrystal Nucleation and Growth

Abstract

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.

Magic-Sized Cd3P2 II−V Nanoparticles Exhibiting Bandgap Photoemission

“…The investigation on the reactants leading to the formation of nanocrystals such as CdSe and PbSe can be found elsewhere. [18][19][20] It is easy to understand that, in ODE, the Cd and P monomers, oligomers, and nanoparticles are "stabilized" by a number of ligands present throughout the reaction. Figure 1 shows the temporal evolution of the optical properties of the as-prepared Cd 3 P 2 nanoparticles sampled from one synthetic batch with the feed molar ratio of 4OA-4Cd-1P and the concentration of (TMS) 3 P of 10 mmol/kg in5gofODE.…”

Molecular Control of the Nanoscale: Effect of Phosphine–Chalcogenide Reactivity on CdS–CdSe Nanocrystal Composition and Morphology

“…26 A kinetic model was used to describe combined nanocrystal nucleation and growth phenomena. 27 Reaction of Pb(oleate) 2 and trioctylphosphine selenide (TOPSe) at low temperature produced spherical PbSe nanocrystals, while reaction with hexaethylphosphorustriamidetriamide (HPT, also called tris(diethylamino)phosphine selenide) at high temperature produced PbSe nanorods. Coupled thermogravimetric mass spectrometry analysis (TGA-MS) showed that HPT accelerates precursor decomposition by releasing amines.…”

An accurate scheme to solve cluster dynamics equations using a Fokker–Planck approach

“…4.1. To solve this problem, upwind schemes [28,29] or related schemes such as the Chang-Cooper scheme [30] can be used [31,11]. Essentially, the Chang-Cooper scheme automatically and seamlessly switches from a centered scheme to an upwind scheme as the advective flux increases, so that the resulting scheme remains stable.…”