A Comparative Study of Theoretical Methods to Estimate Semiconductor Nanoparticles’ Size

Abstract

In this paper, we compare four different methods to estimate nanoparticle diameters from optical absorption measurements, using transmission electron microscopy (TEM) images as a reference for the nanoparticle size. Three solutions of colloidal nanoparticles coated with thiophenol with different diameters were synthesized by thiolate decomposition. The nanoparticle sizes were controlled by the addition of a certain volume of a 1% sulphur solution in toluene. TEM measurements showed that the average diameter for each type of these nanoparticles was 2.8 nm, 3.2 nm, and 4.0 nm. The methods studied for the calculation of the nanoparticles diameter were: The Brus model, the hyperbolic band model (HBM), the Henglein model, and the Yu equation. We evaluated the importance of a good knowledge of the nanoparticle bandgap energy, and the nature of electronic transitions in the semiconductor. We studied the effects that small variations in the electron and hole effective mass values produced in the Brus equation and in the HBM model for CdS, PbS, and ZnS nanoparticles. Finally, a comparison was performed between the data provided by these models and the experimental results obtained with TEM images. In conclusion, we observed that the best approximation to the experimental results with TEM images was the Brus equation. However, when the bandgap energy was close to the bulk bandgap energy, the theoretical models did not adjust correctly to the size measured from the TEM images.