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.

Optical Properties of Synthesized Hexagonal CdTe Nanoparticles Having Hexagonal Phase: Density Functional Theory‐Supported Calculation of Bandgap and Density of States

“…Here, the bandgap has been determined using Tauc's plot [ 35 ] and the particle size has been calculated using different models, such as Brus model, hyperbolic band model (HBM), Henglein‐suggested formula, and empirical formula suggested by Yu et al, as given in refs. [36,37].…”

“…HBM [ 37 ] is another model, which also relates the bandgap of the nanoparticle with the particle size. In the HBM model, simplified single mass is introduced with respect to the effective masses of the electron and holes by the given relation…”

Big Data in a Nano World: A Review on Computational, Data-Driven Design of Nanomaterials Structures, Properties, and Synthesis

“…88,92,93 In nanostructures where quantum confinement effects are present, the effective masses derived from the bulk band structures can be inaccurate (or undefined) due to the modified band structure. 123 When the crystal size is limited, the electron (hole) wave functions are confined within the crystal boundaries and the effective mass becomes energydependent 124,125 As a general trend, the effective mass is expected to increase as crystal size decreases due to reduced dispersion at band edges; however, as shown in a literature comparison of ZnS NCs, this is not always the case experimentally due to crystal orientations, impurities, and other factors. 123 Carrier mobilities have been shown to decrease with NC size, 126 most likely due to enhanced surface scattering; in these cases, surface passivation is useful to reduce carrier trapping.…”

PROFICIENT PHOTOCATALYTIC DEGRADATION OF METHYLENE BLUE DYE USING Ti-DOPED CdSe NANOPARTICLES UNDER SOLAR LIGHT IRRADIATION

“…After doping Ti impurities absorption intensity was slightly different than undoped, this leads to the distortion of host materials. The absorption edge was transformed to the lower wavelength region than the bulk materials providing a blue shift according to quantum confinement effect [24][25][26].…”