Size-dependent bandgap and particle size distribution of colloidal semiconductor nanocrystals

TL;DR

This paper introduces a new analytical model for the size-dependent bandgap of colloidal semiconductor nanocrystals, enabling more accurate size distribution estimates from optical data, especially in strong confinement regimes.

Contribution

It presents a novel analytical expression within the finite-depth square-well approximation to improve size estimation from optical spectra in quantum-confined nanocrystals.

Findings

The model accurately estimates particle sizes from optical spectra.

Size distributions inferred match well with microscopy measurements.

Applicable to various semiconductor nanocrystal systems.

Abstract

A new analytical expression for the size-dependent bandgap of colloidal semiconductor nanocrystals is proposed within the framework of the finite-depth square-well effective mass approximation in order to provide a quantitative description of the quantum confinement effect. This allows one to convert optical spectroscopic data (photoluminescence spectrum and absorbance edge) into accurate estimates for the particle size distributions of colloidal systems even if the traditional effective mass model is expected to fail, which occurs typically for very small particles belonging to the so-called strong confinement limit. By applying the reported theoretical methodologies to CdTe nanocrystals synthesized through wet chemical routes, size distributions are inferred and compared directly to those obtained from atomic force microscopy and transmission electron microscopy. This analysis can be used as a complementary tool for the characterization of nanocrystal samples of many other systems such as the II-VI and III-V semiconductor materials.