Determination of the Quantum Dot Band Gap Dependence on Particle Size from Optical Absorbance and Transmission Electron Microscopy Measurements

This work addresses the determination of arbitrarily shaped particle size distributions (PSDs) from PbS and PbSe quantum dot (QD) optical absorbance spectra in order to arrive at a relationship between band gap energy and particle size over a large size range. Using a modified algorithm which was previously developed for ZnO, we take only bulk absorption data from the literature and match the PSDs derived from QD absorbance spectra with those from transmission electron microscopical (TEM) image analysis in order to arrive at the functional dependence of the band gap on particle size. Additional samples sized solely from their absorbance spectra with our algorithm show excellent agreement with TEM results. We investigate the influence of parameters of the TEM image analysis such as threshold value on the final result. The band gap versus size relationship developed from analysis of just two samples lies well within the bounds of a number of published data sets. We believe that our methodology provides an attractive shortcut for the study of various novel quantum-confined direct band gap semiconductor systems as it permits the band gap energies of a broad size range of QDs to be probed with relatively few synthetic experiments and without quantum mechanical simulations.