Dielectric function of colloidal lead chalcogenide quantum dots obtained by a Kramers-Krönig analysis of the absorbance spectrum

Abstract

We combined the Maxwell-Garnett effective medium theory with the Kramers-Kr\"onig relations to obtain the complex dielectric function $ϵ$ of colloidal PbS, PbSe, and PbTe quantum dots (Qdots). The method allows extracting both real $({ϵ}_{R})$ and imaginary $({ϵ}_{I})$ parts of the dielectric function from the experimental absorption spectrum. This enables the quantification of the size-dependent oscillator strength of the optical transitions at different critical points in the Brillouin zone, strongly improving our understanding of quantum confinement effects in these materials. In addition, the static-limit sum rule yields the electronic dielectric constant from the ${ϵ}_{I}$ spectrum. Interestingly, values for lead chalcogenide Qdots remain close to the bulk dielectric constant. To verify these trends, we determined the dielectric constant of thin lead chalcogenide layers by ab initio calculations, and the results agree with the experimental data.