Impact of stoichiometry on the electronic structure of PbS quantum dots

Although the stoichiometry of bulk lead sulfide (PbS) is exactly 1:1, that of quantum dots (QDs) can be considerably different from this crystalline limit. Employing first-principles calculations, we show that the impact of PbS QD stoichiometry on the electronic structure can be enormous, suggesting that control over the overall stoichiometry in the QD will play a critical role for improving the efficiency of optoelectronic devices made with PbS QDs. In particular, for bare PbS QDs, we find that: (i) stoichiometric PbS QDs are free from midgap states even without ligand passivation and independent of shape, (ii) off stoichiometry in PbS QDs introduces new states in the gap that are highly localized on certain surface atoms, and (iii) further deviations in stoichiometry lead to QDs with "metallic" behavior, with a dense number of energy states near the Fermi level. We further demonstrate that this framework holds for the case of passivated QDs by considering the attachment of ligand molecules as stoichiometry variations. Our calculations show that an optimal number of ligands makes the QD stoichiometric and heals unfavorable electronic structure, whereas too few or too many ligands cause effective off stoichiometry, resulting in QDs with defect states in the gap.