The dynamics of energy and charge transfer in lead sulfide quantum dot solids

We report on a systematic time-resolved photoluminescence study of the competing energy and charge transfer rates in PbS QDs of differing sizes in the same QD solid as a function of both temperature and ligand-controlled different inter-QD average separations. This complements previous studies that typically varied only one parameter and reveals new aspects while also confirming some known features. For the smallest PbS QDs, the dominant decay process is nonradiative resonant energy transfer (NRET) to adjacent larger dots for all separations but at a rate that increases with decreasing temperature. For the largest QDs, NRET being forbidden, the decay is found to be exponential in the inter-QD separation consistent with carrier tunneling but, for each fixed tunneling distance, exhibiting a thermally activated tunneling carrier population with the activation energy dependent upon the ligand length controlling the inter-QD separation. A consistent understanding of this expanded and rich decay rate behavior of both large and small QDs, we show, can be obtained by accounting for the ligand length dependent (a) dielectric environment of the QD solid modeled using an effective medium description, (b) the energy cost of dissociating the exciton into electron and hole in neighboring QDs, and (c) the potential participation of midgap states. Implications of the findings for NRET based photovoltaics are discussed.