A Heterogeneous Kinetics Model for Triplet Exciton Transfer in Solid-State Upconversion.

High internal quantum efficiency semiconductor nanocrystal (NC)-based photon upconversion devices are currently based on a single monolayer of active NCs. Devices are therefore limited in their external quantum efficiency based on the low number of photons absorbed. Increasing the number of photons absorbed is expected to increase the upconversion efficiency, yet experimentally increasing the number of layers does not appreciably increase the upconverted light output. We unravel this mystery by combining kinetic modeling and transient photoluminescence spectroscopy. The inherent energetic disorder stemming from the polydispersity of the NCs means that the kinetics are governed by a stochastic transfer matrix. By drawing the rates from a probabilistic distribution and constructing a reaction network with realistic connectivity, we are able to fit complex photoluminescence traces with a very simple model. We use this model to explain the thickness-dependent performance of the upconversion devices and can attribute the reduced efficiencies to the low excitonic diffusivity of the exciton within the NC layers and increased back transfer of the created singlets from the organic annihilator rubrene. We suggest some avenues for overcoming these limitations in future devices.