A framework for extracting the rates of photophysical processes from biexponentially decaying photon emission data

There is strong interest in designing and realizing optically-active semiconductor nanostructures of greater complexity for applications in fields ranging from biomedical engineering to quantum computing. While these increasingly complex nanostructures can implement progressively sophisticated optical functions, the presence of more material constituents and interfaces also leads to increasingly complex exciton dynamics. In particular, the rates of carrier trapping and detrapping in complex heterostructures are critically important for advanced optical functionality, but they can rarely be directly measured. In this work, we develop a model that includes trapping and release of carriers by optically inactive states. The model explains the widely observed biexponential decay of the photoluminescence signal from neutral excitons in low dimensional semiconductor emitters. The model also allows determination of likelihood intervals for all the transition rates involved in the emission dynamics, without the use of approximations. Furthermore, in cases for which the high temperature limit is suitable, the model leads to specific values of such rates, outperforming reduced models previously used to estimate those quantities. We demonstrate the value of this model by applying it to time resolved photoluminescence measurements of CdSeTe/CdS heterostructures. We obtain values not only for the radiative and nonradiative lifetimes, but also for the delayed photoluminescence originating in trapping and release.