Critical Power Density: A Metric To Compare the Excitation Power Density Dependence of Photon Upconversion in Different Inorganic Host Materials

In photon upconversion (UC) based on triplet-triplet annihilation, the upconversion photoluminescent quantum yield (UC-PLQY) depends on the excitation power density in a way that can be described by a single figure of merit. This figure of merit, the threshold value, allows the excitation power density required for efficient UC-PLQY to be compared between different triplet-triplet annihilation systems. Here, we investigate the excitation power density dependence of two-photon UC processes in a series of four lanthanide-doped inorganic host materials (oxides, fluorides, and chlorides) all doped with 18 mol % Yb3+ sensitizer ions and 2 mol % Er3+ activator ions. We demonstrate that an analogous figure of merit, which we call the critical power density (CPD), accurately describes the UC power dependence of these samples. Better CPD values are obtained when the lifetime of the intermediate states is long. The UC-PLQY at the CPD is linked to the saturation UC-PLQY. Thus, a measurement of the UC-PLQY at this low power density can be used to estimate the theoretical saturation UC-PLQY in the absence of deleterious effects such as laser-induced heating. This is compared to another method to estimate the saturation based on the CPD model, namely, taking half of the level's PLQY under direct excitation. Our careful analysis of the upconversion spectra as a function of excitation power density gives several insights into the differing upconversion pathways in the hosts and proves to be a useful tool for their comparison.