Limits of emission quantum yield determination

The development of new fluorescent molecules and dyes requires precise determination of their emission efficiency, which ultimately defines the potential of the developed materials. For this, the photoluminescence quantum yield (QY) is commonly used, given by the ratio of the number of emitted and absorbed photons, where the latter can be determined by subtraction of the transmitted signal by the sample and by a blank reference. In this work, we show that when the measurement uncertainty is larger than 10% of the absorptance of the sample, the QY distribution function becomes skewed, which can result in underestimated QY values by more than 200%. We demonstrate this effect in great detail by simulation of the QY methodology that implements an integrating sphere, which is widely used commercially and for research. Based on our simulations, we show that this effect arises from the non-linear propagation of the measurement uncertainties. The observed effect applies to the measurement of any variable defined as Z=X/Y, with Y=U-V, where X, U and V are random, normally distributed parameters. For this general case, we derive the analytical expression and quantify the range in which the effect can be avoided.