Relation between Excitation Power Density and Er3+ Doping Yielding the Highest Absolute Upconversion Quantum Yield

The upconversion quantum yield (UCQY) is one of the most significant parameters for upconverter materials. A high UCQY is essential for a succesful integration of upconversion in many applications, such as harvesting of the solar radiation. However, little is known about which doping level of the rare-earth ions yields the highest UCQY in the different host lattices and what are the underlying causes. Here, we investigate which Er3+ doping yields the highest UCQY in the host lattices beta-NaYF4 and Gd2O2S under I-4(15/2) -> I-4(13/2) excitation. We show for both host lattices that the optimum Er3+ doping is not fixed and it actually decreases as the irradiance of the excitation increases. To find the optimum Er3+ doping for a given irradiance, we determined the peak position of the internal UCQY as a function of the average Er-Er distance. For this purpose, we used a fit on experimental data, where the average Er-Er distance was calculated from the Er3+ doping of the upconverter samples and the lattice parameters of the host materials. We observe optimum average Er-Er distances for the host lattices beta-NaYF4 and Gd2O2S with differences <14% at the same irradiance levels, whereas the optimum Er3+ doping are around 2x higher for beta-NaYF4 than for Gd2O2S. Estimations by extrapolation to higher irradiances indicate that the optimum average Er-Er distance converges to values around 0.88 and 0.83 nm for beta-NaYF4 and Gd2O2S, respectively. Our findings point to a fundamental relationship and focusing on the average distance between the active rare-earth ions might be a very efficient way to optimize the doping of rare-earth ions with regard to the highest achievable UCQY.