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 Er 3+ doping yields the highest UCQY in the host lattices β-NaYF 4 and Gd 2 O 2 S under 4 I 15/2 → 4 I 13/2 excitation. We show for both host lattices that the optimum Er 3+ doping is not fixed and it actually decreases as the irradiance of the excitation increases. To find the optimum Er 3+ 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 Er 3+ doping of the upconverter samples and the lattice parameters of the host materials. We observe optimum average Er–Er distances for the host lattices β-NaYF 4 and Gd 2 O 2 S with differences <14% at the same irradiance levels, whereas the optimum Er 3+ doping are around 2× higher for β-NaYF 4 than for Gd 2 O 2 S. 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 β-NaYF 4 and Gd 2 O 2 S, 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.