Stark level analysis of the spectral line shape of electronic transitions in rare earth ions embedded in host crystals

Rare earth ions embedded in host crystals are of great interest for many applications. Due to the crystal field of the host material, the energy levels of the rare earth ions split into several Stark levels. The resulting broadening of the spectral line shapes of transitions between those levels determines the upconversion phenomena, especially under broad-spectrum illumination, which are relevant for photovoltaics for instance. In this paper, we present a method to determine the spectral line shape of energy level transitions of rare earth ions from the absorption spectrum of the investigated material. A parameter model is used to describe the structure of the individual energy levels based on a representation of the Stark splitting. The parameters of the model are then determined with an evolutionary optimization algorithm. The described method is applied to the model system of beta-NaEr0.2Y0.8F4. The results indicate that for illumination with a wavelength around 1523 nm, simple upconversion processes such as two-step absorption or direct energy transfer are less efficient than commonly assumed. Hence a sequence of efficient processes is suggested as an explanation for the high upconversion quantum yield of beta-NaEr0.2Y0.8F4, which has not yet been reported in the literature.