Energies of 4f$^{N}$ and 4f$^{N-1}$5d States Relative to Host Bands in Rare-earth-doped Fluorides*

Energies of 4f$^{N}$ states relative to crystal band states were measured for rare-earth ions in the optical host materials LiYF$_{4}$, Na$_{0.4}$Y$_{0.6}$F$_{2.2}$, and LaF$_{3}$ using x-ray photoemission spectroscopy. Spectra were modeled to determine the valence band maximum and 4f$^{ }$electron binding energies in each material. These results were combined with 4f$^{N}$ to 4f$^{N-1}$5d transition energies to determine 5d binding energies for the lowest levels of excited 4f$^{N-1}$5d configurations. While 4f$^{N}$ ground-state energies vary within several eV of the valence band maximum for different rare-earth ions in each host, the lowest 4f$^{N-1}$5d states have similar energies and are several eV below the bottom of the conduction band. A simple model accurately described 4f$^{N}$ and 4f$^{N-1}$5d binding energies across the entire series of rare-earth ions. These results improve the understanding of optical materials for lasers, phosphors, and spectral hole burning applications for optical signal processing and data storage.