Energy level modeling of lanthanide materials: review and uncertainty analysis

Abstract

Energy level schemes are an essential tool for the description and interpretation of atomic spectra. During the last 40 years, several empirical methods and relationships were devised for constructing energy level schemes of lanthanide defects in wide band gap solids, culminating in the chemical shift model by Thiel and Dorenbos. This model allows us to calculate the electronic and optical properties of the considered materials. However, an unbiased assessment of the accuracy of the obtained values of the calculated parameters is still lacking to a large extent. In this paper, error margins for calculated electronic and optical properties are deduced. It is found that optical transitions can be predicted within an acceptable error margin, while the description of phenomena involving conduction band states is limited to qualitative interpretation due to the large error margins for physical observables such as thermal quenching temperature, corresponding to standard deviations in the range 0.3–0.5 eV for the relevant energy differences. As an example, the electronic structure of lanthanide doped calcium thiogallate (CaGa₂S₄) is determined, taking the experimental spectra of CaGa₂S₄:Ln^Q+ (Ln^Q+ = Ce³⁺, Eu²⁺, Tm³⁺) as input. Two different approaches to obtain the shape of the zig-zag curves connecting the 4f levels of the different lanthanides are explored and compared.