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+) = Ce(3+), Eu(2+), Tm(3+)) 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.

Microscopic Study of Dopant Distribution in Europium Doped SrGa2S4: Impact on Thermal Quenching and Phosphor Performance

“…42,43 These values are prone to large uncertainties of 0.3-0.4 eV. 37 Due to the large uncertainties on calculated energy differences and the large density of excited states in the relevant energy range, it still remains almost impossible to reliably pinpoint which states contribute to phenomena such as thermal quenching. There is hence an ongoing need for more accurate models as well as reliable experimental data, corresponding to optimized systems.…”

“…In order to facilitate the data interpretation, all obtained thermal quenching profiles -both at the single pixel level as for the average behavior -were fitted by means of a standard single-barrier model, a widely used prescription to model thermal quenching behavior: [35][36][37] …”

Nonequivalent lanthanide defects: Energy level modeling

“…This was pioneered by Thiel in the context of photoelectron spectroscopy and further developed by Dorenbos, mostly based on optical spectroscopy [13,14,15,11]. The uncertainties associated with these empirical models and the accuracy by which experimental quantities can be predicted have recently been addressed in detail [8].…”

“…These correspond to the value of the electronic chemical potential at which the formal charge of the lanthanide ion changes [12]. The exact meaning of the empirical energy levels is further elucidated in [8].…”

“…incident photons. Two important classes of energy level schemes exist [8]. Firstly, there are many-body schemes in which the energy level represents the total energy of the complete system.…”