Phonon-Mediated Temperature Dependence of Er³⁺ Optical Transitions in Er₂O₃

Characterization of the atomic level processes that determine the observed optical transitions in emerging materials is critical to the development of new platforms for classical and quantum networking. Such understanding often emerges from studies of the temperature dependence of the transition probabilities. We report new measurements of the temperature dependent Er³⁺ photoluminescence in single crystal Er₂O₃ thin films epitaxially grown on Si(111). Our focus is on transitions that involve the closely spaced Stark-split levels determined by the crystal field. Radiative intensities are compared to a model that includes these relevant Stark-split states, single phonon-assisted excitations, and the well-established level population redistribution due to thermalization. This approach, applied to the individual Stark-split states and employing Er₂O₃ specific single-phonon-assisted excitations, gives good agreement with the experimental results. This model allows us to demonstrate the difference in the electron-phonon coupling of the ⁴S_3/2 and ²H_11/2 state of Er³⁺ in E₂O₃ and suggests that the temperature dependence of Er³⁺ emission intensity may vary significantly with the wavelength of the excitation source.