Fundamental lessons on upconversion spectroscopy in rare-earth ions

Common models describing energy-transfer-upconversion processes fail to treat two spectroscopically distinct ion classes. Reasons are discussed and an alternative model is presented. Energy-transfer processes among neighboring rare-earth ions, such as energy migration and energy-transfer upconversion (ETU), strongly impact the spectroscopy of rare-earth-ion-doped dielectric materials and their performance as amplifier and laser devices. Over the past decades, immense scientific efforts have been made to understand and quantitatively model energy-transfer processes. All commonly used models, the macroscopic rate-equation model by Grant, the microscopic models by Inokuti-Hirayama, Zusman, and Burshteîn, as well as Zubenko’s model which combines both approaches fundamentally assume that all active ions have the same local environment, i.e., they are spectroscopically identical, thereby keeping mathematical complexity at a reasonable level and allowing for analytical solutions. In a case study in Al2O3:Er3+ thin films it is shown that, while only Zubenko’s model succeeds in modeling the pump-power and concentration dependence of measured luminescence decay curves under the influence of energy migration and ETU, even this model is unable to describe a second, spectroscopically distinct class of ions. An extension to Zubenko’s model that takes into account the spectroscopically distinct class of ions provides excellent agreement within the frame of a single theoretical description.