A Theoretical Framework for Ratiometric Single Ion Luminescent Thermometers—Thermodynamic and Kinetic Guidelines for Optimized Performance

Luminescence (nano)thermometry is an increasingly important field for remote temperature sensing with high spatial resolution. Most typically, ratiometric sensing of the luminescence emission intensities of two thermally coupled emissive states based on a Boltzmann equilibrium is used to detect the local temperature. Dependent on the temperature range and preferred spectral window, various choices for potential candidates appear possible. Despite extensive experimental research in the field, a universal theory covering the basics of luminescence thermometry is virtually nonexistent. In this manuscript, a general theoretical framework of single ion luminescent thermometers is presented that offers simple, user-friendly guidelines for both the choice of an appropriate emitter and respective embedding host material for optimum temperature sensing. The results show that the optimum performance (thermal response and sensitivity) around T₀ is realized for an energy gap ∆E₂₁ between thermally coupled levels between 2k_BT₀ and 3.41k_BT₀. Analysis of the temperature-dependent excited state kinetics shows that host lattices in which ∆E₂₁ can be bridged by one or two phonons are preferred over hosts in which higher order phonon processes are required. Such a framework is relevant for both a fundamental understanding of luminescent thermometers but also the targeted design of novel and superior luminescent (nano)thermometers.