image: Figure 1. Impact of lower-lying levels on Boltzmann compliance. a Energy separation ΔElower between the lower thermally coupled level L1 and the nearest lower-lying level Llower for representative Ln3+ ions, together with the ratio of ΔElower to ΔE, where ΔE denotes the TCLs gap. b Extended rate-equation scheme that includes nonradiative relaxation from the two TCLs to Llower. c Simulated LIR in logarithmic form as a function of inverse temperature (1/T), and d corresponding temperature-dependent LIR curves for the ratio of ΔElower to ΔE between 0.1-fold and 3.0-fold.
Credit: Zuoling Fu et al.
Accurate temperature readout is essential in microelectronics, energy conversion, and biomedical processes, where local heating can reshape transport, reaction kinetics, and therapeutic outcomes. Luminescent nanothermometry offers remote optical temperature sensing by encoding thermal information into emission signals. A widely used approach relies on thermally coupled energy levels of lanthanide ions. When two excited states exchange population rapidly enough, an emission intensity ratio follows Boltzmann statistics and enables self-referenced ratiometric thermometry.
In practice, Boltzmann-type thermometers based on thermally coupled levels with gaps in the widely used 200 to 2000 cm-1 range can still deviate markedly from ideal Boltzmann behavior. A major reason is incomplete thermalization. Population exchange between the two levels competes with radiative decay, multiphonon relaxation, and leakage to nearby states, so the ideal two-level picture can break down over a large temperature interval.
In this work, researchers establish a population-dynamics framework to quantify when Boltzmann behavior becomes valid. The model defines an onset temperature and a thermal-coupling window by comparing nonradiative exchange rates with radiative decay. A key mechanistic outcome is a simple stability rule for energy-level selection: robust coupling is expected only when the nearest lower-lying level lies more than twice the energy gap of the thermally coupled pair. This criterion explains why nominally suitable pairs can fail and provides a practical screening tool for new thermometric pairs.
Predictive design also requires linking host-lattice chemistry with thermometric performance. The study introduces a splitting factor that connects the energy separation of thermally coupled levels with microscopic chemical-bond parameters. This bridge enables rational host selection and crystal-field engineering to steer the energy gap and sensitivity beyond empirical trial and error.
To demonstrate practical impact, the framework guides the design of dual thermally coupled architectures that combine a thermally enhanced channel with a thermally quenched channel to amplify ratiometric contrast. In fluoride hosts, an optimized Er3+ and Nd3+ codoped system achieves a relative sensitivity of up to 6.17 % K-1, together with sub-0.1 K resolution.
The work further delivers high-brightness, ultrathin, flexible thermosensing patches based on phosphor particles embedded in a polymer film. The patch operates under near-infrared excitation and supports real-time, noncontact temperature readout on curved surfaces. In situ tests during a heated reaction setup show a maximum deviation below 0.8 K and high repeatability, highlighting potential for temperature mapping in chemical synthesis, microelectronic thermal management, and other demanding environments.
Journal
Light Science & Applications
Article Title
Boltzmann luminescent nanothermometry: mechanistic criteria and predictive design of thermally coupled levels