Thermometric Limits and Artefact Sensitivity of Er³⁺/Yb³⁺ Upconversion Fluorescence-Intensity-Ratio Thermometers in Calcium Aluminate Hosts: A Theoretical and Simulation Study

Er³⁺/Yb³⁺ co-doped upconversion (UC) phosphors read temperature from the Boltzmann-coupled ²H₁₁/₂ and ⁴S₃/₂ green emission bands, and calcium aluminates (CaAl₂O₄, CaAl₄O₇, CaAl₁₂O₁₉, Ca₁₂Al₁₄O₃₃) are attractive refractory hosts for this purpose. Reported performance in such hosts is, however, difficult to compare because laser heating, spectral overlap and signal-to-noise limits are rarely quantified together. Here we build a compact physical model of the fluorescence intensity ratio (FIR) method and use it to map four limits relevant to aluminate hosts: (i) the intrinsic relative sensitivity Sr = ΔE/(kBT²) and the temperature uncertainty it implies, (ii) the shot-noise-limited usable temperature range once thermal quenching of the emission is included, (iii) the calibration error caused by pump-induced heating, and (iv) the bias introduced by fixed-window integration of overlapping, broadened green bands. For ΔE = 750 cm⁻¹ the model gives Sr = 1.20 % K⁻¹ at 300 K, falling to 0.11 % K⁻¹ at 1000 K. With 10⁶ detected photons at 300 K, a temperature uncertainty of 2 K or better is maintained only up to about 625 K, and the ceiling moves to roughly 500 K and 770 K for 10⁵ and 10⁷ photons. A heating coefficient of 0.3 K cm² W⁻¹ at 50 W cm⁻² underestimates the fitted energy gap by about 7 %, and a power-induced offset of 15 K. Overlap between symmetric bands of 300 cm⁻¹ width changes the fitted gap by under 1 %, but 400 cm⁻¹ bands reduce it by about 3 % and Sr at 300 K by about 7 %. A parameter-free phonon-order analysis indicates that the temperature acceleration of multiphonon quenching depends strongly on the host phonon energy. The results define quantitative acceptance criteria and a minimum reporting standard for future experimental work on Er³⁺/Yb³⁺ calcium aluminate thermometers.