Understanding Energy Transfer Mechanisms for Tunable Emission of Yb³⁺-Er³⁺ Codoped GdF₃ Nanoparticles: Concentration-Dependent Luminescence by Near-Infrared and Violet Excitation

Energy transfer (ET) is an important route to manage the population density of excited states, giving rise to spectrally tunable emission that is valuable for multicolor imaging and biological tracking. In this paper, a case study of GdF₃ nanoparticles (NPs) codoped with Yb³⁺ and Er³⁺ was used to experimentally and theoretically investigate the ET mechanisms under near-infrared and violet excitation. Red-to-green ratio (RGR) is used as a primary evaluating protocol, and the power-dependent luminescence and Er^{3+ 4}I_13/2 luminescence behavior are used to identify the corresponding conjectures about ET mechanisms. Compared with the four common upconversion (UC) models, a joint effect of energy-back-transfer, multiphonon relaxation, and linear decay depletion mechanisms for the Er^{3+ 4}I_13/2 manifold was proposed for the UC process based on UC spectra for samples with different dopant concentrations. Meanwhile, the varying RGR could also be observed from downshifting (DS) emission spectra. The ET mechanism for the DS process, where three cross-relaxation processes coexisted including the Yb^{3+ 2}F_5/2 manifold as energy in-transit state, was proposed for the first time. The findings are expected to provide an approach for understanding ET mechanisms in many Yb³⁺/Er³⁺ codoped UC and DS systems and enable spectrally tunable emission properties for applications that require precisely defined optical transitions.