Electronic structures of alkaline rare earth fluoride-based upconversion nanomaterials

In this chapter, we discuss the electronic structures of β-NaLnF₄ (Ln=Y, Gd, and Lu). We unveil that the difference in the experimentally observed band gap arises from the different positions of 4f orbital levels relative to the valence band maximum. The 4f empty state of lanthanide ions, such as Gd³⁺, is discussed in relation to the positions within the optical band gap. By projecting the components of self-energy and wavefunction relaxation in 4f orbitals, we indicate the 4f level of Gd and Lu ions in the β-lattices, giving a brief explanation of the reason for the highly efficient upconversion (UC) luminescence for such materials. This analysis helps us to understand the essential mechanism and modified energy migration-mediated UC model. Meanwhile, the chapter also proposes a convenient route and fundamental analysis for future investigation of the interface states that potentially quench the UC luminescence.