Crystal field analysis of rare-earth ions energy levels in GaN

Much effort has been put to achieve optoelectronic devices based on Er doped GaN, operating on the intra-4f-shell transitions of erbium. The key issue for good understanding of energy transfer mechanisms to Er and its luminescence properties is the position of Er³⁺ ions in the crystalline lattice of GaN. After doping, Er³⁺ ions are assumed to be placed in substitutional position for Ga³⁺ in GaN. Although Ga is positioned in high symmetry, tetrahedral [ErN₄]⁹ - cluster, deviations from this after doping are impossible to avoid because of a large difference in ionic radii of Ga³⁺ (47 pm) and Er³⁺ (89 pm). In this work we report on crystal field analysis of Er ion energy levels in cubic and hexagonal GaN. It is shown that local symmetry of Er in cubic GaN is D₂, whereas calculations reveal that in hexagonal GaN local symmetry is C_3V. Some trends in crystal field parameters of trivalent lanthanides in hexagonal GaN are discussed.