Theory of Trapped-Hole Centers in Aluminum Oxide

Energy levels of trapped-hole centers in gamma- and reactor-irradiated Al₂{O}₃$ are calculated in order to verify models proposed to account for some of the electron-spin resonance (ESR) spectra and to correlate these with optical-absorption spectra. Crystal-field theory is employed in the calculation of energy levels, including a priori calculation of the crystal field on the point-ion model. Lattice distortion by the defect is considered only qualitatively; nevertheless, a number of conclusions are possible. The calculated zero-field splitting of interstitial O⁰, which is 0.268 cm^-1 without distortion and substantially larger with distortion, could account for the absence of an ESR spectrum at X band. A single optical band associated with this center is correlated with a measured band of 2.0 eV. Interstitial O⁺ has a calculated zero-field splitting of 0.174 cm^-1 without distortion, but outward displacement of the two nearest Al³⁺ ions by only 0.17 {} accounts for the observed zero-field splitting of 0.074 cm^-1. No optical absorption is associated with this center. For O^- adjacent to a charge-deficient cation site, the assumption of a cation vacancy leads to an optical band at Δ=2.93 eV which correlates with an observed band at 3.08 eV. The calculated value of λΔ, where λ is the spin-orbit constant, is -0.0057 compared with the ESR value of -0.0073.