Theory of Trapped-Hole Centers in Aluminum Oxide

Energy levels of trapped-hole centers in gamma- and reactor-irradiated ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ 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 ${\mathrm{O}}^0$, which is 0.268 ${\mathrm{cm}}^{-1\mathrm{}}$ 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 ${\mathrm{O}}^{+}$ has a calculated zero-field splitting of 0.174 ${\mathrm{cm}}^{-1\mathrm{}}$ without distortion, but outward displacement of the two nearest ${\mathrm{Al}}^{3+}$ ions by only 0.17 Å accounts for the observed zero-field splitting of 0.074 ${\mathrm{cm}}^{-1\mathrm{}}$. No optical absorption is associated with this center. For ${\mathrm{O}}^{-}$ adjacent to a charge-deficient cation site, the assumption of a cation vacancy leads to an optical band at $\Delta =2.93\mathrm{}$ eV which correlates with an observed band at 3.08 eV. The calculated value of $\frac{\lambda }{\Delta }$, where $\lambda$ is the spin-orbit constant, is -0.0057 compared with the ESR value of -0.0073.