Self-consistent-field-complete-neglect-of-differential-overlap cluster calculations of deep impurities in semiconductors

A self-consistent-field method to calculate energy levels of deep transition-metal centers in semiconductors based on the complete-neglect-of-differential-overlap (CNDO) approximation is presented. The method can be used for a quantitative interpretation of optical transitions between strongly localized states at the impurity center, which are usually interpreted by crystal-field theory in terms of unknown parameters like the crystal-field splitting parameter $\Delta =10\mathrm{}{D}_q$. Special emphasis is laid on the formulation of correct boundary conditions for the cluster of 17 atoms in II-VI compounds. In case of Cu centers in cubic ZnS $\Delta$ is calculated to be 0.84 eV compared with the experimental value of 0.77 eV. The method does not use any parameter which is adjusted to properties of the center or the crystal, as has to be done using the extended Hückel approximation.