Calculation of the spin-orbit-coupling parameter of deep impurities in semiconductors in the complete neglect of differential overlap approximation

A complete neglect of differential overlap (CNDO) self-consistent-field calculation of the crystal-field-splitting parameter 10Dq is used to find the spin-orbit-coupling parameter and the orbital reduction factor. The general spin-orbit-coupling theory has been rewritten in terms of the CNDO approximation and applied to the systems ZnS:Cu²⁺ and CdS:Cu²⁺. The examination of 10Dq and the spin-orbit-coupling parameter {ζ} in terms of the wave functions and some parameters involved shows that it is important to consider not only the effective charges but also the distribution of charge among the different atomic orbitals. The calculated spin-orbit-coupling parameters 600 cm^-1 for ZnS:Cu²⁺ and 620 cm^-1 for CdS:Cu²⁺ agree quite well with the experimental values of 600 and 565 cm^-1, respectively. The orbital reduction factors also agree with experiment. It must be emphasized, however, that our method does not include additional quenching of the spin-orbit-coupling parameter and the orbital reduction factor due to the Jahn-Teller effect. The method presented here can be used to find the quenching of various electronic properties due to covalency and is a uniform procedure for calculating the crystal-field and fine-structure parameters in the framework of the CNDO approximation.