Interrelation between quasi-band and resonant scattering methods of calculating 3d impurity states in semiconductors

Analytical resonance scattering and numerical quasi-band approaches in the theory of semiconductors doped by transition metal ions are compared and the qualitative equivalence of the main results of both theories is demonstrated. A simplified illustrative model is considered in which both resonance scattering from the atomic d-levels and singlesite Koster-Slater potential scattering are included on an equal footing. The analytical solution of this model containing the dangling bond hybrids and crystal field resonances in the valence and forbidden energy bands is presented. The multiplet corrections to the mean- field one-electron levels and the applicability of the scaling parameters J. in calculating the Racah coefficients are discussed. The connection between different possible theoretical schemes and real experimental situations as occurring in elemental Si and Ge on the one hand and III-V and II-VI compounds on the other hand is established.