Energy levels of thed*8electron andd*2hole system

Abstract

In the investigation of the optical and magnetic properties of the semiconductors containing transition-metal ions, the one-electron orbital cannot be treated with a pure d orbital because of a strong covalence. This paper presents the energy matrix of the d*(8) and d*(2) (d* means a modified d function) system, in which the covalence is described by two covalent factors. The differences between the matrix diagonal elements of the t(2)(m)e(n) term of the d*(8) system and the t(2)(6-m)e(4-n) term of the d*(2) system vary with m and n. The d(N) electron system can be explained with the d(10-N) hole system because the difference between the energy matrix of the d(N) and d(10-N) systems has a fixed value. However, this kind of simple relation does not exist for the d*(N) and d*(10-N) systems when the covalence is considered. A numerical calculation shows that the variation of the energy levels with the covalence for Ni2+ in the d*(8) electron system is larger than that in the d*(2) hole system. The calculated energy levels obtained from the d*(8) matrix are in good agreement with the experimental data of the Ni2+ ion for ZnS:Ni and ZnSe:Ni. This suggests that the d*(8) electron system instead of the d*(2) hole system should be used in the investigation of optical and magnetic properties of semiconductor containing Ni2+ ions.