Calculations of exchange interaction in the impurity band of two-dimensional semiconductors with out-of-plane impurities

We calculate the singlet-tripler splitting for a couple of two-dimensional electrons in the potential of two positively charged impurities, which are located out of plane. We consider different relations between vertical dist ances of impurities h(1) and h(2) and their lateral distance R. Such a syst em has never been studied in atomic physics but the methods, worked out for regular two-atomic molecules and helium atom, have been found to be useful . Analytical expressions for several different limiting configurations of i mpurities are obtained and an interpolated formula for intermediate range o f parameters is proposed. The R dependence of the splitting is shown to bec ome weaker with increasing h(1) ,h(2) [S0163-1829(99)01847-0].