It was recalled that exchange interactions among defects in semiconductors were usually treated within effective-mass theory by using a scaled hydrogenic wave function. However, such a function was applicable only to shallow impurities. A simple and robust generalization for treating deep-donors was presented here, in which the long-range part of the wave-function was treated by using well-established quantum defect theory and a model central-cell correction for fixing the bound-state eigenvalue at the experimentally observed value. This permitted the computation of the effect of binding energy upon exchange interactions as a function of donor distance. As expected, the exchange interactions were suppressed (or increased), compared to the hydrogenic case, by greater localization (or delocalization) of the wave-functions of deep-donors or so-called super-shallow donors having a binding energy which was less than the hydrogenic value. The calculated results were compared with a simple scaling of the Heitler-London hydrogenic exchange. The scaled hydrogenic results gave the correct order of magnitude, but failed to reproduce the calculations quantitatively. The donor exchange in silicon was calculated, including inter-valley interference terms, for donor pairs along the {100} direction. The influence of donor-type upon the distribution of nearest-neighbour exchange constants at various concentrations was also shown. The present methods could be used to compute the exchange interactions between two donor electrons with arbitrary binding energy.

Exchange between Deep Donors in Semiconductors - a Quantum Defect Approach. W.Wu, A.J.Fisher: Physical Review B, 2008, 77[4], 045201