It was recalled that exchange interactions among defects in semiconductors were commonly treated within effective-mass theory, using a scaled hydrogenic wave function. However, such a wave function was applicable only to shallow impurities. Here, a simple but robust generalization was presented for treating deep donors. That is, the long-range part of the wave function was treated using well-established quantum defect theory, and a model central-cell correction was included to fix 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. Exchange interactions were suppressed/increased (compared to the hydrogenic case) by the greater localization/delocalization of the wave functions of deep donors (or so-called super-shallow donors with binding energy 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 Si was calculated, including intervalley interference terms for donor pairs along the {100} direction. The influence of the donor type upon the distribution of nearest-neighbor exchange constants at various concentrations was also shown. The present method could be used to compute the exchange interactions between 2 donor electrons of 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 (11pp)