Exchange between deep donors in semiconductors: A quantum defect approach

Abstract

Exchange interactions among defects in semiconductors are commonly treated within effectivemass theory using a scaled hydrogenic wave-function. However such a wave-function is only applicable to shallow impurities; here we present a simple but robust generalization to treat deep donors, in which we treat the long-range part of the wavefunction using the well established quantum defect theory, and include a model central-cell correction to fix the bound-state eigenvalue at the experimentally observed value. This allows us to compute the effect of binding energy on exchange interactions as a function of donor distance; this is a significant quantity given recent proposals to carry out quantum information processing using deep donors. As expected, exchange interactions are suppressed (or increased), compared to the hydrogenic case, by the greater localization (or delocalization) of the wavefunctions of deep donors (or 'super-shallow' donors with binding energy less then the hydrogenic value). The calculated results are compared with a simple scaling of the Heitler-London hydrogenic exchange; the scaled hydrogenic results give the correct order of magnitude but fail to reproduce quantitatively our calculations. We calculate the donor exchange in silicon including inter-valley interference terms for donor pairs along the {100} direction, and also show the influence of the donor type on the distribution of nearest-neighbour exchange constants at different concentrations. Our methods can be used to compute the exchange interactions between two donor electrons with arbitrary binding energy.

Excited states of defect linear arrays in silicon: A first-principles study based on hydrogen cluster analogs

“…Figure 2(d) shows the averaged oscillator strength as a function of energy for a distribution of nearest-neighbor distances corresponding to random donor placements with a range of donor densities, where donor pairs are important [22,42,43]. This gives an approximate description of the absorption of a randomly doped crystal under the assumption that pairwise interactions dominate (at least, in the low-energy regime where transitions to other bound states dominate; our basis set is not designed to describe bound-to-continuum transitions at higher energies).…”

Half-filled orbital and unconventional geometry of a common dopant in Si(001)

“…This difference is significant for the 4-dimer spacing, but falls below the accuracy of our calculations for 6 and 8 dimers. The calculations indicate that the interactions are ferromagnetic, in contrast to the antiferromagnetic interaction of around +0.06 eV estimated for Bi at the same separation in bulk Si, 27 with considerable overlap of the associated Rydberg atoms. The difference is a result of the bonding of the Bi and hence its electronic structure.…”

Optically controlled entangling gates in randomly doped silicon

“…The exchange interaction energy calculated using the Heitler-London approximation [34,51] taking into account the multi-valley coupled wavefunction and central cell correction can be found in Appendix A. The maps in Fig.…”