Exchange between deep donors in semiconductors: a quantum defect approach

TL;DR

This paper introduces a quantum defect theory-based approach to accurately compute exchange interactions between deep donors in semiconductors, improving upon traditional hydrogenic models especially for quantum information applications.

Contribution

It generalizes the effective-mass theory for deep donors by incorporating quantum defect theory and a central-cell correction, enabling precise calculation of exchange interactions across various binding energies.

Findings

Exchange interactions vary significantly with donor binding energy.

Quantum defect approach provides more accurate exchange estimates than scaled hydrogenic models.

Results applicable to quantum information processing with deep donors in semiconductors.

Abstract

Exchange interactions among defects in semiconductors are commonly treated within effective-mass 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.