Shallow dopant pairs in silicon: An atomistic full configuration interaction study

Abstract

The two-electron states and exchange couplings are investigated for a phosphorous donor pair in silicon using an atomistic full configuration interaction method for donor separations spanning from 0.4 to 15 nm. Three distinct donor separation regimes appear from our large basis calculations, from which the validity of simplified methods such as Heitler-London and Hartree-Fock type approaches can be assessed. For bulk donors, the exchange coupling saturates below 5 nm due to excited bonding orbital contributions to the wave functions. Ionic contributions to the two-electron state decrease between 5 and 14 nm, and a fully correlated Heitler-London-like state is reached from 14 nm onwards. Oscillations in exchange couplings can be strongly suppressed by placing the donors in the same $z$ plane and at a small depth, $D$, from the surface. This is a consequence of the $z$-valley terms becoming dominant within the dopant's wave function and of small changes with $x$ and $y$ separations no longer having much effect. We find the depth to be an important parameter in determining the exchange coupling for subsurface dopants, not only through valley repopulation ($D<10$ nm) but also through additional interface effects for ultrashallow depths ($D<2.5$ nm). Our full configuration interaction method provides insights in the exchange interaction for various regimes of donor separation and depths, from the Heitler-London limit at large distances to the 0.4--5 nm range relevant for scanning tunneling microscope based quantum state imaging and spectroscopy experiments. The precise control of electron-electron quantum correlations in such engineered atoms in the solid state is useful to design quantum logic gates and quantum simulators.