The improved point-charge model for dopants in Si and applications to atomic-scale system simulations

Dopants in silicon are strong candidates for qubits in scalable solid-state quantum systems. Tight-binding (TB) theory has been used to provide a good atomic-scale model when a central cell correction is fit to experimental binding energies for one choice of the bulk Si TB parameters. However, this model fails to predict the correct dopant level energy degeneracies for other well-established TB models. We argue that the point-charge dopant model with a simple central cell correction is missing vital contributions from the dopant potential. We have developed a first principles-based dopant model with several new corrections that are obtained explicitly through self-consistent field calculations to evaluate the appropriate dopant matrix elements rather than by fitting to experiment. We find that these new corrections greatly improve our predictability of the underlying dopant physics, as all bulk Si TB parameters produce the correct ordering of dopant levels in our new model, and give us flexible tunability of numerical values of the dopant level to arbitrary precision. Results are discussed to show the effect on inter-dopant exchange coupling and the level structure of dopant clusters. Finally, we discuss how these models can effectively simulate many-body physics in atom arrays.