Revising the 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 with reasonable precision when a central cell correction is adjusted to fit to experimental binding energies for one choice of the bulk Si TB parameters. However, this simple model fails to predict the correct dopant level energy degeneracies for many other well-established bulk Si TB models. We argue that the point-charge dopant model with a simple central cell correction is missing vital contributions from the dopant potential that must be included to encapsulate the underlying physics. We have developed a dopant model that includes several new corrections that are obtained explicitly using atomic orbitals to evaluate the appropriate dopant matrix elements rather than by fitting to experiment. We find that these new corrections play a critical role in defining the dopant physics, as all bulk Si TB parameters predict the correct ordering of dopant levels in our new model. Results are discussed to show the effect on interdopant exchange coupling and the level structure of dopant clusters. Finally, we discuss how these models can be utilized to effectively simulate many-body physics in atom chains and arrays.