Tight-Binding Configuration Interaction Formalism for P-Doped Silicon Nanodevices

Atom-scale Silicon quantum devices incorporating dopants with atomic precision are promising platforms for future quantum computing technologies. This dopant placement precision allows for fine-tuning device properties, such as tunnel couplings and charging energies, making dopant array structures ideal for exploring many-body physics. Additional control is achieved with atomically aligned contacts. Accurate electronic structure calculations are needed to understand how the dopant placement determines state properties.  We introduce an efficient formalism for calculating the electronic and transport properties on realistic devices. Our approach combines tight-binding calculations for the silicon matrix and configuration interaction level theory for the multielectron charged states of dopant structures, incorporating electron-electron interactions and corrections due to exchange and correlation. We present detailed calculations of devices with two, three, and four P atoms in different configurations and their corresponding stability diagrams. By comparing with the Fermi-Hubbard model and Hartree-Fock level theory predictions, we show when exchange and correlation effects and coupling to higher energy orbitals are relevant in predicting the stability diagrams of these devices.