The electronic structure and transport properties of phosphorus arrays and phosphorus clusters in silicon nanodevices.

Donor-based quantum devices in silicon are attractive for universal quantum computing and analog quantum simulations, providing great control over the quantum states of these devices. We present theoretical atomistic calculations and a detailed analysis of the electronic and transport properties of phosphorus dopant arrays and clusters in Si quantum devices. Our method consists of self-consistent calculations of the electron energy levels in P-doped Si devices using representative tight-binding Hamiltonians with solutions to the Poisson equation to account for external potentials. We identify the electronic states and charge distribution in linear, triangular, and square dopant arrays of different sizes and under the influence of a range of gate and source/drain potentials. We rationalize our findings in terms of dopant wavefunction overlaps, symmetries of electronic states, and group-theory methods. For large dopant spacing, arrays act as weakly-coupled distinct sites. For small dopant spacing, arrays act as giant clusters. We identify this transition and discuss how it affects transport. Our simulations allow us to understand the stability diagrams in these devices, demonstrating that our approach accurately describes transport through multi-dopant quantum devices.