Large-scale atomistic density functional theory calculations of phosphorus-doped silicon quantum bits

TL;DR

This study uses large-scale density functional theory to analyze phosphorus-doped silicon, revealing detailed electronic structures and potentials crucial for quantum computing applications, especially in understanding donor electron behavior and device modeling.

Contribution

The paper introduces an explicit density functional theory approach that includes lattice relaxation and detailed electronic structure analysis of phosphorus donors in silicon, improving upon previous models.

Findings

Electron density around dopants shows non-spherical features affecting potentials.

Doping potentials exhibit trigonal lobes at specific energy scales.

Results provide detailed parameters for large-scale device simulations.

Abstract

We present density functional theory calculations of phosphorus dopants in bulk silicon and of several properties relating to their use as spin qubits for quantum computation. Rather than a mixed pseudopotential or a Heitler-London approach, we have used an explicit treatment for the phosphorus donor and examined the detailed electronic structure of the system as a function of the isotropic doping fraction, including lattice relaxation due to the presence of the impurity. Doping electron densities and spin densities are examined in order to study the properties of the dopant electron as a function of the isotropic doping fraction. Doping potentials are also calculated for use in calculations of the scattering cross-sections of the phosphorus dopants, which are important in the understanding of electrically detected magnetic resonance experiments. We find that the electron density around the dopant leads to non-spherical features in the doping potentials, such as trigonal lobes in the (001) plane at energy scales of +12 eV near the nucleus and of -700 meV extending away from the dopants. These features are generally neglected in effective mass theory and will affect the coupling between the donor electron and the phosphorus nucleus. Our density functional calculations reveal detail in the densities and potentials of the dopants which are not evident in calculations that do not include explicit treatment of the phosphorus donor atom and relaxation of the crystal lattice. These details can also be used to parameterize tight-binding models for simulation of large-scale devices.