Hyperfine Constant and Binding Energy Calculation of Shallow Donor in Silicon from Pseudopotential and All-Electron Mixed Approach

Design of robust silicon-processing infrastructure based on spin qubits requires an accurate modeling of hyperfine coupling interaction and s manifold energy levels for donors in silicon. However, the well-known ab-initio methods have so far been lacking the accuracy in predicting these properties due to the large spatial extent of wavefunction of shallow donors in silicon. The present work employs density functional theory (DFT) with pseudopotential and all-electron mixed approach as well as hybrid functional working in tandem and permits efficient calculations for systems containing more than 4000 atoms. Remarkable accuracy in the prediction of hyperfine coupling interaction and s manifold energy levels has been achieved for single phosphorus donor in silicon, including: Fermi contact hyperfine constant (116.0MHz), quadratic Stark coefficient (-2.65×10^-3μm²/V²), binding energy of the ground state (44.8meV), and energies of  the excited 1sT₂ (35.9meV) and 1sE (34.5meV) states. Additionally, accurate computations of super-hyperfine parameters have been achieved, showing excellent agreement with the well-known Green’s functional approach.