First-principles calculations of hyperfine interaction, binding energy, and quadrupole coupling for shallow donors in silicon

Spin qubits based on shallow donors in silicon are a promising quantum information technology with enormous potential scalability due to the existence of robust silicon-processing infrastructure. However, the most accurate theories of donor electronic structure lack predictive power because of their reliance on empirical fitting parameters, while predictive ab initio methods have so far been lacking in accuracy due to size of the donor wavefunction compared to typical simulation cells. We show that density functional theory with hybrid and traditional functionals working in tandem can bridge this gap. Our first-principles approach allows remarkable accuracy in binding energies (67 meV for bismuth and 54 meV for arsenic) without the use of empirical fitting. We also obtain reasonable hyperfine parameters (1263 MHz for Bi and 133 MHz for As) and superhyperfine parameters. We demonstrate the importance of a predictive model by showing that hydrostatic strain has much larger effect on the hyperfine structure than predicted by effective mass theory, and by elucidating the underlying mechanisms through symmetry analysis of the shallow donor charge density.