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

Shallow impurities are central to semiconductor technology. A thorough understanding of the physics of shallow impurities has taken on new urgency in the context of quantum information science, where they form key components of qubits. Because of the large spatial extent of the wave function, first-principles calculations of shallow centers have proved elusive. In addition, the “central cell corrections” that are crucial for accurately describing binding energies and hyperfine parameters are not adequately captured by traditional semi-local functionals in density functional theory, requiring advanced approaches that have proven too computationally demanding. We have developed a methodology that is capable of accurately predicting properties of shallow impurities. It is based on a combination of extrapolating results from supercell calculations carried out using a semi-local functional with performing select calculations using a hybrid functional. We will illustrate the power of this approach with results that provide an explanation for an observed unexpected strain dependence of the hyperfine properties of shallow donors in silicon, a system with applications in atomic clock transitions for silicon-based spin qubits.