Coherence limit due to hyperfine interaction with nuclei in the barrier material of Si spin qubits

On the quest to understand and reduce environmental noise in Si spin qubits, hyperfine interactions between electron and nuclear spins impose a major challenge. Silicon is a promising host material because one can increase the spin coherence time by removing spinful 29Si isotopes. As more experiments rely on isotopic purification of Si, the role of other spinful atoms in the device should be clarified. This is not a straightforward task, as the hyperfine interactions with atoms in the barrier layers are poorly understood. We use density-functional theory to determine the hyperfine tensors of both Si and Ge in a crystalline epitaxial Si/SiGe quantum well as well as Si and O atoms in an amorphous Si/SiO2 (MOS) interface structure. On the basis of the results, we estimate the dephasing time T2 - due to magnetic noise from the spin bath and show that the coherence is limited by interactions with non-Si barrier atoms to a few microseconds in Si/SiGe (for nonpurified Ge) and about 100 μs in Si-MOS. Expressing these numbers alternatively, we find in Si/SiGe the interactions with Ge dominate below a 29Si content of 1000 ppm, and, due to low natural concentration of the spinful oxygen isotopes, the interactions with oxygen in Si-MOS become significant only below a 29Si content of 1 ppm.