Singlet-Triplet Relaxation in Two-electron Silicon Quantum Dots

We investigate the singlet-triplet relaxation process of a two electron silicon quantum dot. In the absence of a perpendicular magnetic field, we find that spin-orbit coupling is not the main source of singlet-triplet relaxation. Relaxation in this regime occurs mainly via virtual states and is due to nuclear hyperfine coupling. In the presence of an external magnetic field perpendicular to the plane of the dot, the spin-orbit coupling is important and virtual states are not required. We find that there can be strong anisotropy for different field directions: parallel magnetic field can increase substantially the relaxation time due to Zeeman splitting, but when the magnetic field is applied perpendicular to the plane, the enhancement of the spin-orbit effect shortens the relaxation time. We find the relaxation to be orders of magnitude longer than for GaAs quantum dots, due to weaker hyperfine and spin-orbit effects.