  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.
