  We study two-electron singlet-triplet relaxation of donor-bound electrons in
Silicon. Hyperfine interaction of the electrons with the phosphorus (P) nuclei,
in combination with the electron-phonon interaction, lead to relaxation of the
triplet states. Within the Heitler-London and effective mass approximations, we
calculate the triplet relaxation rates in the presence of an applied magnetic
field. This relaxation mechanism affects the resonance peaks in current
Electron Spin Resonance (ESR) experiments on P-dimers. Moreover, the estimated
time scales for the spin decay put an upper bound on the gate pulses needed to
perform fault-tolerant two-qubit operations in donor-spin-based quantum
computers (QCs).
