Spin Relaxation of P Dimer Electrons in Silicon

We study the transition rates from different energy states of two P donor electrons to the ground state singlet. By considering the full set of the states of the two donor electrons within the Heitler-London approximation, we classify them according to their hyperfine interaction with P nuclei. Here the electron spin-flip is assisted by hyperfine interaction with the phosphorus nuclei and phonon emissions. This study is crucial in order to find an upper bound for the relaxation time of the silicon-based qubits, and finding various regimes to decelerate the spin decay rate.