  An electron spin qubit in a silicon donor atom is a promising candidate for
quantum information processing because of its long coherence time. To be sensed
with a single-electron transistor, the donor atom is usually located near an
interface, where the donor states can be coupled with interface states. Here we
study the phonon-assisted spin-relaxation mechanisms when a donor is coupled to
confined (quantum-dot-like) interface states. We find that both Zeeman
interaction and spin-orbit interaction can hybridize spin and orbital states,
each contributing to phonon-assisted spin relaxation in addition to the spin
relaxation for a bulk donor or a quantum dot. When the applied magnetic field
$B$ is weak (compared to orbital spacing), the phonon assisted spin relaxation
shows the $B^5$ dependence. We find that there are peaks (hot-spots) in the
$B$-dependent and detuning dependent spin relaxation due to strong
hybridization of orbital states with opposite spin. We also find spin
relaxation dips (cool-spots) due to the interference of different relaxation
channels. Qubit operations near spin relaxation hot-spots can be useful for the
fast spin initialization and near cool-spots for the preservation of quantum
information during the transfer of spin qubits.
