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Decoherence of a shallow donor electron spin in silicon caused byelectron-lattice interaction is studied. We find that there are two time scalesassociated with the evolution of the electron spin density matrix: the fast butincomplete decay due to the interaction with non-resonant phonons followed byslow relaxation resulting from spin flips accompanied by resonant phononemission. We estimate both time scales as well as the magnitude of the initialdrop of coherence for P donor in Si and argue that the approach used issuitable for evaluation of phonon induced decoherence for a general class oflocalized spin states in semiconductors.Comment: in Plain Tex, 10 pages, 1 figure, submitted to Phys. Rev.

Time scales of phonon-induced decoherence of semiconductor spin qubits