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We propose a model for spectral diffusion of localized spins insemiconductors due to the dipolar fluctuations of lattice nuclear spins. Eachnuclear spin flip-flop is assumed to be independent, the rate for this processbeing calculated by a method of moments. Our calculated spin decoherence time$T_{M}=0.64$ ms for donor electron spins in Si:P is a factor of two longer thanspin echo decay measurements. For $^{31}$P nuclear spins we show that spectraldiffusion is well into the motional narrowing regime. The calculation for GaAsquantum dots gives $T_{M}=10-50$ $\mu$s depending on the quantum dot size. Ourtheory indicates that nuclear induced spectral diffusion should not be aserious problem in developing spin-based semiconductor quantum computerarchitectures.Comment: 15 pages, 9 figures. Accepted for publication in Phys. Rev.

Theory of nuclear-induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots