Uniaxial compressive strain along the [001] direction strongly suppresses the spin relaxation in silicon. When the strain level is large enough so that electrons are redistributed only in the two valleys along the strain axis, the dominant scattering mechanisms are quenched and electrons mainly experience intra-axis scattering processes (intravalley or intervalley scattering within valleys on the same crystal axis). We first derive the spin-flip matrix elements due to intra-axis electron scattering off impurities, and then provide a comprehensive model of the spin relaxation time due to all possible interactions of conduction-band electrons with impurities and phonons. We predict nearly three orders of magnitude improvement in the spin relaxation time of $sim10^{19}text{cm}^{-3}$ antimony-doped silicon (Si:Sb) at low temperatures.
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