Electron spin coherence of phosphorus donors in silicon: Effect of environmental nuclei

We report electron paramagnetic resonance EPR experiments of phosphorus donors in isotopically controlled silicon single crystals. By varying the concentration of the 29 Si isotope, f, from 0.075% to 99.2%, we systematically study the effect of the environmental nuclear spins on the donor-electron spin. We find excellent agreement between experiment and theory for decoherence times due to nuclear-induced spectral diffusion, clarifying that the nuclear-induced decoherence is dominant in the range of f studied. We also observe that the EPR linewidth shows a transition from the square-root dependence to the linear dependence on f, in agreement with theoretical predictions.