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 ²⁹Si 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.