Electron spin-echo relaxation and envelope modulation of shallow phosphorus donors in silicon

Abstract

Spins of single donor atoms are attractive candidates for large scale quantum information processing in silicon, since quantum computation can be realized through the manipulation of electron and/or nuclear spins. In this paper we report on two-pulse electron spin-echo experiments on phosphorus shallow donors in natural and $^{28}\mathrm{Si}$-enriched silicon epilayers doped with ${10}^{16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ P donors. The experiments address the spin-spin relaxation times and mechanisms and provide, through the electron spin-echo envelope modulation (ESEEM) effect, information on the donor electron wave function. Experiments performed as a function of the pulse turning angle allowed us to measure the exponential relaxation and spectral diffusion times depurated by instantaneous diffusion. According to these results, isotopically purified samples are necessary to reduce the spectral diffusion contribution and the P shallow donors concentration plays a fundamental role in determining the intrinsic phase memory time. ESEEM peaks have been assigned to hyperfine-coupled silicon-29 nuclei at specific crystallographic positions on the basis of a spectral fit procedure including instrumental distortions.