Electron Spin-Relaxation Times of Phosphorus Donors in Silicon

We study the low-temperature dynamics of a shallow donor, e.g., $^{31}$P, impurity electron spin in silicon, interacting with the bath of nuclear spins of the $^{29}$Si isotope. For small applied magnetic fields, the electron spin relaxation is controlled by the steady state distribution of the nuclear spins. We calculate the relaxation times $T_1$ and $T_2$ as functions of the external magnetic field, and conclude that nuclear spins play an important role in the donor electr...

Spectral diffusion arising from $^{29}$Si nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on $^{31}$P nuclear spin coherence is measured as a function of $^{29}$Si concentration using X-band pulsed electron nuclear double resonance (ENDOR). The $^{31}$P nuclear spin echo decays show that decoherence is cont...

We demonstrate the coherent control and electrical readout of the nuclear spins of ionized phosphorus donors in natural silicon. By combining pulsed illumination with coherent electron spin manipulation, we selectively ionize the donor depending on its nuclear spin state, exploiting a spin-dependent recombination process via a spin pair at the Si/SiO2 interface. The nuclear-spin coherence time of the ionized donor is 18 ms, two orders of magnitude longer than in the neutral d...

Coherence times of electron spins bound to phosphorus donors have been measured, using a standard Hahn echo technique, to be up to 20 ms in isotopically pure silicon with [P]$ = 10^{14}$ cm$^{-3}$ and at temperatures $\leq 4 $K. Although such times are exceptionally long for electron spins in the solid state, they are nevertheless limited by donor electron spin-spin interactions. Suppressing such interactions requires even lower donor concentrations, which lie below the detec...

The ability to probe the spin properties of solid state systems electrically underlies a wide variety of emerging technology. Here, we extend electrical readout of the nuclear spin states of phosphorus donors in silicon to the coherent regime with modified Hahn echo sequences. We find that, whilst the nuclear spins have electrically detected phase coherence times exceeding 2 ms, they are nonetheless limited by the artificially shortened lifetime of the probing donor electron.

We report on the 29Si nuclear spin decoherence time at room temperature for a pure (99.99999%, 7N) and carrier-less (p-type, doping level of 10^15cm-3) silicon in which 29Si nuclei are naturally abundant (4.7%). Despite the experimental difficulties coming from the extremely long spin-lattice relaxation time T1 (of the order of 10^4 s), we have successfully observed a series of spin-echoes of which the time dependence is characterized by the decoherence time T2. We found that...

Silicon is promising for spin-based quantum computation because nuclear spins, a source of magnetic noise, may be eliminated through isotopic enrichment. Long spin decoherence times, $T_2$, have been measured in isotope-enriched silicon but come far short of the $T_2 = 2 T_1$ limit. The effect of nuclear spins on $T_2$ is well established. However, the effect of background electron spins from ever present residual phosphorus impurities in silicon can also produce significant ...

The electrical detection of spin echoes via echo tomography is used to observe decoherence processes associated with the electrical readout of the spin state of phosphorus donor electrons in silicon near a SiO$_2$ interface. Using the Carr-Purcell pulse sequence, an echo decay with a time constant of $1.7\pm0.2 \rm{\mu s}$ is observed, in good agreement with theoretical modeling of the interaction between donors and paramagnetic interface states. Electrical spin echo tomograp...

Silicon is undoubtedly one of the most promising semiconductor materials for spin-based information processing devices. Its highly advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of an isotopically-purified $^{28}$Si form with no magnetic nuclei overcomes what is a main source of spin decoherence in many other materials. Nevertheless, the coherence lifetimes of electron spins in the solid state...

We experimentally demonstrate the inductive readout of optically hyperpolarized phosphorus-31 donor nuclear spins in an isotopically enriched silicon-28 crystal. The concentration of phosphorus donors in the crystal was 1.5 x 10$^{15}$ cm$^{-3}$, three orders of magnitude lower than has previously been detected via direct inductive detection. The signal-to-noise ratio measured in a single free induction decay from a 1 cm$^3$ sample ($\approx 10^{15}$ spins) was 113. By transf...