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Electron spin coherence exceeding seconds in high-purity silicon

Abstract

Silicon is one of the most promising semiconductor materials for spin-based information processing devices1,2. Its advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of a 28Si form with no magnetic nuclei overcomes a primary source of spin decoherence in many other materials3,4. Nevertheless, the coherence lifetimes of electron spins in the solid state have typically remained several orders of magnitude lower than that achieved in isolated high-vacuum systems such as trapped ions5. Here we examine electron spin coherence of donors in pure 28Si material (residual 29Si concentration <50 ppm) with donor densities of 1014–1015 cm−3. We elucidate three mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime T2 up to 2 s. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. A magnetic field gradient suppresses such interactions, producing an extrapolated electron spin T2 of 10 s at 1.8 K. These coherence lifetimes are without peer in the solid state and comparable to high-vacuum qubits, making electron spins of donors in silicon ideal components of quantum computers2,6, or quantum memories for systems such as superconducting qubits7,8,9.

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Figure 1: Summary of measured spin relaxation times, T1 and T2 for phosphorus donors in silicon at cryogenic temperatures.
Figure 2: Electron spin echo decays of phosphorus donors in 28Si crystal with 50 ppm 29Si.
Figure 3: ‘Intrinsic’ T2 obtained by suppressing instantaneous diffusion.
Figure 4: Applying an external magnetic field gradient suppresses donor flip-flops and leads to an extended T2.

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Acknowledgements

We thank W. M. Witzel and A. Morello for helpful discussions. Work at Princeton was supported by the National Science Foundation (NSF) through the Princeton Materials Research Science and Engineering Center (DMR-0819860) and the National Security Agency (NSA)/Laboratory for Physical Sciences through Lawrence Berkley National Laboratory (LBNL) (100000080295), at Keio by the Grant-in-Aid for Scientific Research and Project for Developing Innovation Systems by the Ministry of Education, Culture, Sports, Science and Technology, the FIRST Program by the Japan Society for the Promotion of Science, and the Japan Science and Technology Agency/UK Engineering and Physical Sciences Research Council (EPSRC) (EP/H025952/1), at Oxford by the EPSRC through the Centre for Advanced Electron Spin Resonance (EP/D048559/1), at LBNL by the US Department of Energy (DE-AC02-05CH11231) and the NSA (100000080295), and at Simon Fraser University by the Natural Sciences and Engineering Research Council of Canada. J.J.L.M. is supported by the Royal Society.

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A.M.T., S.T., J.J.L.M., T.S., M.L.W.T., K.M.I. and S.A.L. conceived and designed the experiments. A.M.T., S.T. and J.J.L.M. performed the ESR experiments. A.M.T., J.J.L.M. and S.A.L. analysed the measurements. H.R., N.V.A., P.B., H-J.P., M.L.W.T. and K.M.I. prepared the 28Si samples. A.M.T., J.J.L.M. and S.A.L. wrote the manuscript with input from the other co-authors.

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Correspondence to S. A. Lyon.

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Tyryshkin, A., Tojo, S., Morton, J. et al. Electron spin coherence exceeding seconds in high-purity silicon. Nature Mater 11, 143–147 (2012). https://doi.org/10.1038/nmat3182

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