Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Spatially resolving valley quantum interference of a donor in silicon

Nature Materials volume 13, pages 605–610 (2014)Cite this article

Subjects

Abstract

Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements have only probed wavefunctions indirectly, preventing direct experimental access to valley population, donor position and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunnelling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley-perturbation-induced enhancement of spin relaxation will be negligible for depths greater than 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest for emerging schemes proposing to encode information directly in valley polarization.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Spatial measurement of single quantum states of a subsurface donor.
Figure 2: Valley interference of a single quantum state in reciprocal space.
Figure 3: Valley population.
Figure 4: Valley interference of a single quantum state in real space.

Similar content being viewed by others

References

  1. Morello, A. et al. Single-shot readout of an electron spin in silicon. Nature 467, 687–691 (2010).

    Article  CAS  Google Scholar 

  2. Fuechsle, M. et al. A single-atom transistor. Nature Nanotech 7, 242–246 (2012).

    Article  CAS  Google Scholar 

  3. Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012).

    Article  CAS  Google Scholar 

  4. Pla, J. J. et al. High-fidelity readout and control of a nuclear spin qubit in silicon. Nature 496, 334–338 (2013).

    Article  CAS  Google Scholar 

  5. Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).

    Article  CAS  Google Scholar 

  6. Koiller, B., Hu, X. & Das Sarma, S. Exchange in silicon-based quantum computer architecture. Phys. Rev. Lett. 88, 027903 (2001).

    Article  Google Scholar 

  7. Wellard, C. & Hollenberg, L. Donor electron wave functions for phosphorus in silicon: Beyond effective-mass theory. Phys. Rev. B 72, 085202 (2005).

    Article  Google Scholar 

  8. Goswami, S. et al. Controllable valley splitting in silicon quantum devices. Nature Phys. 3, 41–45 (2006).

    Article  Google Scholar 

  9. Calderón, M., Koiller, B., Hu, X. & Das Sarma, S. Quantum control of donor electrons at the Si–SiO2 interface. Phys. Rev. Lett. 96, 096802 (2006).

    Article  Google Scholar 

  10. Rahman, R. et al. High precision quantum control of single donor spins in silicon. Phys. Rev. Lett. 99, 036403 (2007).

    Article  Google Scholar 

  11. Lansbergen, G. P. et al. Gate-induced quantum-confinement transition of a single dopant atom in a silicon FinFET. Nature Phys. 4, 656–661 (2008).

    Article  CAS  Google Scholar 

  12. Saraiva, A., Calderón, M., Hu, X., Das Sarma, S. & Koiller, B. Physical mechanisms of interface-mediated intervally coupling in Si. Phys. Rev. B 80, 081305 (2009).

    Article  Google Scholar 

  13. Morton, J. J. L., McCamey, D. R., Eriksson, M. A. & Lyon, S. A. Embracing the quantum limit in silicon computing. Nature 479, 345–353 (2011).

    Article  CAS  Google Scholar 

  14. Yang, C. H. et al. Spin-valley lifetimes in a silicon quantum dot with tunable valley splitting. Nature Commun. 4, 2069 (2013).

    Article  CAS  Google Scholar 

  15. Roche, B. et al. Detection of a large valley-orbit splitting in silicon with two-donor spectroscopy. Phys. Rev. Lett. 108, 206812 (2012).

    Article  CAS  Google Scholar 

  16. Zwanenburg, F. A. et al. Silicon quantum electronics. Rev. Mod. Phys. 85, 961–1019 (2013).

    Article  CAS  Google Scholar 

  17. Roth, L. g factor and donor spin-lattice relaxation for electrons in germanium and silicon. Phys. Rev. 118, 1534–1540 (1960).

    Article  CAS  Google Scholar 

  18. Hasegawa, H. Spin-lattice relaxation of shallow donor states in Ge and Si through a direct phonon process. Phys. Rev. 118, 1523–1534 (1960).

    Article  CAS  Google Scholar 

  19. Gunawan, O. et al. Valley susceptibility of an interacting two-dimensional electron system. Phys. Rev. Lett. 97, 186404 (2006).

    Article  CAS  Google Scholar 

  20. Takashina, K. et al. Impact of valley polarization on the resistivity in two dimensions. Phys. Rev. Lett. 106, 196403 (2011).

    Article  CAS  Google Scholar 

  21. Isberg, J. et al. Generation, transport and detection of valley-polarized electrons in diamond. Nature Mater. 12, 760–764 (2013).

    Article  CAS  Google Scholar 

  22. Young, A. F. et al. Spin and valley quantum Hall ferromagnetism in graphene. Nature Phys. 8, 550–556 (2012).

    Article  CAS  Google Scholar 

  23. Gunawan, O., Habib, B., De Poortere, E. & Shayegan, M. Quantized conductance in an AlAs two-dimensional electron system quantum point contact. Phys. Rev. B 74, 155436 (2006).

    Article  Google Scholar 

  24. Soykal, Ö., Ruskov, R. & Tahan, C. Sound-based analogue of cavity quantum electrodynamics in silicon. Phys. Rev. Lett. 107, 235502 (2011).

    Article  CAS  Google Scholar 

  25. Culcer, D., Saraiva, A., Koiller, B., Hu, X. & Das Sarma, S. Valley-based noise-resistant quantum computation using Si quantum dots. Phys. Rev. Lett. 108, 126804 (2012).

    Article  Google Scholar 

  26. Rycerz, A., Tworzydło, J. & Beenakker, C. W. J. Valley filter and valley valve in graphene. Nature Phys. 3, 172–175 (2007).

    Article  CAS  Google Scholar 

  27. Tombros, N. et al. Quantized conductance of a suspended graphene nanoconstriction. Nature Phys. 7, 697–700 (2011).

    Article  CAS  Google Scholar 

  28. Pei, F., Laird, E. A., Steele, G. A. & Kouwenhoven, L. P. Valley-spin blockade and spin resonance in carbon nanotubes. Nature Nanotech. 7, 630–634 (2012).

    Article  CAS  Google Scholar 

  29. Kohn, W. & Luttinger, J. Theory of donor states in silicon. Phys. Rev. 98, 915–922 (1955).

    Article  CAS  Google Scholar 

  30. Pantelides, S. & Sah, C. Theory of localized states in semiconductors. I. New results using an old method. Phys. Rev. B 10, 621–637 (1974).

    Article  CAS  Google Scholar 

  31. Tyryshkin, A. M. et al. Electron spin coherence exceeding seconds in high-purity silicon. Nature Mater. 11, 143–147 (2011).

    Article  Google Scholar 

  32. Steger, M. et al. Quantum information storage for over 180 s using donor spins in a 28Si ‘semiconductor vacuum’. Science 336, 1280–1283 (2012).

    Article  CAS  Google Scholar 

  33. Pitters, J. L., Piva, P. G. & Wolkow, R. A. Dopant depletion in the near surface region of thermally prepared silicon (100) in UHV. J. Vacuum Sci. Technol. B 30, 021806 (2012).

    Article  Google Scholar 

  34. Koenraad, P. M. & Flatté, M. E. Single dopants in semiconductors. Nature Materials 10, 91–100 (2011).

    Article  CAS  Google Scholar 

  35. Van Mieghem, P. Theory of band tails in heavily doped semiconductors. Rev. Mod. Phys. 64, 755–793 (1992).

    Article  Google Scholar 

  36. Foxman, E. et al. Effects of quantum levels on transport through a Coulomb island. Phys. Rev. B 47, 10020–10023 (1993).

    Article  CAS  Google Scholar 

  37. Mol, J. A., Salfi, J., Miwa, J. A., Simmons, M. Y. & Rogge, S. Interplay between quantum confinement and dielectric mismatch for ultrashallow dopants. Phys. Rev. B 87, 245417 (2013).

    Article  Google Scholar 

  38. Sinthiptharakoon, K. et al. Investigating individual arsenic dopant atoms in silicon using low-temperature scanning tunnelling microscopy. J. Phys.: Condens. Matter 26, 012001 (2014).

    Google Scholar 

  39. Chen, C. J. Tunneling matrix elements in three-dimensional space: the derivative rule and the sum rule. Phys. Rev. B 42, 8841–8857 (1990).

    Article  CAS  Google Scholar 

  40. Teichmann, K. et al. Controlled charge switching on a single donor with a scanning tunneling microscope. Phys. Rev. Lett. 101, 076103 (2008).

    Article  CAS  Google Scholar 

  41. Lee, D.-H. & Gupta, J. A. Tunable field control over the binding energy of single dopants by a charged vacancy in GaAs. Science 330, 1807–1810 (2010).

    Article  CAS  Google Scholar 

  42. Cohen, M. & Bergstresser, T. Band structures and pseudopotential form factors for fourteen semiconductors of the diamond and zinc-blende structures. Phys. Rev. 141, 789–796 (1966).

    Article  CAS  Google Scholar 

  43. Rahman, R. et al. Engineered valley-orbit splittings in quantum-confined nanostructures in silicon. Phys. Rev. B 83, 195323 (2011).

    Article  Google Scholar 

  44. Crommie, M. F., Lutz, C. P. & Eigler, D. M. Imaging standing waves in a 2-dimensional electron-gas. Nature 363, 524–527 (1993).

    Article  CAS  Google Scholar 

  45. Sprunger, P. T., Petersen, L., Plummer, E., Leasgsgaard, E. & Besenbacher, F. Giant Friedel oscillations on the beryllium(0001) surface. Science 275, 1764–1767 (1997).

    Article  CAS  Google Scholar 

  46. Rahman, R. et al. Gate-induced g-factor control and dimensional transition for donors in multivalley semiconductors. Phys. Rev. B 80, 155301 (2009).

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank J. Verduijn for helpful discussions. This work is supported by the European Commission Future and Emerging Technologies Proactive Project MULTI (317707) and the ARC Centre of Excellence for Quantum Computation and Communication Technology (CE110001027), and in part by the US Army Research Office (W911NF-08-1-0527). This work is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organization for Scientific Research (NWO). S.R. acknowledges a Future Fellowship (FT100100589). M.Y.S. acknowledges a Laureate Fellowship. The use of nanoHUB.org computational resources operated by the Network for Computational Nanotechnology funded by the US National Science Foundation under grant EEC-0228390 is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Centre for Quantum Computation and Communication Technology, School of Physics, The University of New South Wales, Sydney, New South Wales 2052, Australia

    J. Salfi, J. A. Mol, M. Y. Simmons & S. Rogge

  2. Purdue University, West Lafayette, Indiana 47906, USA

    R. Rahman & G. Klimeck

  3. Centre for Quantum Computation and Communication Technology, School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia

    L. C. L. Hollenberg

Authors
  1. J. Salfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. A. Mol
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Rahman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Klimeck
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Y. Simmons
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. L. C. L. Hollenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. S. Rogge
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.S., J.A.M. and S.R. designed and conducted the experiments. R.R. performed the multi-million atom calculations. J.S., L.C.L.H. and S.R. made the key contributions to the Fourier analysis. All the authors contributed to analysis and writing the paper.

Corresponding author

Correspondence to S. Rogge.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1319 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Salfi, J., Mol, J., Rahman, R. et al. Spatially resolving valley quantum interference of a donor in silicon. Nature Mater 13, 605–610 (2014). https://doi.org/10.1038/nmat3941

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat3941

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing