Local variations in the charge distribution at semiconductor interfaces can lead to energy level band bending in the structure’s band diagram. Measuring this band bending is important in semiconductor electronics and quantum technologies, but current methods are typically only surface sensitive and are unable to probe the extent of band bending at a depth within the semiconductor. Here, we show that nitrogen–vacancy centres in diamond can be used as in situ sensors to spatially map band bending in a semiconductor device. These nitrogen–vacancy quantum sensors probe the electric field associated with surface band bending, and we map the electric field at different depths under various surface terminations. Using a two-terminal device based on the conductive two-dimensional hole gas formed at a hydrogen-terminated diamond surface, we also observe an unexpected spatial modulation of the electric field, which is attributed to the interplay between charge injection and photo-ionization effects (from the laser used in the experiments). Our method offers a route to the three-dimensional mapping of band bending in diamond and other semiconductors that host suitable quantum sensors.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Data availability

The data underlying the present work are available upon request from the corresponding authors.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


  1. 1.

    Zhang, Z. & Yates, J. T. Band bending in semiconductors: chemical and physical consequences at surfaces and interfaces. Chem. Rev. 112, 5520–5551 (2012).

  2. 2.

    Kotadiya, N. B. et al. Universal strategy for Ohmic hole injection into organic semiconductors with high ionization energies. Nat. Mater. 17, 329–334 (2018).

  3. 3.

    Simon, J., Protasenko, V., Lian, C., Xing, H. & Jena, D. Polarization-induced hole doping in wide-band-gap uniaxial semiconductor heterostructures. Science 327, 60–64 (2010).

  4. 4.

    Stathis, J. & Zafar, S. The negative bias temperature instability in MOS devices: a review. Microelectron. Reliab. 46, 270–286 (2006).

  5. 5.

    Zhang, P. et al. Electronic transport in nanometre-scale silicon-on-insulator membranes. Nature 439, 703–706 (2006).

  6. 6.

    Kaczer, B. et al. A brief overview of gate oxide defect properties and their relation to MOSFET instabilities and device and circuit time-dependent variability. Microelectron. Reliab. 81, 186–194 (2018).

  7. 7.

    Weber, J. R. et al. Quantum computing with defects. Proc. Natl Acad. Sci. USA 107, 8513–8518 (2010).

  8. 8.

    Kaviani, M. et al. Proper surface termination for luminescent near-surface NV centers in diamond. Nano. Lett. 14, 4772–4777 (2014).

  9. 9.

    Usman, M. et al. Spatial metrology of dopants in silicon with exact lattice site precision. Nat. Nanotech. 11, 763–768 (2016).

  10. 10.

    Kronik, L. & Shapira, Y. Surface photovoltage phenomena: theory, experiment, and applications. Surf. Sci. Rep. 37, 1–206 (1999).

  11. 11.

    Ishii, H. et al. Kelvin probe study of band bending at organic semiconductor/metal interfaces: examination of Fermi level alignment. Phys. Stat. Sol. A 201, 1075–1094 (2004).

  12. 12.

    Butler, C. J. et al. Mapping polarization induced surface band bending on the Rashba semiconductor BiTeI. Nat. Commun. 5, 4066 (2014).

  13. 13.

    Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

  14. 14.

    Schirhagl, R., Chang, K., Loretz, M. & Degen, C. L. Nitrogen–vacancy centers in diamond: nanoscale sensors for physics and biology. Annu. Rev. Phys. Chem. 65, 83–105 (2014).

  15. 15.

    Rondin, L. et al. Magnetometry with nitrogen–vacancy defects in diamond. Rep. Prog. Phys. 77, 056503 (2014).

  16. 16.

    Casola, F., Van Der Sar, T. & Yacoby, A. Probing condensed matter physics with magnetometry based on nitrogen–vacancy centres in diamond. Nat. Rev. Mater. 3, 17088 (2018).

  17. 17.

    Tetienne, J.-P. et al. Nanoscale imaging and control of domain-wall hopping with a nitrogen–vacancy center microscope. Science 344, 1366–1369 (2014).

  18. 18.

    Du, C. et al. Control and local measurement of the spin chemical potential in a magnetic insulator. Science 357, 195–198 (2017).

  19. 19.

    Kolkowitz, S. et al. Probing Johnson noise and ballistic transport in normal metals with a single-spin qubit. Science 347, 1129 (2015).

  20. 20.

    Tetienne, J.-P. et al. Quantum imaging of current flow in graphene. Sci. Adv. 3, e1602429 (2017).

  21. 21.

    Doherty, M. W. et al. The nitrogen–vacancy colour centre in diamond. Phys. Rep. 528, 1–45 (2013).

  22. 22.

    Dolde, F. et al. Electric-field sensing using single diamond spins. Nat. Phys. 7, 459–463 (2011).

  23. 23.

    Dolde, F. et al. Nanoscale detection of a single fundamental charge in ambient conditions using the NV–center in diamond. Phys. Rev. Lett. 112, 097603 (2014).

  24. 24.

    Pezzagna, S. et al. Creation of colour centres in diamond by collimated ion implantation through nano-channels in mica. Phys. Stat. Sol. A 208, 2017–2022 (2011).

  25. 25.

    Ohno, K. et al. Engineering shallow spins in diamond with nitrogen delta-doping. Appl. Phys. Lett. 101, 082413 (2012).

  26. 26.

    Lesik, M. et al. Production of bulk NV centre arrays by shallow implantation and diamond CVD overgrowth. Phys. Stat. Sol. A 213, 2594–2600 (2016).

  27. 27.

    Iwasaki, T. et al. Direct nanoscale sensing of the internal electric field in operating semiconductor devices using single electron spins. ACS Nano 11, 1238–1245 (2017).

  28. 28.

    Zhang, Q. et al. Single rare-earth ions as atomic-scale probes in ultra-scaled transistors. Preprint at https://arXiv.org/abs/1803.01573 (2018).

  29. 29.

    Falk, A. L. et al. Electrically and mechanically tunable electron spins in silicon carbide color centers. Phys. Rev. Lett. 112, 187601 (2014).

  30. 30.

    Wolfowicz, G., Whiteley, S. J. & Awschalom, D. D. Electrometry by optical charge conversion of deep defects in 4H-SiC. Preprint at https://arXiv.org/abs/1803.05956 (2018).

  31. 31.

    Tetienne, J.-P. et al. Spin properties of dense near-surface ensembles of nitrogen–vacancy centers in diamond. Phys. Rev. B 97, 085402 (2018).

  32. 32.

    Lehtinen, O. et al. Molecular dynamics simulations of shallow nitrogen and silicon implantation into diamond. Phys. Rev. B 93, 35202 (2016).

  33. 33.

    Stacey, A. et al. Evidence for primal sp2 defects at the diamond surface: candidates for electron trapping and noise sources. Preprint at https://arXiv.org/abs/1807.02946 (2018).

  34. 34.

    Doherty, M. W. et al. Theory of the ground-state spin of the NV center in diamond. Phys. Rev. B 85, 205203 (2012).

  35. 35.

    Strobel, P., Riedel, M., Ristein, J. & Ley, L. Surface transfer doping of diamond. Nature 430, 439 (2004).

  36. 36.

    Maier, F., Riedel, M., Mantel, B., Ristein, J. & Ley, L. Origin of surface conductivity in diamond. Phys. Rev. Lett. 85, 3472–3475 (2000).

  37. 37.

    Pakes, C. I., Garrido, J. A. & Kawarada, H. Diamond surface conductivity: Properties, devices, and sensors. MRS. Bull. 39, 542–548 (2014).

  38. 38.

    Hauf, M. V. et al. Chemical control of the charge state of nitrogen–vacancy centers in diamond. Phys. Rev. B 83, 081304 (2011).

  39. 39.

    Dhomkar, S., Jayakumar, H., Zangara, P. R. & Meriles, C. A. Charge dynamics in near-surface, variable-density ensembles of nitrogen–vacancy centers in diamond. Nano. Lett. 18, 4046–4052 (2018).

  40. 40.

    Chicot, G. et al. Hole transport in boron delta-doped diamond structures. Appl. Phys. Lett. 101, 162101 (2012).

  41. 41.

    Scharpf, J. et al. Transport behaviour of boron delta-doped diamond. Phys. Stat. Sol. A 210, 2028–2034 (2013).

  42. 42.

    Kawarada, H. High-current metal oxide semiconductor field-effect transistors on H-terminated diamond surfaces and their high-frequency operation. Jpn. J. Appl. Phys. 51, 090111 (2012).

  43. 43.

    Kasu, M. Diamond field-effect transistors for RF power electronics: Novel NO2 hole doping and low-temperature deposited Al2O3 passivation. Jpn. J. Appl. Phys. 56, 01AA01 (2017).

  44. 44.

    Edmonds, M. T. et al. Spin–orbit interaction in a two-dimensional hole gas at the surface of hydrogenated diamond. Nano. Lett. 15, 16–20 (2015).

  45. 45.

    Akhgar, G. et al. G-factor and well width variations for the two-dimensional hole gas in surface conducting diamond. Appl. Phys. Lett. 112, 042102 (2018).

  46. 46.

    Myers, B. A. et al. Probing surface noise with depth-calibrated spins in diamond. Phys. Rev. Lett. 113, 027602 (2014).

  47. 47.

    Rosskopf, T. et al. Investigation of surface magnetic noise by shallow spins in diamond. Phys. Rev. Lett. 112, 147602 (2014).

  48. 48.

    Romach, Y. et al. Spectroscopy of surface-induced noise using shallow spins in diamond. Phys. Rev. Lett. 114, 017601 (2015).

  49. 49.

    Rose, B. C. et al. Observation of an environmentally insensitive solid-state spin defect in diamond. Science 361, 60–63 (2018).

  50. 50.

    Chang, K., Eichler, A., Rhensius, J., Lorenzelli, L. & Degen, C. L. Nanoscale imaging of current density with a single-spin magnetometer. Nano. Lett. 17, 2367–2373 (2017).

  51. 51.

    Lovchinsky, I. et al. Nuclear magnetic resonance detection and spectroscopy of single proteins using quantum logic. Science 351, 836–841 (2016).

  52. 52.

    Kim, C. K. et al. Temperature control for the gate workfunction engineering of TiC film by atomic layer deposition. Solid. State. Electron. 114, 90–93 (2015).

  53. 53.

    Hauf, M. V. et al. Low dimensionality of the surface conductivity of diamond. Phys. Rev. B 89, 115426 (2014).

  54. 54.

    Akhgar, G. et al. Strong and tunable spin–orbit coupling in a two-dimensional hole gas in ionic-liquid gated diamond devices. Nano. Lett. 16, 3768–3773 (2016).

  55. 55.

    Simpson, D. A. et al. Magneto-optical imaging of thin magnetic films using spins in diamond. Sci. Rep. 6, 22797 (2016).

Download references


We thank M. Barson, D. Simpson and L. Hall for useful discussions. We acknowledge support from the Australian Research Council (grants CE110001027, DE170100129, FL130100119, DP170102735). J.-P.T acknowledges support from the University of Melbourne through an Early Career Researcher Grant. D.A.B, A.T, S.E.L and C.T.-K.L are supported by an Australian Government Research Training Program Scholarship. This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF).

Author information

Author notes

  1. These authors contributed equally: D. A. Broadway, N. Dontschuk.


  1. School of Physics, University of Melbourne, Parkville, VIC, Australia

    • D. A. Broadway
    • , N. Dontschuk
    • , A. Tsai
    • , S. E. Lillie
    • , C. T.-K. Lew
    • , J. C. McCallum
    • , B. C. Johnson
    • , L. C. L. Hollenberg
    •  & J.-P. Tetienne
  2. Centre for Quantum Computation and Communication Technology, School of Physics, University of Melbourne, Parkville, VIC, Australia

    • D. A. Broadway
    • , N. Dontschuk
    • , S. E. Lillie
    • , C. T.-K. Lew
    • , B. C. Johnson
    • , A. Stacey
    •  & L. C. L. Hollenberg
  3. Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, ACT, Australia

    • M. W. Doherty
  4. Melbourne Centre for Nanofabrication, Clayton, VIC, Australia

    • A. Stacey


  1. Search for D. A. Broadway in:

  2. Search for N. Dontschuk in:

  3. Search for A. Tsai in:

  4. Search for S. E. Lillie in:

  5. Search for C. T.-K. Lew in:

  6. Search for J. C. McCallum in:

  7. Search for B. C. Johnson in:

  8. Search for M. W. Doherty in:

  9. Search for A. Stacey in:

  10. Search for L. C. L. Hollenberg in:

  11. Search for J.-P. Tetienne in:


NV measurements and analysis were performed by D.A.B and J.-P.T, with inputs from M.W.D. The devices were fabricated by N.D and D.A.B, H-terminated by A.T and A.S, and electrically characterized by C.T-K.L and B.C.J. The band bending model was developed by N.D with inputs from D.A.B, J.-P.T, A.S and L.C.L.H. All authors contributed to interpreting the data and writing the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to L. C. L. Hollenberg or J.-P. Tetienne.

Supplementary information

  1. Supplementary Information

    Supplementary Tables 1 and 2, Supplementary Figures 1–15, Supplementary Methods 1 and 2, and Supplementary Data 1–3

About this article

Publication history




Issue Date



Further reading