Reversible writing of high-mobility and high-carrier-density doping patterns in two-dimensional van der Waals heterostructures


A key feature of two-dimensional materials is that the sign and concentration of their carriers can be externally controlled with techniques such as electrostatic gating. However, conventional electrostatic gating has limitations, including a maximum carrier density set by the dielectric breakdown, and ionic liquid gating and direct chemical doping also suffer from drawbacks. Here, we show that an electron-beam-induced doping technique can be used to reversibly write high-resolution doping patterns in hexagonal boron nitride-encapsulated graphene and molybdenum disulfide (MoS2) van der Waals heterostructures. The doped MoS2 device exhibits an order of magnitude decrease of subthreshold swing compared with the device before doping, whereas the doped graphene devices demonstrate a previously inaccessible regime of high carrier concentration and high mobility, even at room temperature. We also show that the approach can be used to write high-quality p–n junctions and nanoscale doping patterns, illustrating that the technique can create nanoscale circuitry in van der Waals heterostructures.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Electron-beam-induced doping effect in graphene and MoS2 vdW heterostructures.
Fig. 2: Energy dependence of electron-beam-induced doping effect in graphene and MoS2 vdW heterostructures.
Fig. 3: Transport characteristics and spatially controlled nanoscale doping patterns of BN/Gr/BN heterostructures by electron-beam-induced doping.
Fig. 4: Energy dependence and proposed mechanism for the electron-beam-induced doping effect in graphene and MoS2 vdW heterostructures.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Hu, C. Modern Semiconductor Devices for Integrated Circuits (Pearson, 2010).

  2. 2.

    Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    Article  Google Scholar 

  3. 3.

    Lui, C. H., Li, Z., Mak, K. F., Cappelluti, E. & Heinz, T. F. Observation of an electrically tunable band gap in trilayer graphene. Nat. Phys. 7, 944–947 (2011).

    Article  Google Scholar 

  4. 4.

    Williams, J. R., DiCarlo, L. & Marcus, C. M. Quantum Hall effect in a graphene p–n junction. Science 317, 638–641 (2007).

    Article  Google Scholar 

  5. 5.

    Özyilmaz, B. et al. Electronic transport and quantum Hall effect in bipolar graphene p–n–p junctions. Phys. Rev. Lett. 99, 2–5 (2007).

    Article  Google Scholar 

  6. 6.

    Huard, B. et al. Transport measurements across a tunable potential barrier in graphene. Phys. Rev. Lett. 98, 8–11 (2007).

    Article  Google Scholar 

  7. 7.

    Liu, G., Velasco, J., Bao, W. & Lau, C. N. Fabrication of graphene p–n–p junctions with contactless top gates. Appl. Phys. Lett. 92, 1–4 (2008).

    Google Scholar 

  8. 8.

    Dubey, S. et al. Tunable superlattice in graphene to control the number of Dirac points. Nano Lett. 13, 3990–3995 (2013).

    Article  Google Scholar 

  9. 9.

    Efetov, D. K. & Kim, P. Controlling electron–phonon interactions in graphene at ultrahigh carrier densities. Phys. Rev. Lett. 105, 2–5 (2010).

    Google Scholar 

  10. 10.

    Ye, J. et al. Accessing the transport properties of graphene and its multilayers at high carrier density. Proc. Natl Acad. Sci. USA 108, 13002–13006 (2011).

    Article  Google Scholar 

  11. 11.

    Shi, W. et al. Superconductivity series in transition metal dichalcogenides by ionic gating. Sci. Rep. 5, 12534 (2015).

    Article  Google Scholar 

  12. 12.

    Zhao, S. Y. F. et al. Controlled electrochemical intercalation of graphene/h-BN van der Waals heterostructures. Nano Lett. 18, 460–466 (2018).

    Article  Google Scholar 

  13. 13.

    Xia, Y., Xie, W., Ruden, P. P. & Frisbie, C. D. Carrier localization on surfaces of organic semiconductors gated with electrolytes. Phys. Rev. Lett. 105, 36802 (2010).

    Article  Google Scholar 

  14. 14.

    Ovchinnikov, D. et al. Disorder engineering and conductivity dome in ReS2 with electrolyte gating. Nat. Commun. 7, 12391 (2016).

    Article  Google Scholar 

  15. 15.

    Lohmann, T., Von Klitzing, K. & Smet, J. H. Four-terminal magneto-transport in graphene p–n junctions created by spatially selective doping. Nano Lett. 9, 1973–1979 (2009).

    Article  Google Scholar 

  16. 16.

    Ojeda-Aristizabal, C. et al. Molecular arrangement and charge transfer in C60/graphene heterostructures. ACS Nano 11, 4686–4693 (2017).

    Article  Google Scholar 

  17. 17.

    Ju, L. et al. Photoinduced doping in heterostructures of graphene and boron nitride. Nat. Nanotechnol. 9, 348–352 (2014).

    Article  Google Scholar 

  18. 18.

    Velasco, J. et al. Nanoscale control of rewriteable doping patterns in pristine graphene/boron nitride heterostructures. Nano Lett. 16, 1620–1625 (2016).

    Article  Google Scholar 

  19. 19.

    Wong, D. et al. Characterization and manipulation of individual defects in insulating hexagonal boron nitride using scanning tunnelling microscopy. Nat. Nanotechnol. 10, 949–953 (2015).

    Article  Google Scholar 

  20. 20.

    Zhou, Y. et al. Programmable graphene doping via electron beam irradiation. Nanoscale 9, 8657–8664 (2017).

    Article  Google Scholar 

  21. 21.

    Childres, I. et al. Effect of electron-beam irradiation on graphene field effect devices. Appl. Phys. Lett. 97, 173109 (2010).

    Article  Google Scholar 

  22. 22.

    Yu, X., Shen, Y., Liu, T., Wu, T. & Jie Wang, Q. Photocurrent generation in lateral graphene p–n junction created by electron-beam irradiation. Sci. Rep. 5, 12014 (2015).

    Article  Google Scholar 

  23. 23.

    Iqbal, M. Z., Anwar, N., Siddique, S., Iqbal, M. W. & Hussain, T. Formation of p–n-junction with stable n-doping in graphene field effect transistors using e-beam irradiation. Opt. Mater. 69, 254–258 (2017).

    Article  Google Scholar 

  24. 24.

    Stará, V., Procházka, P., Mareček, D., Šikola, T. & Čechal, J. Ambipolar remote graphene doping by low-energy electron beam irradiation. Nanoscale 10, 17520–17524 (2018).

    Article  Google Scholar 

  25. 25.

    Teweldebrhan, D. & Balandin, A. A. Modification of graphene properties due to electron-beam irradiation. Appl. Phys. Lett. 94, 92–95 (2009).

    Article  Google Scholar 

  26. 26.

    Hwang, E. H. & Sarma, S. Das Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene. Phys. Rev. Lett. 77, 1–6 (2008).

    Google Scholar 

  27. 27.

    Katagiri, Y. et al. Gate-tunable atomically thin lateral MoS2 Schottky junction patterned by electron beam. Nano Lett. 16, 3788–3794 (2016).

    Article  Google Scholar 

  28. 28.

    Xie, X. et al. Designing artificial 2D crystals with site and size controlled quantum dots. Sci. Rep. 7, 9965 (2017).

    Article  Google Scholar 

  29. 29.

    Sule, N. & Knezevic, I. Phonon-limited electron mobility in graphene calculated using tight-binding Bloch waves. J. Appl. Phys. 112, 053702 (2012).

    Article  Google Scholar 

  30. 30.

    Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    Article  Google Scholar 

  31. 31.

    Ausman, G. A. & McLean, F. B. Electron–hole pair creation energy in SiO2. Appl. Phys. Lett. 26, 173–175 (1975).

    Article  Google Scholar 

  32. 32.

    Curtis, O. L., Srour, J. R. & Chiu, K. Y. Hole and electron transport in SiO2 films. J. Appl. Phys. 45, 4506–4513 (1974).

    Article  Google Scholar 

Download references


We thank Y. Chen, W. Ruan, S. Zhao, and J. Jung for useful discussions. This work was supported in part by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, and Molecular Foundry of the US Department of Energy under contract no. DE-AC02-05-CH11231, primarily within the van der Waals Heterostructures Program (KCWF16), which provided for development of the concept and device fabrication, electron-beam doping and transport characterization, and within the sp2-Bonded Materials Program (KC2207), which provided for s-SNOM measurements, and by the National Science Foundation, under grant no.1542741, which provided for AFM topography and SdH measurements, and under grant no.1807233, which provided for EFM measurements.

Author information




A.Z., M.C., W.S., S.K., H.-Z.T. and D.W. conceived the experiment. S.K., W.S. and S.-Y.W. contributed to device fabrication. W.S. and S.K. performed all electrical measurements, EFM measurements and data analysis. K.W. and T.T. provided the BN crystals. L.J. and F.W. contributed to the s-SNOM measurements. W.S., S.K. and A.Z. co-wrote the manuscript, with inputs and comments from all authors.

Corresponding author

Correspondence to Alex Zettl.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Notes 1–18, Figs. 1–27 and Table 1.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shi, W., Kahn, S., Jiang, L. et al. Reversible writing of high-mobility and high-carrier-density doping patterns in two-dimensional van der Waals heterostructures. Nat Electron 3, 99–105 (2020).

Download citation

Further reading