Skip to main content

Thank you for visiting 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.

Resonant tunnelling diodes based on twisted black phosphorus homostructures

An Author Correction to this article was published on 09 July 2021

This article has been updated


Atomically thin materials can be used to build novel forms of conventional semiconductor heterostructure devices. One such device is a resonant tunnelling diode, which can exhibit negative differential resistance and usually consists of a quantum-well structure between two barrier layers. Here, we show that a twisted black phosphorus homostructure can be used to create a resonant tunnelling diode. The devices have a trilayer structure in which a thin non-degenerate black phosphorus layer is sandwiched between two thicker degenerate black phosphorus layers. The interlayer coupling strength depends sensitively on the twist angle between the layers, and thus the twist angle can be used to control the vertical transport behaviour, from ohmic to tunnelling. Because resonant tunnelling through quantum-well states occurs without the need for a physical tunnelling barrier, our devices exhibit a higher tunnelling conductance and negative differential resistance peak-to-valley current ratio than resonant tunnelling diodes based on van der Waals heterostructures.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Device and band structures of BP homojunctions with twist angles of ~90° and 0°.
Fig. 2: Current transport across BP bilayer and trilayer homojunctions.
Fig. 3: Quantum-well formation and resonant tunnelling in the trilayer orthogonal homojunction.
Fig. 4: Temperature-dependent resonant tunnelling in a BP homojunction device.

Data availability

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

Change history


  1. 1.

    Kluksdahl, N. C., Kriman, A. M. & Ferry, D. K. Self-consistent study of the resonant-tunnelling diode. Phys. Rev. B 39, 7720–7735 (1989).

    Google Scholar 

  2. 2.

    Mendez, E. E., Wang, W. I., Ricco, B. & Esaki, L. Resonant tunnelling of holes in AlAs–GaAs–AlAs heterostructures. Appl. Phys. Lett. 47, 415–417 (1985).

    Google Scholar 

  3. 3.

    Schmidt, O. G. et al. Resonant tunnelling diodes made up of stacked self-assembled Ge/Si islands. Appl. Phys. Lett. 77, 4341–4343 (2000).

    Google Scholar 

  4. 4.

    Izumi, R., Sato, T., Suzuki, S. & Asada, M. Resonant-tunnelling-diode terahertz oscillator with a cylindrical cavity for high-frequency oscillation. AIP Adv. 9, 085020 (2019).

    Google Scholar 

  5. 5.

    Alkeev, N. V., Averin, S. V., Dorofeev, A. A., Golant, E. I. & Pashkovskii, A. B. New terahertz mixer based on resonant-tunneling diode. In Proc. 2007 International Kharkov Symposium Physics and Engineering of Millimeter and Sub-Millimeter Waves (MSMW) 192–194 (IEEE, 2007).

  6. 6.

    Alkeev, N. V., Averin, S. V., Dorofeev, A. A., Gladysheva, N. B. & Torgashin, M. Y. GaAs/AlAs resonant-tunnelling diode for subharmonic mixers. Russ. Microelectron. 39, 331–339 (2010).

    Google Scholar 

  7. 7.

    Fan, S. et al. Tunable negative differential resistance in van der Waals heterostructures at room temperature by tailoring the interface. ACS Nano 13, 8193–8201 (2019).

    Google Scholar 

  8. 8.

    Nourbakhsh, A., Zubair, A., Dresselhaus, M. S. & Palacios, T. Transport properties of a MoS2/WSe2 heterojunction transistor and its potential for application. Nano Lett. 16, 1359–1366 (2016).

    Google Scholar 

  9. 9.

    Yan, R. et al. Esaki diodes in van der Waals heterojunctions with broken-gap energy band alignment. Nano Lett. 15, 5791–5798 (2015).

    Google Scholar 

  10. 10.

    Kim, K. et al. Spin-conserving resonant tunnelling in twist-controlled WSe2-hBN-WSe2 heterostructures. Nano Lett. 18, 5967–5973 (2018).

    Google Scholar 

  11. 11.

    Burg, G. W. et al. Coherent interlayer tunnelling and negative differential resistance with high current density in double bilayer graphene–WSe2 heterostructures. Nano Lett. 17, 3919–3925 (2017).

    Google Scholar 

  12. 12.

    Xiong, X. et al. A transverse tunnelling field-effect transistor made from a van der Waals heterostructure. Nat. Electron. 3, 106–112 (2020).

    Google Scholar 

  13. 13.

    Shim, J. et al. Phosphorene/rhenium disulfide heterojunction-based negative differential resistance device for multi-valued logic. Nat. Commun. 7, 13413 (2016).

    Google Scholar 

  14. 14.

    Srivastava, P. K. et al. Multifunctional van der Waals broken-gap heterojunction. Small 15, 1804885 (2019).

    Google Scholar 

  15. 15.

    Mishchenko, A. et al. Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures. Nat. Nanotechnol. 9, 808–813 (2014).

    Google Scholar 

  16. 16.

    Britnell, L. et al. Resonant tunnelling and negative differential conductance in graphene transistors. Nat. Commun. 4, 1794 (2013).

    Google Scholar 

  17. 17.

    Fallahazad, B. et al. Gate-tunable resonant tunnelling in double bilayer graphene heterostructures. Nano Lett. 15, 428–433 (2015).

    Google Scholar 

  18. 18.

    Luo, Z. et al. Anisotropic in-plane thermal conductivity observed in few-layer black phosphorus. Nat. Commun. 6, 8572 (2015).

    Google Scholar 

  19. 19.

    Lee, S. et al. Anisotropic in-plane thermal conductivity of black phosphorus nanoribbons at temperatures higher than 100 K. Nat. Commun. 6, 8573 (2015).

    Google Scholar 

  20. 20.

    Li, L. et al. Quantum oscillations in a two-dimensional electron gas in black phosphorus thin films. Nat. Nanotechnol. 10, 608–613 (2015).

    Google Scholar 

  21. 21.

    Li, L. et al. Black phosphorus field-effect transistors. Nat. Nanotechnol. 9, 372–377 (2014).

    Google Scholar 

  22. 22.

    Li, L. et al. Quantum Hall effect in black phosphorus two-dimensional electron system. Nat. Nanotechnol. 11, 593–597 (2016).

    Google Scholar 

  23. 23.

    Hu, Z. X., Kong, X., Qiao, J., Normand, B. & Ji, W. Interlayer electronic hybridization leads to exceptional thickness-dependent vibrational properties in few-layer black phosphorus. Nanoscale 8, 2740–2750 (2016).

    Google Scholar 

  24. 24.

    Mattevi, C. et al. Evolution of electrical, chemical and structural properties of transparent and conducting chemically derived graphene thin films. Adv. Funct. Mater. 19, 2577–2583 (2009).

    Google Scholar 

  25. 25.

    Liu, X. et al. Modulation of quantum tunnelling via a vertical two-dimensional black phosphorus and molybdenum disulfide p–n junction. ACS Nano 11, 9143–9150 (2017).

    Google Scholar 

  26. 26.

    Gaberle, J. & Shluger, A. L. Structure and properties of intrinsic and extrinsic defects in black phosphorus. Nanoscale 10, 19536–19546 (2018).

    Google Scholar 

  27. 27.

    Kou, L., Ma, Y., Smith, S. C. & Chen, C. Anisotropic ripple deformation in phosphorene. J. Phys. Chem. Lett. 6, 1509–1513 (2015).

    Google Scholar 

  28. 28.

    De Sousa, D. J. P., De Castro, L. V., Da Costa, D. R., Pereira, J. M. & Low, T. Multilayered black phosphorus: from a tight-binding to a continuum description. Phys. Rev. B 96, 155427 (2017).

    Google Scholar 

  29. 29.

    Cao, T., Li, Z., Qiu, D. Y. & Louie, S. G. Gate switchable transport and optical anisotropy in 90° twisted bilayer black phosphorus. Nano Lett. 16, 5542–5546 (2016).

    Google Scholar 

  30. 30.

    Liu, N., Zhang, J., Zhou, S. & Zhao, J. Tuning the electronic properties of bilayer black phosphorene with the twist angle. J. Mater. Chem. C 8, 6264–6272 (2020).

    Google Scholar 

  31. 31.

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Google Scholar 

  32. 32.

    Shishkin, M. & Kresse, G. Self-consistent GW calculations for semiconductors and insulators. Phys. Rev. B 75, 235102 (2007).

    Google Scholar 

  33. 33.

    Perdew, J. P. Density functional theory and the band gap problem. Int. J. Quantum Chem. 28, 497–523 (1985).

    Google Scholar 

  34. 34.

    Low, T. et al. Plasmons and screening in monolayer and multilayer black phosphorus. Phys. Rev. Lett. 113, 106802 (2014).

    Google Scholar 

  35. 35.

    Bhattacharyya, S. et al. Resonant tunnelling and fast switching in amorphous-carbon quantum-well structures. Nat. Mater. 5, 19–22 (2006).

    Google Scholar 

  36. 36.

    Schuberth, G. et al. Resonant tunnelling of holes in Si/SixGe1 − x quantum-well structures. Phys. Rev. B 43, 2280 (1991).

    Google Scholar 

  37. 37.

    Rudenko, A. N., Yuan, S. & Katsnelson, M. I. Toward a realistic description of multilayer black phosphorus: from GW approximation to large-scale tight-binding simulations. Phys. Rev. B 92, 199906 (2015).

    Google Scholar 

  38. 38.

    Rudenko, A. N. & Katsnelson, M. I. Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus. Phys. Rev. B 89, 201408R (2014).

    Google Scholar 

  39. 39.

    Pereira, J. M. & Katsnelson, M. I. Landau levels of single-layer and bilayer phosphorene. Phys. Rev. B 92, 075437 (2015).

    Google Scholar 

  40. 40.

    Sevik, C., Wallbank, J. R., Gülseren, O., Peeters, F. M. & Çakir, D. Gate induced monolayer behavior in twisted bilayer black phosphorus. 2D Mater. 4, 035025 (2017).

    Google Scholar 

  41. 41.

    Vdovin, E. E. et al. Phonon-assisted resonant tunnelling of electrons in graphene–boron nitride transistors. Phys. Rev. Lett. 116, 186603 (2016).

    Google Scholar 

  42. 42.

    Shen, G. D., Xu, D. X., Willander, M. & Hansson, G. V. The origin of the temperature dependence in resonant tunnelling transport. In Proc. 1991 IEEE/Cornell Conference on Advanced Concepts in High Speed Semiconductor Devices and Circuits 84–93 (IEEE, 1991)

  43. 43.

    Ridley, B. K. Quantum Processes in Semiconductors 4th edn (Oxford Univ. Press, 1999).

  44. 44.

    Choi, W. S., Lee, S. A., You, J. H., Lee, S. & Lee, H. N. Resonant tunnelling in a quantum oxide superlattice. Nat. Commun. 6, 7424 (2015).

    Google Scholar 

  45. 45.

    Nguyen, L. N. et al. Resonant tunnelling through discrete quantum states in stacked atomic-layered MoS2. Nano Lett. 14, 2381–2386 (2014).

    Google Scholar 

  46. 46.

    Li, L. L., Partoens, B. & Peeters, F. M. Tuning the electronic properties of gated multilayer phosphorene: a self-consistent tight-binding study. Phys. Rev. B 97, 155424 (2018).

    Google Scholar 

  47. 47.

    Forte, J. D. S., de Sousa, D. J. P. & Pereira, J. M. Dirac spectrum in gated multilayer black phosphorus nanoribbons. Physica E 114, 113578 (2019).

    Google Scholar 

Download references


This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF; grants NRF-2016K1A1A2912707, 2016R1A6A3A11934734, 2016R1A2B4012931, 2018R1D1A1B07049669, 2019R1I1A1A01061466 and 2020R1A2C2014687), funded by the Ministry of Science and ICT of Korea, Samsung Research Funding Center of Samsung Electronics (project no. SRFC-TB1803-04) and the KISTI supercomputing centre (grant no. KSC-2018-CRE-0119).

Author information




B.S., P.K.S. and C.L. conceived the project. Y.H. prepared the devices with help from Y.Z. for electron-beam lithography. P.K.S. and Y.H. carried out electrical measurements. D.J.P.d.S. and T.L. carried out quantum transport simulations. Y.G. and M.J. carried out DFT calculations for twisted and non-twisted BP bilayer band structures. F.A. and W.J.Y. helped with the glove box facility and its use. P.K.S., D.J.P.d.S., S.G., J.T.T., B.S., T.L. and C.L. discussed and analysed the data. P.K.S., C.L., B.S., D.J.P.d.S. and T.L. co-wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Budhi Singh, Tony Low or Changgu Lee.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Electronics thanks Yuerui Lu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–6, Discussion and Tables 1–3.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Srivastava, P.K., Hassan, Y., de Sousa, D.J.P. et al. Resonant tunnelling diodes based on twisted black phosphorus homostructures. Nat Electron 4, 269–276 (2021).

Download citation

Further reading


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