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.

Approaching the intrinsic exciton physics limit in two-dimensional semiconductor diodes


Two-dimensional (2D) semiconductors have attracted intense interest for their unique photophysical properties, including large exciton binding energies and strong gate tunability, which arise from their reduced dimensionality1,2,3,4,5. Despite considerable efforts, a disconnect persists between the fundamental photophysics in pristine 2D semiconductors and the practical device performances, which are often plagued by many extrinsic factors, including chemical disorder at the semiconductor–contact interface. Here, by using van der Waals contacts with minimal interfacial disorder, we suppress contact-induced Shockley–Read–Hall recombination and realize nearly intrinsic photophysics-dictated device performance in 2D semiconductor diodes. Using an electrostatic field in a split-gate geometry to independently modulate electron and hole doping in tungsten diselenide diodes, we discover an unusual peak in the short-circuit photocurrent at low charge densities. Time-resolved photoluminescence reveals a substantial decrease of the exciton lifetime from around 800 picoseconds in the charge-neutral regime to around 50 picoseconds at high doping densities owing to increased exciton–charge Auger recombination. Taken together, we show that an exciton-diffusion-limited model well explains the charge-density-dependent short-circuit photocurrent, a result further confirmed by scanning photocurrent microscopy. We thus demonstrate the fundamental role of exciton diffusion and two-body exciton–charge Auger recombination in 2D devices and highlight that the intrinsic photophysics of 2D semiconductors can be used to create more efficient optoelectronic devices.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Atomically thin WSe2 p–n diode with atomically clean vdW contacts.
Fig. 2: Doping-dependent optoelectronic performance of a 2D WSe2 p–n diode.
Fig. 3: Doping-dependent TRPL and exciton–charge Auger.
Fig. 4: Correlation between photocurrent and exciton lifetime.

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.


  1. 1.

    Ross, J. S. et al. Electrical control of neutral and charged excitons in a monolayer semiconductor. Nat. Commun. 4, 1474 (2013).

    ADS  PubMed  PubMed Central  Google Scholar 

  2. 2.

    He, K. et al. Tightly bound excitons in monolayer WSe2. Phys. Rev. Lett. 113, 026803 (2014).

    ADS  CAS  PubMed  Google Scholar 

  3. 3.

    Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).

    ADS  CAS  PubMed  Google Scholar 

  4. 4.

    Yuan, L. & Huang, L. Exciton dynamics and annihilation in WS2 2D semiconductors. Nanoscale 7, 7402–7408 (2015).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  5. 5.

    Paul, K. K., Kim, J.-H. & Lee, Y. H. Hot carrier photovoltaics in van der Waals heterostructures. Nat. Rev. Phys. 3, 178–192 (2021).

    CAS  Google Scholar 

  6. 6.

    Ross, J. S. et al. Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p–n junctions. Nat. Nanotechnol. 9, 268–272 (2014).

    ADS  CAS  PubMed  Google Scholar 

  7. 7.

    Baugher, B. W., Churchill, H. O., Yang, Y. & Jarillo-Herrero, P. Optoelectronic devices based on electrically tunable p–n diodes in a monolayer dichalcogenide. Nat. Nanotechnol. 9, 262–267 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  8. 8.

    Pospischil, A., Furchi, M. M. & Mueller, T. Solar-energy conversion and light emission in an atomic monolayer p–n diode. Nat. Nanotechnol. 9, 257–261 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  9. 9.

    Cheng, R. et al. Electroluminescence and photocurrent generation from atomically sharp WSe2/MoS2 heterojunction p–n diodes. Nano Lett. 14, 5590–5597 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  10. 10.

    Lee, C.-H. et al. Atomically thin p–n junctions with van der Waals heterointerfaces. Nat. Nanotechnol. 9, 676–681 (2014).

    ADS  CAS  Google Scholar 

  11. 11.

    Li, M.-Y. et al. Epitaxial growth of a monolayer WSe2–MoS2 lateral p–n junction with an atomically sharp interface. Science 349, 524–528 (2015).

    ADS  CAS  Google Scholar 

  12. 12.

    Zhang, Z. et al. Robust epitaxial growth of two-dimensional heterostructures, multiheterostructures, and superlattices. Science 357, 788–792 (2017).

    CAS  Google Scholar 

  13. 13.

    Massicotte, M. et al. Dissociation of two-dimensional excitons in monolayer WSe2. Nat. Commun. 9, 1633 (2018).

    ADS  PubMed  PubMed Central  Google Scholar 

  14. 14.

    Wen, X., Xu, W., Zhao, W., Khurgin, J. B. & Xiong, Q. Plasmonic hot carriers-controlled second harmonic generation in WSe2 bilayers. Nano Lett. 18, 1686–1692 (2018).

    ADS  CAS  Google Scholar 

  15. 15.

    Livache, C. et al. A colloidal quantum dot infrared photodetector and its use for intraband detection. Nat. Commun. 10, 2125 (2019).

    ADS  PubMed  PubMed Central  Google Scholar 

  16. 16.

    Khan, Q. et al. Overcoming the electroluminescence efficiency limitations in quantum-dot light-emitting diodes. Adv. Opt. Mater. 7, 1900695 (2019).

    CAS  Google Scholar 

  17. 17.

    Hong, X. et al. Ultrafast charge transfer in atomically thin MoS2/WS2 heterostructures. Nat. Nanotechnol. 9, 682–686 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  18. 18.

    Yuan, L., Wang, T., Zhu, T., Zhou, M. & Huang, L. Exciton dynamics, transport, and annihilation in atomically thin two-dimensional semiconductors. J. Phys. Chem. Lett. 8, 3371–3379 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  19. 19.

    Steinhoff, A. et al. Biexciton fine structure in monolayer transition metal dichalcogenides. Nat. Phys. 14, 1199–1204 (2018).

    CAS  Google Scholar 

  20. 20.

    Zhu, X.-Y. How to draw energy level diagrams in excitonic solar cells. J. Phys. Chem. Lett. 5, 2283–2288 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. 21.

    Pólya, G. Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz. Math. Ann. 84, 149–160 (1921).

    MathSciNet  MATH  Google Scholar 

  22. 22.

    Doyle, P. G. Application of Rayleigh’s Short-cut Method to Polya’s Recurrence Problem. PhD thesis, Dartmouth College (1982).

  23. 23.

    Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  24. 24.

    Chen, P. et al. Band evolution of two-dimensional transition metal dichalcogenides under electric fields. Appl. Phys. Lett. 115, 083104 (2019).

    ADS  Google Scholar 

  25. 25.

    Liu, Y. et al. Approaching the Schottky–Mott limit in van der Waals metal–semiconductor junctions. Nature 557, 696–700 (2018).

    ADS  CAS  Google Scholar 

  26. 26.

    Chow, C. M. E. et al. Monolayer semiconductor Auger detector. Nano Lett. 20, 5538–5543 (2020).

    ADS  CAS  Google Scholar 

  27. 27.

    Wang, Y. et al. Van der Waals contacts between three-dimensional metals and two-dimensional semiconductors. Nature 568, 70–74 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  28. 28.

    Luque, A. & Hegedus, S. Handbook of Photovoltaic Science and Engineering 2nd edn (John Wiley, 2011).

  29. 29.

    Allen, T. G., Bullock, J., Yang, X., Javey, A. & De Wolf, S. Passivating contacts for crystalline silicon solar cells. Nat. Energy 4, 914–928 (2019).

    ADS  CAS  Google Scholar 

  30. 30.

    Das, S., Gupta, G. & Majumdar, K. Layer degree of freedom for excitons in transition metal dichalcogenides. Phys. Rev. B 99, 165411 (2019).

    ADS  CAS  Google Scholar 

  31. 31.

    Lien, D.-H. et al. Electrical suppression of all nonradiative recombination pathways in monolayer semiconductors. Science 364, 468–471 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  32. 32.

    David, A., Young, N. G., Lund, C. & Craven, M. D. The physics of recombinations in III-nitride emitters. ECS J. Solid State Sci. Technol. 9, 016021 (2019).

    ADS  Google Scholar 

  33. 33.

    Elbaz, G. A. et al. Unbalanced hole and electron diffusion in lead bromide perovskites. Nano Lett. 17, 1727–1732 (2017).

    ADS  CAS  Google Scholar 

  34. 34.

    Chuang, S. L. Physics of Optoelectronic Devices (John Wiley, 1995).

  35. 35.

    Passari, L. & Susi, E. Recombination mechanisms and doping density in silicon. J. Appl. Phys. 54, 3935–3937 (1983).

    ADS  CAS  Google Scholar 

  36. 36.

    Altermatt, P. P., Schmidt, J., Heiser, G. & Aberle, A. G. Assessment and parameterisation of Coulomb-enhanced Auger recombination coefficients in lowly injected crystalline silicon. J. Appl. Phys. 82, 4938–4944 (1997).

    ADS  CAS  Google Scholar 

  37. 37.

    Richter, A., Glunz, S. W., Werner, F., Schmidt, J. & Cuevas, A. Improved quantitative description of Auger recombination in crystalline silicon. Phys. Rev. B 86, 165202 (2012).

    ADS  Google Scholar 

  38. 38.

    Kadlec, E. et al. Effects of electron doping level on minority carrier lifetimes in n-type mid-wave infrared InAs/InAs1−xSbx type-II superlattices. Appl. Phys. Lett. 109, 261105 (2016).

    ADS  Google Scholar 

  39. 39.

    Cadiz, F. et al. Exciton diffusion in WSe2 monolayers embedded in a van der Waals heterostructure. Appl. Phys. Lett. 112, 152106 (2018).

    ADS  Google Scholar 

  40. 40.

    Mouri, S. et al. Nonlinear photoluminescence in atomically thin layered WSe2 arising from diffusion-assisted exciton–exciton annihilation. Phys. Rev. B 90, 155449 (2014).

    ADS  Google Scholar 

  41. 41.

    Uddin, S. Z. et al. Neutral exciton diffusion in monolayer MoS2. ACS Nano 14, 13433–13440 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  42. 42.

    Martin, J. et al. Observation of electron–hole puddles in graphene using a scanning single-electron transistor. Nat. Phys. 4, 144–148 (2008).

    CAS  Google Scholar 

  43. 43.

    Chen, K. et al. Experimental evidence of exciton capture by mid-gap defects in CVD grown monolayer MoSe2. npj 2D Mater. Appl. 1, 15 (2017).

    ADS  Google Scholar 

  44. 44.

    Liu, E. et al. Gate tunable dark trions in monolayer WSe2. Phys. Rev. Lett. 123, 027401 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  45. 45.

    Nguyen, P. V. et al. Visualizing electrostatic gating effects in two-dimensional heterostructures. Nature 572, 220–223 (2019).

    CAS  Google Scholar 

  46. 46.

    Tea, E. & Hin, C. Charge carrier transport and lifetimes in n-type and p-type phosphorene as 2D device active materials: an ab initio study. Phys. Chem. Chem. Phys. 18, 22706–22711 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  47. 47.

    Palummo, M., Bernardi, M. & Grossman, J. C. Exciton radiative lifetimes in two-dimensional transition metal dichalcogenides. Nano Lett. 15, 2794–2800 (2015).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  48. 48.

    Ye, Z. et al. Efficient generation of neutral and charged biexcitons in encapsulated WSe2 monolayers. Nat. Commun. 9, 3718 (2018).

    ADS  PubMed  PubMed Central  Google Scholar 

  49. 49.

    Sundararaman, R. et al. JDFTx: Software for joint density-functional theory. SoftwareX 6, 278–284 (2017).

  50. 50.

    Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 196, 36–44 (2015).

  51. 51.

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

  52. 52.

    Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).

  53. 53.

    Groenendijk, D. J. et al. Photovoltaic and photothermoelectric effect in a double-gated WSe2 device. Nano Lett. 14, 5846–5852 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

Download references


Xiangfeng Duan acknowledges the support from the Office of Naval Research through Award N00014-18-1-2707. J.R.C. acknowledges NSF Career grant number 1945572. Y.H. acknowledges the financial support from the Office of Naval Research through award N00014-18-1-2491. Y.P. acknowledges the support from Air Force Office of Scientific Research under AFOSR award no. FA9550-YR-1-XYZQ.

Author information




Xiangfeng Duan and P.C. conceived the research. P.C., T.L.A., J.R.C. and Xiangfeng Duan designed the experiment. P.C. fabricated the devices and performed optoelectrical measurements. Z.L., P.W., S.-J.L., Z.H., Xidong Duan and Y.H. contributed to materials, device fabrications, measurements and discussions. J.X. and Y.P. conducted band structure calculations. T.L.A. and P.C. conducted the time-resolved photoluminescence and photocurrent scanning measurements. P.C., T.L.A., J.R.C. and Xiangfeng Duan performed the data analysis. P.C., T.L.A., J.R.C. and Xiangfeng Duan co-wrote the manuscript. All authors discussed the results and commented on the manuscripts.

Corresponding authors

Correspondence to Justin R. Caram or Xiangfeng Duan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Andrey Chaves, Lain-Jong Li 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.

Extended data figures and tables

Extended Data Fig. 1 Band diagram and photocurrent generation in diode.

a, The carriers generated by the Schottky barrier are blocked by the barrier at the p–n interface. b, The carriers generated by the p–n junction may tunnel through the Schottky junction and contribute to the photocurrent.

Extended Data Fig. 2 Fitting the IDSVDS characteristic of p–n junction diode.

Black dot: experimental data; solid red line: fit of diode equation. a, The fit of p–n configuration; we extract the RS = 36 MΩ, RSH = 47 GΩ, IS = 4.6 × 10−22 A and η = 1.18; b, The fit of NP configuration; we extract the RS = 28 MΩ, RSH = 35 GΩ, IS = 8.1 ×10−21 A and η = 1.3.

Extended Data Fig. 3 Apparent external quantum efficiency (EQE) of 2D diodes by assuming the device area as the active area.

a, EQE dependence on charge density for the evap-diode (red dots) and the vdW-diode (black dots) at VG1 = −5 V. The line serves as a guide for the eyes. b, EQE dependence on charge density for the evap-diode (red dots) and the vdW-diode (black dots) at VG1 = 5 V. The EQE is calculated as EQE =ISCEph/(ePin), where ISC is the short circuit photocurrent, Eph is the energy per photon, e is the elementary charge and Pin is the input power. Pin = power density (Pd) × illuminated exciton-collection area (A). Note we estimated the apparent EQE by using the device area (the entire WSe2 area between the source and drain electrodes) as A for simplicity, which may lead to a considerably underestimated EQE value as the device area is usually larger than the active area. If we consider the exciton diffusion model with a total exciton collection length of ~1 μm, the maximum EQE is estimated ~21%.

Extended Data Fig. 4

Fitting lifetimes and doping dependence of relative PL intensity and lifetime for different components. a, An example of biexponential fit: (VG = −0.8 V, P = 244 nW). The top panel is the residuals of tri-exponential fitting. The middle panel is the residuals of bi-exponential fitting. The bi-exponential residual is identical to the tri-exponential implying the tri-exponential is an over-fit confirmed by the error in k3 being larger than the value of k3 (Extended Data Table 1); therefore, we used the bi-exponential fit. The bottom panel is the TRPL data and bi-exponential and tri-exponential fitting curve. b, An example of triexponential fit: (VG= −4 V, P= 244 nW). The top panel is the residuals of tri-exponential fitting. The middle panel is the residuals of bi-exponential fitting. The tri-exponential residual is better than the bi-exponential without fit errors larger than the fit values; there we used the tri-exponential fit. The bottom panel is the TRPL data and bi-exponential and tri-exponential fitting curve. c, Doping dependence of relative PL intensity for different components. There are three components, which are t1, t2 and t3. d, Doping dependence of the PL lifetime for different components. The inset shows the lifetime of t3.

Extended Data Fig. 5 A highly simplified band diagram showing the relevant states for band-edge carriers in WSe2.

EF,0 denotes the Fermi level of undoped system; EF,t denotes the Fermi level at turning point.

Extended Data Fig. 6 Deconvolution of the exciton diffusion from scanning photocurrent microscopy studies.

Specifically, we used VG1 = 4 V and VG2 = −4 V (black line) as our measure of laser spot size since the photocurrent collection is exclusively from the diode interface, which is much smaller than our laser spot size (instrument response function, IRF) and fit (red dashed line) it to a single Gaussian function. We fit (pink dashed line) VG1 = 4 V and VG2 = −0.4 V (blue line) with a function being convolution of the IRF Gaussian with an exponential centred at the middle of the interface (X = 0 μm) for the low-doping limit. The decay constant for the fit corresponds to exciton diffusion length Lexc = 0.72 ± 0.10 μm. The yellow square denotes the position of electrodes.

Extended Data Fig. 7 Gate dependent ISC in monolayer, bilayer and four-layer WSe2 vdW-diodes.

a, IDSVDS curve of the monolayer WSe2 diode under illumination. b, IDSVDS curve of the bilayer WSe2 diode under illumination. c, IDSVDS curve of the four-layer WSe2 diode under illumination. d, Gate dependent ISC in monolayer diode. e, Gate dependent ISC in bilayer diode. f, Gate dependent ISC in four-layer diode.

Extended Data Fig. 8

Power dependent apparent EQE in a bilayer diode at VG1 = 5 V and different VG2.

Extended Data Table 1 Fitting parameters for Extended Data Fig. 4a, 4b
Extended Data Table 2 Summary of the diode parameters in different studies

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, P., Atallah, T.L., Lin, Z. et al. Approaching the intrinsic exciton physics limit in two-dimensional semiconductor diodes. Nature 599, 404–410 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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