Synthesis and properties of free-standing monolayer amorphous carbon


Bulk amorphous materials have been studied extensively and are widely used, yet their atomic arrangement remains an open issue. Although they are generally believed to be Zachariasen continuous random networks1, recent experimental evidence favours the competing crystallite model in the case of amorphous silicon2,3,4. In two-dimensional materials, however,  the corresponding questions remain unanswered. Here we report the synthesis, by laser-assisted chemical vapour deposition5, of centimetre-scale, free-standing, continuous and stable monolayer amorphous carbon, topologically distinct from disordered graphene. Unlike in bulk materials, the structure of monolayer amorphous carbon can be determined by atomic-resolution imaging. Extensive characterization by Raman and X-ray spectroscopy and transmission electron microscopy reveals the complete absence of long-range periodicity and a threefold-coordinated structure with a wide distribution of bond lengths, bond angles, and five-, six-, seven- and eight-member rings. The ring distribution is not a Zachariasen continuous random network, but resembles the competing (nano)crystallite model6. We construct a corresponding model that enables density-functional-theory calculations of the properties of monolayer amorphous carbon, in accordance with observations. Direct measurements confirm that it is insulating, with resistivity values similar to those of boron nitride grown by chemical vapour deposition. Free-standing monolayer amorphous carbon is surprisingly stable and deforms to a high breaking strength, without crack propagation from the point of fracture. The excellent physical properties of this stable, free-standing monolayer amorphous carbon could prove useful for permeation and diffusion barriers in applications such as magnetic recording devices and flexible electronics.

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Fig. 1: Morphology of MAC.
Fig. 2: Atomic structure of MAC from TEM.
Fig. 3: Mechanical properties of MAC.
Fig. 4: Insulating properties of MAC.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The code used in this study is available upon request from the corresponding author.


  1. 1.

    Zachariasen, W. H. The atomic arrangement in glass. J. Am. Chem. Soc. 54, 3841–3851 (1932).

    Article  CAS  Google Scholar 

  2. 2.

    Voyles, P. M. & Abelson, J. R. Medium-range order in amorphous silicon measured by fluctuation electron microscopy. Sol. Energy Mater. Sol. Cells 78, 85–113 (2003).

    Article  CAS  Google Scholar 

  3. 3.

    Gibson, J. M., Treacy, M. M. J., Sun, T. & Zaluzec, N. J. Substantial crystalline topology in amorphous silicon. Phys. Rev. Lett. 105, 125504 (2010).

    ADS  Article  CAS  Google Scholar 

  4. 4.

    Treacy, M. M. J. & Borisenko, K. B. The local structure of amorphous silicon. Science 335, 950–953 (2012).

    ADS  Article  CAS  Google Scholar 

  5. 5.

    Herman, I. P. Laser-assisted deposition of thin films from gas-phase and surface-adsorbed molecules. Chem. Rev. 89, 1323–1357 (1989).

    Article  CAS  Google Scholar 

  6. 6.

    Wright, A. C. Neutron scattering from vitreous silica. V. The structure of vitreous silica: what have we learned from 60 years of diffraction studies? J. Non-Cryst. Solids 179, 84–115 (1994).

    ADS  Article  CAS  Google Scholar 

  7. 7.

    Wright, A. C. The great crystallite versus random network controversy: a personal perspective. Int. J. Appl. Glass Sci. 5, 31–56 (2014).

    Article  Google Scholar 

  8. 8.

    Roorda, S. & Lewis, L. J. Comment on “The Local Structure of Amorphous Silicon”. Science 338, 1539 (2012).

    ADS  Article  CAS  Google Scholar 

  9. 9.

    Eder, F. R., Kotakoski, J., Kaiser, U. & Meyer, J. C. A journey from order to disorder—atom by atom transformation from graphene to a 2D carbon glass. Sci. Rep. 4, 4060 (2014).

    ADS  Article  CAS  Google Scholar 

  10. 10.

    Kotakoski, J., Krasheninnikov, A. V., Kaiser, U. & Meyer, J. C. From point defects in graphene to two-dimensional amorphous carbon. Phys. Rev. Lett. 106, 105505 (2011).

    ADS  Article  CAS  Google Scholar 

  11. 11.

    Turchanin, A. et al. Conversion of self-assembled monolayers into nanocrystalline graphene: structure and electric transport. ACS Nano 5, 3896–3904 (2011).

    Article  Google Scholar 

  12. 12.

    Joo, W.-J. et al. Realization of continuous Zachariasen carbon monolayer. Sci. Adv. 3, e1601821 (2017).

    ADS  Article  CAS  Google Scholar 

  13. 13.

    Zandiatashbar, A. et al. Effect of defects on the intrinsic strength and stiffness of graphene. Nat. Commun. 5, 3186 (2014).

    ADS  Article  CAS  Google Scholar 

  14. 14.

    Araujo, P. T., Terrones, M. & Dresselhaus, M. S. Defects and impurities in graphene-like materials. Mater. Today 15, 98–109 (2012).

    Article  CAS  Google Scholar 

  15. 15.

    Zhang, C., Hao, X.-L., Wang, C.-X., Wei, N. & Rabczuk, T. Thermal conductivity of graphene nanoribbons under shear deformation: a molecular dynamics simulation. Sci. Rep. 7, 41398 (2017).

    ADS  Article  CAS  Google Scholar 

  16. 16.

    Lichtenstein, L. et al. The atomic structure of a metal-supported vitreous thin silica film. Angew. Chem. Int. Ed. 51, 404–407 (2012).

    Article  CAS  Google Scholar 

  17. 17.

    Lusk, M. T. & Carr, L. D. Nanoengineering defect structures on graphene. Phys. Rev. Lett. 100, 175503 (2008).

    ADS  Article  CAS  Google Scholar 

  18. 18.

    Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).

    ADS  Article  CAS  Google Scholar 

  19. 19.

    Mahvash, F., Paradis, E., Drouin, D., Szkopek, T. & Siaj, M. Space-charge limited transport in large-area monolayer hexagonal boron nitride. Nano Lett. 15, 2263–2268 (2015).

    ADS  Article  CAS  Google Scholar 

  20. 20.

    Kim, D. Y., Jeong, H., Kim, J., Han, N. & Kim, J. K. Defect-mediated in-plane electrical conduction in few-layer sp 2-hybridized boron nitrides. ACS Appl. Mater. Interfaces 10, 17287–17294 (2018).

    Article  CAS  Google Scholar 

  21. 21.

    Rodin, A. S. & Fogler, M. M. Apparent power-law behavior of conductance in disordered quasi-one-dimensional systems. Phys. Rev. Lett. 105, 106801 (2010).

    ADS  Article  CAS  Google Scholar 

  22. 22.

    Rodin, A. S. & Fogler, M. M. Hopping transport in systems of finite thickness or length. Phys. Rev. B 84, 125447 (2011).

    ADS  Article  CAS  Google Scholar 

  23. 23.

    Morozov, S. V. et al. Giant intrinsic carrier mobilities in graphene and its bilayer. Phys. Rev. Lett. 100, 016602 (2008).

    ADS  Article  CAS  Google Scholar 

  24. 24.

    Kapko, V., Drabold, D. A. & Thorpe, M. F. Electronic structure of a realistic model of amorphous graphene. Phys. Status Solidi B 247, 1197–1200 (2010).

    Article  CAS  Google Scholar 

  25. 25.

    Tauc, J. Optical properties and electronic structure of amorphous Ge and Si. Mater. Res. Bull. 3, 37–46 (1968).

    Article  CAS  Google Scholar 

  26. 26.

    Rusli Amaratunga, G. A. J. & Silva, S. R. P. Photoluminescence in amorphous carbon thin films and its relation to the microscopic properties. Thin Solid Films 270, 160–164 (1995).

    ADS  Article  Google Scholar 

  27. 27.

    Zhuang, J., Zhao, R., Dong, J., Yan, T. & Ding, F. Evolution of domains and grain boundaries in graphene: a kinetic Monte Carlo simulation. Phys. Chem. Chem. Phys. 18, 2932–2939 (2016).

    Article  CAS  Google Scholar 

  28. 28.

    Stuart, S. J., Tutein, A. B. & Harrison, J. A. A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112, 6472–6486 (2000).

    ADS  Article  CAS  Google Scholar 

  29. 29.

    Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    ADS  Article  CAS  Google Scholar 

  30. 30.

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

    ADS  Article  CAS  Google Scholar 

  31. 31.

    Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    ADS  Article  CAS  Google Scholar 

  32. 32.

    Ruiz-Vargas, C. S. et al. Softened elastic response and unzipping in chemical vapor deposition graphene membranes. Nano Lett. 11, 2259–2263 (2011).

    ADS  Article  CAS  Google Scholar 

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B.Ö. acknowledges support by the National Research Foundation, Prime Minister’s Office, Singapore, under its Competitive Research Programme (CRP award number NRF-CRP9-2011-3), NRF Investigatorship (NRFI award number NRF-NRFI2018-08) and Medium-Sized Centre Programme. Work at Vanderbilt University (H.S., Y.W. and S.T.P.) was supported by US Department of Energy grant DE-PG02-09ER46554 and by the McMinn Endowment. Computations were performed at the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under contract number DE-AC02-05CH11231, and at the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by US National Science Foundation grant number ACI-1053575. J.L. and K.S. acknowledge JSPS KAKENHI (JP16H06333 and P16823) for financial support. This work was also supported by the Pico Center at MCPC of SUSTech that receives support from Presidential fund and Development and Reform Commission of Shenzhen Municipality. We thank X. Yu and Singapore Synchrotron Light Source (SSLS, SINS beamline) for assistance with angle-resolved XPS measurements, D. Vella and G. Eda for assistance with photoluminescence measurements and G. K. W. Koon for assistance with ellipsometry measurements. B.Ö. thanks J. Fabian for discussions.

Author information




B.Ö. initiated and coordinated the work. C.-T.T. and H.Z. contributed equally to the work. C.-T.T., C.O. and B.Ö. designed the experiments. H.Z., D.B.F., C.O., C.-T.T., N.K. and I.H.A. synthesized the material. H.Z., D.B.F. and C.O. performed the Raman, XPS and AFM characterizations. J.L., Z.G. and K.S. performed the DF-TEM, HR-TEM and STEM characterizations. H.S., Y.P.W. and S.T.P. performed the density functional theory calculations and Monte Carlo simulations. D.B.F. and H.A. fabricated the device and performed the indentation experiment. A.S.M. fabricated the device and performed the electrical measurements. C.-T.T. performed the optical measurements. C.-T.T., S.T.P. and B.Ö. analysed all data and wrote the paper. All authors discussed and commented on the manuscript.

Corresponding author

Correspondence to Barbaros Özyilmaz.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature thanks Volker Deringer, Jannik Meyer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Optical image and Raman mapping of MAC film transferred on Si/SiO2 substrate.

a, MAC transferred to SiO2/Si wafer. Crease and fold at MAC edge from transfer process. b, Contrast-enhanced image in greyscale shows no topological features visible on MAC. c, Raman mapping shows that the intensity ratio of the D to G band, ID/IG, is uniform at the edge of transferred MAC on a Si/SiO2 substrate. This ratio is slightly higher than the expected ratio of 0.82, as the Raman background signal is not subtracted during Raman mapping. d, Raman map (50 × 50 µm2, with 2,500 data points) of ID/IG shows uniform quality over a large area (standard deviation is ±1.8%).

Extended Data Fig. 2 Comparison of large-area TEM data.

a, Polycrystalline graphene with grain size 200–500 nm. b, Nanocrystalline graphene (sample in Fig. 2i) with grain size 1–3 nm. c, MAC (sample in Fig. 2h). Left, bright-field TEM; centre, DF-TEM with false-colour image overlay showing crystal domains; right, SAED patterns. Both polycrystalline and nanocrystalline graphene show crystal domains under DF-TEM and have well defined SAED diffraction patterns. MAC has no visible domains in DF-TEM. Only MAC has the characteristic amorphous halo from SAED diffraction.

Extended Data Fig. 3 Thickness of MAC.

a, AFM topography of MAC transferred onto an atomically flat, exfoliated BN crystal. b, Close-up of the region indicated by the white box in a, with a scan length of 3 µm. c, Height profile of MAC, obtained by averaging vertically over the entire image scan in b, shows a thickness of about 0.6 nm. d, Optical image of MAC grown on gold substrates and transferred onto SiO2 by wet transfer with KI/I2 solution as gold etchant and followed by 7 h annealing in Ar/H2 at 300 °C. For MAC transferred from gold, residues from the gold etching cannot be fully removed owing to the non-optimized transfer process. e, AFM topography of a folded MAC edge in d to obtain one and two layers. f, The height profile along the red dotted line in e gives the thickness of MAC grown on gold as about 0.8 nm. Residual contamination from the transfer step and difference in substrate interactions may account for the higher thickness of MAC when transferred from gold.

Extended Data Fig. 4 Current–voltage measurement and gate dependence.

a, Nonlinear IV curves in Fig. 4b shown in linear scale. b, Gate dependence of MAC with electrostatic gating by SiO2/Si back gate shows ambipolar behaviour and strong temperature dependence, increasing from 100 GΩ per square at room temperature to 1 TΩ per square at 200 K.

Extended Data Fig. 5 Resistivity of samples as a function of the temperature.

a, Temperature dependence of the resistivity for a set of devices with two- and three-layer MAC (denoted BL and TL, respectively). b, The linear fit of the resistivity of offset α and power N, as described by the formula ρ = αTN, shows a linear correlation, N = 2.2(±0.6) − 0.33(±0.02)logα. The data in a, b are provided in Supplementary Table. c, d, Resistivity of tri-layer MAC sample (sample ID TL0) as a function of temperature plotted in a linear scale. The Mott plot (c) shows a temperature limit of 135 K (indicated by the black arrow) up to which it can be applied, as opposed to a power-law dependence (d). The red lines are the best linear fits.

Extended Data Fig. 6 Universal scaling of nonlinear I–V characteristics for ML1 sample.

All I–V curves are collapsed to a single curve indicating apparent power-law dependence in a disordered quasi-one-dimensional system. The equation for the universal scaling curve is from ref. 21.

Extended Data Fig. 7 Selection of MAC theoretical model.

The configuration for the MAC structure at the 20,000th iteration is chosen as the theoretical model, shown in Fig. 2c, for its similarity to experimental HRTEM images of MAC. Previous steps also show an unstable ring structure (for example, rings with fewer than four carbon atoms, or ill-defined rings). Furthermore, the ring size distribution from 10,000 steps is similar . Colour overlay is added for identification of pentagons (red), heptagons/octagons (blue) and strained hexagons (purple or green) that are omnipresent. Crystallites (green) separate regions with non-hexagons. Crystallites are defined to consist of at least one hexagonal ring surrounded by six hexagonal rings.

Extended Data Fig. 8 Modulus square of electronic wavefunctions.

The lowest unoccupied wavefunctions (blue) are shown for ten states with energies closest to the Fermi energy. This shows localization on non-hexagon rings that are separated by crystallites.

Extended Data Fig. 9 Optical measurements of MAC on SiO2/Si.

a, Photoluminescence spectra were measured with an excitation wavelength of 473 nm. The peaks marked by asterisks correspond to the Raman signal from MAC. The emission spectrum of the film has a broad peak centred at 600 nm. b, Relative permittivity of MAC on SiO2/Si substrate by ellipsometry measurements. Eg is taken where the imaginary part equals zero, at about 590 nm (2.1 eV), at which the real part of the relative permittivity is approximately 11.

Supplementary information

Supplementary Information

This file contains Supplementary Notes 1-4, Supplementary Table, Supplementary Figures 1-11 and Supplementary References.

Supplementary Data

Atomic coordinates for the theoretical model of MAC constructed using the kinetic Monte Carlo method at the 20,000th iteration. This is used for calculations in Fig. 4d–f. Data are provided in the internal XCrySDen structure format (XSF).

Video 1

The video shows a 4 cm × 4 cm unsupported monoatomic layer of carbon (MAC) floating on the surface of water. For visibility, black dots were marked on the corners and edge of the sheet before removal of growth substrate. MAC is nudged to move around the water surface without incurring any damage.

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Toh, CT., Zhang, H., Lin, J. et al. Synthesis and properties of free-standing monolayer amorphous carbon. Nature 577, 199–203 (2020).

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