Abstract
Correlating atomic configurations—specifically, degree of disorder (DOD)—of an amorphous solid with properties is a long-standing riddle in materials science and condensed matter physics, owing to difficulties in determining precise atomic positions in 3D structures1,2,3,4,5. To this end, 2D systems provide insight to the puzzle by allowing straightforward imaging of all atoms6,7. Direct imaging of amorphous monolayer carbon (AMC) grown by laser-assisted depositions has resolved atomic configurations, supporting the modern crystallite view of vitreous solids over random network theory8. Nevertheless, a causal link between atomic-scale structures and macroscopic properties remains elusive. Here we report facile tuning of DOD and electrical conductivity in AMC films by varying growth temperatures. Specifically, the pyrolysis threshold temperature is the key to growing variable-range-hopping conductive AMC with medium-range order (MRO), whereas increasing the temperature by 25 °C results in AMC losing MRO and becoming electrically insulating, with an increase in sheet resistance of 109 times. Beyond visualizing highly distorted nanocrystallites embedded in a continuous random network, atomic-resolution electron microscopy shows the absence/presence of MRO and temperature-dependent densities of nanocrystallites, two order parameters proposed to fully describe DOD. Numerical calculations establish the conductivity diagram as a function of these two parameters, directly linking microstructures to electrical properties. Our work represents an important step towards understanding the structure–property relationship of amorphous materials at the fundamental level and paves the way to electronic devices using 2D amorphous materials.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
All related data generated and/or analysed in this study are available from the corresponding author on reasonable request.
Code availability
Code is provided at GitHub (https://github.com/vipandyc/AMC_Monte_Carlo; https://github.com/ningustc/AMCProcessing).
References
Zallen, R. The Physics of Amorphous Solids (Wiley, 1983).
Miracle, D. B. A structural model for metallic glasses. Nat. Mater. 3, 697–702 (2004).
Sheng, H. W., Luo, W. K., Alamgir, F. M., Bai, J. M. & Ma, E. Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006).
Greer, A. L. in Physical Metallurgy 5th edn (eds Laughlin, D. E. & Hono, K.) 305–385 (Elsevier, 2014).
Ma, E. Tuning order in disorder. Nat. Mater. 14, 547–552 (2015).
Joo, W. J. et al. Realization of continuous Zachariasen carbon monolayer. Sci. Adv. 3, e1601821 (2017).
Hong, S. et al. Ultralow-dielectric-constant amorphous boron nitride. Nature 582, 511–514 (2020).
Toh, C. T. et al. Synthesis and properties of free-standing monolayer amorphous carbon. Nature 577, 199–203 (2020).
Tilley, R. J. D. Crystals and Crystal Structures (Wiley, 2006).
Schorr, S. & Weidenthaler, C. (eds) Crystallography in Materials Science: From Structure-Property Relationships to Engineering (De Gruyter, 2021).
Yang, Y. et al. Determining the three-dimensional atomic structure of an amorphous solid. Nature 592, 60–64 (2021).
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).
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).
Huang, P. Y. et al. Imaging atomic rearrangements in two-dimensional silica glass: watching silica’s dance. Science 342, 224–227 (2013).
Li, X. et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324, 1312–1314 (2009).
Reina, A. et al. Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition. Nano Lett. 9, 30–35 (2009).
Nandamuri, G., Roumimov, S. & Solanki, R. Chemical vapor deposition of graphene films. Nanotechnology 21, 145604 (2010).
Sun, Z. et al. Growth of graphene from solid carbon sources. Nature 468, 549–552 (2010).
Cai, J. et al. Atomically precise bottom-up fabrication of graphene nanoribbons. Nature 466, 470–473 (2010).
Kolmer, M. et al. Rational synthesis of atomically precise graphene nanoribbons directly on metal oxide surfaces. Science 369, 571–575 (2020).
Yazyev, O. V. A guide to the design of electronic properties of graphene nanoribbons. Acc. Chem. Res. 46, 2319–2328 (2013).
Jang, J. et al. Low-temperature-grown continuous graphene films from benzene by chemical vapor deposition at ambient pressure. Sci. Rep. 5, 17955 (2015).
Choi, J. H. et al. Drastic reduction in the growth temperature of graphene on copper via enhanced London dispersion force. Sci. Rep. 3, 1925 (2013).
Wu, T. et al. Continuous graphene films synthesized at low temperatures by introducing coronene as nucleation seeds. Nanoscale 5, 5456–5461 (2013).
Zhang, P. F. et al. Parent B2N2‐perylenes with different BN orientations. Angew. Chem. Int. Ed. 60, 23313–23319 (2021).
Malard, L. M., Pimenta, M. A., Dresselhaus, G. & Dresselhaus, M. S. Raman spectroscopy in graphene. Phys. Rep. 473, 51–87 (2009).
Zachariasen, W. H. The atomic arrangement in glass. J. Am. Chem. Soc. 54, 3841–3851 (1932).
Egami, T. & Billinge, S. J. Underneath the Bragg Peaks: Structural Analysis of Complex Materials (Elsevier, 2003).
Xu, Z. et al. Electrical conductivity, chemistry, and bonding alternations under graphene oxide to graphene transition as revealed by in situ TEM. ACS Nano 5, 4401–4406 (2011).
Wang, W. H., Dong, C. & Shek, C. H. Bulk metallic glasses. Mater. Sci. Eng. R Rep. 44, 45–89 (2004).
Mott, N. F. & Davis, E. A. Electronic Processes in Non-crystalline Materials (Oxford Univ. Press, 2012).
Kaiser, A. B., Gomez-Navarro, C., Sundaram, R. S., Burghard, M. & Kern, K. Electrical conduction mechanism in chemically derived graphene monolayers. Nano Lett. 9, 1787–1792 (2009).
Ambegaokar, V., Halperin, B. I. & Langer, J. S. Hopping conductivity in disordered systems. Phys. Rev. B 4, 2612–2620 (1971).
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).
Thapa, R., Ugwumadu, C., Nepal, K., Trembly, J. & Drabold, D. A. Ab initio simulation of amorphous graphite. Phys. Rev. Lett. 128, 236402 (2022).
Mott, N. F. Conduction in non-crystalline materials. III. Localized states in a pseudogap and near extremities of conduction and valence bands. Philos. Mag. 19, 835–852 (1969).
Tuan, D. V. et al. Insulating behavior of an amorphous graphene membrane. Phys. Rev. B 86, 121408(R) (2012).
Li, Y., Inam, F., Kumar, A., Thorpe, M. F. & Drabold, D. A. Pentagonal puckering in a sheet of amorphous graphene. Phys. Status Solidi B 248, 2082–2086 (2011).
Liu, L. et al. Heteroepitaxial growth of two-dimensional hexagonal boron nitride templated by graphene edges. Science 343, 163–167 (2014).
Imada, I., Fujimori, A. & Tokura, Y. Metal-insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998).
Siegrist, T. et al. Disorder-induced localization in crystalline phase-change materials. Nat. Mater. 10, 202–208 (2011).
Krivanek, O. L. et al. Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy. Nature 464, 571–574 (2010).
Kresse, G. & Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).
Acknowledgements
This work was supported by the National Key R&D Program of China (2021YFA1400500, 2018YFA0305800, 2019YFA0307800, 2020YFF01014700, 2017YFA0206300), the National Natural Science Foundation of China (U1932153, 51872285, 11974001, 22075001, 11974024, 11874359, 92165101, 11974388, 51991344), the Beijing Natural Science Foundation (2192022, Z190011), the Beijing Outstanding Young Scientist Program (BJJWZYJH01201914430039), the Key-Area Research and Development Program of Guangdong Province (2019B010934001), the Strategic Priority Research Program of Chinese Academy of Sciences under grant no. XDB33000000 and the Key Research Program of Frontier Sciences, CAS (QYZDB-SSW-JSC019). J.C. is grateful for the support of the Beijing Natural Science Foundation (JQ22001). L.W. is grateful for the support from the Youth Innovation Promotion Association of CAS (2020009). A portion of this work was performed at the Steady High Magnetic Field Facilities, High Magnetic Field Laboratory, Chinese Academy of Sciences and supported by the High Magnetic Field Laboratory of Anhui Province. Computational resources were provided by the Peking University supercomputing platform, Shanghai Supercomputer Center and the TianHe-1A supercomputer.
Author information
Authors and Affiliations
Contributions
L.Liu and H.T. conceived the project. H.T., J.C., W.Z. and L.Liu designed the experiments and calculations. P.-F.Z., K.Z., J.-Y.W., T.L. and J.P. synthesized the molecule precursors. H.T. performed the CVD growth, with assistance from J.Liu, H.T., R.L., P.L., S.Y., S.L., Y.L., X.H., K.L., Y.J., Y.Zhang and Y.Hou performed the Raman, XPS, atomic force microscopy and other general characterizations. X.L., J.W., Z.X., P.G., L.Lin, L.W. and X.B. performed the SAED characterizations. Y.M., S.N., M.X., X.Z., S.J.P. and W.Z. performed the STEM and NBED experiments and data analysis. M.C., E.H., E.W. and J.C. performed the density functional theory calculations and other theoretical calculations. H.T., Z.L., Z.Y., J.G. and W.F. fabricated the device and performed the room-temperature electrical measurements. Y.Zou, D.D., Y.Huang, J.Lu, Y.Han, Z.W. and Z.G.C. performed the low-temperature transport measurements. H.T., M.C., M.L., J.C., W.Z. and L.Liu wrote the paper. All authors discussed and commented on the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature thanks David Drabold, Jannik Meyer, Hyeon Suk Shin and Chee-Tat Toh for their contribution to the peer review of this work.
Additional information
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 Molecule synthesis and characterization.
a, Organic synthesis route of BN-doped 1,8-dibromonaphthalene, which was used as the main precursor for the growth. (a) C3H5MgBr (2 equiv), 70%; (b) (Cy3P)2Cl2Ru=CHPh (0.8 mol%), CH2Cl2, 92%; (c) 2,3-dicyano-5,6-dichlorobenzoquinone (2 equiv), hexane, 60 °C, 17%; (d) AlBr3, N-bromosuccinimide, CH2Cl2, 62%. b, Molecular structure of 1,8-dibromonaphthalene used as the growth precursor in the control experiment. c, 1H nuclear magnetic resonance spectrum of compound 5 (400 MHz, CDCl3, 298 K).
Extended Data Fig. 2 Characterizations of AMC samples grown at different temperatures.
a, Representative optical images of AMC samples, showing the limited coverage at low temperature (275 °C and 300 °C), continuous and uniform films at medium temperatures (325–500 °C) and films with bilayer regions at high temperatures (600–800 °C). b, Raman spectra of AMC samples, showing the similar feature, that is, broad D and G peaks without G′ signals. At 850 °C, a weak G′ peak was found at about 2,690 cm−1. c, Raman mapping of ID/IG for AMC-300, AMC-400 and AMC-500, demonstrating the spatial uniformity. d, Statistics of ID/IG as a function of growth temperature, showing no monotonic, or apparent, temperature dependence. Considering the DOD differences among AMC samples as shown by STEM characterizations, ID/IG is probably not a good indicator of DOD. Scale bars, 200 μm (a), 5 μm (c).
Extended Data Fig. 3 Characterizations of AMC′ samples with 1,8-dibromonaphthalene as the precursors.
a, Optical images of AMC′ samples transferred onto SiO2/Si substrates. No AMC′ sample was obtained at 300 °C or 325 °C. Continuous and uniform AMC’ films were obtained at intermediate temperatures and samples with the continuous first layer and the partially covered second layer were obtained when T ≥ 600 °C. b, Raman spectra of AMC′ samples, showing the complete absence of G′ peaks. c, I–V curves of two-terminal AMC′ devices, showing varied conductivities for AMC′ samples. d, Diagram of Rs as a function of growth temperature, naturally exhibiting three zones. Scale bar, 200 μm (a).
Extended Data Fig. 4 Density functional theory calculations of catalytic (on Cu) and thermal (in vacuum) cracking of two molecules.
a,b, The predicted reaction process and energy profiles of splitting the molecules (without Br) without (a) and with (b) BN doping into carbon chains. The reaction energy is defined as the energy of the final state minus that of the initial state. c, The calculated decomposition route and energy barriers for A3-2 (CH3-CH2-CH3) cracking on Cu. d, The formation energy (ΔE) per carbon atom on the Cu(100) surface for C, C-C and C-C-C. For n carbon atoms, ΔE is defined as ΔE = (Etotal − nEC − ECu)/n, in which Etotal, EC and ECu are the energies of the absorbed system, a single carbon atom in vacuum and a Cu surface, respectively. e, The absorption energy (ΔE) of CxHy species on the Cu(100) surface. The absorption energy ΔE is defined as ΔE = (Etotal − nECxHy − ECu)/n. f, Reaction enthalpies for 1D linear chains forming 2D compact clusters. mCx + nCy on the x label means the combination of m Cx and n Cy carbon chains. C5-C6 (containing nine carbon atoms) represents a pentagon sharing an edge with a hexagon and the same notation applies for C6-C6, C5-C7 and C6-C7.
Extended Data Fig. 5 Region-averaged 4D-STEM NBED patterns of AMC-300 from two different areas, one area with in situ heating (a–c) and one without heating (d–f).
The scanning region of the 4D-STEM dataset is 36 × 36 nm2. Averaged NBED patterns are obtained by dividing the whole scanning regions into 6 × 6 (a,d), 3 × 3 (b,e) and 1 × 1 (c,f) subregions. The NBED patterns of different subregions in a and d show strong diffuse halos, along with occasional broadened diffraction spots, demonstrating the random spatial distribution of crystallites and glassy structures at the small scale of 6 nm. The diffraction spots gradually become broadened and disappear when increasing the size of the averaging region from 6 × 6 nm2 (a,d) to 12 × 12 nm2 (b,e) and 36 × 36 nm2 (c,f), in agreement with the SAED result in Fig. 2a. The results of a–c were obtained using in situ heating at 650 °C and the dark strips in the centre of convergent-beam electron diffraction patterns are minor gain artefacts from the CMOS camera. The results of d–f were obtained at room temperature. Scale bars, 5 nm−1 (a–f).
Extended Data Fig. 6 Region-averaged 4D-STEM NBED patterns of AMC-400 from two different areas, one area with in situ heating (a–c) and one without heating (d–f).
The scanning region of the 4D-STEM dataset is 36 × 36 nm2. Averaged NBED patterns are obtained by dividing the whole scanning regions into 6 × 6 (a,d), 3 × 3 (b,e) and 1 × 1 (c,f) subregions. Diffuse halos are the dominant features of subregion NBED patterns (a,d), indicating the distinctive structure difference between AMC-300 (Extended Data Fig. 5) and AMC-400 at the sub-10-nm scale. The halos become more diffuse when increasing the size of the averaging region from 6 × 6 nm2 (a,d) to 12 × 12 nm2 (b,e) and exhibit no apparent difference with AMC-300 and AMC-500 at the scale of 36 × 36 nm2 (c,f). Region-averaged NBED results strongly confirm the greater DOD in AMC-400, consistent with the conclusion from real-space STEM images in the main text. The results of a–c were obtained using in situ heating at 650 °C and the dark strips in the centre of convergent-beam electron diffraction patterns are minor gain artefacts from the CMOS camera. The results of d–f were obtained at room temperature. Scale bars, 5 nm−1 (a–f).
Extended Data Fig. 7 Region-averaged 4D-STEM NBED patterns of AMC-500 from two different areas, a–c in one area and d–f in the other.
The scanning region of the 4D-STEM dataset is 36 × 36 nm2. Averaged NBED patterns are obtained by dividing the whole scanning regions into 6 × 6 (a,d), 3 × 3 (b,e) and 1 × 1 (c,f) subregions, respectively. Diffuse halos with blurry spots are found as the main features of subregion NBED patterns a and d, showing the intermediate DOD that agrees with the finding from STEM images. The halos become more diffuse when increasing the size of the averaging region from 6 × 6 nm2 (a,d) to 12 × 12 nm2 (b,e) and exhibit no apparent difference with AMC-300 and AMC-400 at the scale of 36 × 36 nm2 (c,f). The results were obtained at room temperature. Scale bars, 5 nm−1 (a–f).
Extended Data Fig. 8 Denoised ADF-STEM images and the corresponding structural mapping of the AMC-300 (a,b), AMC-400 (c,d) and AMC-500 (e,f) samples, respectively.
Pentagons are filled with red. Heptagons and octagons are filled with blue. Hexagons are filled with bright green or dark green to show crystallites or isolated areas, respectively. The results of a–d were obtained using in situ heating at 650 °C and the results of e and f were obtained by first annealing the sample at 650 °C for 2 h in the JEOL 2100Plus transmission electron microscope, cooling down to room temperature and quickly transferring into the Nion U-HERMES100 microscope for characterization at room temperature. Scale bars, 1 nm (a–f).
Extended Data Fig. 9 Thermostability of AMC-300 (a), AMC-400 (b) and AMC-500 samples (c) in air shown by Raman spectroscopy.
The monolayers were transferred onto SiO2/Si substrates and then consecutive Raman measurements were performed by 4 mW of laser (continuous wave, 532 nm). The acquisition time of a single spectrum was 10 s, with the interval duration of 100 s for AMC-300 and no breaks for AMC-400 and AMC-500. We noticed that, with longer laser irradiation, the Raman intensities from the same spot gradually decayed owing to the structural damage by the heating effect. By tracing the evolution of Raman spectra, we found that AMC-300 held the highest thermostability, whereas AMC-400 suffered severely from the radiolysis. The results of the thermostability evaluation are consistent with our atomic-level structure characterizations.
Extended Data Fig. 10 Electrical measurements of conductive AMC samples.
a–f, Measurements of Rs by the TLM for AMC samples in zones II and IV, showing the temperature-dependent conductivities. Insets, optical images of as-fabricated devices. g, Rs (black circles) as a function of T in one device of AMC in zone IV (550 °C). Inset, natural logarithm of the current as a function of T−1/3. The red lines are the fits to the 2D variable-range-hopping model. h, Results of room-temperature Hall measurements, showing the p-type semiconductor behaviour with a mobility of about 0.1 cm2 V−1 S−1. Inset, optical image of the device with the standard Hall bar configuration. Scale bars, 20 μm (insets of a–f,h).
Extended Data Fig. 11 Electrical measurements of insulating AMC samples.
a, Optical images of as-fabricated AMC devices with the sample highlighted by dashed blue lines. b, Two-terminal I–V curves with a bias sweep from −10 V to 10 V. AMC samples from zone III, including AMC-325, AMC-350, AMC-375 and AMC-400, show <2 pA of the current, comparable with that from the bare SiO2 substrate, strongly suggesting the highly insulating behaviours. By contrast, AMC-450 from zone IV manifests an almost linear current response. We note that we treat this I–V curve of AMC-450 (the normal linear response to applied voltage but with the lowest current in all AMC devices) as the detection limit of our instruments for the AMC system. c, Temperature-dependent I–V curves for AMC-350, showing no increase of the current at elevated temperatures. d, Raman mapping of the sum of G and D peaks (in area), corresponding to the channel region of the AMC-350 device marked by the dashed red lines in the top-middle panel of a, demonstrating the continuity of AMC across two electrodes. e,f, Atomic force microscopy results of the AMC-375 channel area (indicated by the dashed red line in the top-right panel of a) in height (e) and phase (f), both showing the absence of any apparent structural cracks or holes. By confirming the AMC continuity in the device channel from the Raman and atomic force microscopy characterizations, we conclude that AMC samples from zone III are indeed electrically insulating with the comparable level with SiO2, or at least in the limit of our instruments. Scale bars, 20 μm (a), 5 μm (d–f).
Supplementary information
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tian, H., Ma, Y., Li, Z. et al. Disorder-tuned conductivity in amorphous monolayer carbon. Nature 615, 56–61 (2023). https://doi.org/10.1038/s41586-022-05617-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41586-022-05617-w
This article is cited by
-
Ultrathin quasi-2D amorphous carbon dielectric prepared from solution precursor for nanoelectronics
Communications Engineering (2023)
Comments
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.
