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Thermally conductive ultra-low-k dielectric layers based on two-dimensional covalent organic frameworks


As the features of microprocessors are miniaturized, low-dielectric-constant (low-k) materials are necessary to limit electronic crosstalk, charge build-up, and signal propagation delay. However, all known low-k dielectrics exhibit low thermal conductivities, which complicate heat dissipation in high-power-density chips. Two-dimensional (2D) covalent organic frameworks (COFs) combine immense permanent porosities, which lead to low dielectric permittivities, and periodic layered structures, which grant relatively high thermal conductivities. However, conventional synthetic routes produce 2D COFs that are unsuitable for the evaluation of these properties and integration into devices. Here, we report the fabrication of high-quality COF thin films, which enable thermoreflectance and impedance spectroscopy measurements. These measurements reveal that 2D COFs have high thermal conductivities (1 W m−1 K−1) with ultra-low dielectric permittivities (k = 1.6). These results show that oriented, layered 2D polymers are promising next-generation dielectric layers and that these molecularly precise materials offer tunable combinations of useful properties.

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Fig. 1: Templated colloidal polymerization of boronate ester-linked COF films.
Fig. 2: Optoelectronic properties of COF films.
Fig. 3: COF-5 dielectric layer impedance measurements.
Fig. 4: Thermal properties of 2D COF thin films.
Fig. 5: Meta-analysis of thermal conductivities in low-k dielectrics.

Data availability

Source data are provided with this paper. Additional data are available from the corresponding authors upon request.


  1. Krishtab, M. et al. Vapor-deposited zeolitic imidazolate frameworks as gap-filling ultra-low-k dielectrics. Nat. Commun. 10, 3729 (2019).

    Article  Google Scholar 

  2. Volksen, W., Miller, R. D. & Dubois, G. Low dielectric constant materials. Chem. Rev. 110, 56–110 (2010).

    Article  CAS  Google Scholar 

  3. Maex, K. et al. Low dielectric constant materials for microelectronics. J. Appl. Phys. 93, 8793–8841 (2003).

    Article  CAS  Google Scholar 

  4. International Roadmap for Devices and Systems (IRDS) (IEEE, 2017);

  5. Arden, W. M. The international technology roadmap for semiconductors—perspectives and challenges for the next 15 years. Curr. Opin. Solid State Mater. Sci. 6, 371–377 (2002).

    Article  Google Scholar 

  6. Miller, R. D. In search of low-k dielectrics. Science 286, 421–423 (1999).

    Article  CAS  Google Scholar 

  7. Veres, J., Ogier, S. D., Leeming, S. W., Cupertino, D. C. & Mohialdin Khaffaf, S. Low-k insulators as the choice of dielectrics in organic field-effect transistors. Adv. Func. Mater. 13, 199–204 (2003).

    Article  CAS  Google Scholar 

  8. Hopkins, P. E., Kaehr, B., Piekos, E. S., Dunphy, D. & Brinker, C. J. Minimum thermal conductivity considerations in aerogel thin films. J. Appl. Phys. 111, 113532 (2012).

    Article  Google Scholar 

  9. Erickson, K. J. et al. Thin film thermoelectric metal–organic framework with high Seebeck coefficient and low thermal conductivity. Adv. Mater. 27, 3453–3459 (2015).

    Article  CAS  Google Scholar 

  10. Xie, X. et al. Thermal conductivity, heat capacity, and elastic constants of water-soluble polymers and polymer blends. Macromolecules 49, 972–978 (2016).

    Article  CAS  Google Scholar 

  11. Kim, G.-H. et al. High thermal conductivity in amorphous polymer blends by engineered interchain interactions. Nat. Mater. 14, 295–300 (2015).

    Article  CAS  Google Scholar 

  12. Evans, A. M. et al. Buckling of two-dimensional covalent organic frameworks under thermal stress. Ind. Eng. Chem. Res. 58, 9883–9887 (2019).

    Article  CAS  Google Scholar 

  13. Bisbey, R. P. & Dichtel, W. R. Covalent organic frameworks as a platform for multidimensional polymerization. ACS Cent. Sci. 3, 533–543 (2017).

    Article  CAS  Google Scholar 

  14. Sick, T. et al. Oriented films of conjugated 2D covalent organic frameworks as photocathodes for water splitting. J. Am. Chem. Soc. 140, 2085–2092 (2018).

    Article  CAS  Google Scholar 

  15. Colson, J. W. et al. Oriented 2D covalent organic framework thin films on single-layer graphene. Science 332, 228–231 (2011).

    Article  CAS  Google Scholar 

  16. Burke, D. W. et al. Acid exfoliation of imine-linked covalent organic frameworks enables solution processing into crystalline thin films. Angew. Chem. Int. Ed. 59, 5165–5171 (2019).

    Article  Google Scholar 

  17. Chen, X. et al. High-lithium-affinity chemically exfoliated 2D covalent organic frameworks. Adv. Mater. 31, 1901640 (2019).

    Article  Google Scholar 

  18. Dey, K. et al. Selective molecular separation by interfacially crystallized covalent organic framework thin films. J. Am. Chem. Soc. 139, 13083–13091 (2017).

    Article  CAS  Google Scholar 

  19. Sasmal, H. S. et al. Covalent self-assembly in two dimensions: connecting covalent organic framework nanospheres into crystalline and porous thin films. J. Am. Chem. Soc. 141, 20371–20379 (2019).

    Article  CAS  Google Scholar 

  20. Rodríguez-San-Miguel, D. & Zamora, F. Processing of covalent organic frameworks: an ingredient for a material to succeed. Chem. Soc. Rev. 48, 4375–4386 (2019).

    Article  Google Scholar 

  21. Shao, P. et al. Flexible films of covalent organic frameworks with ultralow dielectric constants under high humidity. Angew. Chem. Int. Ed. 57, 16501–16505 (2018).

    Article  CAS  Google Scholar 

  22. Evans, A. M. et al. Seeded growth of single-crystal two-dimensional covalent organic frameworks. Science 361, 52–57 (2018).

    Article  CAS  Google Scholar 

  23. Li, H. et al. Nucleation–elongation dynamics of two-dimensional covalent organic frameworks. J. Am. Chem. Soc. 142, 1367–1374 (2020).

    Article  CAS  Google Scholar 

  24. Smith, B. J. et al. Colloidal covalent organic frameworks. ACS Cent. Sci. 3, 58–65 (2017).

    Article  CAS  Google Scholar 

  25. Cao, S., Li, B., Zhu, R. & Pang, H. Design and synthesis of covalent organic frameworks towards energy and environment fields. Chem. Eng. J. 355, 602–623 (2019).

    Article  CAS  Google Scholar 

  26. Ikeda, M., Takeuchi, M. & Shinkai, S. Unusual emission properties of a triphenylene-based organogel system. Chem. Commun. 9, 1354–1355 (2003).

    Article  Google Scholar 

  27. Sangwan, V. K. et al. Quantitatively enhanced reliability and uniformity of high-κ dielectrics on graphene enabled by self-assembled seeding layers. Nano Lett. 13, 1162–1167 (2013).

    Article  CAS  Google Scholar 

  28. Huang, B. L., McGaughey, A. J. H. & Kaviany, M. Thermal conductivity of metal-organic framework 5 (MOF-5): Part I. Molecular dynamics simulations. Int. J. Heat Mass Transf. 50, 393–404 (2007).

    Article  CAS  Google Scholar 

  29. Wang, X., Liman, C. D., Treat, N. D., Chabinyc, M. L. & Cahill, D. G. Ultralow thermal conductivity of fullerene derivatives. Phys. Rev. B 88, 075310 (2013).

    Article  Google Scholar 

  30. Klemens, P. G. The scattering of low-frequency lattice waves by static imperfections. Proc. Phys. Soc. A 68, 1113 (1955).

    Article  Google Scholar 

  31. Gaskins, J. T. et al. Investigation and review of the thermal, mechanical, electrical, optical, and structural properties of atomic layer deposited high-k dielectrics: beryllium oxide, aluminum oxide, hafnium oxide, and aluminum nitride. ECS J. Solid State Sci. Technol. 6, N189 (2017).

    Article  CAS  Google Scholar 

  32. Scott, E. A., Gaskins, J. T., King, S. W. & Hopkins, P. E. Thermal conductivity and thermal boundary resistance of atomic layer deposited high-k dielectric aluminum oxide, hafnium oxide, and titanium oxide thin films on silicon. APL Mater. 6, 058302 (2018).

    Article  Google Scholar 

  33. Giri, A., Tomko, J., Gaskins, J. T. & Hopkins, P. E. Large tunability in the mechanical and thermal properties of carbon nanotube-fullerene hierarchical monoliths. Nanoscale 10, 22166–22172 (2018).

    Article  CAS  Google Scholar 

  34. McGaughey, A. J. H. & Kaviany, M. Thermal conductivity decomposition and analysis using molecular dynamics simulations: Part II. Complex silica structures. Int. J. Heat Mass Transf. 47, 1799–1816 (2004).

    Article  CAS  Google Scholar 

  35. Jiang, Z. GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films. J. Appl. Crystallogr. 48, 917–926 (2015).

    Article  CAS  Google Scholar 

  36. Gajdoš, M., Hummer, K., Kresse, G., Furthmüller, J. & Bechstedt, F. Linear optical properties in the projector-augmented wave methodology. Phys. Rev. B 73, 045112 (2006).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  40. Hoover, W. G. & Posch, H. A. Direct measurement of Lyapunov exponents. Phys. Lett. A 113, 82–84 (1985).

    Article  Google Scholar 

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W.R.D., J.-L.B. and F.W. thank the Army Research Office of the United States for a Multidisciplinary University Research Initiatives (MURI) award under grant no. W911NF-15-1-0447. A.M.E. is supported by a National Science Foundation (NSF) Graduate Research Fellowship under grant no. DGE-1324585. N.P.B. also acknowledges an NSF Graduate Research Fellowship. A.G. and P.E.H. appreciate support from the Office of Naval Research (grant no. N00014-20-1-2686). M.B., J.A.M. and A.J.H.M. gratefully acknowledge support from the Army Research Office, grant W911NF-17-1-0397. The electron microscopy work was supported by the United States Department of Energy (DOE DE-SC0019356), and the impedance spectroscopy work was supported by the NSF (DMR-1720139). This study made use of the Integrated Molecular Structure Education and Research Center (IMSERC) and the Electron Probe Instrumentation Center (EPIC) at Northwestern University, both of which have received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF NNCI-1542205 and NSF ECCS1542205, respectively), the Materials Research Science and Engineering Center (NSF DMR-1720139), the State of Illinois, and the International Institute for Nanotechnology. Portions of this work were performed at the DuPont–Northwestern–Dow Collaborative Access Team (DND-CAT) located at Sector 5 and Sector 8 of the Advanced Photon Source (APS). DND-CAT is supported by Northwestern University, E.I. DuPont de Nemours & Co. and the Dow Chemical Company. This research used resources of the Advanced Photon Source and Center for Nanoscale Materials, both of which are DOE Office of Science User Facilities operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. Resources at the Advanced Photon Source were funded by the NSF under award no. 0960140. This research used resources of the Advanced Light Source, a DOE Office of Science User Facility under contract no. DE-AC02-05CH11231.

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Authors and Affiliations



A.M.E. prepared and characterized all COF films. A.G. performed all thermal property characterization and simulations. V.K.S. prepared COF-5 devices and performed impedance spectroscopy. S.X. and H.L. performed and interpreted density functional theory calculations. M.B. performed thermal property characterization. C.G.T.-C. performed and interpreted the X-ray reflectivity experiments. H.B.B. performed synchrotron X-ray scattering experiments. M.S.R. prepared EG/SiC substrates used for COF devices. N.P.B. imaged the COF devices using scanning electron microscopy. E.V. assisted with monomer syntheses. D.W.B. assisted with synchrotron X-ray characterization. V.K.S., H.L., M.J.B., F.W., J.-L.B., J.A.M., A.J.H.M., M.C.H., W.R.D. and P.E.H. supervised this work. All authors contributed to the conception of the study, data interpretation and manuscript preparation.

Corresponding authors

Correspondence to William R. Dichtel or Patrick E. Hopkins.

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Competing interests

Northwestern University and the University of Virginia have filed a preliminary patent application (provisional application no. 6314014) related to the discoveries disclosed here.

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Peer review information Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

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Source data for Fig. 4a–d

Source Data Fig. 5

Source data for Fig. 5

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Evans, A.M., Giri, A., Sangwan, V.K. et al. Thermally conductive ultra-low-k dielectric layers based on two-dimensional covalent organic frameworks. Nat. Mater. 20, 1142–1148 (2021).

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