Advertisement

Journal of Computational Electronics

, Volume 12, Issue 4, pp 722–729 | Cite as

Multiscale modeling of screening effects on conductivity of graphene in weakly bonded graphene-dielectric heterostructures

  • Neerav Kharche
  • Timothy B. Boykin
  • Saroj K. Nayak
Article

Abstract

Graphene is often surrounded by different dielectric materials when integrated into realistic devices. The absence of dangling bonds allows graphene to bond weakly via the van der Waals interaction with the adjacent material surfaces and to retain its peculiar linear band structure. In such weakly bonded systems, however, the electronic properties of graphene are affected by the dielectric screening due to the long-range Coulomb interaction with the surrounding materials. Including the surrounding materials in the first principles density functional theory (DFT) calculations is computationally very demanding due to the large supercell size required to model heterogeneous interfaces. Here, we employ a multiscale approach combining DFT and the classical image-potential model to investigate the effects of screening from the surrounding materials (hBN, SiC, SiO2, Al2O3, and HfO2) on the dielectric function and charged impurity scattering limited conductivity of graphene. In this approach, the graphene layer is modeled using DFT and the screening from the surrounding materials is incorporated by introducing an effective dielectric function. The dielectric function and conductivity of graphene calculated using the simplified two-band Dirac model are compared with DFT calculations. The two-band Dirac model is found to significantly overestimate the dielectric screening and charged impurity scattering limited conductivity of graphene. The multiscale approach presented here can also be used to study screening effects in weakly bonded heterostructures of other emerging two-dimensional materials such as metal dichalcogenides.

Keywords

Graphene Non-local screening van der Waals interaction 2D layered materials DFT 

Notes

Acknowledgements

This work was supported in part by New York State Focus Center and in part by the NSF PetaApps grant number 0749140, and an anonymous gift from Rensselaer. The work was partly supported by Army Research Laboratory under the cooperative agreement number W911NF-12-2-0023. Computing resources of the Computational Center for Nanotechnology Innovations at Rensselaer partly funded by State of New York and of nanoHUB.org funded by the NSF have been used for this work.

References

  1. 1.
    Riedl, C., Coletti, C., Iwasaki, T., Zakharov, A.A., Starke, U.: Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation. Phys. Rev. Lett. 103, 246804 (2009) CrossRefGoogle Scholar
  2. 2.
    Elias, D.C., Nair, R.R., Mohiuddin, T.M.G., Morozov, S.V., Blake, P., Halsall, M.P., et al.: Control of graphenes properties by reversible hydrogenation: evidence for graphane. Science 323, 610–613 (2009) CrossRefGoogle Scholar
  3. 3.
    Robinson, J.T., Burgess, J.S., Junkermeier, C.E., Badescu, S.C., Reinecke, T.L., Perkins, F.K., et al.: Properties of fluorinated graphene films. Nano Lett. 10, 3001–3005 (2010) CrossRefGoogle Scholar
  4. 4.
    Li, B., Zhou, L., Wu, D., Peng, H.L., Yan, K., Zhou, Y., et al.: Photochemical chlorination of graphene. ACS Nano 5, 5957–5961 (2011) CrossRefGoogle Scholar
  5. 5.
    Robinson, J.A., Hollander, M., LaBella, M., Trumbull, K.A., Cavalero, R., Snyder, D.W.: Epitaxial graphene transistors: enhancing performance via hydrogen intercalation. Nano Lett. 11, 3875–3880 (2011) CrossRefGoogle Scholar
  6. 6.
    Caldwell, J.D., Anderson, T.J., Culbertson, J.C., Jernigan, G.G., Hobart, K.D., Kub, F.J., et al.: Technique for the dry transfer of epitaxial graphene onto arbitrary substrates. ACS Nano 4, 1108–1114 (2010) CrossRefGoogle Scholar
  7. 7.
    Britnell, L., Gorbachev, R.V., Jalil, R., Belle, B.D., Schedin, F., Katsnelson, M.I., et al.: Electron tunneling through ultrathin boron nitride crystalline barriers. Nano Lett. 12, 1707–1710 (2012) CrossRefGoogle Scholar
  8. 8.
    Britnell, L., Ribeiro, R.M., Eckmann, A., Jalil, R., Belle, B.D., Mishchenko, A., et al.: Strong light-matter interactions in heterostructures of atomically thin films. Science 340, 1311–1314 (2013) CrossRefGoogle Scholar
  9. 9.
    Gao, G.H., Gao, W., Cannuccia, E., Taha-Tijerina, J., Balicas, L., Mathkar, A., et al.: Artificially stacked atomic layers: toward new van der Waals solids. Nano Lett. 12, 3518–3525 (2012) CrossRefGoogle Scholar
  10. 10.
    Haigh, S.J., Gholinia, A., Jalil, R., Romani, S., Britnell, L., Elias, D.C., et al.: Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices. Nat. Mater. 11, 764–767 (2012) CrossRefGoogle Scholar
  11. 11.
    Kharche, N., Nayak, S.K.: Quasiparticle band gap engineering of graphene and graphone on hexagonal boron nitride substrate. Nano Lett. 11, 5274–5278 (2011) CrossRefGoogle Scholar
  12. 12.
    Neaton, J.B., Hybertsen, M.S., Louie, S.G.: Renormalization of molecular electronic levels at metal-molecule interfaces. Phys. Rev. Lett. 97, 216405 (2006) CrossRefGoogle Scholar
  13. 13.
    Thygesen, K.S., Rubio, A.: Renormalization of molecular quasiparticle levels at metal-molecule interfaces: trends across binding regimes. Phys. Rev. Lett. 102, 046802 (2009) CrossRefGoogle Scholar
  14. 14.
    Kaasbjerg, K., Flensberg, K.: Strong polarization-induced reduction of addition energies in single-molecule nanojunctions. Nano Lett. 8, 3809–3814 (2008) CrossRefGoogle Scholar
  15. 15.
    Stokbro, K.: First-principles modeling of molecular single-electron transistors. J. Phys. Chem. C 114, 20461–20465 (2010) CrossRefGoogle Scholar
  16. 16.
    Franceschetti, A., Zunger, A.: Addition energies and quasiparticle gap of CdSe nanocrystals. Appl. Phys. Lett. 76, 1731–1733 (2000) CrossRefGoogle Scholar
  17. 17.
    Jiang, X., Kharche, N., Kohl, P., Boykin, T.B., Klimeck, G., Luisier, M., et al.: Giant quasiparticle bandgap modulation in graphene nanoribbons supported on weakly interacting surfaces. Appl. Phys. Lett. 103, 133107 (2013) CrossRefGoogle Scholar
  18. 18.
    Niquet, Y.M., Lherbier, A., Quang, N.H., Fernandez-Serra, M.V., Blase, X., Delerue, C.: Electronic structure of semiconductor nanowires. Phys. Rev. B 73, 165319 (2006) CrossRefGoogle Scholar
  19. 19.
    Das Sarma, S., Adam, S., Hwang, E.H., Rossi, E.: Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011) CrossRefGoogle Scholar
  20. 20.
    Ong, Z.Y., Fischetti, M.V.: Theory of interfacial plasmon-phonon scattering in supported graphene. Phys. Rev. B 86, 165422 (2012) CrossRefGoogle Scholar
  21. 21.
    Konar, A., Fang, T.A., Jena, D.: Effect of high-κ gate dielectrics on charge transport in graphene-based field effect transistors. Phys. Rev. B 82, 115452 (2010) CrossRefGoogle Scholar
  22. 22.
    Hwang, E.H., Das Sarma, S.: Dielectric function, screening, and plasmons in two-dimensional graphene. Phys. Rev. B 75, 205418 (2007) CrossRefGoogle Scholar
  23. 23.
    Ando, T.: Screening effect and impurity scattering in monolayer graphene. J. Phys. Soc. Jpn. 75, 074716 (2006) CrossRefGoogle Scholar
  24. 24.
    Das Sarma, S., Hwang, E.H.: Conductivity of graphene on boron nitride substrates. Phys. Rev. B 83, 121405 (2011) CrossRefGoogle Scholar
  25. 25.
    Ando, T., Fowler, A., Stern, F.: Electronic-properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982) CrossRefGoogle Scholar
  26. 26.
    Gonze, X., Amadon, B., Anglade, P.M., Beuken, J.M., Bottin, F., Boulanger, P., et al.: ABINIT: first-principles approach to material and nanosystem properties. Comput. Phys. Commun. 180, 2582–2615 (2009) CrossRefGoogle Scholar
  27. 27.
    Troullier, N., Martins, J.L.: Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991) CrossRefGoogle Scholar
  28. 28.
    Goedecker, S., Teter, M., Hutter, J.: Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 54, 1703–1710 (1996) CrossRefGoogle Scholar
  29. 29.
    Ismail-Beigi, S.: Truncation of periodic image interactions for confined systems. Phys. Rev. B 73, 233103 (2006) CrossRefGoogle Scholar
  30. 30.
    Kharche, N., Boykin, T.B., Nayak, S.K.: First-principles investigation of nonlocal screening and its implications for conductivity of graphene embedded in weakly interacting dielectrics (2013, submitted) Google Scholar
  31. 31.
    Morozov, S.V., Novoselov, K.S., Katsnelson, M.I., Schedin, F., Elias, D.C., Jaszczak, J.A., et al.: Giant intrinsic carrier mobilities in graphene and its bilayer. Phys. Rev. Lett. 100 (2008) Google Scholar
  32. 32.
    Hwang, E.H., Adam, S., Das Sarma, S.: Carrier transport in two-dimensional graphene layers. Phys. Rev. Lett. 98, 186806 (2007) CrossRefGoogle Scholar
  33. 33.
    Nomura, K., MacDonald, A.H.: Quantum transport of massless Dirac fermions. Phys. Rev. Lett. 98, 076602 (2007) CrossRefGoogle Scholar
  34. 34.
    Lherbier, A., Biel, B., Niquet, Y.M., Roche, S.: Transport length scales in disordered graphene-based materials: strong localization regimes and dimensionality effects. Phys. Rev. Lett. 100, 036803 (2008) CrossRefGoogle Scholar
  35. 35.
    Lherbier, A., Blase, X., Niquet, Y.M., Triozon, F., Roche, S.: Charge transport in chemically doped 2D graphene. Phys. Rev. Lett. 101, 036808 (2008) CrossRefGoogle Scholar
  36. 36.
    Wehling, T.O., Yuan, S., Lichtenstein, A.I., Geim, A.K., Katsnelson, M.I.: Resonant scattering by realistic impurities in graphene. Phys. Rev. Lett. 105, 056802 (2010) CrossRefGoogle Scholar
  37. 37.
    Sachs, B., Wehling, T.O., Katsnelson, M.I., Lichtenstein, A.I.: Adhesion and electronic structure of graphene on hexagonal boron nitride substrates. Phys. Rev. B 84, 195414 (2012) CrossRefGoogle Scholar
  38. 38.
    Olsen, T., Thygesen, K.S.: Random phase approximation applied to solids, molecules, and graphene-metal interfaces: from van der Waals to covalent bonding. Phys. Rev. B 87, 075111 (2013) CrossRefGoogle Scholar
  39. 39.
    Silkin, V.M., Zhao, J., Guinea, F., Chulkov, E.V., Echenique, P.M., Petek, H.: Image potential states in graphene. Phys. Rev. B 80, 121408 (2009) CrossRefGoogle Scholar
  40. 40.
    van Schilfgaarde, M., Katsnelson, M.I.: First-principles theory of nonlocal screening in graphene. Phys. Rev. B 83, 081409 (2011) CrossRefGoogle Scholar
  41. 41.
    Pitarke, J.M., Nazarov, V.U., Silkin, V.M., Chulkov, E.V., Zaremba, E., Echenique, P.M.: Theory of acoustic surface plasmons. Phys. Rev. B 70, 205403 (2004) CrossRefGoogle Scholar
  42. 42.
    Barrera, R.G., Guzman, O., Balaguer, B.: Point charge in a three-dielectric medium with planar interfaces. Am. J. Phys. 46, 1172–1179 (1978) CrossRefGoogle Scholar
  43. 43.
    Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999) MATHGoogle Scholar
  44. 44.
    Fischetti, M.V.: Long-range Coulomb interactions in small Si devices. Part II. Effective electron mobility in thin-oxide structures. J. Appl. Phys. 89, 1232–1250 (2001) CrossRefGoogle Scholar
  45. 45.
    Xu, Y.N., Ching, W.Y.: Calculation of ground-state and optical properties of boron nitrides in the hexagonal, cubic, and wurtzite structures. Phys. Rev. B 44, 7787–7798 (1991) CrossRefGoogle Scholar
  46. 46.
    Fratini, S., Guinea, F.: Substrate-limited electron dynamics in graphene. Phys. Rev. B 77, 195415 (2008) CrossRefGoogle Scholar
  47. 47.
    Fischetti, M.V., Neumayer, D.A., Cartier, E.A.: Effective electron mobility in Si inversion layers in metal-oxide-semiconductor systems with a high-κ insulator: the role of remote phonon scattering. J. Appl. Phys. 90, 4587–4608 (2001) CrossRefGoogle Scholar
  48. 48.
    Hollander, M.J., LaBella, M., Hughes, Z.R., Zhu, M., Trumbull, K.A., Cavalero, R., et al.: Enhanced transport and transistor performance with oxide seeded high-κ gate dielectrics on wafer-scale epitaxial graphene. Nano Lett. 11, 3601–3607 (2011) CrossRefGoogle Scholar
  49. 49.
    Chen, F., Xia, J.L., Ferry, D.K., Tao, N.J.: Dielectric screening enhanced performance in graphene FET. Nano Lett. 9, 2571–2574 (2009) CrossRefGoogle Scholar
  50. 50.
    Chen, J.H., Jang, C., Adam, S., Fuhrer, M.S., Williams, E.D., Ishigami, M.: Charged-impurity scattering in graphene. Nat. Phys. 4, 377–381 (2008) CrossRefGoogle Scholar
  51. 51.
    Ong, Z.Y., Fischetti, M.V.: Charged impurity scattering in top-gated graphene nanostructures. Phys. Rev. B 86, 121409 (2012) CrossRefGoogle Scholar
  52. 52.
    Ong, Z.Y., Fischetti, M.V.: Top oxide thickness dependence of remote phonon and charged impurity scattering in top-gated graphene. Appl. Phys. Lett. 102 (2013) Google Scholar
  53. 53.
    Gamiz, F., Fischetti, M.V.: Remote Coulomb scattering in metal-oxide-semiconductor field effect transistors: screening by electrons in the gate. Appl. Phys. Lett. 83, 4848–4850 (2003) CrossRefGoogle Scholar
  54. 54.
    Jena, D., Konar, A.: Enhancement of carrier mobility in semiconductor nanostructures by dielectric engineering. Phys. Rev. Lett. 98, 136805 (2007) CrossRefGoogle Scholar
  55. 55.
    Dean, C.R., Young, A.F., Meric, I., Lee, C., Wang, L., Sorgenfrei, S., et al.: Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010) CrossRefGoogle Scholar
  56. 56.
    Berger, C., Song, Z.M., Li, T.B., Li, X.B., Ogbazghi, A.Y., Feng, R., et al.: Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J. Phys. Chem. B 108, 19912–19916 (2004) CrossRefGoogle Scholar
  57. 57.
    Moon, J.S., Curtis, D., Hu, M., Wong, D., McGuire, C., Campbell, P.M., et al.: Epitaxial-graphene RF field-effect transistors on Si-face 6H-SiC substrates. IEEE Electron Device Lett. 30, 650–652 (2009) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Neerav Kharche
    • 1
    • 2
    • 3
  • Timothy B. Boykin
    • 4
  • Saroj K. Nayak
    • 3
    • 5
  1. 1.Computational Center for Nanotechnology InnovationsRensselaer Polytechnic InstituteTroyUSA
  2. 2.Chemistry DepartmentBrookhaven National LaboratoryUptonUSA
  3. 3.Department of Physics, Applied Physics and AstronomyRensselaer Polytechnic InstituteTroyUSA
  4. 4.Department of Electrical and Computer EngineeringUniversity of Alabama in HuntsvilleHuntsvilleUSA
  5. 5.School of Basic SciencesIndian Institute of TechnologyBhubaneswarIndia

Personalised recommendations