Graphene applications in electronics and photonics
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Carrier transport in graphene Graphene has some outstanding physical properties that make it extremely appealing for applications in electronics. Of these, the extraordinarily rapid charge-carrier transport of graphene has received the most attention, and mobilities1,2 in excess of 200,000 cm2 V–1 s–1 and saturation velocities3 of ∼5 × 107 cm s–1 have been reported. In addition, the one-atom thickness, mechanical strength, flexibility, high current-carrying capacity (up to 109 A/cm2), and high thermal conductivity (up to 50 W cm–1 K–1)4 of graphene all contribute to its appeal. Most of these record properties refer to a pristine material under somewhat idealized conditions. In technology, however, graphene is part of a more complex structure and is used under conditions that are dictated by the application. Under such realistic conditions, electronic transport is subject to a variety of scattering interactions,5–10 including long-range interactions with charged impurities on graphene or the supporting insulator substrate and short-range interactions
involving neutral defects or adsorbates, surface roughness, and phonons. Which of these mechanisms dominates the scattering depends on both the quality of the graphene sample and the characteristics of its environment.11 For instance, Coulomb scattering from charged impurities typically dominates at low temperatures for graphene on insulating substrates (e.g., SiO2, SiC, Al2O3).7 Even in suspended graphene, transport is influenced by adsorbed species, so the mobility is greatly enhanced after these species are volatilized by heating.1,2 When all impurities and structural defects are eliminated, phonon scattering remains. The magnitude of the carrier mobility (μ) and its dependence on temperature (T) and carrier density (n) are indicative of the dominant scattering mechanism.11 Thus, mobilities that are greater than about 100,000 cm2 V–1 s–1 and are proportional to 1/nT indicate transport dominated by acoustic-phonon scattering, whereas Coulomb scattering typically leads to mobilities on the
Phaedon Avouris, IBM, Watson Research Center; [email protected] Fengnian Xia, IBM, Watson Research Center; [email protected] DOI: 10.1557/mrs.2012.206
© 2012 Materials Research Society
MRS BULLETIN • VOLUME 37 • DECEMBER 2012 • www.mrs.org/bulletin
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GRAPHENE APPLICATIONS IN ELECTRONICS AND PHOTONICS
order of 1000–10,000 cm2 V–1 s–1 that are independent of n, and short-range scattering by neutral defects leads to a temperatureindependent mobility that is proportional to 1/n.5,9,12–14 Although a number of different electronic devices based on graphene can be envisioned, we focus here on the most widely explored concept, that of field-effect transistors. Transport in graphene is intrinsically ambipolar, meaning that both positive and negative carriers are important. As illustrated in Figure 1a–b, when, through application of the appropriate gate bias, the Fermi level, EF, is brought below the neutrality point, ENP (the energy of the Dirac point), transport involves holes, whereas
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