Advertisement

Electronic Transport in Graphene

Chapter

Abstract

This chapter provides an experimental overview of the electrical transport properties of graphene and graphene nanoribbons, focusing on phenomena related to electronics applications. Section 2.1 gives a brief description of the band structure. Section 2.2 discusses the effect of various scattering mechanisms in 2D sheets and nanoribbons and compares the characteristics of exfoliated and synthesized graphene. The physics of high-bias transport in graphene field effect transistors is described in Sect. 2.3. Section 2.4 gives a brief summary and outlook.

Keywords

Graphene Sheet Dirac Point Graphene Nanoribbons Epitaxial Graphene Electron Drift Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author acknowledges helpful discussions with Bill Cullen, Michael Fuhrer, Philip Kim, Elena Polyakova and Arend Van Der Zande. The assistance of my student Ke Zou in preparing the figures is much appreciated and I thank Vincent Crespi for a careful reading of the manuscript. This work is supported by NSF Grants No. NIRT ECS-0609243 and No. CAREER DMR-0748604.

References

  1. 1.
    Wallace, P. The Band Theory of Graphite. Physical Review 71, 622–634 (1947).MATHCrossRefGoogle Scholar
  2. 2.
    Bostwick, A., Ohta, T., Seyller, T., Horn, K. & Rotenberg, E. Quasiparticle dynamics in graphene. Nature Physics 3, 36–40 (2006).CrossRefGoogle Scholar
  3. 3.
    Castro Neto, A., Guinea, F., Peres, N., Novoselov, K. & Geim, A. The electronic properties of graphene. Reviews of Modern Physics 81, 109–162 (2009).CrossRefGoogle Scholar
  4. 4.
    Park, C., Giustino, F., Spataru, C., Cohen, M. & Louie, S. Angle-resolved photoemission spectra of graphene from first-principles calculations. Nano letters 9, 4234–4239 (2009).CrossRefGoogle Scholar
  5. 5.
    Borghi, G., Polini, M., Asgari, R. & MacDonald, A. Fermi velocity enhancement in monolayer and bilayer graphene. Solid State Communications 149, 1117–1122 (2009).CrossRefGoogle Scholar
  6. 6.
    Peres, N. Colloquium: The transport properties of graphene: An introduction. Reviews of Modern Physics 82, 2673 (2010).CrossRefGoogle Scholar
  7. 7.
    Brey, L. & Fertig, H. Electronic states of graphene nanoribbons studied with the Dirac equation. Physical Review B 73, 235411 (2006).CrossRefGoogle Scholar
  8. 8.
    Nakada, K., Fujita, M., Dresselhaus, G. & Dresselhaus, M.S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Physical Review B 54, 17954–17961 (1996).CrossRefGoogle Scholar
  9. 9.
    Son, Y., Cohen, M. & Louie, S. Half-metallic graphene nanoribbons. Nature 444, 347–349 (2006).CrossRefGoogle Scholar
  10. 10.
    Barone, V., Hod, O. & Scuseria, G. Electronic structure and stability of semiconducting graphene nanoribbons. Nano Lett 6, 2748–2754 (2006).CrossRefGoogle Scholar
  11. 11.
    Ando, T., Fowler, A. & Stern, F. Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982).CrossRefGoogle Scholar
  12. 12.
    Piscanec, S., Lazzeri, M., Mauri, F. & Ferrari, A. Optical phonons of graphene and nanotubes. The European Physical Journal-Special Topics 148, 159–170 (2007).CrossRefGoogle Scholar
  13. 13.
    Charlier, J.C., Eklund, P., Zhu, J. & Ferrari, A. Electron and phonon properties of graphene: Their relationship with carbon nanotubes. Carbon Nanotubes, 673–709 (2008).Google Scholar
  14. 14.
    Hwang, E. & Das Sarma, S. Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene. Physical Review B 77, 115449 (2008).CrossRefGoogle Scholar
  15. 15.
    Efetov, D.K. & Kim, P. Controlling Electron-Phonon Interactions in Graphene at Ultrahigh Carrier Densities. Physical Review Letters 105, 256805 (2010).CrossRefGoogle Scholar
  16. 16.
    Chen, J., Jang, C., Xiao, S., Ishigami, M. & Fuhrer, M. Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nature Nanotechnology 3, 206–209 (2008).CrossRefGoogle Scholar
  17. 17.
    Zou, K., Hong, X., Keefer, D. & Zhu, J. Deposition of high-quality HfO2 on graphene and the effect of remote oxide phonon scattering. Physical Review Letters 105, 126601 (2010).CrossRefGoogle Scholar
  18. 18.
    Fischetti, M., Neumayer, D. & Cartier, E. Effective electron mobility in Si inversion layers in metal-oxide-semiconductor systems with a high-kappa insulator: The role of remote phonon scattering. Journal of Applied Physics 90, 4587–4608 (2001).CrossRefGoogle Scholar
  19. 19.
    Fratini, S. & Guinea, F. Substrate-limited electron dynamics in graphene. Physical Review B 77, 195415 (2008).CrossRefGoogle Scholar
  20. 20.
    Deal, B. The current understanding of charges in the thermally oxidized silicon structure. Journal of the Electrochemical Society 121, 198C (1974).CrossRefGoogle Scholar
  21. 21.
    Zhuravlev, L. The surface chemistry of amorphous silica. Zhuravlev model. Colloids and Surfaces A: Physicochemical and Engineering Aspects 173, 1–38 (2000).CrossRefGoogle Scholar
  22. 22.
    Romero, H.E. et al. n-Type behavior of graphene supported on Si/SiO(2) substrates. ACS NANO 2, 2037–44 (2008).CrossRefGoogle Scholar
  23. 23.
    Kim, W. et al. Hysteresis caused by water molecules in carbon nanotube field-effect transistors. Nano Lett 3, 193–198 (2003).CrossRefGoogle Scholar
  24. 24.
    Aguirre, C. et al. The Role of the Oxygen/Water Redox Couple in Suppressing Electron Conduction in Field-Effect Transistors. Adv. Mater. 21, 3087–3091 (2009).CrossRefGoogle Scholar
  25. 25.
    Adam, S., Hwang, E., Galitski, V. & Das Sarma, S. A self-consistent theory for graphene transport. Proceedings of the National Academy of Sciences 104, 18392 (2007).CrossRefGoogle Scholar
  26. 26.
    Hwang, E., Adam, S. & Das Sarma, S. Carrier transport in two-dimensional graphene layers. Physical Review Letters 98, 186806 (2007).CrossRefGoogle Scholar
  27. 27.
    Ando, T. Screening effect and impurity scattering in monolayer graphene. Journal of the Physical Society of Japan 75, 074716 (2006).Google Scholar
  28. 28.
    Nomura, K. & MacDonald, A. Quantum transport of massless dirac fermions. Physical Review Letters 98, 076602 (2007).Google Scholar
  29. 29.
    Hong, X., Zou, K. & Zhu, J. Quantum scattering time and its implications on scattering sources in graphene. Physical Review B 80, 241415 (2009).CrossRefGoogle Scholar
  30. 30.
    Chen, J. et al. Charged-impurity scattering in graphene. Nature Physics 4, 377–381 (2008).CrossRefGoogle Scholar
  31. 31.
    Shon, N.H. & Ando, T. Quantum transport in two-dimensional graphite system. Journal of the Physical Society of Japan 67, 2421–2429 (1998).CrossRefGoogle Scholar
  32. 32.
    Monteverde, M. et al. Transport and Elastic Scattering Times as Probes of the Nature of Impurity Scattering in Single-Layer and Bilayer Graphene. Physical Review Letters 104, 126801 (2010).CrossRefGoogle Scholar
  33. 33.
    Dean, C. et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotechnology 5, 722–726 (2010).CrossRefGoogle Scholar
  34. 34.
    Bolotin, K. et al. Ultrahigh electron mobility in suspended graphene. Solid State Communications 146, 351–355 (2008).CrossRefGoogle Scholar
  35. 35.
    Du, X., Skachko, I., Barker, A. & Andrei, E.Y. Approaching ballistic transport in suspended graphene. Nature Nanotechnology 3, 491–495 (2008).CrossRefGoogle Scholar
  36. 36.
    Zhang, Y., Brar, V., Girit, C., Zettl, A. & Crommie, M. Origin of spatial charge inhomogeneity in graphene. Nature Physics 5, 722–726 (2009).CrossRefGoogle Scholar
  37. 37.
    Deshpande, A., Bao, W., Miao, F., Lau, C. & LeRoy, B. Spatially resolved spectroscopy of monolayer graphene on SiO2. Physical Review B 79, 205411 (2009).CrossRefGoogle Scholar
  38. 38.
    Stolyarova, E. et al. High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface. Proceedings of the National Academy of Sciences 104, 9209 (2007).CrossRefGoogle Scholar
  39. 39.
    Stauber, T., Peres, N. & Guinea, F. Electronic transport in graphene: A semiclassical approach including midgap states. Phys. Rev. B 76, 205423 (2007).CrossRefGoogle Scholar
  40. 40.
    Wehling, T.O., Katsnelson, M.I. & Lichtenstein, A.I. Adsorbates on graphene: Impurity states and electron scattering. Chem Phys Lett 476, 125–134 (2009).CrossRefGoogle Scholar
  41. 41.
    Chen, J.-H., Cullen, W., Jang, C., Fuhrer, M. & Williams, E. Defect Scattering in Graphene. Phys. Rev. Lett. 102, 236805 (2009).CrossRefGoogle Scholar
  42. 42.
    Ni, Z. et al. On resonant scatterers as a factor limiting carrier mobility in graphene. Nano letters 10, 3868–3872 (2010).CrossRefGoogle Scholar
  43. 43.
    Hong, X., Cheng, S.-H., Herding, C. & Zhu, J. Colossal negative magnetoresistance in dilute fluorinated graphene. Phys. Rev. B 83, 085410 (2011).CrossRefGoogle Scholar
  44. 44.
    Lucchese, M. et al. Quantifying ion-induced defects and Raman relaxation length in graphene. Carbon 48, 1592–1597 (2010).CrossRefGoogle Scholar
  45. 45.
    Katsnelson, M. & Geim, A. Electron scattering on microscopic corrugations in graphene. Philosophical Transactions A 366, 195 (2008).CrossRefGoogle Scholar
  46. 46.
    Geringer, V. et al. Intrinsic and extrinsic corrugation of monolayer graphene deposited on SiO2. Physical Review Letters 102, 076102 (2009).CrossRefGoogle Scholar
  47. 47.
    Cullen, W.G. et al. High-Fidelity Conformation of Graphene to SiO2 Topographic Features. Phys Rev Lett 105, 215504 (2010).CrossRefGoogle Scholar
  48. 48.
    Meyer, J.C. et al. The structure of suspended graphene sheets. Nature 446, 60–63 (2007).CrossRefGoogle Scholar
  49. 49.
    Lui, C., Liu, L., Mak, K., Flynn, G. & Heinz, T. Ultraflat graphene. Nature 462, 339 (2009).Google Scholar
  50. 50.
    Bao, W. et al. Controlled ripple texturing of suspended graphene and ultrathin graphite membranes. Nature nanotechnology 4, 562–566 (2009).CrossRefGoogle Scholar
  51. 51.
    Schedin, F. et al. Detection of individual gas molecules adsorbed on graphene. Nature Materials 6, 652–655 (2007).CrossRefGoogle Scholar
  52. 52.
    Lohmann, T., Von Klitzing, K. & Smet, J. Four-Terminal Magneto-Transport in Graphene pn Junctions Created by Spatially Selective Doping. Nano letters 9, 1973–1979 (2009).CrossRefGoogle Scholar
  53. 53.
    Wei, D. et al. Synthesis of N-doped graphene by chemical vapor deposition and its electrical properties. Nano letters 9, 1752–1758 (2009).CrossRefGoogle Scholar
  54. 54.
    Pi, K. et al. Electronic doping and scattering by transition metals on graphene. Physical Review B 80, 075406 (2009).CrossRefGoogle Scholar
  55. 55.
    Wehling, T. et al. Molecular doping of graphene. Nano Lett 8, 173-177 (2008).CrossRefGoogle Scholar
  56. 56.
    Leenaerts, O., Partoens, B. & Peeters, F. Adsorption of H2O, NH3, CO, NO2, and NO on graphene: A first-principles study. Physical Review B 77, 125416 (2008).CrossRefGoogle Scholar
  57. 57.
    Chen, W., Chen, S., Qi, D.C., Gao, X.Y. & Wee, A.T.S. Surface transfer p-type doping of epitaxial graphene. Journal of the American Chemical Society 129, 10418–10422 (2007).CrossRefGoogle Scholar
  58. 58.
    Choi, J., Lee, H., Kim, K., Kim, B. & Kim, S. Chemical Doping of Epitaxial Graphene by Organic Free Radicals. The Journal of Physical Chemistry Letters 1, 505–509 (2009).CrossRefGoogle Scholar
  59. 59.
    Bae, S. et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nature nanotechnology 5, 574 (2010).CrossRefGoogle Scholar
  60. 60.
    Park, H., Rowehl, J.A., Kim, K.K., Bulovic, V. & Kong, J. Doped graphene electrodes for organic solar cells. Nanotechnology 21, 505204 (2010).CrossRefGoogle Scholar
  61. 61.
    Gomez De Arco, L. et al. Continuous, highly flexible, and transparent graphene films by chemical vapor deposition for organic photovoltaics. ACS nano 4, 2865–2873 (2010).CrossRefGoogle Scholar
  62. 62.
    Yang, Y. & Murali, R. Impact of size effect on graphene nanoribbon transport. Electron Device Letters, IEEE 31, 237–239 (2010).CrossRefGoogle Scholar
  63. 63.
    Campos-Delgado, J. et al. Bulk production of a new form of sp2 carbon: Crystalline graphene nanoribbons. Nano Letters 8, 2773–2778 (2008).CrossRefGoogle Scholar
  64. 64.
    Li, X., Wang, X., Zhang, L., Lee, S. & Dai, H. Chemically derived, ultrasmooth graphene nanoribbon semiconductors. Science 319, 1229 (2008).CrossRefGoogle Scholar
  65. 65.
    Kosynkin, D. et al. Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons. Nature 458, 872–876 (2009).CrossRefGoogle Scholar
  66. 66.
    Jiao, L., Zhang, L., Wang, X., Diankov, G. & Dai, H. Narrow graphene nanoribbons from carbon nanotubes. Nature 458, 877–880 (2009).CrossRefGoogle Scholar
  67. 67.
    Cai, J. et al. Atomically precise bottom-up fabrication of graphene nanoribbons. Nature 466, 470–473 (2011).Google Scholar
  68. 68.
    Han, M., Brant, J. & Kim, P. Electron transport in disordered graphene nanoribbons. Physical review letters 104, 056801 (2010).CrossRefGoogle Scholar
  69. 69.
    Gallagher, P., Todd, K. & Goldhaber-Gordon, D. Disorder-induced gap behavior in graphene nanoribbons. Physical Review B 81, 115409 (2010).CrossRefGoogle Scholar
  70. 70.
    Stampfer, C. et al. Energy gaps in etched graphene nanoribbons. Phys Rev Lett 102, 056403 (2009).CrossRefGoogle Scholar
  71. 71.
    Han, M.Y., Özyilmaz, B., Zhang, Y. & Kim, P. Energy band-gap engineering of graphene nanoribbons. Physical Review Letters 98, 206805 (2007).CrossRefGoogle Scholar
  72. 72.
    Evaldsson, M., Zozoulenko, I.V., Xu, H. & Heinzel, T. Edge-disorder-induced Anderson localization and conduction gap in graphene nanoribbons. Physical Review B 78, 161407 (2008).CrossRefGoogle Scholar
  73. 73.
    Martin, J. et al. Observation of electron–hole puddles in graphene using a scanning single-electron transistor. Nature physics 4, 144–148 (2008).CrossRefGoogle Scholar
  74. 74.
    Sols, F., Guinea, F. & Neto, A.H.C. Coulomb blockade in graphene nanoribbons. Physical Review Letters 99, 166803 (2007).CrossRefGoogle Scholar
  75. 75.
    Mucciolo, E.R., Castro Neto, A. & Lewenkopf, C.H. Conductance quantization and transport gaps in disordered graphene nanoribbons. Physical Review B 79, 075407 (2009).CrossRefGoogle Scholar
  76. 76.
    Querlioz, D. et al. Suppression of the orientation effects on bandgap in graphene nanoribbons in the presence of edge disorder. Applied Physics Letters 92, 042108 (2008).CrossRefGoogle Scholar
  77. 77.
    Martin, I. & Blanter, Y.M. Transport in disordered graphene nanoribbons. Physical Review B 79, 235132 (2009).CrossRefGoogle Scholar
  78. 78.
    Adam, S., Cho, S., Fuhrer, M. & Das Sarma, S. Density inhomogeneity driven percolation metal-insulator transition and dimensional crossover in graphene nanoribbons. Physical Review Letters 101, 046404 (2008).CrossRefGoogle Scholar
  79. 79.
    Zou, K. & Zhu, J. Transport in gapped bilayer graphene: the role of potential fluctuations. Physical Review B 82, 081407 (2010).CrossRefGoogle Scholar
  80. 80.
    Taychatanapat, T. & Jarillo-Herrero, P. Electronic Transport in Dual-Gated Bilayer Graphene at Large Displacement Fields. Physical Review Letters 105, 166601 (2010).CrossRefGoogle Scholar
  81. 81.
    Yan, J. & Fuhrer, M.S. Charge Transport in Dual Gated Bilayer Graphene with Corbino Geometry. Nano Letters 10, 4521–4525 (2010).CrossRefGoogle Scholar
  82. 82.
    Chen, Z., Lin, Y.-M., Rooks, M.J. & Avouris, P. Graphene nano-ribbon electronics. Physica E 40, 228–232 (2007).CrossRefGoogle Scholar
  83. 83.
    Wang, X. et al. Room-temperature all-semiconducting sub-10-nm graphene nanoribbon field-effect transistors. Physical review letters 100, 206803 (2008).CrossRefGoogle Scholar
  84. 84.
    Basu, D., Gilbert, M., Register, L., Banerjee, S. & MacDonald, A. Effect of edge roughness on electronic transport in graphene nanoribbon channel metal-oxide-semiconductor field-effect transistors. Applied Physics Letters 92, 042114 (2008).CrossRefGoogle Scholar
  85. 85.
    Fang, T., Konar, A., Xing, H. & Jena, D. Mobility in semiconducting graphene nanoribbons: Phonon, impurity, and edge roughness scattering. Physical Review B 78, 205403 (2008).CrossRefGoogle Scholar
  86. 86.
    Murali, R., Yang, Y., Brenner, K., Beck, T. & Meindl, J.D. Breakdown current density of graphene nanoribbons. Applied Physics Letters 94, 243114 (2009).CrossRefGoogle Scholar
  87. 87.
    First, P. et al. Epitaxial Graphenes on Silicon Carbide. MRS Bulletin 35, 296 (2010).CrossRefGoogle Scholar
  88. 88.
    Reina, A. et al. Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition. Nano letters 9, 30–35 (2008).CrossRefGoogle Scholar
  89. 89.
    Li, X. et al. Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science 324, 1312–1314 (2009).CrossRefGoogle Scholar
  90. 90.
    Emtsev, K.V. et al. Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide. Nature Materials 8, 203–207 (2009).CrossRefGoogle Scholar
  91. 91.
    Jobst, J. et al. Quantum oscillations and quantum Hall effect in epitaxial graphene. Physical Review B 81, 195434 (2010).CrossRefGoogle Scholar
  92. 92.
    Shen, T. et al. Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001). Applied Physics Letters 95, 172105 (2009).CrossRefGoogle Scholar
  93. 93.
    Riedl, C., Coletti, C., Iwasaki, T., Zakharov, A. & Starke, U. Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation. Physical Review Letters 103, 246804 (2009).CrossRefGoogle Scholar
  94. 94.
    Miller, D.L. et al. Observing the Quantization of Zero Mass Carriers in Graphene. Science 324, 924–927 (2009).CrossRefGoogle Scholar
  95. 95.
    Orlita, M. et al. Approaching the Dirac point in high-mobility multilayer epitaxial graphene. Physical Review Letters 101, 267601 (2008).CrossRefGoogle Scholar
  96. 96.
    Wu, X. et al. Half integer quantum Hall effect in high mobility single layer epitaxial graphene. Applied Physics Letters 95, 223108 (2009).CrossRefGoogle Scholar
  97. 97.
    Lee, D.S. et al. Raman spectra of epitaxial graphene on SiC and of epitaxial graphene transferred to SiO2. Nano letters 8, 4320–4325 (2008).CrossRefGoogle Scholar
  98. 98.
    Yazyev, O.V. & Louie, S.G. Electronic transport in polycrystalline graphene. Nature Materials 9, 806–809 (2010).CrossRefGoogle Scholar
  99. 99.
    Huang, P.Y. et al. Grains and grain boundaries in single-layer graphene atomic patchwork quilts. Nature 469, 389–92 (2011).CrossRefGoogle Scholar
  100. 100.
    Nienhaus, H., Kampen, T. & Mönch, W. Phonons in 3 C-, 4 H-, and 6 H-SiC. Surface science 324, L328–L332 (1995).CrossRefGoogle Scholar
  101. 101.
    Hwang, J., Kuo, C., Chen, L. & Chen, K. Correlating defect density with carrier mobility in large-scaled graphene films: Raman spectral signatures for the estimation of defect density. Nanotechnology 21, 465705 (2010).CrossRefGoogle Scholar
  102. 102.
    Li, X. et al. Large-Area Graphene Single Crystals Grown by Low-Pressure Chemical Vapor Deposition of Methane on Copper. Journal of the American Chemical Society 133, 2816–2819 (2011).Google Scholar
  103. 103.
    Meric, I. et al. Current saturation in zero-bandgap, top-gated graphene field-effect transistors. Nature Nanotechnology 3, 654–659 (2008).CrossRefGoogle Scholar
  104. 104.
    Tse, W. & Das Sarma, S. Energy relaxation of hot Dirac fermions in graphene. Phys. Rev. B 79, 235406 (2009).Google Scholar
  105. 105.
    Bistritzer, R. & MacDonald, A. Hydrodynamic theory of transport in doped graphene. Physical Review B 80, 085109 (2009).CrossRefGoogle Scholar
  106. 106.
    Barreiro, A., Lazzeri, M., Moser, J., Mauri, F. & Bachtold, A. Transport properties of graphene in the high-current limit. Physical Review Letters 103, 076601 (2009).CrossRefGoogle Scholar
  107. 107.
    DaSilva, A., Zou, K., Jain, J. & Zhu, J. Mechanism for current saturation and energy dissipation in graphene transistors. Physical Review Letters 104, 236601 (2010).Google Scholar
  108. 108.
    Perebeinos, V. & Avouris, P. Inelastic scattering and current saturation in graphene. Phys. Rev. B 81, 195442 (2010).CrossRefGoogle Scholar
  109. 109.
    Freitag, M. et al. Energy dissipation in graphene field-effect transistors. Nano letters 9, 1883–1888 (2009).CrossRefGoogle Scholar
  110. 110.
    Yao, Z., Kane, C. & Dekker, C. High-field electrical transport in single-wall carbon nanotubes. Physical Review Letters 84, 2941–4 (2000).CrossRefGoogle Scholar
  111. 111.
    Javey, A., Guo, J., Wang, Q., Lundstrom, M. & Dai, H. Ballistic carbon nanotube field-effect transistors. Nature 424, 654–657 (2003).CrossRefGoogle Scholar
  112. 112.
    Park, J.Y. et al. Electron-phonon scattering in metallic single-walled carbon nanotubes. Nano Letters 4, 517–520 (2004).CrossRefGoogle Scholar
  113. 113.
    Canali, C., Majni, G., Minder, R. & Ottaviani, G. Electron and hole drift velocity measurements in silicon and their empirical relation to electric field and temperature. Electron Devices, IEEE Transactions on 22, 1045–1047 (1975).CrossRefGoogle Scholar
  114. 114.
    Meric, I. et al. Channel Length Scaling in Graphene Field-Effect Transistors Studied with Pulsed Current–Voltage Measurements. Nano Letters 11, 1093 (2011).CrossRefGoogle Scholar
  115. 115.
    Mak, K.F., Lui, C.H. & Heinz, T.F. Measurement of the thermal conductance of the graphene/SiO2 interface. Applied Physics Letters 97, 221904 (2010).CrossRefGoogle Scholar
  116. 116.
    Haugen, H., Huertas-Hernando, D. & Brataas, A. Spin transport in proximity-induced ferromagnetic graphene. Physical Review B 77, 115406 (2008).CrossRefGoogle Scholar
  117. 117.
    Hong, X., Posadas, A., Zou, K., Ahn, C.H. & Zhu, J. High-Mobility Few-Layer Graphene Field Effect Transistors Fabricated on Epitaxial Ferroelectric Gate Oxides. Physical Review Letters 102, 136808 (2009).CrossRefGoogle Scholar
  118. 118.
    Zheng, Y. et al. Gate-controlled nonvolatile graphene-ferroelectric memory. Applied Physics Letters 94, 163505 (2009).CrossRefGoogle Scholar
  119. 119.
    Ohno, Y., Maehashi, K., Yamashiro, Y. & Matsumoto, K. Electrolyte-gated graphene field-effect transistors for detecting pH and protein adsorption. Nano Lett 9, 3318–3322 (2009).CrossRefGoogle Scholar

Further Reading

  1. N. W. Ashcroft, and N. D. Mermin, Solid State Physics (Brooks Cole, 1976).Google Scholar
  2. C. Weisbuch, and B. Vinter, Quantum Semiconductor Structures: Fundamentals and Applications (Academic Press, 1991).Google Scholar
  3. Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications, edited by Ado Jorio, Gene Dresselhaus and Milred S. Dresselhaus, (Springer, 2008).Google Scholar
  4. B. I. Shklovskii, and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer, 1984).Google Scholar
  5. Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures, edited by H. Grabert, and M. H. Devoret, (Plenum Press, New York, 1992).Google Scholar

Copyright information

© Springer Science+Business Media, LLC  2012

Authors and Affiliations

  1. 1.Department of PhysicsPenn State UniversityUniversity ParkUSA

Personalised recommendations