Carrier Transport in Two-Dimensional Graphene Layers

Hwang, E. H.; Adam, Shaffique; Sarma, S. Das

doi:10.1103/physrevlett.98.186806

Cited by 1,175 publications

(1,169 citation statements)

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“…Coulomb scattering in 2D TMDCs is caused by random charged impurities located within the 2D TMDC layer or on its surfaces, and is the dominant scattering effect at low temperatures, as it is for graphene 105 . Engineering the dielectric environment can enhance mobilities 106 , as has been demonstrated for graphene 107,108 and for MoS 2 (ref.…”

Section: Electrical Transport and Devicesmentioning

confidence: 99%

“…Graphene placed on a dielectric material such as SiO 2 , however, experiences scattering due to surface polar phonons in the SiO 2 (ref. 102), and in freely suspended graphene 105,109 the primary scattering is due to out-of-plane flexural phonons 112 . Additionally, freestanding MoS 2 has been shown to have similar ripples 113 to those in graphene, which may also contribute to scattering and mobility reduction.…”

Section: Electrical Transport and Devicesmentioning

confidence: 99%

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Electronics and optoelectronics of two-dimensional transition metal dichalcogenides

et al. 2012

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699M any two-dimensional (2D) materials exist in bulk form as stacks of strongly bonded layers with weak interlayer attraction, allowing exfoliation into individual, atomically thin layers 1 . The form receiving the most attention today is graphene, the monolayer counterpart of graphite. The electronic band structure of graphene has a linear dispersion near the K point, and charge carriers can be described as massless Dirac fermions, providing scientists with an abundance of new physics 2,3 . Graphene is a unique example of an extremely thin electrical and thermal conductor 4 , with high carrier mobility 5 , and surprising molecular barrier properties 6,7 .Many other 2D materials are known, such as the TMDCs 8,9 , transition metal oxides including titania-and perovskite-based oxides 10,11 , and graphene analogues such as boron nitride (BN) 12,13 . In particular, TMDCs show a wide range of electronic, optical, mechanical, chemical and thermal properties that have been studied by researchers for decades 9,14,15 . There is at present a resurgence of scientific and engineering interest in TMDCs in their atomically thin 2D forms because of recent advances in sample preparation, optical detection, transfer and manipulation of 2D materials, and physical understanding of 2D materials learned from graphene.The 2D exfoliated versions of TMDCs offer properties that are complementary to yet distinct from those in graphene. Graphene displays an exceptionally high carrier mobility exceeding 10 6 cm 2 V -1 s -1 at 2 K (ref. 16) and exceeding 10 5 cm 2 V -1 s -1 at room temperature for devices encapsulated in BN dielectric layers 5 ; because pristine graphene lacks a bandgap, however, fieldeffect transistors (FETs) made from graphene cannot be effectively switched off and have low on/off switching ratios. Bandgaps can be engineered in graphene using nanostructuring [17][18][19] , chemical functionalization 20 and applying a high electric field to bilayer graphene 21 , but these methods add complexity and diminish mobility. In contrast, several 2D TMDCs possess sizable bandgaps around 1-2 eV (refs 9,14), promising interesting new FET and optoelectronic devices.TMDCs are a class of materials with the formula MX 2 , where M is a transition metal element from group IV (Ti, Zr, Hf and so on), group V (for instance V, Nb or Ta) or group VI (Mo, W and so on), and X is a chalcogen (S, Se or Te). These materials form layered structures of the form X-M-X, with the chalcogen atoms in two hexagonal planes separated by a plane of metal atoms, as shown in Fig. 1a. Adjacent layers are weakly held together to form the bulk crystal in a variety of polytypes, which vary in stacking orders and metal atom coordination, as shown in Fig. 1e. The overall symmetry of TMDCs is hexagonal or rhombohedral, and the metal atoms have octahedral or trigonal prismatic coordination. The electronic properties of TMDCs range from metallic to semiconducting, as summarized in Table 1. There are also TMDCs that exhibit exotic behaviours such as charge density waves ...

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Section: Electrical Transport and Devicesmentioning

confidence: 99%

Section: Electrical Transport and Devicesmentioning

confidence: 99%

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides

et al. 2012

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“…5, k F is the Fermi wavevector, and the dimensionless function F (a) is defined in ref. [24]. κ avg is given by the average relative dielectric constant of the two regions surrounding graphene: κ avg = (κ top + κ bottom )/2.…”

Section: Ionized Impurity Scatteringmentioning

confidence: 99%

“…If a nominal charged impurity concentration of n imp ∼ 10 11 /cm 2 is present at a graphene/high-κ dielectric interface, for carrier concentrations ≤ 10 12 /cm 2 , acoustic phonon scattering at RT is also relatively insignificant owing to the low density of states of graphene at the Fermi energy (see [21][22][23][24]). In this technologically relevant regime, the competing effects of impurity and SO-phonon scattering are responsible for the low-field transport properties of graphene.…”

Section: Introductionmentioning

confidence: 99%

Effect of high-κgate dielectrics on charge transport in graphene-based field effect transistors

Konar¹,

Tian²,

Jena³

2010

Phys. Rev. B

279

214

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The effect of various dielectrics on charge mobility in single layer graphene is investigated. By calculating the remote optical phonon scattering arising from the polar substrates, and combining it with their effect on Coulombic impurity scattering, a comprehensive picture of the effect of dielectrics on charge transport in graphene emerges. It is found that though high-κ dielectrics can strongly reduce Coulombic scattering by dielectric screening, scattering from surface phonon modes arising from them wash out this advantage. Calculation shows that within the available choice of dielectrics, there is not much room for improving carrier mobility in actual devices at room temperatures.

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“…This shows that the emergent divergent longitudinal resistivity at the graphene Dirac point could equally well be considered a putative Hall insulator phase, which in this context, is equivalent to the zero Fermi energy ν = 0 QHE in graphene with σ xx = 0 and ρ xy ∼ 0. The only (qualitative) difference between graphene and 2D semiconductor systems is that the graphene Dirac point is known to be dominated by density inhomogeneities associated with the electronhole puddles, 25,26,27,28,29 which lead to considerable density fluctuations around the average (expected) zero density at the Dirac point. This means that there will be considerable fluctuations around the expected ρ xy = 0 value in the graphene Hall insulator phase.…”

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confidence: 99%

The enigma of the quantum Hall effect in graphene

Sarma

Yang

2009

Solid State Communications

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We apply Laughlin's gauge argument to analyze the ν = 0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν = 0 quantized Hall effect. We argue that this ν = 0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.A single two-dimensional (2D) layer of carbon atoms forming a honeycomb lattice, i.e., a graphene layer, has unusual physical properties attracting a great deal of current interest. 1 Among its intriguing properties, the effective low-energy dispersion is linear in 2D momentum: E = v|k|, where v, the graphene Fermi velocity, is a constant (v ∼ c/300 where c is speed of light), and electron wave functions formally obey a Dirac-like continuum equation with zero Dirac mass, rather than the Schrodinger's equation. Associated with this Dirac nature is the fact that the single-particle spectrum has a two-fold pseudo-spin (or valley) degeneracy, in addition to the usual (double) spin degeneracy. Thus the lowenergy spectrum of graphene is made of particle or hole excitations near a double-cone Fermi surface; the apex of the cones are the Dirac points where electron and hole dispersions cross each other, or where the valence and conduction bands become degenerate. The combined 4-fold spin/pseudospin degeneracy gives rise to an emergent SU(4) symmetry, which is useful in analyzing the low-energy properties of graphene and plays a central role in our discussion below. Obviously this is a very unusual band structure, which has attracted much attention both theoretically and experimentally.The observation of quantum Hall effect (QHE) 2,3 when an external, perpendicular magnetic field (B) is applied, provides the most compelling evidence for the 2D massless Dirac nature of electrons in graphene. In particular, such a system is predicted 4,5,6 to support integer QHE with quantized values of Hall conductance given by:with n = 0, 1, 2, · · · is an integer, and g s = g v = 2 are respectively the spin and pseudospin/valley degeneracies; the latter is inherent in the chiral, massless Dirac equation describing 2D graphene. The half integer form in Eq.(1) arises from the Berry phase associated with the pseudospin index, and the experimental observation of the sequence predicted in the form of Eq. (1) is a direct reflection of the massless chiral Dir...

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Carrier Transport in Two-Dimensional Graphene Layers

Cited by 1,175 publications

References 14 publications

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides

Effect of high-κgate dielectrics on charge transport in graphene-based field effect transistors

The enigma of the quantum Hall effect in graphene

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