Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

The rise of graphene

This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

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Two-dimensional gas of massless Dirac fermions in graphene

Two-dimensional materials are attractive for use in next-generation nanoelectronic devices because, compared to one-dimensional materials, it is relatively easy to fabricate complex structures from them. The most widely studied two-dimensional material is graphene, both because of its rich physics and its high mobility. However, pristine graphene does not have a bandgap, a property that is essential for many applications, including transistors. Engineering a graphene bandgap increases fabrication complexity and either reduces mobilities to the level of strained silicon films or requires high voltages. Although single layers of MoS(2) have a large intrinsic bandgap of 1.8 eV (ref. 16), previously reported mobilities in the 0.5-3 cm(2) V(-1) s(-1) range are too low for practical devices. Here, we use a halfnium oxide gate dielectric to demonstrate a room-temperature single-layer MoS(2) mobility of at least 200 cm(2) V(-1) s(-1), similar to that of graphene nanoribbons, and demonstrate transistors with room-temperature current on/off ratios of 1 × 10(8) and ultralow standby power dissipation. Because monolayer MoS(2) has a direct bandgap, it can be used to construct interband tunnel FETs, which offer lower power consumption than classical transistors. Monolayer MoS(2) could also complement graphene in applications that require thin transparent semiconductors, such as optoelectronics and energy harvesting.

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Single-layer MoS2 transistors

The remarkable mechanical properties of carbon nanotubes arise from the exceptional strength and stiffness of the atomically thin carbon sheets (graphene) from which they are formed. In contrast, bulk graphite, a polycrystalline material, has low fracture strength and tends to suffer failure either by delamination of graphene sheets or at grain boundaries between the crystals. Now Stankovich et al. have produced an inexpensive polymer-matrix composite by separating graphene sheets from graphite and chemically tuning them. The material contains dispersed graphene sheets and offers access to a broad range of useful thermal, electrical and mechanical properties. Individual sheets of graphene can be readily incorporated into a polymer matrix, giving rise to composite materials having potentially useful electronic properties. Graphene sheets—one-atom-thick two-dimensional layers of sp2-bonded carbon—are predicted to have a range of unusual properties. Their thermal conductivity and mechanical stiffness may rival the remarkable in-plane values for graphite (∼3,000 W m-1 K-1 and 1,060 GPa, respectively); their fracture strength should be comparable to that of carbon nanotubes for similar types of defects1,2,3; and recent studies have shown that individual graphene sheets have extraordinary electronic transport properties4,5,6,7,8. One possible route to harnessing these properties for applications would be to incorporate graphene sheets in a composite material. The manufacturing of such composites requires not only that graphene sheets be produced on a sufficient scale but that they also be incorporated, and homogeneously distributed, into various matrices. Graphite, inexpensive and available in large quantity, unfortunately does not readily exfoliate to yield individual graphene sheets. Here we present a general approach for the preparation of graphene-polymer composites via complete exfoliation of graphite9 and molecular-level dispersion of individual, chemically modified graphene sheets within polymer hosts. A polystyrene–graphene composite formed by this route exhibits a percolation threshold10 of ∼0.1 volume per cent for room-temperature electrical conductivity, the lowest reported value for any carbon-based composite except for those involving carbon nanotubes11; at only 1 volume per cent, this composite has a conductivity of ∼0.1 S m-1, sufficient for many electrical applications12. Our bottom-up chemical approach of tuning the graphene sheet properties provides a path to a broad new class of graphene-based materials and their use in a variety of applications.

Graphene-based composite materials

We have produced ultrathin epitaxial graphite films which show remarkable 2D electron gas (2DEG) behavior. The films, composed of typically three graphene sheets, were grown by thermal decomposition on the (0001) surface of 6H−SiC, and characterized by surface science techniques. The low-temperature conductance spans a range of localization regimes according to the structural state (square resistance 1.5 kΩ to 225 kΩ at 4 K, with positive magnetoconductance). Low-resistance samples show characteristics of weak localization in two dimensions, from which we estimate elastic and inelastic mean free paths. At low field, the Hall resistance is linear up to 4.5 T, which is well-explained by n-type carriers of density 1012 cm-2 per graphene sheet. The most highly ordered sample exhibits Shubnikov−de Haas oscillations that correspond to nonlinearities observed in the Hall resistance, indicating a potential new quantum Hall system. We show that the high-mobility films can be patterned via conventional lithographic...

Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics.

We have produced ultrathin epitaxial graphite films which show remarkable 2D electron gas (2DEG) behavior. The films, composed of typically 3 graphene sheets, were grown by thermal decomposition on the (0001) surface of 6H-SiC, and characterized by surface-science techniques. The low-temperature conductance spans a range of localization regimes according to the structural state (square resistance 1.5 kOhm to 225 kOhm at 4 K, with positive magnetoconductance). Low resistance samples show characteristics of weak-localization in two dimensions, from which we estimate elastic and inelastic mean free paths. At low field, the Hall resistance is linear up to 4.5 T, which is well-explained by n-type carriers of density 10^{12} cm^{-2} per graphene sheet. The most highly-ordered sample exhibits Shubnikov - de Haas oscillations which correspond to nonlinearities observed in the Hall resistance, indicating a potential new quantum Hall system. We show that the high-mobility films can be patterned via conventional lithographic techniques, and we demonstrate modulation of the film conductance using a top-gate electrode. These key elements suggest electronic device applications based on nano-patterned epitaxial graphene (NPEG), with the potential for large-scale integration.

Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics

http://absimage.aps.org/image/MAR05/MWS_MAR05-2004-006526.pdf

Asmerom Ogbazghi

Papers

Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics.

Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics

Ultrathin epitaxial graphite layers : 2D electron gas properties and a route towards graphene based nanoelectronics