Graphene Wikipedia, the f

Graphene

Graphene is an atomic-scale honeycomb lattice made of

carbon atoms.

Image of graphene in a transmission electron microscope.

From Wikipedia, the free encyclopedia

Graphene is a one-atom-thick planar sheet of sp

-bonded carbon atoms that are densely packed in a

honeycomb crystal lattice. It can be visualised as an atomic-scale chicken wire made of carbon atoms and
their bonds. The name comes from graphite + -ene; graphite itself consists of many graphene sheets stacked
together.

The carbon-carbon bond length in graphene is about 0.142 nm. Graphene is the basic structural element of
some carbon allotropes including graphite, carbon nanotubes and fullerenes. It can also be considered as an
infinitely large aromatic molecule, the limiting case of the family of flat polycyclic aromatic hydrocarbons
called graphenes.

Contents

1 Description
2 Occurrence and production

2.1 Drawing method
2.2 Epitaxial growth on silicon
carbide
2.3 Epitaxial growth on metal
substrates
2.4 Hydrazine reduction
2.5 Sodium reduction of ethanol
2.6 From nanotubes

3 Properties

3.1 Atomic structure
3.2 Electronic properties
3.3 Electronic transport
3.4 Optical properties

3.4.1 Saturable absorption

3.5 Spin transport
3.6 Anomalous quantum Hall
effect
3.7 Nanostripes: Spin-polarized
edge currents
3.8 Graphene oxide
3.9 Chemical modification
3.10 Thermal properties
3.11 Mechanical properties

4 Potential applications

4.1 Single molecule gas detection
4.2 Graphene nanoribbons
4.3 New graphene devices
4.4 Integrated circuits
4.5 Transparent conducting
electrodes

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4.6 Ultracapacitors
4.7 Graphene biodevices

5 Pseudo-relativistic theory
6 History and experimental discovery
7 See also
8 References
9 External links

Description

A simple, non-technical definition has been given in a recent review on graphene:

Graphene is a flat monolayer of carbon atoms tightly packed into a two-dimensional (2D)
honeycomb lattice, and is a basic building block for graphitic materials of all other dimensionalities.
It can be wrapped up into 0D fullerenes, rolled into 1D nanotubes or stacked into 3D graphite.

[1]

Previously, graphene was also defined in the chemical literature as follows:

A single carbon layer of the graphitic structure can be considered as the final member of the series
naphthalene, anthracene, coronene, etc. and the term graphene should therefore be used to
designate the individual carbon layers in graphite intercalation compounds. Use of the term
"graphene layer" is also considered for the general terminology of carbons.

[2]

The IUPAC compendium of technology states: "previously, descriptions such as graphite layers, carbon
layers, or carbon sheets have been used for the term graphene...it is not correct to use for a single layer a
term which includes the term graphite, which would imply a three-dimensional structure. The term graphene
should be used only when the reactions, structural relations or other properties of individual layers are
discussed". In this regard, graphene has been referred to as an infinite alternant (only six-member carbon
ring) polycyclic aromatic hydrocarbon (PAH). The largest molecule of this type consists of 222 atoms and is

10 benzene rings across.

[3]

Also, a definition of "isolated or free standing graphene" has recently been proposed - "Graphene is a single
atomic plane of graphite, which —and this is essential— is sufficiently isolated from its environment to be

considered free-standing".

[4]

This definition is narrower than the definitions given above and refers to

cleaved, transferred and suspended graphene monolayers. Other forms of graphene, e.g. graphene grown on
various metals can also become free-standing if transferred to, for example, SiO

or suspended.

Occurrence and production

In 2004 physicists from University of Manchester and Institute for Microelectronics Technology,

Chernogolovka, Russia, found

[5]

a way to isolate graphene by peeling it off from graphite with Scotch tape

and optically identify it by transferring them to a silicon dioxide layer on Si. In 2005 the same Manchester

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group together with researchers from the Columbia University (see the History chapter below) would
demonstrate that quasiparticles in graphene are massless Dirac fermions. It is now presumed that tiny
fragments of graphene sheets are produced (along with quantities of other debris) whenever graphite is

abraded, such as when drawing a line with a pencil.

[6]

Graphene produced by exfoliation is presently one of the most expensive materials on Earth, with a sample
that can be placed at the cross section of a human hair costing more than $1,000 as of April 2008 (about

$100,000,000/cm

[6]

The price may fall dramatically, though, if commercial production methods are

developed in the future. On the other hand, the price of epitaxial graphene on SiC is dominated by the silicon

carbide substrate price which is approximately $100/cm

as of 2009. This is about 1,000,000 times cheaper

than exfoliated graphene. Even cheaper graphene produced by transfer from Ni. Korean researchers
reported 20" graphene wafers.

In the literature, specifically that of surface science community, graphene has also been commonly referred
to as monolayer graphite. This community has intensely studied epitaxial graphene on various surfaces (over
300 articles prior to 2004). In some cases, these graphene layers are coupled to the surfaces weakly enough

(by Van der Waals forces) to retain the two dimensional electronic band structure of isolated graphene,

[7][8]

as also happens

[5]

with exfoliated graphene flakes with regard to silicon dioxide.

For example, experiments on epitaxial graphene monolayers on silicon carbide,

[9][10]

have provided the

demonstration of the spectrum of massless Dirac particles in graphene, which is the hallmark signature of its
electronic structure. It was recently shown that even without being transferred graphene on SiC exhibits the

properties of massless Dirac fermions such as the anomalous quantum Hall effect

[11][12][13][14][15]

. The

weak van der Waal forces that provide the cohesion of multilayer graphene stacks do not always affect the
electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of

certain multilayered epitaxial graphenes are identical to that of a single graphene layer,

[16]

in other cases the

properties are affected

[9][10]

as they are for graphene layers in bulk graphite. This effect is theoretically

well understood and is related to the symmetry of the interlayer interactions.

[16]

Drawing method

The British researchers obtained relatively large graphene crystallites (first, only a few microns in size but,
eventually, larger than 1 mm and visible by a naked eye) by mechanical exfoliation (repeated peeling) of 3D
graphite crystals; their motivation was allegedly to study the electrical properties of thin graphite films and,
as purely two-dimensional crystals were unknown before and presumed not to exist(reference required),
their discovery of individual planes of graphite was presumably accidental. Both theory and experiment
previously suggested that perfect two-dimensional (2D) structures could not exist in the free state. It is
believed that intrinsic microscopic roughening on the scale of 1 nm could be important for the stability of 2D

crystals.

[17]

The results obtained in work

[18]

have been confirmed by several groups. Not only graphene but

free-standing atomic layers of boron nitride, mica and dichalcogenides were demonstrated in this paper. For
an example of what graphene looks like, see its photograph below.

Epitaxial growth on silicon carbide

Yet another method is to heat silicon carbide to high temperatures (>1100 °C) to reduce it to graphene.

[19]

This process produces a sample size that is dependent upon the size of the SiC substrate used. The face of
the silicon carbide used for graphene creation, the silicon-terminated or carbon-terminated, highly influences
the thickness, mobility and carrier density of the graphene.

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Many important graphene properties have been identified in graphene produced by this method. For
example, the electronic band-structure (so-called Dirac cone structure) has been first visualized in this

material.

[9][10][20]

Weak anti-localization is observed in this material and not in exfoliated graphene

produced by the pencil trace method.

[21]

Extremely large, temperature independent mobilities have been

observed in SiC epitaxial graphene. They approach those in exfoliated graphene placed on silicon oxide but
still much lower than mobilities in suspended graphene produced by the drawing method. Most recently, the

anomalous quantum Hall effect has been observed in graphene on Si-face and C-face silicon carbide

[12]

[13][14][15]

Epitaxial graphene on silicon carbide can be patterned using standard microelectronics methods. The

possibility of large integrated electronics on SiC epitaxial graphene was first proposed in 2004

[22]

researchers at the Georgia Institute of Technology, only a couple of months after the discovery of isolated
graphene made the drawing method. (A patent for graphene based electronics was applied for in 2003 and
issued in 2006). Since then, important advances have been made. In 2008, researchers at MIT Lincoln Lab

have produced hundreds of transistors on a single chip

[23]

and in 2009 and very high frequency transistors

have been produced at the Hughes Research Laboratories on monolayer graphene on silicon carbide.

[24]

Epitaxial growth on metal substrates

This method uses the atomic structure of a metal substrate to seed the growth of the graphene (epitaxial
growth). Graphene grown on ruthenium doesn't typically yield a sample with a uniform thickness of
graphene layers, and bonding between the bottom graphene layer and the substrate may affect the properties

of the carbon layers.

[25]

Graphene grown on iridium on the other hand is very weakly bonded, uniform in

thickness, and can be made highly ordered. Like on many other substrates, graphene on iridium is slightly
rippled. Due to the long-range order of these ripples generation of minigaps in the electronic band-structure

(Dirac cone) becomes visible.

[26]

High-quality sheets of few layer graphene exceeding 1 cm

(0.2 sq in) in

area have been synthesized via chemical vapor deposition on thin nickel films. These sheets have been
successfully transferred to various substrates, demonstrating viability for numerous electronic

applications.

[11]

. An improvement of this technique has been found in copper foil where the growth

automatically stops after a single graphene layer, and arbitrarily large graphene films can be created

[27]

Hydrazine reduction

Researchers have developed a method of placing graphene oxide paper in a solution of pure hydrazine (a
chemical compound of nitrogen and hydrogen), which reduces the graphene oxide paper into single-layer

graphene.

[28]

Sodium reduction of ethanol

A recent publication has described a process for producing gram-quantities of graphene, by the reduction of
ethanol by sodium metal, followed by pyrolysis of the ethoxide product, and washing with water to remove

sodium salts.

[29]

From nanotubes

Experimental methods for the production of graphene ribbons are reported consisting of cutting open

nanotubes.

[30]

In one such method multi walled carbon nanotubes are cut open in solution by action of

potassium permanganate and sulfuric acid.

[31]

In another method graphene nanoribbons are produced by

plasma etching of nanotubes partly embedded in a polymer film

[32]

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Properties

Atomic structure

The atomic structure of isolated, single-layer graphene was studied by transmission electron microscopy

(TEM) on sheets of graphene suspended between bars of a metallic grid.

[17]

Electron diffraction patterns

showed the expected hexagonal lattice of graphene. Suspended graphene also showed "rippling" of the flat
sheet, with amplitude of about one nanometer. These ripples may be intrinsic to graphene as a result of the

instability of two-dimensional crystals,

[33][34][1]

or may be extrinsic, originating from the ubiquitous dirt

seen in all TEM images of graphene. Atomic resolution real-space images of isolated, single-layer graphene

on silicon dioxide substrates were obtained

[35][36]

by scanning tunneling microscopy. Graphene processed

using lithographic techniques is covered by photoresist residue, which must be cleaned to obtain atomic-

resolution images.

[35]

Such residue may be the "adsorbates" observed in TEM images, and may explain the

rippling of suspended graphene. Rippling of graphene on the silicon dioxide surface was determined by

conformation of graphene to the underlying silicon dioxide, and not an intrinsic effect.

[35]

Graphene sheets in solid form (density > 1 g/cm

) usually show evidence in diffraction for graphite's

0.34 nm (002) layering. This is true even of some single-walled carbon nanostructures.

[37]

However,

unlayered graphene with only (hk0) rings has been found in the core of presolar graphite onions.

[38]

Transmission electron microscope studies show faceting at defects in flat graphene sheets,

[39]

and suggest a

possible role in this unlayered-graphene for two-dimensional dendritic crystallization from a melt.

Electronic properties

Graphene is quite different from most conventional three-dimensional materials. Intrinsic graphene is a
semi-metal or zero-gap semiconductor. Understanding the electronic structure of graphene is the starting
point for finding the band structure of graphite. It was realized early on that the E-k relation is linear for low
energies near the six corners of the two-dimensional hexagonal Brillouin zone, leading to zero effective mass

for electrons and holes.

[40]

[41]

Due to this linear “dispersion” relation at low energies, electrons and holes

near these six points, two of which are inequivalent, behave like relativistic particles described by the Dirac

equation for spin 1/2 particles.

[42][43]

Hence, the electrons and holes are called Dirac fermions, and the six

corners of the Brillouin zone are called the Dirac points.

[42]

The equation describing the E-k relation is

; where the Fermi velocity v

~ 10

m/s.

[43]

Electronic transport

Experimental results from transport measurements show that graphene has a remarkably high electron

mobility at room temperature, with reported values in excess of 15,000 cm

−1

[1]

Additionally, the

symmetry of the experimentally measured conductance indicates that the mobilities for holes and electrons

should be nearly the same.

[41]

The mobility is nearly independent of temperature between 10 K and

100 K,

[44][45][46]

which implies that the dominant scattering mechanism is defect scattering. Scattering by

the acoustic phonons of graphene places intrinsic limits on the room temperature mobility to

200,000 cm

−1

at a carrier density of 10

−2

[46][47]

The corresponding resistivity of the graphene

sheet would be 10

−6

Ω·cm, less than the resistivity of silver, the lowest resistivity substance known at room

temperature.

[48]

However, for graphene on silicon dioxide substrates, scattering of electrons by optical

phonons of the substrate is a larger effect at room temperature than scattering by graphene’s own phonons,

and limits the mobility to 40,000 cm

−1

[46]

Despite the zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the

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Photograph of graphene in

transmitted light. This one atom thick
crystal can be seen with the naked eye

because it absorbs approximately

2.3% of white light, which is π times

fine-structure constant.

order of 4e

/h. The origin of this minimum conductivity is still unclear. However, rippling of the graphene

sheet or ionized impurities in the SiO

substrate may lead to local puddles of carriers that allow

conduction.

[41]

Several theories suggest that the minimum conductivity should be 4e

/πh; however, most

measurements are of order 4e

/h or greater

[1]

and depend on impurity concentration.

[49]

Recent experiments have probed the influence of chemical dopants on the carrier mobility in graphene.

[49][50]

Schedin, et al. doped graphene with various gaseous species (some acceptors, some donors), and

found the initial undoped state of a graphene structure can be recovered by gently heating the graphene in

vacuum. Schedin, et al. reported that even for chemical dopant concentrations in excess of 10

−2

there

is no observable change in the carrier mobility.

[50]

Chen, et al. doped graphene with potassium in ultra high

vacuum at low temperature. They found that potassium ions act as expected for charged impurities in

graphene,

[51]

and can reduce the mobility 20-fold.

[49]

The mobility reduction is reversible on heating the

graphene to remove the potassium.

Due to its two-dimensional property, charge fractionalization (the fractioning of electrons into anyons) is
thought to occur in graphene. It is though that it may therefore be a suitable material for the construction of

quantum computers using anyonic circuits.

[52][53]

Optical properties

Graphene's unique electronic properties produce an unexpectedly high
opacity for an atomic monolayer, with a startlingly simple value: it
absorbs πα ≈ 2.3% of white light, where α is the fine-structure

constant.

[54]

This is "a consequence of the unusual low-energy

electronic structure of monolayer graphene that features electron and
hole conical bands meeting each other at the Dirac point ... [which] is
qualitatively different from more common quadratic massive

bands".

[55]

Based on the Slonczewski-Weiss-McClure (SWMcC) band

model of graphite, the interatomic distance, hopping value and
frequency cancel when the optical conductance is calculated using the
Fresnel equations in the thin-film limit.

This has been confirmed experimentally, but the measurement is not
precise enough to improve on other techniques for determining the

fine-structure constant.

[56]

Recently it has been demonstrated that the bandgap of graphene can
be tuned from 0 to 0.25 eV (about 5 micron wavelength) by applying

voltage to a dual-gate bilayer graphene field-effect transistor (FET) at room temperature.

[57]

. The optical

response of graphene nanoribbons has also been shown to be tunable into the terahertz regime by an applied

magnetic field

[58]

Saturable absorption

It is further confirmed that such unique absorption could become saturated when the input optical intensity
is above a threshold value. This nonlinear optical behavior is termed saturable absorption and the threshold
value is called the saturation fluency. Graphene can be saturated readily under strong excitation over the
visible to near-infrared region, due to the universal optical absorption and zero band gap. This has relevance
for the mode locking of fiber lasers, where wideband tuneability may be obtained using graphene as the
saturable absorber. Due to this special property, graphene has wide application in ultrafast photonics.

[59][60][61]

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Spin transport

Graphene is thought to be an ideal material for spintronics due to small spin-orbit interaction and near
absence of nuclear magnetic moments in carbon. Electrical spin-current injection and detection in graphene

was recently demonstrated up to room temperature.

[62][63][64]

Spin coherence length above 1 micron at

room temperature was observed,

[62]

and control of the spin current polarity with an electrical gate was

observed at low temperature.

[63]

Anomalous quantum Hall effect

The quantum Hall effect is relevant for accurate measuring standards of electrical quantities, and in 1985
Klaus von Klitzing received the Nobel prize for its discovery. The effect concerns the dependence of a
transverse conductivity on a magnetic field, which is perpendicular to a current-carrying stripe. Usually the
phenomenon, the quantization of the so-called Hall conductivity σ

at integer multiples of the basic quantity

/h (where e is the elementary electric charge and h is Planck's constant) can be observed only in very

clean Si or GaAs solids, and at very low temperatures around -270 °C, and at very high magnetic fields.

Graphene in contrast, besides its high mobility and minimum conductivity, and because of certain pseudo-
relativistic peculiarities to be mentioned below, shows particularly interesting behavior just in the presence
of a magnetic field and just with respect to the conductivity-quantization: it displays an anomalous quantum
Hall effect with the sequence of steps shifted by 1/2 with respect to the standard sequence, and with an
additional factor of 4. Thus, in graphene the Hall conductivity is

, where

is the above-mentioned integer "Landau level" index, and the double valley and double spin degeneracies

give the factor of 4.

[1]

Moreover, in graphene these remarkable anomalies can even be measured at room

temperature, i.e. at roughly 20 °C.

[44]

This anomalous behavior is a direct result of the emergent massless

Dirac electrons in graphene. In a magnetic field, their spectrum has a Landau level with energy precisely at
the Dirac point. This level is a consequence of the Atiyah-Singer index theorem. and is half-filled in neutral

graphene,

[42]

leading to the "+1/2" in the Hall conductivity.

[65]

Bilayer graphene also shows the quantum

Hall effect, but with the standard sequence, i.e. with

i.e. with only one of the two

anomalies. Interestingly, concerning the second anomaly, the first plateau at N = 0 is absent, indicating that

bilayer graphene stays metallic at the neutrality point.

[1]

Unlike normal metals, the longitudinal resistance of graphene shows maxima rather than minima for integral
values of the Landau filling factor in measurements of the Shubnikov-de Haas oscillations, which show a

phase shift of π, known as Berry’s phase.

[41][44]

The Berry’s phase arises due to the zero effective carrier

mass near the Dirac points.

[66]

Study of the temperature dependence of the Shubnikov-de Haas oscillations

in graphene reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass from

the E-k relation.

[44]

Nanostripes: Spin-polarized edge currents

Nanostripes of graphene (in the "zig-zag" orientation), at low temperatures, show spin-polarized metallic
edge currents, which also suggests applications in the recent field of spintronics. (In the "armchair"

orientation, the edges behave semiconducting.

[67]

)

Graphene oxide

By oxidizing and chemically processing graphene, and then floating them in water, the graphene flakes form
a single sheet and bond very powerfully. These sheets, called Graphene oxide paper have a measured Tensile

Modulus of 32 GPa.

[68]

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Chemical modification

Soluble fragments of graphene can be prepared in the laboratory

[69]

through chemical modification of

graphite. First, microcrystalline graphite is treated with a strongly acidic mixture of sulfuric acid and nitric
acid. A series of steps involving oxidation and exfoliation result in small graphene plates with carboxyl
groups at their edges. These are converted to acid chloride groups by treatment with thionyl chloride; next,
they are converted to the corresponding graphene amide via treatment with octadecylamine. The resulting
material (circular graphene layers of 5.3 angstrom thickness) is soluble in tetrahydrofuran,
tetrachloromethane, and dichloroethane.

Full hydrogenation from both sides of graphene sheet results in graphane, but partial hydrogenation leads to

hydrogenated graphene

[70]

Thermal properties

The near-room temperature thermal conductivity of graphene was recently measured to be between

(4.84±0.44) ×10

to (5.30±0.48) ×10

−1

. These measurements, made by a non-contact optical

technique, are in excess of those measured for carbon nanotubes or diamond. It can be shown by using the

Wiedemann-Franz law, that the thermal conduction is phonon-dominated.

[71]

However, for a gated graphene

strip, an applied gate bias causing a Fermi energy shift much larger than k

T can cause the electronic

contribution to increase and dominate over the phonon contribution at low temperatures. The ballistic

thermal conductance of graphene is isotropic.

[72]

Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has
basal plane thermal conductivity of over a 1000 W/mK (comparable to diamond). In graphite, the c-axis (out
of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal

planes as well as the larger lattice spacing.

[73]

In addition, the ballistic thermal conductance of a graphene is

shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon

nanotubes.

[74]

Despite its 2-D nature, graphene has 3 acoustic phonon modes. The two in-plane modes (LA, TA) have a
linear dispersion relation, whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to

this, the T

dependent thermal conductivity contribution of the linear modes is dominated at low

temperatures by the T

1.5

contribution of the out of plane mode.

[74]

Some graphene phonon bands display

negative Grüneisen parameters.

[75]

At low temperatures (where most optical modes with positive Grüneisen

parameters are still not excited) the contribution from the negative Grüneisen parameters will be dominant
and thermal expansion coefficient (which is directly proportional to Grüneisen parameters) negative. The
lowest negative Grüneisen parameters correspond to the lowest transversal acoustic ZA modes. Phonon
frequencies for such modes increase with the in-plane lattice parameter since atoms in the layer upon
stretching will be less free to move in the z direction. This is similar to the behaviour of a string which is
being stretched will have vibrations of smaller amplitude and higher frequency. This phenomenon, named

"membrane effect", was predicted by Lifshitz in 1952.

[76]

Mechanical properties

As of 2009, graphene appears the strongest material ever tested. Measurements have shown that graphene

has a breaking strength 200 times greater than steel.

[77]

However, the process of separating it from graphite,

where it occurs naturally, will require some technological development before it is economical enough to be

used in industrial processes.

[78]

Utilizing an atomic force microscope (AFM), the spring constant of suspended graphene sheets have been

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measured. Graphene sheets, held together by van der Waals forces, were suspended over silicon dioxide
cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was in the range
1-5 N/m and the Young's modulus was 0.5 TPa, which differs from that of the bulk graphite. These high
values make graphene very strong and rigid. These intrinsic properties could lead to utilizing graphene for

NEMS applications such as pressure sensors, and resonators.

[79]

As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative
displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of
infinite size), the Mermin-Wagner theorem shows that the amplitude of long-wavelength fluctuations will
grow logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of
infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in
relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral
tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in

suspended layers of graphene,

[17]

and it has been proposed that the ripples are caused by thermal

fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether

graphene is truly a 2D structure.

[33][34][1]

Potential applications

Single molecule gas detection

Graphene makes an excellent sensor due to its 2D structure. The fact that its entire volume is exposed to its
surrounding makes it very efficient to detect adsorbed molecules. Molecule detection is indirect: as a gas
molecule adsorbs to the surface of graphene, the location of adsorption experiences a local change in
electrical resistance. While this effect occurs in other materials, graphene is superior due to its high electrical
conductivity (even when few carriers are present) and low noise which makes this change in resistance

detectable.

[50]

Graphene nanoribbons

Graphene nanoribbons (GNRs) are essentially single layers of graphene that are cut in a particular pattern to
give it certain electrical properties. Depending on how the un-bonded edges are configured, they can either
be in a zigzag or armchair configuration. Calculations based on tight binding predict that zigzag GNRs are
always metallic while armchairs can be either metallic or semiconducting, depending on their width.
However, recent density functional theory calculations show that armchair nanoribbons are semiconducting

with an energy gap scaling with the inverse of the GNR width.

[80]

Indeed, experimental results show that the

energy gaps do increase with decreasing GNR width.

[81]

However, as of February 2008, no experimental

results have measured the energy gap of a GNR and identified the exact edge structure. Zigzag nanoribbons
are also semiconducting and present spin polarized edges. Their 2D structure, high electrical and thermal
conductivity, and low noise also make GNRs a possible alternative to copper for integrated circuit
interconnects. Some research is also being done to create quantum dots by changing the width of GNRs at

select points along the ribbon, creating quantum confinement.

[82]

Due to its high electronic quality, graphene has also attracted the interest of technologists who see them as a
way of constructing ballistic transistors. Graphene exhibits a pronounced response to perpendicular external

electric fields allowing one to built FETs (field-effect transistors). In their 2004 paper,

[5]

the Manchester

group demonstrated FETs with a "rather modest" on-off ratio of ~30 at room temperature. In 2006, Georgia

Tech researchers announced that they had successfully built an all-graphene planar FET with side gates.

[83]

Their devices showed changes of 2% at cryogenic temperatures. The first top-gated FET (on-off ratio of <2)

was demonstrated by researchers of AMICA and RWTH Aachen University in 2007.

[84]

Graphene

nanoribbons may prove generally capable of replacing silicon as a semiconductor in modern technology.

[85]

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New graphene devices

Facing the fact that current graphene transistors show a very poor on-off ratio, researchers are trying to find
ways for improvement. In 2008 researchers of AMICA and University of Manchester demonstrated a new
switching effect in graphene field-effect devices. This switching effect is based on a reversible chemical
modification of the graphene layer and gives an on-off ratio of greater than six orders of magnitude. These

reversible switches could potentially be applied to nonvolatile memories.

[86]

In 2009 researchers at the Politecnico di Milano demonstrated four different types of logic gates, each

comprised of a single graphene transistor.

[87]

In the same year, the Massachusetts Institute of Technology

researchers built an experimental graphene chip known as a frequency multiplier. It is capable of taking an
incoming electrical signal of a certain frequency and producing an output signal that is a multiple of that

frequency.

[88]

Although these graphene chips open up a range of new applications their practical use is

limited by a very small voltage gain (typically, the amplitude of the output signal is about 40 times less than
that of the input signal). Moreover, none of these circuits was demonstrated to operate at frequencies higher
than 25 kHz.

Integrated circuits

Graphene has the ideal properties to be an excellent component of integrated circuits. Graphene has a high
carrier mobility, as well as low noise allowing it to be utilized as the channel in a FET. The issue is that single
sheets of graphene are hard to produce, and even harder to make on top of an appropriate substrate.
Researchers are looking into methods of transferring single graphene sheets from their source of origin
(mechanical exfoliation on SiO

/ Si or thermal graphitization of a SiC surface) onto a target substrate of

interest.

[89]

In 2008, the smallest transistor so far, one atom thick, 10 atoms wide was made of graphene.

[90]

IBM announced in December 2008 that they have fabricated and characterized graphene transistors

operating at GHz frequencies.

[91]

In May 2009 a team from Stanford University, University of Florida and

Lawrence Livermore National Laboratory announced that they have created an n-type transistor, which

means that both and n and p-type transistors have now been created with graphene.

[92]

At the same time,

the researchers at the Politecnico di Milano demonstrated the first functional graphene integrated circuit – a

complementary inverter consisting of one p- and one n-type graphene transistor.

[93]

However, this inverter

also suffered from a very low voltage gain.

Transparent conducting electrodes

Graphene's high electrical conductivity and high optical transparency make it a candidate for transparent
conducting electrodes, required for such applications as touchscreens, liquid crystal displays, organic
photovoltaic cells, and Organic light-emitting diodes. In particular, graphene's mechanical strength and
flexibility are advantageous compared to indium tin oxide, which is brittle, and graphene films may be

deposited from solution over large areas.

[94][95]

Large-area, continuous, transparent, and highly conducting few-layered graphene ﬁlms were produced by
chemical vapor deposition and used as anode for application in photovoltaic devices. A greatly improved
power conversion efficiency (PCE) up to 1.71% was demonstrated, which is 55.2% of the PCE of a control

device based on indium-tin-oxide.

[96]

Ultracapacitors

Due to the incredibly high surface area to mass ratio of graphene, one potential application is in the
conductive plates of ultracapacitors. It is believed that graphene could be used to produce ultracapacitors

with a greater energy storage density than is currently available.

[97]

Graphene - Wikipedia, the free encyclopedia

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10 z 20

2009-11-29 15:57

Energy of the electrons with

wavenumber k in graphene,

calculated in the Tight Binding-

approximation. The unoccupied

rsp. occupied states, coloured

in blue-red rsp. yellow-green,

touch each other without

energy gap exactly at the above-

mentioned six k-vectors.

Graphene biodevices

Graphene's modifiable chemistry, large surface area, atomic-thickness and molecularly-gatable structure
make antibody-functionalized-graphene-sheets excellent candidate for mammalian and microbial detection

and diagnosis.

[98]

Pseudo-relativistic theory

The electrical properties of graphene can be described by a conventional
tight-binding model; in this model the energy of the electrons with
wavenumber k is

[40][42]

with the nearest-neighbor hopping energy γ

≈ 2.8 eV and the lattice constant a ≈ 2.46 Å. Conduction and

valence band, respectively, correspond to the different signs in the above dispersion relation; they touch
each other in six points, the "K-values". However, only two of these six points are independent, whereas the
rest is equivalent by symmetry. In the vicinity of the K-points the energy depends linearly on the
wavenumber, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms,
the wave function even has an effective 2-spinor structure. As a consequence, at low energies, even
neglecting the true spin, the electrons can be described by an equation which is formally equivalent to the
massless Dirac equation. Moreover, in the present case this pseudo-relativistic description is restricted to the

chiral limit, i.e., to vanishing rest mass M

, which leads to interesting additional features:

[42]

Here v

~ 10

is the Fermi velocity in graphene which replaces the velocity of light in the Dirac theory; is

the vector of the Pauli matrices,

is the two-component wave function of the electrons, and E is their

energy.

[67]

History and experimental discovery

The term graphene first appeared in 1987

[99]

in order to describe single sheets of graphite as one of the

constituents of graphite intercalation compounds (GICs); conceptually a GIC is a crystalline salt of the

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11 z 20

2009-11-29 15:57

intercalant and graphene. The term was also used in early descriptions of carbon nanotubes,

[100]

as well as

for epitaxial graphene,

[101]

and polycyclic aromatic hydrocarbons.

[102]

Larger graphene molecules or sheets (so that they can be considered as true isolated 2D crystals) cannot be
grown even in principle. An article in Physics Today reads:

"Fundamental forces place seemingly insurmountable barriers in the way of creating [2D crystals] ...
Nascent 2D crystallites try to minimize their surface energy and inevitably morph into one of the rich
variety of stable 3D structures that occur in soot. But there is a way around the problem. Interactions
with 3D structures stabilize 2D crystals during growth. So one can make 2D crystals sandwiched
between or placed on top of the atomic planes of a bulk crystal. In that respect, graphene already exists
within graphite ... One can then hope to fool Nature and extract single-atom-thick crystallites at a low
enough temperature that they remain in the quenched state prescribed by the original higher-temperature
3D growth."

[103]

Single layers of graphite were previously (starting from the 1970s) grown epitaxially on top of other

materials.

[104]

This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp

-bonded

carbon atoms, as in free-standing graphene. However, there is significant charge transfer from the substrate
to the epitaxial graphene, and, in some cases, hybridization between the d orbitals of the substrate atoms and
π orbitals of graphene, which significantly alters the electronic structure of the epitaxial graphene.

Single layers of graphite were also observed by transmission electron microscopy within bulk materials (see

section Occurrence), in particular inside soot obtained by chemical exfoliation.

[6]

There have also been a

number of efforts to make very thin films of graphite by mechanical exfoliation (starting from 1990 and

continuing until after 2004)

[6]

but nothing thinner than 50 to 100 layers was produced during these years.

A key advance in the science of graphene came when Andre Geim and Kostya Novoselov at Manchester

University managed to extract single-atom-thick crystallites (graphene) from bulk graphite in 2004.

[5]

The

Manchester researchers pulled out graphene layers from graphite and transferred them onto thin silicon
dioxide on a silicon wafer in a process sometimes called micromechanical cleavage or, simply, the Scotch
tape technique. The silicon dioxide electrically isolated the graphene, and was weakly interacting with the
graphene, providing nearly charge-neutral graphene layers. The silicon beneath the silicon dioxide could be
used as a "back gate" electrode to vary the charge density in the graphene layer over a wide range.

The micromechanical cleavage technique led directly to the first observation of the anomalous quantum Hall

effect in graphene,

[44][66]

which provided direct evidence of the theoretically predicted pi Berry's phase of

massless Dirac fermions in graphene. The anomalous quantum Hall effect in graphene was reported
simulataneously by Geim and Novoselov as well as Philip Kim and Yuanbo Zhang from Columbia
University.

Geim has received several awards for his pioneering research on graphene including the 2007 Mott medal
for the "discovery of a new class of materials – free-standing two-dimensional crystals – in particular
graphene", the 2008 EuroPhysics Prize (together with Novoselov) "for discovering and isolating a single
free-standing atomic layer of carbon (graphene) and elucidating its remarkable electronic properties", and
the 2009 Körber Prize for "develop[ing] the first two-dimensional crystals made of carbon atoms". In 2008
and 2009, the Reuters (which also runs a bibliometric service Web of Science) tipped him as one of the

front-runners for a Nobel prize in Physics

[105]

The theory of graphene was first explored by Philip R Wallace in 1947 as a starting point for understanding
the electronic properties of more complex, 3D graphite. The emergent massless Dirac equation was first

pointed out by Gordon W. Semenoff

[42]

and David P. DeVincenzo and Eugene J. Mele.

[106]

Semenoff

emphasized the occurrence in a magnetic field of an electronic Landau level precisely at the Dirac point.

This level is responsible for the anomalous integer quantum Hall effect.

[44][65][66]

Later, single graphene

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12 z 20

2009-11-29 15:57

layers were also observed directly by electron microscopy.

[17]

More recently, graphene samples prepared on nickel films, and on both the silicon face and carbon face of

silicon carbide, have shown the anomalous quantum Hall effect directly in electrical measurements.

[11][12]

[13][14][15]

Graphitic layers on the carbon face of silicon carbide show a clear Dirac spectrum in angle-

resolved photoemission experiments, and the anomalous quantum Hall effect is observed in cyclotron

resonance and tunneling experiments.

[107]

Even though graphene on nickel and on silicon carbide have both

existed in the laboratory for decades, it was graphene mechanically exfoliated on silicon dioxide that
provided the first proof of the Dirac fermion nature of electrons in graphene.

See also

Aromaticity
Exfoliated graphite
nano-platelets
Fullerenes

Polycyclic aromatic
hydrocarbons
Carbon nanotubes
Graphene nanoribbons

Graphene Oxide Paper
Graphite
List of software for
nanostructures modeling

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External links

BBC News report (http://news.bbc.co.uk/2/hi/science/nature/3944651.stm)
BBC News report, latest 18-APR-2008 (http://news.bbc.co.uk/2/hi/science/nature/7352464.stm)
Electrons lose their mass in carbon sheets (http://physicsworld.com/cws/article/news/23538) Physics
Web (09-Nov-2005)
Potential for graphene computer chips, with explanation of technical issues/problems
(http://gtresearchnews.gatech.edu/newsrelease/graphene.htm)
Quantum weirdness on the end of your pencil (http://www.newscientist.com/channel/fundamentals
/mg19125591.700) Philip Ball, New Scientist Magazine issue 2559, (8 July 2006)
Talks (http://online.kitp.ucsb.edu/online/graphene_m07/) at the Electronic Properties of Graphene
conference (January 8-19, 2007)
"Experiment finds graphene's missing pi (http://physicsworld.com/cws/article/news/31136) ".
physicsworld.com. 2007-09-14. http://physicsworld.com/cws/article/news/31136. Retrieved
2009-08-15.
Carbon nanosheets promise super-fast chips (http://technology.newscientist.com/channel
/tech/dn13158-carbon-nanosheets-promise-superfast-chips.html?feedId=online-news_rss20) Graphene
has the highest electronic quality among all known materials, New Scientist, 8 January 2008
Most of graphene papers published by Andre Geim's group are downloadable here
(http://onnes.ph.man.ac.uk/nano/Publications.html#Graphene)
Researchers leap a nano hurdle - ABC Online (Australia) (http://www.abc.net.au/science/articles
/2008/01/29/2148939.htm?site=science&topic=latest) Development of a simpler method of graphene
production.
Is Graphene the New Silicon? (http://www.nsf.gov/news/news_summ.jsp?cntn_id=111341&
org=NSF&from=news) National Science Foundation, March 27, 2008
"Band structure of graphene (http://www.nanohub.org/resource_files/2005/12/00723/2004.10.20-
l21-ece453.pdf) " (PDF). http://www.nanohub.org/resource_files/2005/12/00723/2004.10.20-
l21-ece453.pdf. Retrieved 2009-08-15.
General notes on graphene (http://heybryan.org/graphene.html)
Katherine Bourzac (17 July 2008). "Strongest Material Ever Tested: Graphene, praised for its
electrical properties, has been proven the strongest known material
(http://www.technologyreview.com/Nanotech/21098/?a=f) ". Technology Review magazine.
http://www.technologyreview.com/Nanotech/21098/?a=f.
Antonio H. Castro Neto (12 May 2009). "Pauling’s dreams for graphene (http://physics.aps.org
/articles/v2/30) ". http://physics.aps.org/articles/v2/30.

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