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Graphene is one of the crystalline forms of carbon, alongside diamond, graphite, carbon
nanotubes and fullerenes. In this material, carbon atoms are arranged in a regular hexagonal pattern.
Graphene can be described as a one-atom thick layer of the layered mineral graphite. High-quality
graphene is very strong, light, nearly transparent, and an excellent conductor of heat and electricity.
Its interaction with other materials and with light, and its inherently two-dimensional nature, produce
unique properties.
At the time of its isolation in 2004,[1] many researchers studying carbon nanotubes were already
familiar with the composition, structure and properties of graphene, which had been calculated
decades earlier. The combination of familiarity, extraordinary properties and surprising ease of
isolation enabled an explosion in graphene research. Andre Geim andKonstantin Novoselov at
the University of Manchester won the Nobel Prize in Physics in 2010 "for groundbreaking experiments
regarding the two-dimensional material graphene".
Description[edit]
Graphene is an allotrope of carbon whose structure is a single planar sheet of sp2-bonded carbon
atoms, that are densely packed in a honeycomb crystal lattice.[3] The termgraphene was coined as a
combination of graphite and the suffix -ene by Hanns-Peter Boehm,[4] who described single-layer
carbon foils in 1962.[5] Graphene is most easily visualized as an atomic-scale chicken wire made of
carbon atoms and their bonds.
The carbon-carbon bond length in graphene is about 0.142 nanometers.[6] Graphene sheets stack to
form graphite with an interplanar spacing of 0.335 nm. Graphene is the basic structural element of
some carbon allotropes including graphite, charcoal, carbon nanotubes and fullerenes. It can also be
considered as an indefinitely large aromatic molecule, the limiting case of the family of flat polycyclic
aromatic hydrocarbons.
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 incorrect 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."[7] In this regard, graphene has been referred to as an infinite
alternant (only six-member carbon ring) polycyclic aromatic hydrocarbon (PAH). The largest known
isolated molecule of this type consists of 222 atoms and is 10 benzene rings across. [8] It has proven
difficult to synthesize even slightly bigger molecules, and they still remain "a dream of many organic
and polymer chemists".[9]
Furthermore, ab initio calculations show that a graphene sheet is thermodynamically unstable with
respect to other fullerene structures if its size is less than about 20 nm (“graphene is the least stable
structure until about 6000 atoms”) and becomes the most stable one (as within graphite) only for sizes
larger than 24,000 carbon atoms.[10] The flat graphene sheet is also known to be unstable with respect
to scrolling i.e. curling up, which is its lower-energy state.[11]
A definition of "isolated or free-standing graphene" has also 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."[12] This definition is narrower than the definitions given
above and refers to cleaved, transferred and suspended graphene monolayers. [citation needed]
Other forms of graphene, such as graphene grown on various metals, can also become free-standing
if, for example, suspended or transferred to silicon dioxide (SiO2). A new example of isolated
graphene is graphene on silicon carbide (SiC) after its passivation with hydrogen.[13]
Occurrence and production[edit]
A lump of graphite, a graphene transistor and a tape dispenser. Donated to the Nobel Museum in Stockholm by Andre
Geim and Konstantin Novoselov in 2010.
In essence, graphene is an isolated atomic plane of graphite. From this perspective, graphene has
been known since the invention of X-ray crystallography. Graphene planes become even better
separated in intercalated graphite compounds. In 2004, physicists at the University of Manchester and
the Institute for Microelectronics Technology, Chernogolovka, Russia, first isolated individual
graphene planes by using adhesive tape.[14] They also measured electronic properties of the obtained
flakes and showed their unique properties.[15] In 2005 the same Manchester Geim group together with
the Philip Kim group from Columbia University (see the History section) demonstrated
thatquasiparticles in graphene were massless Dirac fermions. These discoveries led to an explosion
of interest in graphene.
Since then, hundreds of researchers have entered the area, resulting in an extensive search for
relevant earlier papers. The Manchester researchers themselves published the first literature
review.[3] They cite several papers in which graphene or ultra-thin graphitic layers
wereepitaxially grown on various substrates. Also, they note a number of pre-2004 reports in which
intercalated graphite compounds were studied in a transmission electron microscope. In the latter
case, researchers occasionally observed extremely thin graphitic flakes ("few-layer graphene" and
possibly even individual layers). An early detailed study on few-layer graphene dates back to
1962.[16] The earliest TEM images of few-layer graphene were published by G. Ruess and F. Vogt in
1948.[17] In 1859 Benjamin Collins Brodie was aware of the highly lamellar structure of thermally
reduced graphite oxide.[18] It was studied in detail by V. Kohlschütter and P. Haenni in 1918, who also
described the properties of graphite oxide paper.[19]
It is now well known 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. [14] There was
little interest in this graphitic residue before 2004/05 and, therefore, the discovery of graphene is often
attributed to Andre Geim and colleagues[20] who introduced graphene in its modern incarnation.
In 2008, graphene produced by exfoliation was 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 2).[14] Since then, exfoliation procedures have been scaled up, and now
companies sell graphene in large quantities.[21][22] On the other hand, the price of epitaxial graphene
on SiC is dominated by the substrate price, which is approximately $100/cm 2 as of 2009. Byung Hee
Hong and his team in South Korea pioneered the synthesis of large-scale graphene films using
chemical vapour deposition (CVD) on thin nickel layers, which triggered chemical researches toward
the practical applications of graphene,[23][24] with wafer sizes up to 30 inches (760 mm) reported.[25]
In 2011 the Institute of Electronic Materials Technology and Department of Physics, Warsaw
University announced a joint development of acquisition technology of large pieces of graphene with
the best quality so far.[26][27]
In the literature, specifically that of the 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,[28][29] as also happens[15] with exfoliated
graphene flakes with regard to SiO2. An example of weakly coupled epitaxial graphene is the one
grown on SiC (see below).
Exfoliated graphene[edit]
In 2004, the Manchester group obtained graphene by micro-mechanical alleviation of graphite. They
used adhesive tape to repeatedly split graphite crystals into increasingly thinner pieces. They may not
have been the first to use this technique—US Patent 6,667,100, filed in 2002, describes the process
in detail, applied to commercially available flexible expanded graphite sheet, to achieve a graphite
thickness of 0.01 thousandth of an inch. The tape with attached optically transparent flakes was
dissolved in acetone, and, after a few further steps, the flakes including monolayers were sedimented
on a silicon wafer. Individual atomic planes were then hunted with an optical microscope. A year later,
the researchers simplified the technique and started using dry deposition, avoiding the stage when
graphene floated in a liquid. Relatively large crystallites (first, only a few micrometres in size but
eventually larger than 1 mm and visible to the naked eye) were obtained with the technique. It is often
referred to as a scotch tape or drawing method. The latter name appeared because the dry deposition
resembles drawing with a piece of graphite.[30] The key for the success probably was the use of highthroughput visual recognition of graphene on a properly chosen substrate, which provides a small but
noticeable optical contrast. The optical properties section below contains a photograph of what
graphene looks like.
The isolation of graphene led to the current research boom. Previously, free-standing atomic planes
were often "presumed not to exist"[15] because they are thermodynamically unstable on a nanometer
scale[10] and, if unsupported, have a tendency to scroll and buckle.[9] It is currently believed that
intrinsic microscopic roughening on the scale of 1 nm could be important for the stability of purely 2D
crystals.[31]
There were a number of previous attempts to make atomically thin graphitic films by using exfoliation
techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were
obtained. These efforts were reviewed in 2007.[3] Furthermore, a couple of very old papers were
recently unearthed[16] in which researchers tried to isolate graphene starting with intercalated
compounds (see History and experimental discovery). These papers reported the observation of very
thin graphitic fragments (possibly monolayers) by transmission electron microscopy. Neither of the
earlier observations was sufficient to "spark the graphene gold rush", until the Science paper did so by
reporting not only macroscopic samples of extracted atomic planes but, importantly, their unusual
properties such as the bipolar transistor effect, ballistic transport of charges, large quantum
oscillations, etc. The discovery of such interesting qualities intrinsic to graphene gave an immediate
boost to further research and several groups quickly repeated the initial result and moved further.
These breakthroughs also helped to attract attention to other production techniques, such as epitaxial
growth of ultra-thin graphitic films. In particular, it has later been found that graphene monolayers
grown on SiC and Ir are weakly coupled to these substrates (how weakly remains debated) and the
graphene–substrate interaction can be passivated further.[13]
Not only graphene but also free-standing atomic planes of boron nitride, mica, dichalcogenides and
complex oxides were obtained by using the drawing method.[32] Unlike graphene, the other 2D
materials have so far attracted surprisingly little attention.
Epitaxial growth on silicon carbide[edit]
Main article: Carbide-derived Carbon
Another method of obtaining graphene is to heat silicon carbide (SiC) to high temperatures
(>1,100 °C) under low pressures (~10−6 torr) to reduce it to graphene.[33] This process produces
epitaxial graphene with dimensions dependent upon the size of the SiC substrate (wafer). The face of
the SiC used for graphene formation, silicon- or carbon-terminated, highly influences the thickness,
mobility and carrier density of the graphene.
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.[34][35][36] Weak anti-localization is observed in this material and not in exfoliated graphene
produced by the pencil-trace method.[37] 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. 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.[38][39][40][41][42][43]
The weak van der Waals force that provides the cohesion of multilayer graphene stacks does 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,[44] in other cases the properties are affected[34][35] 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.[44]
Epitaxial graphene on SiC can be patterned using standard microelectronics methods. The possibility
of large integrated electronics on SiC-epitaxial graphene was first proposed in 2004,[45] and a patent
for graphene-based electronics was filed provisionally in 2003 and issued in 2006. [46] Since then,
important advances have been made. In 2008, researchers atMIT Lincoln Lab produced hundreds of
transistors on a single chip[47] and in 2009, very high frequency transistors were produced at the
Hughes Research Laboratories on monolayer graphene on SiC.[48] Band gap of the epitaxial graphene
can be tuned by irradiating with laser beams; modified graphene has a lot of advantages in device
application.[49]
Epitaxial growth on metal substrates[edit]
This method uses source and 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.[50] On the other hand, graphene grown
on iridium 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.[51] Highquality sheets of few-layer graphene exceeding 1 cm2 (0.2 sq in) in area have been synthesized via
chemical vapor deposition on thin nickel films with methane as a carbon source. These sheets have
been successfully transferred to various substrates, demonstrating viability for numerous
applications.[25][38][52]
An improvement of this technique has employed copper foil; at very low pressure, the growth of
graphene automatically stops after a single graphene layer forms, and arbitrarily large graphene films
can be created.[25][53] The aforementioned single layer growth is also due to the low concentration of
carbon in methane. Larger hydrocarbon gasses, such as ethaneand propane, will lead to the growth
of bilayer graphene.[54] In this light, it is obvious that at atmospheric-pressure CVD growth, multilayer
graphene will also form on copper (similar to that grown on nickel films).[55] Growth of graphene has
been demonstrated at temperatures compatible with conventional CMOS processing, using a nickelbased alloy with gold as catalysts.[56]
Graphite oxide reduction[edit]
Graphite oxide reduction was probably historically the first method of graphene synthesis. P. Boehm
reported monolayer flakes of reduced graphene oxide already in 1962.[57] In this early work existence
of monolayer reduced graphene oxide flakes was demonstrated. The contribution of Boehm was
recently acknowledged by Nobel prize winner for graphene research, Andre Geim: (Many Pioneers in
Graphene Discovery). Graphite oxide exfoliation can be achieved by rapid heating and yields highly
dispersed carbon powder with a few percent of graphene flakes. Reduction of graphite oxide
monolayer films e.g. by hydrazine, annealing in argon/hydrogen was reported to yield graphene films.
However, the quality of graphene produced by graphite oxide reduction is lower compared to e.g.
scotch-tape graphene due to incomplete removal of various functional groups by existing reduction
methods. Furhermore, the oxidation protocol introduces permanent defects due to over-oxidation.
Recently, the oxidation protocol was essentially enhanced to yield graphene oxide with an almost
intact carbon framework that allows the highly efficient removal of functional groups. The measured
mobility of charge carriers exceeded 1000 cm2/Vs for the best quality of flakes.[58] Some spectroscopic
analysis of reduced graphene oxide can be found in the literature. [59][60] Applying a layer of graphite
oxide film to a DVD disc and burning it in a DVD writer resulted in a thin graphene film with high
electrical conductivity (1738 siemens per meter) and specific surface area (1520 square meters per
gram), besides being highly resistant and malleable.[61][62] In February 2013 researchers from UCLA,
led by professor Richard Kaner, announced a novel technique to produce graphene supercapacitors
based on the DVD burner approach.[63]
Growth from metal-carbon melts[edit]
The general idea in this process is to dissolve carbon atoms inside a transition metal melt at a certain
temperature, and then allow the dissolved carbon to precipitate out at lower temperatures as single
layer graphene (SLG).[64] The metal is first melted in contact with a carbon source. This source could
be the graphite crucible inside which melting is carried out or it could be the graphite powder or chunk
sources, which are simply placed in contact with the melt. Keeping the melt in contact with carbon
source at a given temperature will give rise to dissolution and saturation of carbon atoms in the melt
based on the binary phase diagram of metal-carbon. Upon lowering the temperature, solubility of the
carbon in the molten metal will decrease and the excess amount of carbon will precipitate on top of
the melt. The floating layer can be either skimmed or allowed to freeze for removal afterwards.
Different morphology including thick graphite, few layer graphene (FLG) and SLG were observed on
metal substrate. The Raman spectroscopy proved that SLG has been successfully grown on nickel
substrate. The SLG Raman spectrum featured no D and D′ band, indicating the pristine and highquality nature of SLG. Among transition metals, nickel provides a better substrate for growing SLG.
Since nickel is not Raman active, the direct Raman spectroscopy of graphene layers on top of the
nickel is achievable. The graphene-metal composite could be utilized in thermal interface materials for
thermal management applications.[64]
Pyrolysis of sodium ethoxide[edit]
A 2008 publication 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.[65]
From nanotubes[edit]
Experimental methods for the production of graphene ribbons are reported consisting of cutting
open nanotubes.[66] In one such method multi-walled carbon nanotubes are cut open in solution by
action of potassium permanganate and sulfuric acid.[67] In another method graphene nanoribbons are
produced by plasma etching of nanotubes partly embedded in apolymer film.[68]
From graphite by sonication[edit]
It consists in dispersing graphite in a proper liquid medium that is then sonicated. Non exfoliated
graphite is eventually separated from graphene by centrifugation. This method was first proposed by
Hernandez et al.[69] who obtained graphene concentration up to 0.01 mg/ml in N-methylpyrrolidone
(NMP). The method was then largely improved by several groups, in particular, by the Italian group of
Alberto Mariani. Mariani et al. reached the concentration of 2.1 mg/ml in NMP (the highest in this
solvent).[70] The same group published the highest graphene concentrations reported so far in any
liquid and obtained by any method. An example is the use of a suitable ionic liquid as the dispersing
liquid medium for graphite exfoliation;[71] in this medium the very high concentration of 5.33 mg/ml was
obtained.
Carbon dioxide reduction method[edit]
This synthesis process involves a highly exothermic reaction in which magnesium is combusted in an
oxidation-reduction reaction with carbon dioxide, producing a variety of carbon nanoparticles including
graphene and fullerenes. The carbon dioxide reactant may be either solid (dry-ice) or gaseous. The
products of this reaction are carbon and magnesium oxide. Issued patents are held on this
process.[72][73]
Atomic structure[edit]
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.[31]Electron
diffraction patterns showed the expected honeycomb 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,[3][74][75] 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 SiO2 substrates were
obtained[76][77] by scanning tunneling microscopy. Graphene processed using lithographic techniques
is covered by photoresist residue, which must be cleaned to obtain atomic-resolution images.[76] Such
residue may be the "adsorbates" observed in TEM images, and may explain the rippling of suspended
graphene. Rippling of graphene on the SiO2 surface was determined to be caused by conformation of
graphene to the underlying SiO2, and not an intrinsic effect.[76]
Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This
is true even of some single-walled carbon nanostructures.[78] However, unlayered graphene with only
(hk0) rings has been found in the core of presolar graphite onions.[79] TEM studies show faceting at
defects in flat graphene sheets,[80] and suggest a possible role in this unlayered graphene for twodimensional crystallization from a melt.
Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, like
hydrocarbons. When bombarded with pure carbon atoms, the holes in graphene sheets are
completely filled, with carbon atom snapping to the gaps and perfectly aligning into hexagon
shapes.[81][82]
Properties[edit]
Electronic[edit]
GNR band structure for zig-zag orientation. Tightbinding calculations show that zigzag orientation is always metallic.
GNR band structure for arm-chair orientation. Tightbinding calculations show that armchair orientation can be
semiconducting or metallic depending on width (chirality).
Graphene differs from most conventional three-dimensional materials. Intrinsic graphene is a semimetal or zero-gapsemiconductor. Understanding the electronic structure of graphene is the starting
point for finding the band structure of graphite. It was realized as early as 1947 by P. R.
Wallace[83] that the energy-momentum relation (dispersion 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.[84] Due to this linear (or “conical") 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.[85][86] Hence, the electrons and holes are called
Dirac fermions and the six corners of the Brillouin zone are called the Dirac points. [85] The equation
describing the electrons' lineardispersion relation is
; where the Fermi
6
velocity vF ~ 10 m/s, and the wavevector k is measured from the Dirac points (the zero of energy is
chosen here to coincide with the Dirac points).[86]
Electron transport[edit]
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 cm2·V−1·s−1.[3] Additionally, the symmetry of the experimentally measured conductance
indicates that the mobilities for holes and electrons should be nearly the same. [84] The mobility is
nearly independent of temperature between 10 K and 100 K,[87][88][89] 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 cm2·V−1·s−1 at a carrier density
of 1012 cm−2.[89][90] The corresponding resistivity of the graphene sheet would be 10−6 Ω·cm. This is
less than the resistivity of silver, the lowest resistivity substance known at room
temperature.[91] However, for graphene on SiO2 substrates, scattering of electrons by optical phonons
of the substrate is a larger effect at room temperature than scattering by graphene’s own phonons.
This limits the mobility to 40,000 cm2·V−1·s−1.[89]
Despite the zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on
the order of
. The origin of this minimum conductivity is still unclear. However, rippling of the
graphene sheet or ionized impurities in the SiO2 substrate may lead to local puddles of carriers that
allow conduction.[84] Several theories suggest that the minimum conductivity should be
however, most measurements are of order
concentration.[92]
;
or greater[3] and depend on impurity
Recent experiments have probed the influence of chemical dopants on the carrier mobility in
graphene.[92][93]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. They reported that even for chemical dopant concentrations in
excess of 1012 cm2 there is no observable change in the carrier mobility.[93] 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,[94] and can reduce the mobility 20-fold.[92] The mobility
reduction is reversible on heating the graphene to remove the potassium.
Due to its two-dimensional property, charge fractionalization (where the apparent charge of individual
pseudoparticles in low-dimensional systems is less than a single quantum [95]) is thought to occur in
graphene. It may therefore be a suitable material for the construction of quantum
computers[96] using anyonic circuits.[97][98]
Optical[edit]
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.
Graphene's unique optical properties produce an unexpectedly high opacity for an atomic monolayer
in vacuum, absorbing πα ≈ 2.3% of white light, where α is the fine-structure constant.[99] 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".[100] 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.[101]
The band gap of graphene can be tuned from 0 to 0.25 eV (about 5 micrometre wavelength) by
applying voltage to a dual-gate bilayer graphene field-effect transistor (FET) at room
temperature.[102] The optical response of graphene nanoribbons has also been shown to be tunable
into the terahertz regime by an applied magnetic field.[103] It has been shown that graphene/graphene
oxide system exhibitselectrochromic behavior, allowing tuning of both linear and ultrafast optical
properties.[104]
Recently, a graphene-based Bragg grating (one-dimensional photonic crystal) has been fabricated
and demonstrated its capability for excitation of surface electromagnetic waves in the periodic
structure by using 633 nm He-Ne laser as the light source.[105]
Saturable absorption[edit]
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 fluence. 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 fullband mode
locking has been achieved by graphene-based saturable absorber. Due to this special property,
graphene has wide application in ultrafast photonics. Moreover, the ultrafast optical response of
graphene/graphene oxide layers can be tuned electrically.[104][106][107] Furthermore, Saturable
absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband
optical absorption property. The microwave saturable absorption in graphene demonstrates that
graphene microwave and Terahertz photonics devices could emerge, such as: microwave saturable
absorber, modulator, polarizer,microwave signal processing,and broad-band wireless access
networks.[108]
Nonlinear Kerr effect[edit]
Under more intensive laser illumination, graphene could also possess a nonlinear phase shift due to
the optical nonlinear Kerr effect, besides the well-known saturable absorptionproperty. Based on a
typical open and close aperture z-scan measurement, graphene is found to possess a giant nonlinear Kerr coefficient of 10−7 cm2·W −1, almost nine orders of magnitude larger than that of bulk
dielectrics.[109] This suggests that graphene may be a very promising nonlinear Kerr medium, paving
the way for graphene-based nonlinear Kerr photonics such as soliton in graphene.
Excitonic[edit]
First-principle calculations with quasiparticle corrections and many body effects are performed to
study the electronic and optical properties of graphene-based materials. The approach is described
as three stages.[110] With GW calculation, the properties of graphene-based materials are accurately
investigated, including graphene,[111] graphene nanoribbons,[112][113][114] edge and surface
functionalized armchair graphene nanoribbons,[115] hydrogen saturated armchair graphene
nanoribbons,[116] Josephson effect in graphene SNS junctions with single localized defect,[117][118] and
scaling properties in armchair graphene nanoribbons.[119]
Thermal[edit]
The near-room temperature thermal conductivity of graphene was measured to be between
(4.84±0.44) × 103 to (5.30±0.48) × 103 W·m−1·K−1. These measurements, made by a non-contact
optical technique, are in excess of those measured for carbon nanotubes or diamond. The isotopic
composition, the ratio of 12C to 13C, has a significant impact on thermal conductivity, where isotopically
pure 12C graphene has higher conductivity than either a 50:50 isotope ratio or the naturally occurring
99:1 ratio.[120] It can be shown by using theWiedemann–Franz law, that the thermal conduction
is phonon-dominated.[121] However, for a gated graphene strip, an applied gate bias causing a Fermi
energy shift much larger than k BT can cause the electronic contribution to increase and dominate over
the phonon contribution at low temperatures. The ballistic thermal conductance of graphene is
isotropic.[122][123]
Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that
has basal planethermal conductivity of over a 1,000 W·m−1·K−1 (comparable todiamond). 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.[124] 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.[125]
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 T2 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.[125] Some graphene
phonon bands display negative Grüneisen parameters.[126] 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 behavior of a string, which, when it is stretched, will
have vibrations of smaller amplitude and higher frequency. This phenomenon, named "membrane
effect", was predicted by Lifshitz in 1952.[127]
Mechanical[edit]
As of 2009, graphene appears to be one of the strongest materials ever tested. Measurements have
shown that graphene has a breaking strength over 100 times greater than a hypothetical steel film of
the same (incredibly thin) thickness,[128] with a tensile modulus (stiffness)
of 1 TPa (150,000,000 psi).[129] 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,[130] though this may be changing soon.[131] Graphene is very light, weighing only
about 0.77 milligrams per square meter. The Nobel announcement illustrated this by saying that a 1
square meter graphene hammock would support a 4 kg cat but would weigh only as much as one of
the cat's whiskers, at 0.77 mg (about 0.001% of the weight of 1 m2 of paper).[128]
Graphene paper or GP has recently been developed by a research department from the University of
Technology Sydney by Guoxiu Wang, that can be processed, reshaped and reformed from its original
raw material state. Researchers have successfully milled the raw graphite by purifying and filtering it
with chemicals to reshape and reform it into nano-structured configurations, which are then processed
into sheets as thin as paper, according to a university statement. Lead researcher Ali Reza
Ranjbartoreh said: 'Not only is it lighter, stronger, harder and more flexible than steel, it is also a
recyclable and sustainably manufacturable product that is eco-friendly and cost effective in its use.'
Ranjbartoreh said the results would allow the development of lighter and stronger cars and planes
that use less fuel, generate less pollution, are cheaper to run and ecologically sustainable. He said
large aerospace companies have already started to replace metals with carbon fibres and carbonbased materials, and graphene paper with its incomparable mechanical properties would be the next
material for them to explore.[citation needed]
Using an atomic force microscope (AFM), the spring constant of suspended graphene sheets has
been measured. Graphene sheets, held together by van der Waals forces, were suspended over SiO
2 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 using
graphene for NEMS applications such as pressure sensors and resonators.[132]
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, [31] 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. [3][74][75][133][134]
Spin transport[edit]
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 (as well as a weak hyperfine interaction). Electrical
spin-current injection and detection in graphene was recently demonstrated up to room
temperature.[135][136][137] Spin coherence length above 1 micrometre at room temperature was
observed,[135] and control of the spin current polarity with an electrical gate was observed at low
temperature.[136]
Anomalous quantum Hall effect[edit]
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 currentcarrying stripe. Usually the phenomenon, the quantization of the so-called Hall conductivity
at
integer multiples of the basic quantity
(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 3 K, and at very high magnetic fields.
Graphene in contrast, besides its high mobility and minimum conductivity, and because of certain
peculiarities explained in Pseudo-relativistic theory 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
, whereN is the above-mentioned integer "Landau level"
index, and the double valley and double spin degeneracies give the factor of 4. [3] Moreover, in
graphene these remarkable anomalies can even be measured at room temperature, i.e. at
roughly 20 °C.[87] 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,[85] leading to the "+1/2" in the Hall conductivity.[138] Bilayer graphene also shows the
quantum Hall effect, but with only one of the two anomalies (i.e.
).
Interestingly, concerning the second anomaly, the first plateau at N = 0 is absent, indicating that
bilayer graphene stays metallic at the neutrality point.[3]
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.[84][87] The Berry’s phase arises due to the zero
effective carrier mass near the Dirac points.[139] 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.[87]
Strong magnetic fields[edit]
The quantum Hall effect in graphene in sufficiently strong magnetic fields (above 10 Teslas or so)
reveals additional interesting features. Additional plateaus of the Hall conductivity
at
at
with
[141]
are observed.[140] Also, the observation of a plateau
and the fractional quantum Hall effect at
were reported.[141][142]
These observations of the quantum Hall effect with
indicate that the four-fold
degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or
completely lifted. According to one of the suggestions, it is the magnetic catalysis of symmetry
breaking that is responsible for lifting the degeneracy of the Landau levels.
Forms[edit]
Nanostripes[edit]
Nanostripes of graphene (in the "zig-zag" orientation), at low temperatures, show spin-polarized
metallic edge currents, which also suggests applications in the new field ofspintronics. (In the
"armchair" orientation, the edges behave like semiconductors.[143])
Graphene oxide[edit]
Further information: Graphite oxide
By dispersing oxidized and chemically processed graphite in water, and using paper-making
techniques, the monolayer flakes form a single sheet and bond very powerfully. These sheets,
called graphene oxide paper have a measured tensile modulus of 32 GPa.[144] The peculiar chemical
property of graphite oxide is related to the functional groups attached to graphene sheets. They even
can significantly change the pathway of polymerization and similar chemical processes. [145] Graphene
Oxide flakes in polymers also shown enhanced photo-conducting properties.[146] A team at
Manchester University led by Andre Geim published findings showing that graphene-based
membranes are impermeable to all gases and liquids (vacuum-tight). However, water evaporates
through them as quickly as if the membranes were not there at all.[147]
Chemical modification[edit]
Photograph of single-layer graphene oxide undergoing high temperature chemical treatment, resulting in sheet folding
and loss of carboxylic functionality, or through room temperature carbodiimide treatment, collapsing into star-like
clusters.
Soluble fragments of graphene can be prepared in the laboratory[148] 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 angstromthickness) is soluble
in tetrahydrofuran, tetrachloromethane and dichloroethane. Refluxing single-layer graphene oxide
(SLGO) in solvents leads to size reduction and folding of the individual sheets as well as loss of
carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets
dependant on their preparation methodology. When using thionyl chloride, acyl chloride groups result,
which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%.
Boehm titration results for various chemical reactions of single-layer graphene oxide, which reveal reactivity of the
carboxylic groups and the resultant stability of the SLGO sheets after treatment.
Hydrazine reflux is commonly used for reducing SLGO to SLG(R), but titrations show that only around
20–30% of the carboxylic groups are lost leaving a significant number of COOH groups available for
chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable
and using a room temperature stirring with HCl (< 1.0 M) leads to around 60% loss of COOH
functionality. Room temperature treatment of SLGO with carbodiimides leads to the collapse of the
individual sheets into star-like clusters, which exhibited poor subsequent reactivity with amines (ca. 3–
5% conversion of the intermediate to the final amide).[149] It is apparent that conventional chemical
treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that
leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis.
Therefore, other types of chemical reactions have been explored. SLGO has also been grafted with
polyallylamine, cross-linked through epoxy groups. When filtered into graphene oxide paper, these
composites exhibit sheets increased stiffness and strength relative to unmodified graphene oxide
paper.[150]
Full hydrogenation from both sides of graphene sheet results in graphane, but partial hydrogenation
leads to hydrogenated graphene.[151] Similarly, both-side fluorination of graphene (or chemical and
mechanical exfoliation of graphite fluoride) leads to fluorographene (graphene fluoride), while partial
fluorination (generally halogenation) provides fluorinated (halogenated) graphene.
Casimir effect and dispersion[edit]
The Casimir effect is an interaction between any disjoint neutral bodies provoked by the fluctuations
of the electrodynamical vacuum. Mathematically it can be explained by considering the normal modes
of electromagnetic field, which explicitly depend on the boundary (or matching) conditions on the
surfaces of the interacting bodies. Since the interaction of graphene with electromagnetic field is
surprisingly strong for a one-atom-thick material, the Casimir effect in the graphene systems is of
growing research interest.[152][153]
The related van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic
asymptotic power law in contrast to the usual inverse quartic.[154]
Bilayer graphene[edit]
Main article: Bilayer graphene
Bilayer graphene is two layers of graphene and it has been shown to have interesting electrical
properties, such as the quantum hall effect, a tunable band gap,[155] and potential forexcitonic
condensation[156] – making them promising candidates for optoelectronic and nanoelectronic
applications. Bilayer graphene typically can be found either in twisted configurations where two layer
are rotated relative to each other or a graphitic Bernal stacked configurations where half the atoms in
one layer lie atop half the atoms in the other. Stacking order and orientation greatly influence the
optical and electronic properties of bilayer graphene. One way to synthesize bilayer graphene is
via chemical vapor deposition, and can produce large area bilayer regions that almost exclusively
conform to a Bernal stack geometry.[157]
3D graphene[edit]
In 2013, a three-dimensional honeycomb of hexagonally arranged carbon was termed 3D
graphene.[158][159]
Potential applications[edit]
Several potential applications for graphene are under development, and many more have been
proposed. These include lightweight, thin, flexible, yet durable display screens, electric circuits, and
solar cells, as well as various medical, chemical and industrial processes enhanced or enabled by the
use of new graphene materials.[160]
In 2013, graphene researchers led by Prof. Jari Kinaret from Sweden's Chalmers University of
Technology, secured a €1 billion grant from the European Union to be used for further research into
development of potential applications of graphene.[161] In 2013 was formed Graphene Flagship
consortium including Chalmers University of Technology and next seven European universities and
research centers, and Finland company Nokia.[162][163] Nokia has also been working on graphene
technology for several years.[164]
Medicine[edit]
Graphene is reported to have enhanced PCR by increasing the yield of DNA product.[165] Experiments
have revealed that the outstanding thermal conductivity of graphene could be the main reason behind
this result. Furthermore, graphene yields DNA product equivalent to positive control with up to 65%
reduction in the PCR cycles.
Integrated circuits[edit]
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 used as the channel in a field-effect
transistor. 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 2 / Si or thermal
graphitization of a SiC surface) onto a target substrate of interest.[166] In 2008, the smallest transistor
so far, one atom thick, 10 atoms wide was made of graphene.[167] IBM announced in December 2008
that they fabricated and characterized graphene transistors operating at GHz frequencies. [168] In May
2009, an n-type transistor was announced meaning that both n and p-type transistors have now been
created with graphene.[169][170] A functional graphene integrated circuit was also demonstrated – a
complementary inverter consisting of one p- and one n-type graphene transistor.[171] However, this
inverter also suffered from a very low voltage gain.
According to a January 2010 report,[172] graphene was epitaxially grown on SiC in a quantity and with
quality suitable for mass production of integrated circuits. At high temperatures, the Quantum Hall
effect could be measured in these samples. See also the 2010 work by IBM in the transistor section
above in which 'processors' of 100 GHz transistors on 2-inch (51 mm) graphene sheets were
made.[173]
In June 2011, IBM researchers announced that they had succeeded in creating the first graphenebased integrated circuit, a broadband radio mixer.[174] The circuit handled frequencies up to 10 GHz,
and its performance was unaffected by temperatures up to 127 degrees Celsius.
In June 2013 an 8 transistor 1.28 GHz ring oscillator circuit was described. [175]
Transistors[edit]
Graphene exhibits a pronounced response to perpendicular external electric fields, potentially
forming field-effect transistors. A 2004 paper documented FETs with an on-off ratio of ~30 at room
temperature.[citation needed] A 2006 paper announced an all-graphene planar FET with side
gates.[176] Their devices showed changes of 2% at cryogenic temperatures. The first top-gated FET
(on–off ratio of <2) was demonstrated in 2007.[177] Graphene nanoribbons may prove generally
capable of replacing silicon as a semiconductor.[178]
A 2008 paper demonstrated a new switching effect based on a reversible chemical modification of the
graphene layer that gives an on–off ratio of greater than six orders of magnitude. These reversible
switches could potentially be applied to nonvolatile memories. [179]
In 2009, researchers demonstrated four different types of logic gates, each composed of a single
graphene transistor.[180]
Practical uses for these circuits are limited by the very small voltage gain they exhibit. Typically, the
amplitude of the output signal is about 40 times less than that of the input signal. Moreover, none of
these circuits operated at frequencies higher than 25 kHz.
In the same year, tight-binding numerical simulations[181] demonstrated that the band-gap induced in
graphene bilayer field effect transistors is not sufficiently large for high-performance transistors for
digital applications, but can be sufficient for ultra-low voltage applications, when exploiting a tunnelFET architecture.[182]
In February 2010, researchers announced transistors with an on/off rate of 100 gigahertz, far
exceeding the rates of previous attempts, and exceeding the speed of silicon transistors with an equal
gate length. The 240 nm devices were made with conventional silicon-manufacturing
equipment.[183][184][185]
In November 2011, researchers used ink-jet printing (additive manufacturing) as a method for
fabricating graphene devices.[186]
In 2013, researchers demonstrated graphene's high mobility in a detector that allows broad band
frequency selectivity ranging from the THz to IR region (0.76-33THz)[187] A separate group created a
terahertz-speed transistor with bistable characteristics, which means that the device can
spontaneously switch between two electronic states. The device consists of two layers of graphene
separated by an insulating layer of boron nitride just a few atomic layers thick. Electrons move
through this barrier by quantum tunneling. These new transistors exhibit “negative differential
conductance,” whereby the same electrical current flows at two different applied voltages. [188][189]
Graphene does not have an energy band-gap, which presents a hurdle for its applications in digital
logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface
functionalization have not resulted in a breakthrough. A team of researchers at the University of
California has shown that the negative differential resistance experimentally observed in graphene
field-effect transistors of "conventional" design allows for construction of viable non-Boolean
computational architectures with the gap-less graphene. The negative differential resistance observed under certain biasing schemes - is an intrinsic property of graphene resulting from its
symmetric band structure. The obtained results present a conceptual change in graphene research
and indicate an alternative route for graphene's applications in information processing. [190]
Also in 2013, researchers reported the creation of transistors printed on flexible plastic that operate at
25-gigahertz, sufficient for communications circuits and can be fabricated at scale. To make the
transistors, the researchers first fabricate all the non-graphene-containing structures—the electrodes
and gates—on sheets of plastic. Separately, they grow large sheets of graphene on metal, then peel it
off and transfer it to the plastic. Finally, they top the sheet with a waterproof layer. The devices still
work after being soaked in water, and they’re flexible enough to be folded up. [191]
Redox[edit]
Graphene oxide can be reversibly reduced and oxidized using electrical stimulus. Controlled reduction
and oxidation in two-terminal devices containing multilayer graphene oxide films are shown to result in
switching between partially reduced graphene oxide and graphene, a process that modifies the
electronic and optical properties. Oxidation and reduction are also shown to be related to resistive
switching.[192][193]
Transparent conducting electrodes[edit]
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.[194][195]
Large-area, continuous, transparent, and highly conducting few-layered graphene films were
produced by chemical vapor deposition and used as anodes for application in photovoltaic devices. A
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.[196]
Organic light-emitting diodes (OLEDs) with graphene anodes have also been demonstrated.[197] The
electronic and optical performance of devices based on graphene are shown to be similar to devices
made with indium-tin-oxide.
An all carbon-based device called a light-emitting electrochemical cell (LEC) was demonstrated with
chemically derived graphene as the cathode and the conductive polymer PEDOTas the anode by
Matyba et al.[198] Unlike its predecessors, this device contains no metal, but only carbon-based
electrodes. The use of graphene as the anode in LECs was also verified in the same publication.
Ethanol distillation[edit]
Graphene oxide membranes allow water vapor to pass through, but have been shown to be
impermeable to all other liquids and gases including helium .[147] This phenomenon has been used for
further distilling of vodka to higher alcohol concentrations, in a room-temperature laboratory, without
the application of heat or vacuum normally used in traditionaldistillation methods.[199] Further
development and commercialization of such membranes could revolutionize the economics
of biofuel production and the alcoholic beverage industry.
Desalination[edit]
Research suggests that graphene filters could outperform other techniques of desalination by a
significant margin.[200]
Solar cells[edit]
Graphene has a unique combination of high electrical conductivity and optical transparency, which
make it a good candidate for use in solar cells. A single sheet of graphene is a zerobandgap semiconductor whose charge carriers are delocalized over large areas, implying that carrier
scattering does not occur. Because this material only absorbs 2.3% of visible light, it is a candidate for
applications as a transparent conductor.[201] Graphene can be assembled into a film electrode with low
roughness. However, in practice, graphene films produced via solution processing contain lattice
defects and grain boundaries that act as recombination centers and decrease the electrical
conductivity of the material. Thus, these films must be made thicker than one atomic layer in order to
obtain sheet resistances that are sensible. This added resistance can be combatted by incorporating
conductive filler materials, such as a silica matrix. Reduced Graphene film's electrical conductivity can
also be improved by attaching large aromatic molecules such as pyrene-1-sulfonic acid sodium
salt (PyS) and the disodium salt of 3,4,9,10-perylenetetracarboxylic diimide bisbenzenesulfonic
acid (PDI). These large aromatic molecules, under high temperatures, facilitate better πconjugation of the graphene basal plane. Graphene films have high transparency in the visible and
near-infrared regions, and are also highly chemically and thermally stable. [201]
In order for graphene to be put to use in solar cells commercially, large-scale production of the
material would need to be achieved. However, the peeling of pyrolytic graphene does not seem to be
a simple process to scale up. An alternative method with potential for scalable production of graphene
that has been suggested is the thermal decomposition of silicon carbide.[201]
Other than graphene's use as a transparent conducting oxide (TCO), it has also exhibited high charge
mobilities that lead one to conclude that it could be put to use as a charge collector and transporter in
PVs. The use of graphene in OPVs as a photoactive material requires the bandgap to be tuned to
within the range of 1.4-1.9eV. In 2010, Yong & Tour reported single cell efficiencies of nano structured
graphene-based PVs of over 12%.[201] According to P. Mukhopadhyay and R. K. Gupta the future of
graphene in OPVs could be "devices in which semiconducting graphene is used as the photoactive
material and metallic graphene is used as the conductive electrodes". [202]
The USC Viterbi School of Engineering lab reported the large scale production of highly
transparent graphene films by chemical vapor deposition in 2008. In this process, researchers create
ultra-thin graphene sheets by first depositing carbon atoms in the form of graphene films on a nickel
plate from methane gas. Then they lay down a protective layer ofthermoplastic over the graphene
layer and dissolve the nickel underneath in an acid bath. In the final step they attach the plasticprotected graphene to a very flexible polymer sheet, which can then be incorporated into an OPV cell
(graphene photovoltaics). Graphene/polymer sheets have been produced that range in size up to 150
square centimeters and can be used to create dense arrays of flexible OPV cells. It may eventually be
possible to run printing presses laying extensive areas covered with inexpensive solar cells, much like
newspaper presses print newspapers (roll-to-roll).[203][204]
While silicon has long been the standard for commercial solar cells, new research from the Institute of
Photonic Sciences (ICFO) in Spain has shown that graphene could prove far more efficient when it
comes to transforming light into energy. The study found that unlike silicon, which generates only one
current-driving electron for each photon it absorbs, graphene can produce multiple electrons. Solar
cells made with graphene could offer 60% solar cell efficiency – double the widely-regarded maximum
efficiency of silicon cells.[205]
Single-molecule gas detection[edit]
Theoretically 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 adsorbedmolecules. However,
similar to carbon nanotubes, graphene has no dangling bonds on its surface. Gaseous molecules
cannot be readily adsorbed onto graphene surface. So intrinsically graphene is insensitive. [206] The
sensitivity of graphene chemical gas sensors can be dramatically enhanced by functionalizing
graphene, for example, coating with a thin layer of certain polymers. The thin polymer layer acts like a
concentrator that absorbs gaseous molecules. The molecule absorption introduces a local change
in electrical resistanceof graphene sensors. 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.[93]
Quantum dots[edit]
Graphene quantum dots (GQDs) use graphene with all dimensions less than 10 nm. Their size and
edge crystallography govern their electrical, magnetic, optical and chemical properties. GQDs can be
produced via graphite nanotomy[207] or via bottom-up, solution-based routes (Diels-Alder,
cyclotrimerization and/or cyclodehydrogenation reactions).[208]Several studies[167] have indicated that
GQDs with controlled structure can be incorporated into applications in electronics, optoelectronics
and electromagnetics. quantum confinement can be created by changing the width of GNRs at select
points along the ribbon.[209]
Frequency multiplier[edit]
In 2009, researchers built experimental graphene frequency multipliers that take an incoming signal of
a certain frequency and outputs a signal at a multiple of that frequency.[210][211]
Optical modulators[edit]
When the Fermi level of graphene is tuned, the optical absorption of graphene can be changed. In
2011, researchers at UC Berkeley reported the first graphene-based optical modulator. Operating
at 1.2 GHz without any temperature controller, this modulator has a broad bandwidth (from 1.3 to 1.6
μm) and small footprint (~25 μm2).[212]
Additives in coolants[edit]
Owing to high thermal conductivity of graphene, it could be used as additives in coolants. Preliminary
research work has shown that 5.0 volume percentage graphene can enhance the thermal conductivity
of a base fluid by 86%.[213] Another application due to enhanced thermal conductivity of graphene was
found in polymerase chain reaction.[214]
Reference Material[edit]
Graphene shows properties that enable it to be used as a reference material for characterizing
electroconductive and transparent materials. One layer of graphene absorbs 2.3% of white
light.[215] This property was used to define the conductivity of transparency that combines the sheet
resistance and the transparency. This parameter was used to compare different materials without the
use of two independent parameters.[216]
Thermal management materials[edit]
In 2011, researchers in Georgia Institute of Technology reported that a three-dimensional vertically
aligned functionalized multilayer graphene architecture can be an approach for graphenebased thermal interfacial materials (TIMs) with superior equivalent thermal conductivity and ultralow interfacial thermal resistance between graphene and metal.[123]
Energy storage[edit]
Ultracapacitors[edit]
Due to the extremely 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. [217]
Electrode for Li-ion batteries (microbatteries)[edit]
Stable Li-ion cycling has recently been demonstrated in bi and few layer graphene films grown on
Nickel substrates,[218][219] while single layer graphene films have been demonstrated as a protective
layer against corrosion in battery components such as the steel casing. [220] This opens up the
possibilities for flexible electrodes for microscale Li-ion batteries where the anode acts as the active
material as well as the current collector.[221]
Engineered piezoelectricity[edit]
Density functional theory simulations predict that depositing certain adatoms on graphene can render
it piezoelectrically responsive to an electric field applied in the vertical (i.e. out-of-plane) direction. This
type of locally engineered piezoelectricity is similar in magnitude to that of bulk piezoelectric materials
and make graphene a candidate tool for control and sensing in nanoscale devices. [222][223]
Biodevices[edit]
Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly gatable
structure make antibody-functionalized graphene sheets excellent candidates for mammalian and
microbial detection and diagnosis devices.[224]
Energy of the electrons with wavenumber k in graphene, calculated in the Tight Binding-approximation. The unoccupied
(occupied) states, colored in blue–red (yellow–green), touch each other without energy gap exactly at the abovementioned six k-vectors.
The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA
sequencing. Integration of graphene (thickness of 0.34 nm) layers as nanoelectrodes into a
nanopore[225] can solve one of the bottleneck issues of nanopore-based single-molecule DNA
sequencing.
Pseudo-relativistic theory[edit]
The electrical properties of graphene can be described by a conventional tight-binding model; in this
model the energy of the electrons with wave vector k is[83][85]
with the nearest-neighbor hopping energy γ0 ≈ 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 wave vector, 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 that 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 M0, which leads to interesting additional features:[85][226]
Here vF ~ 106 is the Fermi velocity in graphene, which replaces the velocity of light in the
Dirac theory; is the vector of the Pauli matrices,
of the electrons, and E is their energy.[143]
is the two-component wave function
History and experimental discovery[edit]
The term graphene first appeared in 1987[227] 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 intercalant and graphene. The term was also used in early descriptions
of carbon nanotubes,[228] as well as for epitaxial graphene,[229] and polycyclic aromatic
hydrocarbons.[230]
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]... The 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 highertemperature 3D growth.[30]
Single layers of graphite were previously (starting from the 1970s) grown epitaxially on top of
other materials.[231] This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice
of sp2-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.[14] 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) [14] but nothing
thinner than 50 to 100 layers was produced during these years.
Andre Geim and Konstantin Novoselov, 2010
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.[15] The Manchester researchers pulled out graphene
layers from graphite and transferred them onto thin SiO 2 on a silicon wafer in a process
sometimes called micromechanical cleavage or, simply, theScotch tape technique. The
SiO2 electrically isolated the graphene, and was weakly interacting with the graphene,
providing nearly charge-neutral graphene layers. The silicon beneath the SiO2 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,[87][139]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 around the same time by Geim
and Novoselov and by Philip Kim and Yuanbo Zhang in 2005. These simple experiments
started after the researchers watched colleagues who were looking for quantum Hall
effect[232] and Dirac fermions[233] in bulk graphite.
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 twodimensional 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, Reuters tipped him as one of the front-runners for a Nobel prize in Physics.[234] On
October 5, 2010, the Nobel Prize in Physics for the year was awarded to Andre
Geim andKonstantin Novoselov from the University of Manchester for their work on
graphene.[235]
The theory of graphene was first explored by P. R. Wallace in 1947 as a starting point for
understanding the electronic properties of more complex, 3D graphite. The
emergentmassless Dirac equation was first pointed out by Gordon Walter Semenoff and
David P. DeVincenzo and Eugene J. Mele.[236] 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.[87][138][139] Later, single graphene
layers were also observed directly by electron microscopy. [31]
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.[38][39][40][41][42][43] 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.[237] Even though graphene on nickel and on silicon carbide have both existed in
the