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Graphene — An exciting two-dimensional material for science and
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DOI: 10.1007/s12045-011-0029-9
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238 RESONANCE ¨March 2011
GENERAL ¨ARTICLE
Gra
p
hene – An Excitin
g
Two-Dimensional Material for
Science and Technolo
gy
Mandar M Deshmukh and Vibhor Singh
Keywords
Graphene, nanoelectronics,
massless electrons, NEMS.
Vibhor is a PhD student at
TIFR and
g
ot his MSc
from IIT Roorkee.
Mandar is a facult
y
member at TIFR and is
interested in the broad
area of nanoscience. His
hobbies include
p
hoto
g
ra–
p
h
y
and lon
g
distance
runnin
.
One
a
tom thick gr
a
phene is derived
f
rom gr
a
phite
a
nd is
a
new m
a
teri
a
l; however, gr
a
phite h
a
s
been
a
p
a
rt o
f
hum
a
nhistory
f
or centuries. In
this
a
rticle we discuss why it gener
a
tes so much
excitement in
a
wide v
a
riety o
f
scientific disci-
plines. We emph
a
size its electronic
a
nd mech
a
n-
ic
a
l properties with
a
neyetow
a
rds
a
pplic
a
tions
th
a
tm
a
yimp
a
ct our lives sooner, r
a
ther th
a
n
l
a
ter. We
a
lso review methods to m
a
ke this won–
der m
a
teri
a
l, including the
f
a
mous `scotch-t
a
pe‘
technique th
a
t led to the Nobel-Prize winning
rese
a
rch.
1. Introduction
An intriguing question th
a
trese
a
rchers working in n
a
no-
science
a
re trying to
a
nswer is
{
how do electrons flow
differently when they
a
re confined to flow through struc-
tures th
a
t
a
re only
a
bout 10 nm in one o
f
their dimen-
sions? In most contempor
a
ry electronic devices, s
a
yin
a
computer’s processor, the electrons flow through the
devices
a
nd interconnects in
a
m
a
nner very simil
a
rto
w
a
ter flowing through the pipes in the plumbing system
o
f
a
typic
a
lhome. Wh
a
t the confinement
a
tn
a
nometer
lengthsc
a
le does is to
a
ccentu
a
te the w
a
ve-like n
a
ture
o
f
electrons, described by qu
a
ntum mech
a
nics. Answers
to questions like these
a
re very pertinent
a
stheywill
help in the development o
f
the next gener
a
tion o
f
m
a
–
teri
a
ls
a
nd devices
{
this will
a
id in the mini
a
turiz
a
tion
a
nd sc
a
ling o
f
electronic components in line with the
prediction o
f
Moore’s l
a
w[1]. Someo
f
the
a
nswers to
the question
a
lso suggest th
a
t
a
completely new kind o
f
device b
a
sedonqubits
{
sm
a
llest unit o
f
comput
a
tion
239
RESONANCE ¨March 2011
GENERAL ¨ARTICLE
b
a
sedontheide
a
s in the field o
f
qu
a
ntum computing
{
a
re re
a
liz
a
ble in rese
a
rch l
a
bs.
In this quest
f
or studying n
a
nostructures sever
a
lbre
a
k-
throughs h
a
ve been m
a
de in the field o
f
m
a
teri
a
ls sci-
ence. The Nobel Prize winning discovery in 1996 o
f
a
new
f
orm o
f
c
a
rbon, C60, in the sh
a
pe o
f
a
soccer
b
a
ll, besides
a
lre
a
dy-known
a
llotropes like di
a
mond
a
nd
gr
a
phite, h
a
sledto
a
renewed
f
ocus on c
a
rbon-b
a
sed
n
a
nostructures. C
a
rbon with
a
n
a
tomic number o
f
6h
a
s
a
n electronic configur
a
tion o
f
1s22s22p2. The outer shell
o
f
2s22p2is very
a
d
a
pt
a
ble
a
nd c
a
n hybridize to
f
orm
molecul
a
rorbit
a
ls (st
a
rting with h
a
l
f
-filled 2s12p3)th
a
t
h
a
ve the hybridized ch
a
r
a
cter o
f
both s
a
nd porbit
a
ls.
A hybridiz
a
tion o
f
sp3ch
a
r
a
cter le
a
ds to
f
our orbit
a
ls
with tetr
a
hedr
a
l symmetry
a
sseenindi
a
mond, sp2hy–
bridiz
a
tion le
a
ds to
a
hex
a
gon
a
l symmetry
a
sseenin
gr
a
phite, gr
a
phene (we will revisit this in
f
urther det
a
il
shortly), c
a
rbon n
a
notubes
a
nd C60,
a
nd sp hybridiz
a
–
tion le
a
ds to org
a
nic molecules like
a
cetylene.
The m
a
lle
a
ble n
a
ture o
f
c
a
rbon‘s molecul
a
rorbit
a
ls c
a
n
be seen in the world
a
round us domin
a
ted by c
a
rbon
which is the key ingredient o
f
the living world. As
a
result o
f
the discovery o
f
C60, there is
a
push to devel-
opment o
f
electronics b
a
sedonc
a
rbon. Ijim
a
discovered
in 1991
a
nother
a
llotrope o
f
c
a
rbon c
a
lled c
a
rbon n
a
n-
otubes. C
a
rbon n
a
notubes (CNT) with single w
a
lls con-
sist o
f
a
single
a
tom thick sheet o
f
gr
a
phite (
a
lso c
a
lled
gr
a
phene) rolled into
a
se
a
mless cylinder. Depending on
the di
a
meter
a
nd the
a
xis o
f
rolling, these c
a
rbon n
a
n-
otubes were either met
a
llic or semiconducting. As
a
n
a
t-
ur
a
l sequence o
f
scientific evolution rese
a
rchers worked
in sever
a
lte
a
ms
a
ll over the world to isol
a
te
a
single
l
a
yer o
f
gr
a
phene. This w
a
s
a
d
a
unting t
a
sk
a
sm
a
king
m
a
teri
a
ls th
a
t
a
re
a
tomic
a
lly thick h
a
d not been done
be
f
ore
{
cert
a
inly not
a
tthesc
a
le required to m
a
ke elec-
tronic devices [2].
sp2hybridization
leads to a
hexagonal
symmetry as seen
in graphite,
graphene, carbon
nanotubes and
C60.
Carbon nanotubes
(CNT) with single
walls consist of a
single atom thick
sheet of graphite
(also called
graphene) rolled
intoaseamless
cylinder.
240 RESONANCE ¨March 2011
GENERAL ¨ARTICLE
Figure 1. The lattice struc
–
ture of graphene has hex
–
agonal symmetry as indi
–
cated by the red and blue
colored ‘atoms’ taken to
–
gether. This class of lattice
is not a Bravais lattice bu
t
can be constructed from
two interpenetrating lat-
tices of equilateral tri-
angles.
Andre Geim
a
nd Konst
a
ntin Novolselov c
a
me up with
a
n ingenious method
a
f
ter ye
a
rs o
f
effort [3] to isol
a
te
monol
a
yer gr
a
phene fl
a
kes. As we discuss in more det
a
il
l
a
ter, they developed the `scotch t
a
pe‘ method which
relies on t
a
king
a
l
a
rge cryst
a
lo
f
gr
a
phite
a
nd peeling
the cryst
a
lrepe
a
tedlybyusing
a
n
a
dhesive t
a
pe to gen–
er
a
te
a
l
a
rge number o
f
thin cryst
a
ls. Depositing this
t
a
pe on
a
substr
a
te o
f
choice, like the 300 nm co
a
ting o
f
SiO2on silicon
a
llows one to optic
a
lly im
a
ge the l
a
yers
a
nd
f
a
bric
a
te electric
a
l devices. This simple ide
a
behind
the discovery h
a
sledto
a
new field th
a
t is growing very
r
a
pidly
a
nd recently Geim
a
nd Novolselov were
a
w
a
rded
the Nobel Prize
f
or their discovery [4]. It is import
a
nt to
underst
a
nd the underlying science behind the m
a
teri
a
l
to
a
ppreci
a
te the imp
a
ct o
f
this discovery.
2. Underst
a
nding Gr
a
phene’s Electronic Prop-
erties
It is interesting to note th
a
ttheb
a
sicstructureth
a
t
gives rise to gr
a
phite, c
a
rbon n
a
notubes
a
nd C60 is
gr
a
phene with sp2hybridized molecul
a
rorbit
a
l; how-
ever, it w
a
sthel
a
st to be isol
a
ted. F
i
g
u
re 1 shows the
hex
a
gon
a
ll
a
ttice structure o
f
gr
a
phene th
a
tresults
f
rom
A
ndre Geim and
Konstantin Novolselov
came up with the
‘scotch tape’ method
which relies on taking
a large crystal of
graphite and peeling
the crystal repeatedly
by using an adhesive
tape to generate a
large number of thin
crystals.
GENERAL ¨ARTICLE
It is the half-filled
shell of unhybridized
p
z
that gives the
state its unique
electrical property
due to the overlap
with nearest
neighbours to form
S
orbital.
the sp2hybridiz
a
tion o
f
the molecul
a
rorbit
a
ls st
a
rting
f
rom the h
a
l
f
-filled outer shell o
f
2s12p3(one c
a
n think
o
f
this
a
s
a
nintermedi
a
te st
a
te
f
rom the outer shell 2s2
2p2prior to hybridiz
a
tion). The porbit
a
lth
a
tisnothy–
bridized is the p
z
orbit
a
l
a
nd is oriented perpendicul
a
r
to the pl
a
ne o
f
the two-dimension
a
l sheet. The hex
a
go-
n
a
ll
a
ttice is not
a
Br
a
v
a
is l
a
ttice
a
nd th
a
timpliesth
a
t
one c
a
n describe it only in terms o
f
two interpenetr
a
ting
l
a
ttices o
f
equil
a
ter
a
l tri
a
ngles
{
one
a
tom o
f
red l
a
ttice
a
t the centroid o
f
thebluel
a
ttice (see F
i
g
u
re 1). The
sp2bonds between the ne
a
rest neighbour
a
toms h
a
ve
a
strong w
a
ve
f
unction overl
a
p
a
nd give rise to
a
very
strong cov
a
lent bond. However, it is the h
a
l
f
-filled shell
o
f
unhybridized p
z
th
a
t gives the st
a
te its unique electri-
c
a
l property due to the overl
a
pwithne
a
rest neighbours
to
f
orm ¼orbit
a
l.
In order to better underst
a
nd the electronic properties
o
f
a
ny m
a
teri
a
litisimport
a
nt to underst
a
nd the energy
(
E
)
a
nd momentum (¡!
k)rel
a
tionship
f
or different ¡!
k
{
a
lso known
a
sb
a
nd structure o
f
the m
a
teri
a
l. The ori-
gin o
f
the b
a
nd structure is simply rel
a
ted to the
f
a
ct
a
z
a
a
a
a
f
a
a
a
a
a
f
a
a
a
f
f
a
a
a
a
a
a
a
a
a
f
a
f
a
a
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a
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