Lectures 15-16

Graphene and

carbon nanotubes

Graphene is atomically thin crystal of carbon which is stronger than steel but flexible, is transparent for light, and conducts electricity (gapless semiconductor).

D.I.Y.Graphene

Geim & Novoselov(Manchester) 2004

Graphene from a nanopensilKim (Columbia Univ) 2005Kim (Columbia Univ) 2005

Ultra-thin graphitic films mechanically exfoliated from bulk graphite

Novoselov & Geim (Manchester)Science 306, 666 (2004)

Geim & Novoselov - Nature Materials 6, 183 (2007)Geim & MacDonald Physics Today 60 35 41 (2007)

, ( )

Geim & MacDonald, Physics Today 60, 35-41 (2007)Geim & Kim, Scientific American 90-97 (April 2008)

10 nm

hybridisation forms strong directed bonds2sp

Carbon has 4 electrons in the outer s-p shell

hybridisation forms strong directed bonds which determine a honeycomb lattice structure.p

C

- bonds

*Strong hybridised bonds

make graphene mechanically strong.It takes 48,000 kN·m·kg−1

2sp empty

?- conduction properties

(compare to best steel's 154 kN·m·kg−1). Also, it is chemically resilient.

strong covalent bonds

full

hexagonal Bravais lattice unit cell – can be u t ce ca bechosen differently

2 full

221121ananR nn

6 x 1/3 sites

2 full sites

6 x 1/3 sites

hybridisation forms strong directed bonds2sp

Carbon has 4 electrons in the outer s-p shell

hybridisation forms strong directed bonds which determine a honeycomb lattice structure.p

C

- bonds

)(zp orbitals determine conduction properties of graphite

eV3~0

)(p orbitals determine conduction properties of graphite

*

eV10~pz-bands

Bragg scattering conditions

GNGNG

RGi

Reciprocal lattice

MRG nn 221

221121GNGNG NN 121 nnRGieaGaG 1

1112||;

G

21

unitcell

aGaG

S

2222

111

2||;

||;

2GunitcellS

GaG 222 ||;

Hexagonal Bravais lattice determines a hexagonal reciprocal lattice, with

a 42

1G

aaaGG

34

2/32||||

221

Reciprocal lattice

GNGNG

)()( kGk

Hexagonal

221121GNGNG NN )()(

21kGk NN

Hexagonal reciprocal lattice corresponding to

the hexagonalG the hexagonal

Bravais lattice2G

1st Brilloun zone

1G

1G

Fermi ‘point’in graphenein graphene

FEk )(

G Valley G y

'G

Graphene (monolayer of graphite)Graphene (monolayer of graphite) is an atomically thin zero-gap

two-dimensional semiconductor with linear dispersion ofwith linear dispersion of

conduction and valence band electrons.

22cond ppvvp yx ppvvp

pElectronic dispersion in the vicinity of the corner of

xpyp

22val ppvvp

the Brillouin zone: the same in both valleys.

yx ppvvp

high-energy photon ħω~100-1000eV

Simultaneous detection of the energy, E and

ti l θ fħω 100-1000eV propagation angle θ of photo-electrons enablesonemEp cos2|| one

to restorecompletely

the band structure.EAp

mEp )(

cos2

||

||

A l l d h i i (ARPES)

the band structure.

work function

Angle-resolved photo-emission spectroscopy (ARPES) of heavily doped graphene synthesized on silicon carbide

A. Bostwick et al – Nature Physics, 3, 36 (2007)

DoS

Graphene: gapless semiconductorDoS

h l l t

gatecarriers Vn

holes electronsWallace, Phys. Rev. 71, 622 (1947)

Graphene-based field-effect transistor: GraFET GraFET

Geim and Novoselov, Nature Mat. 6, 183 (2007)

Graphene-based pixels

When embedded in polymers, graphene reinforces them, remains

grapheneg p ,conducting and, since it’s thin, it is

highly transparent.Thus it is an ideal material to makeThus, it is an ideal material to make

flexible liquid crystal screens

or to be used in conducting coating.Blake (Graphene Industries Ltd), et al

Nano Lett. 8, 1704, (2008)

Graphene: state of the art in applicaitons

G exfoliated from bulk graphite into

G grown on copper andtransferred into various media

G sublimated on inch-size SiC is used g p

suspensions is used to enhance mechanical

properties of light-weight

transferred into various media is used for flexible optoelectronics,

LCD displays, touch screens.

for manufacturing THz circuits. IBM & HRL (USA)IBM & HRL (USA)

materials (for aerospace and medical implants ).

(Samsung)

Carbon nanotubes

Iijima 1991Smalley 1993

STM images of carbon nanotubesT.W. Odom, J.-L. Huang, P.Kim, C.Lieber, Nature 391 (1998)

Nanotubes growth

Nanotube typesNanotube types

armchair (n,n) metallic

i ( 0) i d tzig-zag (n,0) semiconductor

chiral (n m) small gapchiral (n,m) small-gap with n-m=3 semiconductors

LyyLyi

)()0(/21

Metallic nanotubes (n,n)

Mp

e LyiL

2

~ /21

perimeter, 2πr

ML

py

22yx

cond ppv 2

222

LMhpv x

condn1n

yx pp

p

3210n0nF

xpyp

22Mh

,....3,2,1,0nxp

22yx

val ppv 22

LMhpv x

valn

1M

Metallic nanotubes (m,m’) with m=m’ truly 1D conductors

d it

0M

p

density of states

11M 1M|| xpvxp

v

DoS1

0M

1M|| xp

Yao et al (TUDelft)1999

Semicondutor-type nanotubes(different n and m)

D di h th b h t i ll d i tDepending on how the carbon sheet is rolled into a nanotube, the resulting nanotube may have a gap in

the electron spectrum. A gap in the nanotube spectrum is determined by its radius r, which offers p y ,

a direct root towards engineering semiconductor wires with a prescribed band gap, for use in

electronic and optoelectronic devices.

v

gap

rv

xpgap

tunnelling currentT.W. Odom, J.-L. Huang, P. Kim, C. Lieber, Nature 391 (1998)

Potential applications of carbon nanotubes:

In surface tunnelling microscopy – used as a tip.

Make excellent tips for field-effect electron guns for plasma. displays (SONY).

equi-potential linesequ pote t a es

Northwest Doctoral Training Centre

in Nanoscience

Initial training designed to demonstrate the breadth and potential of nanoscience, before focusing on one specific area of the subject.nanoscience, before focusing on one specific area of the subject.

Research and training in fundamental nanoscience, practical nano-engineering, and nanotechnology in medicine.

Interdisciplinary PhD projects which span from development and studies (exp and th) of fundamental properties of new materials and structures to making devices for applications in electronics and medicine. g pp

Development of skills in nanofabrication, low-temperature physics, materials science and data storage, synthetic chemistry, cell &tissue biology biophysics nanophotonics and materials science – this will be biology, biophysics, nanophotonics and materials science – this will be your choice!