Lectures Graphene and

Transcription

1 Lectures 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).

2 D.I.Y. Graphene Geim & Novoselov (Manchester) 004

3 Graphene from a nanopensil Kim (Columbia Univ) 005

4 Ultra-thin graphitic films mechanically exfoliated from bulk graphite Novoselov & Geim (Manchester) Science 306, 666 (004) Geim & Novoselov - Nature Materials 6, 183 (007) Geim & MacDonald, Physics Today 60, (007) Geim & Kim, Scientific American (April 008) 10 nm

5 Carbon has 4 electrons in the outer s-p shell sp hybridisation forms strong directed bonds which determine a honeycomb lattice structure. - bonds C sp Strong hybridised bonds make graphene mechanically strong. It takes 48,000 kn m kg 1 (compare to best steel's 154 kn m kg 1 ). Also, it is chemically resilient. strong covalent bonds * empty?- conduction properties full

6 hexagonal Bravais lattice R n 1 n n1a1 na unit cell can be chosen differently full sites 6x1/3sites

7 Carbon has 4 electrons in the outer s-p shell sp hybridisation forms strong directed bonds which determine a honeycomb lattice structure. * p z - bonds ( ) C 0 ~ 3eV orbitals determine conduction properties of graphite p z -bands ~ 10eV

8 Bragg scattering conditions G R Reciprocal lattice G N N1 G1 N G 1 N a1 G 1 a 1 ; G 1 S a G a ; G ig R 1n e n 1 n n M 1 1 G G G unitcell S unitcell G 1 Hexagonal Bravais lattice determines a hexagonal reciprocal lattice, with G 1 G a a 4 3 / 3a

9 Reciprocal lattice ( k G ) ( k ) ( N k 1N G G N N N1 G1 N G 1 G Hexagonal reciprocal lattice corresponding to the hexagonal Bravais lattice 1 st Brilloun zone G 1

10 Fermi point in graphene ( k ) E F

11 G Valley G '

12 Graphene (monolayer of graphite) is an atomically thin zero-gap two-dimensional semiconductor with linear dispersion of conduction and valence band electrons. cond vp v p x py p y p x Electronic dispersion in the vicinity of the corner of the Brillouin zone: the same in both valleys. val vp v p x p y

13 Simultaneous detection high-energy photon of the energy, E and ħω~ ev propagation angle θ of photo-electrons enables me cos one to restore ( p ) A E completely the band structure. p work function Angle-resolved photo-emission spectroscopy (ARPES) of heavily doped graphene synthesized on silicon carbide A. Bostwick et al Nature Physics, 3, 36 (007)

14 Graphene: gapless semiconductor DoS Wallace, Phys. Rev. 71, 6 (1947) hl holes electrons ncarriers V gate Graphene-based field-effect transistor: GraFET Geim and Novoselov, Nature Mat. 6, 183 (007)

15 Graphene-based pixels graphene When embedded in polymers, graphene reinforces them, remains conducting and, since it s thin, it is highly transparent. Thus, it is an ideal material to make flexible liquid crystal screens Blake (Graphene Industries Ltd), et al Nano Lett. 8, 1704, (008) or to be used in conducting coating.

16 Graphene: state of the art in applicaitons G sublimated on inch-size SiC is used G grown on copper and transferred into various media G exfoliated from bulk graphite into for manufacturing THz circuits. IBM & HRL (USA) is used for flexible optoelectronics, suspensions is used to enhance mechanical LCD displays, touch screens. properties of light-weight (Samsung) materials (for aerospace and medical implants ).

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18 Carbon nanotubes Iijima 1991 Smalley 1993 STM images of carbon nanotubes T.W. Odom, J.-L. Huang, P.Kim, C.Lieber, Nature 391 (1998)

19 Nanotubes growth

20 Nanotube types armchair (n,n) metallic zig-zag (n,0) semiconductor chiral (n,m) with n-m=3 small-gap semiconductors

21 ( y 0) ( y L ) Metallic nanotubes (n,n) ~ p y 1 L e L i y / L M perimeter, πr cond v p x p y n 1 cond n v p x h M L p y p x F n 0 p x n 0,1,,3,... M val val v px p n v px y L h M

22 M 1 Metallic nanotubes (m,m ) with m=m truly 1D conductors density of states v p x M 0 p x M 11 M 1 1 DoS v M 0 Yao et al (TUDelft)1999

23 Semicondutor-type nanotubes (different n and m) Depending 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 a direct root towards engineering semiconductor wires with a prescribed band gap, for use in electronic and optoelectronic devices. gap v r p x tunnelling current T.W. Odom, J.-L. Huang, P. Kim, C. Lieber, Nature 391 (1998)

24 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 t lines

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