Carbon nanostructures: Carbon nanostructures: functional properties functional properties and characterization and characterization

F. Banhart, IPCMSF. Banhart, IPCMS

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• The carbon atom

• The modifications of carbon

• Graphene

• Fullerenes

• Nanotubes

• Diamond

• Characterization

Hybridization of carbonHybridization of carbon

Hybridization of orbitals:

Ψhyb = C1Ψ2s + C2Ψ2p , C1 + C2 = 1 (normalization)

linear combination is also eigenfunction of the same eigen value

2p

1s

2sx y z

ground state1s2 2s2 2p2

first excited state1s2 2s1 2p3

2p

1s

2sx y z

4 valence electrons

Hybrid orbitalsHybrid orbitals

ss pp spsp++ ==

sp3 -hybridization4 sp orbitals

4 σ bonds

diamond

sp2 -hybridization3 sp orbitals+ 1 p-orbital

3 σ-bonds+ 1 π-bond

graphiteconductivity !

p-orbitals

π-bond

σ-bond

sp2-bonding betweentwo carbon atoms

The phases: The phases: graphite and diamondgraphite and diamond

diamond graphite

Phase diagram of carbonPhase diagram of carbonpressure

[GPa]

temperature [103K]

[kbar]

graphite

diamond

liq.liq.

gasgas

Modifications of carbonModifications of carbon

Graphene / Graphite Diamond

Fullerenes Onions Nanotubes Exotics

Structure of grapheneStructure of graphene

crystallography of graphene:

thinnest possible sheet of graphitic carbon thickness of one atom

a1, a2: basal unit vectors

(10,3)

ripples:

instabilities due tophonon confinement in 2D

graphene is not flat!

Structural defects in grapheneStructural defects in graphene

non-hexagonal rings

57

75

non-hexagonal rings induce curvaturebasis of closed graphitic nanoparticles

Stone-Wales transformation

Structural transformation:rearrangement of rings

5

5

5 56 6

6

6

making nanoarchitectures by defect engineering

Topology of defective grapheneTopology of defective graphene

Hypothetical molecule

pentagonspositive curvature

heptagonsnegative curvature

hexagonsflat or cylindrical curvature

Nanotube junction

Defects in graphene: pentagons, heptagons induce curvature

C60

Properties of grapheneProperties of graphenemechanical:

- fracture strength: 40 N/m (extreme!)- strength: 200 times greater than steel- Young's modulus: E ≈ 1 TPa (elasticity modulus E = dσ/dε)- elastic stretching: up to 20% (record for crystalline materials)- high flexibility (bending)- impermeable to gases

thermal:

- thermal conductivity: ~ 5000 W/m K (record, twice diamond)- thermal expansion negative at all temperatures (membrane phonons normal to plane dominate)

electronic:

- band structure 2D symmetry- semiconductor with zero bandgap- charge carriers: quasiparticles, behave like massless Dirac fermions (move at relativistic speed)

- ballistic charge transport at room temperature- quantum phenomena robust at room temperature (perfection, meff = 0)

Electronic properties of grapheneElectronic properties of graphenesemiconductor with zero bandgap (without external field: Eg = 0 semimetal)

effective mass = 0

vF: Fermi velocity (in graphene: c/vF ≈ 300)σ: Pauli matrix (2-dimensional with linear components of k) k: quasiparticle momentum

linear energy relation:

22yxFF kkvkvE +== hh

Schrödinger fermions: meff ≠ 0

Dirac fermionsmeff = 0

Brillouin zone of graphene

KΓ

Production of grapheneProduction of grapheneExfoliation from graphite

- mechanical exfoliation with Scotch tape from graphite

- chemical exfoliation: separation of layers by solvents

Chemical vapour depositionhydrocarbon (CH4) over catalyst (Fe, Ni, Co) at high T

graphene

W (011)

Ni (111)

CH4C 2 H2

Applications of grapheneApplications of graphene- electronic devices:

ballistic transport at room T charge transport source drain in FET only 0.1 ps (100 nm channel)no bandgap on/off ratios only 10-100, but sufficient for analog electronicshigh mobilities, low noise

- electron conductors with low resistance (wiring in devices)

- transparent conductive electrodes (replaces ITO)one monolayer of graphene absorbs 2.3% of white light

- gas sensor: electrical properties change (doping!) when molecules attached

- …

GraphiteGraphite

crystallography of graphite

multi-layer graphene

Carbon NanoparticlesCarbon Nanoparticles

single-shell

multi-shellNanotubes

SWNT

MWNT

1.4 nm

7 nm

Fullerenes

C60

"Onions"

0.7 nm

5 nm

Structure of fullerenesStructure of fullerenes

icosahedron truncated icosahedron

cage-like molecule C60

20 hexagons12 pentagons closure

60 vertices

distance between C-atoms:between 2 hexagons: 0.139 nm between pentagons and hexagons: 0.143 nm

stronger bond between hexagons (double bonds)distribution of π-electrons not uniform

Higher fullerenesHigher fullerenes

C60 C70

C60

C240C540

spherical shape: minimization of surface/strain energy minimization of π-electron energy (delocalization)

C60 most stabledestabilization: strain in σ-bonds (adjacent pentagons)

similar molecules: C28, C32, C50, C70, C76, C84, C240, ….

CC6060 dimers, polymersdimers, polymers

dimer polymer

covalent inter-cage bonds

made by - UV irradiation (photopolymeris.)- electron irradiation or plasma- high pressure

polymer: extremely hard material at high pressure (?)

CC6060 crystals: Fulleritescrystals: Fullerites

C60

fcc latticea = 1.4 nm

K3C60 K6C60

intercalation compoundssuperconductorsK3C60: Tc = 19 KCs2RbC60: Tc = 33 K

molecular C60 crystalvan der Waals-bonded

Endohedral fullerenesEndohedral fullerenes

Encapsulation of foreign atoms:He, N, Ne, Ca, Sc, Y, La, Gd, U ...

"real" structure: asymmetric position

Sc2@C84:encapsulation of 2 atoms

made by evaporation of metal atoms together with carbon

(possible) Applications of fullerenes(possible) Applications of fullerenes

Mechanics:- plasma treatment of C60: generation of diamond films- cross-linked C60: extremely hard materials

Optics:- light limiter- solar cell applications

Electronics:- lithography, photo resists- superconductors

biological / medical applications ?

MultiMulti--shell fullerenes: Carbon onionsshell fullerenes: Carbon onions

C60@C240@C540

pentagons, hexagons, heptagons

TEM image

2 … >100 shells

Applications of carbon onionsApplications of carbon onions

pressure cells for diamonddiamond nucleation encapsulation of metal crystals

Au

Types of carbon nanotubesTypes of carbon nanotubes

single wall (SWNT)single wall (SWNT)

1.4 nm1.4 nm

multi wall (MWNT)multi wall (MWNT)7 nm7 nm

Crystallography of carbon nanotubesCrystallography of carbon nanotubes

(n,m)(n,m)--tubes tubes

nana11

mama22aa22

aa11

R = na1 + ma2 each nanotube is characterized by (n,m)

R

Rolling up a graphene layerRolling up a graphene layer

1111

77

(11,7)-tube

Chirality of nanotubesChirality of nanotubes

armchairarmchair

chiralchiral

zigzagzigzag

Properties of carbon nanotubesProperties of carbon nanotubes

mechanical:- strongest known fiber

(fracture strength: 100 GPa)- low weight- high elasticity (E = 1 – 5 TPa)- capillary action

electrical:- metallic or semiconducting- ballistic electron transport- quantum wires

thermal:

- high thermal conductivity (axis)

Data of carbon nanotubesData of carbon nanotubes

Nanotubes for comparisonsize diameter: 0.5-100 nm

length: > cmelectron beam lithogr.:lines with some 10 nm

density 1.4 g/cm3 Al: 2.7 g/cm3

ultimate strength 100 GPa steel: 2 GPa

max. current density 1010 A/cm2 Cu: 107 A/cm2

field emission 1-3 V at 1µm distance Mo tips: 100 V/µm

thermal conductivity 6000 W/m⋅K Diamond: 3300 W/m⋅K

temperature stablity 2800°C in vacuum750°C in air

metal wires in devices:ca. 600-1000°C

costs ca. 1 - 100 €/g gold: 10 €/g

Conductor or semiconductor ?Conductor or semiconductor ?

(n,m) - tube:

- if n = m or (n-m)/3 integer metallic conductor(5,5); (9,0)

- else semiconductor(10,5); (10,0)band gap 0.4 – 0.7 eV (depends inversely on diameter)

Band structure of carbon nanotubesBand structure of carbon nanotubes

Dispersion relations:

metallic semiconducting(5,5) (9,0) (10,0)

metallic

many one-dim. subbands due to quantization around circumference

Measurement of electrical propertiesMeasurement of electrical propertiessingle nanotubes on electrodessingle nanotubes on electrodes

test circuitstest circuits

Electronic propertiesElectronic properties

metallic semiconducting

dens

ity o

f sta

tes

dens

ity o

f sta

tes

energy [eV] energy [eV]

density of states

Ballistic conductance: - calculated and observed in armchair (metallic) nanotubes- based on the absence of defect scattering- mean free path between scattering (localization length) of > 10μm

Quantum behaviour: - quantization along circumference (standing waves) - conductance jumps by increments of G0 = 2e2/h = (12.9kΩ)-1 found in MWNTs

Production of carbon nanotubesProduction of carbon nanotubes

arc discharge evaporationarc discharge evaporationof graphiteof graphite

CVD: carbonCVD: carbon--containing gasescontaining gaseson catalytically active materialson catalytically active materials

CVD synthesis of carbon nanotubesCVD synthesis of carbon nanotubes

root growth

tip growth

1. dissociation of CH4 on metal surface: CH4 C + 2H22. dissolution of carbon in metal3. nucleation of CNT (hemispherical cap) on metal surface4. tip or root growth of SWNT

metal catalyst: Fe, Co, Ni, Pt, … T = 600 – 1000°C

metal remainsas rooton substrate

metal on tipof growing tube

CVD growth of nanotubes on patterned CVD growth of nanotubes on patterned substratessubstrates

nanotube bundle

pattern on Si substrate

SWNT array

Possible applications of nanotubesPossible applications of nanotubes

-- ultrastrong fiber for composite materialsultrastrong fiber for composite materials-- electrically conducting nanowireselectrically conducting nanowires-- semiconducting devices semiconducting devices channel in FETschannel in FETs-- heat conductors in electronicsheat conductors in electronics-- tips for field emissiontips for field emission-- tips for tunneling microscopestips for tunneling microscopes-- electrodes in batterieselectrodes in batteries-- electromechanical actuatorselectromechanical actuators-- chemically activated sensorschemically activated sensors-- shells for metal nanowiresshells for metal nanowires-- gears for nanomechanics ?gears for nanomechanics ?-- nanotweezers ?nanotweezers ?-- superconductors ??superconductors ??

Nanotube devicesNanotube devices

connection oftwo SWNTs

with different conductivity

diode transistor "AND" logic gate

T-junction oftwo SWNTs

with different conductivity

network ofseveral SWNTs with different conductivity

Hybrid nanotube electronics Hybrid nanotube electronics

Nanotubes as channel in FET:Nanotubes as channel in FET:similar characteristics as Sisimilar characteristics as Si--FET, FET, but:but: -- much smallermuch smaller

-- much faster (THz)much faster (THz)-- much lower energy consumptionmuch lower energy consumption

IBMIBM

nanotubes in combination with other materials

Display technologyDisplay technology „„light at the end of the tubelight at the end of the tube““

field emission from nanotubesfield emission from nanotubes

nanotubenanotube

screenscreen

-- field emission at room temp.field emission at room temp.-- operation at some Voltsoperation at some Volts-- high emission, stabilityhigh emission, stability-- high brightness, lifetimehigh brightness, lifetime-- low power consumptionlow power consumption-- low demands on vacuumlow demands on vacuum

tubes as electron emitterstubes as electron emitters prototype

Carbon nanocompositesCarbon nanocomposites

• atoms/molecules in carbon nanotubes• crystals in/on nanotubes

contacts with metals

nanotube-DNA composites

atoms/molecules in nanotubes

Chemistry of carbon nanotubesChemistry of carbon nanotubes

adding molecules to nanotubes

connecting a molecule to a graphene surface

local change of C-hybridization

doublehelix

peptiderings

functionalgroups

Metals in carbon nanotubesMetals in carbon nanotubes

Fe in carbon nanotubes

Nanotubes as templates for the production of metallic nanowires

Filling nanotubes with fullerenes: Filling nanotubes with fullerenes: peapodspeapods

EndohedralfullerenesGd@C82in nanotubes

Mechanical applicationsMechanical applications

single-wall nanotubes: - extreme strength- extreme structural fexibility

"space elevator"

Applications in microscopyApplications in microscopy

AFM / STM tip field emitterfor TEM / SEM

DiamondDiamond

cubic hexagonal

Crystallography of diamond:

a = 0.357 nm

Defects in diamond:- vacancies: formation energy: E = 7.5 eV, generation: irradiation- diamond: almost no plasticity (hardness, dense packing)- stacking faults, twins- impurity atoms on substitutional sites doping with B, N

Properties of diamondProperties of diamondmechanical :- high elasticity modulus E = 108 GPa- strong in all directions, hardest bulk material

electrical:- large bandgap insulator (Eg = 5.5 eV)- doping with B, N possible

optical:- highly transpartent from IR to UV (best window material)- absorption at 5.5 eV (bandgap) 230 nm (UV)- n = 2.42 (at 550 nm)

thermal:- high vibration frequency- best isotropic heat conductor (although pure phonon-type)

Electronic properties of diamondElectronic properties of diamond

N: n-doping difficult (1.7 eV!)

B: p-doping possible

VB

CB

Eg = 5.5 eV

B

N1.7 eV

0.4 eV

pure diamond: large bandgap insulatordoped diamond: applicable as semiconductor

B, N atoms on interstitial sites

diamond transistor p-diamond

Au/Ti contact

Au contactSiO2

Comparison with some Comparison with some semiconductorssemiconductors

Si GaAs ß-SiC diamond

bandgap [eV] 1.1 1.4 2.2 5.5e-mobility [cm2/V s] at RT 1500 8500 900 2200h-mobility 600 400 20-100 1600

therm. conduct. [W/cm K] 1.45 0.46 4 20max. temp. of device [°C] 200 400 800 1200

Applications of diamondApplications of diamond

- gemstones- hard tools (grinding, cutting, drilling, sawing, polishing …)- medicine: ultrasharp scalpels- protective coatings- semiconducting devices for high temperatures- heat sink in microelectronics- windows for spectroscopy

Other modifications of carbonOther modifications of carbon

• amorphous carbon• carbon fibers

amorphous network

fibers