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Carbon nanostructures: Carbon nanostructures: functional properties functional properties and characterization and characterization
F. Banhart, IPCMSF. Banhart, IPCMS
© not for publication in the internet or elsewhereimages protected by copyrights
• 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