carbon nanostructures: functional properties and ...qmmrc.net/winter-school-2010/pdf/banhart.pdf ·...
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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© not for publication in the internet or elsewhereimages protected by copyrights
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• The carbon atom
• The modifications of carbon
• Graphene
• Fullerenes
• Nanotubes
• Diamond
• Characterization
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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
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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
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The phases: The phases: graphite and diamondgraphite and diamond
diamond graphite
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Phase diagram of carbonPhase diagram of carbonpressure
[GPa]
temperature [103K]
[kbar]
graphite
diamond
liq.liq.
gasgas
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Modifications of carbonModifications of carbon
Graphene / Graphite Diamond
Fullerenes Onions Nanotubes Exotics
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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!
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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
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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
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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)
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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
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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
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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
- …
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GraphiteGraphite
crystallography of graphite
multi-layer graphene
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Carbon NanoparticlesCarbon Nanoparticles
single-shell
multi-shellNanotubes
SWNT
MWNT
1.4 nm
7 nm
Fullerenes
C60
"Onions"
0.7 nm
5 nm
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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
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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, ….
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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 (?)
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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
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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
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(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 ?
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MultiMulti--shell fullerenes: Carbon onionsshell fullerenes: Carbon onions
C60@C240@C540
pentagons, hexagons, heptagons
TEM image
2 … >100 shells
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Applications of carbon onionsApplications of carbon onions
pressure cells for diamonddiamond nucleation encapsulation of metal crystals
Au
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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
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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
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Rolling up a graphene layerRolling up a graphene layer
1111
77
(11,7)-tube
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Chirality of nanotubesChirality of nanotubes
armchairarmchair
chiralchiral
zigzagzigzag
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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)
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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
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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)
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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
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Measurement of electrical propertiesMeasurement of electrical propertiessingle nanotubes on electrodessingle nanotubes on electrodes
test circuitstest circuits
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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
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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
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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
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CVD growth of nanotubes on patterned CVD growth of nanotubes on patterned substratessubstrates
nanotube bundle
pattern on Si substrate
SWNT array
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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 ??
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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
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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
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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
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Carbon nanocompositesCarbon nanocomposites
• atoms/molecules in carbon nanotubes• crystals in/on nanotubes
contacts with metals
nanotube-DNA composites
atoms/molecules in nanotubes
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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
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Metals in carbon nanotubesMetals in carbon nanotubes
Fe in carbon nanotubes
Nanotubes as templates for the production of metallic nanowires
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Filling nanotubes with fullerenes: Filling nanotubes with fullerenes: peapodspeapods
EndohedralfullerenesGd@C82in nanotubes
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Mechanical applicationsMechanical applications
single-wall nanotubes: - extreme strength- extreme structural fexibility
"space elevator"
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Applications in microscopyApplications in microscopy
AFM / STM tip field emitterfor TEM / SEM
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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
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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)
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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
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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
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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
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Other modifications of carbonOther modifications of carbon
• amorphous carbon• carbon fibers
amorphous network
fibers