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Graphene: Properties and Application
ISSP-INERA-30-06-2014
Valentin PopovFaculty of Physics, Sofia University
[email protected]://www.phys.uni-sofia.bg/~vpopov
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IntroductionPropertiesApplicationOutlook
Outline
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IntroductionPropertiesApplicationOutlook
Outline
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FULLERENESKCS, 1985NP 1996
0D
Introduction
GN, NP 2010“…for groundbreaking experiments regarding the two-dimensional material graphene…"
NANOTUBESIijima, 1991
1D
GRAPHENEGeim, Novoselov,
Science 306, 666 (2004)
Graphene is a perspective material for atomic-thin metallic field-effect transistors which would havesmaller size, lesser power consumption, higher operation frequencies.
GRAPHITE3D
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IntroductionPropertiesApplicationOutlook
Outline
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Properties
P. R. Wallace, 1947
Wallace model
( ) | |FE v± ≈ ±k k
( ) ( )E t f± = ±k k
( ) 3 2cos( ) 4cos( / 2)cos( 3 / 2)y y xf k a k a k a= + +k
( ),
ˆˆ ˆ . .i ji j
H t a b h c+= − +∑
±→ electrons/ holes
FLG - SWM model for graphite: Slonczewski and Weiss, 1958; J.W. McClure, 1957.
Dirac cones, Dirac points
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PropertiesWeyl equation
( ) ( )Fi v Eψ ψ− ⋅∇ =σ r r
/2
, /2
1( )2
i
K i
ee
θ
θψ
−
±
⎛ ⎞= ⎜ ⎟
±⎝ ⎠
k
kk
arctan( / )x yk kθ =k
± → electrons/ holes
Helicity operator ½ħσ·k/|k| → helicity ±½ for e/h
“QED on a table”: Klein tunneling, Zitterbewegung…
Semenoff, 1984Haldane, 1988
Two-component wavefunction → spinor → pseudospin
Observation of Dirac cones by ARPES: Zhou et al., Nature Physics 2006.
спиралност
A
B
ψψ
ψ⎛ ⎞
= ⎜ ⎟⎝ ⎠
ψψ
ψ↑
↓
⎛ ⎞= ⎜ ⎟⎝ ⎠
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PropertiesKlein tunneling
Theory: Katsnelson, Nature Physics 2006; Observation: Stander, PRL 2009, Young, Nature Physics 2009
The electrons can tunnel through potential barrier with probability of unity (Klein paradox).
ϕ – incident angleqx – electron momentum
V0 = 200 meV (blue)V0 = 285 meV (red)
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PropertiesElectrical transport
Scanning electron microscope image of the experimental device
Schematic of the experimental device
Novoselov et al., Science 306, 666 (2004)
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PropertiesZero-field transport
Novoselov et al., Science 306, 666 (2004)
Ambipolar field effect in 2D zero-gap semiconductor:
ρ(Vg) – sharp peak, σ(Vg) – linear dependence
ρ-1 = σ = neμ, n ~ Vg (theory) → σ ~ Vg (exptl.) μ - weak dependence on T, mainly limited by defects; μ = 3,000 - 10,000 cm2/V.s
σmin ≈ e2/h
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PropertiesAnomalous quantum Hall effect
Landau quantization
Novoselov et al., Science, 2007
Novoselov et al., Nature, 2005
Zhang et al., Nature, 2005
Quantum Hall effect Shubnikov – de Haas oscillations
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PropertiesGraphene quantum dots
Single electron transistor (SET)
Ponomarenko et al., Science, 2008
Coulomb blockade < 10 K
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PropertiesOptical absorption
Graphene is almost transparent
Mak et al., SSC, 2012
Absorbance πα ≈ 2.3%, α=πe2/ħc≈1/137
Nair et al., Science, 2008
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PropertiesPhonon dispersion
Raman-active phonon E2g
Wirtz et al., SSC, 2004
E2g
Malard et al., PR, 2009
Raman scattering
- first-order spectra – the G band- second-order spectra – two-phonon and
defect-induced bands excited by the double-resonance mechanism
Experimental data: inelastic neutron scattering, high resolution electron energy loss spectroscopy, double-resonance Raman scattering, inelastic x-ray scattering.
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PropertiesDoping effects
G band damping and energy renormalization
Yan et al., PRL, 2007
LO/TO branch @Γ and TO branch @K damping and renormalization
Popov et al., PRB, 2010
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PropertiesSpecific heat
Specific heat:saturates to the Dulong-Petit limit of 2.1 J/gK at high temperatures
Pop et al., MRS Bull., 2012
Theory:Electronic contribution - negligiblePhonon contribution: C ~ T2 for ω ~ q (LA, TA phonons)C ~ T for ω ~ q2 (ZA phonons)ω(ZA) < ω(LA,TA) → C ~ T below ~100 K
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PropertiesThermal expansion
Negative thermal expansion coefficient Experiment: < 350 K; Bao, 2009Theory: < 2300 K; Mounet, 2005
Bao et al., Nature Nanotechnology, 2009
This behavior is explained by the negative Grüneisen parameter of the ZA phonon mode γ (γ ~ α). This effect was predicted in membranes by Lifshitz, 1952.
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PropertiesThermal conductivity
Intrinsic thermal conductivity limited by only phononsdiamond ~2000 W/mKCNT ~2300 W/mKsuspended graphene ~2000 W/mK
Extrinsic thermal conductivity limited by defects, impurities, boundariesamorphous carbon ~0.01 W/mKsupported graphene ~600 W/mK
2j j j
j
K C v dτ ω=∑∫
Theory:Electronic contribution - negligiblePhonon contribution:
Chen, Nature Materials, 2012
Seol, Science, 2010
Pop et al., MRS Bull., 2012
Thermoelectricity:FoM: ZT = S2σT/KS ~ 100 µV/K (Zuev, PRL 2009)Increase ZT by suppressing thermal conductivityPredicted ZT~4 in graphene ribbons, not measured
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Density: 0.77 mg/m2; 1 m2 -> 0.77 mg
Optical transparency: almost transparentabsorbs only πα ≈ 2.3%
Mechanical strength:42 N/m; 1 m2 -> 4 kg100 times stronger than steel (same thickness)
Electrical conductivity:2D conductivity σ = enμμ = 200,000 cm2V-1s-1 limited by acoustic phonons at n = 1012 cm-2
2D sheet resistivity ρ = 31 Ω/3D conductivity: 0.96 x 106 Ω-1cm-1 higher than for copper of 0.60 x 106 Ω-1cm-1
Thermal conductivity:2D thermal conductivity: 5000 Wm-1K-1 dominated by phonons, higher than for copper of 400 Wm-1K-1
PropertiesSummary
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IntroductionPropertiesApplicationOutlook
Outline
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ApplicationGraphene production
Graphene dot, flakes, ribbons, sheets…: graphene electronics
-Mechanical exfoliation of HOPG (low yield, mainly for basic research) (Novoselov et al., Science 306, 666 (2004))
-Thermal exfoliation (graphene nanoribbons) (Wang et al., Science 319, 1229 (2008)).
-Electrochemical exfoliation (processing with sulphuric acid – high-quality, large-area, large yield of unoxidized defect-free few-layer graphene) (Paton et al., Nature Mater. (2014))
-Thermal decomposition of SiC (graphitization of Si-terminated SiC wafer) (Emtsev et al., Nature Mater. 8, 203 (2009)).
-Chemical vapor deposition (decomposition of hydrocarbons – large-scale production of few-layer graphene on copper and nickel foils; etching for removal of catalyst) (Kim et al., Nature 457, 706 (2009)).
Zhang et al., Accounts Chem. Res. 46, 2329 (2012)
CVD
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ApplicationGraphene production
Graphene oxide: composites, energy conversion and storage
-Graphene oxide GO) – produced by Hummer and Offeman method (mixture of sulphuric acid H2SO4, sodium nitrite NaNO3, and potassium permanganate KMnO4 as an oxidizing agent) (J. Am. Chem. Soc., 1958). GO structure – not established well: Hofmann, 1939 (repeat unit, epoxide groups C2O); Ruess, 1946 (incl. hydroxyl groups -OH); Lerf-Klinowski, 1998 (amorphous model, may include carboxyl groups -CO2H)
-Reduced graphene oxide (rGO) – chemical reduction with sodium borohydride (NaBH4) or hydrazine (N2H4), thermal reduction, electrochemical reduction, microwave-assisted reduction… resulting in partial removal of oxygen and recovery of aromatic rings.
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ApplicationGraphene composites
Rafiee et al., ACS Nano, 2009
Composites with improved mechanical properties
0.1% graphene filler in epoxy matrix → >20% increase of Young’s modulus and tensile strength
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ApplicationGraphene composites
Composites with improved electrical properties
Φc ~0.1vol% percolation threshold for polystyrene-graphene compositeandσc ~0.1S/m – sufficient for many electrical applications
Stankovich et al., Nature, 2006
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ApplicationGraphene composites
Composites with improved thermal properties
Verdejo et al., J.Mater.Chem., 2008
0.25 vol% graphene filler in silicon foam matrix→ ~6% increase of thermal conductivity
Composites with metals, metal oxides, nanoparticles (attaching nanoparticles to graphene, wrapping nanoparticles in graphene) for various applications
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ApplicationTransparent electrodes
Transparent electrodes are needed for LCD displays, touch panel displays, LEDs, solar cells, sensors, detectors, etc.
Most popular material for transparent electrodes is ITO (indium tin oxide).-Advantages: transparent, conducting-Drawbacks: rare element, brittle, poor adhesion to organic materials, expensive production technique by magnetron sputtering
Challenges:-Cheaper production technique, e.g., by chemical vapor deposition or deposition from solution-Cheaper materials, e.g., conductive polymers, metallic nanowires, nanowire-polymer composites, carbon nanotubes, graphene-Flexible electrodes
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ApplicationTransparent electrodes
material Sheet resistance Ω/ Transparency %
ITO on glass ~20 ~90
ITO on PET ~40-80 ~80PEDOT on PET ~200 ~90
Nanowires on glass/PET ~10 ~85Graphene on PET (CVD) ~30 ~90
Yong et al., Nature Nanotechnology, 2010; Hu et al., ACS Nano, 2010
PET=polyethylene terephthalate PEDOT=poly(3,4-ethylenedioxythiophene)
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ApplicationTransparent electrodes
Bae et al., Nature Nanotechnology, 2010; CVD at 1000 °C for 16 h, PET film of size 100 m x 0.2 mKim et al., APL, 2011, PECVD, at 500 °C
Chemical vapor deposition (CVD) method. ‐Decomposition of hydrocarbons, mainly methane and ethylene, in the presence of transition metal catalysts, mainly copper or nickel. Solubility problems with nickel. ‐Transfer of the graphene by etching the catalyst, removing graphene using polymer film (PET, PMMA, PDMS) by pressing the film, pressing the film onto target substrate, and removing the polymer film.
PMMA=poly(methyl methacrylatePDMS=polydimethylsiloxane
Graphene-based electrodes for ITO replacement
Improvement of electrical conductivity by doping with nitric acid (HNO3) – sheet resistance of 30 Ω/ at 90%.
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ApplicationTransparent electrodes
Bae et al., Nature Nanotechnology, 2010
Touchscreen displays:
a. Copper foil wrapping around a 7.5-inch quartz tube to be inserted into an 8-inch quartz reactor. The lower image shows the stage in which the copper foil reacts with CH4 and H2 gases at high temperatures.b. Roll-to-roll transfer of graphene films from a
thermal release tape to a PET film at 120 °C.c. A transparent ultralarge-area graphene film transferred on a 35-inch PET sheet.d. Screen printing process of silver paste electrodes on graphene/PET film. The inset shows 3.1-inch graphene/PET panels patterned with silver electrodes before assembly.e. An assembled graphene/PET touch panel showing outstanding flexibility.f. A graphene-based touch-screen panel connected to a computer with control software.
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ApplicationTransparent electrodes
Zhu et al., ACS Nano, 2011
Graphene layer was grown on copper foil by CVD and transferred on top of a metal grid of size ~0.1 mm x 0.1 mm prepared on glass or PET films. Sheet resistance: 20 Ω/ at 90%
Graphene-based electrodes for ITO replacement
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ApplicationSolar cells
Handbook of Photovoltaic Sci. & Eng., ed. A. Luque and S. Hegedus, John Willey & Sons, 2003
Theoretical limit of the efficiency of single-junction solar cell: max ~32% at band gap of 1.1 eV (Shockley).The efficiency is limited by blackbody radiation losses, radiative recombination, and incident light spectrum losses.
Shockley and Queisser, JAP, 1961
Conventional solid state solar cells implement a p-n junction between two electrodes; at least one of the electrode should be transparent; incident photon creates an electron-hole pair, which travel to the electrodes; the e.m.f. is equal to the quasi-Fermi level separation.
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ApplicationSolar cells
Electrochemical solar cells (Grätzel cells) use a photosensitizer; incident photons are absorbed by the photosensitizer, which is excited; the excited electrons are injected into the TiO2 electrode, thus oxidizing the photosensitizer; the electrons travel over the circuit to the other electrode, where they reduce the photosensitizer. Also: perovskite sensitizer; Mitzi et al., Nature, 1994
*Grätzel, Nature, 1991
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ApplicationSolar cells
Solar Cell Efficiency %
SiliconSi (crystalline) 25Si (multicryst., thin film) 20Si (amorphous) 10III-VGaAs (thin film) 29GaS (multicrystalline) 18InP (crystalline) 22
Solar Cell Efficiency %
Thin-film chalcogenideCIGS 20CdTe 20MultijunctionInGaP/GaAs/InGaAs 44OrganicDye sensitized 12Perovskite sensitized 14
Green et al., Prog. Photovolt: Res. Appl. 2014
Challenges:-Cheaper production method of the solar cells,-Cheaper materials,-Flexible electrodes
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ApplicationSolar cells
Graphene as ITO replacement
Ramuz et al., ACS Nano. 2012
P3DDT=poly(3-dodecylthiophene-2,5-diyl)
Active layer: Sc-SWNT(absorber and p-type)/C60(n-type)
Silver cathode+ITOEfficiency ~0.46%
All-carbonEfficiency ~0.004%
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ApplicationSolar cells
Graphene as ITO replacement
Park et al., Nano Lett.. 2013
P3HT=poly(3-hexylthiophene)
Active layer: PbS QD (P3HT) (absorber and p-type)/ZnO(n-type)
PbS QD (P3HT) Efficiency 4.2% (0.5%)
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ApplicationSolar cells
Graphene as ITO replacement
Park et al., Nature Sci. Rep., 2013
PEDOT:PSS=poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate)PEDOT:PEG (PC)=poly(3,4-ethylenedioxythiophene)-block-poly(ethylene glycol) (perchlorate)
Anode: grapheneActive layer: PEDOT:PSS (absorber and p-type)/C60(n-type)
Efficiency 10-15% of ITO
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ApplicationSolar cells
Graphene as ITO replacement
Wang et al., Nano Lett.. 2014
Active layer: Perovskite(absorber and p-type)/graphene-TiO2(n-type)
Efficiency 15.6%
Superstructured perovskite solar cellSolution-based fabrication at < 150 ºC
FTO=fluorine doped tin oxide coated glassPerovskite=Al2O3/CH3NH3PbI3-xClx
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ApplicationFuel cells
Proton exchange membrane (PEM) fuel cell: hydrogen enters the cell at the anode, where it is oxidized to ions and electrons; the electrons travel from anode to cathode, the hydrogen ions pass through the PEM to the cathode, where they meet oxygen and are reduced to water. Variant: Direct Methanol Fuel Cells. Catalyst of redox reactions: platinum
Advantages:-high energy density,-cheap fuelDrawback: -Pt is very expensive!
Challenges: replacement of bulk Pt with-Pt nanoparticles-cheaper metal catalyst-non-metal catalyst
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ApplicationFuel cells
Graphene as Pt nanoparticles support: advantage - higher surface area, lower production costs
Seger, J. Phys. Chem. C Lett., 2009
Pt nanoparticles on rGO support:Increase of catalyst activity by 80%
Non-platinum catalysts:N-doped graphene (Liang, Nature Mater., 2011)
Non-metal catalysts:edge-halogenated (Cl, Br, I) graphene nanoplatelets (Jeon, Nature Sci. Rep., 2013)
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ApplicationSupercapacitors
Electrochemical capacitors (supercapacitors):Double-layer capacitors: electrostatic storage through charge separation in a Helmholzdouble layer at each electrode;Pseudocapacitors: Electrochemical storage through faradaic charge transfer via redox reactions; desolvated alkali metal cations pervade the double layer, adsorb on the transition metal oxide layer (RuO2, MnO2, etc.) of the anode and transfer charge to it.Hybrid supercapacitors: capacitors with asymmetric electrodes (Li-ion capacitor).
←→ Helmholz double layer, formed by the electrode, solvent and solvated ions of the electrolyte
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ApplicationSupercapacitors
Ragone (1968) chart
Advantages: -fast charging,-unlimited cycle life,-quick operation mode.Drawback:-low energy density-rapid voltage drop
Challenge:-increase the energy density by increasing surface-to-volume ratio of anode for redox reactions
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ApplicationSupercapacitors
Yoo et al., Nano Lett. 2011
Transition-metal-oxide nanowire/single-walled carbon nanotubes thin-film electrodes: capacitance of 184 F/g, energy density of 25.5 Wh/kg (Chen et al., ACS Nano, 2010).
Vertically aligned and electrochemically oxidized carbon nanotube electrodes: capacitance of ~158 F/g and energy density of ~53 Wh/kg (Kim et al., Nanotechnology, 2012).
Graphene oxide electrodes: capacitance of 154 F/g and energy density of 85.6 Wh/kg (Liu et al., Nano Lett. 2011). (Also: Zhu et al., Science, 2011)
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ApplicationBatteries
Li-ion batteries (Sony, 1991): consist of a graphite anode, transition metal oxide cathode (LiXO2, X = Mn, Fe, Co, Ni), and an electrolyte (Li salt, such as LiPF6, LiBF4, or LiClO4, in an organic solvent, such as ether). The storage is based on a faradaic redox reaction. Upon charging Li ions percolate the anode and are reduced on it, upon discharge Li ions percolate back to the cathode and are oxidized on it.
Advantages: -high energy density-low self discharge-no memory effect.Drawback:-special charging and exploitation conditions-expensive
Challenge:-cheaper production-increase of charging cycles-increase of energy density
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ApplicationBatteries
Kucinskis et al. , J. Power Sources, 2013
The electrochemical activity can be improved by anchoring, mixing, wrapping or encapsulating the active cathode material particles in graphene, which forms a 3D conducting network
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ApplicationBatteries
Song, Nano Lett., 2013
The Li-S batteries: increase of electrochemical activity by using sulphur as cathode constituent; advantages – sulphur is nontoxic, safe, and inexpensive ; reduction of deterioration with cetyltrimethyl ammonium bromide (CTAB)-modified sulfur-graphene oxide nanocomposite cathode; twice larger energy density than Li-ion batteries.
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ApplicationGas sensors
Field effect transistors based on graphene are promising devices for high signal-to-noise ratio detection of various local electrical and chemical influences due to high carrier mobility and low intrinsic noise of graphene.
Schedin et al., Nature Mater., 2007
Measurement of NO2: resistance – 1 ppb, Hall resistance – 1 molecule!Optimal device size ~ 1 μm
Measurement of NH3, NO2, CO, CO2, O2, etc.Potyrailo, Chem. Rev. 2011.
Precise discrimination between the different gases by analyzing the low-frequency noiseRumyantsev et al., Nano Lett. 2012.
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ApplicationCharge sensors
Charge sensor: device, consisting of a quantum dot and a single electron transistor, fabricated by oxygen reactive ion etching of single layer graphene (dark areas).
Wang et al., Appl. Phys. Lett. 2010
Measurement of charges at the QD: once an electron occupies the QD, it is detected by the SET because of capacitive coupling with the dot: the conductance of the SET changes by ~ 30%.
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ApplicationHumidity sensors
Sreeprasad et al., Nano. Lett. 2013
Humidity sensor: graphene nanoribbons were assembled into polyallylminehydrochloride (PAH) nanofibers to form a percolating network
Measurement of humidity and temperature: graphene oxide is deposited by drop casting or spray coating on silver electrodes printed on a polyethylene naphthalate (PEN) substrate;. device resistance is proportional to temperature and humidity in the range 10-40 °C and 30-80%.Borini et al., ACS Nano 2012
Measurement of humidity and pressure: fibers swell on absorbing water, fiber volume increases,tunneling distance increases, current decreases;Pressure is proportional to water-to-fiber ratio.humidity range 0-40%.
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ApplicationTransistors
Schwierz, Nature Nanotech. 2010
Planar field-effect transistor (FET): the planar FET consists of a gate, a channel connecting source and drain electrodes, and a barrier separating the gate from the channel; application in digital logic (FoM = Ion/Ioff ratio) and radiofrequency devices (FoM = cut-off frequency).
Moore’s Law (1965):Component density doubles every 18 months (blue line). Reducing gate length and pitch is accompanied by increasing current leakage. Limit on gate length ~ 20 nm.
Solution: FinFET
Graphene – an option for post-silicon electronics?
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ApplicationTransistors
E=2.2 V/nm, ∆=130 meV, Ion/Ioff~100 @RT; Xia et al., Nano Lett. 2010
Graphene field-effect transistor for logic circuit devices
Challenge: high Ion/Ioff ratio → bandgap
Electric field Graphene nanoribbons
W=15 nm, ∆=200 meVHan et al., PRB 2007
Zhang et al., Nature 2009
W=10 nm, ∆=80 meVIon/Ioff~107 @RTLi et al., Science 2008
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ApplicationTransistors
Lin et al., Science 2010
Gate=240 nm, f=100 GHz Gate=40 nm, f=133 GHz
Wu et al., Nature 2011
Graphene field-effect transistor for r.f. applications
Challenge: high cut-off frequency
Gate=140 nm, f=300 GHz
Duan et al., Nature, 2010
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ApplicationOther applications
Light-emitting diodesEM radiation sensorsStrain sensorsEtc.
NTT
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IntroductionPropertiesApplicationOutlook
Outline
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OutlookGraphene publications (Web of Knowledge, June 2014)
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OutlookGraphene dreams
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Acknowledgments
This work was supported by Project #316309: INERA— Research and Innovation Capacity Strengthening of ISSP-BAS in Multifunctional Nanostructures.
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Thank you!