Physics of Nanotubes, Graphite and Graphene Mildred Dresselhaus

Quantum Transport and Dynamics in Nanostructures The 4 th Windsor Summer School on Condensed Matter Theory 6-18 August 2007, Great Park Windsor (UK) Physics of Nanotubes, Graphite and Graphene Mildred Dresselhaus Massachusetts Institute of Technology, Cambridge, MA

Physics of Nanotubes, Graphite and Graphene Outline of Lecture 1 - Nanotubes Brief overview of carbon nanotubes Review of Photophysics of Nanotubes Phonon assisted Photoluminescence Double wall carbon nanotubes Nano-Metrology

Carbon Nanotube researchstill a growing field 1991 nanotube observation by Sumio Iijima (NEC) opening field number of publications is still growing exponentially 6000 5000 4000 3000 2000 1000 0 1991 1996 2001 2006 number of publications containing Carbon Nanotube vs. time Iijima, S., Helical Microtubules of Graphitic Carbon. Nature, 1991. 354(6348): p. 56-58.

Carbon Nanotubes (5,5) Armchair Nanotube (9,0) Zigzag Nanotube (6,5) Chiral Nanotube (n,m) notation focuses on symmetry of cylinder edge

Carbon materials Diamond Graphite (hexagonal, rhombohedral) HOPG (highly oriented pyrolytic graphite) Pyrolytic graphite Turbostratic graphite Kish graphite Liquid carbon Amorphous carbon Carbon and graphitic foams Carbon fibers Fullerenes Nanotubes Nanohorns Graphene fibers and scrolls Graphene Graphene ribbons

3D, 2D, 1D Carbon Materials Diamond sp 3 (3D) 1332 cm -1 Graphite sp 2 (2D) 1582 cm -1 Chain sp 1 (1D) 1855 cm -1 All are Raman active with characteristic frequencies

Unique Properties of Carbon Nanotubes within the Nanoworld graphene sheet SWNT armchair zigzag chiral Size: Nanostructures with dimensions of ~1 nm diameter (~10 atoms around the cylinder) Electronic Properties: Can be either metallic or semiconducting depending on diameter and orientation of the hexagons Mechanical: Very high strength, modulus, and resiliency. Good properties on both compression and extension. Physics: 1D density of electronic states Single molecule Raman spectroscopy and luminescence. Single molecule transport properties. Heat pipe, electromagnetic waveguide.

One Dimensional Systems: High aspect ratio Enhanced density of states Single wall carbon nanotubes SWNT: Nanowire Chirality and diameter-dependent properties Nanotube D. O. S. D. O. S. D. O. S. D. O. S. E E E E 3D Bulk Semiconductor 2D Quantum Well 1D Quantum Wire 0D Quantum Dot

Nanotube Structure in a Nutshell (4,2) Graphene Sheet SWNT Rolled-up graphene layer Large unit cell. C na ma ( n, m) h = 1 + 2 θ = L a dt = = n + nm + m π π 1 3m tan 2n + m 2 2 Each (n,m) nanotube is a unique molecule R.Saito et al, Imperial College Press, 1998

Electronic structure of a carbon nanotube Rolling up 2D graphene sheet Confinement of 1D electronic states 1D van Hove singularities - high density of electronic states (DOS) at well defined energies Graphene ribbons resemble nanotubes in some ways

Metal or Semiconductor? R. Saito et al., Appl. Phys. Lett. 60, 2204 (1992) Density of States Depending on Chirality, Diameter 3p n m = 3 p ± 1 metal semiconductor E gap 1/ d t Each (n,m) nanotube is a unique molecule Armchair graphene ribbons can be M or S

Resonance Raman Spectroscopy (RRS) A.M. Rao et al., Science 275 (1997) 187 RRS: R.C.C. Leite & S.P.S. Porto, PRL 17, 10-12 (1966) Enhanced Signal Raman spectra from SWNT bundles Optical Absorption e-dos peaks E = 0.94eV = 1.17eV π π diameter-selective resonance process ω RBM = α /d t = 1.58eV = 1.92eV = 2.41eV

Resonant Raman Spectra of Carbon Nanotube Bundles M. A. Pimenta (UFMG) et al., Phys. Rev. B 58, R16016 (1998) G-band resonant Raman spectra laser energy G-band Diameter dependence of the Van-Hove singularities d t = 1.37 ± 0.18 nm

RBM Single Nanotube Spectroscopy yields E ii, (n,m( n,m) Resonant Raman spectra for isolated single-wall carbon nanotubes grown on Si/SiO 2 substrate by the CVD method A. Jorio (UFMG) et al., Phys. Rev. Lett. 86, 1118 (2001) Semiconducting Metallic ' Each nanotube has a unique DOS because of trigonal warping effects Raman signal from one SWNT indicates a strong resonance process R. Saito et al., Phys. Rev. B 61, 2981 (2000) (ω RBM, E ii ) (n,m)

Raman Spectra of SWNT Bundles G-band Metallic G-band G - G + G + Raman Intensity RBM: ω RBM 1/d t G - D-band G + G -band o Raman Shift (cm 1 ) RBM gives tube diameter and diameter distribution Raman D-band characterizes structural disorder G - band distinguished M, S tubes and G + relates to charge transfer G band (2nd order of D-band) provides connection of phonon to its wave vector

Water, 1.1 g/cm 3 SDS 1.0 g/cm 3 Band Gap Fluorescence M. J. O Connell O et al., Science 297 (2002) 593 S. M. Bachilo et al., Science 298 (2002) 2361. Energy [ev] 2 c 1 c 2 1.2 g/cm 3 SDS=Sodium Dodecyl Sulfate 0 fluorescence absorption v 1 v 2 Excitation (nm) Peaks only Emission (nm) 2 0 Density of Electronic States e-dos of (n, m) = (10,5) Initially (n,m) assignments were made by empirical excitation-emission pattern

PHOTOLUMINESCENCE SDS-wrapped HiPco nanotubes in solution S. M. Bachilo et al., Science 298, 2361 (2002) 2n+m=constant family patterns are observed in the PL excitation-emission spectra Identification of ratio problem Showed value of mapping optical transitions Perhaps this technique can be applied to study graphene ribbons

Raman Mapping of a Nanotube G-band @ 1600cm -1 x 10 40 4 20 2 2.5 RBM 40 @ 173cm -1 4 2 20 1000 Silicon @ 520cm -1 4 2 40 x 10 9 8 20 7 0 0 2 0 0 800 0 0 6 (µm) -20-2 1.5 (µm) -2-20 600 (µm) -2-20 5-40 -4 1-4 -40 400-4 -40 4 3-60 -6-80 -8 0.5-100 -20 0 20-2 0 2 (µm) -10 0-6 -8-60 -80-100 -20 0 20 200-2 0 2 (µm) -10 H. Son et al. unpublished (2006) 0-6 -8-60 -80 1-100 -20 0 20-2 0 2 (µm) -10 2 0

Resonance Raman Spectroscopy on the same sample used for PL E 33 S E 11 M E 22 S RRS 2n+m = constant family behavior is observed E 33 S Fantini (UFMG) et al. PRL (2004) showed RRS and PL give the same E ii Family effects are mainly due to trigonal warping E 11 M E 22 S simple tight binding (stb) stb γ 0 =2.9eV The simple TB does not describe E ii correctly!

EXTENDED TIGHT BINDING MODEL Kataura plot is calculated within the extended tight-binding approximation using Popov/Porezag approach: Transition Energy (ev) curvature effects (ssσ, spσ, ppσ, ppπ) long-range interactions (up to ~4Å) geometrical structure optimization The extended tight-binding calculations show family behavior (differentiation between S1 & S2 and strong chirality dependence) similar to that of the PL empirical fit Inverse Diameter (1/nm) M 2n+m=3p S1 2n+m=3p+1 S2 2n+m=3p+2 Family behavior is strongly influenced by the trigonal warping effect Ge.G. Samsonidze et al., APL 85, 5703 (2004) N.V. Popov et al Nano Lett. 4, 1795 (2004) & New J. Phys. 6, 17 (2004)

Brillouin zone (BZ) 2D graphene BZ 2n+m families in SWNTs R. Saito et al., Phys. Rev. B, 72, 153413 (2005) SWNT BZ K K Family mod (2n+m, 3) = type I 0 : metal 1 : type I SC 2 : type II SC type II (example) 2n+m = const family type I type II separation (8,0), (7,2), (6,4) 2n+m = 16 type I family

DNA wrapping of SWNTs DNA Wrapping: provides good separation of CoMoCAT SWNT sample Subsequent fractionation: results in sample strongly enriched in (6,5) species M. Zheng, et al. Science 302, 1546 (2003) Average DNA helical pitch ~ 11nm, height ~ 1.08nm.

DNA-Assisted Assisted SEPARATION M. Zheng et al., Science, 302,1546 (2003). column containing stationary phase load sample add eluant collect samples Raman characterization shows that DNA wrapping removes metallic (M) SWNTs Chromatography further removes M SWNTs preferentially Ion-exchange chromatography (IEC) Hybrid DNA-SWNTs: M-SWNT different surface charge density, higher polarizability, elute before S-CNTs RBM Spectra Taken at E laser = 2.18eV CoMoCAT CNT (No DNA) DNA-CNT M (6,5) S Fractionated DNA-CNT 150 200 250 300 350 400 Raman Shift (cm -1 )

Nanotube PL Spectroscopy Most Measurements - excitation at E 22, emission at E 11 - measured with Xe lamp - (2n+m) family patterns provide (n, m) identifications. Our Measurements (6,5) enriched sample Intense light source (laser) Allows observation of phonon assisted processes PL map of SDS- dispersed HiPco CNTs Maruyama et al. NJP (2003) Maruyama s work suggests study of detailed phonon-assisted excitonic relaxation processes for different phonon branches.

PL Spectra of (6,5) Nanotubes 1.64 8 Excitation Energy (ev) 1.6 7.5 7 1.56 6.5 1.52 6 1.48 5.5 5 1.44 1.05 1.1 1.15 1.2 1.25 Emission Energy (ev) 1.3 Phonon-assisted transitions on an expanded scale Chou, et al PRL 94, 127402 (2005) E11 = 1.26eV E22 = 2.18eV

Excitons in Carbon Nanotubes Experimental Justification for excitons 2-photon excitation to a 2A + symmetry exciton (2p) and 1-photon emission from a 1A exciton (1s) cannot be explained by the free electron model 1A E 11 (1s) 2A+ E 11 (2p) BAND-EDGE ABSORPTION (a.u.) 1.2 1.4 1.6 1.8 2.0 2-PHOTON EXCITATION ENERGY The observation that excitation and emission are at different frequencies supports exciton model 1A E 11 (1s) EMISSION ENERGY 1.4 (9,1) (8,3) 1.3 (6,5) (7,5) 1.2` 1.2 1.4 1.6 1.8 2-PHOTON EXCITATION ENERGY Wang et al. Science 308, 838 (2005)

The exciton-phonon sidebands further support exciton model HiPco + SDS solution E 22 S -E 11 S Sideband F. Plentz Filho (UFMG) et al, PRL 95, 247401 (2005) E 11 S -E 11 S Perebeinos, Tersoff and Avouris, PRL 94, 027402 (2005)

Emission Identified with One and Two Phonon Processes: 2 ilo/ito near Γ Phonon dispersion relations of graphite 2 ito near K (G band) 2 ilo/ila near K 2 oto near Γ(M-band) 1iLO/iTO near Γ (G-band) Chou et al., PRL 94, 127402 (2005) Two phonon process One phonon process

Non-degenerate Pump-probe probe Frequency domain S. G. Chou et al. PRL 94 127402 (2005) Fast optics, Time domain E pump = 1.57±0.01eV, ~E 11 (6,5)+2ħω D E probe = around E 11 of (6,5) nanotube (Instrument resolution ~250fs) E Pump ~E 11(6,5) + 2ħω ph, D Eprobe =E 11(6,5) Pump Intraband relaxation Probe Interband relaxation S. G. Chou et al. Phys. Rev. B (2005)

Pump Probe Studies at Special E pump E pump = 1.57±0.01eV E 11 1A- (6,5) +2ħω D E probe = around E 11 1Aof (6,5) nanotube Intraband relaxation Pump Probe at band edge Exciton population at E 11 1A- (6,5): Quick rise (within 200fs) Three decay components: τ fast ~680fs (dominant process) τ int ~2-3ps (dominant process) τ slow ~50ps (weak during first 20ps). K

Exp. (n,m) E Probe FluenceJ/m 2 fast % Int % Slow % O 5 (8,3) 1.27eV 0.3 900fs 70 Several ps Traces mixed 30ps 30 O 4 (6,5) 1.25eV 0.3 700fs 45 3ps 45 50ps 10 O 2 (7,5) 1.20eV 0.1 800fs 90 N/A N/A 40ps 10 Probing at Different Energies: -Pump at 1.57±0.01 ev 1.27eV(8,3) E ii j E 1A- 11 E 1A- 11 (6, 1A- (8,3) + 2hw D 6,5) + 2hw D 1.25eV(6,5) u E 11 1A- (7,5) + 2hw D 1A- (7 1.22eV 1.20eV(7,5) 1.16eV o 5 o 4 o 3 o 2 o 1 E 11 1A- E 11 1A- 1A- (6 E 11 1A- 1A- (8.3) (6,5) (7,5) 1A- (7 z 0 K

Why? More on Excitons Large binding energy (0.5eV) Even at room temperature, excitons exist. Exciton specific phenomena dark excitons, two photon, environment What can we know or imagine? Near cancellation by self energy ETB + many body effects reproduce Eii Localized exciton wave function enhancement of optical process Length dependence. Wang et al. Science 308, 838 (2005) 2+ A 1-11 (2p) A 11 (1s)

Exciton exists only in the 3M-triangle E11S E22S E55S E44S E33S Energy minima for the π band exist only in 3MΔ. Cutting lines occur around K-point.

Centre of mass motion Symmetry considerations J. Jiang et al. Phys. Rev. B75 035405 (2007) :Good quantum number Relative motion A symmetry excitons Bright and dark excitons A - : bright exciton A +, E and E *: dark excitons K K Γ K e h K e h C Γ 2 K Γ e hk K A ±

E symmetry exciton and its dispersion E exciton h K E* exciton K K e K K e K K K h Bright and dark excitons A - : bright exciton A +, E, E *: dark excitons Dispersion for (6,5) NT

Lowest energy but not symmetry allowed Dark state has the lowest energy J. Jiang et al. Phys. Rev. B75 035405 (2007) A - : bright exciton A - : bright exciton A +, E and E *: dark excitons 11 11 11 11

Raman Spectra of SWNT Bundles G-band Metallic G-band G - G + Raman Intensity RBM: ω RBM 1/d t G - D-band G + G -band o Raman Shift (cm 1 ) Photophysics of SWNTs is now at an advanced stage Photophysics of MWNTs (DWNTs) is at an early stage

Motivation for studying DWNTs Applications world shows much interest Synthesis world has made major progress Promising for fundamental physics Study of the interface between DWNTs and bilayer graphene should enrich both areas

Approaches to DWNTs simplest assumption + = Suggests using Kataura plots for SWNTs as first approximation for DWNTs, but E(k) of monolayer and bilayer graphene say more detail is needed

Br 2 -doped double-wall nanotubes TEM images (a) Pristine DWNTs (b) Br 2 -DWNTs Highly pure samples (99% of DWNTs + 1% of SWNTs + catalysts particles) 5 nm (c) 5 nm (d) SEM images 100nm 100nm Endo et al. Nanolett. 4,1451 (2004)

Kataura plot: undoped vs. doped SWNTs using Extended Tight Binding Model Outer tubes Inner tubes 2.4 2.0 d t (nm) 1.6 1.2 0.8 Doped (+0.04 e - /C) 2.5 29 26 21 18 17 Undoped E ii (ev) 2.0 1.5 E M 11 E S 33 35 38 36 39 E S 22 32 30 33 29 28 31 27 26 25 24 23 22 E S 11 19 20 16 Different configurations for outer/inner nanotubes depending on laser energy 1.0 100 150 200 250 300 350 Frequency (cm 1 )

Semiconducting outer/metallic inner configuration M S RBM properties at E laser =2.33 ev Breathing mode spectrum from the Br 2 dopant Resonance with Bromine electronic transitions Can identify individual (n,m) inner tubes from Kataura plot Raman Intensity (arb. units) 1.0 (a) E Laser = 2.33 ev (12,3) (11,5) (9,6) (7,7) Pristine (8,5) (9,3) Raman Intensity (arb. units) 1.4 (b) E laser = 2.33 ev 100 150 200 250 300 350 Frequency (cm -1 ) A.Souza-Filho. et al PRB (2006) Br 100 150 200 250 300 350 Br 2 -doped 2 Frequency (cm -1 ) 26 29 21 32 24 35 22 38 27 23 150 200 250 Frequency (cm 1 )

Metallic outer/semiconducting inner configuration Raman Intensity (arb. units) 1.0 Raman Intensity (arb. units) 1.4 100 150 200 250 300 350 Frequency (cm -1 ) 3 (a) 1.0 E laser = 1.58 ev (9,4) 240 250 260 270 280 Frequency (cm -1 ) 39 S (10,2) 36 * 33 31 M RBM properties at E laser =1.58 ev 29 * (11,0) 28 25 22 pristine (9,1) E S 11 Intensity enhancement after bromine doping Doping changing relative intensities of (n,m) tubes The Kataura plot for SWNTs gives identification for inner wall tubes and shows doping effect (b) E laser = 1.58 ev Br 2 doped 1.4 (9,4) (10,2) 240 250 260 270 280 Frequency (cm -1 ) * * (11,0) E S 22 150 200 250 Frequency (cm 1 ) 100 150 200 250 300 350 Frequency (cm -1 )

Metallic shielding effects Metallic outer/semiconducting inner wall D and G band (DWNTs) E laser =1.58 ev S M Raman Intensity 1500 1550 1600 1650 Frequency (cm -1 ) 1301 Br 2 -doped D band 1554 Pristine 1200 1300 1400 1500 1600 1700 Frequency (cm -1 ) The G-band is predominantly from semiconducting Nanotubes (based on diameter dependence) No shift in the G-band for semiconducting inner tubes The inner tubes are shielded by the metallic outer tubes

Charge transfer effects Semiconducting outer/metallic inner E laser =2.33 ev D and G band (DWNTs) Br 2 -doped 1581 1570 1599 M S Raman Intensity D band 1341 1545 1450 1500 1550 1600 1650 Frequency (cm -1 ) 1592 1575 x0.5 Pristine 1485 1562 1537 1519 1200 1400 1600 Frequency (cm -1 ) 1450 1500 1550 1600 1650 Frequency (cm -1 ) The G-band profile is a mixing of semiconducting and metallic profiles; Shift in the G-band from semiconducting outer tubes indicates charge transfer to the Br 2 molecules The BWF (Breit Wigner Fano) decreases after doping. The decrease in the overall intensity indicates depletion of states

Charge transfer and screening effects Raman Intensity (a) M Br 2 doped Pristine S x0.3 Raman Intensity 1450 1500 1550 1600 1650 Frequency (cm -1 ) Metallic inner tubes highly affected by doping E laser 2.33 ev (b) G band Raman spectra of Br 2 doped DWNTs. S M E laser 1.58 ev Semiconducting inner tubes is not affected when shielded by metallic tubes 1450 1500 1550 1600 1650 Frequency (cm -1 )

Calculated electronic charge density difference (ρ doped - ρ undoped ) of DWNTs Calculation supports experimental observations about charge transfer A.G. Souza Filho et al Nano Letters (2007)

Outer tubes Undoping experiments on bromine doped DWNTs Br 2 -adsorbed DWNTs Br 2 Inner tubes E laser =2.33 ev Br 2 Energy needed for removing Br 2 is ~ 25 mev Raman Intensity cooling 21 o C heating 600 o C 100 200 300 400 500 Frequency (cm -1 ) 21 o C The dopant is completely removed after heat treatment Souza Filho et al, PRB (2006)

Spectrum for RBM for pristine and H 2 SO 4 doped DWNTs Outer Walls M Inner Walls H 2 SO 4 doped E laser =2.052 ev Pristine Raman Intensity S 150 200 250 300 350 400 Frequency (cm -1 ) Outer walls strongly affected by doping Inner semiconducting (S) tubes weakly interact with dopant Inner metallic (M) tubes more strongly interact with dopant E. Barros et al, PRB (2007)

What we learned from intercalation studies of DWNTs The Kataura plot from SWNTs provides a semi-quantitive interpretation of frequencies for inner wall tubes for DWNTs The M/S configuration shields inner semiconducting tubes from the effect of the dopant The S/M configuration allows charge transfer to inner metallic tubes S M M S This work potentially relates to bilayer graphene

Laser Energy Dependence of G -band Spectra The ~2450 cm -1 peak (TO+LA) in DWNTs is downshifted relative to the corresponding peak in SWNTs The SWNT G band corresponds to peak 3 of DWNTs Frequency (cm -1 ) 2700 2650 2600 2550 2500 2450 SWNTs 2.186 ev inner outer 2400 2600 2800 Frequency (cm -1 ) 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 Excitation Energy (ev) 4 3 2 1 0 Some resemblance to bilayer graphene E. B. Barros et al., PRB in press (2007)

The problem of Nano-metrology Why do we need metrology for nanotechnology? Why do we need reference standards? What is new about metrology at the nano-scale? What does nanoscience have to do with metrology? World wide production of Carbon Nanotubes MWNTs 270 tons/yr (2.45 10 5 kg/year) SWNTs 7 tons/yr (6.35 10 3 kg/year) 8K US$ / kg to 5.0 10 5 US$ / kg (R. Blackmon, http://www.wtec.org/cnm/)

Metrology is guided by applications Potential Applications of Carbon Nanotubes by M. Endo, M. S. Strano, P. M. Ajayan @ Springer TAP111 Large Volume Applications Limited Volume Applications (Mostly based on Engineered Nanotube Structures) Present Near Term (less than ten years) Long Term (beyond ten years) - Battery Electrode Additives (MWNT) - Composites (sporting goods; MWNT) - Composites (ESD* applications; MWNT) *ESD Electrical Shielding Device - Battery and Super-capacitor Electrodes - Multifunctional Composites - Fuel Cell Electrodes (catalyst support) - Transparent Conducting Films - Field Emission Displays / Lighting - CNT based Inks for Printing - Power Transmission Cables - Structural Composites (aerospace and automobile etc.) - CNT in Photovoltaic Devices - Scanning Probe Tips (MWNT) - Specialized Medical Appliances (catheters) (MWNT) - Single Tip Electron Guns - Multi-Tip Array X-ray Sources - Probe Array Test Systems - CNT Brush Contacts - CNT Sensor Devices - Electro-mechanical Memory Device - Thermal Management Systems - Nano-electronics (FET,Interconnects) - Flexible Electronics - CNT based bio-sensors - CNT Fitration/Separation Membranes - Drug-delivery Systems

What should we measure? At which scale? Quantity vs. mass Mass remaining Remaining, % (%) 100 90 80 70 60 50 40 30 20 10 0 Quality Statistical Comparison QCM shows SWNTs are non-homogeneous already at the μg scale TGA (375 C) ~mg Experiment Number 77.90 % 5 9 13 17 21 1 experiment number 25 mass remaining (%) Thermogravimetric analysis (TGA) Quartz cyrstal microbalance (QCM) Mass Remaining, % 100 90 80 70 60 50 40 30 20 10 QCM (375 C) ~µg 75.88 % 0 1 5 9 13 17 21 1 experiment Experiment Number number 25

Can we trust the measurements? What do we use for measuring nanomaterials properties? 4-PROBES TRANSPORT 2 R 14 R 12 +R 23 +R 34 1 3 4 SCANNING PROBES ELECTRON MICROSCOPY Purewal et al.,prl 98,186808 (2007) IBM Website LIGHT: Raman and photoluminescence LOCALIZED LIGHT EMISSON 50nm From Achim Hartschuh From Hubert - FEI

Can we trust the measurements? What is the ideal environment? Encapsuled by micelles Suspended in air Sitting on a substrate Within a forest Nano-metrology is a wide open area for development requiring collaboration between metrology and nanoscience experts