1. Boris Altshuler
Igor Aleiner
David Reichman
Laura Kaufman
Mike Steigerwald
Stephen O’Brien
Ruben Gonzalez
Mark Hybertsen

2. Excited Electronic States of Carbon Nanotubes
Gordana Dukovic, Matt Sfeir, Louis Brus
Chemistry Dept, Columbia University, New York, NY
Collaboration among Heinz, O’Brien, Hone, Turro, Friesner, and Brus groups at Columbia, and Zhu TEM group at Brookhaven.
1.Band Structure and Electron-Hole Binding – Excitons
2. Sidewall Endoperoxides and Auger non-radiative recombination
2.Resonant Rayleigh Scattering from individual tubes and
Spectral Assignment
3 Growth, Short Tubes, and the Diffuse Interstellar Bands

3. SWNTs – a family of long molecules
Ch = n a1 + m a2  (n,m)
(4,2)
>100 distinct SWNT structures defined by indices (n,m)
Defining structural features: diameter and chirality
Each physical structure has a unique electronic structure

4. Huckel π and π* MOs (Band structure) of graphite MO Energies are a function of good quantum number electron momentum k(x,y) in the plane of graphite Electron momentum k is continuous for infinite plane of graphite
α = 0
γ0 = eV
(fitted to reproduce
ab initio results) π* π
Semi-metallic behavior at K-points
Saito and Kataura, Topics Appl. Phys. 2001, 80, 213

5. Electron momentum k quantized around circumference.
Independent Electron Model: for one (n,m) tube, only a series of momentum stripes from graphite are possible
Metallic:
Nanotube:
Electron momentum k quantized around circumference.
Electron momentum remains continuous along length
Semiconducting:
empty
filled

6. Molecular Tubes– some Chiral
(10,10) Arm-chair
Metallic Wire
(18,0) Zig-zag
Small gap
Semimetallic Wire
(7,12)
Chiral
Semiconductor
Images from Hongjie Dai

7. How are SWNTs made? Chemical Vapor Deposition 800 C on a metallic Fe particle catalyst
CnHm
CnHm Fe
Catalyst Support
Images from Hongjie Dai
Synthesis makes a broad range of (n,m) values in the gas phase. These must then be solubilized

8. Experimental Micellar Optical Spectra of Semiconductor SWNTs : What are these transitions –delocalized HOMO to LUMO, or localized Bound Excitons?
(7,6)
(12,1)
(11,3)
(10,5)
(9,7)
Pump wavelength 800 nm
[(n,m) assignment according to S.M. Bachilo et al. Science 298, 2361 (2002)]

9. Excitons Due to electron-hole attraction?
Exciton Bound states below
the van Hove Band Edge
Exciton envelope wavefunction:
Neutral excited state moves as a unit along the SWNT?

10. Selection Rules for two photon and one photon spectra
No Exciton:
Exciton: 1s 2p
Band edge
Band edge
Density of states:
(DOS)
Fluorescence:
no shift
large shift X
Two photon absorption:
forbidden
onset
onset
Experiment: Measure fluorescence intensity as a function of 2-photon excitation energy with tunable femtosec laser

11. Two-photon excitation spectroscopy
800 nm (1.55 eV)
130 fs
Ti:sapphire
Spectr.
+ CCD
+ InGaAs
Pump
OPA
Spitfire
amplifier
sample
1200 – 2500 nm
(0.5 – 1.0 eV)
Peak power ~ 108 W

12. Two Photon Excitation spectra of individual fluorescence peaks
F. Wang etal, Science 308, 838(2005)
Energy levels of transitions observed directly from 2-photon excitation spectra and emission peak energy 1s 2p
Band edge

13. Exciton energies band gap 1.7 eV 1g 2u (6,5) nanotube Continuum states
Ebinding
0.43 eV
band gap 1.7 eV
E2p – E1s
0.31 eV
(6,5) nanotube
dt = 0.76 nm
For comparison:
Poly(phenylene vinylene) ~ 0.35 eV
Semiconductor nanowires ~ tens of meV

14. Scaling of exciton binding energy
Consistent with theoretical predictions
(Perebeinos, V.; Tersoff, J.; Avouris, P. PRL 2004, 92, )
Dukovic, G. et al; Nano Letters 2005, 5, 2314.

15. Topic 2: Photochemistry: Absorption bleaching and luminescence quenching at low pH
Overall increase in intensity with increasing pH – hole doping at acid pH due to a protonated surface oxide(??) (also observed by Strano et al, J. Phys. Chem, 2003, 107, 6979)
Luminescence more sensitive to H+ than optical absorption
What exactly is on the surface??

16. Crucial role of oxygen Heating under Ar at 97 ˚C recovers fluorescence
Both O2 and H+ necessary to quench fluorescence
Hypothesis: quenching due to “protonated oxide”
Dukovic etal, J. Am. Chem. Soc. 126, (2004)

17. SWNT Surface Endoperoxide hypothesis
Many large aromatic molecules reversibly bind diatomic oxygen +
DFT calculation
ENDOPEROXIDE
PROTONATED OXIDE

18. Endoperoxide Energetics by DFT for short SWNT section
1 eV
1.3 eV
0.1 eV
Controlled oxidation for further chemical modification.

19. SWNT re-oxidation with 1 O2 from naphthalene endoperoxide thermal decomposition in solution. How many sidewall endoperoxides necessary to quench luminescence??
Luminescence quenched
Absorption NOT bleached

20. Effect of holes from protonated oxide on SWNT
Exciton and/or hole mobile along length of SWNT
Fluorescence quenching – ~ 10 holes per 400 nm tube – experimental result
Absorption bleaching – ~ 250 holes per 400 nm tube – from band filling theory.
Difference in sensitivities to holes in absorption and luminescence explained by Auger non-radiative recombination
exciton + h+  h+ + kinetic energy
fsec luminescence decay shows Auger recombination also:
Exciton + Exciton  Exciton + kinetic energy

21. Topic 3: Optical Spectroscopy of Single Nanotubes : Can we identify individual tubes?
Existing techniques:
Resonance Raman spectroscopy.
Fluorescence Excitation Spectroscopy.
We perform white light Rayleigh scattering spectroscopy.
Advantages:
Direct probe of electronic transitions, intrinsically stronger than Raman Scattering.
Present for both semiconductor and metallic nanotubes.
Data recorded in parallel – 1 minute signal averaging

22. Theoretical Rayleigh Scattering from a Cylinder
e = e1 + ie2
(23,0) eV
Peaks in the Rayleigh scattering spectrum are due to the peaked dielectric function, from interband transitions (above) or possibly excitons.
The scattering cross section for a single nanotube is ~ 0.1 % of total extinction. The two become comparable at a diameter of around 40 nm.

23. High brightness – like laser
Supercontinuum White Light Radiation generated in a microstructured core optical fiber
Spectral range:
High brightness – like laser
Large spectrum bandwidth – like a light bulb nm
Microstructured fiber: core ~ 2 m

24. Rayleigh Scattering: Experimental Setup Supercontinuum Generation
laser system
Mode-locked Ti:Saph coupled to microstructured fiber optic.
nonlinear fiber
piezo (oscillating in z)
supercontinuum light
Laser brightness
polarizers
spectrograph and CCD
Spectral range: nm
Scattered light is corrected by the supercontinuum spectral profile giving the Rayleigh spectrum
reference beam
polarizers
excitation and collection objectives
spatial filter (pinhole)
sample
scattered light
transmitted light

25. Growth and Imaging CVD Growth Process Imaging 10 mm
Si/SiO2 substrates with slits patterned by optical lithography and wet etching.
Directional growth determined by flow direction of feed gas, lengths > 100 microns:
CO, methane, and ethanol gas
Fe, FeMo, and CoMo catalysts
Isolated SWNT
slit edges
Imaging
Look at total integrated intensity on CCD to find tubes. Correlates to SEM images.
nanotube scattering
Single tubes scatter light much less than bundles. Distinguishable from the number of peaks in the spectra and width of features.

26. Experimental Single SWNT Resonance Rayleigh Spectra
M. Sfeir etal, Science 306, 1540 (2004)
Scattering
DOS
E33
Semiconducting Carbon Nanotube
E44
Two well separated E33 and E44 transitions for larger diameter tubes, E33 and E22 for smaller diameters. eV
Metallic Carbon Nanotube
E22
Single E22 transition observed in the visible – sometimes split into two very close peaks by trigonal warping effect eV

28. T. Beetz, Y. Zhu Brookhaven – M. Sfeir Columbia Science 312, 554 (2006)

29. Topic 4: SWNT Nucleation, Short Tubes, and the Diffuse Interstellar Bands
Electronic Transitions due to an Unidentified Family of Large Aromatic Molecules
Perhaps flat aromatic PAHS.
Could they be due to tubular PAHs , that is , short stubs of SWNTs, grown on Fe clusters?

30. Graphite dust and PAHs are present in the Interstellar Medium
PAHs emit vibrational luminescence following electronic excitation
under collision free conditions
How are they formed?

31. Astrophysical Graphite Formation at High Temperature
Graphite and PAH formation in the outflows of Carbon Rich Stars:
Graphite condenses from acetylene at about 1700 K in equilibrium thermodynamics -- probably supercools to about 1200 K.
Fe in about 10% abundance compared to carbon. Fe predicted to be present as neutral metallic clusters.
Perhaps short stubs of SWNT are formed on Fe clusters.
Sharp and Wasserburg, Geochem. Cosmochem. Acta 59, 1633 (1995)

32. Astrophysical Fe/C ratio is 1/10 SWNT Growth on Fe cluster at Acetylene pressure of 10-6 torr
TEM images acquired after growth and cooling
Catalyst:
Ni supported on MgO
C-source:
C2H2 –10-6 torr
particle diameter < 6nm  SWNTs
Particle vs. nanotube diameter = 2-1:1
bigger particles  nanocages
Lin etal Nanoletters 6, 449 (2006)

33. Figure 2. Snapshots during SWNT growth at 900 K
Figure 2. Snapshots during SWNT growth at 900 K. The cluster contains fifty Fe atoms, and one carbon atom is added to the central part of the
cluster every 40 ps. Iron atoms are represented as balls and carbon atoms as a stick-like structure. Carbon atoms inside the tubular structure are
shown in red. The time dependence of the dissolved carbon content is shown in the inset.
Ding, Bolton and Rosen, J. Phys. Chem. B108, (2004)

34. Geometrically optimized DFT calcuations on short sections of
Perhaps short sections of SWNTs are the DIB carriers
Geometrically optimized DFT calcuations on short sections of
(5,5) metallic tube

35. Length quantization Energy bands of (5,5) CNT y L=(N+1)a/2
kF=0.673π/a
L=(N+1)a/2 y
a/2
Quantum confinement: sin(kJL)=0
Allowed states: kJ=2Jp/(N+1)a
Ding, Yan, Cao PRB 2002

36. Size Dependence of MO States
Van Hove states
Linear states
Van Hove states

37. Linear band transitions
Intense, charge transfer, end-to-end optical transition moves to lower energy as tube lengthens
Linear band transitions
Strength vs. N

38. Perhaps short stubs of metallic carbon nanotubes are carriers of DIBs

39. Summary
Exciton binding energy about 0.4 eV -- SWNT optical peaks are excitons.
Protonated Endoperoxides dope tubes with holes.
Exciton Auger recombination extremely fast.
For suspended nanotubes, it is possible to detect very strong resonance Rayleigh scattering in short times
Rayleigh scattering clearly shows exciton optical transitions and distinguishes between metallic and semiconducting tubes and provides a structure identification tool
Astrophysical nucleation of graphite and PAHs should be controlled by Fe clusters – short SWNTs may be carriers for Diffuse Interstellar Bands