Probing the Electronic Structure of Carbon Nanotubes using Rayleigh Scattering

1
Probing the Electronic Structure of Carbon
Nanotubes using Rayleigh Scattering
Matthew Y. Sfeir
Feng Wang Limin Huang X. M. H. Huang Mingyuan
Huang Jim Hone Stephen OBrien Tony Heinz Louis
Brus
Tobias Beetz Lijun Wu Yimei Zhu Jim Misewich
2
Imagining the Carbon Nanotube Structure
Family of closely related molecules with hundreds
of members and diameters ranging from 0.4 - 3.0
nm.
Each nanotube is uniquely described by its
diameter dt and chiral angle q.
Also can be labeled by (n,m)
3
Motivation and Open Questions
Our understanding of SWNTs mainly comes from
Kataura Plot

1. Single-particle theory. (LEFT)
2. Assignments of luminescence data (Box 1) based on
   predictions from single-particle theory.
3. Measurement and calcs. confirming the existence
   of many-body effects.

All allowed nanotube transitions (eV)
SWNT diameter
What is the real electronic structure of an
arbitrary SWNT?
4
Experimental Detemination of Excitons in SWNTs
Two photon excitation spectra of individual
fluorescence peaks
Energy levels of transitions observed directly
from 2-photon excitation and emission spectra
The optical transitions in nanotubes are
excitons, NOT interband transitions.
F. Wang et al, Science 308, 838(2005)
5
Motivation and Open Questions
1. Assign the optical spectra of all SWNTs.
As there is no accurate theory to guide optical
assignments this requires independent measurement
of electronic and physical structure. 2. From
assignments, develop understanding of the
influence of many-body and chirality effects in
both metals and semiconductors.
Theory
Experiment
?
6
Optical Methods to Probe SWNTs
O'Connell, et al. Science 297, 593-596 (2002).
1) Absorption
Small cross section, has only previously been
measured in ensemble samples.
2) Luminescence
Only applicable to small diameter semiconducting
tubes.
3) Resonance Raman Scattering
Need to satisfy unknown resonance condition very
weak.
Raman
4) Rayleigh Scattering
Can probe all frequencies simultaneously with
white light can we observe resonant enhancement?
cm-1
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Linear Light Scattering Processes
Resonance Rayleigh Scattering

• Elastic light scattering white light
  scattering
• wscattered wincident
• Probe electronic structure detectable at all
  w, but enhanced at electronic transition energies
  ? similar to absorption spectra

w
Resonance Raman Scattering

• Inelastic light scattering momentum transfer
  via fundamental excitations in material
  (monochromatic)
• Vibrational Raman probe Raman active phonons
• wscattered wincident ? wphonon
• Strongly enhanced at energies in resonance with
  an electronic transition ? Resonance Raman

cm-1 shift from w
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Rayleigh Scattering From Nanostructures
Resonance Rayleigh scattering shown to closely
resemble the absorption spectra.
Silver Particles
SWNT Bundles
Michaels, Amy M. Nirmal, M. Brus, L. E. JACS
121(43) 9932-9939. (1999)
Yu, Z. and Brus, L. J. Phys. Chem. B 105(6)
1123-1134. (2001)
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Supercontinuum Radiation for Spectroscopy
Smaller cross-section of carbon nanotubes demands
a brighter light source compatible with confocal
microscopy methods.
Solution white-light generation in an optical
fiber laser brightness with a large spectral
bandwidth (450 - 1450 nm)
log Intensity
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Sample Fabrication and Characterization
Growing Suspended Nanotubes
Imaging
Look at total integrated intensity on CCD to find
tubes. Correlate to electron microscopy images.
Substrates with slits patterned by optical
lithography and wet etching.
CVD directional growth with lengths gt 100 microns
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Resonance Rayleigh Scattering Spectra
M. Sfeir et al, Science 306, 1540 (2004)
Semiconducting Carbon Nanotube
Two well separated S33 and S44 transitions for
larger diameter tubes, S33 and S22 for smaller
diameters.
Metallic Carbon Nanotube
Single M11 or M22 transition observed in the
visible sometimes split into two very close
peaks by trigonal warping effect
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Theoretical Rayleigh Scattering from a SWNT
Treat SWNT as an infinite right cylinder with
effective dielectric function.
e e1 ie2
Band Model
Exciton Model
Energy
Energy
Peaks in the dielectric function give rise to
peaks in the Rayleigh spectrum resulting
lineshape is similar for exciton or interband
model.
13
Assigning the Optical Spectra
For unambiguous assignment of optical
transitions, we need a technique compatible with
our sample geometry that provides an independent
structural verification.
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Determining SWNT Structure by Electron Diffraction
Analyze electron scattering signal from 20 nm
collimated electron beam.
Gao, et. al., Appl. Phys. Let., 82(16) 2703.
(2003)
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Direct Correlation of the Electronic and Physical
Structure
M. Sfeir et al, Science accepted (2006)
(16, 11)
Optical Transitions S33 2.0 eV S44 2.3 eV
Diameter 1.83 nm Chiral Angle 23.9 o
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(16,11) Electronic Structure
Comparisons to some commonly used theoretical
treatments.
Substantial differences in the absolute energies
from theory Semis gt 200 meV Metals gt 150 meV
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Testing Fundamental Predictions of Electronic
Structure
A predicted chirality dependence leads to
systematic deviations as a function of (n,m). Do
many-body effects (which shift absolute energies)
disrupt this pattern?
Zoom of region of Kataura plot
Ignoring chirality and many-body effects
S33
M11
However, the graphene energy dispersion is not a
linear function of k.
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Testing Fundamental Predictions of Electronic
Structure
A predicted chirality dependence leads to
systematic deviations as a function of (n,m). Do
many-body effects (which shift absolute energies)
disrupt this pattern?
Zoom of region of Kataura plot
Spread within a transition series is not random
and depends on chirality (n,m).
S33
2nm46
Semiconducting family behavior
2nm44

• Within certain structural "families" (changing d
  and q), energies evolve in a predictable way
  within that group.

M11
Metals trigonal warping effect

• Splitting of transitions within a series with
  increasing chiral angle

It is difficult to measure these effects
experimentally because of little correlation
between optical and physical data!
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Semiconducting SWNTS
1. Constant Chiral Angle
2. Constant Diameter
D dt 0.12 nm
D q 5.3o
We can use these three patterns to indirectly
assign many of our spectra!
3. Families of Constant 2nm
Our data confirms some family behavior the
relationships between SWNTs with different
diameters and chiral angles.
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Metallic SWNTs
Experimental Verification of the Trigonal Warping
Effect
Not detectable by luminescence of Raman
scattering - shows unique capabilities of the
Rayleigh scattering method.
M22
M11
M11
q 24o
q 30o
q 25o
DE 90 meV
DE 140 meV
DE 0 meV
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Connecting Different Data Sets
How do we compare nanotubes from different
regions of the Kataura plot to develop a
universal picture of excited states?

• We have optical data for
• Small diameter semi SWNTs. diameters lt 1 nm
• Strong many-body effects
• Large diameter semi SWNTs diameters gt 1.6 nm
• Unknown many-body effects?
• Metallic nanotubes with diameters in between 1.3
  nm
• No many body-effects???

2
3
1
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Connecting Different Data Sets
Kane CL, Mele EJ. PRL 93 197402 (2004).
Nanotube electronic structure dominated by 2D
many-body effects (REAL graphene dispersion). 1D
are negligible.
We dont know the real graphene energy
dispersion E(k) For SWNT transitions with
energy E, determine k, and compare different
nanotubes with similar k. If 1D effects are
strong, this treatment will give large errors
(metal vs. semi diameter dependence).
k
This is the best theoretical fit to our data and
implies that metals and semiconductors not very
different!!!
23
SWNT Project Synergy
Many projects have contributed to and benefitted
from the Rayleigh scattering project and
furthered our understanding of SWNTs.
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Conclusions

• We have developed an optical method useful for
  identifying the optically allowed electronic
  transitions in individual carbon nanotubes.
• Rayleigh scattering spectra can be interpreted
  qualitatively using theory as a guide but direct
  structual characterization is necessary for
  assignments.
• We have begun building a set of assignments from
  correlated electron diffraction measurements and
  extending those using the expected evolution .
• An interesting picture of the excited states is
  emerging we invite theoretical help with this
  problem!!!

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Acknowledgements
Production and Growth Jim Hone Limin
Huang Henry Huang Mingyuan Huang
Optical Experiments Feng Wang Yang Wu Tony
Heinz Louis Brus
Electron Microscopy Limin Huang Lijun Wu,
BNL Yimei Zhu, BNL Tobias Beetz, BNL
Discussion Mark Hybertsen Philip Kim Gordana
Dukovic Jim Yardley Jim Misewich, BNL
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Extra Slides
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Examining Family Relations
We have seen that our data progresses in the
expected way for diameter and chirality changes.
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Chirality Dependence in a Non-interacting Model
Metal
Semiconductor - I
Semiconductor - II
mod (n m, 3) 1
mod (n m, 3) 2
mod (n m, 3) 0
Metals trigonal warping effect Semiconductors
family behavior
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Trigonal Warping Effect in Metallic SWNT
Constant energy contours of graphene dispersion
? 30o
Saito et. al., PRB 61, 2981 (2000). Reich and
Thomsen, PRB 62, 4273 (2000).
? 0o
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Can we extend this technique to a single nanotube?
The nanotube has an extremely small scattering
cross-section.
Silver (50 nm)
SWNT (40 ?m long)
N2
10-27 cm2
10-14 cm2
10-10 cm2
Need a sufficiently bright broadband excitation
source and a single nanotube in a controlled
geometry and environment.
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Structural Information from Raman Scattering
Rayleigh Identifies MULTIPLE electronic
transitions which can be used to satisfy the
resonance condition needed for Raman.
Resonance Raman
(21,4) nanotube?
Low chiral angle
Phonon frequency (cm-1)
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(n,m) Eii (eV) Transition p-TB theory ETB theory ETBMB correction
(16,11) 2.00 S33 1.79 1.63 1.88
  2.30 S44  2.14 1.93 2.15
(15,10) 2.15 S33 1.92 1.77 2.01
  2.44 S44 2.29  2.06 2.26
(13,12) 2.09 S33 1.9 1.73 1.97
  2.52 S44  2.36 2.15 2.35
(13,11) 2.19 S33 1.99 1.82 2.06
  2.56 S44  2.42 2.19 2.38
(10,10) 1.93 M11 1.79 1.63 1.88
(11,8) 1.93 M11(-) 1.84 1.66 1.91
2.02 M11() 1.9 1.74 1.99
(20,14) 2.22 M22(-) 2.04
M22() 2.13
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Using Rayleigh Information To Engineer Nanotube
Devices
Henrys Transfer Method
X. M. H. Huang, R. Caldwell, L. Huang, S. Jun, M.
Huang, M.Y. Sfeir, L. Brus, S.P. OBrien, J.
Hone, Submitted, 2005.
This gives us the ability to select a nanotube
with specific properties and place it on a
surface with spatial accuracy of several microns.
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An Example with Electronic Transport Data
1. Optical Characterization

• Semiconducting Nanotube
• dt 1.9 nm
• (17,10) possible assignment from family plots

2. Transfer to Si substrate for transport
measurements

• Confirms semiconducting character

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Scattering Spectra along the Nanotube Single
Tube to Small Bundle
B
A
Semiconducting
Metallic
Transitions red-shift by 20 - 50 meV upon
bundling.
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Nanotube Bundling in a Y-Junction
A Moderate sized bundle structure. B Single
semiconducting nanotube with dt 1.9 nm. AB
Merged structure.
The resonances in tube B are red-shifted by 35
and 47 meV. The resonances in tube A are
shifted by much less in the combined
structure. This effect is consistent with
dielectric screening of manybody effects.
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Metallic Armchair Tubes - Lineshape
M11 M22
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Polarization Dependence of Rayleigh Scattering
X 5
Polarization along nanotube axis Selection rules
allow symmetric transitions between singularities
in the DOS, ?J 0.
Perpendicular to nanotube axis Selection rules
allow ?J 1 transitions, but quenched due to
depolarization effect.
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Lineshape Analysis
Rayleigh Scattering
Exciton Model
Band Model
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Dielectric Function
Optical response is dominated by the peaked joint
density of states.
We observe Rayleigh scattering that is resonantly
enhanced near the absorption maxima.
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Rayleigh Spectra Collected with a QTH Lamp
Collection time gt 4.5 hours per graph.
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Lineshape Analysis
Rayleigh Scattering
Exciton Model
Band Model