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 O’Brien
Tony Heinz
Louis Brus
Tobias Beetz
Lijun Wu
Yimei Zhu
Jim Misewich
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 .
[Also can be labeled by (n,m)]
S22
S44S33
S11
M11
M22
1
Motivation and Open Questions
Our understanding of SWNTs mainly comes from:
A. Single-particle theory. (LEFT)
B. Assignments of luminescence data (Box 1) based on predictions from single-particle theory.
C. Measurement and calcs. confirming the existence of many-body effects.
All
allo
wed
nan
otub
e tr
ansi
tions
(eV
)
SWNT diameter
What is the real electronic structure of an arbitrary SWNT?
Kataura Plot
Two photon excitation spectra of individual fluorescence peaks
Band edge1s 2p
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)
Experimental Detemination of Excitons in SWNTs
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
??
1) Absorption
2) Luminescence
3) Resonance Raman Scattering
4) Rayleigh Scattering
4002000-200-400
cm-1
Optical Methods to Probe SWNTs
Small cross section, has only previously been measured in ensemble samples.
Only applicable to small diameter semiconducting tubes.
Need to satisfy unknown resonance condition; very weak.
Can probe all frequencies simultaneously with white light; can we observe resonant enhancement?
O'Connell, et al. Science 297, 593-596 (2002).
Raman
Resonance Raman Scattering
Resonance Rayleigh Scattering
• Elastic light scattering [white light scattering]
• scattered = ncident
• Probe electronic structure – detectable at all , but enhanced
at electronic transition energies similar to absorption spectra
• Inelastic light scattering – momentum transfer via
fundamental excitations in material (monochromatic)
• Vibrational Raman – probe Raman active phonons
• scattered = incident phonon
• Strongly enhanced at energies in resonance with an electronic
transition Resonance Raman
Linear Light Scattering Processes
cm-1 shift from 4002000-200-400
Rayleigh Scattering From Nanostructures
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)
Resonance Rayleigh scattering shown to closely resemble the absorption spectra.
Solution: white-light generation in an optical fiber: laser brightness with a large spectral bandwidth (450 - 1450 nm)
Supercontinuum Radiation for Spectroscopy
Smaller cross-section of carbon nanotubes demands a brighter light source compatible with confocal microscopy methods.
log
Inte
nsi
ty
Growing Suspended Nanotubes Imaging
CVD directional growth with lengths > 100 microns:
Substrates with slits patterned by optical lithography and wet etching.
Look at total integrated intensity on CCD to find tubes.
Correlate to electron microscopy images.
Sample Fabrication and Characterization
Isolated SWNT
10 m
nanotube scattering
slit edges
Metallic Carbon Nanotube
Semiconducting Carbon Nanotube
Single M11 or M22 transition observed in the visible – sometimes split into two very close peaks by trigonal warping effect
Two well separated S33 and S44 transitions for larger diameter tubes, S33 and S22 for smaller diameters.
Resonance Rayleigh Scattering SpectraM. Sfeir et al, Science 306, 1540 (2004)
3
23 1
r
Qsca
Theoretical Rayleigh Scattering from a SWNT
Peaks in the dielectric function give rise to peaks in the Rayleigh spectrum; resulting lineshape is similar for exciton or interband model.
= 1 + i2
Exc
ito
n M
od
el
Ban
d M
od
elTreat SWNT as an infinite right cylinder with effective dielectric function.
Energy Energy
Assigning the Optical SpectraFor unambiguous assignment of optical transitions, we need a
technique compatible with our sample geometry that provides an independent structural verification.
Collaboration with the electron microscopy group
@ Brookhaven National Labs.
TEM
Image
Diffraction
Determining SWNT Structure by Electron Diffraction
arctand2 d1
d3
Equatorial Oscillation
J02(RD0)
Gao, et. al., Appl. Phys. Let., 82(16) 2703. (2003)
Analyze electron scattering signal from ~ 20 nm collimated electron beam.
Direct Correlation of the Electronic and Physical Structure
Energy (eV)
Inte
nsi
ty
a: experimental diffractionb: simulated diffraction
Diameter: 1.83 nm
Chiral Angle: 23.9 o
Optical Transitions:
S33 = 2.0 eVS44 = 2.3 eV
M. Sfeir et al, Science accepted (2006)
(16, 11)
(16,11) Electronic Structure
S33 S44
Rayleigh Spectrum
Resonance Energy Fit
-Tight Binding Calcs
Extended Tight Binding
ETB + Many-body Corr.
1.99 2.27
2.00 2.30
1.79 2.14
1.63 1.93
1.88 2.15
Transition Energies (eV)
Substantial differences in the absolute energies from theory:
Semis: > 200 meVMetals: > 150 meV
Comparisons to some commonly used theoretical treatments.
Testing Fundamental Predictions of Electronic Structure
Zoom of region of Kataura plot
S33
M11
Ignoring chirality and many-body effects:
11S5~44S
11S4~33S
11S2~22S
11S6~22M
11S3~11M
td
1~11S
However, the graphene energy dispersion is not a linear function of k.
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?
Semiconducting: “family” behavior
Metals: trigonal warping effect
Zoom of region of Kataura plot
S33
M11
Spread within a transition series is not random and depends on chirality [(n,m)].
• Within certain structural "families" (changing d and ), energies evolve in a predictable way within that group.
• 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!
Testing Fundamental Predictions of Electronic Structure
2n+m=46
2n+m=44
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?
1. Constant Chiral Angle 2. Constant Diameter dt = 0.12 nm = 5.3o
We can use these three patterns to indirectly assign many of our spectra!
We can use these three patterns to indirectly assign many of our spectra!
Semiconducting SWNTS
3. Families of Constant 2n+m
Our data confirms some “family” behavior – the relationships between SWNTs with different diameters and chiral angles.
Experimental Verification of the Trigonal Warping Effect
= 30o = 25o = 24o
M11 M11 M22
= 0 meV = 90 meV = 140 meV
Not detectable by luminescence of Raman scattering - shows unique capabilities of the Rayleigh scattering method.
Metallic SWNTs
S22
S44
S33
S11
M11
M22
Connecting Different Data Sets
We have optical data for:
1. Small diameter semi SWNTs. [diameters < 1 nm]Strong many-body effects
2. Large diameter semi SWNTs [diameters > 1.6 nm]Unknown many-body effects?
3. Metallic nanotubes with diameters in between [1.3 nm]No many body-effects???
How do we compare nanotubes from different regions of the Kataura plot to develop a universal picture of excited states?
1
3 2
Nanotube electronic structure dominated by 2D many-body effects (REAL graphene dispersion). 1D are negligible.
We don’t 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).
Kane CL, Mele EJ. PRL 93 197402 (2004).
This is the best theoretical fit to our data and implies that metals and semiconductors not very different!!!
S33 M11S22
0.8 nm 1.3 nm1.7nm
2.00
1.95
1.90
1.85
2.302.252.202.152.10
(10,10)(14,13)(7,6)
k
Connecting Different Data Sets
SWNT Project SynergyMany projects have contributed to and benefitted from the Rayleigh scattering
project and furthered our understanding of SWNTs.
Mechanical
Electro-optics
Transport
Intertube Interactions
Theory
Raman Scattering
Transfer Technology
Heinz, BrusHone
Hone, Kim
Heinz, Hone, BNL
Heinz, Hone
NSEC
Heinz, Brus
Synthesis and FabricationO’Brien, Hone
Conclusions
1. We have developed an optical method useful for identifying the optically allowed electronic transitions in individual carbon nanotubes.
2. Rayleigh scattering spectra can be interpreted qualitatively using theory as a guide but direct structual characterization is necessary for assignments.
3. We have begun building a set of assignments from correlated electron diffraction measurements and extending those using the expected evolution .
4. An interesting picture of the excited states is emerging – we invite theoretical help with this problem!!!
Acknowledgements
Production and Growth:Jim HoneLimin HuangHenry HuangMingyuan Huang
Production and Growth:Jim HoneLimin HuangHenry HuangMingyuan Huang
Optical Experiments:Feng WangYang WuTony HeinzLouis Brus
Optical Experiments:Feng WangYang WuTony HeinzLouis Brus
Electron Microscopy:Limin HuangLijun Wu, BNLYimei Zhu, BNLTobias Beetz, BNL
Electron Microscopy:Limin HuangLijun Wu, BNLYimei Zhu, BNLTobias Beetz, BNL
Discussion:Mark HybertsenPhilip KimGordana DukovicJim YardleyJim Misewich, BNL
Discussion:Mark HybertsenPhilip KimGordana DukovicJim YardleyJim Misewich, BNL
Extra Slides
We have seen that our data progresses in the expected way for diameter and chirality changes.
4741 37
4440
43
37
40
38
4144
47
4346
1/dt
Eii (eV)
Examining “Family” Relations
Metal Semiconductor - I Semiconductor - II
mod (n – m, 3) = 0 mod (n – m, 3) = 1 mod (n – m, 3) = 2
Chirality Dependence in a Non-interacting Model
Metals: “trigonal warping effect”Semiconductors: “family” behavior
Trigonal Warping Effect in Metallic SWNT
= 30o
= 0o
Constant energy contoursof graphene dispersion
Saito et. al., PRB 61, 2981 (2000).
Reich and Thomsen, PRB 62, 4273 (2000).
Can we extend this technique to a single nanotube?
The nanotube has an extremely small scattering cross-section.
Need a sufficiently bright broadband excitation source and a single nanotube in a controlled geometry and environment.
N2 SWNT (40 m long) Silver (50 nm)
10-27 cm2 10-14 cm2 10-10 cm2
1640160015601520
4002000-200-400
Low chiral angle
Resonance Raman:
Phonon frequency (cm-1)
eV 2.62.42.22.01.81.61.4
Resonantly excite at ONE energy (1.96 eV)
dt = 1.89 nm
Rayleigh
Identifies MULTIPLE electronic transitions which can be used to satisfy the resonance condition
needed for Raman.
Structural Information from Raman Scattering
(21,4) nanotube?
(n,m) Eii (eV) Transition -TB theory ETB theoryETB+MB
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
2.02M11(+) 1.9
1.741.99
(20,14) 2.22M22(-) 2.04
M22(+) 2.13
Henry’s Transfer Method
Using Rayleigh Information To Engineer Nanotube Devices
This gives us the ability to select a nanotube with specific properties and place it on a surface with spatial accuracy of several microns.
X. M. H. Huang, R. Caldwell, L. Huang, S. Jun, M. Huang, M.Y. Sfeir, L. Brus, S.P. O’Brien, J. Hone, Submitted, 2005.
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
Scattering Spectra along the Nanotube: Single Tube to Small Bundle
B A
Semiconducting Metallic
Transitions red-shift by 20 - 50 meV upon bundling.
B A
A
B
A+BA
B
A+B
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.
A: Moderate sized bundle structure.
B: Single semiconducting nanotube with dt ~ 1.9 nm.
A+B: Merged structure.
Nanotube Bundling in a Y-Junction
Metallic Armchair Tubes - Lineshape
2.62.42.22.01.81.6 2.62.42.22.01.81.6
M11M22
Polarization Dependence of Rayleigh Scattering
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.”
X 5
eV
Lineshape AnalysisE
xcit
on
Mo
del
Ban
d M
od
el
Rayleigh Scattering
1.0
0.8
0.6
0.4
0.2
0.0
800700600500400
'' '' 'Scattering Spectra'
(23,0)
Optical response is dominated by the peaked joint density of states.
Dielectric Function
We observe Rayleigh scattering that is resonantly enhanced near the absorption maxima.
2 2
2 A( )( )
1 0 2
1 1( ) ( ') P( ) '
'd
Collection time > 4.5 hours per graph.
Rayleigh Spectra Collected with a QTH Lamp
eV
Lineshape AnalysisE
xcit
on
Mo
del
Ban
d M
od
el
Rayleigh Scattering