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