Recent Advances in the Optical Spectroscopy of Carbon Nanotubes

Tony F. Heinz

Departments of Physics and Electrical Engineering

Nanoscale Science and Engineering Center

Columbia University, New York, NY

tony.heinz@columbia.edu

http://heinz.phys.columbia.edu

Columbia University CollaborationOptical Characterization

Tony Heinz: Daohua Song, Feng Wang, Yang Wu, Hugen Yan

Louis Brus: Gordana Dukovic, Matt Sfeir (Chemistry)

Fabrication (for individual nanotube measurements)

Jim Hone:Jim Hone::C. C. Chuang, M. Huang, Henry Huang (Mech. Eng.)

Nanotube CVD Growth (for individual nanotube measurements)

Stephen O’Brien: Limin Huang (Materials Science)

Oxygen Photochemistry

Nick Turro: Brian White, Steffen Jockush (Chemistry)

Electronic Structure Calculations for Surface Chemistry

Rich Friesner, Mike Steigerwald: Zhiyong Zhou (Chemistry)

Brookhaven National Lab: TEM- Yimei Zhu, Jim Misewich, Toby Beetz

Funding: Columbia NSF Nanocenter and DOE- BES

Optical Properties of Nanotubes

Why the interest?

Optical Properties of Nanotubes

(1) Spectroscopic signature of nanotube structure

and quality

Absorption, Emission, Raman ..

Raman RBM andG mode spectrafor 1.89 nm diametertube (Columbia)

PLE excitation spectraWeisman et al., Rice U.

Optical Properties of Nanotubes

• (2) Spectroscopic and optoelectronic applications:

• Tunable band gap (fiber optics, tissue transp., …)• Integratable 1D nanostructures• Variety of material forms

Fluorescing agents, LEDs, detectors,

nonlinear optical elements

Avouris et al., IBM[Science 300, 783 (2003)]

Optical Properties of Nanotubes(3) Probe of the fundamental physics of the excited states and their dynamics

• The position and character of excited electronic states.

• Rate and mechanisms of light emission

• Carrier-carrier interaction and consequences

• Nanotube environment interaction and consequences

• Phonons and electron-phonon interactions

Topics

0. Fundamentals of electronic states and optical transitions in nanotubes

1. Nature of electronic resonances in nanotubes: excitons or band-to-band transitions? The role of many-body effects

2. Dynamics: radiative and nonradiative processes

3. Measurements of individual nanotubes

Electronic States of Electronic States of Carbon NanotubesCarbon Nanotubes

Armchair θ = 30º

Zigzag θ = 0

Chiral

0 < θ < 30º

Basic schema: Derive states from those of graphene that satisfy required boundary conditions

Graphene Electronic Structure

Zero-gap semiconductor

Nanotube Electronic Structure

Metallic:

Semiconducting:

Density of States

DOS = dN/dE

~ dk/dE (1-D)

For linear bands (metallic behavior near EF):

DOS = Constant

For parabolic bands (E ~ k2 ):

DOS ~ 1/[dE/dk] ~ 1/k ~ E-1/2

van Hove singularity in DOS at band edge in 1-D

Density of Statesin Different Dimensions

Parabolic bands

0-D 1-D 2-D 3-D

δ(E) E-1/2 θ(E) E1/2

Sub-bands and Optical Transitions

E1

E3

E2

H1H2

H3

E11 E22 E33

For transitions polarized perpendicular to the nanotubeaxis, we have E12, E23, etc. as allowed transitions

Nanotube Optical Transitions

H. Kataura et al. Proceedings of the International Winter School on Electronics Properties of Novel Materials (1999)

E11s

E22s

E11m = M11

E33s

E44s

E22m = M22

Refinements to Single-Particle Picture of Optical Transitions

• Curvature effects for small diameter tubes

π-σ interactions• More correct description of graphene bands:

– Non strictly conical near K point

Split metallic peaks expected, exceptfor high-symmetry armchair tubes

Family behavior for two classes of Semiconducting tubes

Photoluminescence Excitation Spectra for Single-Walled Nanotube Ensemble

Weisman et al, Rice U.

Beyond the Single-ParticlePicture of Optically Excited

States:

Optical emission/absorption always involves an electron and a hole do they interact?

Excitons

Electron-hole interaction gives rise to a series of correlated states analogous to hydrogenic atom

In 3D: En = (μ/m0) (1/ε)2 Ryd/n2

(μ/m0) (1/ε)2 13.6 eV/ n2

E1 ~ meV in typical bulk semiconductors

3 D Materials: Optical Transitions

Ab

sorp

tio

n

Photon energy

ExcitonicRydberg Series

Continuum band-to-band

ExcitonsElectron-hole interaction gives rise to a series of correlated states analogous to hydrogenic atom

In 3D: En = (μ/m0) (1/ε)2 Ryd/n2

(μ/m0) (1/ε)2 13.6 eV/ n2

E1 ~ meV in typical bulk semiconductors

Nanotube: μ = 0.05 m0 and ε ~ 4

E1 ~ 40 meV

Expect enhanced e-h interaction in quasi-1D systems:Ando; Avouris, Perebeinos, Tersoff; Kane and Mele; Louie; Mazumdar; Molinari; Pederson; …

Nature of Observed Optical Transitions in SWNTs?

van Hove singularity in JDOS

Energy

Band-to-band transitions

Band edge1s 2p

Energy

Excitonic picture with strong e-h interaction

Strong e-h interaction →Transfer of oscillator strength to exciton

SWNT Emission and Absorption Spectra

Rice group: Science 298, 2361 (2002)

Energy

c1v1

Evidence for Excitons

• Fluorescence decay dynamics (UC Berkeley)

• Transition linewidth and lineshape (Los Alamos)

• Observation of phonon sidebands (IBM)

Two-photon spectroscopy: Direct demonstration of excitonic nature

of transitions and measurementexciton binding energy.Two-photon transitions obey differentselection rules and only connect with excited Rydberg states of exciton

Two-Photon Excitation Spectroscopy

Different selection rulesfor one and two-photon transitions – allows accessto excited exciton states.

Two-photon transition to ground exciton state isforbidden

Two-Photon Photoluminescence Excitation Spectroscopy

Excite with tunable femtosecond laser aroundhalf E11 transition energy; monitor fluorescence

[Heinz, Brus groupsScience 308, 838 (2005).]

Similar results byMaultzsch et al., TU Berlin

Diameter Dependence of Excitonic Effects

Exciton BE 1/d

Coulomb interaction most significant when diameter is small.

Consistent with theoretical prediction: Perebeinos, Tersoff, Avouris, PRL 92, 257402 (2004)

Dukovic, Wang, Heinz, BrusNano Lett. 5, 2314 (2005)

Strong Excitonic Effects

• Localized exciton: e-h correlation length ~ 1- 2 nm

•Optical transition energy ≠ single particle bandgap

Exciton BE ~ 300 – 400 meV for 1 nm diameter SWNT

Eopt ~ 1.5 eV, Eqp ~ 1.8 – 1.9 eV

• Consequences for optoelectronics

• Behavior of electroluminescent devices• Weak photoconductivity - must break excitons• Strong transitions, nonlinear optical effects

Origin of Strong Excitonic Effects

• Intrinsically strong Coulomb interactions in 1D

• Relatively weak dielectric screening

Full Picture of Optical Transitions

Each allowed band-to-band transition Eii producesRydberg series of excitons + free-carrier continuum

Emission: Fast internal relaxation → dominated by E11 (1s) exciton

Excitation: Linear Eii (1s), Eii (3s), + continuum 2-photon Eii (2p), Eii (4p), + continuum

Fuller Picture for Optical Transitions

(0) Each allowed band-to-band transition Eii

produces Rydberg series of excitons + continuum

(1) EIJ with cross polarization

(2) Coupling to phonons – sidebands appear

(3) Coupling between K and K’ points:

Each exciton is 4 fold degenerate (neglecting spin)

Critical for emission properties, minoreffects on absorption spectra rules

Avouris et al.

Exciton Dynamics:

Radiative and Non-Radiative Decay

Two specific questions

• Why is the fluorescence quantum efficiency as low as 10-4 -10-3 ?

• Can we observe exciton-exciton interactions

Expect high emission efficiency for direct-gap semiconductor, particularly with excitonic enhancement

But: Experimental fluorescence quantum efficiency

η = 10-4 - 10-3

= rrad / (rrad + rnonrad ) ≈ rrad / rnonrad

What is happening?

- Low radiative emission rate? or

- Very rapid competing non-radiative process?

Efficiency of Light Emission

Time-Resolved Fluorescence

• Decay time: ~10 ps - non-radiative process

• Determination of radiative rate: ~ 10 - 100 ns

Wang, Dukovic,Brus, and Heinz“Time-Resolved Fluorescence …,” PRL 92, 177401 (2004).

Related results reported by Fleming et al., UC Berkeley(fluorescence upconversion);Hartschuh, Hertel, …;Heben, Rumbles, ..(time-resolved photon counting)

Radiative Lifetime

τrad ~ 10 - 100 ns

• Rate comparable to that for allowed transitions in direct-gap semiconductors, including nanoparticles with high quantum efficiency of emission

Theoretically: Comparable to naïve calculation based on free carriers!

What about exciton enhancement of rate?

~ L/a = (length of tube)/(size of exciton)•\

Radiative Emission with Excitons

(1) Center of mass motion of excitons:

- Only K < (1/λ) states can radiate

(2) Role of dark excitons

- K/K’ degeneracy

- Possible Singlet/triplet spin states?

Louie, Avouris/Perebeinos/Tersoff

Both factors decrease radiative rate compared to simple model, but have opposite temperature depedences

Avouris et al.

Nature of Fast Nonradiative Decay?

One effective trapping site for non-radiative decay can explain the fast rate:

In 10 ps excitons at thermal velocity travels ~ 1 μm

Evidence suggests that better quality tubes will

radiate more efficiently.

Possible role of multiphonon decay, but no clear

experimental signature.

Fluorescence Sensitivity to Defects

G. Dukovic and Columbia team, "Reversible Surface Oxidation and Efficient Luminescence Quenching in Semiconductor Single-Wall Carbon Nanotubes," JACS 126, 15269 (2004)

8

6

4

2

0

Flu

ore

sce

nce

(a

.u.)

12080400Time (min)

(8,3)

(6,5)

(9,7)

(7,5)

(10,2)

(9,4)

(10,5)(12,1)

(11,3)

Fluorescence quencedwith just a few adsorbedchemisorbed oxygenmolecules/nanotubeIn acidic solution

(Dosed with 1 Δ oxygen)

Multiple Excitons in Carbon Nanotubes?

Decay for Multiple Excitons

• Additional fast decay initially

• Identical decay at later times, independent of fluence

Related results reported by Fleming et al., UC Berkeley;Krauss et al,Rochester

Wang, Dukovic,Brus, and Heinz, "Observation of rapid Auger recombination in optically excited semiconducting carbon nanotubes," Phys. Rev. B 70, 241403 (2004)

At low excitation density:

Fluorescence # of excited SWNTs pump fluence

At high excitation density:

Fast exciton-exciton annihilation process until one only one excitation per nanotube

Initial decay differs; tail of decay is equivalent.

Exciton-Exciton Annihiliation (or Auger recombination)

Lifetime for 2 excitons in 1 μm nanotube: ~ 1 ps

Model with effective carrier-carrier interaction scaled to exciton binding energy predicts annihilation rate with factor of 5 -- Another manifestation of multi-body physics

[F. Wang, Y. Wu, M. S. Hybertsen, and T. F. Heinz, Auger Recombination of Excitons in One-Dimensional Nanostructures, Phys. Rev. B (in press)]

Implications of Exciton-Exciton Annihiliation

• Unfavorable for population inversion and lasing

• This strong multibody effect in nanotubes: possibility of multi-exciton generation from a single photon well above gap, as recently demonstrated in semiconductor nanoparticles by Klimov et al.,

Efros et al.

Summary: Dynamics of Light Emission

• Strong optical transitions from ground-state exciton (~ 10 - 100 ns radiative lifetime at room temperature)

• Fast non-radiative decay channel (10 – 100 ps) limits the fluorescence yield - Strong sensitivity to

defects and external environment

• Extremely efficient exciton-exciton annihilation

Advantages:

Simplify spectroscopy (species and orientation)

Examine influence of local environment

Interface with other measurements:

- Complementary microscopy (TEM, STM, …)

- Transport measurements

3. Spectroscopy of Individual Nanotubes

Optical Spectroscopy of Individual Nanotubes

• Fluorescence (Rice, Rochester, Los Alamos, …)

• Resonance Raman spectroscopy (MIT/BU, …)

Here:

Rayleigh (or elastic) light scattering

M.Y. Sfeir ,F. Wang ,L.M. Huang ,C.C. Chuang ,J. Hone ,S.P. O'Brien ,T.F. Heinz ,L.E. Brus, "Probing electronic transitions in individual carbon nanotubes by Rayleigh scattering," Science 306 1540-1543 (2004)

Individual Nanotube Rayleigh Scattering Spectroscopy

Dark-field imaging

Suspended Individual Nanotubes

Reduced background Suspended nanotube across slit

SEM

slit edges

nanotube scattering

OpticalScattering

In-situ CVD growthacross etched slit

F. Wang, G. Dukovic, L. E. Brus, and T. F. Heinz, “The Optical Resonances in Carbon Nanotubes Arise from Excitons,” Science 308, 838 (2005).

Rayleigh Spectra from Individual Nanotubes

Semiconducting

Metallic

(M11 or M22)

2.62.42.22.01.8 2.62.42.22.01.82.62.42.22.01.8

Energy (eV)

a b c(16,11)(15,10)(13,12)

2.52.32.11.91.7

'(11,8)'

2.52.32.11.91.7

'(10,10) Tube 1' '(10,10) Tube 2'

a b

Energy (eV)

(E33, E44)

Independent Structural Determination on Same Nanotube

Columbia and Brookhaven National Lab. collaboration

M. Y. Sfeir, T. Beetz, F. Wang, L. Huang, X. M. H. Huang, M. Huang, J. Hone, S. P. O’Brien, J. A. Misewich, T. F. Heinz, L. Wu, Y. Zhu, and L. E. Brus, “Optical Spectroscopy of Individual Single-Walled Carbon Nanotubes of Defined Chiral Structure,” Science (in press).

Comparison of Spectra as Function of Chirality: Semiconducting Tubes

2.62.42.22.01.8 2.62.42.22.01.8 2.62.42.22.01.8 2.62.42.22.01.8

Energy (eV)

a b(16,11)(15,10)

(13,12)(15,10)

First direct confirmation of expected family behavior -- Critical for accepted assignments of tube indices

M. Y. Sfeir et al. (Columbia and Brookhaven Team), “Optical Spectroscopy of Individual Single-Walled Carbon Nanotubes of Defined Chiral Structure,” Science (in press).

Comparison of Spectra as Function of Chirality: Metallic Tubes

2.52.32.11.91.7

'(11,8)'

2.52.32.11.91.7

'(10,10) Tube 1' '(10,10) Tube 2'

a b

Energy (eV)

Direct demonstration of predicted splitting of metallic peaks from trigonal warping effect.

M. Y. Sfeir et al. (Columbia and Brookhaven Team), “Optical Spectroscopy of Individual Single-Walled Carbon Nanotubes of Defined Chiral Structure,” Science (in press).

Single-Particle Models:Tight-Binding, Extended Tight-Binding

• Correct trends, but numerically inaccurate (10-20%)

• Rigorous calculations are difficulty:* Many-body effects* Large unit cell

• Exciton binding energy partially offsets effect of upward band gap renormalization

ε = ∞h

e

ε

e

Exciton binding

h

Single Nanotube Rayleigh Spectroscopy: Polarization Dependence

030

60

90

120

150180

210

240

270

300

330

Light scattering is strongly polarized along the nanotube.

Polarization Perpendicular to the Nanotube: Depolarization Effect

E║0

E║total E┴0

+++

- - -

E┴ind P┴= ( -1) 2

1 +E┴

0

P║=( -1) E║0

x5

Scattering Spectra along a given Nanotube

40 m

substrate

Also observed M/S chirality change:

Using transfer mechanism

studied complete transport

behavior in different regions

This case shows preservationof nanotube chirality overthe length

Tube-Tube Interactions

Shift of 47 meV

b

c

A+B A

aA: Isolated SWNT

A+B: SWNT A bundled with SWNT B

SEM Image

RayleighScatteringSpectrum

Dielectricscreening byadjacent SWNTinducesred-shiftin bandgap

F. Wang and Columbia team,Phys. Rev. Lett. (in press)

A

B

A+BA

B

A+B

a b

c

Tube-Tube Interaction: Y- Junction

F. Wang and Columbia team,Phys. Rev. Lett. (in press)

Influence of Dielectric Screening on Coulomb Interactions in Nanotubes

Calculation of electrostatic potentialas a function of thedistance from a disk of charge

A: isolated nanotubeB: with adjacent nanotube

F. Wang and Columbia team,Phys. Rev. Lett. (in press)

Rayleigh Spectra of Individual Nanotubes

General technique: semiconducting and metallic nanotubes with rapid data collection

Signature of electronic structure → physical structure

Transitions polarized along the nanotube direction

Study tube-tube interaction and other environmental effects

Probing mechanical displacements

Combine with other single molecule measurements

Electron diffraction structural analysis

Electric transport

Optical Spectroscopy of Carbon Nanotubes

Many body effects are critically important in carbon nanotubes

Optical transitions are excitonic in character

Strong exciton-exciton interactions, rapid Auger process

Coupling of nanotube to external environment is significant

Importance of single molecule spectroscopy is growing

Simplified spectra and heightened control

Probe of local environment

Coupling to complementary measurements

Publications by Columbia Team• F. Wang, G. Dukovic, L. E. Brus, and T. F. Heinz, “

Time-Resolved Fluorescence in Carbon Nanotubes and Its Implication for Radiative Lifetimes,” Phys. Rev. Lett. 92, 177401 (2004).

• G. Dukovic, B. E. White, Z. Zhou, F. Wang, S. Jockusch, M.L. Steigerwald, T.F. Heinz, R.A. Friesner, N.J. Turro, L.E. Brus, "Reversible Surface Oxidation and Efficient Luminescence Quenching in Semiconductor Single-Wall Carbon Nanotubes," JACS 126 15269-15276 (2004)

• M.Y. Sfeir ,F. Wang ,L.M. Huang ,C.C. Chuang ,J. Hone ,S.P. O'Brien ,T.F. Heinz ,L.E. Brus, "Probing electronic transitions in individual carbon nanotubes by Rayleigh scattering," Science 306 1540-1543 (2004)

• F. Wang, G. Dukovic, E. Knoesel, L.E. Brus, T.F. Heinz, "Observation of rapid Auger recombination in optically excited semiconducting carbon nanotubes," Phys. Rev. B 70, 241403 (2004)

• F. Wang, G. Dukovic, L. E. Brus, and T. F. Heinz, “The Optical Resonances in Carbon Nanotubes Arise from Excitons,” Science 308, 838 (2005).

• B. H. Hong, J. P. Small, M. S. Purewal, A. Mullokandov, M. Y. Sfeir, F. Wang, J. Y. Lee, T. F. Heinz, L. E. Brus, P. Kim, and K. S. Kim, “Extracting Subnanometer Single Shells from Ultralong Multiwalled Carbon Nanotubes,” Proc. Nat. Acad. Sci. 102, 14155 (2005). 

• G. Dukovic, F. Wang, D. H. Song, M. Y. Sfeir, T. F. Heinz, and L. E. Brus, “Structural Dependence of Excitonic Optical Transitions and Band-Gap Energies in Carbon Nanotubes,” Nano Lett. 5, 2314 (2005).

• F. Wang, M. Y. Sfeir, L. Huang, X. M. H. Huang, Y. Wu, J.  Kim, J. Hone, S.  O'Brien, L. E. Brus, and T. F. Heinz, “

Interactions between Individual Carbon Nanotubes  Studied by Rayleigh Scattering Spectroscopy,” Phys. Rev. Lett. (in press).

• M. Y. Sfeir, T. Beetz, F. Wang, L. Huang, X. M. H. Huang, M. Huang, J. Hone, S. P. O’Brien, J. A. Misewich, T. F. Heinz, L. Wu, Y. Zhu, and L. E. Brus, “Optical Spectroscopy of Individual Single-Walled Carbon Nanotubes of Defined Chiral Structure” Science (in press).

• F. Wang, Y. Wu, M. S. Hybertsen, and T. F. Heinz, Auger Recombination of Excitons in One-Dimensional Nanostructures, Phys. Rev. B (in press).