recent advances in the optical spectroscopy of carbon nanotubes tony f. heinz departments of physics...
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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
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).