optical spectroscopy of nanostructures of c nanotubes.pdfoptical spectroscopy of nanostructures y....
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![Page 1: Optical Spectroscopy of Nanostructures of C nanotubes.pdfOptical Spectroscopy of Nanostructures Y. Ron Shen Physics Department ... nanoparticles, nanorods, nanotubes, etc. Carbon nanotubes,](https://reader030.vdocument.in/reader030/viewer/2022041003/5ea4de2762caa85676386f33/html5/thumbnails/1.jpg)
Optical Spectroscopy of Nanostructures
Y. Ron ShenPhysics Department
University of California at Berkeley
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Nanophotonics
• Optical characterization of nanostructures: nanoparticles, nanorods, nanotubes, etc.Carbon nanotubes, graphenes, metamaterials
• Applications of Nanostructures to optics: nano-lasers, nano-lithography, metamaterials, etc.
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Optical Characterization of Individual Carbon Nanotubes
Feng Wang
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Single-Wall Nanotube (SWNT): A Quasi-1D System
Hundreds of species depend on how it is folded.
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Characteristics of Carbon Nanotubes
• Nearly ideal 1D systems
• High mechanical strength
• High thermal conductivity
• High current-carrying capacity
• Existence of both metals and semiconductors
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A Family of StructuresGraphene:
(n,m): Chiral indicesd = R/π (tube diameter)θ (chiral angle)
Over hundred species with diameters less than 2 nanometer
1n a
2m a
R(5,4)
1a2a
θ
1 2
2 2
2 2 21 2 1 2
| | 2
R n a m a
R a n m nma a a a a
= ⋅ + ⋅
= + +
= = = ⋅
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Optical Characterization of Single SWNTs
Avoiding complications from a bundle of nanotubes
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Determination of Tube DiameterRaman spectrum of radial breathing mode (RBM)
(A. Jorio et al, New J. Physics 5, 139 (2003))
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/RBM tA d Bω = +
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Determination of Chiral Indices
Optical Transitions ⇐⇒ Chiral Indices (S.M. Bachilo et al., Science 298, 2361 (2002)
Tube can have same diameter but different chiral indices
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Graphene Electronic Structure
Fermi surface: K and K’ points(Zero-gap semiconductor)
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Metallic and SemiconductingNanotubes
Γ
Brillouin zone
If K points are on the lines, mod(n-m)≡n-m-3(interger)=0, no energy gap⇒⇒ metallic nanotubes
If K points are not on the lines, mod(n-m)=1 or 2energy gap appears⇒⇒ semiconducting nanotubes
For SWNT, cyclic or periodic boundary condition in the rolling direction ⇒⇒
only states on the red lines in the 2D BZ can exist. (k=2Nπ/R)
R
2π/R
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Γ
SWNT Electronic Structure
Brillouin zone
Metallic:
E11E22
Semiconducting:
E11
E33
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Categorization of SWNTs
Bandgap: d Metallic or semiconducting: n-m (chiral angle θ )
Metallic
mod(n-m,3)=0 mod(n-m,3)=1 mod(n-m,3)=2
Semiconducting Semiconducting
e.g. (15,15), (18, 15) (16,15) (17,15)
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SWNT Electronic Structure
Γ
Brillouin zone
Semiconducting:
E11
E33
• Lower-energy transitions can appear in the visible if the tube diameter is sufficiently small.
• Transitions would be characterized by 1D van Hove singularities unless exciton formation dominates.
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Optical Spectroscopy of Single Nanotubes
Resonance Raman spectroscopy: Intrinsically weak.
Fluorescence: Only possible for semiconducting tubes.
Elastic (Rayleigh) light scattering
Absorption spectroscopy
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Elastic Scattering Spectroscopy
1
2
E12ω ω
Elastic Scattering:21σ ε∝ −
E12
Resonances correspond to electronic transitions.
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Experiment Arrangement
dark field imaging
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Suspended Carbon NanotubesReduced background Suspended nanotube across slit
SEM
slit edges
nanotubescattering
OpticalScattering
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Rayleigh Spectrum
Energy (eV)
M. Sfeir*, F. Wang* et al. Science, 306, 1540 (2004)
(13,12): d = 1.70 nm mod(n-m,3)=1
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Correlation with Electron Diffraction
(16, 11) tubeM. Sfeir, T. Beetz, F. Wang et al. Science, 312, 554 (2006)
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Γ
SWNT Electronic Structure
Brillouin zone
Metallic:
E11E22
Semiconducting:
E11
E33
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Family Trend
E11
E33
1. Diameter dependence:Smaller diamter, larger Eii .
Semiconducting: Eii
mod(n-m,3)=1 < Eiimod(n-m,3)=2 , i = odd integer.
Eiimod(n-m,3)=1 > Eii
mod(n-m,3)=2 , i = even integer.Differences increase with n-m value.
Metallic:Degeneracy with n-m=0. Peak splitting increases with n-m.
2. n-m (chiral angle) dependence:
( Derived from tight binding calculation. Dresselhaus, Kataura, Weisman and others)
A set of qualitative rules:
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n-m Dependence:Semiconducting Nanotubes
E44 E44
E33
E33
(13,12): d = 1.70 nm mod(n-m,3)=1
(15,10): d = 1.71 nm mod(n-m,3)=2
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n-m Dependence:Metallic Nanotubes
d=1.36 nm d=1.30 nm
Degenerate transitions for (n-m)=0,Degeneracy lifted for (n-m)≠0
2.52.32.11.91.7
'(11,8)''(10,10) Tube 1'a b
Energy (eV)
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Nature of Optical Transitionsvan Hove Singularities ?
Prevailing experimental interpretation
Strong e-h interaction ⇒⇒Excitons?
e h Theoretical prediction
(Avouris, Louie and others)
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Confirmation of Existence of Excitonsin Semiconducting Nanotubes
Allowed two-photon excitation to 2p exciton state relaxes to 1s and results in
fluorescence from 1s.
hν
hν 1s2p
continuum
x
Energy difference between 2p and 1s ⇒⇒exciton binding energy
F. Wang et al. Science, 308, 838 (2005)
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1s
2p
Two-photon Excitation Spectrum
1s-2p separation: ~ 300 meV,
(6,5) tube
continuum states
Ebinding ≅ 420 meV
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Strong e-h Interaction in 1D⇒⇒ large exciton binding energy
electron and hole confined in 1D with ineffective screening
h e
electric fields lying outside of the tube
Exciton may even exist in metallic nanotoubes
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Identification of Excitonsfrom Absorption Spectrum
Density of states:(DOS)
Absorption spectrum:
Free carrier picture: van Hove singularity
Exciton picture:1s 2p
Measure absorption spectrum of individual nanotubes.
(possible even for metallic tubes)
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Interference between the real and imaginary part complicates the lineshape.
Example: A Lorentzian line with non-resonant background.
Absorption Spectroscopy vs. Elastic Scattering Spectroscopy
21scaσ ε∝ −Im( )absσ ε∝
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Experimental Setup
suspended nanotube across slit
Schematic
transmission
Tunable laser
position modulated
20 nm
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(16,15) Semiconducting SWNTs
Absorption into continuum Appears at much higher energy and weak
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Optical Characterization of a Metallic SWNT
Rayleigh Raman
RBM mode G mode
(21,21) d = 2.9 nm armchair
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Absorption Spectrum of (21,21) Metallic SWNT
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Lineshape Analysis
Signature of excitonic transitionEbinding ~ 50 meV
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Exciton Spectra of Semiconductingand Metallic SWNT
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Reasons for Exciton Formation (even in metallic nanotubes):
Strong e-h Interaction in 1D
Electron and hole are confined in 1D
Ineffective dielectric screening
h e
electric fields lying outside of the tube
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Theoretical Model21( )
( 0.3 )eV z
z dε= ⋅
+Coulomb potential:
Ebinding = 50 meVRex = 3.1 nm
fitting: ε ~10
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Free Electron Screening in 1D
3 2( )~(1/ )D q qε
Thomas-Fermi Method: (q wavevector)
3D:
1D:
For q ~ 1/ Rex, ε = 7
1D metal: free electron screening is far from perfect !
1 ( ) ~ ln (1/ )D q qε
( , ) ( , ) ( , )( ) ( , ) / ( , )
ext ind
ext
q r q r q rq q R q R
φ φ φ
ε φ φ
= +
=
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Theoretical Absorption Spectrum of Excitonic Transition in Metallic SWNT
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Multi-Phonon Raman Scattering in Single SWNTs
F. Wang et al. PRL 98, 047402 (2006)
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Experiment Arrangement
dark field imaging
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Raman Spectrum of SWNT
One phonon Two phonon
Brar et al. Phys. Rev. B 66, 155418 (2002)
RBM
G
X 103
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Multi-Phonon Raman Spectra of Single SWNTs
Excitation at 473 nm on two nanotubeswith d ~ 2 nm
optical phonon
Γ K
D
Freq
. (cm
-1)
1600G
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Raman Spectra with Different Excitation Wavelengths
E33 E22
d ~ 2 nm
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Individual Nanotube Characteristics
Resonance enhancement for outgoing photons
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Comparison of Raman Strengths between SWNT and Graphite
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Characteristics of Multi-Phonon Raman Spectra of SWNTs
• Combinations of zone-center and even number of zone-edge modes observed (result of momentum conservation)
• Narrow combination modes up to 6 phonons observed; mode strength decreasing slowly with increasing order (near intermediate resonances in multi-phonon scattering likely to be important)
• Mode strengths much stronger than those from graphite (stronger electron-phonon scattering in 1D systems)
• Relative mode strengths depend on tubes and excitation wavelength (resonant enhancement dominant)
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Multiphonon Raman Scattering
inω outω
ΔE, Δk
Three important factors:
1. Electron-phonon interactions
2. Resonance enhancement
3. Phonon density of states
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Resonant Enhancement in Multi-phonon Raman Scattering
Γ
( ) ~ ( ) or ( ')in G D ii iim n E K E Kω ω ω− −
K K’
Initial and final transitions:near K points
Intermediate resonances: near K or K’D
D
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Summary
• Optical spectroscopy can be used to characterize single SWNTs.
• Electronic properties of SWNT vary significantly depending on chiral indices.
• Excitons exists with high binding energy even in metallic tubes.
• Resonant enhancement leads to observation of multi-phonon Raman scattering.