Transcript Slide 1

Nano-Optics Journal Club
January 12, 2006
Andy Walsh
“Probing Electronic Transitions in Individual
Carbon Nanotubes by Rayleigh Scattering”
Matthew Y. Sfeir,1 Feng Wang,2 Limin Huang,3
Chia-Chin Chuang,4 J. Hone,4 Stephen P. O’Brien,3
Tony F. Heinz,2 Louis E. Brus1
1Department
of Chemistry, 2Departments of Physics
and Electrical Engineering, 3Department of Applied
Physics and Applied Mathematics, 4Department of
Mechanical Engineering, Columbia University
Science, Vol 306, 1540, 26 November 2004
Outline
Motivation - Why I Selected This Paper
Brief Overview of Carbon Nanotube Electronic Structure
The Experiment
Supercontinuum Generation
Results
Summary
Why I Selected This Paper
1
As stated by the authors, Raleigh scattering is usually discounted
as a method for probing nano-scale objects since it is assumed
that the signals will be prohibitively small. This is shown not to
be the case (at least for carbon nanotubes).
2
If I start using nanotube
The experimentterminology
uses a highthat
power
broadband
I have
failed supercontinuum
generated by femtosecond
pulses
to define,laser
please
stopand
me!a photonic crystal fiber.
1
+
2
= An elegant technique with a broad range of possible applications
I intend to focus on the experimental technique which I believe
will be of more interest to most of the group than the actual
nanotube-specific results. Having said that, here’s a quick
overview of carbon nanotube electronic structure…
Carbon Nanotube Electronic Structure I
Real Space
• kz along tube axis is continuous
• k is quantized since  must be
single valued
kz
k
(x=0) = (x=L)
eikx = eik(x+L)
k=2mp/L
k - Space
m=-N/2 to N/2
kz
Dk
Different wrappings lead to
different optical and electronic
properties…
Carbon Nanotube Electronic Structure II
TB Graphene
Electronic Band
Structure
+
Quantized K┴
=
Bands
This is obviously a first
approximation and there are many
corrections that should be
included, such as curvature
effects, excitonic effects, etc. but,
for our purposes, this picture is
sufficient for now…
J. Menendez, et al, ASU
Carbon Nanotube Electronic Structure III
Fluorescence
Empty
Full
For single tube spectroscopy, this
technique is time consuming and
yields the energies of only two
transitions E22 (or higher) and E11
Ref 2
The Experiment I
(My interpretation….)
( from Ref 3 )
Femtosecond
Ti:Sapphire
Photonic
Crystal
Fiber
Focusing
Objective
Sample
Collection
To spectrometer and CCD
Collecting elastically
scattered photons
Normalize by the
excitation spectrum
The Experiment II
SEM
Optical Image
Slit Edges
Raleigh
Scattering
Nanotube
Supercontinuum Generation I
“Supercontinuum generation is the formation of broad continuous spectra by
propagation of high power pulses through nonlinear media … The term
supercontinuum does not cover a specific phenomenon but rather a plethora
of nonlinear effects, which, in combination, lead to extreme pulse broadening.”
Ref 3
Supercontinuum Generation II
Ref 3
Supercontinuum Generation III
Ref 4
Supercontinuum Generation IV
According to Ref 4:
“These simulations and measurements clearly showed that, while the input
pulse can propagate large distances in these fibers without distortion, the
continuum cannot. Thus- the optimal approach to supercontinuum
generation is to use a short, ~1 cm, fiber. Indeed, using such a fiber, we
have recently succeeded in generating a supercontinuum pulse only 25 fs
long-considerably shorter than the 40-fs pulse that created it-and also
much smoother and much more stable. This short-fiber continuum is not
only a nearly ideal pulse for most broadband applications, but it is also
potentially compressible to a few fs.”
“In particular, for SC generated with femtosecond pulse pumping, the
dominant contribution to the long wavelength extension of the SC has
been shown to be associated with soliton break up combined with the
Raman self-frequency shift whilst an important contribution to the shortwavelength portion of the SC is due to the associated transfer of energy
into the normal dispersion regime via the generation of non-solitonic
dispersive wave radiation.”
Ref 5
Supercontinuum Generation V
Ref 3
Results I
σ(ω) ~ r4 ω3 | Є(ω)-1 |2
Intensity
“E33” “E44” DOS
“E22M ”
Cross-section follows the
dielectric function which
“reflects the wavefunctions
and electronic transitions”
DOS
Excitonic Model
Free-carrier Model
( Inconclusive )
Multiple Tubes
Energy
“E33” in (a)
Results II
Results III
Raman spectra taken in reflection mode with a single laser line
using a sharp notch filter to reject the laser light
“Radial Breathing Mode”
ωRBM = a + b / dt
where dt is the nanotube diameter
and a and b are fit parameters
“G Band”
Raman provides
complementary information
(especially the RBM
energy) to help make (n,m)
identification
Summary
The authors demonstrate that “Rayleigh scattering spectra … can be
obtained with high signal to noise ratio” from nano-scale sized objects.
Those spectra can be obtained quickly (<1 min) over broad
spectral ranges by use of a “white light source of laser brightness”
directly probing the electronic levels of the sample.
Though the results were inconclusive as to the nature of the electronic
transitions (excitonic or free-carrier) in carbon nanotubes, the method
allows for (1) quick discrimination between individual nanotube and bundles
and (2) better (n.m) determination when coupled with Raman spectroscopy.
Additional References
2. S. Bachilo, et al, Science, Vol 298, 2361 (2002)
3. Hansen & Kristiansen, www.blazephotonics.com,
“Application Note: Supercontinuum Generation in Photonic Crystal Fibers”
4. A. Yariv, et al, Optics Letters, 24, 711 (1999)
5. Dudley, et al, Optics Express, 10, 1215 (2002)
6. E. Yablonovitch, PRL, 58, 2059 (1987)
7. S. John, PRL, 58, 2486 (1987)
8. J. C. Knight, et al, Optics Letters, 21, 1547 (1996)
Questions?