january 24, 2005szfki-mfa carbon nanotube learning seminar1 optical properties of carbon nanotubes...
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January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 1
Optical properties of carbon nanotubes I.(Absorption)
Kamarás Katalin MTA SzFKI
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 2
Outline
1. Basics of optical properties2. Selection rules3. Polarization effects4. Kataura plot5. Isolated nanotubes
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 3
10 – 400 nm
15 – 1000
20 keV – 12 MeV
1 – 2.5
3 – 120 eV
>0.3 mm
1 – 4 meV
0.5 – 1.5 eV
-sugárzás
400 - 4000
12000 - 24000
<1012 Hz
Tartomány Frekvencia Hullámszám (cm-1) Energia Hullámhossz
Rádióhullámok, mikrohullámok
Szubmilliméter 1011 – 1012 Hz 10 -30 0.3 – 1 mm
Távoli infravörös (FIR) 0.1 – 10 THz 10 - 700 1 – 90 meV
Infravörös (MIR) 12 – 120 THz 0.05 – 0.5 eV 2.5 – 25
Közeli infravörös (NIR) 120 – 400 THz 4000 - 12000
Látható (VIS) 1.5 – 3 eV 400 – 800 nm
Ultraibolya (UV)
Röntgen 50 eV – 120 keV 0.01 – 10 nm
0.1 – 10 pm
m
m
m
The electromagnetic spectrum
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 4
I0
IT
IR
Reflexiós Abszorpciósspektroszkópia (transzmissziós)
spektroszkópiaBolometrikus
(direkt abszorpciós)spektroszkópia
IA
Td IeIRRII
000 )1(
Typical optical measurement arrangements
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 5
Basics of optical properties
We want to determine the complex dielectric function:
relrelrel i "'~
~
0
SI ! (RTM not in SI)
through the complex index of refraction:
"'~~ innn rel RTM: in
or the absorption coefficient:
EED rel 0~~
0~ kcn
00
"'
~)( c
zn
c
zin
eezE
dispersion absorption
zeIzEzEzI )0()()()( *
dz
dI
I
1
00 '
""2
cnc
n rel Measured: , n”, calculated:
f n’ is slowly varying with , ~ ”BEWARE!
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 6
22
22
0 ")1'(
")1'(
nn
nn
I
IR R
’, ”
n’, n”
Frequency dependence of optical functions
i ii
pi
iiii
erel ii
NVm
e
22
2
220
2
11
1
R
Drude-Lorentz dielectric function:
from independent oscillators additive, but n not!because of square root) where absorption is strong, n’ also varies strongly!(because of dispersion relations) where absorption is strong, reflectance is also high!
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 7
0TI Fresnel’s equations for normal incidence:
22
22
0 ")1'(
")1'(
nn
nn
I
IR R
R large, if n’>>1or n”>>n’
Reflectance spectroscopy
Extraction of optical constants from reflectance: use of dispersion relations
Kramers-Kronig (KK) transformation:
d
d
Rdd
R )(lnln
2
1)(ln)(
0022
PP
ieRinn
innr
'''1
'''1
i
r
E
En’, n” ’, ”, ...
Because of the integral, broad spectral range or reasonable extensions are needed!
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 8
if R<<1, dT eI
IT
0
cddTA log Beer’s law(Lambert-Beer)
specific (molar) absorption coefficient
1][ cm .//1][ konccm
dT log
Absorption spectroscopy (from transmittance)
not a definition! (measured sometimes called “extinction coefficient”)
Transmission can also be subject to KK analysis, if the spectral range is broad enough:
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 9
Optical functions of a transparent nanotube
~ -log T and ” ~ is a good approximationabove 3000 cm-1 only!
-log T is a reasonable approximation for the optical conductivity ’=” rather than ”
100 1000 100000
20
40
60
80
100
120
Transparent nanotube
-log T, scaled from KK, scaledReflectance from KK from KK, scaled
,, from KK, scaled
Frequency (cm-1)
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 10
Optical functions for extended bands
k-dependence: Ec(k) – conduction band, Ev(k) – valence band, Mcv(k) – dipole matrix elementk=0, but k is not restricted
If we neglect the k-dependence of the matrix elements, we obtain an expression containing the joint density of states nj(E):
Parallel bands contribute most to the absorption
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 11
Band structure of nanotubes
n,n (armchair)metallic
n,msemiconducting
n-m=mod 3small-gap
N. Hamada, S. Sawada, A.Oshiyama:PRL 68, 1579 (1992)
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 12
Density of states of nanotubesJ.W. Mintmire, C.T. White: PRL 81, 2506 (1998)
First approximation: (see talk of M. Veres)
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 13
Selection rules
Selection rules:for Ez: m=0, parity changefor Exy: m= 1, no parity change
z: 13 13,14 14,15 15xy: 12 13, but not 13 14
z-polarized light: 0A0- xy-polarized light: 0E+1
+
u
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 14
Depolarization (antenna effect)
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 15
Polarized absorption in nanotubes
Due to depolarization, only tubes with their axis parallel to the field show a structured response
Calculation: S. Tasaki, K. Maekawa, T. Yamabe: Phys. Rev. B 57, 9301 (1998)
Experiment: N. Wang, Z.K. Tang, G.D. Li, J.S. Chen: Nature 408, 50 (2000)
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 16
Optical spectra of carbon nanotubesSelection rules: only symmetric transitons are allowed
0 5000 10000 15000 20000 25000
Ab
sorb
an
ce
Frequency (cm-1)
Semiconducting nanotube
0 5000 10000 15000 20000 25000
Abs
orba
nce
Frequency (cm-1)
Metallic nanotube
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 17
Optical spectra of macroscopic nanotube samples
Háttér: -plazmon
0 5000 10000 15000 20000 250000
1
2
3
4
M11S
22
S11
M00
Rinzler nanotube filmmeasurement:F. Borondics, M. Nikolou, K. Kamarás, D.B. Tanner
Ab
sorb
an
ce
Frequency (cm-1)
P. Petit, C. Mathis, C. Journet, P. Bernier:Chem. Phys. Lett. 305, 370 (1999)
1 eV = 8000 cm-1F
IR MIR
NIR
VIS
UV
Baseline subtraction of high-frequencyabsorption:•“plasmons” (•perpendicular polarization•tube-tube interaction in bundles
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 18
Kataura plot - calculated
H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu,S. Suzuki, Y. Ohtsuka, Y. Achiba:Synthetic Metals 103, 2555 (1999)
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 19
Kataura plot – improved (RTM)
Tubes with the same diameter but different chiralities have different transition energies!
Optical measurements (NIR,VIS)
experimental Kataura plot
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 20
Transmission of nanotube film
Z. Wu, Z. Chen, X. Du, J.M. Logan,J. Sippel, M. Nikolou, K. Kamaras, J.R. Reynolds, D.B. Tanner, A. F. HebardA.G. Rinzler: Science 305, 1273 (2004)
January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 21
Isolated nanotubes: absorption
M.J. O’Connell, S.M. Bachilo, C.B. Huffmann, V.C. Moore, M.S. Strano, E.H. Haroz, K.L. Rialon, P.J. Boul, W.H. Noon, C. Kittrell, J. Ma, R.H. Hauge, R.B. Weisman, R.E. Smalley:Science 297, 593 (2002)