January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar1 Optical properties of carbon nanotubes I. (Absorption) Kamarás Katalin MTA SzFKI

January 24, 2005 SZFKI-MFA Carbon Nanotube Learning Seminar 1

Optical properties of carbon nanotubes I.(Absorption)

Kamarás Katalin MTA SzFKI


Outline

1. Basics of optical properties2. Selection rules3. Polarization effects4. Kataura plot5. Isolated nanotubes


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


I0

IT

IR

Reflexiós Abszorpciósspektroszkópia (transzmissziós)

spektroszkópiaBolometrikus

(direkt abszorpciós)spektroszkópia

IA

Td IeIRRII

000 )1(

Typical optical measurement arrangements


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!


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!


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!


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:


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)


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


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)


Density of states of nanotubesJ.W. Mintmire, C.T. White: PRL 81, 2506 (1998)

First approximation: (see talk of M. Veres)


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


Depolarization (antenna effect)


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)


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


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


Kataura plot - calculated

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu,S. Suzuki, Y. Ohtsuka, Y. Achiba:Synthetic Metals 103, 2555 (1999)


Kataura plot – improved (RTM)

Tubes with the same diameter but different chiralities have different transition energies!

Optical measurements (NIR,VIS)

experimental Kataura plot


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)


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)

Documents

January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar1 Optical properties of carbon nanotubes I. (Absorption) Kamarás Katalin MTA SzFKI