Abstract: Present thesis reports the Raman investigation of the Raman scattering in MWNTs as function of laser power. Raman spectra of MWNT were taken at laser parameters (514.5nm, 0.1- 0.6 w). The mathematical analysis of graphitic Raman peaks was done based on Einstein model. Earlier we chose Gaussian and Lorentzian weighting function to investigate Raman graphitic peaks. Earlier we discussed about size dependent Raman scattering in CNTs. When the laser power is increased from a minimum value, it causes the increase in induced temperature in the sample. In this section we have discussed Temperature dependence on Raman spectra. The temperature dependence of linewidth has been interpreted as due to decay of optical phonon into two LA phonons at half optical frequency. Temperature rise in the sample was calculated theoretically as well as experimentally.

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Study of Raman Scattering in Carbon nanotubes
Ajay Singh (2010PH10821)
Ankit Singla (2010PH10826)
Supervisor: Dr. A. K. Shukla
Abstract: Present thesis reports the Raman investigation of the Raman scattering in MWNTs as function
of laser power. Raman spectra of MWNT were taken at laser parameters (514.5nm, 0.1- 0.6 w). The
mathematical analysis of graphitic Raman peaks was done based on Einstein model. Earlier we chose
Gaussian and Lorentzian weighting function to investigate Raman graphitic peaks. Earlier we discussed
about size dependent Raman scattering in CNTs. When the laser power is increased from a minimum
value, it causes the increase in induced temperature in the sample. In this section we have discussed
Temperature dependence on Raman spectra. The temperature dependence of linewidth has been
interpreted as due to decay of optical phonon into two LA phonons at half optical frequency.
Temperature rise in the sample was calculated theoretically as well as experimentally.
Email:ph1100821@physics.iitd.ac.in, ph1100826@physics.iitd.ac.in
1. INTRODUCTION
Carbon exists in different allotropic forms that give rise to its versatile behaviour.
Graphite is the most stable form of carbon at room temperature and atmospheric
pressure. Graphite is characterized by double bonds between sp2 hybridized carbon
atoms [4]. There are so many new form or allotrope of carbon, like
buckminsterfullerene (C60) or Bucky ball [5], Carbon nanotubes (CNTs) [7] etc.
Graphene is a honeycomb structure made out of hexagons like benzene rings
stripped out from their hydrogen atoms. CNTs are made by rolling graphene in
cylindrical shape reconnecting the carbon bonds. Hence carbon nanotubes, which
have only hexagon sand, can be thought of as 1D object.
Nanoparticles or Nano crystals made of semiconductors, metals or oxides are of
interest for their optical, electrical and chemical properties. These are of great
scientific interest because they are effectively a bridge between atomic or molecular
structures and bulk materials. In nanoparticles, size-dependent properties are
observed such as surface Plasmon resonance in some metal particles quantum
confinement in semiconductor particles, and super paramagnetism in magnetic
materials. Especially, the applications of one dimensional nanostructure such as
carbon nanotubes play a important role in nanoelectronics. Changes in properties of
the semiconductor are not only sensitive with the reduction in size of the material but

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also with the shape of the materials. There are three main categories of low
dimensional semiconductors, which involve:
1. One-dimensional confinement (quantum wells)
2. Two-dimensional confinements (quantum wires)
3. Three-dimensional confinements (quantum dots)
The quantum mechanical effects dominate at nanoscale when the size approaches
the de Broglie wavelength of the carriers. Quantum mechanical feature of low
dimensional systems is another unique the phonon confinement. Phonon
confinement effects can be studied by Raman spectroscopy.
Aim of this thesis is to investigate the temperature dependence on the Raman
spectra and ultimately the laser power dependence. The temperature rise in the
sample of carbon nanostructures have been estimated here by Raman spectroscopy
and the evolution of the Raman spectra with probing laser power density. The
Raman spectra is analysed mathematically using phonon dispersion equations and
different weighing function such as Lorentzian and Gaussian distributions. And the
temperature dependence is studied using Einstein model for harmonic oscillator.
2. CARBON NANOTUBES
Carbon nanotubes are layers of graphite wrapped into cylinders of few nanometres
in diameters, and approximately 10-20 microns in length. There are mainly two types
of carbon nanotubes single wall nanotubes [SWNT] and multi wall nanotubes
[MWNT]. Rolling a single graphite sheet in to a cylinder forms SWMT. MWNT
comprised of several nested cylinder with an interlayer spacing of approximately
0.34 to 0.36nm [3].
The structure of nanotubes can be defined by using a chiral vector. Three types of
carbon-nanotubes are possible known as armchair, zigzag and chiral nanotubes,
depending on the rolling of the two-dimension graphene [4]. Chirality causes different
properties for different types of tubes. These different types are explained in terms of
the unit cell of a carbon nanotube. Nanotubes made up of carbon are of great
interest for their electrical, optical, and chemical properties.

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Fig. 1. Multiwall carbon nanotubes (MWNT) [23].
3. THE RAMAN EFFECT
When a material is exposed to monochromatic light, phonons goes through Raleigh
and Raman scattering. The Raman Effect occurs when incident photon interacts
with the electron cloud of the bonds of a molecule. The incident photon gives energy
to one of the electrons to excite it into a virtual state. In case of spontaneous Raman
Effect, the molecules are excited from the ground state to a virtual energy state, and
relax into a vibrational excited state, generating Stokes Raman scattering. If the
molecule is already in an excited vibrational energy state, the Raman scattering is
then anti-Stokes Raman scattering as shown in Fig. (3). A molecular polarizability
modifies the amount of the electron cloud deformation, with respect to the vibrational
coordinate. The amount of the change in polarizability determines the intensity, and
the Raman shift is equal to the energy of the vibrational level that is involved in
scattering.
Fig.2. Raman and Rayleigh phonon scatterings [24]

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In last section we investigated mathematical formula for graphitic peaks in Raman
scattering. For that we considered phonon confinement model and found size
dependent Raman scattering. There, we considered constant laser power.
When we increase laser power, spectra no more remains same. While increasing
laser power the induced temperature in the sample rises. This increase in
temperature leads to anharmonicity in phonon vibrations. So in this section we have
studied temperature rise in the sample as a function of laser power. We also studied
spatial distribution of the temperature. When temperature increases, we observed
that FWHM tends to its maximum value and Raman peak shift to its lower values.
Temperature dependence of the line width has been interpreted as due to the decay
of optical phonon into two LA phonons at half the optical frequency.
4. WORK DONE DURING LAST SEMESTER
In last part we investigated mathematical formulation for graphitic Raman peaks and
studied size dependence of Raman spectra. From phonon confinement model
proposed by Ritcher et. al, in previous part of the project we formulated Raman
peaks using Lorentzian and Gaussian weighing function. We suggested the Raman
intensity as:
∫
( )
(1)
∫
( )
(2)
Above for an optical branch, (q) is the phonon dispersion relation (Fig.3) and is
given by
( ) (3)
Where A=2356297.67 cm-2
, B=149700 cm-2
, Ɵ=0.23and (q=0)=1582 cm-1(peak
position)

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Fig.3. Phonon dispersion relation for graphite [25]
Using the expression of w(q) from equation (3) into equation (2)
∫
[ ( ( ) ) ]
(4)
Eq. (1) represents Raman intensity as a function of Raman shift while using
Gaussian weighing function and Eq. (2) represents Raman intensity while using
lorentzian weighing function.
Fig.4. Raman spectra for different size of CNTs at constant laser power for (a) Gaussian Weighting function (b)
Lorentzion Weighting function.
In last semester our project work was concern on the analysis of G peak. So using
Phonon confinement model, we find FWHM and Peak position by varying the
diameter of the CNTs which are shown below:

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Table 1 shows the variation in peak shiftng and change in broadening while using Gaussian weighing function.
CNT Diameter
L(nm)
1 1.5 2 2.5 3 3.5 4 5
Peak position
cm
-1
1552.46 1552.74 1554.91 1558.63 1561.22 1564.08 1568.31 1570
FWHM cm
-1
185.12 156.6 134.7 127.65 119.32 110.9 107.2 104
Table 2 shows the variation in peak shiftng and change in broadening while using Lorentzian weighing function.
CNT diameter L
(nm)
1 1.5 2 2.5 3
Peak position
(cm
-1
)
1584 1586.4 1587.5 1588 1589
WHM(cm
-1
) 73 68.4 64.5 65 53
5. TEMPERATURE DEPENDANCE OF HARMONICE OSCILLATOR
The Raman peaks and the FWHM of Raman intensity are also function of
temperature. When temperature changes, position of Raman peaks and the value of
FWHM also changes. This is because of temperature dependence of the phonon
vibrations. Earlier we considered phonon vibration as harmonic vibrations .When we
increase laser power, induced temperature raises in the sample. To study the
temperature dependence we take quantum theory of harmonic oscillator into
account.
Energy of harmonic oscillator is given by Einstein model. Average energy of a
harmonic oscillator and hence of a lattice mode of angular frequency at temperature
T
(5)
Where Energy of oscillator is given by ( ) (6)
And the probability of the oscillator being in this level at temperature T is given by the
Boltzman factor (7)
From eq. (5)
(8)
n
n
nP  
_
_
0
0
1 1
exp /
2 2
1
exp /
2
B
n
B
n
n n k T
n k T
 






    
      
    
  
   
  



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(9)
The average number of phonons is given by the Bose-Einstein distribution as
(10)
So the temperature dependence of Harmonic oscillator energy will lead to change
the Raman shift frequency and the FWHM while changing the incident optical power.
Temperature dependence of the line width has been interpreted as due to the decay
of optical phonon into two LA phonons at half the optical frequency. The FWHM as
function of temperature is given as
* + (11)
Where -1
, is Intrinsic FWHM at room temperature when slit width 0.
Fig.5 Plot between FWMH and the temperature.
Anhaomonicity: When rise in temperature associated with harmonic oscillator takes
place, it changes the frequency of phonon vibration which leads to change in FWHM
and Raman shift during Raman scattering process.as the temperature increases ,
energy versus distance behaviour changes and it shows asymmetric behaviour as
shown in fig. 6.
_
/
1
2 1Bk T
e 

  

1
1
)(


TBk
e
n  

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Fig.6 Energy versus displacement of harmonic oscillator [21]
6. THEORITICAL WORK
I. Temperature dependence of linewidth and Raman shift: According to the
anharmonic theory of phonon scattering suggested by Hart et al, light scattering due
to optical phonons in CNTs leading to the change in phonon frequency and line width.
While taking anharmonicity into account, FWHM Γ(T) of the phonon line is given by
* + [
( )
] (12)
And Raman Peak position is given by
* + [
( )
] (13)
Where Ci ‘s are found from experimental values [table 3] .
Fig.7 (a) Calculated FWHM as function of temperature (b) Calculated Raman shift as function of temperature
C
1
= 0.9866
C
2
= 0.00348
C
3
= -0.08
C
4
= -0.0074

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Putting the expression of FWHM and Raman shift form eq. (12) and (13) into our
original expression (eq. 2):
∫
[[
[ ]
[
( )
] ]
(
* +
[
( )
])
]
(14)
Fig.8 Theoretically calculated Raman Spectra for a MWNT sample.
II. Temperature rise induced by laser beam
When a laser beam is incident on a material, it causes rise in temperature. The laser
beam has Gaussian intensity distribution I0 exp(-r2
/w2
). Near the beam waist, w will
be less dependent on z, the beam depth that we shall treat the band width w as
constant. If attenuation constant is α then energy absorbed per unit volume per
second
G(r, z) =α exp(-α z) I0 f(r/w)

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We shall take f(R) = exp (-R2
). So the spatial temperature distribution will be given as
(15)
Here represents the maximum temperature induced by the laser beam at the
center , and it is given as
( ) ( ) (16)
Where, for a laser beam
( ) (∫ ) (∫ )
( ) (17)
is the mean inverse distance from a point on the surface at the beam center to the
remaining points on the surface using a weight factor f(R)R proportional to the
intensity incident (weighted by area) on the surface.f(R) describes the shape of the
beam in the dimensionless variable R. The thermal conductivity is K. With the
notation. is beam width. is sufficiently small varying function of z, so near the
beam waist we consider equal to the beam waist . For our case ].
For a laser beam the total optical power carried by the beam is the integral of the
optical intensity over a transverse plane (say at a distance z)
∫ ∫
∫ (18)
Finally
→ (
∫
) (∫ )

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(∫ )(∫ ) (19)
Where is Bessel transform of f(R), given as
∫ (20)
Using eq. (20) can be written as
( ) ( ) (
⁄
) ( )
Now
 ( ) ( ) (21)
The conductivity of the carbon nanotubes shows weak dependence on temperature
for higher temperature. Though for smaller values of temperatures conductivity has
strong dependence on temperature [14] as shown in fig.9.
Fig.9 Calculated MWNT thermal conductivity (solid line) compared to the thermal conductivity of a 2-D graphene
sheet (dot–dashed line) and 3-D graphite (dotted line) [14].
In the temperature range 400-1000o
C, considering conductivity to be constant
(3000W/m-K) .So the induced temperature in the CNT sample increases linearly with
power and decrease with spatial coordinates R,Z as shown in fig.10.

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Fig.10 (a) Theoretically calculated maximum temperature rise as function of laser power, (b) Temperature
distribution with R and Z (laser parameter 541.5nm, 0.1w)
7. EXPERIMENTAL WORK
We recorded Raman spectra of MWNTs sample for different laser power by the
Raman spectrometer. The system consists of a laser as a continuous wave argon-
ion laser (COHERENT, INNOVA-90-5, 514.5nm), sample chamber, a double
monochromator (high transmission of 75 % with a band pass of 1.0 nm) to disperse
the signal into its constituent scattered wavelengths, Triple monochromator and a
detector (Photomultiplier tube –HUMAMATSU-R 943-02, Operating voltage- 2000 V,
Amplifier and discriminator, Chart recorder) to detect photons at various
wavelengths. The lab apparatus used to record Raman spectra is shown below:
Fig.11 Experimental Set up of Raman spectrometer .

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Scattered light from the sample is analyzed by triple monochromator. A systamatic
diagram of the triple monochromatic used in the Raman spectrometer is shown
below.
Fig.12 Schematic diagram of the triple monochromatic Raman spectrometer
The recorded Raman spectra for different laser powers taking other parameters
constant were recorded. The spectra were recorded for 0.1, 0.2, 0.3, 0.4, 0.5, 0.6
watt. The shift in Raman peak and linewidth broadening were observed clearly.
Fig.13 Recorded Raman spectra for a MWNT sample using laser wavelength 541.5nm.
Table3. Variation in Raman peak and change in FWMH for the graphitic mode.
S.No. Laser power (w) Raman peak (cm
-1
) FWHM (cm
-1
)
1 0.1 1583.89 53
2 0.2 1581.71 59
3 0.3 1575.78 62
4 0.6 1572.45 70
Triple Monochromator (T64000)

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Variation of Raman peaks and the FWHM with the laser power were observed
experimentally from the recorded Raman spectra. And Raman temperature was
calculated using those datas. The laser power dependence of FWHM and Raman
Peak is graphically shown below:
Fig.14 (a) Graphitic Raman peaks as function of laser power, (b) Linewidth as function of laser power for
wavelength 541.5nm for Graphitic Raman peaks
Table2. Calculated temperature from experimental recorded spectra: using equation (11)
S.No. Laser Power FWHM (cm
-1
) Temp.(
o
C)
1 0.1 53 705
2 0.2 59 780
3 0.3 62 820
4 0.6 70 930
Calculated Raman temperature is graphically shown below:
Fig.15 Experimentally obtained Raman temperature.

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8. RESULT AND DISCUSSION
From the recorded Raman spectra we observed that line width tends to its maximum
value while increasing laser power and Raman peaks shift towards lower values.
Raman peak of graphitic mode at 0.1W laser power was observed at 1583.89 cm-1
while it was observed at 1572.45 cm-1
for . W. The pea shifts significantly ( cm-
1
) while changing laser power .FWHM for 0.1W laser power was recorded 53 cm-1
less compared to 70 cm-1
which was observed for 0.6W laser power. The change in
the position of peake and line width happens because of increasing in the tempreture
while increasing the laser light. Temperature rise causes anharmonicity in the
phonon vibrations.
Temperature rise due to laser light and temperature distribution were calculated
considering beam width as constant. For higher temperatures thermal conductivity
was also taken as independent on temperature. The values of laser beam waist and
thermal conductivity of the sample were taken 5 μm and 3000W m- respectively.
From the calculations we find that the maximum temperature due laser heating at
. W is too high ( o
C).which is much enough to burn the sample . The burning
sample can also be seen at this much of laser power. The temperature distribution
was calculated which shows lorentzian distribution with peak at the centre (R=0,
Z=0). For higher values of R and Z, temperature decreases very fast and it
approaches room temperature for R, Z values greater than that of beam diameter.
Experimental results show that temperature observed by phonon mechanism is
much less than that of temperature rise calculated theoretically. For 0.2W laser
power Raman temperature was found 780o
and the temperature rise was
calculated o
C .the reason for that a large difference is that the conduction of
heat is dominated by electrons. The total heat generated by laser heating is
conducted by both phonons and electrons.The major part of the heat goes to
electrons.The calculated temperature rise is combined of both electrons and
phonons. While the experimentally found Raman temperature is the temperature due
to heat transfer by the phonons only. For higher laser energies this difference in
temperature increases up to order of magnitudes.
The temperature dependence of line width has been interpreted as due to decay of
optical phonon into two LA phonons at half optical frequency. Raman peak shift can

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be interpreted as due to increase in energy of harmonic oscillator associated with the
phonons which cause Raman scattering due to resonance with incident light.
Increase in energy will lead to increase in frequency of harmonic oscillator so the
lower frequency oscillators will now cause resonance with incident light, ultimately at
lower wavenumber phonons will show the Raman scattering.
9. FUTURE SCOPE
Graphene is expected to be a future material for the semiconductor industry.
Graphite has been used as target for CNT as well as graphene .properties of
graphite and carbon nanotubes ,which are studied here, have large potential
apllication in industry, nano electronic due to electrical properties, thernal properties,
field emission.Carbon nanotube based nano electronics is very emerging field in
semiconductor device industry.The Raman spectra which we studied here, gives
various informations of the CNTs like order of defects, type of the nanotubes
(semiconducting, insulating, metallic, multiwalls / single wall ), size of nanotubes,
thermal concucting properties of the nanotubes. Therefore , one can study carbon
nano tube and graphene by Raman spectrometer to attain various informations.
10. ACKNOWLEDGEMENTS
We express our gratitude and heartiest thanks to our supervisor Dr. A. K.
Shukla for his active involvement at every stage of the project work carried out in
this thesis. His invaluable guidance, encouragement and moral support was always
be a source inspiration for us. We also thank him for his easy availability for
discussion at any time.
We thank to Mr. Kapil Saxena, Mr. Pawan kumar, for beautiful moments kept
our laboratory a beautiful place to work. With their presence, project work was more
than enjoyable. For their ever available help and giving me the necessary guidance,
useful discussion during all stages of my project work and their important help during
the laser operation and Raman spectrometer handling.
Last but not least we are indebted to our project coordinator Dr. Vijaya
Prakash G. for his timely advice. Lively suggestion and important discussions with
him helped us a lot in completing project work.

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REFERENCES
[1] Bundy, F. P., Journal of Chemical Physics Vol 38, 631-643 (1963).
[2] DeVries, R.C., Annual Review of Materials Science, Vol 17,161-187 (1987).
[3] Angus, J.C. and Hayman, C.C., Science, Vol 241, 913-921 (1988).
[4] Vole, O. et al., John Wiley & Sons Inc, (2002)
[5] Kroto, H.W. et al., Nature, Vol 318, 162-163 (1985).
[6] Krätschmer, W. et al., Nature, Vol 347, 354-358 (1990).
[7] S. Iijima, Nature Vol 56, 354 (1991)
[8] C.N.R. Rao, A. Govindaraj, Nanotubes and Nanowires, RSC Nanoscience and Nanotechnology Series, RSC
Publishing, Cambridge, UK, 2005
[9] Alan C., Colin P., Terry R., Baker K and. Rodriguez N.M., J.Phys.Chem.B, 102 (22),4253-4256.
[10] Sation R.Dresselhaus, G.Dresselhaus M.S., Physical properties of nanotubes Imperia College Press. 2003.
[11] P.J.Harris, carbon nanotubes and related structures, Department of chemistry, Cambridge University press.
[12] H.S. Harriselhaus, G .Dresselhaus, R. Satio, A.Jorio, Raman spectroscopy of carbon nanotubes, Elsevier,
2004
[13] Temperature rise induced by a laser beam by M. Lax, Journal of Applied Physics 48, 3919 (1977)
[14] Carbon Nanotubes: Thermal Properties J. Hone Columbia University, New York, New York, U.S.A.
[15] http://cnx.org/content/m22925/latest/
[16] http://www.google.co.in/imges/arc discharge method
[17] http://www.google.co.in/imges/chemical vapour deposition
[18] C.N.Banwell, atomic and molecular spectroscopy
[19] http://www.citycollegiate.com/allotropyXIIb.htm
[20]http://en.wikipedia.org/wiki/Carbon_nanotube
[21] (http://idea.sns.it/research/spectroscopy/IR)
[22] http://hone.mech.columbia.edu/pdf/hone_thermal_ency_nano.pdf
[23]http://www.crystalsoftcorp.com/gallery.php
[24]http://www.webexhibits.org/causesofcolor/14D.html
[25]http://flex.phys.tohoku.ac.jp/~pourya/gcnt.html