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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 1exp /

2 2

1exp /

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 Te

1

1)(

TBken

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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

C1 = 0.9866

C2 = 0.00348

C3 = -0.08

C4 = -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 400-1000oC, 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.(oC)

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 ( oC).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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