89

CHAPTER 4

RAMAN SPECTROSCOPY OF ZnO NANORODS AND NANOTUBES

4.1 Introduction

Raman spectroscopy is widely used to investigate the vibrational properties of

nanomaterials [1-14]. Nanocrystalline systems are very interesting from a fundamental

point of view owing to the changes in their vibrational properties related to the spatially

confined grain size effects [1-18]. The vibrational spectra of nanostructured materials are

generally different from the spectra of the corresponding bulk materials due to its large

surface to volume ratio [1-3]. The small size of nanomaterials will cause the breakdown

of vibrational selection rule that results in the vibrational lines becoming broad and with

frequency shifted when compared to those of bulk materials [4]. Hence the vibrational

spectra of nanomaterials are influenced by the surface and size effect of nanophase

materials [4-6]. Raman spectroscopy refers to the scattering of light and can be observed

in (almost) any direction with respect to the incident radiation. In order to extract the

information about the scattering by the molecules, obviously, a monochromatic light

source should be used. This technique is widely used for the study of phonon

confinement effects, strain and substitutional effects, the effect of the increase of local

temperature, porosity and nonstoichiometry in different types of nanomaterials [7].

Raman spectroscopy is a nondestructive characterisation method for many recent

studies on the vibrational properties of ZnO crystals, thin films, micro and nanostructures

[8-14]. The confined optical phonons within the grains of ZnO nanostructures lead to an

interesting change in its vibrational spectra as compared to that of their bulk counterparts.

For crystals of reduced dimensionality, some peak shifts and broadenings in the Raman

90

spectra may occur. The Raman spectra of ZnO nanostructures always show such a shift

and broadening from the bulk phonon frequencies. In previous works on ZnO

nanocrystals, some authors attribute these changes to confinement effects [15,16] whereas

others claim that the shifts are due to local heating, compressive stress or strain rather

than to spatial confinement [17,18]. In analogy with electron confinement, phonon

confinement has also been found to show interesting changes in the vibrational spectra.

Understanding the nature of the observed shift is important for interpretation of

the Raman spectra and understanding properties of ZnO nanostructures. Despite practical

importance, current knowledge of vibrational (phonon) properties of ZnO nanostructures

is rather limited. Understanding the peculiarities of phonon spectrum of ZnO

nanostructures can help in the development of ZnO based optoelectronic devices. In this

chapter, the phonon spectra of ZnO nanorods and nanotubes are compared with that of

the bulk and the effect of confinement on phonons of different symmetry are examined

theoretically. By means of optical phonon model, the line shape, peak position and

FWHM of ZnO nanorods and nanotubes was calculated and are compared with the

experimental result.

4.2 Raman Spectroscopy

Raman scattering consists of two types of radiation; Stokes radiation, where the

scattered photons have a lower frequency than the incident photons, anti-Stokes radiation,

where the scattered photons have a higher frequency than the incoming photons. The

intensity of anti-Stokes scattering is generally lower than the intensity of Stokes radiation

since the molecules have to be in an excited state for anti-Stokes scattering to occur.

91

Therefore, normally, only the Stokes radiation is recorded. Energy level representation of

Raman scattering is shown in figure 4.1.

Fig 4.1 Energy level diagram for Raman scattering; (a) Stokes scattering, (b) Anti-

Stokes scattering

For a rotation or vibration to be infrared or microwave active, the motion must

produce a change in the electric dipole of the molecule. In order to be Raman active, a

molecular rotation or vibration must cause some change in a component of the molecular

polarizability. The schematic representation of conventional Raman spectrometer is

shown in figure 4.2. Both conventional and FT Raman spectroscopies are based on the

same principle. FT Raman differs from conventional Raman in two important ways; (1)

the laser wavelength used to excite samples lies in the near-IR (most often a 1064 nm Nd:

YAG laser) and (2) instead of using dispersive gratings a Michelson interferometer is

used to analyze scattered light. FT Raman instrument also consists of one or more filters

to effectively block the Rayleigh scattering.

92

Fig 4.2 Schematic diagram of Conventional Raman Spectrometer

The Raman spectrum of the samples was measured using a Jobin–Yvon Horibra

LABRAM-HR visible (400 nm-1100 nm) confocal micro Raman spectrometer equipped

with a charge coupled detector. The He-Ne laser with wavelength 633 nm was used as a

source of excitation.

4.2.1 The Raman Effect

All collective vibrations that occur in crystals can be viewed as the superposition

of plane waves that virtually propagate to infinity [19, 20]. These plane waves, the so-

called normal modes of vibration, are commonly modelled by quasi-particles called

phonons. For a three-dimensional solid containing N unit cells with p atoms each, (3pN-

6) different phonons can propagate and their wave vectors (k) all point in a volume of the

reciprocal space called the Brillouin Zone (BZ). The phonons are referred to as being

93

longitudinal or transverse depending on whether the atoms move parallel or

perpendicular to the direction of the wave propagation given by k. The vibrational modes

with in-phase oscillations of neighbouring atoms are acoustic modes and that with out of

phase oscillations are optical modes [19, 20]. The polarisation of the dipoles excited in

solids when a laser beam of amplitude E0 and frequency νlas interacts with phonons of

frequency νvib depends on the polarizability tensor α

0 lasP= × E cos (2 t)α πν ………………………………………………………… (1)

Where α terms can be individually described as a function of the normal vibration

coordinates Q using a Taylor approximation [19, 20]:

0

0 ( , , , )i j

i j ij

Q Q

Q i j x y zQ

αα α

=

∂ = + × =

∂ ……………………………………… (2)

The classical electromagnetic theory of radiations from an oscillating dipole demonstrates

that Raman peaks have a Lorentzian shape and Raman intensity can be written as [19, 20]

30 ( ) 2

2 0

( )

[( ( )]2

BZ

d kI I

k

ω

ω ω

= ×Γ

− +

∫ ………………………………………… (3)

In equation (3), ω(k) represents the dispersion branch to which the mode belongs and Γ0

is the half-width for the ordered reference structure. According to equation (2),

i j

Q

α∂

∂ must be different from zero and this condition is governed by the symmetry of

the crystals. Raman activity can therefore be predicted through Group theory [21]. All

observed vibrational modes; both first order and higher order scattering are assigned on

the basis of group theoretical analysis.

94

The higher order phonon processes arise from mutual interaction between first

order phonons. The phonon-phonon interaction caused by the anharmonic terms in the

crystal potential is called Multiphonon processes (second and third order phonons) [22].

Generally, it originates from the entire BZ (excluding point Γ) and may produce phonons

at point Γ. Multiphonon process results from two and three phonon scattering processes

or combinations and overtones. Combinations bands occur at positions that are simple

additions of the two fundamental bands involved. Overtones occur at slightly less than

twice the fundamental depending on the degree of anharmonicity in the bond

vibrations. Overtones and combination bands, in some circumstances, may be stronger

than fundamentals, so it is important to be able to assign these bands when present.

4.2.2 Optical Phonon Confinement

The spatial confinement of optical phonons show that the Raman spectra are red

shifted (in wave numbers) and broadens due to the relaxation of the q-vector selection

rule in finite size nanocrystals. When the crystallite is reduced to nanometer scale, the

momentum selection rule, k=0, will be relaxed [17]. This allows the phonon with wave

vector | k | = |k´|±2π/L to participate in the first order Raman scattering, where k´ is the

wave vector of the incident light and L is the size of the crystal. The phonon scattering

will not be limited to the center of the Brillouine zone, and the phonon dispersion near

the zone center must be considered. That means for a particle of size L, the phonon wave

function must decay to a very small value close to the boundary. This restriction on the

spatial extent of the wave function, via a relationship of the uncertainty principle type,

leads to discrete values of wave vector k, of which the smallest k is π/L, and its multiples.

As a result, the shift, broadening and the asymmetry of the first order optical phonon can

95

be observed [17]. The phonons of several k’s over the complete Brillouin zone contribute

to the spectral line shape; however, their relative contributions gradually diminish as k

approaches the Brillouin-zone boundary. The phonons in nanomaterials are spatially

confined by its small size, grain boundaries and surface disorder. This finite size effect

give rise to phonon confinement, causing an uncertainty in the phonon wave vector,

which typically produces a frequency shift and a line shape broadening and leads to the

asymmetrical shape of the Raman spectrum. Such an asymmetrical shape of the Raman

modes is associated with the phonon confinement.

Three different types of approaches have been used to theoretically investigate

the consequences of confinement on phonon spectra

1) Gaussian confinement model

2) Continuum theory

3) Microscopic lattice dynamical calculation.

In analogy with the spatial correlation model originally developed for disordered material,

the phenomenological phonon confinement model (Gaussian confinement model) was

proposed by Richter et.al. [23] which was extended to rod like geometry by Cambell and

Fauchet [16], to take into account the contribution from phonons away from the zone

centre. Continuum theory was proposed by Roca et.al. [24] which considers the coupling

between the mechanical vibrational amplitude and electrostatic potential to obtain the

vibrational modes of nanomaterials especially in spherical quantum dots. Microscopic

lattice dynamical calculation provide more insight about the nature of the vibrations of

nanoparticles containing up to a few thousands atoms [25]. Among the above three

models Gaussian confinement model is the simplest approximation for illustrating the

96

optical phonon confinement effect in semiconductor nanostructures especially nanorods

and nanotubes.

4.2.3 Gaussian Confinement Model

4.2.3.1 Theory

The main ingredient of this model is the relaxation of the conservation of

momentum in the creation and decay of phonons in nanocrystals. Consider the wave

function of a phonon with wave vector q0 in an infinite crystal [23]

0 .

0 0( , ) ( , )iq r

q r U q r e−Φ = ……………………………………………………....... … .(4)

Where U (q0, r) has the periodicity of the lattice. Now consider a spherical nanocrystal of

diameter L. A plane-wave-like phonon wavefunction cannot exist within the crystal

because the phonon cannot propagate beyond the crystal surface. Therefore, one must

multiply the phonon wave function Ψ(q0, r) with a confinement function W(r), which

decays to a very small value close to the boundary. Hence, the wavefunction for a phonon

in spherical nanocrystal becomes [23]

0 0 0 0( , ) ( , ) ( , ) ( , ) ( , )q r W r L q r q r u q r′Ψ = Φ = Ψ………………………………… ...... ..(5)

W(r, L) to be Gaussian confinement function written as [23]

2 2( ) exp( / )W r r Lα= − …………………………………………………………... …. (6)

Where the value of α decides how rapidly the wavefunction decays as one approaches the

boundary. There is no physical reason to assume this form of confinement or its

particular value at the boundary. 0( , )q r′Ψ can be expanded in a Fourier series, the Fourier

coefficient being [23]

97

0 .3

0 03

1( , ) ( , )

2

iq rC q q d r q r e

π−′= Ψ∫ ………………………………………….. . . (7)

The nanocrystal wavefunction is a superposition of eigenfunctions with q vectors

centered at q0. For the spherical nanocrystal, the Gaussian weighting function C (q)

becomes [23]

2 2 2 1(0, ) exp( / 2 ) cosC q q L α θ−= − …………………………………………. … (8)

The first-order Raman spectrum is then obtained by integrating these contributions over

the complete Brillouin zone, as:

( )( )

( ) ( )0

23

2 2

0,

/ 2

d q C qI

qω

ω ω=

− + Γ ∫

………………………………………. .(9)

Where ω (q) is the phonon dispersion curve Γ0 is the natural line width, and |C (0, q)| is

the Fourier co-efficient that describes the phonon confinement. According to Campell

and Fauchet [16] the Gaussian confinement function, exp (-αr2/L

2) set as α = 8π

2, so that

the boundary value is zero. If we consider a column shaped crystal, the Fourier co

efficient can be written as [16]

( ) ( ) ( ) ( )( )1 2 1 1 2 2

22 1/ 22 2 2 2 2 2

2 20, , exp /16 exp /16 1 / 32C q q q L q L erf iq Lπ π π= − − −

→ (10)

Where L1 and L2 are the diameter and length of the column shaped (one dimensional)

nanocrystal. The length of the nanostructures is much larger than the diameter, which

means that the confinement effect mainly occurs along the diameter direction.

98

4.2.4 Raman spectrum of Wurtzite ZnO

The wurtzite ZnO belongs to the space group C6ν4 with two formula units in the

primitive cell. Each primitive cell of ZnO has four atoms, each occupying C3ν sites,

leading to 12 phonon branches, 9 optical modes and 3 acoustic modes [26]. At the centre

of the Brillouine zone (Γ point) group theory predicts the following lattice optical

phonons have the following irreducible representation [27]:

opt 1 1 1 2 = 1A + 2B + 1E + 2EΓ ……………………………………………………… (11)

where A1 and E1 are polar modes and are both infrared and Raman active, while E2

modes are non polar and only Raman active. The non polar E2 modes have two wave

numbers, namely, E2 (high) and E2 (low) associated with the motion of oxygen and Zn

sub lattice respectively [26]. Strong E2 (high) mode is characteristic of the wurtzite lattice

and indicates good crystallinity. The vibrations of A1 and E1 modes can polarize in unit

cell, which creates a long range electrostatic field splitting the polar modes into

longitudinal optical (LO) and transverse optical (TO) component. The E1 (LO) mode is

associated with the presence of oxygen vacancies, interstitial Zn or their complexes. The

B1 modes are Raman and infrared inactive (silent modes).

4.2.5 Raman Spectra of ZnO nanorods and nanotubes

Figure 4.3 shows the Raman spectra of ZnO nanorods and nanotubes being

excited using 633 nm UV line of He-Ne laser. The spectrum of ZnO nanorods exhibits 5

prominent peaks at 209, 331, 376, 394 and 437 cm-1

in addition to weak and broad peaks

at 542 and 654 cm-1

. The spectrum of ZnO nanotubes is similar with that of nanorods

except that two modes related to multiphonon process are absent. For comparison, a

99

compilation of the reported frequencies of the Raman active phonon modes in bulk ZnO

[26] is presented in table 4.1.

Table 4. 1 Wave number and symmetries of the modes found in Raman spectrum of ZnO

nanorods and nanotubes and their assignments

Mode of symmetry Peak position

ZnO bulk (cm-1

)

Peak position

Nanorod (cm-1

)

Peak position

Nanotube (cm-1

)

2 TA(M)

2E2(M)

A1(TO)

Quasi A1(TO)

E1(TO)

E2(high)

[E2(high)+E2(low)]

Acoust.overtone

380

395

413

444

209

331

376

394

416

438

542

654

331

375

-

418

437

547

646

By comparing the obtained optical phonon modes of ZnO nanostructures with that

of the bulk, one can assign that the modes at 376 and 438 cm-1

of nanorods and 375 and

437 cm-1

of nanotubes peaks to A1 (TO) and E2 (high) modes respectively. 416 cm-1

of

ZnO nanorods and 418 cm-1

of nanotubes are assigned to E1 (TO) mode. While 209 , 331

and 542 cm-1

peaks of ZnO nanorods are related to multiphonon process and have been

assigned to the second order Raman spectrum arising from the zone boundary phonons ,

2 TA (M), 2E2 (M) or [E2 (high)-E2 (low)] and [E2 (high) +E2 (low)] respectively [28,29].

100

0 200 400 600 800 1000

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500In

ten

sity

Raman Shift (cm-1

)

210

256

331

376

394

438

542

654331

375

437

547646

418

416

Fig 4.3 Raman Spectra of ZnO nanorods and nanotubes

The peak at 394 cm-1

is assigned to quasi A1 (TO) mode of ZnO nanorods [26].

The Raman spectra of ZnO nanotubes also exhibit a combination of both first and second

order features. The second order features at 331 and 547 cm-1

are identified as it in the

ZnO nanorods 2E2 (M) and [E2 (high) +E2 (low)] due to overtones or combination of first

order modes. An acoustic overtone with A1 symmetry is located at 654 and 646 cm-1

for

ZnO nanorods and nanotubes, respectively [28, 29]. The 256 cm

-1 peak is assigned to

laser plasma lines. In this geometry, no LO phonon peaks are seen because the incident

light is perpendicular to the c axis of the samples. A1 (LO) phonon can appear only when

the c axis of wurtzite ZnO is parallel to the sample surface. When perpendicular to the

sample surface, E1 (LO) phonon is observed [26]. Although, each ZnO nanorods /

nanotubes is c axis oriented, all nanorods/ nanotubes are randomly placed. The

101

appearance of well resolved Raman peaks related to multiphonon and resonance

processes and the absence of E1 (LO) peak at 588cm-1

related to oxygen deficiency

indicates that the prepared ZnO nanorods and nanotubes are of good optical quality.

Strong multiphonon scattering reveals quantum confinement in the samples because of

ZnO nanoentities on the surface of the nanostructures. It is well known that the Raman

spectra of ZnO nanorods and nanotubes may contain numerous combination and overtone

bands because of anharmonicity effect.

Figure 4.3 also shows that the E2 (high) mode is red shifted by 6cm-1

for ZnO

nanorods and 7cm-1

for ZnO nanotubes. A1 (TO) mode is also red shifted by 4 cm-1

for

ZnO nanorods and 5 cm-1

ZnO nanotubes. The E2 (high) and A1 (TO) modes are not only

broadened, but also show an asymmetric broadening towards the low frequency side.

Generally the three possible mechanisms that may be responsible for the observed

phonon peak shifts in the corresponding Raman spectra are :-

(1) Spatial confinement within the nanorods/ nanotubes boundaries.

(2) Phonon localization by defects such as oxygen deficiency, zinc excess, surface

impurities etc.

(3) Laser induced heating in nanostructure ensembles and tensile strain.

The broadening of the spectra, the asymmetry of line shape and strong red shifts of the

E2 (high) and A1 (TO) mode towards lower frequency side are strongly attributed to the

optical phonon confinement effect [23, 30]. Therefore among these three mechanisms the

most important effect is the spatial confinement in ZnO nanorods and nanotubes.

Gaussian confinement model is extensively used to characterise and interpret the

observed peak shift due to spatial confinement [31]. Therefore this model has been used

102

to calculate the observed peak shift and asymmetric broadening in Raman peaks of ZnO

nanorods and nanotubes arise due to phonon confinement effect.

4.2.5.1 Gaussian Confinement Model in ZnO nanorods and nanotubes

This confinement model is used for calculating the spectral line shapes of

confined optical phonons of different symmetries such as E2 (high) and A1 (TO) modes.

Figure 4.4 and 4.5 shows the calculated and experimental Raman spectra of ZnO

nanorods and nanotubes.

Fig 4.4 Calculated and experimental Raman spectra of ZnO nanorods

Scattered lines: Experimental Raman spectra

Solid line: calculated spectra, it is the sum of all contribution

103

Fig 4.5 Calculated and experimental Raman spectra of ZnO nanotubes

Scattered lines: Experimental Raman spectra

Solid line: calculated spectra, it is the sum of all contribution

Fitting equation (6) to the experimental E2 (high) and A1 (TO) modes of ZnO nanorods

and nanotubes are shown in figure 4.6 and 4.7. As the intensity of E1 (TO) mode is

extremely small, due to the little orientation deviation of the crystal lattice from the axis

of the rods/ tubes, fitting of confined phonon line shape and consequent estimation of

unambiguous parameters is rather difficult. Three parameters are used to describe the

Raman line shape:

(a) Γa/ Γb, the ratio of the half width at half maximum (HWHM) on the low energy side to

HWHM on the high energy side, which is the measure of asymmetric broadening.

(b) Γ – the full width at half maximum

(c) ∆ω- the difference between the zone centre and zone boundary frequencies of the

phonon dispersion curve of interest.

104

425 430 435 440 445 450 455

3000

4000

5000

6000

experimental

fitIn

ten

sity

Raman shift (cm-1)

ZnO nanorod

ZnO nanotube

Fig 4.6 Scattered lines: Experimental E2 (high) modes

Solid lines: Calculated E2 (high) modes

375.0 375.5 376.0 376.5 377.0

3000

4000

5000

6000

Inte

nsi

ty

Raman shift ( cm-1)

experimental

fit

ZnO nanorod

ZnO nanotube

Fig 4.7 Scattered lines: Experimental A1 (TO) mode

Solid lines: Calculated A1 (TO) mode.

105

The results of the peak position, FWHM and Γa/ Γb of ZnO nanorods and nanotubes

obtained by this model are listed in table 4.2.

Table 4.2 The observed and calculated peak position, FWHM and Γa/ Γb of different

symmetries.

From this it is evident that there is a good agreement between the experimental

and calculated Raman shift and FWHM for E2 (high) and A1 (TO) mode of ZnO nanorods

and nanotubes. It is obvious that the calculated FWHM of the Raman modes are similar

to that of the measured values which mean that the phonon confinement effect is the only

physical mechanism that causes the peak broadening. This analysis clearly see the trend

that the Raman peaks [E2 (high) and A1 (TO)] have a large red shift and broadening as the

nanorods become transformed into nanotubes and the asymmetry of the line shapes

attributed to optical phonon confinement is more precise in ZnO nanotubes. Large

surface to volume ratio and smaller diameter contributed to this enhanced optical phonon

confinement effect in the as prepared ZnO nanotubes.

ZnO

Optical

phonon

Reported

Peak

position

(cm-1

)

Observed

Peak

position

(cm-1

)

Calculated

peak

position

(cm-1

)

Observed

FWHM

(cm-1

)

Calculate

d

FWHM

(cm-1

)

Γa/ Γb

Nanorod

A1(TO)

E2(high)

380

444

375.98

438

376.02

437

0.46

11

0.45

11.1

0.87

1.2

Nanotube

A1(TO)

E2(high)

380

444

375.67

437

375.86

436

0.78

12

0.71

15.2

1.44

1.4

106

4.3 Conclusions

The Raman spectra of ZnO nanorods and nanotubes have been recorded and

analyzed. The strong red shift observed in E2 (high) and A1 (TO) modes of ZnO

nanorods and nanotubes can be attributed to the phonon confinement effect. The

observed shift and broadening of the Raman peaks have been calculated on the basis of

the Gaussian phonon confinement model which is in good agreement with the measured

spectra. This analysis clearly shows that the strong shift and broadening of the Raman

peaks are dominated by the anharmonic effects originating from quantum phonon

confinement effect. The phonon confinement effect is more prominent in ZnO nanotubes

than the nanorods. This study on optical phonon confinement effects in ZnO nanorods

and nanotubes should be useful for further investigations of physical properties like

electron phonon interaction and scattering and be of benefit to their application.

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