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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