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Chapter-1
Introduction
0D1D2D3D
Introduction Chapter-1
1
When Neil Armstrong stepped onto the moon, he called it small step for man
and giant leap for mankind. Nano may represent another giant leap for mankind, but
with step so small that it makes Neil Armstrong look the size of solar system!
However, nanoscience and nanotechnology are steering mankind into new realms of
efficient and miniature tools and gadgetry [1]. Nanotechnology: The Future is coming
sooner than we think. Nanotechnology is a technology that deals with small structure
or small sized materials. A typical dimension spans from sub nanometer to several
hundred nanometers. A nanometer (nm) is one billionth of a meter or 10-9
m and is
approximately the length equivalent to few hydrogen or five silicon atoms align in a
line. According to the literature survey the progress of nanomaterials and
nanotechnology can be defined as follows:
The era of 2000-2005 as Passive Nanostructure; during this period products
took the advantage of the passive properties of nanomaterials, including nanotubes and
nanolayers. For example, titanium dioxide is often used in sunscreens because it
absorbs and reflects ultraviolet light. When broken down into nanoparticles it becomes
transparent to visible light, eliminating the white cream appearance associated with
traditional sunscreens.
The era of 2006-2010 as Active Nanostructure; Active nanostructures change
their state during use, responding in predicable ways to the environment around them.
Nanoparticles might seek out cancer cells and then release an attached drug. Products
in this phase required a greater understanding of how the structure of nanomaterials
determines its properties and a corresponding ability to design unique materials. The
era of 2011-2015 as Systems of Nanosystems; Nanostructures could self-assemble into
a lattice on which bone or other tissues could grow.
Why Nanomaterials Chapter-1
2
At this stage significant advancements in robotics, biotechnology, and new
generation information technology will begin to appear in products. The era of 2016-
2020 as Molecular Nanosystems; this stage will involve the intelligent design of
molecular and atomic devices, leading to “unprecedented understanding and control
over the basic building blocks of all natural and man-made things” [2].
2020 and beyond as the singularity; every exponential curve eventually
reaches a point where the growth rate becomes almost infinite. This point is often
called the singularity. If technology continues to advance at exponential rates, what
will happen after 2020? Technology is likely to continue, but at this stage some
observers forecast a period at which scientific advances aggressively assume their own
momentum and accelerate at unprecedented levels, enabling products that today seem
like science fiction. Beyond the singularity, human society is incomparably different
from what it is today. Several assumptions seem to drive predictions of a singularity
[3], there is an assumption that solutions to most of today‟s problems including
material scarcity, human health, and environmental degradation can be solved by
technology, if not by us, and then by the computers we eventually develop.
1.1 Why Nanomaterials?
One of the first and most natural questions to ask when starting to deal with
nanoparticles is: “why are nanomaterials so interesting”? Why even bother to work
with these extremely small structures when handling and synthesis is much more
2000-2005
Passive Nanostructure 2011-2015
Systems of Nanosystems
2016-2020
Molecular Nanosystems 2006-2010
Active Nanostructure
Why Nanomaterials Chapter-1
3
complicated than that of their macroscopic counterparts. The answer lies in the nature
of and unique properties possessed by nanostructures. Small features permit more
functionality in a given space, but nanotechnology is not only a simple contribution of
miniaturization from micron meter scale down to nanometer scale. Materials in the
micrometer scale mostly exhibit physical properties the same as that of bulk form,
however, materials in the nanometer scale may exhibit physical properties distinctively
different from that of bulk. Materials in this size range exhibits some remarkable
specific properties: a transition from atoms or molecules to bulk form takes place in
this size range. For example, crystals in nanometer scale have a low melting point and
reduced lattice constants, since the number of surface atoms or ions becomes a
significant fraction of the total number of atoms or ions and the surface energy plays a
significant role in the thermal stability. Crystal structures stable at elevated
temperatures are stable at much lower temperatures in the nanometer sizes. This may
result in losing the ferroelectricity and ferromagnetism when the materials are shrunk
to nanometer scale. Bulk semiconductors became insulators when the characteristic
dimension is sufficiently small (in a couple of nanometers). Although bulk gold does
not exhibit catalysis properties, but nanocrystals of gold demonstrate to be an excellent
low temperature catalyst.
In our macroscopic everyday experience we observe the phenomena of light
acting in quiet easy predictive way. Light directed at a surface is reflected just at the
angle and with the color that would be expected. This easily predictive behavior
changes dramatically when the reflecting particles become much smaller than the
wavelength of the incident light. Nanomaterials possess a very high surface to volume
ratio. This can be utilized in areas where high surface areas are critical for success.
This could for example be in the catalytic industry; some nanoparticles actually have
Why Nanomaterials Chapter-1
4
proven to be good catalysts. Some nanoparticles also show bactericidal effects and here
a high surface to volume ratio is also important. In biology and biochemistry
nanoparticles have attracted much attention. Nanoparticles are often in the range 10-
100 nm and this is the size as that of human proteins. Scientists from the Chinese
Academy of Science have even suggested using gold nanoparticles to improve
Polymerase Chain Reaction (PCR). The scientific mantra of “structure dictates
function” - a tenet largely taught to biologists and biochemists - is quickly being
adopted by researchers who deal with materials at the nanoscale. In biology, this catch
phrase is exemplified by proteins whose roles in specific chemical pathways are
strictly determined by the way these large biomolecules fold or form hierarchical
structures based on chemical interactions with themselves or other molecules. Another
aspect which is important and plays role for most of the dramatic electronic and
vibrational properties compared to bulk is to check quantum confinement effect. The
most dramatic changes in properties take place in the structures where the
carriers/phonons are confined in the region of a characteristic length of the order of the
electron/phonon wave functions wave length. If the motion of a particle (or quasi
particle), e.g. electron or phonon, is restricted in one or more dimensions by a potential
well, this particle is confined in the well because the probability to traverse the energy
barriers is lower than to remain within it. When the confining dimension is large
compared to the wavelength of the particle, the particle behaves within the confined
area as if it were free. As the confining dimension decreases and reaches the order of
the wave function„s wave length, the particle‟s energy states are modified due to the
overlap of the wave function‟s amplitude reflected from the barriers. This is defined as
"quantum confinement". The free path length of particles in solids is usually much
longer than the particles wave function‟s wave length. In case the confined dimension
Why Nanomaterials Chapter-1
5
reaches the order of the free path length no "quantum size" effect takes place.
However, other characteristics of the particle like lifetime and mobility are affected by
changing e.g. the carrier and heat transport properties.
To chemists, physicists, and engineers, a similar structure-function relationship
is the underlying motive for discovering and characterizing novel nanoscale structures.
Hence, we are interested in the nanoparticles.
Nanostructures can be divided into zero-dimensional (0D when they are
anisotropic, such as spheres and polyhedra), one-dimensional (1D when they are
elongated, such as rods, wires and tubes), and two-dimensional (2D when they are
planar, such as plates and discs) based on their shapes. Besides, these building blocks
with different dimensionality (0D–2D) can self-assemble into more complex
nanostructures, such as nanostructured arrays and dendritic nanostructures [4]. Figure
1.1 illustrates the basic geometrical motifs of inorganic crystals with the
dimensionality from 0D to 3D.
Nanofluidics is often defined as the study and application of fluid flow in
and around nanosized objects. It is not a new, but it didn‟t have the name of its own
until the development of micro fluidics in the 1990s. Nanoparticle material,
concentration, size, and shape all contribute to the nanofluids properties. Noble metal
colloids or nanofluids, especially gold, have a long history of scientific studies. Fig.1.2
presents the schematic of importance of nanofluidics and relevance in different fields.
The earliest scientific work by Faraday on the preparation of gold colloids dates back
to 1857 [5] and this work stimulated tremendous interests in this new form of gold, [6,
7] in particular, about the origin of the beautiful ruby red color of colloidal gold.
Why Nanomaterials Chapter-1
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Figure 1.1: Basic geometrical motifs of inorganic nanocrystals with the
dimensionality from 0D to 3D [4].
Why Nanomaterials Chapter-1
7
It is worth noting that the distinct color of gold had long been utilized in
colorful decoration, even in ancient times (e.g., a few thousand years ago), much
earlier than the 19th
century's scientific studies on gold colloids, but ancient
practitioners certainly had not realized that the attractive ruby color of gold is indeed
due to its nanoscale form. Since Faraday's original work, Mie was the first who
successfully modeled the optical spectra of gold colloids by solving Maxwell's
equations in 1908 [7].
Figure 1.2: Classical disciplines related to nanofluidics and some of the
relevant subjects studied.
Concept of Phonon Engineering Chapter-1
8
1.2 Concept of Phonon Engineering
Phonons, i.e. quanta of lattice vibrational waves affect almost all physical properties in
solids [8]. They do not only affect optical properties of crystalline solids but also limit
the electron mobility near room temperature. The phonons are classified as optical and
acoustic phonons. The acoustic phonons or long wavelength phonons; which give rise
to sound waves explains the name phonons. In bulk materials with n atoms per unit
cell, there are 3n phonon dispersion branches for each wave vector q . The relation
between phonon frequency and wave vector q is known as phonon dispersion
curve q . Therein acoustic phonon branches describe the motion of unit cell,
while (3n-1) optical phonon branches describe the relative motion of atoms inside a
unit cell. The acoustic phonon branches which are the main heat carriers are commonly
referred as longitudinal acoustic (LA) and transverse acoustic (TA). In the case of
graphene the out of plane transverse vibrations are denoted as z-axis acoustic (ZA)
phonons. The acoustic phonons in bulk crystals have linear dispersion in the long
wavelength region, the optical phonons are nearly dispersion less with a small group
velocity,
dq
dVc . The optical phonons are used for determining the number of
atomic planes in the few layer graphene via Raman spectroscopy. The thermal
properties of low dimensional materials can be altered more drastically than in
corresponding bulk crystal due to uniqueness of phonon transport [9]. The phonon
properties of structures with reduced dimensionality are a fascinating area of research
since they give rise to various interesting phenomena including: (a) in clean systems
and at normal temperatures, the carrier mobility and dephasing times are determined by
phonon scattering. (b) when microstructure decreases in size and phonons with lower
Concept of Phonon Engineering Chapter-1
9
wave vectors are involved in the electron-phonon interaction due to which electron
scattering by acoustic phonons becomes mere pronounced as compared to the
scattering of electrons by optical phonons.(c) the scattering by optical phonons, being
dominant in the 3D case, is reduced or suppressed (d) when the number of defects
decreases with improvement of the nanostructure technology, as a result of which the
electron-optical phonon interaction weakens and the minimum linewidth of optical
spectra is determined by the electron-acoustic phonon interaction. Carrier energy
relaxation and non-radiative recombination involve emission of phonons. This makes
them relevant for a number of electronic processes in nanostructures, due to
technological importance. There are several evidences that the phonon interaction is
altered due to the effects of dimensional confinement on the phonon modes in nano-
structures similar to the electron confinement. This dimensional confinement of
phonons modifies the phonon related properties such as melting temperature, specific
heat, low and high frequency Raman spectra, carrier phonon interactions in low
dimensional structures.
Micro- and nanoscale mechanical resonators and semiconductor quantum dots
embedded in micro cavities have established themselves as a new paradigm in cavity
quantum electrodynamics (cavity QED) and emerged as ubiquitous devices for
application in a wide range of technical disciplines including communications, sensing,
metrology, and fundamental scientific endeavors. In many instances the performance
of these devices is limited by the deleterious effects of mechanical damping. Although
much progress has not been made towards the understanding of mechanical dissipation
at the micro- and nanoscale [10-13], obtaining reliable predictions of the fundamental
design-limited quality factor, Q, remains a major challenge. The origins of mechanical
damping in micro- and nanoscale systems have been the subject of numerous studies,
Concept of Phonon Engineering Chapter-1
10
with several relevant loss mechanisms having been investigated. These include: (i)
fundamental anharmonic effects such as electron-phonon interactions, damping, and
the quality factor; (ii) viscous damping, involving interactions with the surrounding
atmosphere or the other hosts matrix; (iii) materials losses driven by the relaxation of
intrinsic or extrinsic defects in either the bulk or surface of the resonator for which the
most commonly studied Lamb‟s model and its modified model where interaction of
soft/hard matrix with nanofluidics has been considered and (iv) support-induced
damping, i.e. the dissipation induced by the unavoidable coupling of the resonator to
the substrate. Enhanced thermal conduction in nanofluids is an observed phenomenon
for which the underlying mechanistic processes are still being debated. In addition, the
technological progress in the design and fabrication of semiconductor cavity-QED
systems has enabled them to be used as components in quantum information
processing [14] and for the generation of indistinguishable photons [15]. These
quantum applications require robust cavity-QED based QD devices that rest on the
ability to manipulate and control the underlying quantum processes. Such quantum
control is usually obtained when the cavity and QD are in the intermediate to strong-
coupling regime [16]. For semiconductor cavity-QED systems, signatures of electron–
acoustic-phonon scattering have been noted with incoherent excitation, resulting in off-
resonant „„cavity feeding‟‟ and an asymmetric (on-resonance) vacuum Rabi doublet
[17].
In the applications of nanostructured materials, an understanding of their
acoustic and mechanical properties is especially important. Furthermore,
technologically important semiconductors and dielectrics, heat is mostly carried by the
acoustic phonons and there will be modification of thermal properties due to the
modified increased phonon-boundary scattering arising from the modification of
Concept of Phonon Engineering Chapter-1
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acoustic phonon energy spectra. For example, the thermal conductivity of the generic
semiconductor nanostructures is smaller than that of constituent bulk materials [18].
This happens due to increased phonon boundary scattering and decrease in the phonon
group velocity [19]. Modification of the acoustic phonon dispersion is particularly
strong in nanostructures embedded into the elastically dissimilar materials [20]. Such
modification may turn out to be desirable for some applications while detrimental for
others. However, the reduction of the thermal conductivity, being a bad news for the
thermal management of downscaled electronic devices, is good news for the
thermoelectric devices, which require materials with the high electrical conductivity
and low thermal conductivity [21]. Recently, the concept of “phonon engineering” has
been introduced which may lead to progress in electronic and optoelectronic devices
[20]. The phonon engineering [21] basically deals with controlling phonon transport
via tuning. Phonons with its dispersion relation having quantized modes of vibration
occurring in a rigid crystal lattice are strongly affected by the spatial confinement in
terms of modified phonon dispersion curves, and allied properties such as phonon
group velocity, density of states, point defects, electron-phonon interaction etc. The
phonon engineering concept proposes that the acoustic phonon spectrum is particularly
strong in nanostructures embedded into elastically dissimilar materials. Thus
nanostructures offer a new ways of controlling phonon transport via tuning its
dispersion. While, earlier the acoustic phonon confinement was only considered useful
for charge carrier mobility and electrical conductivity, it is now found that the
confinement of acoustic phonon modes leads to decrease of the average phonon group
velocity with corresponding increase of the phonon scattering and reduction in thermal
conductivity. This is good news for the thermoelectric devices which needs materials
with high electrical conductivity and low thermal conductivity [21]. However, this can
Concept of Phonon Engineering Chapter-1
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be cured by embedding the nanostructure into acoustically faster or acoustically harder
layers [19-21].
In nanostructures, the role of electron-acoustic phonon interaction on a carrier
relaxation has been discussed in terms of possible slowing of relaxation rates due to the
phonon confinement [22-25]. It is found that the electron-acoustic phonon interaction
is responsible for the decay rate of the excitonic polarization in nanostructures. In
nanostructures, where dimensional confinement is significant, it is possible that the
phase space restrictions may weaken or forbid the optical phonon scattering processes
which would normally dominate in bulk structures. Phonons generally affect the
thermal, optical, mechanical, and electrical properties of materials. While, the phonon
density of states (PDOS) is primarily a function of the local atomic structure, and it is
also sensitive to atomic-level stresses and the microstructure. It is found that the
phonon density of states for nanomaterials is significantly different from its bulk
counterparts [26-32].
The microscopic origins of the observed size effects are, however, very often
not clear. In view of the partially controversial interpretation of the PDOS of
nanostructured materials, a detailed study revealing the role of the various size effects
appears to be a worthwhile task. To understand the vibrational properties of
semiconductor/metal nanocrystals, it is absolutely necessary to consider the zero
dimensional confinement effects on the electronic states in a system. In addition, the
low-frequency phonon modes (acoustic phonons) of nanoparticles bear a unique
signature of their structural and mechanical properties directly reflecting the impact of
confinement on the ionic movement.
Coinage metals, such as Au, Ag, have been important materials throughout
history [33]. Although in ancient cultures they were admired primarily for their ability
Concept of Phonon Engineering Chapter-1
13
to reflect light, their applications have become far more sophisticated with our
increased understanding and control of the atomic world. Today, these metals are
widely used in electronics and catalysis and as structural materials, but when they are
fashioned into structures with nanometer-sized dimensions, they also become enablers
for a completely different set of applications that involve light. These new applications
go far beyond merely reflecting light and have renewed our interest in maneuvering the
interactions between metals and light in a field known as plasmonics [10-13].
Nanofluids are dilute liquid suspensions of nanoparticles with at least one of
their principal dimensions smaller than 100 nm. There is a growth in the use of colloids
which are nanofluidics in the biomedical industry for sensing and imaging purposes.
This is directly related to the ability to design novel materials at the nanoscale level
alongwith recent innovations in analytical and imaging technologies for measuring and
manipulating nanomaterials. Colloidal gold has a long therapeutic history, which is
well rooted in eastern traditions particularly in the India to its subcontinent [34, 35].
The medicinal value of colloidal gold is well documented in the books of ancient
Indian ayurveda like „Charaka Samhita‟ and the „Vedas.‟ Nanofluidics is basically
characterized by two most important and fundamental transport properties: thermal
conductivity and viscosity. The apparent thermal conductivity is the most important
parameter to demonstrate the enhancement potential of heat transfer in nanofluids. It
has been shown that the thermal conductivity of the nanofluids is influenced by the
heat transfer properties of the base fluid and nanoparticle material, the volume fraction,
the size, and the shape of the nanoparticles suspended in the liquid, as well as the
distribution of the dispersed particles [36]. Keblinski et al [37] listed four possible
explanations to understand the heat transfer enhancement in nanofluids: Brownian
motion of the nanoparticle, molecular-level layering of the liquid at the liquid/particle
Confined Acoustic Phonons in Nanostructure Chapter-1
14
interface, the nature of heat transport in the nanoparticles, and the effects of
nanoparticle clustering. Brownian motion, by which particles move through the liquid
and possibly collide, thereby enabling direct solid-solid transport of heat from one
particle to another, can be expected to increase thermal conductivity. Nanofluids with
smaller nanoparticle size exhibit greater thermal conductivity. Nanofluids with metallic
nanoparticles give higher thermal conductivity than nanofluids with non-metallic
nanoparticles [38]. However, it appears from the literature that the origin of thermal
conductivity in nanostructure/nanofluidics system is still unclear. Besides, there is a
need of proper nanofluidics system with less size variation of the nanoparticles in bare
fluids.
As far as the understanding of the thermal conductivity is concerned the role
played by phonons is not disputable. Therefore, it is believed that the investigation of
phonons in either form of colloids or solid will be quite useful. Recent results reveal
that these properties are sensitive to the size, shape, composition, base fluids and size
distribution [36-38]. Therefore, a synthesis of nanoparticles –host (base fluids) system
is desirable for optimum application.
1.3 Confined Acoustic Phonons in Nanostructures
Spatial confinement of acoustic phonons in nanostructures affects their
dispersion. It modifies the acoustic phonon properties such as phonon group velocity,
polarization, density of states and changes the way the acoustic phonons interact with
other phonons, defects and electrons such changes create opportunities for engineering
phonon dispersion spectrum in nanostructures for improving electrical phonon
spectrum at room temperature one needs to have materials at the nanometer length
scale due to being average phonon mean free path and wavelength of thermal phonon
Confined Acoustic Phonons in Nanostructure Chapter-1
15
TK
V
B
sD 48.1 in the range of nanometer ( is the plank‟s constant, BK is the
Boltzmann constant, T is the absolute temperature, sV is the sound velocity in
materials). Engineering of the optical phonon in nanostructures via the boundary
conditions requires different approaches than engineering of the acoustic phonons. In
the long wavelength limit the optical phonons corresponds to the motion of atoms
within the same unit cell and hence change by imposing new outside boundaries is not
possible [39]. However, the electron-phonon scattering rates can be modified by tuning
the confined electronic states energy difference with respect to the optical phonon
energy. This effect is known as “Phonon bottleneck” and is useful in the optimization
of solid state lasers. Although phonon engineering has received attention recently,
interest in modifying the acoustic phonon spectra of layer materials (superlattices) has
a long history [40]. The folded phonons in superlattices of GaAs/AlGaAs have been
experimentally observed by colvard et al [41]. However, interest in the subject
substantially increased when it was pointed out that the confinement induced changes
in the acoustic phonon dispersion can strongly affect the thermal conductivity [42].
In an infinite elastic solid medium, acoustic waves such as longitudinal and
transverse acoustic waves are governed by the Navier equations [43] that describe the
dynamic motions of solids. However, when at least one of the dimensions of a solid
object decreases to be near or smaller than the phonon wavelength, phonon
confinement results in a strong modification of the acoustic phonon spectrum [19]. The
frequencies of the confined acoustic phonons in a nanostructure depend on its shape
and its boundary conditions including the effect of surrounding medium. Thus, the
confined acoustic modes are sensitive to physical structures and should show
significant size-dependent features.
Confined Acoustic Phonons in Nanostructure Chapter-1
16
When the phonon wavelength λ ~ D, i.e the nanostructure dimension, the confined
acoustic phonons no longer have a propagating character and are generally understood
as normal vibrations of the whole nanostructure. In principle, the confined acoustic
phonons in a nanostructure manifest themselves via the appearance of discrete peaks in
inelastic light scattering spectra and the blue shift of these peaks with decreasing
nanostructure size [44-49].
The first observation of confined acoustic modes of nanoparticles was reported
in the Raman study of spinel microcrystallines by Duval in 1986 [44]. One low
frequency peak with a frequency of several cm-1
was observed in the Raman spectrum
and was attributed to the spheroidal mode of the nanospheres. Interestingly, the mode
frequency was found to shift with the variation in the particle size. That is, the mode
frequency is proportional to the inverse diameters of the particles. This size dependent
feature agrees well with the theoretical predictions based on Lamb‟s theory [45]. In the
following years, nanoparticles of different materials, such as CdSe, CdS, Ge, Si, were
studied by Raman scattering [50-51]. However, these Raman experiments only study
the particles of sizes ranging from several nm to few tens of nm because it is very hard
for Raman scattering to detect the vibrations of frequency below 1 cm-1
. Particles of
several hundreds of nanometers or microns were not studied until Brillouin light
scattering was introduced to this field [52]. Using Brillouin light scattering, many more
confined acoustic modes with accurate frequency could be observed [52].
In the above mentioned Brillouin and Raman experiments, the nanoparticles
studied are often, for simplicity, assumed to be spherical and the measured data are
analyzed within the theory formulated by Lamb [45] for a homogeneous elastic sphere.
In this theory, the confined acoustic modes of a sphere are classified as spheroidal or
torsional, which are labeled by l = 0, 1, 2. . . the angular momentum quantum number,
Confined Acoustic Phonons in Nanostructure Chapter-1
17
and n = 1, 2, 3, . . . , the sequence of modes in increasing order of energy. However, in
few early studies [34 -35, 37, 43-45, 50, 52-61], nanoparticles studied did not have free
surfaces. Thus, on the surfaces of these spheres, the stress and strain are not completely
zero and the free surface conditions of the Lamb‟s theory are not fully satisfied in these
studies. Also, the contact between neighboring spheres could lead to vibration damping
and energy loss [53-54, 61-62]. Theoretical studies [47- 48, 56, 63] have shown that,
when the acoustic impedances of matrix material and the embedded spheres are the
same, the vibrational energy loss from the sphere can be very large and low frequency
spectrum will be very broad or almost a straight line [49]. Several other studies have
also showed that the eigenvibrational frequencies of nanospheres embedded in matrix
are different from those of free surface nanospheres [46, 53, 64-67]. Hence, the Lamb‟s
theory has not been experimentally tested under rigorous free surface conditions
though it has been widely applied in most studies. Also, the study of a sphere‟s
eigenvibrations under different surface conditions can help to understand how
environmental factors affect its vibrations, especially the phonon lifetimes.
Apart from Lamb‟s theory, selection rules are fundamentally important for
assigning the low frequency acoustic modes which is observed in Raman and Brilloiun
spectra. Group theory [39] predicts that spherical modes are observed in Raman
scattering where as torsional modes are not observed [55-56]. While, Wu et al [61]
observed the torsional modes (l=1, n=0 and l=2, n=0) in nanocrystalline silicon which
they attributed to the non-spherical shape of the particle, the observation of the
torsional mode (l=1, n=0) in nanocrystal CdS in GeO2 matrix with a frequency ratio of
~ 0.72 and attribution to the particle-matrix interaction was recently argumented by
Ivanda et al [47]. Very recently, Kanehisa pointed out that Duval‟s selection rules are
not correct and stated that only the torsional mode with l = 2 is Raman-active [68]. A
Confined Acoustic Phonons in Nanostructure Chapter-1
18
subsequent comment, by Goupalov et al [66], which refuted Kanehisa‟s model and his
subsequent rebuttal have exacerbated the current controversy. Unfortunately, Raman
experiments are unable to provide adequate evidence to resolve this controversy. The
selection rules are critically important to analyze the Raman results of nanoparticles.
Experiments [45, 50, 52] have shown that Brillouin scattering is more appropriate than
Raman scattering to study the confined acoustic modes of submicron spheres because
their mode frequencies mainly lie in the gigahertz range. In Brillouin experiments, the
sphere sizes are of the order of excitation wavelength, which are normally several
hundred nm. Thus, the Raman selection rules cannot be applied. Furthermore, there are
no convincing theoretical foundations to support their mode assignment models.
Therefore, there is a critical need to establish selection rules to correctly assign the
confined acoustic modes of spheres studied by Brillouin light scattering, which serve
as the basis for determining their mechanical properties.
Another issue to understand the origin of the observed variation of low-
frequency Raman bands of TiO2 nanoparticles with particle size is required. As far as
the investigation of different properties like vibrational and mechanical of titanium
dioxide nanoparticles is concerned the situation is not encouraging. Ivanda et al [47]
performed low-frequency Raman (LFR) experiment and calculated LFR modes
together with a deconvolution treatment of the size distribution. In other paper [47],
they have shown the low-frequency Raman spectra for different size of TiO2
nanoparticles obtained using annealing, but they did not assign any peak. For
experimental measurement of the confined acoustic phonons of nanostructures, thin
films and nanospheres have been extensively studied. However, at the same time, a lot
of new and more complicated nanostructures have been fabricated that call for more
attention, such as core-shell composite spheres, hollow spheres, nanowires and
Objective of the Present Study Chapter-1
19
nanocubes. Very rare experimental study has been done on these nanostructures and
their low-frequency acoustic features are still unknown.
1.4 Objective of the Present Study
Our investigation in the present study focused mainly on the semiconductor and metal
nanoparticles, which are free-standing or embedded in different matrix to understand
the behavior of phonons and the effect of different matrix materials on them. The
nanocrystals of silicon, germanium, titanium dioxide, silver and gold are selected in
view of their electronic, optoelectronic and biological applications. The determination
of the structure is, in general, a hard task, either by the experimental techniques or for
sophisticated total energy calculations and knowledge of the geometrical structure and
shape is required as a basis for understanding many of its properties. In this thesis, low
frequency Raman scattering measurements has been performed to probe the acoustic
vibrations of several nanostructures. The results are analyzed with the help of three
variants of Lamb‟s model. However, the very specific objective of the present work is
listed below.
(i) To investigate low frequency modes in metal nanoparticles
The modes with very low frequency (<30 cm-1
) are difficult to be measured
accurately in Raman scattering and pump probe spectroscopy due to high background
from scattering. Recently, tera-hertz time domain spectroscopy has been used to
observe infrared active l=1 spheriodal mode. Simultaneous observation of Raman
active radial and quadrupolar modes is rare in LFRS. The above facts motivated us to
perform a low frequency Raman scattering from free standing silver nanoparticles. It is
noteworthy that the quadrupolar and breathing modes are simultaneously observed in
the study of Ag nanoparticle which is quite rare and it is presented in Chapter 4.
Objective of the Present Study Chapter-1
20
(ii) To investigate the size distribution of metal nanofluids: UV- Visible
spectroscopic assessment
UV-visible spectroscopy is one of the popular characterization techniques to
determine particle formation and size distribution of the nanoparticles. Furthermore, it
is known that the spectrum surface plasmon resonance of nanoparticles is influenced
by the size, shape, inter-particle interactions, free electron density and surrounding
medium, which indicates that it is an efficient tool for monitoring the electron injection
and aggregation of NPs and is also presented in Chapter 4. A theoretical approach
under the framework of Mie scattering theory is further applied to determine the size of
the metal nanofluidics. Using Mie scattering theory optical spectra can be analyzed to
determine particle size of stable suspension.
(iii) To investigate the formation of Si and Ge nanocrystals during annealing of
implanted SiO2 layer using Low frequency Raman scattering and eigen
frequencies of the free and embedded semiconductor nanoparticles.
A study of the influence of heat treatments on an ion-beam synthesized silicon
and germanium nanocrystals in SiO2 layers by low-frequency Raman scattering
(LFRS) and optical Raman spectra. Spectral analysis along with the theoretical
calculations reveals the occurrence of Si and Ge crystals nuclei in SiO2 matrix in
contrast to the electron microscopic results. The results are surprising as the melting,
binding energy, diffusion length etc are different for both systems indicating same
phenomena of crystal growth. Crystal nuclei of Si and Ge of nanometer size results in
an additional contribution to the density of states associated with surface vibrational
modes of Si and Ge nanocrystals and it is presented in Chapter 5.
In addition, chapter 5 also describes the low frequency Raman scattering study
of the quantized acoustic vibrations in anatase TiO2 semiconductors nanocrystals. The
Objective of the Present Study Chapter-1
21
observed Raman spectra are analyzed with theoretical models. The controversies in the
selection rules are also discussed. Our results show that the observed low-frequency
Raman scattering originates from the spherical (l=0) and quadrupolar vibrations (l=2)
of the spheriodal mode due to the confinement of acoustic vibrations in TiO2
nanoparticles. Furthermore, the low-frequency peak due to the vibrational quadrupolar
and spheriodal modes, a band is also observed, which is assigned to the Raman
forbidden torsional l=2 mode originating from the near spherical shape of the TiO2
(iv) To perform the vibrational dynamics using abinitio calculations
The abinitio calculations based on density functional theory are now being
widely used for the study of structural, vibrational and electronic properties of real
materials ranging from nanoscale up to bulk solids. DFT is basically the process of
solving the Schrödinger equation for many electron systems in practical environmental
settings. The Chapter-6 describes briefly the DFT formulation and analyzes the
electronic and vibrational properties of ZnO nanowire and silver clusters.
The problem proposed in the present thesis is of fundamental in nature, the
outcome is expected to be a detailed understanding of the vibrational properties of the
free and embedded nanoparticles of different shapes and size. The role of dimensional
confinement in modifying acoustic phonon modes and their interactions with charge
carriers despite the fact that electron scattering by acoustic phonons plays the key role
in the physics of nanostructures, and great relevance to understand the phonon
engineering concepts for nanoscale devices has been tried to understand in the present
thesis.
References Chapter-1
22
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