Nanophysics
In 1959, the idea of nanotechnology was introduced first time, when Richard
Feynman, a physicist at Caltech, gave a talk called "There's Plenty of Room at the
Bottom. Feynman suggested that it may eventually be possible to precisely manipulate
atoms and molecules. At such microscopic level, the principles of classical mechanics are
failed to explain the properties and behavior of systems. So, one has to consider the
concepts of quantum mechanics.
It is well understood and accepted universally now that for the solutions of the
problems at the macroscopic level, the principles of classical mechanics are applicable.
But, at microscopic level of atoms, these principles are observed to be fail and the
principles of quantum mechanics must be used for solutions. In fact, quantum mechanics
is valid at all length scales. It is possible to describe the characteristics of macroscopic
objects also with quantum mechanics. Classical mechanics and quantum mechanics give
the same predictions for macroscopic objects so we usually use the simpler classical
mechanics to describe large objects. Nanometer scale objects lie near the boundary
between classical mechanics and quantum mechanics and sometimes it is necessary to
use quantum mechanics to describe phenomena on the scale of nanometers. Therefore,
after having a brief discussion on quantum mechanics, let us now see the different aspects
of nanophysics in detail which essentially is the mathematical way to understand the
science at micro level. Let us now discuss the quantum mechanics with its essential
fundamentals and the applications.
Particle in a box
For the understanding of microscopic properties (e.g. position, momentum) of the
particles like electrons in the atomic structure, we can compare the electron with a
particle which is trapped in the box of finite dimensions. Consider a particle which
bounces back and forth between the walls of a box of width L as shown in the Fig. 1.2.
Suppose that the walls of the box are infinitely hard so that the particle does not loose
energy each time it strikes a wall. Moreover, suppose that particle is moving with
sufficiently low velocity so that the relativistic case can be ignorable. Such particle
behaves like a standing wave in a string stretched between the walls of the box. Further,
the potential energy U of the particle is infinite on both sides of box and is constant inside
the box as shown in the Fig. 1.3. The possible de Broglie wavelengths of the particle in
this case are determined by the width L of the box as shown in the Fig. 1.4. Particle does
not acquire enough energy so that it can go outside the box and so the probability of
finding the particle outside is zero. Hence, its wavefunction   0 for x  0 and x  L .
So to find the value of wavefunction  within the box i.e. within x=0 and x=L we can
start with the Schrödinger equation within the box. The Schrödinger equation within the
box is
 2 2m
(1.30)
 2 E  0
x 2
The solution of above Schrödinger equation is
 2mE 
 2mE 
(1.31)
  A sin 
 x  B cos 
 x




which can be verified by substituting above eq (1.31) in to (1.10). Here, A and B are
constants. Here, in above eq. (1.31),   0 when x=0 and x=L. The second term here can
not describe the particle because cosine (0) =1 and hence it can not vanish at x=0.
Therefore, we can say that, B=0. Here,   0 when x=0 but   0 when x=L only when
2mE
L  n
n=1,2,1,4 ….
(1.32)
This suggests that the energy of the particle can have only certain values known as
eigenvalues. The energy levels of the particle are found by solving the eq. (1.12) which
gives,
n2 2 2
n=1, 2, 1 ….
(1.33)
En 
2mL2
Here, the integer n that specifies an energy level En is called quantum number. Above eq.
(1.33) gives following important conclusions:
(i) A particle trapped in a box can occupy only certain specific energies which are depend
on the mass of the particle and the nature of its trapping. (ii) It can not acquire zero
energy. If it has zero energy means its velocity is zero and hence its de Broglie
wavelength   h
will become infinite but there is no way to reconcile an infinite
mv
wavelength with a trapped particle. Hence, the trapped particle can not acquire zero
kinetic energy.
The wavefunctions of a particle in a box whose energies are En are given with the help of
eq. (1.31) by taking B=0.
 2mEn 
(1.34)
 n  A sin 
x




Substituting eq.(1.31) in eq.(1.34) we have,
n x
 n  A sin
(1.35)
L
Above eq.(1.35) gives the eigenfunctions of the trapped particle in the box of width L for
different quantum number n. Now, the probability density of particle can be derived by
2
taking the integral of  n over all space which in turn gives

L
(1.36)
 A2    1
2

Substituting the value of A from eq.(1.36) into eq. (1.35) we get,
n x
 n  2 L sin
(1.37)
L
2
which gives the normalized wave function of the particle. In every case,  n  0 at x=0
and x=L i.e. at the boundaries of the box.

2
n
Nanoscale systems
Nanoscale systems simply means about the tiny systems with dimensions at
nanometer level (i.e. 10-9m). The technology that relies on Nanoscale systems is known
as nanotechnology. However, the nanotechnology is simply not miniaturizing materials,
and devices at the nanometer scale. At nano-meter length scales new physical properties
emerge in these materials and new techniques are required to make them. Size constraints
often produce qualitatively new behavior in nano-materials. This means that when the
materials (and hence the devices) are manufactured at nanoscale level, all the
corrosponding parameters and properties (e.g. electrical, optical, magnetic, etc.) are
changed with respect to their bulk form. Now let us see the world of nanoscale devices in
detail.
1.7 Nanomaterials
The materials made up of nanoparticles are termed as nanomaterials. The
materials that we are utilizing in our day to day life are in their bulk form. The properties
and hence their behavior under different circumstances are of certain type. But, when the
same material is grown up atom by atom very systematically in a crystal grow machine
by proper method, then all the associated properties as well the behavior are noticed to be
changed dramatically with respect to their corresponding bulk form. One of the main
causes behind this may be the rearrangement of the atoms or molecules. The
combinations of atoms or molecules held together under different circumstances are
known as clusters. In this sense, clusters are artificial molecules that differ from the
molecules that are occurred naturally. Clusters consist of a countable number of atoms
ranging from 50 to 1000.
Importance of nanomaterials:
These materials have created a high interest in recent years by virtue of their unusual
mechanical, electrical, optical and magnetic properties. Some examples are given below:
(i) Nanophase ceramics are of particular interest because they are more ductile at elevated
temperatures as compared to the coarse-grained ceramics.
(ii) Nanostructured semiconductors are known to show various non-linear optical
properties. Semiconductor Q-particles also show quantum confinement effects which
may lead to special properties, like the luminescence in silicon powders and silicon
germanium quantum dots as infrared optoelectronic devices. Nanostructured
semiconductors are used as window layers in solar cells.
(iii) Nanosized metallic powders have been used for the production of gas tight materials,
dense parts and porous coatings. Cold welding properties combined with the ductility
make them suitable for metal-metal bonding especially in the electronic industry.
(iv) Single nanosized magnetic particles are mono-domains and one expects that also in
magnetic nanophase materials the grains correspond with domains, while boundaries on
the contrary to disordered walls. Very small particles have special atomic structures with
discrete electronic states, which give rise to special properties in addition to the
superparamagnetism behavior. Magnetic nanocomposites have been used for mechanical
force transfer (ferrofluids), for high density information storage and magnetic
refrigeration.
(v) Nanostructured metal clusters and colloids have a special impact in catalytic
applications. They may serve as precursors for new type of heterogeneous catalysts
(Cortex-catalysts) and have been shown to offer substantial advantages concerning
activity, selectivity and lifetime in chemical transformations and electro- catalysis (fuel
cells).
(vi)Nanostructured metal-oxide thin films are receiving a growing attention for the
realization of gas sensors (NOx, CO, CO2, CH4 and aromatic hydrocarbons) with
enhanced sensitivity and selectivity. Nanostructured metal-oxide (MnO2) finds
application for rechargeable batteries for cars or consumer goods. Nanocrystalline silicon
films for highly transparent contacts in thin film solar cell and nano-structured titanium
oxide porous films for its high transmission and significant surface area enhancement
leading to strong absorption in dye sensitized solar cells.
(vii) Polymer based composites with a high content of inorganic particles leading to a
high dielectric constant are interesting materials for photonic band gap structure.
Methods for synthesis of nanomaterials
In broad way, there are two approaches for synthesis of nanomaterials: (i) top
down approach in which we start with the bulk (larger) sample and with the help of
various experimental techniques, the size of the sample is allowed to reduce until the
desired size obtained. Following techniques are employed under top down approach:
(a) High energy ball milling, (b) laser ablation (c) Sputtering (d) electron beam
evaporation (e) photolithography. The approach is bottom up approach for the synthesis
of nanomaterials in which the materials are assembled atom by atom to form the clusters
of certain particular size. Following techniques are employed under bottom up approach:
(a) chemical vapor deposition, (b) sol gel method, (c) electro-deposition. Let us now see
some important methods for synthesis of nanomaterials.
Top down approach:
A top-down approach is the breaking down of a system to gain its compositional
sub-systems (Fig. 1.5). A key advantage of the top-down approach is that the parts are
both patterned and built in place, so that no assembly step is needed.
(1) High energy ball milling (Mechanical alloying):
This process was developed by Benjamin and his coworkers at the International
Nickel Company in the late of 1960. In this process a powder mixture placed in the ball
mill is subjected to high-energy collision from the balls. It was found that this method
could successfully produce fine, uniform dispersions of oxide particles (Al2O3, Y2O3,
ThO2) in nickel-base super alloys that could not be made by more conventional powder
metallurgy methods.
Traditionally, a ball mill consists of stainless cylinder and some crushing agents
(e.g. iron balls or silicon carbide balls). After
filling up the samples in the powder form, the
milling chamber is allowed to rotate. The
crushing agents (i.e. balls) continuously move up
and down due to centrifugal and gravitational
forces and impart high amount of energy by
colliding with material powder particles. The
impact energy of the milling balls in the normal
direction attains a value of up to 40 times higher
than that due to gravitational acceleration.
The fig. 1.6 shows the motions of the balls
and the powder. Since the rotation directions of
the bowl and turn disc are opposite, the
centrifugal forces are alternately synchronized.
Thus, friction resulted from the hardened milling
Fig. 1.6 High energy ball milling:
balls and the powder mixture being ground
Motion of balls and powder.
alternately rolling on the inner wall of the bowl
and striking the opposite wall. The synthesis of
nanostructured metal oxides for gas detection is one of the most promising applications of
high-energy ball milling.
Sol Gel method:
Sol is a stable colloidal dispersion of small particles in a liquid (solvent). The
particles may be amorphous or crystalline. Whereas a gel is a state where both liquid and
solid are dispersed in each other, which presents a solid network containing liquid
components. In a colloidal gel, the network is built from agglomeration of colloidal
particles. Generally, the sol particles may interact by van der Waals forces or hydrogen
bonds. A gel may also be formed from linking polymer chains. In most gel systems used
for materials synthesis, the interactions are of a covalent nature and the gel process is
irreversible.
Advantages:
(1) This method produces thin bond-coating to provide excellent adhesion between the
metallic substrate and the top coat.
(2) This method produces thick coating to provide corrosion protection performance.
(3) This method can easily shape materials into complex geometries in a gel state.
(4) Produces high purity products.
(5) This method has low temperature sintering capability, usually 200-600°C.
(6) This method prevents the problems with co-precipitation, which may be
inhomogeneous.
(7) This method provides a simple, economic and effective method to produce high
quality coatings.
(8) Sol-gel synthesis may be used to prepare materials with a variety of shapes, such as
porous structures, thin fibers, dense powders and thin films.
Fig. 1.9 Sol Gel method options
Quantum well:
Quantum well is the two dimensionally confined structures akin to thin film few
nanometers thick. In broad sense, Quantum wells are thin layered semiconductor
structures in which we can observe and control many quantum mechanical effects. They
derive most of their special properties from the quantum confinement of charge carriers
in thin layers (e.g 40 atomic layers thick) of one semiconductor quantum well material
sandwiched between other semiconductor "barrier" layers. They can be made to a high
degree of precision by
modern epitaxial crystal
growth techniques.
Fig.
shows the quantum well
structure of GaAs which is
the sandwich type structure
wherein few nanometers
thick layer of GaAs is
grown between the layers
of
doped
GaAs
by
aluminum. In this way, the
carriers in GaAs are trapped
in the GaAs layer along the
growth direction. This leads
to a confinement of the
electrons in the conduction
band and of the elementary
excitations
of
carriers
(called "holes") in the filled
valence bands. This leads to a quantum well structure. The carriers in the quantum well
are free to move in the in-plane direction.
The important techniques by which quantum well structures can be grown are
molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD).
Both can achieve a layer thickness control close to about one atomic layer. With the help
of eq. (1.33) one can find the energy states of electron when the sides of the quantum
well do not rise immediately to infinity at the boundaries or the potential is non-uniform
within the well.
9 Properties of nanomaterials:
Nanomaterials have the structural features in between of those of atoms and the
bulk materials. While most microstructured materials have similar properties to the
corresponding bulk materials, the properties of materials with nanometer dimensions are
significantly different from those of atoms and bulks materials. This is mainly due to the
nanometer size of the materials which render them: (i) large fraction of surface atoms; (ii)
high surface energy; (iii) spatial confinement; (iv) reduced imperfections, which do not
exist in the corresponding bulk materials. Due to their small dimensions, nanomaterials
have extremely large surface area to volume ratio, which makes a large to be the surface
or interfacial atoms, resulting in more surface dependent material properties. Especially
when the sizes of nanomaterials are comparable to length, the entire material will be
affected by the surface properties of nanomaterials. This in turn may enhance or modify
the properties of the bulk materials. For example, metallic nanoparticles can be used as
very active catalysts. Chemical sensors from nanoparticles and nanowires enhanced the
sensitivity and sensor selectivity. The nanometer feature sizes of nanomaterials also have
spatial confinement effect on the materials, which bring the quantum effects. The energy
band structure and charge carrier density in the materials can be modified quite
differently from their bulk and in turn will modify the electronic and optical properties of
the materials. For example, lasers and light emitting diodes (LED) from both of the
quantum dots and quantum wires are very promising in the future optoelectronics. High
density information storage using quantum dot devices is also a fast developing area.
Reduced imperfections are also an important factor in determination of the properties of
the nanomaterials. Nanostructures and Nanomaterials favors of a self-purification process
in that the impurities and intrinsic material defects will move to near the surface upon
thermal annealing. This increased materials perfection affects the properties of
nanomaterials. For example, the chemical stability for certain nanomaterials may be
enhanced, the mechanical properties of nanomaterials will be better than the bulk
materials. The superior mechanical properties of carbon nanotubes are well known. Due
to their nanometer size, nanomaterials are already known to have many novel properties.
Many novel applications of the nanomaterials rose from these novel properties have also
been proposed.
Applications of nanomaterials:
Nanomaterials having wide range of applications in the field of electronics, fuel
cells, batteries, agriculture, food industry, and medicines, etc... It is evident that
nanomaterials split their conventional counterparts because of their superior chemical,
physical, and mechanical properties and of their exceptional formability.
Carbon nanotubes - Microbial fuel cell
Microbial fuel cell is a device in which bacteria consume water-soluble waste
such as sugar, starch and alcohols and produces electricity plus clean water. This
technology will make it possible to generate electricity while treating domestic or
industrial wastewater. Microbial fuel cell can turn different carbohydrates and complex
substrates present in wastewaters into a source of electricity. The efficient electron
transfer between the
microorganism and the
anode of the microbial
fuel cell plays a major
role in the performance
of the fuel cell. The
organic
molecules
present in the wastewater
posses a certain amount
of chemical energy,
which is released when
converting
them
to
simpler molecules like
CO2. The microbial fuel
cell is thus a device that
converts the chemical
energy present in waterFig. 1.11. Schematic representation of microbial fuel cell
soluble
waste
into
electrical energy by the catalytic reaction of microorganisms. Carbon nanotubes (CNTs)
have chemical stability, good mechanical properties and high surface area, making them
ideal for the design of sensors and provide very high surface area due to its structural
network. Since carbon nanotubes are also suitable supports for cell growth, electrodes of
microbial fuel cells can be built using of CNT. Due to three-dimensional architectures
and enlarged electrode surface area for the entry of growth medium, bacteria can grow
and proliferate and get immobilized. Multi walled CNT scaffolds could offer selfsupported structure with large surface area through which hydrogen producing bacteria
(e.g., E. coli) can eventually grow and proliferate. Also CNTs and MWCNTs have been
reported to be biocompatible for different eukaryotic cells. The efficient proliferation of
hydrogen producing bacteria throughout an electron conducting scaffold of CNT can
form the basis for the potential application as electrodes in MFCs leading to efficient
performance.
Phosphors for High-Definition TV
The resolution of a television, or a monitor, depends greatly on the size of the
pixel. These pixels are essentially made of materials called phosphors, which glow when
struck by a stream of electrons inside the cathode ray tube (CRT). The resolution
improves with a reduction in the size of the pixel, or the phosphors. Nanocrystalline zinc
selenide, zinc sulfide, cadmium sulfide, and lead telluride synthesized by the sol-gel
techniques are candidates for improving the resolution of monitors. The use of
nanophosphors is envisioned to reduce the cost of these displays so as to render high
definition televisions (HDTVs) and personal computers affordable to be purchase.
Elimination of Pollutants
Nanomaterials possess extremely large grain boundaries relative to their grain
size. Hence, they are very active in terms of their chemical, physical, and mechanical
properties. Due to their enhanced chemical activity, nanomaterials can be used as
catalysts to react with such noxious and toxic gases as carbon monoxide and nitrogen
oxide in automobile catalytic converters and power generation equipment to prevent
environmental pollution arising from burning gasoline and coal.
Sun-screen lotion
Prolonged UV exposure causes skin-burns and cancer. Sun-screen lotions
containing nano-TiO2 provide enhanced sun protection factor (SPF) while eliminating
stickiness. The added advantage of nano skin blocks (ZnO and TiO2) arises as they
protect the skin by sitting onto it rather than penetrating into the skin. Thus they block
UV radiation effectively for prolonged duration. Additionally, they are transparent, thus
retain natural skin color while working better than conventional skin-lotions.
Sensors
Sensors rely on the highly active surface to initiate a response with minute change
in the concentration of the species to be detected. Engineered monolayers (few
Angstroms thick) on the sensor surface are exposed to the environment and the peculiar
functionality (such as change in potential as the CO/anthrax level is detected) is utilized
in sensing.
Next-Generation Computer Chips
The microelectronics industry has been emphasizing miniaturization, whereby the
circuits, such as transistors, resistors, and capacitors, are reduced in size. By achieving a
significant reduction in their size, the microprocessors, which contain these components,
can run much faster, thereby enabling computations at far greater speeds. However, there
are several technological impediments to these advancements, including lack of the ultra
fine precursors to manufacture these components; poor dissipation of tremendous amount
of heat generated by these microprocessors due to faster speeds; short mean time to
failures (poor reliability), etc. Nanomaterials help the industry break these barriers down
by providing the manufacturers with Nanocrystalline starting materials, ultra-high purity
materials, materials with better thermal conductivity, and longer-lasting, durable
interconnections (connections between various components in the microprocessors).
Example: Nanowires for junctionless transistors are made so tiny to reduce the size of
sub assemblies of electronic systems and make smaller and smaller devices, but it is
difficult to create high-quality junctions. In particular, it is very difficult to change the
doping concentration of a material over distances shorter than about 10 nm. Researchers
have succeeded in making the junctionless transistor having nearly ideal electrical
properties. It could potentially operate faster and use less power than any conventional
transistor on the market today. The device consists of a silicon nanowire in which current
flow is perfectly controlled by a silicon gate that is separated from the nanowire by a thin
insulating layer. The entire silicon nanowire is heavily n-doped, making it an excellent
conductor. However, the gate is p-doped and its presence has the effect of depleting the
number of electrons in the region of the nanowire under the gate. The device also has
near-ideal electrical properties and behaves like the most perfect of transistors without
suffering from current leakage like conventional devices and operates faster and using
less energy.