Mod-01 Lec-25 Electrical, Magnetic and Optical Properties of Nanomaterials

Mod-01 Lec-25 Electrical, Magnetic and Optical Properties of Nanomaterials


Now, let us go to optical absorption of nano
materials, so to summarize the before we do that let us summarize the brief concepts so
far. We have various phenomena in materials and various like reflection, refraction, and
diffraction etcetera absorption. These phenomena give rise to colors and materials
and they are also responsible for what you may call the overall optical response of the
materials. Then we notice that we have to differentiate the optical behavior of metals
where in there are free electrons, which give rise to plasmons. When we talk about and we have to talk about
the frequency regime. That means the wavelength of the incoming radiation determines
the response of the metal to the incoming radiations. In other words, a metal itself could actually
becoming become somewhat transparent or it could be reflecting, depending on the frequency
of the incoming radiation. We also noted that in the case of semi conductors
we have to worry about the band gap and exciton. If I have to understand how the absorption
of a semi conductor is going to be when a imposed an electromagnetic radiation.
Therefore, and of course the important question that we are going to now ask is that
when we go to nano materials, how is the behavior as compared to a bulk metal going
to change or a bulk semi conductor going to change, when you have a material in the nano
scale. So, when you are talking about size effect
on optical properties, bulk metal absorbs electromagnetic radiations say in a visible
region, thin films of metals may become partially transmitting. This is, because of
the insufficient material effect as we pointed out. So, gold films about ten nanometer thick
can become partially transparent. This is not something very what you might call unexpected.
Apart from the insufficient material effects, there are other important phenomena,
which come into play in nano materials, especially nano freestanding nano crystalline
particles. These include the phenomena of surface plasmon and quantum confinement effects.
So, we will take up these two important phenomena. We already talked about
what is called the bulk plasmon, which is a longitudinal wave.
Now, we will take up the concept of a surface plasmon, because now we know in a
nanostructure nano crystalline material or a nano material freestanding nano particles.
You have a large surface to volume ratio, and therefore surface dominant effects like
surface plasmon come into play. In semi conductor quantum dots optical absorption
and emission actually shift to the blue region of the spectrum, which means to the
higher energies as the size of the dot increases. This we will see in detail, which
implies that inherently, there is something changing in nano structured materials regarding
the what you might call the electromagnetic structure or the band structure.
The size reduction is more prominent in the case of semiconductors as compared to
metals. To see the effect of say quantum confinement in metals we have to go down to
smaller sizes as compared to the thin semiconductor crystals. So, this effect becomes
prominent at larger sizes in semiconducting crystals. Therefore, we will have a lot of
examples of semiconducting crystals being described here.
We had also seen that at very small sizes metal nano particles can develop a band gap
and can become a semiconductor or an insulator. So, this aspect we have seen that,
because of dimensional confinement the density of states, we saw already changes
between a bulk ready semiconductor normal metallic conductor to a 2 D kind of a
system, where you get a stair case kind of a density of states.
Then we saw we got on to 1 D semi conduct 1 D metal, which actually develops a band
gap. That means 1 D metal you talk to a material like copper, which is bulk metallic in
the bulk and reduce its size. You saw that the density of states, now starts to behave
like an e power minus half rather than e minus
half in the bulk, we saw that you actually develop a band gap. In other words, the metal
starts to behave like a semiconductor or an insulator in very small sizes.
Then we also saw the case when we go down to zero dimensional metal again metal in
the bulk, then you actually start to the material starts to behave like an atom. That means
you have discrete energy levels. So, all these possibilities we have already seen before
for the case of a metal. Now, what happens in the case of semiconducting
nano particles and films. So, these are very interesting things, which start to happen
in the case of semiconducting nano particles and films and decreasing. On decreasing
the size the electron gets confined to the particle and you confinement effects starts
to dominating. What is meant by this confinement effect will become clear, when
we discuss what is happening here. This leads to two important effects one is the
increase in the band gap energy, this is very important. This is the heart of the blue shift
we will be talking about the second is the band levels get quantized. So, you have a
bulk semiconductor as shown schematically in
the diagram. So, you have the green region, which is now
my schematic of the valence band. Now, you have the conduction band, which is separated
by E g and this is not the bulk scenario. Now, when you make a nano particle
you can clearly see two things are happening number one is that, when you look
at the band gap originally this was my band gap. Now, the new band gap in a semiconductor
in nano particle is this. So, the band gap has increased when you are talking
about the semiconducting nano particle. The second effect is that the band gap level
gets quantized. Of course, this is an obvious effect, because now you in an nano particle.
Even in a normal bulk material there are these discrete levels, but since they are
placed. So, closely and when there are, because now there are now a mole of atoms or more.
You can continue consider them to be a continuous stage, which is called a band.
So, it is just a mere approximation, but when the number of particles in the system actually
reduces. Obviously, there are not enough levels to make it what you might call a continuous
or a semi continuous level. Therefore, you can see the discretization effect and
you see that these levels start to become discrete.
So, there are two important effects that come into play when you reduce the size of a
nano particle one is in the increase in the band gap energy. Number two is that the band
gap levels, get quantized or start to discreteness of the levels starts to come above or get
starts to be felt another important effect, which comes in semiconducting nano particles
is the fact that surface states or trap states can form, which lie in the band gap and
become important, because now the optical property of nano crystals is going to be
dominated by the surface states. Therefore, there may be absorptions suppose I am
talking about a surface state lying in the band gap.
This is my band gap this implies those surface states will absorb more strongly as
compared to the inherent band gapage or what you might call the inherent E g nano.
Therefore, those will stand to dominate the property optical properties of the
semiconductor. So, the energy level spacing increases with decreasing dimension and
this is called the quantum confinement effect. So, we have now we talking about a semiconductor
nano particle. We have to take in additional factors compared to the bulk. Number
one is that you have insufficient material leading to discretization of the
band into separate energy levels. Number two is
a fact that there is a increase in band gap energy, which means now you have to supply
a higher energy coming of course, through a
electromagnetic radiation like photon to via photon to actually excite an electron. Third
thing we saw is that surface trap states can also start to play an important role in the
absorption properties of the semiconductor. Now, how does the band gap or what you might
call the effective band gap change with particle radius R, when you study this effect
effective radius. Now, we have seen that the effective radius actually increases, so is
these all originally were within the band, now
become part of the band gap. Now, essentially we saw that we know that as r reduces the
E g effective increases. So, we look at the formula of E g effective as a function of
R. There is of course, the band gap energy of
a bulk semi conductor the first term, but there
are two more terms. One depends one is a positive term going as 1 by R square. There is
second columbic term, which is coming from, which is a negative term coming as 1 by
R, but since the 1 by R square term dominates over the 1 by R term. This implies that
though given individual terms given the first term or the second term in that.
So, this my second term and this is my third term, the second term tells you that as the
R decreases the E g effective has to increase.
The third term tells you that as the R decreases the E g effective has to decreases
the columbic attraction term, but as you can see this is R square dependence. Therefore,
this term dominates and overall the band gap energy increases as you decrease the size
or the as you confine the semiconductor. These are the terms in this are all constants, which
we have dealt with before. Now, the signature of this increase of what
you might call the band gap can be seen in this nice interesting example, where in Vijayalaxmi
and co workers studied bulk gallium arsenide and compared it with nano crystalline
gallium arsenide. Typically, they put this nano crystalline gallium arsenide as a thin
film on a i to substrate and studies the absorption properties. If you look at the
absorbance of this, now what you call the nano
gallium arsenide visa be the bulk gallium arsenide. Here the x axis is the wave length
you see that the bulk shows an increase in absorbance with wave length.
That means as the way decrease, that means as the wavelength increases the absorbance
decreases. So, the wavelength is increasing in the right hand direction the energy is
actually increasing on the left hand side direction, so this my energy, so with increase
in energy we see a increase in absorption what
is prominent in this absorption spectrum. Of course, one of the things is that you do
not find an exciton excitonic absorption. Because, this is now at room temperature experiment,
where in you expect that the exciton has been disassociated. However, if
you look at their paper they plot this nano gallium arsenide they actually plot a peak
like this. They call it the excitonic absorption, now what is really and this nano gallium arsenide
has size range about 7 to 15 nano meters size nano crystals. That means this
is not a mono disperse system. In other words I have to consider the size
variations also into take into account. That means now I am not talking about a single
band gap for this material those range of band gaps. Since, there is a range of band gaps
I would expect absorption to take place over a
range of energies. That is the reason and that is the reason that this peak is actually
broader. It is not a very sharp peak as you would expect if you had a mono disperse
crystalline size. So, a broad excitonic peak occurs at about
526 nanometers. This is the range where it occurs and this corresponds the energy of
about 2.36 e V. This is if you compare it with
the band gap of the bulk gallium arsenide. It is about 1.43 e V. That means that the
frequency is blue shifted. That means the band gap has effectively increased right the
shift is 0.93 e V. It is not the net the net is 2.36 e V, that means now my band gap is
2.36 e V in the nano gallium arsenide while in
the bulk gallium arsenide. It is 1.43 V, that means the effective band gap has increased.
We already know that if we are talking about true excitonic absorption.
Then you would know that that has to lie in the band gap of the original semi conductor.
Therefore, that would actually lead to a reduction in the reduction in the band gap. So,
this we can understand as not as excitonic absorption though the terminology is used
as, what you might call purely coming from confinement
effect and increase in the band gap. So, to summarize this importance like
you see that bulk gallium arsenide has a different absorption spectrum as compared
to a nano gallium arsenide, in the nano gallium arsenide.
You observed that there is actually a very strong peak in the absorbance at 526 nano
meters. This strong absorption peak corresponds to a band gap of about 2.36 e V. This is
what you might call blue shifted with respect to the bulk gallium arsenide. That means
now this happens at higher frequencies or in other words at lower wavelengths an
additional fact. That is seen from this curve is a fact that
there is an overall increase in absorption, absorbance of the entire wavelength regime
or the frequency regime in the case of the nano. That means the nano curve is shifted
to higher absorbance values across the
spectrum and this is coming. This is attributed to the enhanced oscillator strength an
oscillator strength is a dimensionless quantity to express the strength of the transition.
Now, we are talking about the transition to the valence band to the conduction band. We
have already noted that, the excitonic peak or the absorption peak is broad due to the distribution of the crystallite sizes. So,
here we have a clear cut example of nano crystallite gallium arsenide film of an I
T O substrate, which shows an absorption property, which is very different from that
of the bulk gallium arsenide. The important thing to note is that the absorption peak
is now blue shifted. That means it is occurring across a higher level larger band gap. There
is a peak, where there was no peak in the case of the bulk gallium arsenide.
So, this is a very important difference between the optical property of what you might
call bulk semi conductor visa V a nano semi conductor. We will take up some more
examples in the coming slides to see the difference between, this what you might call
bulk versus nano in the for semiconductors. After considering the example of gallium
arsenide nano crystalline thin film… We take up an equivalent example the case
of the P b S e nano crystals, where in again we see this dramatic effect of blue shift,
which is coming from quantum confinement effects in these semi conductor nano crystals.
Now, we have already noticed that the density of the state becomes more quantized.
The band gap shifts to higher energies, which is the root cause for this blue shift
in the case of the P b S e nano crystals. Again,
we are plotting the wavelength as a function of the absorbance. We know of course,
these curves have been shifted vertically. So, that we can make a comparison and that
is why the y axis is in arbitrary units. We note that dramatic change in the absorption
peak as you go from say for an instance a 9
nanometer particles of P b S e to 5.5 nanometer particles to 4.5 and to the 3 nanometer
particles. We will soon see a effect with respect to the surface plasmon absorbance
in the case of metals, that there this effect of
shift is actually negligible. It is actually small
when you actually change the particle size. So, here you see that there is actually a
blue shift in the peak and you can see the big
shifts to higher frequencies or in other words lower wavelengths. In other words the
energy of the transition becomes high. Therefore, the material absorbs at higher energies,
when you actually reduce the particle size. This particle size is only by a factor of
about three from 9 nanometer to 3 nanometers. The
wavelength you can see from absorbance shifts to something like about 1000, 100 nanometers
from something more than something 2000 nanometers, so clear cut there
is this quantum confinement effect in these nano crystals, which effects its optical
properties, the counterpart side. The other side of this absorbance is what
is called photo luminescence. In other words if
a material is put into an exited state, then it is going to relax at its ground state.
In the process it may actually emit a photon in some
cases. Of course, there can be radiation less transitions, but if there is a possibility
here that the excited state will relax to the
ground state by the emission of photons. This is the phenomena of photo luminescence
and when this relaxation in a semiconductor takes place by recombination
of electron and hole. The photon is emitted and if this emitted photon’s energy lies
in the range of about 1.8 to 3.1 electron volts.
Then the radiation will be in the visible range and often this phenomena is called
luminescence. Now, by changing the size of the nano particles I have a handle on the
band gap. Now, in other words in the bulk materials I just had one single band gap to
deal with, but now I can tailor the band gap by actually changing the particle size.
Therefore, I can tailor the emission and in other words I get a handle on even on the
color of the particle, which I see, which we will take up a startling example coming
up soon. Even in these cases the emission case
not unexpectedly you observe a blue shift of
frequencies with reduction in particle size. So, when we are talking about photo luminescence,
which is the phenomena, which is called a other side of the coin of absorbance,
which is the emission of a photon when a system is excited. In other words the recombination
of electronic whole takes place and there is a emission of photon. This emission
of photon can actually happen in the visible region in which case you call it luminescence.
Of course, this need not always take place in visible range that depends on the band
gap and the band gap happens to be about 1.8 to 3.1 volts. Then this will happen to be
in visible region. The dramatic effect can be seen in what you
might call the core shell nanostructures, where in there is one semiconductor as the
core. Other semiconductor as the shell some examples of these are cadmium sulfide coated
with most zinc selinide coated with C d S e, C d S e coated with cds etcetera. In this
case we notice that the band gaps are tunable near the I R in which case they can be used
as I R biological luminescent markers also. That means not only the emission can be in
the visible region. It can also be in the I R
region and you have a handle on the frequency of emission.
Therefore, you can tune what you call the frequency, which is emitted in such core shell
structures the luminescent properties are typically, the characteristics of the core.
We will take up an example and the shell actually
leads to an enhancement of the luminescent properties of the core the shell.
We said when we talked about the core shell structure in detail before we said the shell
could actually be performing many roles. One of the roles could be one of mere passive
layer, which is actually protecting the core from the environment, but we also pointed
out that we will take up an example at some later stage, where we will talk about the
enhancement of properties of the core. This is a nice example, where in you will
actually find that there is this enhancement of
the luminescent property of the core. When you have a shell around it of a
semiconductor. Now, typically the disposition of a semiconductor with a larger band gap
than the core results in what you might call the luminescence enhancement. This occurs
due to the suppression of radiation less recombination. This radiation less recombination
is typically mediated by surface states. So, if you had a raw semiconductor then you
have the surface states, which lie in the band gap and the transition to these surface
states may, sometime may not lead to luminescence. Therefore, having a shell layer
enhances your luminescent properties of the semiconductor. The one of the beautiful examples available
is the case of the C d S e nano particles. Now, we are talking about change in C d S
e nano particles size from about 5.5 nanometers, which is on the right hand side
a small nano particle to a size. So, this is my
5.5 nanometer to a size of about 2.3 nanometer particle a factor of about 2 to 3. Now, in
these core shell nano structures of course, there is a shell of zinc sulfide. We will
look at the properties of luminescence in the absence
of the shell. Also, in the presence of the shell, so we have a case where there is no
zinc sulfide. We will compare it to the properties, where there is actually a zinc
sulfide shell. The most beautiful unmarking, what you call
characteristic signature of this change in size is the change in color of the colloid.
This is cited as usually one of the beautiful properties emerging in nano structure, this
is given as one of those what you may call the
typical or the outstanding examples given. Where, in here I have schematically shown
the change in color that on the 5.5 nano particle. On the left hand side you notice that
you have emission or photo emission in the red region of the spectrum. When you reduce
the size to 2.3 nanometer, which is on the right hand side.
You notice that the emission shifts to the blue color. Clearly, that is why the phenomena
is known as blue shift. Because, now there is a change in color from red to the blue.
That means from lower energy to higher energies.
When you reduce the particle size, which again is coming from the phenomena of the
quantum confinement, which is leading to a increase in the band gap.
Now, this is a very striking and startling example and if now if I plot the intensity
versus wavelength. Now, this intensity is not the
absorbing intensity, but the emission intensity. So, it is the other side of the coin of absorbance
we just now saw. Now, again we are plotting it with respect to wavelength. So,
when the particle size is 5.5 nanometer, which is a case corresponding to the figure on the
right hand side. So, this is the case the red case you notice
that, there is an emission in the frequency wavelength region 60 to 600 to 650 in the
red color regime. Now, the important thing is
that in the absence of the shell you see that the emission has a certain intensity, but
when you have a shell around it there is a clear
cut marked enhancement in the intensity in the
presence of the shell. So, I can show that there is an enhancement
in the presence of the shell. So, this is clearly you can see that an important effect
of putting a shell around the core. Now, as you change the particle size, you can see
that the frequencies are seeing a blue shift the
peak is shifting to blue side. You can see that in each one of these cases the core shell
structure has an higher emission as compared to the bare core or the bare core implying
to the only core. The core is shown by the dotted lines the core shell structure is shown
by the peak the overall peak of the emission, does not shift much.
So, there can be a small shift as you can see from the fact that the peak of the bare
core lies slightly to what you call in over the
shell at the slight red shift to this, but that is not
a very significant effect the important effect is the enhancement in the intensity. So, there
is a beautiful example here of a core shell structure, where in the absence of a core
you still have a blue shift when you reduce the
particle size. There is an enhancement of the photon emission
or enhancement in the fluorescence, when you have a shell around the core. This
is as I said typically a beautiful example; there are beautiful nice pictures, where in
they show that how this dramatic effect takes place, because of reduction in particle size.
Here, again note that the particle size reduction is not too much, it is not an order
of 92, it is only by a few factor of few. Now, if you look at on the other hand metallic
nano particles. The metallic nano particles you will see we have pointed out the size
does not effect, it is not. It does not have a very
profound effect. Now, for instance gold nano particles have been used as a pigment,
because of the ruby colored stained glass dating back to the old seventeenth century.
So, if anybody has gone to an old church, where
there is stained glass the color of the stained glass is coming from these nano gold particles.
Typically, about 1 to 10 nanometer in size and we accept that this is this phenomena
is coming this color is coming, because of surface plasmon resonance. We had also pointed
out that the surface plasmon are transverse in nature as compared to the bulk
plasmon, which are longitudinal character. Now, we already noted that the thin films
of gold can be partially transparent about a 100
nanometers or less. They will essentially transmit blue violet light now the color of
these nano metallic particles depends on the size
in the nano scale regime, but again now we have to see the larger size changes to see
the change in color bulk gold is yellow in color
nano particles of gold can have red purple or blue color. So, there is again a possibility
of tuning the color of these gold nano particles
by changing the size not only does the color depend on the size, but it also depends on
the shape. In the next slide we will see that you
will construct two types of particles one cylindrical particles and one spherical particles.
We will see how the shape actually affects the frequency of a emission or frequency of
absorption not only does the particle shape and size play a role in this whole plasmon surface plasmon resonance, but also the dielectric
properties of the medium. Because, as we said that in the case of the stained glass,
this gold nano particles are embedded in a dielectric glass. You may also what you may
call suspend this gold nano particles in the form of a colloidal suspension and in which
case the dielectric property of the suspending medium plays an important role.
Now, in this case of this gold nano particles the surface plasmon are excited by the
incident electromagnetic radiations. We few more points about that are in the next box
surface plasmon have a lower energy than bulk plasmon. Now, when you have a gold or
silver which has a mean free path of about 50 nanometers for smaller particles than this
there will be no scattering within the particle. All the interactions will be on the surface,
in other words when we have extremely small particles. It is the surface, which becomes
important. That means we have to worry about the surface plasmon more than the bulk
plasmon. In other words the bulk plasmon absorbance is going to be small.
It is going to be the surface plasmon, which are going to play key role in determining
the optical properties of such small metallic
nano particles. As we pointed out in particles with shape anisotropy. We are going to give
an example of cylinder in the next slide more than one type of plasmon may be simultaneously
excited. We may observe a absorption peak corresponding to both longitudinal
and transverse plasmon. So, this is a beautiful example in this example, we have
three kinds of objects. One a sphere, one a long cylinder, which is
marked in green. Also, the corresponding curve is also in green and one is a short
cylinder. In other words sphere can be characterized by one dimension, which is just
the radius of the sphere while on the other hand, if you have a long cylinder not only
does you have to specify the diameter of the cylinder, but in addition you have to specify
the length. That means two dimensions characterize a cylinder. This can be the sphere
can be thought of as a quantum dot or a zero dimensional system. Of course, this is
slightly large, but on the other hand a cylinder can be thought of as a one dimensional
nano crystal. Now, in some of the previous curves when we
talked about semi conductors, we initially of course, we plotted what we might call the
absorbance. Then we switch to when we switch when we talked about photo luminescence.
We actually plotting the emission part that means how an excited system relaxes by
emission of light. We use the term fluorescence for that, but here again we are
going back to absorbance. That means what we are plotting here is absorption of wavelength
or absorption as a function of the frequency of the electromagnetic radiation.
Here, typically we are talking about visible regions.
Now, for a sphere of about 15 nanometer diameter and here this blue sphere, which is 15
nanometer diameter. Only transverse plasmon peak is observed at lambda approximately
about 520 nano meter. So, if I look at this blue curve corresponding to my transverse
plasmon absorbance. We see that it has a peak of about 520 nano meter, there is only one
peak that is very important to note. This is coming from transverse plasmon in other
words surface plasmon. So, this absorbance spectra of the sphere is dominated by a
single quantity, which is now the absorbance of, because of sitting up transverse surface
plasmon. So, that is the key phenomena here. Now, as I pointed out there is one key difference
between semiconductor particles and metal nano particles that is the size dependence
the sensitivity to size. Dependence on this absorbance spectrum, we noted in the
case of semiconductors that if I change the size… Just from 3 nanometers to 4.5 nanometer, which
is about a 50 percent increase, You see that the peak shifts drastically. Another
words for the 3 nanometer particle the peak is
round about this may be considered 1200 in that range. This three nanometer particle
is more than 1500. So, there is a drastic change
in the absorbance peak, when you change the particle size in the nano scale regime,
but when you are talking about metal nano particles, this is not the case. We have been
talking about this previously. So, here is the
right example to prove that point. Now, if I double the radius of the sphere
I make it 30 nanometer the transverse plasmon absorption peak will only shift lightly I
have not plotted it on this curve. Because, that
will make it what you may call too much complicated there will be too many curves
lying on top of the other therefore, but the shift is only slight, this is unlike
semiconductor nano particles, where the absorbance is a strong function of the nano
particle size. So, we see that if I make my sphere from 30 nanometer to 50 nanometer or
50 nanometer to 15 to 30. There is not much shift in the peak and this peak is now
coming from surface plasmon resonance. Now, the case of the cylinder is very interesting.
Now, let me start with the long cylinder the 112 nanometer cylinder, in the case of
the 112 nanometer cylinder you would notice that there is two peaks. In fact there are
two peaks one peak in the low wavelength or the
high frequency regime. The other one is in the longer wavelength regime these this
longer wavelength is coming from the longitudinal plasmon, which is along the length of
the cylinder of the along the length of the cylinder. The lower wavelength peak, which
is here close to about maybe 5 slightly more
than a board or close to 500 nanometers. This peak is coming from the transverse plasmon,
another words based on the geometry of the cylinder.
Now, I got two peaks and these two peaks are coming from totally different mechanisms
one from longitudinal plasmon. One is coming from surface plasmon, now if I make the
cylinder short there is o b there is a shift in the longitudinal plasmon on peak. Because,
that is along the length of the cylinder, which is what is sensitive while you can see
that now for the short cylinder, this is the red
curve. We can see that the red curve, so I have
marked points on the red curve. The red curve the surface plasmon is in the same
position, because now if you look at the D of the long and short cylinder, they are the
same place. So, the transverse plasmon peak appears at
the same place as of the long cylinder, but then the longitudinal mode has actually shifted
to shorter wave lengths. In other words higher frequencies, this shift this peak is
coming from the longitudinal plasmon. In other words, now I have in the case of
metal nano particles an important demonstration that the color depends on the
size, obviously as we have seen and also on the shape of the particles. So, size and shape
are the two important factors that we have seen in the previous graph, which is now going
to determine my plasmon absorption. We have already seen that in the case of a shape
the two peaks. We observe one is coming from that means the two peaks are from two
different mechanisms. One is coming from a surface plasmon resonance ant the other is
coming from the longitudinal plasmon. So, there is a nice example here of metal nano
particles, which were in the size and shape are
determining the absorption of the material. Having said this, that we have to be careful,
that we are comparing semiconductors with metals the mechanisms of absorption are obviously
different, but after that we are comparing the sensitivity of two sides. We
are definitely not saying that it is not size dependent. Obviously, we have seen the example
that the absorption spectrum is size dependent, but it is not a sensitive function
of size. That is the important thing we are saying, now we take up another of the core
shell examples. In this core shell example we
have a metal on the dielectric in the previous example of core shell structure.
We saw we considered a semiconductor on a semiconductor and we took up the example
of zinc sulfide shell on a C d S e, which is a semiconducting nano particle. Now, we
take up the example of a metal shell. In this case
we have a gold shell as you can highlighting in a yellow here the gold shell on a silicon
dioxide core S i O 2 core. So, the core is dielectric in other words, it is a non conducting
material and the shell is our metal. We consider a case where we keep the core radius
or the core diameter constant. The core diameter is 60 nanometers. What we do is we
just change the shell size from about you can see that about 20 to 5 nanometers.
We keep on changing the shell size and we study the extinction intensity as a function
of the wavelength. We note that in this case
where you coat the gold on S i O 2 course the
plasmon band shifts on changing the core radius. This depends on obviously the
thickness of the shell, because we are keeping the core radius constant increasing the core to shell ratio, actually red shifts the
plasmon resonance band. Because, I have taken up this example, because this is right opposite
of what we have been talking, so far which is blue shift
In other words, here when I am reducing the metal thickness on this metal thickness of
shell around this dielectric core. Then I am seeing that on decreasing the shell size
I see that there is actually a red shift. That means
that when you have a shell just thick, then the frequency peak lies close to about 800
nanometers, when I make the shell thin of about 5 nanometers. Then I see that there
is a shift towards the red region. That means this is now towards the lower energy region.
So, this shift is actually opposite to what we
have been talking about, so far for the case of the semiconductor nano particles. So, this
is a very interesting case of a core shell structure.
Now, we were when we talked about the refractive index. We said that there are very
interesting class of materials known as materials with negative refractive index. So, meta
materials or negative refractive index refractive index materials or otherwise, we meant
to call them negative refractive index structures have a negative refractive index, when
we say a negative refractive index. Suppose I am assuming ray we said coming from
vacuum or air into a medium, which is colored blue here. Then we note that the refracted
ray lies in the same side of the normal, as the incident ray unlike normal refraction,
which is green line shown here, where in the refracted ray lies on the other side of the
normal. Now, typically these are manmade structures where in the refractive index has
a negative value. This refractive index and negative value typically over some frequency
range and so far this has not been discovered in natural materials. These meta
materials have a negative effective permittivity and permeability. Now, the refractive
index we have noted before can be written as plus or minus epsilon into mu,
where 1 is the permittivity and the other is
permeability. We have to note that, when we are talking
about positive refractive index. Then we take the positive sign outside the square root
and use the both positive of epsilon and mu. So,
the negative refractive index structures use the negative sign outside the square root,
use both the negative signs here an important
property of the negative refractive index materials is shown in the figure below in
normal refraction. What happens, suppose you have a divergent set of rays?
Then these rays of course, even after refraction will continue to be divergent within the
medium, what you might call the angular regime of refraction may come down, but the
rays continue to diverge, but in negative refraction you can see that, this is now my
red material the refraction the refractive index
material. The divergent rays will actually come to convergence in other words such a
material can be used as a convergent lens. Normally, we know that when we you are talking
about a lens, which is converging like a double convex lens than, it is actually
the shape of the lens, which alters what you might call the optical path length, which
is leading to the convergence, but here you are
seeing that this even a flat surface of negative refractive index can act like a converging
lens. This kind of a negative refractive index material can actually be used for focusing
what might be known as a evanescent component of the fields.
Now, what are the typical materials or structure, which show this kind of negative
refractive index there are structures, which are known as magnetic split ring resonators.
There is a schematic of such structures here all these grey regions in the figure below
are these magnetic split rings detectors or split
ring resonators. Now, there is a lattice of these structures. Therefore, I make a crystal
of these and you note that if the scale of these structures happens to be a two of about
200 nanometers. Then such a structure will show negative refractive
index close to the visible range. That means if I change the scale of this structure,
which I am making I can actually tune the regime in the electromagnetic spectrum, where
in it shows what you might call the negative refractive index property.
So, if I make the structure even smaller then it will shift to the visible region, but if
I make the scale of the structure larger. Then
they will start to become negative refractive index only in the microwave or other regimes.
So, these are what you might call very interesting materials, but the important thing
to note from our course point of view, that if I make this structure in the nano scale
about 200 nanometers are less. Each one of these what you might call these entities,
in this is what is called a magnetic split ring
resonator. Then this structure as a whole starts to behave like a negative refractive
index structure.
So, people have been making various kinds of Kieran materials and various kinds of
sculpted structures, which can actually give this kind of a property of negative refractive
index, for that kind of negative refractive index to be in the optical regime. We have
to note that the scale of the structure has to
be about less the about 200 nanometers. So, these are again very interesting materials.
People are interested in this area can investigate further with this we come to an
end of this course. In this course, which Professor Kantesh Bilani and myself are the
instructors. We have tried to give you abroad flavor of
what are nano materials, what are nano structures, what kind of properties can they
have. Of course, briefly we have also been talking about the applications of these materials.
In some cases we have gone into details of these classifications. Some of the properties
we have considered in lot of detail like the magnetic properties, but in many other
cases we have only made a cursory, what you might call a remark or a superficial consideration
of many of these topics. So, students are expected to follow up these with further
reading. Also there is an immense volume of material available in the literature.
Now, regarding the nano materials nano structures their properties one of the biggest
what you might call the mammoth volumes is about… Now, initially there are ten
volumes of the handbook of nano materials by Hari Singh Nalwa. Now, ten more
volumes have been added. That means now you have twenty volumes as reference materials coming from a single handbook. There
are many other such similar handbooks; there are beautiful review papers also available
on any specific given topic. We are also being trying to give reference like for optics.
We had cited a book, which you can refer. Similarly, we have talked about magnetism
what books you can refer, but going through
this course is…

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