 Welcome back to this course on nanostructured materials, synthesis properties, self assembly and applications. This is the ninth lecture of module 4 and today we are going to start our discussion on optical properties of nanostructures. Previous lectures we looked at the magnetic properties of nanostructures of which we had three lectures and now we start a three lecture part of optical properties of nanostructures and in which we will discuss what are the basic optical processes and how the bands are affected by decreasing the size of nanoparticles and how the variation in the bands and several other factors affect the absorption processes and the fluorescence and phosphorescence or luminescence in general and other properties of the nanoparticles and how these optical properties can be applied for useful purposes like in medical devices or as sensors or for other optical encoding devices. Several applications where nanoparticles having variation in their optical processes due to the size and shape of nanoparticles will be discussed. So, today is the lecture 9 of module 4 and we are discussing optical properties. So, the nanoparticles show variation in color with the size of the particle. This is now a very very established fact and has been very attractive to students and practitioners of nanoscience and technology because of the large number of interesting colors which can be generated with nanoparticles and people were making these nanoparticles long back for example, this window is a glass window, but the glass has impregnated with gold nanoparticles. Now, this is there in a cathedral of Notre Dame which is a very famous church and all the glasses have colors and those colors are due to gold nanoparticles which we now know. When it was made in the early years then it was probably not known why these colors are being given by gold. Now, we know that when gold is made into small particles like nanoparticles it can show you different colors. So, many many years ago in the fourth century AD itself this kind of a cup was made where the glass has got gold nanoparticles impregnated. So, it is a glass where gold nanoparticles are there today we know that they are gold nanoparticles and it shows a red color when you have transmitted light that means, when the light is either inside or from coming from the other side and in reflected light if you pass light on this direction and if you observe the reflected light then it looks green and this is due to gold nanoparticles which are embedded in this glass and these kind of structures were known thousands of years ago and give you a reflection of what optical properties of nanostructured materials can be and today people are analyzing these kind of information which has been present for centuries with us and this is only one particular application that you can have different colored glasses with nanoparticles of gold of different sizes giving you different colors. And today we have gone ahead and made many new applications where by the optical properties are being used to for applications. So, again gold is one of the most well studied materials bulb gold is yellow in color all of us know gold is yellow in color, but when you make the particles of gold very small it can have different colors it can have red color pink color violet color and so the first time gold was made in laboratory scientifically was by Michael Faraday around 1856 1857 and this is preserved even today this kind of light pink color of gold solution has nanoparticles of gold which Michael Faraday called at that time gold colloids. So, this was the first scientific or laboratory synthesis of gold, but people had even much before thousands of years before had made colored glasses using gold particles which they did not understand at that time are due to gold particles, but today we know that those kind of colored glasses are made of gold nanoparticles and of course, people have made using silver cobalt etcetera also. So, the area of the colors of nanoparticles is a very old area of course, the understanding was not there today we understand why different size nanoparticles give different color and what other applications can be brought about by this variation of the optical properties of nanoparticles. So, to recap this gold slide you have bulk gold looking yellow solution of gold looking pink made by Michael Faraday and this is a modern synthesis of gold colloids in water and this is a picture where you can see the gold particles. So, 12 nanometer gold particles can be seen in a micrograph and they look red in color in an optical micrograph and which is the same thing as being shown here where you see the pink color. So, this color change of gold from yellow to a different color is due to the variation in the band gap of the material and that we will discuss in the next few slides. Now, there are some other materials where you can see changes in the optical properties like absorption or emission of these materials and one of the examples which people are using to a great extent for applications are kind of creams or lotions where the material will reflect the UV light because the normal rays which come in the from the sun with this lot of UV radiation and UV light is not good for our human beings or any other animal and you want to protect yourself from ultraviolet rays. So, one of the ways you can protect is put a sun screen or a lotion which does not absorb the UV radiation. So, such things are like large zinc oxide particles. So, you make a kind of a suspension with zinc oxide particles and they will block the UV light and they actually scatter visible light and so it appears white in color and the traditional zinc oxide sun screen is white in color because it scatters the visible light. When you make the zinc oxide particles smaller it will also block UV light this blocks UV light the nano size zinc oxide particles also block UV light, but the particles are so small that now they do not scatter visible light because the particles are now smaller than the wavelength of the visible light. So, to scatter you must be of the order of the wavelength of the light that you are planning to scatter when you make the size of the zinc oxide particles much smaller then they do not scatter the visible rays and hence they will look transparent or like shown here it will not show this white color which the large size zinc oxide particles were showing. So, that is a change and it appeals to people because in this kind of lotion with large size zinc oxide although you are protected, but your face is not no more original you will have all these white patches on your body whereas if you have a nano scale zinc oxide it is a clear solution. So, this is another example of how you can make nano particles which can be tuned to absorb or scatter or or flores differently than the bulk size particles or the large size particles and this has been applied zinc oxide is a very very important material this tremendous amount of studies on zinc oxide and one of the applications of nano size zinc oxide is in sun screens or lotions and this is a TEM picture of zinc oxide nano particles which are basically present in a suspension or an emulsion and there are stable emulsion. So, that they do not precipitate out and the particle size is such that it should not precipitate out or settle down in the bottom. So, such a material is of high demand for sun screens now coming to the other properties of nano materials showing variation in its absorption or emission properties this is a particular area which is called the area of quantum confinement and one of the names which is very commonly used in the nano science nano technology area is the term quantum dots. So, what are quantum dots from dots it basically means particles and since the dots are spherical we are talking of spherical particles and why we call them quantum dots because at the size of the particles which we are talking say around 4 nanometers 5 nanometers etcetera at that scale quantum phenomena becomes very important and your energy levels the band diagrams etcetera change. And these are normally shown in this colored view graph where you have solution of the same material all the materials are having only the same cadmium selenide particles, but they are showing you different colors the particles are the same chemical composition is the same, but they are showing you different colors. What is the reason the reason is the optical properties have changed because the size of the particles are different in different solution. So, all of them are crystalline cadmium selenide in the nano region, but their size some are 5 nanometers some are 10 nanometers etcetera and with change in the size they give different colors. So, they can be used as a light source of different wavelengths. So, normally cadmium selenide is a semiconductor. So, these quantum dots are typically semiconductors and they are very small that you can by adding or removing one electron you can change its properties. Because they are so small their properties depend on few electrons and you can tune their properties very, very minutely. And one of the ways that you tune the properties is by changing the size of this quantum dot and you can get a variation of these colors. So, this is one of the most important or and simple property which one can see in a nano material where there is a change in the optical properties as a function of size. And this is an example of cadmium selenide where the color is changing as this size of the particle of cadmium selenide is changing. Now, why so much importance of course this looks very nice and you know if you are a student of chemistry you enjoy seeing colors and you can see all these bright colors just by varying the size of the particle putting the same material. So, it is very pleasing and enjoyable to see this variation of colors with the size of the particles, but what more can you do for an application where it will be of use to mankind. So, that kind of an application is shown here where you have used quantum dots to be used as markers. So, if you can find one particular quantum dot of a particular size going into one area and it is emitting red color then you can identify that side. Now, another sized quantum dot goes to another site and shows a yellow color and something shows a green color. That means, if you can use these quantum dots which are emitting different colors you can and if you can target them to different parts of the body then you can illuminate different parts of the body and if you know which quantum dot will go where you can identify that my this part is having some kind of cells because the red emitting quantum dots will only go there. And if a green emitting quantum dot goes to another specific site then we can identify easily that site. So, quantum dots are being used as medical markers. So, in medicine in biosensing applications there is a tremendous importance of quantum dots and apart from that you can use quantum dots in data storage. So, we have earlier looked at data storage using magnetic nanoparticles which mentioned that magnetic nanoparticles are used in DVDs in CDs etcetera nowadays. And you can also use optical properties of nanoparticles and optical encoding you can do and store data based on these optical properties of quantum dots. So, that is another important area, but the most important area I think is in biosensing and as medical markers to identify specific regions within organs or within a living being which can be identified by the specific emission of a particular wavelength of light by a particular sized nanoparticle. So, what does light because we are talking of optical properties. So, we have to understand how light interacts with solids because all the optical properties you will involve some wavelength of radiation. So, light when it interacts with solids can reflect. So, this is the incident beam it can be reflected the light can be absorbed. So, energy from the light can be absorbed. So, photons can be absorbed photons are quanta of radiation and it can also be transmitted. So, you can have reflection, absorption and transmission. So, I naught which is the incident beam should be equal to the sum of the intensity of the reflected light plus the intensity of the absorbed light and the intensity of the transmitted light. So, if certain energy is absorbed or photons of a certain color are absorbed they would not be seen in the transmitted beam. They would not be seen in the reflected beam and hence it will affect the color of the material because normally the color of the material if you are observing from here depends on what is the beam which is coming to your eyes. So, if something is absorbed then you will not see the exact wavelength which is coming from the incident beam because some wavelength is absorbed and you will see a resultant wavelength minus this wavelength from the incoming beam. So, you will see a different color this basically what happens when light interacts with solids and you look at the light either the reflected light or the transmitted light and that will be different from the incident light because you have lost some radiation due to absorption of the material. Now, so you can write the total intensity as a sum of all these three and you can define what is reflectance by intensity reflected upon intensity you incident intensity. Now, if you have the total of the transmittance absorbance and the reflectance the sum total will be 1 and from that you can calculate what is transmittance. So, this is reflectance and this is transmittance. Now, so if light traversing material is absorbed exponentially then depending on the absorption coefficient because different materials will have different absorption coefficients. If you have water it will absorb differently if you have say you have calcium chloride it will absorb differently. So, the material has some characteristics and the absorption coefficient of the material beta depends on the material apart from that it will depend on how much material is there. So, how thick is the material because the light has to travel through that material. So, if the material is very thick very large. So, x will be large or l is large and so these two factors the absorption coefficient which depends on the materials and the atoms which make the material and the thickness of the material both of them will affect the absorption intensity. So, normally transparent materials things which are transparent have very low absorption coefficient and things which are very strong absorbers will have a very high beta value. So, low beta value means it has good transmittance a high beta value means it has good absorption. So, if you have a initial beam which is i and that will be related to the beta which is the absorption coefficient and the thickness which is x using this relation that you will the transmitted beam which is the non absorbed beam is equal to the initial intensity and then a proportionality exponential of minus beta x because it decreases if you increase beta or x the absorption the transmitted beam intensity will decrease and so there is a negative sign here. So, the initial beam has an intensity i initial and the transmitted beam will have this intensity where you bring in an exponential factor depending on the absorption coefficient and the thickness of the material through which the light is traveling. So, one more thing is that the beta is actually wavelength dependent. So, it the beta value for a material will change whether you are shining u v radiation or you are shining visible light it will change according to the wavelength of the incoming beam, but for many purposes you can consider beta to be constant, but in fact in reality beta is a function of the wavelength. Now, looking at luminescence that is once a radiation is absorbed. So, you have incident radiation and these are energy levels in which the field states are shown and then there are these empty states and this is the gap energy gap. So, if you shine light and there is an absorption of energy then particles or electrons from here the field states will go to the unfilled states and this is what happens when light is absorbed. Now, after sometime that electron which was in the higher energy level can come back or relax back to the empty sites which was created when the electrons went up and then it gives out radiation and that is the spontaneous emission. So, you can have absorption and you can have emission when the electron comes back to the field state. So, what is then luminescence? Luminescence normally is that electrons which are excited and take up some amount of energy, but the electrons which come back to the lower energy level they may generate a different energy new photons by reemission that is due to fluorescence or phosphorescence. So, in luminescence the radiated energy that is the energy which is coming out the energy which is coming out may or may not be equal to the energy being absorbed. So, if it gives out the same energy which it absorbed that is just emission, but if it has a lower energy or a higher wavelength then the energy of the incoming beam then that is called fluorescence or if it is delayed emission then it is called phosphorescence. And both these types of emission with lower energy of photons compared to the incoming photons is together called luminescence. So, in luminescence you can have phosphorescence fluorescence which lasts for less than 1 second it is very fast and when it is delayed that means it is very slow then the emission is called phosphorescence where the photon which is emitted is coming out after 1 second after it was absorbed. So, there is a delay between the absorption and the emission reemission whereas, in fluorescence it lasts only very less than once within 1 second everything is over. So, typically if you shine UV light that means your absorption is in the UV the emission may be in the UV or it may be in the visible that means it will always have less energy the emission. And normally when you shine UV you will get blue emission you can get blue or you can get lower wavelengths higher wavelengths or lower energy. If you shine blue light then you would not get blue if it is fluorescence or phosphorescence you will get red that means lower energy light will be emitted in luminescence. Now, so if the luminescence ends rapidly then the material is fluorescent because it luminescence only as long as it is excited because the fluorescence is very fast. So, if you switch on a light and you are the material is having absorption of energy and it will fluoresce also immediately. So, if you remove that source of light then fluorescence also will stop, but in phosphorescence if you shine light on the material and after sometime you stop the light then also you may see a glow of light coming from the material. And that material is called phosphorescent material because it is giving you a delayed radiation. So, there is what is called a glow after much after the light which was shining has been switched off. So, if the luminescence continues and the material is phosphorescent that means the light emission persists that differentiates it from fluorescence. So, these are two important things about luminescence what is a phosphorescence and what is the fluorescence. Now, this difference between energy gaps is what causes different colors. So, some material may have a large energy gap some materials may have small energy gaps that is one thing. The other thing is the gap also changes with the size of the particle because if you look at it from the atomic scale if you have two atoms you know from simple overlap of atomic orbitals that if you have two atomic orbitals overlapping they will result into molecular orbitals. If you three atomic orbitals are overlapping it will give rise to three molecular orbitals because the adjacent orbitals from nearby atoms will overlap. Now, that depends on number of atoms now if you have a cluster of 20 atoms then you will have 20 orbitals overlapping and the distance between the orbitals energies becomes smaller and smaller. As you see with the increase of number of atoms the difference between the two energy levels is becoming smaller and smaller till we reach a stage when we have so many atoms that we call it an infinite solid. Typically in a solid there will be many millions of atoms because as you know in one gram mole of any substance you will have 10 to the power 23 atoms. So, 10 to the power 23 is a very large number it is a huge number. So, if you look at 44 atoms if this is the situation think at what will happen at 4000 atoms or 40000 atoms and when we are talking of millions of atoms you will hardly be able to see any spacing between them because the more the number of atoms more will be these orbitals which are overlapping. And then we say that we have a continuous band why we say it is a continuous band because it tells you that any energy within this region within this band is acceptable here only one two and three energy levels are acceptable for this three atom system here 14 energy levels are acceptable you cannot put any electron in between these two levels here 44 energy levels are acceptable. But in a solid there are so many energy levels that are acceptable that we say that all the energy levels are acceptable within this energy and within this energy. So, this is called an energy band this forms an energy band this is important to understand. Now, so for in a metal and a semiconductor what is the status with respect to filling of electrons in this bands. Now, if you look at a semiconductor or a metal you will have these two type of diagrams in a semiconductor you will have a band gap. That means you will have electrons this filled orbitals may are blue in color show that the electrons are occupying these orbitals. So, this is the filled valence band and then this some valence internal band or the core band that is also filled. Now, when you go to the higher energy levels there is a gap in energy where you cannot have any band any electron because there is no energy level available. So, this is a band gap here there is also may be a band gap much lower. So, wherever you have a set of orbitals or set of energies available it forms a band and then the next set of energies are available there that forms a band and in between there are no energy levels available. So, that is called the forbidden gap or no electron can occupy any energy in this region. So, if you have an electron here the next higher energy it can occupy is somewhere there. So, the electron has to jump from this energy to this energy that is the band gap in a semiconductor in a metal what happens that the conduction band. Suppose this is the conduction band and this above that also there is an empty band, but the conduction band is not full. There is some electrons in the conduction band and some electrons can still come in the conduction band. Whereas, in semiconductors there is no such band which is partially filled. So, that is the difference in a metal you have partially filled bands in a semiconductor you do not have partially filled bands you have filled bands or empty bands. And the difference in the energy is band gap in metals you do not have a band gap at the energy level at which electrons are present because there are available energy levels just above that. So, electron can easily take this energy or this energy etcetera. So, this is the difference between metals and semiconductors. So, now when you change the size of a particle you change the number of atoms in the particle. So, what will happen instead of having large number of available energy orbitals you will have less number of available energy orbitals when you are decreasing the size of a particle from micron size to nano size and from say 100 nanometer. When you are going to 5 nanometer you will have very few atoms and very few orbitals and. So, you will start getting a larger band gap because the number of available energy levels will become lesser and they will separate from each other and separate by larger distances. So, the band gap will change and if the band gap changes the color which you see will change in the visible region. If the light which is there in the visible region varies from say 0.4 micron there is a wave length of radiation then it shows something like a violet color. If it is higher wave length say 0.5 micron or lower energy this scale shows energy from 3.1 electron volt to 1.7 electron volt which is kind of the visible range of frequencies or energies. And this scale 0.4 micron to 0.7 micron shows you the colors of the visible region these are the wave lengths. So, the wave length of 0.4 micron or 400 nanometers is around violet. When it is 500 nanometers you are in the green and when it is above 600 it is orange and around 600 it is orange and when it is around 780 or 680 nanometers then you are in the red color. So, different wave lengths are give you different colors and the wave length range for the visible region of the spectrum is from around 400 to around 700 nanometers which is 0.4 to 0.7 micron and corresponding energy is from 3.1 electron volts to 1.7 electron volts. So, the band gap if the band gap is 1.7 electron volt the color you may see is red color or it might have gone into lower color which is the near infrared or if you are 0.4 micron which is 400 nanometers. And suppose you go to lower wave length of 0.375 micron that is 375 nanometers then you may not see any color because it is below the wave length of visible light. So, then you have moved into ultraviolet radiation. So, this is the visible region and on this side you have ultraviolet at lower wave lengths and on higher wave lengths you have the infrared radiation. So, you can tune your band gap and you can tune the colors that you see. So, if you apply an energy of h nu which is greater than the band gap or e gap then you can have absorption. So, you have this incident beam and this is the energy gap and if the energy of this incident beam is greater than this gap then you will have electrons which are moving from the filled valence band to the conduction band. And for example, if the energy gap is less than 1.7 electron volts then you can have an absorption from entire visible region because the visible region is starts from 1.7 to 3.1 electron volt. So, if the energy gap is less than 1.7 the entire visible will be absorbed can be absorbed and the material looks black or metallic if the band gap is smaller than 1.7 electron volt. If the band gap is greater than 3.1 electron volt because we mention that 3.1 electron volt is the maximum energy within the visible region. So, if you have a band gap which is more than 3.1 electron volt then there is no absorption in the visible because the visible light is smaller than 3.1 electron volt. And so you will see a material will be looking like transparent material it is not absorbing in the visible and when it is less than 1.7 electron volt all the radiation of the visible is absorbed and the material appears black or metallic in color. So, that is the explanation of these colors and if in between that means the gap is between 1.7 and 3.1 then you can see red color, blue color, green color all the visible colors you can see when you have a band gap in between 1.7 and 3.1 you will see all the possible colors from blue, yellow, green, red, violet etcetera. Now, other than the valence band and conduction band if you add impurities or dopants then what happens you have this valence band and you have this conduction band. If you add impurity then you get some energy levels which are discrete that means there are not too many impurity atoms. So, it cannot form a band. So, they are like a level energy level, but not too many energy levels in the vicinity. So, it cannot form a band there are one or two levels may be there that too separated by some gap of energy. But if you can design your material such that you choose a impurity or a dopant such that you introduce the energy level of the impurity in between the conduction band and the valence band then you can access this energy level. That means now you have ability to transfer an electron with less energy to this level earlier you had to transfer an electron to the conduction band that requires more energy when you transfer to this impurity level you need only this much energy. So, with lower energy you can cause an absorption. So, that is why sometimes this band gap is very high and you cannot see any color, but when you add some impurity then you start seeing some color that is because you can have a transition which is now in the visible whereas the band gap is in the ultraviolet. So, you can have that. So, there are different types of absorption now possible you can have one photon absorption from here to there you can have one photon absorption from here to the conduction band. You can have two photon absorption that means one from here one from there and they can also emit like this. So, one photon comes from here and then you have this transition electron comes down and you have a photon as a result of that emitted. So, you can have this type of one photon or two photon combination of photons emitted due to the presence of impurity levels and how did the impurity levels come the impurity levels came because you took a solid and in that solid you have added some impurity atoms. So, you add a very small amount of impurity atoms. So, if you have a 100 percent solid say you add 1 percent of some impurity material. So, you it is 99 percent of your original materials say zinc oxide in which you add say 1 percent of europium or terbium or some such species which has a energy level which goes right in between or somewhere in between the conduction band and the valence band of the host compound. The host compound here we were discussing was zinc oxide it can be some other oxide some other chalcozonoid etcetera. Now, you can have in inorganic semiconductors like you have organic semiconductors are there what we are discussing now is inorganic semiconductors like zinc oxide or cadmium selenide cadmium sulfide cadmium telluride they are all inorganic semiconductors made of inorganic compounds. But, you can also have organic semiconductors made of carbon chains and may be having unsaturation etcetera. So, inorganic semiconductors what we discussed is that you can have a valence band you can have a conduction band you can have these impurity levels these are also called trap levels are caused by defects and when you cause an electron to go from the valence band to the conduction band then you create a hole in the valence band. So, this is also true that whenever you have an absorption due to the excitation of an electron from the valence band to the conduction band then a hole is created in the valence band a hole is nothing but the absence of an electron. So, if an electron goes away electron has a negative charge. So, what will it leave behind it will leave behind a positive charge that is why the hole is a positively charged unit and you can have this kind of luminescence between trap states or you can have emission from the conduction band to the valence band depending on what kind of energy you are giving to the system. So, typically in these materials a lot we discuss is about the effect of size. So, we said in our earlier slides that you can have all kinds of colors for gold or you can have all kinds of colors for cadmium selenide and we showed you some 10 volumetric flasks field of solutions or field of colloidal solutions of cadmium selenide as a semiconductor and why where the colors different although in all of them if you can find out the material if you analyze the material using any technique a chemical technique or x ray technique or any technique by which you can identify the material you will find only cadmium and selenium in the ratio of 1 is to 1 then what has changed the color the color has been changed because although cadmium and selenium are there in all the flasks volumetric flasks and they show the red green let me show you that figure. So, this is the figure where you see all the flasks of cadmium selenide with different size particles. So, but we have not yet explained exactly why the colors are changing we have said that because of particle size the colors are changing if you change the particle size you will change the color, but why because of particle size the color should change and that is a very very important problem which has been solved for long time using band gaps and that is the slide that we are discussing where we show what happens when the particle size decreases. So, this is say a bulk semiconductor that means a semiconductor which has got large size particles. So, this is a large size particle and we call it a bulk. Now, if I reduce the size of the it has got say a distance a b and c because this is a three dimensional solid. So, you have three directions a b and c and these are very large dimensions say each side is 10 microns or something. So, it is a bulk material. Now, if I try to remove part of the material from this side. So, I remove chop this particle like you are chopping a piece of cake. So, you will make thin slices of this particle and you will get this kind of shape. Now, this kind of shape is like a plate because it has two dimensions one and two which are large, but the third dimension is very small and this kind of a plate like structure is called a quantum well in this kind of nano sized objects. So, in this quantum well what happens in terms of electrons and its energy. In the bulk we know that the energy of the electron changes as the number density. This is called the number of electrons per unit change in energy or energy difference between e and e plus delta e. So, what is the electron density between a small change in the energy. So, that is plotted here that is called rho here is also called the density of states. It is the density of energy states that means how many levels are closely packed that is the density is high or low it varies with the energy. So, if you see for a bulk object the rho of e or the density varies in this manner it is like a parabola where the density is 0 rho e is 0 at 0 energy and it changes and goes up the density increases till a certain value of energy and after that the line stops that means there are no states above this value. Now, this is true for a bulk where you have filled electrons up till this value and in that case that will be called the Fermi level. If you have electrons filled up till this level then that energy is called the Fermi energy and this is the density of states plot for a bulk material which has got three dimensions a b and c are large. Now, when the size decreases now we are talking of confinement or quantum size effects when the size decreases from bulk. Now, you see you have made what we are calling it is a quantum well because the property of the electrons and its energy levels are going to be affected. So, how are they going to be affected the shape of this curve now has this step like feature. So, in a quantum well because you have one dimension very small. So, you can say this is a nano material because one of the dimension is nano sized the other two dimensions are not nano sized in a quantum well. So, when this happens the density of states is in a step wise manner it does not vary continuously like in a bulk solid you have a density of states of this value up till this energy below that there is no density of states below a certain energy. That means electrons cannot have energy of this value only it can have energy above this value till this value you have a certain density of states. When you go to higher energy you have higher density of states and again for a small region of energy the density of states is constant. So, density of state is constant from this energy to this energy then density of states is constant from this energy to another energy. So, now this is called quantum confinement effects because in the bulk density of states is not constant at all for any energy it changes continuously whereas, here density of states is constant over a certain energy range and then it suddenly changes and again becomes constant for another energy range. This happens for a quantum well where one dimension is nano dimension. When you go to a quantum wire where two dimensions are nano sized this is nano sized and this is nano sized and the third dimension is still long. Then we call it a quantum wire and then the nature of this density of states diagram changes again. So, here you have a nano dimensional wire no variation in density of states in this energy region. There is a variation in the density of states in this region and then suddenly it jumps to another density of states and then again there is a small variation. So, this plot of density of states versus e is very characteristic whether you have a bulk particle or a quantum well like structure which is like a 2 d nano structure. This is a 3 d bulk structure this is 2 d nano structure like a plate it is also called a quantum well. This is a quantum wire also called a one dimensional nano structure because in one dimension this is long in the other dimensions it is small and if you reduce this to nano size in all three dimensions 1, 2 and the third one in that case it will become a quantum box or like a particle in a box in three dimensions. In all three dimensions it is now constrained it is confined that is why we call it quantum confinement because the electrons are not allowed to move outside this box. The dimension is so small because the electron cannot go out of the particle and the particle is a nano particle. So, the electron has to be within the nano particle. So, you have got a quantum box or a 3 d quantum object this is a 2 d quantum object this is a 1 d quantum object and it is a 3 d quantum object this is a 3 d bulk object. So, in this case you come back to your atomic structure the energy levels are now discrete. There is no variation of the density of states like in this case or in this case the density of states for a one particular energy is varying, but the density of states cannot change with energy continuously or even in a small band it changes drastically. So, you have discrete energy levels. So, at one energy say E 1 you can have some density of states at another energy E 2 you can have some density of states, but between E 1 and E 1 you cannot have any density of states. So, this is a quantum box a 3 d quantum box and you have now electrons in discrete energy levels in this particular case. So, what we talked about are these energy levels and the variation in the nature of the density of states versus energy plots which cause all the changes in the optical properties of the systems. Because what will happen to electrons when they are absorbed or moved from this level to this level will be very different from shining light and pushing electrons between these levels and again it will be different in this case. So, in all these cases because the energy level diagram is different because of the type or size of the particle and the shape of the particle. Hence the optical properties will be different and with that I will stop my lecture now and we will continue our applications these were the basic properties of nano structures with respect to optical properties. That means, what happens when light is absorbed by different size particles what happens how the colors change and associated properties which all depend on the energy band diagram and the spacing between the energy levels and the shape of the density of states plot as a function of energy. And now in the next two lectures we will discuss on how these are applied to give you useful devices based on these variation of the optical properties in nano structures. So, thank you very much and we will continue our lectures.