 So, let me start with my today's lecture, but before we start let us let me remind you what we discussed yesterday and basically what we discussed yesterday is the how solar cell or how a p-n junction diode can be used as a solar cell what happens when light falls on a p-n junction diode and we have seen that how junction helps in getting the voltage positive current negative right. So, whenever you know semiconductor device if voltage is positive current is negative or you know product the power is negative then the device excessive power generating device otherwise power is consumed. So, that is what we have seen and with the schematic diagram I have showed you that you know this there are some drift diffusion of current and holes minority majority carriers that keeps on happening, but additional to that what happens under the light generated carrier is result is the collection of the positive charges on p side negative charges on one side that is physical separation of positive negative charge which means photo voltage is generated and this generation of photo voltage across p-n junction due to light is called photovoltaic effect. And we also discussed the parameters of solar cell right. So, we have discussed the p-n junction you have discussed open circuit voltage, short circuit current, cell factor, efficiency, maximum power point, two parameters we have not discussed is about series resistance and the shunt resistance that we will discuss in this lecture ok. So, I far I hope that everything is going fine fine. So, this is what we have discussed yesterday operation of a p-n junction solar cell, generation of photovoltaic light generated current and reverse direction parameters of solar cell VOC, ISC, Filth Factor Efficiency. What we will discuss today is so now we are looking going to look at the details of the operation of a solar cell. We have looked at yesterday from the physics point of view now we will look at from the device perspective how the solar cell should be made or designed in order to get the highest possible efficiency. So, before going further so today is two lectures are focused on the design of solar cell mainly. Before we go further we will look at it what are the upper limits of solar cell parameter right. So, there are solar cell parameter this VOC, ISC, FF, Efficiency. So, what is the upper limit? How much is the maximum value of current that you can get? What is the maximum value of open circuit voltage that you can get? What is the maximum value of fill factor that you can get and what is the maximum efficiency that you can get? So, these are the various question you have been asking and today is the day to get the answer to all this question. So, pay your full attention. How to design a solar cell in order to get a highest short circuit current and the next lecture I will say how to design a solar cell in order to get the highest open circuit voltage also ok. So, this is just to recap that this is what we discussed P side get positive and side get negative not all the carriers which are generated due to light get absorbed or contributes to the current. Some of the carriers get recombine also some of the carriers get recombine. So, therefore the diffusion length for electrons in the P side and diffusion length for holes in N side minor to carrier diffusion length are important fine and then we also looked at the various parameters ISC, VOC, VM, IM, PM etcetera. Here ISC if you are I also told you if you are using JSC the current density then you should multiply by the area also and what is the P in? P in is a power density of the solar radiation under the standard phase condition that is 1000 watt per meter square air mass 1.5 G spectrum ok. So, normally a solar cell should perform following jobs right a solar cell should convert light falling light on a solar cell into electricity as much as possible right that is the job of the solar cell that we want. So, we want high efficiency. So, it should actually absorb the light falling on a solar cell ok. It should actually absorb the light all the light falling on a solar cell what does it mean? It should reflect less light and it should transmit also less light and therefore, the once the light is absorbed there has to be. So, let me go back to the whiteboard and tell you what are the main functions that a solar cell should perform? Functions of solar cell ok. First thing it should do is it should absorb as much light as possible absorption of when the light is absorbed what you should do? Absorbing what it should do? It should create electron hole pairs. This is the first thing ok. Second thing once electron hole pairs are created what it should do? See if I draw my solar cell p-injunction a light is falling electron is generated and hole is generated right. We do not want this to be recombined if it is recombining then we are not getting help in the current generation. What we want? We want this electron to go to the other side ok. So, once this electron goes to the other side down the energy it cannot come back right it cannot come back it goes to the other side it cannot come back because it has to increase in its energy and this motion this is and this hole cannot go here this electron cannot go. So, once a minority carrier crosses the junction we call it is a separation of carriers what is called separation of carriers. So, separation of carriers are important if carriers are not separated what will happen they will recombine ok. So, second job a solar cell must do is a separation of carriers which carriers generated carriers light generated carriers. So, light generated carriers should get separated is that enough that is not enough what is the next thing? Finally, we want this current to flow in the external circuit. So, therefore, what we will be doing we should be able to making contacts ok. So, we should make a contact contact with this side contact with this side and we should connect it to the external ok. This so, this carrier electron then actually should go and flow in this contact and this is called the collection of carriers collection of carriers absorption separation and collection. These are the three functions any solar cell must perform be it amorphous silicon cadmium telleride CIGS gallium arsenide organic solar cell thin film solar cell any type of solar cell this three functions must be performed ok. And these three functions are happening in series ok. First absorption takes place second charge separation takes place and third collection takes place ok. So, out of this three if anyone is not performed well by a solar cell then your efficiency of solar cell will be low ok. All these three functions absorption separation collection must be performed as efficiently as possible. So, these are the functions of solar cell ok this we must remember. So, this is what a solar cell do. Now, we want light to get into the solar cell as much as possible and sorry I could not bring the solar cell I will bring it after this lecture. So, light must go inside the solar cell as much as possible. Therefore, my front metal contact is not continuous my front metal contact is in this way. So, there are fingers there are thin metal lines and there is a collection. So, by the way when light falls on a solar cell when light falls on a solar cell this is minus p in junction this is a solar cell basically right. So, I have n and p when light falls current is generated everywhere current is generated everywhere ok. So, current is generated wherever light falls. So, therefore, you should your contact should be almost everywhere, but because we want light to come in. So, you make selected contact ok. So, that your light should come from here otherwise and you know this is the metal contact I am showing you and the metal contact blocks the light ok. So, therefore, front metal contact cannot be continuous contact cannot be continuous contact it is in the form of fingers. The back side if the light is coming from this side this is called the front side the side from where light is entering and the other side is called the rear side. The light the surface from where light is entering called the front side the surface from light. So, the back side you can have a continuous metal contact this H line is a metal contact and this also metal contact. So, back side can be a continuous metal contact and the front side cannot be because you want light to get into, ok. So, this is what a typical solar cell looks like. So, there are fingers on the front side, there is a metal contact on the back side that there is a p-n junction, ok. p-n junction is very thin. I will tell you why, I will discuss in the design why the structure is like this, but it has to actually reflect less light. So, therefore, there is a anti-reflection coating that we do. There is also anti-reflection texturing. We make surface rough also, so that reflection is minimum from the front surface. And this thin lines are called fingers and there is a thick metal lines which collects the current from all these metals called bus bar and then you have the rear contact, ok. These are the terminology. The p side is normally called bass and n is emitter. So, p-n junction is bass and emitter, ok. So, now, let us look at what is the highest efficiency we can get. Now, efficiency of the solar cell is a function of V o c, I s c and fell factor. And therefore, highest efficiency means high value of V o c, high value of I s c and high value of fell factor, right. So, highest value of efficiency means how the value of parameters, how much is the highest value of parameters, how much is the highest value of open circuit voltage, how much is the highest value of short circuit current, how much is the highest value of field factor ideally, what is the upper limit? Now, upper limit of ISE short circuit current, now upper limit of short circuit current, what is happening in a solar cell, light is coming, a photon is falling on a solar cell. A photon is, see if I look at the solar cell like this, a photon is falling having energy h nu, it gives one electron hole pairs, this electron hole pair gets separated. And if everything goes well, there is no recombination taking place, everything goes well, for one photon, one electron will come out, for one photon, one electron will come out, this is what is happening right and hole will go this way. So, for one photon, one electron is coming right and the rate of flow of electron is current. So, once we want to find out what is the highest value of current, what we should know, we should know how many number of photons are there in my spectrum. And we would like to find out highest value of current under standard test condition, under standard test condition the value, the power density is 1000 watt per meter square, but 1000 watt per meter square of not any photon, it is of the air mass 1.5 spectrum, 1.5 g, g for the global right. So, this is in this spectrum air mass 1.5 g of having intensity 1000 watt per meter square, how many photons are there, that will determine what is the upper limit of the short circuit current. Remember one photon is giving one electron, if you know how many photons are there, we know how many electrons are generated and collected. And once you know how many electrons are generated, we can find out the limit for the current ok. So, that is why it is important to know the number of photons or the photon flux, how many photons are coming per unit area, per unit time on the solar cell and this is my spectrum ok. And actually what I have plotted here, there is the photon flux right. So, actually if you can see here this axis is a photon flux axis ok. Unfortunately numbers are not visible, but you can see that the photon flux in the range of tens for 18, tens for 19, 17, number of photons per unit area, per unit time ok. So, that is what is the photon flux is there. And if you assume that each photon ok, here it is clear, here you get the wattage per meter square per nanometer, why per nanometer because this scale is a wavelength scale ok. So, this is a radiation density, this is watt per meter square per nanometer. Now, if you know that this many watts are coming. So, for example, at this 500 wavelength, if your radiation is coming at 1500 watt per meter square, 1500 watt per meter square, how many numbers of photons are coming ok, how you will get that. So, total energy is you know total energy if you divide by the energy of one photon, you will find that total number of photons coming in that. In that way you will find out the total photon flux ok, number of photons per unit area per unit time. So, divide the energy in a given spectrum width and this spectrum is very easily available. If you go to the NASA side, the spectrum will be available, the spectrum will give you ok. From 400 to 410 nanometer, the energy falling is so and so and therefore, if you divide the energy of the 410 nanometer photon, which you can find out, you can find out the how many photons are then in that spectrum ok. Now, if you assume that each photon is giving me one electron in the external circuit that is the highest limit right. I know that each photon will not give you one electron, why not some photon will get absorbed away from the diffusion length and therefore, they will recombine right and therefore, some of the photon energy will be lost because of the recombination. Some of the photons will get reflected also right. So, whatever photons are coming, some photons will get reflected because reflection will not be 0, some will get transmitted ok, transmission will not be 0 and some will recombine ok, some of the electron hole pair will recombine. So, electrons will hold recombine. So, this is the loss due to reflection, this is the loss due to recombination, this is the loss due to transmission. So, not every photon in reality will actually result in one electron, but the highest limit will be achieved when every photon gives me one electron. So, this is the graph every photon gives me one electron ok. Now, look at the interesting aspect of this graph is that and I will zoom it to show you the little bit clear. What is the interesting aspect of this graph? As the band gap increasing, as the band gap increasing, the short circuit current is decreasing. Why it is so? As the band gap increasing, the upper limit of short circuit current is decreasing. So, the short circuit current, the maximum short circuit current that you can get from your solar cell depends on the band gap. An answer is very simple. If the band gap is higher, if the band gap is higher, if the band gap is this much, let us say band gap is 2 electron volt and if a light falling is 2.5 electron volt, it will get absorbed. But if light falling is 1.5 electron volt, it will not get absorbed. If the light falling is 1.2 electron volt, it will not get absorbed ok. So, because when you increase the band gap, there are less number of photon which can cross that energy level and more number of photon will pass. So, this photon, this 1.5 electron volt photon just will pass. It will be transparent and therefore, as you increase the band gap, less and less number of photons get absorbed and your short circuit current decreases ok. Then somebody will say that in our spectrum, in solar spectrum, we have the photons in our spectrum. We have photons from as high as 3.5 electron volt and as low as 0.3 electron volt. So, why not to take a semiconductor which is 0.3 electron volt? So, that each and every photon gets absorbed in a solar cell. Each and every photon get absorbed in a solar cell and what will happen? Your current will also be very high. Is this a good idea? Take a very low band gap solar cell or semiconductor, so that each and every photon will get absorbed, so that your current is higher. But remember what is our efficiency? It is not only current, it is also voltage and therefore, we will come back to that. But learn this from this slide that lower is the band gap of the material, higher is the current that you can get very nice. So, that is upper limit of current you can calculate. You will find that for a material of 1.12 electron volt for silicon which is having a band gap of 1.12 electron volt, the upper limit maximum value of I s c or actually J s c current density is about 46 milli ampere per centimeter square. Never in the world, never in the world you will achieve the current density higher than 46 milli ampere per centimeter square for silicon. That is the highest, highest. Whatever you do, you can only get maximum 46 milli ampere per centimeter square. So, that is upper limit for silicon and you can actually find out upper limit for any other band gap material or something. What about the upper limit for the open circuit voltage? What about the upper limit for the open circuit voltage? Look at this band diagram. The open circuit voltage is actually the first of all the whenever you divide the potential energy by q, you get voltage. So, when you divide the potential energy by q, you get the voltage. I told you earlier. So, potential energy is q sorry q into v. So, voltage is actually your potential energy into divided by q. So, if I have a semiconductor which is having a band gap of e g, the maximum potential difference from this level to this level is e g by q. Therefore, the maximum possible voltage if at all it can be band gap divided by the q that is the unit of voltage. So, if it is silicon, my silicon is having band gap of 1.12 electron volt. So, 1.12 divided by q, 1.12 electron volt, 1.12 electron volt divided by 1 electron that is q the charge of the you get actually 1.12 volt. So, that is the maximum, maximum, possible voltage that you can get. But in practice even that is not achievable. So, e g by q it should be the highest limit of EOC, higher band gap means higher value of EOC. You are getting some hint when your material band gap is higher, you are getting higher voltage because that is the that is the energy that you separate your electron. If your band gap is higher, actually you are getting you are shifting it to higher energy level and therefore, you can get more work done by the electron. And this in practice the possible voltage that you can get is actually from the two difference of the two Fermi level P side and N side and basically quasi Fermi level under the operation of a solar cell. The difference between the two Fermi level E f N Fermi level at the N side Fermi level at the P side divide by q, what is E? Capital E is a symbol of potential energy. So, potential energy of the Fermi level at the N side minus potential energy of the Fermi level P side divide by q that is the highest value of EOC that you can achieve, but the upper upper limit is band gap divided by q that is nothing but the band gap in terms of voltage. If you look at this expression, the open circuit voltage you have seen yesterday is a function of I L divided by I 0, light generated current and I 0 plus 1. I L is the light generated current and light generated current depends on what? Intensity of the light depends on the band gap, right. So, first of all your open circuit voltage is the function of current itself, keep this point. Your open circuit voltage is a function of current itself, right. Light generated current will be higher. So, open circuit voltage will be also higher in practice, right. But open circuit voltage increases as a log of a light generated current as a log function of a light generated current, ok. So, 10 time increase in the light generated current will actually double the open circuit voltage. So, though the open circuit voltage is a function of light generated current, it is not a linear function. It is a log function. Look at here what is there in numerator? I 0, I 0, ok. What is I 0? Reverse saturation current, remember? Reverse saturation current that we discussed and I 0 is a function of many parameters, ok. Diffusion coefficient, diffusion length, doping level of acceptor, intrinsic carrier concentration, intrinsic carrier concentration is function of temperature, diffusion coefficient you can correlate with the lifetime and diffusion length. Diffusion coefficient you can also correlate with mobility, diffusion length you can correlate with lifetime. So, I 0 is a function of many, many parameters, ok. And look, I 0 also depends on N i. N i depends on what? Intrinsic carrier concentration I told you. Intrinsic carrier concentration also depends on the band gap. If I have one material like this and I have another material like this, this is having smaller band gap, this is having larger band gap. What will happen to N i in this case? In this case N i will be higher than N i in this case. Why? Because of the lower band gap, more electron will get excited because of the thermal energy. In this case, because of the higher band gap, less electron will get excited. So, N i in the lower band gap material is higher as compared to the higher band gap material. So, therefore, if your I 0 is higher, what is your low? V O C is lower, very important. If your I 0 is higher, reverse situation current is higher, your V O C is higher. So, I 0 depends on what? N i. N i depends on what? Temperature. So, if your temperature is higher, N i is higher, N i is higher, I 0 is lower. Let me put on the paper here. So, your V O C is k T by q log of I L divided by I 0 plus 1. Light I L is a light generated current. So, first of all V O C is a function of I L. More light means more I L, more I L means more V O C and that you see that when you are actually using solar module. In the morning, intensity is lower. So, light, so current is lower. So, your voltage will be little lower. In the afternoon, in the afternoon time when your current is higher, because your light is higher, your current is higher and when your current is higher, your open circuit voltage is higher. So, if light intensity is higher, then your I L is higher. When your I L is higher, your V O C is higher, but this V O C is a function of log function. Remember, then this is a very important. The next parameter depends on I 0. So, your V O C is function of I 0. I 0 is a reverse situation current and I 0 is function of many parameters. Function of N i, function of mobility, function of tau, function of B, function of N A, function of N D, everything. Your N i is a function of band gap. So, it becomes a function of band gap also. So, what will happen? If especially look at the temperature and many people have been asking what happens as a temperature. So, as the temperature increases, N i that is intrinsic carrier concentration will increase, because more and more electrons will get thermal energy to get excited from valence band to conduction band. So, as the temperature increases, N i increases. As the N i increases, I 0 increases. As the I 0 increases, what will happen? As the I 0 increases, what will happen? V O C decreases. Open circuit voltage will decrease. Fine. So, this is important discussion and that will be useful. So, the more important thing is N i is also function of band gap. Higher band gap, higher band gap. So, if I look in terms of band gap, higher is the band gap. N i is the lower. Lower is the N i. I 0 is lower. I 0 is lower means open circuit voltage is higher. So, contradiction. I want higher efficiencies. So, I want higher short circuit current. I want higher open circuit voltage. I want higher fill factor. What is the contradiction? If I have lower band gap, what is the contradiction? So, high efficiency means V O C should be high, I S C should be high, fill factor should be high. That is meaning of high efficiency, high efficiency. Especially, if I look at the function of. So, when I look at the band gap, when the band gap increases, what happens? The lower band gap means higher short circuit current that we have seen. Lower band gap, I will go take you to the back to the slide. Lower band gap here means higher short circuit current. But from here, lower band gap means lower open circuit voltage. Lower band gap means lower open circuit voltage. So, if my band gap increases, my open circuit voltage increases, but my short circuit current decreases. So, this is the contradiction with the choice of the material. So, there is a contradiction. What I want? I want high efficiency means I want high V O C, I want high I S C, I want high fill factor. But the open circuit voltage is higher for the higher band gap material and short circuit, sorry, open circuit voltage is higher for the high band gap material, short circuit current is lower for the high band gap material. And therefore, therefore, optimum value of E G is required. Optimum value of band gap should not be very high, it should not be very low. So, you have to find the optimum for which your efficiency is maximum. You have to find the optimum for which your efficiency is maximum. And I will come back to this again. Have you already got this? There has to be a optimum band gap value. It cannot be very high, it cannot be very low. Fine. So, upper limit of open circuit voltage depends on the band gap. But for all practical operation, the upper limit of open circuit depends on I 0. I L value, V O C depends on I L and I 0. I L value cannot change significantly. But I 0 value can change significantly. Orders of magnitude. Your I 0 can easily change 1000 times, 500 times, 10,000 times depending on the parameters of your material, depending on the processing. And in brief, I 0 can be given as a empirical formulae as a function of band gap like this, considering the best value. And this is for the silicon. So, if you put the value of band gap of silicon here, you can find out the value of I 0. You know the upper limit of I L for silicon. I told you already, what is the upper limit of I L for silicon? What is the upper limit of I L for silicon? 46 milliampere per centimeter square. So, you put this numbers and you can actually find out what is the upper limit for open circuit voltage. You can do this. What is the upper limit for open circuit voltage for silicon? You do it in your free time. You will find that this value comes about. So, these are the practical values by this. This values comes about 750 milliold, about 0.75. You can do this calculation on your own. So, we have looked at the upper limit for current. We have looked at the upper limit for voltage. And now, upper limit for the fill factor. Fill factor is determined by the series losses in the solar cell, ok, resistive losses, series resistance and shunt resistance. But people have also shown that fill factor is also dependent on the open circuit voltage. So, if you define a number called V O C divided by K T by Q, by the way K T by Q has units of volt, ok. K T has a unit of electron volt and if you divide by Q, K T by Q has the unit of volt. And you know that all of you know that room temperature is K T by Q is. So, K T I told you earlier also has a unit of electron volt. K T by Q has a unit of volt. And at room temperature R T of 300 Kelvin, the value of K T is 0.0256 electron volt or by K T by Q is 0.0256 volt. That is the value you can normally use standard values in the calculations also. K T, K is the Boltzmann constant, T is the temperature at 300 Kelvin. It is 25 millilectron volt, the K T or K T by Q is 25 milliold. So, here the kind of V O C divided by K T by Q it is plotted in that way. And you can see that as the V O C increases, your fill factor also increases. As the V O C increases, your fill factor also increases. You can look it in the little bit clear. So, the units and numbers become clear. If fill factor is a function of V O C, mainly it depends on the series resistance losses, but this is another relation. Fill factor is very much affected by the series resistance. And I will come back to that. Higher the series resistance of the solar cell, lower is the fill factor. So, normally a lot of people actually work to design a solar cell with the low series resistance. So, this is how the upper limit of fill factor. Upper limit of fill factor as we can, as we discussed the from the, from the I V curve, upper value of fill factor. Normally, if my curve should be square, my curve should be square. And so, this is my I S C and this is my V O C as a solar cell, but in practice my curve is something like this. And therefore, this is my point. So, the ratio of the two curves, two squares is what is the fill factor. So, ideally you can have 100 percent fill factor if the curve become, but that will never occur. That will never occur. So, your fill factor we have seen V M I M divided by V O C I S C. Typically, highest value that you can go is about 85 percent, 86 percent. So, 85, 86 percent is what fill factor you can get this really, really, really high value. Ideally, square I V curve means 100 percent, but you will never reach that. Fill factor is a function of series resistance of a solar cell. It is a function of shunt resistance of a solar cell and it is also depends on the V O C that we have shown in the earlier cases. So, highest limit of current, highest limit of voltage, highest limit of fill factor will give me highest limit of efficiency. So, I told you that there has to be optimum value of the band gap. It cannot be lower band gap, very low band gap, cannot be very high band gap. First of all, look at this point very clearly. When we say efficiency, the standard efficiency means many things. When we say efficiency, first of all we talk about spectrum air mass 1.5. If your spectrum is different, then your efficiency will be different. When you talk about efficiency, we say either efficiency of single junction or multiple junction. So, typically, standard practice is to give efficiency of a single junction solar cell. Also, when we give efficiency, we give efficiency with concentration or without concentration. As you concentrate more light in a solar cell, if time permits, I will show you that actually your efficiency increases. So, therefore, when you are giving efficiency and as a student of this course, you should never make a mistake. So, efficiency is given for air mass 1.5 g spectrum 1000 watt per meter square. Never get confused. Some people also give efficiency for some other spectrum. For example, concentrate the solar cell, people use some air mass 1 spectrum, air mass 0 spectrum and something else. For all our applications, typically what people understand is the efficiency of air mass 1.5 g 1000 watt per meter square. As a course of a student of this course, never make a mistake. Efficiency of a single junction. When you say upper limit of a solar cell efficiency is 29 percent, I am referring to the upper limit of efficiency of a single junction. But when you go to multiple junction or ideally when you go to infinite number of junctions, your solar cell efficiency can be 86 percent. We will discuss it later if time permits. But whenever mentioning the efficiency, I am mentioning single junction efficiency or if it is specific, then I should say it is a multiple junction efficiency. And that is the different. Upper limit of the efficiency will be different for single junction. Upper limit of efficiency will be different for the double junction triple junction. And with without concentration, when I am making the efficiency without concentration of light, which means efficiency also depends on the light concentration. So, when you concentrate light efficiency is increases. But normally all our practical purpose, when I am talking about silicon, I am talking about efficiency air mass 1.5 g 1000 watt per meter square single junction without light concentration, of course, I am mentioning it at 25 degree centigrade. Some people go one step further and say what is the wind speed? So, wind speed because wind speed also have a result of cooling. So, 1 meter per second wind speed approximately this is the value. So, these are the parameter under which your single junction solar cell efficiencies are defined never magnetics. Single junction without concentration air mass 1.5 1000 watt per meter square 25 degree centigrade. Cool. So, you have then you have then the efficiency depends on the band gap. And you should not have very low band gap, you should not have very high band gap. Very low band gap means high shock circuit current, but lower open circuit voltage very high band gap means high open circuit voltage, but lower shock circuit. So, somewhere there is optimum. Where is the optimum? Optimum value comes air mass 1.5 curve we should look this curve. Optimum comes about 1.45 electron volt. What is the optimum value of the band gap to get the highest efficiency air mass 1.5 I am sorry band gap 1 about 1.45 electron. And what is the value of highest efficiency? I am looking at the air mass 1.5 curve do not look at air mass 0 curve or black body curve here. So, this is the highest value almost and this value comes to about 29 percent as I said ok. So, the highest value of single junction solar cell is about 29 percent that is possible. Where is your silicon? Silicon is not sitting at the highest value. So, the ideal. So, what is ideal band gap? So, ideal semiconductor band gap for solar cell is 1.45 electron volt. Is silicon is having ideal band gap? No. Then why silicon use? I have already answered there are many advantage that silicon provides. So, just here for the convenience I am writing again silicon has the band gap of 1.12 electron volt. Chetmium telluride has the band gap almost about 1.42 electron very close to the ideal. Gellium arsenide has the band gap of 1.45 electron volt very close to the ideal almost ideal. Amorphous silicon has the band gap of 1.7 electron volt. CIGS has a band gap about 1 electron volt. So, these two materials are the best suited in as far as the band gap matching is concerned. Silicon is not suited, but silicon is still not bad look at the efficiency curve. Silicon is here very close to the maximum body can gets. People have demonstrated that with silicon you have people have almost achieved 25 percent efficiency ok. So, upper limit of parameter is clear why the why the band gap optimum band gap is 1.145 electron volt should be clear to all of you now. So, let us move it, but we cannot actually we people we do not reach to the ideal efficiency particularly in the commercial scenario because there are many losses that takes place in a solar cell. I have divided losses in two categories. One is called the fundamental losses that takes place which nobody can help us, other is called technological losses ok. Fundamental losses yes we will discuss later. Fundamental losses the loss of energy which energy low energy photons. If your band gap is 1.45 ideal all the photons which are having energy less than 1.45 electron will pass will transmit and therefore, not contributing to the current not contributing to the voltage. So, that is your loss losses of excess energy. So, if your band gap is 1.12 electron volt and if your photon is 1.2 electron volt ok or let me come to this this losses I will come to. So, loss of voltage and loss of fill factor loss of fill factor there is bound to have some see resistance you cannot help and because you are going to make a metal contact you are going to have some losses. So, the two most important losses if this is your band gap. Suppose, I am talking about ideal band gap of 1.45 electron volt this is 1.45 electron volt. What is my spectrum? Solar spectrum what is the length it contains as the energy contains 3.5 electron volt to 0.3 electron volt ok. Which means all the photons which are having energy 1.45 electron volt and lower than that will be loss that is loss transmission loss ok. So, those photons which are electric just pass by refers as a transmission loss. You know how much is the transmission loss? 23 percent of your incoming energy is just transmitting passing by for the ideal band gap semiconductor 1.45 electron volt 23 percent ok. That is 1 loss. Now, suppose you have a photon which is 3.5 electron volt which is falling. So, this will give actually give rise to electron how much energy it will give rise or 3.5 electron volt right because all its energy it will give right, but eventually this extra energy. So, what I need is only equal to the band gap energy ok energy that I need is equal to the band gap energy only eventually all the photon. So, this excited electron will actually lose its energy will come back here. So, your requirement is 1.45 electron only you are supplying 3.5 electron volt. So, almost 2 electron volt of extra energy is getting wasted it is not being utilized. So, your band gap is 1.45 electron and any photon having energy higher than the band gap any surplus of energy than the band gap energy is wasted in the form of heat ok. This loss is called thermalization loss thermalization loss you know how much is this loss? 33 percent. Wow 33 percent plus 23 percent 33 plus 23 equal to 56 percent. Thermalization loss is 33 percent, transmission loss is 23 percent 56 percent of the incoming energy is getting lost and what is the bad thing that it is not in your control you cannot do anything it is a fundamental loss. So, I tell my student that even if you pray a lot to the god and in a lot Shiva gets happy and comes to you and say ask what you want and if you say give me a solar cell of more than 44 percent efficiency he said he will say sorry I cannot do that ok. So, even lot cannot help because it is as per the law of physics you cannot get. So, 56 percent is your losses what you can get is only 44 percent. So, only 44 percent of the incoming radiation is in your control and again out of this you are going to get losses because of the metal contact you have to have your Fermi level is always lower than the valence band and conduction band and therefore, you are going to have losses. So, therefore, all after you. So, this is the what is possible and then you reduce the losses and you get about 29 percent ideal right. So, that is how the number 29 percent comes getting it. So, lot of losses occurs which are not in your control is there any possibility by which I can avoid this losses transmission and thermalization losses yes there are possibilities by which you can avoid the transmission thermalization losses. How you can do that? By making multiple junctions by making multiple junctions. So, 2 junctions 3 junctions 4 junctions 5 junctions infinite junctions if you have infinite junctions you will get 86 percent efficiency. But as far as the single junction is considered 56 percent energy is just getting lost ok. So, what you see is this is the ideal what you can get. So, these are the losses fundamental losses fundamental losses, but out of this then you have to reduce the technological losses. What is technological losses? You want reflection to be 0, but can you achieve 0 reflection technologically? Very difficult you can achieve, but very difficult ok. You want a recombination to be 0, but can you achieve 0 recombination? You can achieve, but very difficult because your impurity levels are very high ok. You want series resistance of your solar cells to be 0, but can you achieve 0 series resistance? Very difficult not possible. So, therefore, out of 29 percent there are lot of technological losses that occurs which is not which is very difficult to achieve 0 resistance is very difficult to achieve or low resistance is very difficult low reflection is the. So, when you minimize when you reduce the technological losses your solar cell as of today that what people are making in industry is about 15 to 16 percent efficient on an average and I am talking about crystalline silicon solar cell. 15 to 16 percent is the efficiency of the commercially available crystalline silicon solar cell you get. So, considering all these losses you come here fine ok. So, fine because I go into the explanation in the wide board I actually lose a trick of time and I am not able to finish my slides which are designed. But anyway I think it is important to give you the concept slides are always going to be with you you can read more and more whenever your time. So, there are fundamental losses which we cannot avoid there are technological losses which is in our control, but very difficult because we have to also look at the commercial aspect financial aspect of it. So, typically I divide losses in three categories optical losses which occurs because. So, this is how your junction looks like right your end the red is n blue is p type your metal contact and then your back metal contact your metal contact. So, some of the light will either get absorbed in the metal contact or reflected that is optical loss some of the light get transmitted that is optical loss some of the light will get reflected from the front surface that is optical loss. Recombination losses there will the recombination occur it will occur everywhere it will occur at the rear side it will occur in the bulk of the material it will occur in the emitter. Remember what is the emitter n layer is referred as emitter and this thick layer is p type is referred as a base so base and emitter p n junction is base and emitter. So, your recombination will occur at the metal contact at the front surface in the emitter in the everywhere recombination occurs everywhere and your resistive losses your series resistance. Series resistance is a contribution of all the parts of the solar cell and therefore, losses will occur there and researchers and scientists always keep try to minimize the this kind of losses in all kind of solar cells. So, when you refer to the design of cadmium tolderite CIGS copper indium gallium selenide crystalline silicon you minimize try to minimize optical losses recombination losses and the CIGS colossal. The design of solar cell is all about two in two terms you can actually summarize the design the design of solar cell the design of solar cell is all about two things. What are the two things one minimize recombination and maximize absorption. Maximize recombination wherever it is happening maximize absorption wherever wherever possible these are the two main mantras of solar cell design everything everything everything is related to this whatever we will discuss minimize absorption I am sorry minimize recombination maximize absorption. So, these are the just summary of the losses that I have discussed here the losses optical and electrical only can recombination losses.