Hello, in the last class we looked at the IV characteristics of a solar cell. In particular, we understood or we recognized the fact that the IV characteristic of a solar cell is a complex relationship it is not a simple relationship, in terms of what current and voltage is seen on the external circuit. And therefore, we recognize the fact that the simply looking at the open circuit potential and then you know looking at the open-circuit voltage and making a judgment on a solar cell is a very incorrect way of going about it. You are likely going to make an incorrect decision based on just the open-circuit voltage. You can have a wide range of solar cells all of which have either the same or very nearly the same open-circuit voltage, but their performance characteristic could be dramatically different. And as a result, a much more useful parameter to follow was the fill factor which recognized you know how much of you know possible power that is available in the solar cell can be tapped from that particular solar cell given its specific iv characteristic. So, this is what we looked at. In an earlier class, we also looked at how the solar the p-n junction is made, how it is you know put together, how do you start and you know create either a single crystalline or a polycrystalline or an amorphous material, how do you do the doping and how do you create this situation where you have a p-n junction which is you know perfect at an atomic level or near-perfect at an atomic level. So, you can do some meaningful electronic characterization across it or you can see is a meaningful electronic characteristic across it. We also saw that you know how we make those single crystals essentially creates cylindrical structures from which we slice out the wafers and as a result, if you look at solar panels, large solar panels you will see some hint of the circular shape in each of those cells. If you may even see the complete you know very distinctly circular shape except for some notches or even otherwise you will see a reasonable hint of that circular shape when you look at that panel based on how it has been made. So, these are some of the things that we have seen. What we will see today, is over and beyond what we have already seen in terms of how you make those single crystals and slice them. Today you will see how you make the solar cell itself given that you have a single crystal let us say you have a wafer and then from there what would you do to create a solar cell after you have already done the doping. So, we are now going to look at the doping, but beyond the doping, we will look at the solar cell construction. (Refer Slide Time: 02:55) In this context, what our learning objectives for this class are the following. We will start actually by looking at the limitations, limitations of a single junction solar cell. So, single-junction solar cells which is what we have discussed for the most of this class, course, as it relates to photovoltaic activity, is we have looked at single-junction solar cells because which means there is a single p-n junction in that solar cell and that is how we are capturing electricity. So, that is what we have, saw through this class. But inherent to the idea that it is a single junction solar cell, it has some specific limitations. So, we will first start by actually looking at those limitations and then we will keep that in our mind, with that in our mind, we will describe how solar cells even if they are single-cell single-junction solar cells how are they constructed, what are some things that we need to keep in mind as we construct that solar cell. So, that is the second thing that we will look at. Then we will have done these two, we will see how we can overcome the limitation of a single junction solar cell, how we can overcome that limitation and the idea that we will be used is this idea called a tandem solar cell and so that is something that we will look at towards the end of this class. So, those are the three things we will look at. What is the limitation of a single junction solar cell? How we put that single-junction solar cell together. And then how do we overcome that limitation? So, these are the three things will come. (Refer Slide Time: 04:23) So, we will begin by looking at the first part. There is something referred to as the Shockley Queisser Limit. So, this is named after the people who studied this extensively and put this you know indicated this in a theoretical sense as to what sort of a limit is there for a single-junction solar cell and that is what is referred to as a Shockley Queisser Limit. And most of the solar cells we tend to see commercially happen to be single-junction solar cells at this point, most of them are and therefore, many of them do subscribe to this limit, I mean in the sense they are not capable of doing better than this limit. So, we will look briefly at that. In this context, there is a terminology we should become familiar with because in the solar energy context they use it a lot, that is what you see here is followed by a number am in this case it says AM 1.5, AM 1.5 is a technique you know specification that is indicated there. The AM stands for air mass. So, it stands for air mass and the full term, there is the air mass coefficient. So, what is this addressing or what is this conveying to us? What is it trying to refer to rather? It is referring to the amount of distance or path that the sunlight has to travel through atmosphere before it reaches us in a relative sense in the sense that it assumes that if it is coming, the shortest path it can take is when the sun is directly above us right. So, the shortest path that the sunlight can take to reach us is when the sun is directly above us which means it goes through the thickness of the atmosphere just straight down the thickness of the atmosphere it comes to us. On the other hand, if we are obliquely situated. So, you have that is the atmosphere and this is the surface of the earth and that let us say that is the atmosphere. So, sunlight that is coming straight down takes the shortest path down and comes here. So, we are here now. So, midday this is how it would be. So, in the same location, in the same location if you want to see the sunlight that some other point of time in the day sunlight would come obliquely and it would travel this distance before it reaches the same location. So, if you compare you will find this distance here is larger than this distance here. Ok, because it is coming at an angle it has to travel a much longer distance through the atmosphere and therefore, sees much more, more of the atmosphere before it reaches that point. So, this is captured by this idea of this air mass coefficient which simply talks of the optical path length relative to the path length vertically upward. Ok, So, optical path length relative to the path length vertically upward. So, AM1 refers to the idea that it is coming straight down on us. So, AM1 means both the path lengths are the same it was straight coming down vertically from vertically upward and that is what we are comparing against. So, that is AM1. So 1.5 refers to some other point of time in the day were roughly one and a half times you know the distance you are travelling before you reach that point, relative to what you travel if you are coming vertically down. Now, it turns out that in most places for much of the studies that are carried out where they are trying to figure out how well some particular solar cell will function, they typically prefer to use AM 1.5 solar radiation. So, they simulate or create AM 1.5 solar radiation which would refer to solar radiation which has travelled one and a half times the thickness of the atmosphere to reach the point. Primarily to a sort of average out for the fact that you are going to get AM 1 only during the middle of the day rest of the day you are not going to get this. So, you are going to get you to know much less much higher numbers am, much higher numbers on either side of the middle of the day. So, an average number of 1.5 is used to you know sort of capture the range that is possible. Also, it is all got to do with the fact that when you look at you know latitudes that are significantly away from the equator, anyway they are not going to get direct overhead sunlight. So, with for them also using AM 1 it is not a very you know the representative way of figuring out how much sunlight they are getting and figuring out how well this solar unit will function in their place right. So, to figure out how much the; how the solar unit will function in their place you have to simulate the sunlight that is arriving at their place and therefore, usually AM1.5 use used as a generic number under which a lot of testing is done. So, that is stands for this air mass coefficient. It is, I mean, I thought we should we become aware of this term, but because when you read solar energy-related literature you will see this term showing up here and there. So, now, returning to our discussion on the Shockley Queisser Limit. Just to go over the sentence that is stated right at the beginning in un-concentrated AM1.5 solar radiation with a bandgap of 1.34 electron volts, 33.4 efficiency is per cent efficiency is obtained. So, this is just a statement, as we discuss this slight you will get a better sense of this statement. The statement simply says in un-concentrated AM 1.5 solar radiation with a bandgap of 1.34 electron volts 33.4 per cent efficiency is obtained. So, what they are trying to convey here is that first of all we are using radiation as it is coming in we are not using reflectors to concentrate the radiation. So, we are setting some standard condition under which we are doing this measurement. So, the standard condition is there is no concentration, no reflection or a no lens, and no such thing is being used to concentrate the sunlight, just ambient sunlight as it comes down it's being used and we are replicating the idea that it is one point coming through 1.5 times the thickness of the atmosphere and so AM1.5 is used. And then this radiation is being captured by a material which has a bandgap of 1.34 electron volts. So, 1.34 electron volts is the bandgap that is being used. If you do that the efficiency you will get is 33.4 per cent. So, 33.4 per cent of the solar radiation that arrives will get converted to electricity and therefore, that is what we are talking off in terms of 33.4 per cent efficiency. So, 1000 watts of a solar energy 1000 watts per meter square of solar energy is arriving on the surface 334 watts is what you will capture as electricity as your usable electricity. So, that is what we are referring to as 33.4 per cent efficiency is obtained. So, the point is this there are a bunch of reasons why this happens and incidentally, this 33.4 per cent is considered the best possible efficiency you can get theoretically, theoretically the best possible efficiency you can get with a single junction solar cell. So, if you have one p-n junction in it and you use that solar cell put it out in the sun under the under these conditions the best possible efficiency you can get is 33.4 per cent. You typically get less than this. So, we typically get less than this. And this is some kind of a theoretical limit based on various phenomena that are occurring within the system. So, that is the point. So, therefore, we have to work with this as being the upper limit. And in fact, what this says is that you know if you plot the efficiency versus the band gap, so I just put an efficiency here as eta and this is the bandgap Eg then you will see some curve which goes like that, something like that you will see a curve that looks like that and this maximum that you see will be at this you know 1.34 electron volts and you know efficiency that will correspond to is this 33.4 per cent. So, on either side of it, you can have materials with a bandgap higher than that you can have materials with a bandgap lower than that. On either side of this, you will have an efficiency that is less than this as per theoretical considerations. So, this is what the Shockley Queisser Limit is. We will now briefly look at why this limit exists, what are all the phenomena that are creating the situation then you end up having this limit. So, we will look at that in just a moment. So, this, by the way, is a curve that is you know you can you know figure this there is a way in which I mean to do this across various materials, they do some calculation they arrive at this value of 1.34 electron volts. The material that we tend to use much of the material that we use in the commercial sense for the solar cells, as we have been discussing through this course the most commonly used material is silicon. So, for silicon, the bandgap is not 1.34 electron volts, but it is exactly 1.1 electron volts. So, 1.1 electron volt is what you have. So, see somewhere here at 1.1 electron volt. So, for 1.1, you will not even get, even the theoretical value will not even be 33.4 per cent you are looking at an only about 32 per cent. So, you are only going to get about 32 per cent efficiency there for the theoretically if you are using silicon as your material and which is what we are going to typically use. So, that is a limit. And if you see practically what is normally being accomplished is only about 24 per cent, 24 per cent efficiency is what is being accomplished. So, it means about three-quarters of the energy that falls on the solar cell is lost. It is not being converted to electricity, only a quarter is being converted to an if electricity a in a single junction solar cell. So, this is the situation that we face. However, I mean, it may on the one hand it may look you know not so impressive you know which means you are only capturing 24 per cent of a whatever is following and in fact, yes from know from a research perspective from a technology perspective people are constantly working on finding ways to increase this efficiency. So, they obviously, you are putting something out there you would like to get as much you know power captured by that unit as you can for the same meter square of that unit that you put out there. So, that efficiency should be as high as possible and people will work towards it. But at the same time, we keep in mind the fact that you know every hour we are receiving enough energy from the sun that covers the entire energy requirements of the planet for a full year right. So, for a full year, whatever humanity needs are being received by us every hour. So, even if let us say you have only 24 per cent efficiency. So, or even let us say 20 per cent efficiency, I will not even say 24, let us say 20 per cent efficiency, we have 20 per cent efficiency, it simply means in 5 hours you will get all the energy that you require to serve the entire you know words needs if you are capturing all the solar energy that is falling on the planet right. So, that is just to give you a sense of perspective. I mean even there are lot of things that you have to keep in mind because, for example, all the energy that comes to the planet is not falling on the land, quite a bit of it is falling in the sea. So, we have to do many other corrective factors in it, but just to give you some sense of you know what are we dealing with. So, what is you know, what we spoke of as a 1 hour for the whole year may become 5 hours. If your account for the fact that you know maybe even much more than half is oceans. So, instead of 5 hours let us say it will take 15 hours, 15 hours to get all the energy we require for the entire year. So, still, you put in all that maybe you are instead looking at a day, in a day you can capture on all the energy that you require for the entire year if you would if it is set up that way. So, that is just a thought to keep in mind. I mean there may be other factors that you and you need to throw in, but you can see the room available for error wherein you still have the ability to serve the needs of the entire planet. So, now, this is some general information that I have given you up here on the idea that you take this, there is this upper limit. So, now, we will just briefly see why this limit comes about. So, we need to see where is it that the solar cell is losing energy once you have incident energy why is it getting lost why it is not all of it being captured. So, to start, to consider that the first thing that you have to keep in mind is that the solar cell is not sitting at absolute 0, it is sitting at room temperature. It is not even sitting at room temperature because sunlight is falling on it typically the solar cell may heat up. So, and various processes are happening inside it, it will tend to heat up. So, you are looking at a solar cell which is typically sitting maybe closer to say 60, 70 degrees centigrade. So, that is the kind of temperature it's sitting at, which means it will lose heat by radiation, as a blackbody it will lose heat by radiation. So, somehow, where is that heat coming from? The heat is coming from whatever came into it right. So, it is not the magically generating this heat and putting it out. It is the heat, part of the heat and energy that reached it is being re-released by it in the form of the radiation corresponding to its temperature being that of a black body right. So, it turns out that about 7 per cent given the temperature it is a 10 whatnot, even at room temperature it is giving out about 7 per cent. So, at least about 7 per cent of the energy that is coming in is lost by the system simply as you know blackbody radiation leaving the system. So, that is the first source of loss. So, which means already you will not capture a 100 per cent, only 93 per cent of what is coming to the cell can now be captured that is the first loss. The second loss is recombination loss, which means of the energy that falls on the solar cell which ends up creating the electron-hole pairs, some of the electron-hole pairs recombine. So, we discussed this earlier, so we have the conduction band and we have the valence band and then you have this incoming solar radiation then that takes an electron from here and pushes it up. So, you end up having an electron up there and here you have the hole right. So, this is what you end up creating. So, you take the electron push it up into the conduction band you create a hole in the valence band. So, if you give it some chance these two can recombine, the electron can fall right back into the hole and you know you will no longer have a charge carrier available you have you know that is called recombination. It has recombined with the hole and no longer you can tap it as electricity. So, this recombination is a statistical process it will happen some amount of recombination will keep happening although you are put in a p-n junction and you are trying to stabilize the electrons and holes were moving them away and doing all that still some amount of recombination will occur, that recombination has been estimated theoretically to be at around 10 per cent. So, 10 per cent of whatever falls on it will undergo recombination. So, now what was, you know maximum possible was 93 per cent just now we saw after you accounted for blackbody radiation after you account for recombination the maximum that is possible is 83 per cent. So, this is what we have. But a very significant amount of the loss that happens in a semiconductor device is associated with this loss referred to as the spectrum loss, spectrum loss. So, what is the spectrum loss? So, we need to have an idea of what is the spectrum loss. Again it has got to do with this band diagram. So, this band diagram is what decides spectrum loss. Let me just put that up here. So, we have a conduction band we have valence band and we have this bandgap Eg. So, this is, sorry, this is a conduction band, this is a valence band. Now, a single junction device, single-junction p-n junction device has a single bandgap which is this Eg that we have. So, this Eg you can link up with a particular frequency. So, we have Eg equals h υ. So, this is an equation of the possible energy that an incoming photon has and the frequency corresponding to that photon and how that matches up with the bandgap. So, the way this system works is, as long as Eg is greater than or equal to, I am sorry as long as the Eg is less than or equal to the h υ, then that frequency is absorbed, right. So, if you have a single junction semiconductor being used as your p-n junction, single p-n junction material being used as your solar cell. Let us say it is a silicon-based cell of bandgap 1.1 electron volts. As long as h υ is greater than 1.1 electron volt, so for silicon if h υ is greater than 1.1 electron volt that a photon is going to get absorbed, but in our solar spectrum, we have a wide range of wavelengths right. So, we have a full range of wavelengths. So, any frequency that is less than the frequency required for h υ to be greater than 1.1. So, any frequency that is less than this does not have sufficient energy. So, therefore, h υ is not less than 1.1 right. So, if you have h υ less than 1.1 for υ such that h υ is less than 1.1 electron volt, the radiation is not going to get absorbed it will just go through, right. So, if you look at the spectrum, the solar spectrum and how much energy is available at frequencies which correspond to this such υ that range of frequencies which are all less than the a value required for h υ equal to 1.1 that entire range of frequencies if you take into account, it turns the turns out that 19 per cent of the incoming radiation can not be in a position to get a be absorbed by the silicon semiconductor. 19 per cent of that radiation will not have enough energy to enable the transition between the valence band in the conduction band and therefore, it will sort of the material will sort of being transparent to it, it will just not participate in the process it will be lost. So, therefore, that you have lost that by having that, by specifying the bandgap you have completely lost that. Now, look at the other extreme. So, that is not even going to participate in the process. So, it is left. Now, let us look at all values of a υ where Eg is, where h υ is greater than Eg. So, so supposing h υ is greater than Eg. So, supposing h υ is such that it is much greater than Eg let us just say it is much greater than Eg. We will consider a case where h υ is much much greater than Eg. Then what happens is the electron that leaves goes to a much higher level. So, you have done a transition, but you have pushed the electron to a much higher level above the lowest available energy level in the conduction band, it has gone to a much much higher level. So, normally once you do that, that is not going to be a stable situation because there are a lot of energy levels below this position which are all sitting vacant right, which is all sitting vacant because that is by definition how the conduction band is being set up most of it is sitting vacant. So, you have pushed an electron very high up because you had that much energy available in the incoming photon. So, what normally happens is it will just come straight down and it will land here. So, it will come back to the, you know sort of the edge of that bandit will just come straight down will come to that location of that a bottom of that conduction band and so that is sort of where it will eventually settle down. So, this extra energy that you have is lost right. So, that extra energy that you pushed into the conduction band is lost, it just is it is no longer useful for us because it just picked it up and then just dropped right back that extra energy it loses its heat. So, this comes off as heat. So, it is lost as heat. So, you end up seeing a situation that even though you have kept a bandgap such that everything with energy greater than the bandgap can be absorbed by the material and it does get absorbed by the material. It turns out that only energy close to the bandgap value is usably available all the extra energy that we have got over and above the bandgap is getting lost as ahead. And again if you look at you know a range of wavelengths available in the solar spectrum if you take whatever corresponds to 1.1 electron volt and then look at all the energies that are available higher than that for all those energies the extra energy is lost. So, essentially you are capturing mostly close to that 1.1 electron volt that is really what you are capturing most of the rest of it you are losing right. And if you look at the spectrum and you analyze the spectrum of how much energy is available in all those wavelengths that are higher, how much extra energy is available and the fact that all that extra energy is lost you find the 33 per cent of excess, a 33 per cent is lost by using frequencies which are higher than what is required for that a bandgap. So, for all frequencies corresponding to values that are greater than that of the band, bandgap required frequency all that energy is lost and that corresponds to a 33 per cent that is lost. So, if you simply look at the 19 per cent that is unabsorbed and 33 per cent excess that is lost because only the close to the bandgap value is going to get used to being captured between the two of them you already have lost 52 per cent. So, the spectrum losses itself just the spectrum losses just the fact that you have one band gap and it cannot absorb wavelengths of no lower energy and wavelengths of higher energy it will waste some of that energy if you just take that into account 52 per cent of the incoming energy is lost ok. So, now you do the total you have lost 52 per cent due to spectrum, spectrum losses, you lost another ten per cent due to the recombination losses because of the electron-hole pair recombining and another seven per cent you have lost due to blackbody radiation. So, this is 52, this is a 62 and if you add all that that comes to 69. So, something like that. So, you are just less than seventy per cent you can I mean based on the exact details that you take into account exact numbers will be slightly different. But if you do, you find that approaching about 70 per cent somewhere between 65 and 70 per cent is the number you will arrive at which represents the total loss that is there from the system simply because of the various phenomena that are occurring based on, you take the exact you know details of what is the temperature what is the material all those things you work on for you get somewhere between 65 and 70. So, that is the loss that you will have. So, the and that, therefore, what you are capturing is just over 30 per cent, so 33. So, that is how they came this they arrived at this number 33.4 per cent is the more you know more precise calculation you arrive at that number, 33.4 per cent is what is usably capture. So, you have about you know 66.6 per cent that is lost. So, 33.4 per cent is all you can capture. So, that is what the Shockley Queisser Limit is about. It conveys to us the idea that even though solar energy is incident on the solar cell there is an upper limit to what can be captured. So, this is a basic limit. It is there inherent to most of the solar cells that you see around if you go see a solar panel anywhere around in your city chances are it is subject to this limit. So, that is something that you can keep in mind, all right. So, now, that we know that there is a limit and it is not a very impressive limit we are sitting at 33.4 per cent let us see how a cell is constructed. (Refer Slide Time: 28:40) So, the starting point is the p-n junction. So, I will say this is the p material and that is the n material that is there. So, this is p and that is n. So, that is what we have. So, you have all, you know you have a, you have solar radiation that is coming in and it penetrates this material comes arrives at the junction and then at the junction you have the electricity, I mean you have the charges getting distributed and then you have the buildup of charges you have electrons getting built up in the n side, holes being built up in the p side and then you can tap, tap it to the external circuit. So, what do we need to tap? So, the first thing we what we need is we need a contact we need to make electrical contact with this material right. So, that is how we will be in a position to tap the electricity. (Refer Slide Time: 29:31) So, the first thing we need is contact and in this case, I have pointed out that we have put material at the bottom which I should call the positive contact. So, some metal I mean you could put say an aluminium, for example, a layer of aluminium at the bottom or anything else you which is a high conducting material and then make a contact to it, make an electrical contact which takes us out to the external circuit. Now, this can be a flat piece, this is a flat surface of saying some of the metal, some metal metallic surface which is flat and then, therefore, you can get electricity out of it. Now, there is a problem in the sense that you cannot put the same flat surface on top. If you put the frame flat surface on top, you will block access to sunlight. So, this junction needs to receive sunlight. So, sunlight should arrive at this material, it should penetrate through the top layer and reach that junction. So, therefore, your top layer should first of all be very thin. So, that you know permits the sunlight to go through and then thin and transparent it should arrive at that junction.
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