You can use it any which way you want, but this is the orientation of the solar cell that you should associate as supposed to this horizontal orientation you should associate this vertical orientation with this band diagram. So, then you have it all lined up correctly this is your p side and this is your n side similarly you have the p; p side here and you have the n side here n side here right. So, p and n are there and that lines up with the band diagram that you are seeing here also in terms of scale this is a very expanded band diagram that I am showing you from left to right for sake of clarity this is all going to I mean from p to n is, of course, going to be that extent of that sample that you have we spoke about that being you know just about 0.2 millimetres or 0.5 millimetres or even less those are all those are there wafers that you start with you can even make it much smaller and also this zone in the middle the depletion zone is going to be an extremely tiny zone centred along with this the interface that you see here right. So, this interface that you see here at that interface is where the depletion layer is going to exist. So, you are thinking of looking at a very narrow region. So, please understand keep in mind the orientation of the cell relative to the orientation of this band diagram and the fact that you know dimensions are all exaggerated okay. So, for sake of clarity that’s the reason why it is being exaggerated. So, this is something that you should keep in mind. So, that it doesn’t confuse you that you know; why is it in one way in the other way. So, solar radiation falling on this has created the situation that you have more holes on the n side of the sample and more I am sorry more electrons on the n side of the sample and more holes on the p side of the sample. Now, as I mentioned right at the beginning when I when we spoke about the forward bias of the sample okay forward bias of a p-n junction I told you that we put a battery there to create more electrons on the n side of the sample and more holes on the p side of the sample and that created a forward bias for that p-n junction, but I also told you that that is not the only way you can do that in any manner if you create more electrons on the n side of the sample and more holes on the p side of the sample more relative to what was there before that you know shortly after the junction was formed in in in all those cases you have created a forward bias. So, if you look at a diagram that you have here you have created a situation where the p-n junction is now in forwarding bias. So, all that we discussed the forward bias and reverse bias was not in vain there was a purpose for it. So, this is the purpose, the purpose is that when you use the p-n junction and you subject it to solar radiation it’s a natural position that it arrives at a natural position that it settles into which is what you see on the diagram in front of you is a position which is which corresponds to this junction being in forwarding bias. So, that is something that you have to keep in mind. (Refer Slide Time: 38:54) So, when you use this sample as a p-n junction what as I mentioned there are a few things that we have to keep in mind one is that we would like to minimize the recombination okay. So, recombination, as I said, will more easily happen when you have only a single semiconductor it is much less likely to happen when you have a p-n junction, but it is not 0. So, recombination will happen. It does happen even in a p-n junction. So, recombination simply means you brought in this energy you created some electrons on the n side you created some holes on the p side, hopefully, you can tap this as external electricity, but before you can tap it as external electricity internally itself the p and n are you know cancelling each other out or the or rather the hole and the electron are cancelling each other out. So, that is recombination this recombination occurs much more when you have defects okay. So, when you have defects you have dangling bonds when you have dangling bonds it traps all these electrons and holes and then it creates a situation where they more easily annihilate each other. So, presence of defects is a bad thing in a semiconductor and that’s the specific reason why there is such interest in using single crystalline silicon as the best possible you know if you think within the silicon system single crystal silicon is your; is the distinctly better sample for you to work with for creating a solar cell, but as I mentioned in our earlier class that you know when you will do single crystalline silicon simply because of the process involved in creating it is expensive okay. So, your next bet is your polycrystalline silicon, but clearly, that has grain boundaries and that’s the reason why it is called polycrystalline sample and that has many more defects than single crystalline silicon naturally many more of the electrons are annihilated within this electron-hole pairs are annihilated in that sample and therefore, its effectiveness is less and finally, you have amorphous silicon which is distinctly cheaper than the single crystal or polycrystalline silicon to make and more than that it is also very flexible in the sense you can put it on any surface of any kind of contour and use it and therefore, there is a lot of interest in working with amorphous silica, but by nature again amorphous means those atoms have a lot of dangling bonds and. So, on and there are more defects, of course, we saw how hydrogen can be used to stabilize those defects. Nevertheless it off the three the single-crystalline sample the polycrystalline sample and the amorphous sample the amorphous is the least effective in capturing the solar radiation in a manner that you can continue to use as an external you know power source. So, it is a tradeoff between cost and efficiency okay and with the idea being that you would like to minimize recombination you will never eliminate it, but you would simply want to minimize it okay. So, this is something that we would like to keep in mind ok. (Refer Slide Time: 41:45) So, if you look at this now that you have created this the p-n junction and you have seen how you can you know to separate the charges you can generate electricity I mean you can tap this that now that you have separated the charges that’s basically what it is even in a battery that is what you have got you have got a source of electrons and those electrons will come through the external circuit and it will come to the other side. So, anode-cathode you have and then you have some process by which you know to utilize the thing in the external circuit. So, similarly, with the solar cell, you have a now created situation by putting this p-n junction that you have separated the charges and this charges can flow in the external circuit the one important aspect of a solar cell that we have to keep in mind which we will discuss in greater detail in one of our immediately succeeding classes is the fact that a solar cell is a current source okay as opposed to most of the units that we get for any from any other purpose which happened to be voltage sources. So, when you buy a cell a battery from a shop which is an electrochemical device that’s typically a voltage source whereas, this is typically a current source meaning that you are first generating the current and then the voltage is whatever happens because of the current okay. So, the current is what drives the behaviour of this sample and this is because the charge carriers are being created by the sunlight that is received and. So, essentially you first generate this thing called the photocurrent okay because of the incoming solar radiation. So, when you don’t have any external load. So, you have just put the solar cell out there you just buy the solar cell you put it out in the sun you don’t connect anything to it you just put it out in the sun when you put it out in the sun you have created done exactly what I said which is put more electrons on the n side more holes on the p side which means when you just take a p-n junction or solar cell and put it out in the sun without even putting any external load you have created a forward-biased solar cell okay. You have not connected a battery and then the forward bias you just left it out in the sun you left it out in the sun it became forward-biased because more holes are sitting on the p side more electrons sitting on the n side, not just more holes and electrons sitting there in there is solar radiation coming in and; that means, it is creating, even more, it just continues to create more holes and more electrons and both on both sides of the sample and they are and the electrons are continuing to slide one way the holes are just continuing to slide the other way. So, you are building this up as you build this up you have now got this sample sitting in this is junction sitting in forwarding bias as long as it is in forwarding bias you will have a current going through it corresponding to the characteristic that we just saw here you are now in forwarding bias. So, you will have a current going through that sample this is a current going internally through the sample please keep that in mind we have not connected anything external to the circuit it is internal to that sample you have current going through the sample and it is an internal short circuit okay. So, it says you can think of it that way it is an internal short circuit internally this current is going and that is how the electrons and holes are getting consumed ok. So, so and it is behaving as a forward bias diode. So, when you simply take the solar cell and put it out in the sun then this is the circuit that you are dealing with this that solar energy is coming in and creating this photocurrent that you see the photocurrent is flowing through the circuit internally. So, this is not an external circuit this diode that you see here is sitting internal it is it’s an internal diode inside that sample and through that, the electron holes are getting consumed ok. So, it is itself powering its self. So, it is itself powering a forward bias within itself as opposed to an external battery powering the forward bias. So, this is what happens when you put it out in the sun. (Refer Slide Time: 45:40) Now, on this slide, I would like to show you what happens when you try to take this solar cell which is what you see on your left-hand top corner and then use it to do something useful externally. So, to do that given that you know in ten intent I mean by itself this is the situation it is going to face you when you put it out in the sun over and above this we now try to attach an external load. So, RL is your road load resistor. Okay so, you put this load resistor. So, now what do you have a situation where you are generating more electrons and more holes on the p side more electrons on the n side they have 2 options they can internally do you know the short circuit. So, internal diode they can go and you know complete this short circuit they can also go in the external circuit. So, this is what they can do so. They do both. So, that’s the point they. They end up doing both you have some electrons going through the external load which does the job that you want to do and you have some electrons going through your electrons and holes going through the diode in the forward bias and they are also lost there. So, ideally, you want to minimize what goes through that diode maximize what goes through your external rule that’s the idea that you want to do, but there are some you know restrictions which is what this diagram is about which shows you progressively what are all the different parameters that are involved in this process okay. So, this is what is going on now in addition to this external load even though we have put this external load here by nature of you know just the electronics of what is happening there you are not going to have only the external load okay. So, the current has to flow, it has to flow through that sample and come out. So, there is an internal resistance and that internal resistances exist in any you know even in a battery there is internal resistance. There is always an internal resistance because it is not that there is because the battery is in the current path the solar cell is also in the current path. So, if you complete the circuit; there is a physical dimension to the solar cell the current has to physically flow through that dimension right. So, there is a resistance associated with that. So, that is your internal resistance. So, to speak and that resistance is in series; so, you will always have a series resistance which will add to your load resistance; so, this is something that you cannot escape in this sample; so, in addition to the diode that is sitting here you know you have all these additional parameters which is this series resistance associated load resistance. The one other aspect that we have not accounted for here is that recombination that I spoke to you about earlier okay. So, that recombination is even without any without this forward bias aspect of it that does not involve any biasing aspect of it; it simply means you created electron and hole even before they let’s say even before the electron could go off to you know n side and the hole could go off to the p side it might get annihilated in internally itself. On the p side itself they may get annihilated on the n side itself they may get annihilated, but it’s all got to do with the same solar energy that came in. So, say solar energy created all this thing it created the possibility that you could have all this current, but some of the current got lost within itself right. So, that photocurrent some of it got lost internally because of the internal short circuit or internal recombination. So, to speak and. So, that is what this is ok. So, this is like a shunt resistor. So, it adds to the internal aspect of you know recombination that is going on. So, this is from the forward bias this is from the recombination this is the series resistance that you have and this is the load resistor okay. So, this is how the circuit looks. So, you buy a solar cell and you connect an external load to it. So, you buy a solar cell and you connect a bulb to it, let’s say you connect an led to it. So, then what you have done is you have taken essentially a solar cell and you. So, you only are aware of the solar cell being present here okay. So, you have a p and you have an n and then you have taken this and connected it to a bulb right. So, I am just notionally showing that here. So, you have some bulb here. So, this is what you have done internally this is what is happening if you take the whole thing into account this is what is happening. So, you are you have a lot of processes going on you have the photocurrent that is generated you have the diode operating internally itself the diode is there it is operating in forwarding bias you have a shunt resistor which is representing the recombination events that are happening you have a resistor in series which represents the idea that there is currently going through that solar cell before it even comes out of the circuit and then and then finally, you have your load resistor. So, this is your overall circuit okay. So, these are all the various parameters of how the solar cell behaves when you have incoming radiation. So, the purpose of this class was to look at how the p-n junction and therefore, the solar cell based on the p-n junction how does it behave concerning the incoming solar radiation. So, in conclusion, what the main points that we see here are that the p-n junction stabilizes the electron-hole pair okay. (Refer Slide Time: 50:43) So, this is very critical and that is why it is preferred over simply having a semiconductor and then it the p-n junction is as I mean p-n junction solar cell is a current source because the photocurrent is being generated and therefore, it has to be used accordingly and what that accordingly is we will see how do you maximize the potential know how do you maximize the ability of the solar cell to function for a particular induce or how do you match the induced to function to the characteristics of the solar cell. It’s a little bit tricky. So, we have to understand some parameters associated, then we will understand how that matching is done or even why that matching is required; how do you match some endue to a solar panel it is a bit different from what you would do concerning a battery and that is why it’s of interest. So, so in summary that’s what it is we wanted to see how it functions in the presence of radiation and that is the detail that we looked in considerable detail through this class going forward we will see something more on how it can be utilized what other parameters come into place when you put that solar cell plus end-user together okay. So, with that, we will conclude today’s lass. Thank you. Hello, in the last class we looked at how the p-n junction interacts with incoming radiation. So, we have a p-n junction based solar cell, which is our typical photovoltaic solar cell and then you have incoming radiation, we looked at what happens across the boundary, we looked at you know how the charges are, charge carriers are created on each side of the boundary and the fact that because there is a boundary, because there is a depletion region of a space charge region, and because there is band bending; the negative charges accumulate to one side, the positive charges accumulate to the other side and that is how we have the charge separation and therefore, you have some stabilization of the charges and then you are in a position to tap it for electricity outside. We also understood the fact that this is you know p-n junction, it is functioning as a diode and so, you know if you have the charges appropriately positioned, you have excess positive charges on the p side and excess negative charges on the n side, then you have automatically no forward bias the diode and this does not have to be necessary using a battery in an external circuit, even internally due to incoming solar radiation when you do that, you create a forward-biased p-n junction and therefore, that has some characteristics associated with it. So, in this context, we also looked at you know circuit elements that describe what is happening concerning p-n junction, when you attach a load to it, p-n junction based solar cell when you attach a load to it, what are all the various components that sort of show up in that circuit, and what are they representing, you know how the current flow etcetera we had some diagrams that we put up. So, from there we will take it a little forward here, in this class, we are going to look at the solar cell characteristics and usage; sort of from an external circuit perspective we looked at it only as a p-n junction previously. Now, we will take that I mean fundamentally it is a p-n junction. So, those characteristics are going to be there. So, we are going to try and see what we can understand; in terms of you know given that these are the characteristics of the inherent junction, what are you likely to see in the external circuit and what are some you know ideas associated with that. So, that is the point that we are going to see and that is what I mean by saying solar cell characteristics and usage, in terms of usage also how those characteristics, because that is what the external circuit says. So, we have to understand in terms of using what are the implications. (Refer Slide Time: 02:44) So, our learning objectives are to determine the operational characteristics of a p-n junction based solar cell, which is what as I said is how the solar cell will behave concerning an external circuit. So, once an external circuit is hooked up to it, what is the behaviour that the cell will display towards it, what can the external circuit expect out of it. So, that is one important thing that we are going to look at. And once you understand that, we are also going to look at, using that information using hat understanding, we are going to see what is the best way to use the solar cell. We are going to look at what is the best way to use the solar cell because the solar cell has some characteristics and as you are going to see in this class, if you ignore those characteristics you could use the cell in a very poor way, very ineffective way, and as a result, you will not get the full benefit of the solar cell. So, you have to be conscious of those characteristics and only then you can make the best use of the solar cell and you have to keep that in mind both in terms of you know when you buy the solar cell, what to expect from it when you use the solar cell, what to expect from it, how do you compare solar cells that are available all those things are intricately related to this idea that it has some characteristics and you need to know those characteristics to; characteristics meanings it is behaviour, when how much current it will give at what voltage it will give that is what I am referring to as it is characteristic. So, as the voltage changes, the current changes and so, there is some graph that comes out of it. So, you have to know that, only then using that plot for you know different solar cells you can compare them, you can compare this as you know the function of time as the solar cell ages, and also what is going to happen to that characteristic as the sun moves. So, let us say you have a bright sunny day, you are going to see some behaviour, cloud goes on top of it some period, on top of the solar cell and therefore, blocks the sunlight a little bit. So, is going to be a drop in the intensity of the sunlight. So, then naturally the behaviour of the solar cell is going to change. So, how do you understand that behaviour and therefore, how do you keep that also in mind when you operate the solar cell. So, these are the kinds of things that we are going to look at when I say; what is the best way to use the solar cell? So, these are the operational parameters that we are going to look at in this class. (Refer Slide Time: 04:58) Okay, so, as we already plotted once in one of our earlier classes we looked at this plot, this is the current-voltage characteristic for diode and so, you can see that this is the forward bias and this is the reverse bias. As we discussed in the forward bias we reduce the space charge region or the depletion region and then pretty soon the current starts flowing. So, for up to some voltage you are fighting you know a voltage that was in inbuilt in the system, and then eventually you overcome it and then you start flowing current and so, after some point you see a steady increase in current. So, this is what you see. In the reverse direction, you have a very small reverse saturation current which is almost negligible in the scale, you do not see it here and then from there on you have known you keep building potential in the negative direction, it keeps growing the space charge region and therefore, becoming more and more of I mean resistor or more and more of a blockage to the flow of current, and then eventually this material breaks down and then you have this sort of you know breakdown voltage after which you see very high current, but that is not the mode in which we want to typically operate this diode. So, if you want to; for this class, we are going to look at some equations and the main thing that we need to look at here is this equation that you see up here, which relates the diode current Id to the diode voltage that is shown here. So, diode current to the diode voltage is the relationship. So, this may look a little complicated, but we are not going to derive this if you look at semiconductor textbooks they derive this. Primarily to derive this they are looking at you know how the charge carriers are created, how the charge carriers move from one side to the other and from the other side to this side, the majority charge carriers, minority charge carriers, what role are they playing all of that is looked at and based on that you come up with this idea of what is current when you have some amount of voltage. Now, you will see here there is an I0, this is the reverse saturation current, the small value that you will see somewhere out here, it's the reverse saturation current and you see here some parameter. So, you have q that is the charge on the electron, the Vd is the voltage on the diode. So, that is what we have there and k, of course, is Boltzmann’s constant, T is the absolute temperature. So in fact, we even talk of this you see this kT by q or q by kT, that is listed here, but if you write it as kT by q that is referred to as a thermal voltage ok. So, you have a parameter like that, which we will, we are not deeply interested in that and one constant here gamma, in different books they call it gamma, eta, n and so on, which deals with ideality or non-ideality of the system. Usually, gamma has values between 1 and 2, 1 to 2. So, that is sort of the number that we are looking at for gamma, it is something representing how ideal or non-ideal the system is it relates to all at the discussion that we had on direct bandgap semiconductors, indirect bandgap semiconductors and so on. So, there are some terms out here and this whole exponential part, this is the fact that you have an e power something. So, e power some you know e power something you are having right. So, this e power something comes from the equation for the charge carrier concentration. So, the behaviour of the charge carrier concentration is what results in this e; e power something and that is how we know eventually when you and you have to you need these charge carriers to do the current to you know carry the current so, to speak. And therefore, in the current equation, the sum term corresponding to the charge carriers is going to show up and therefore, you end up having this exponential term that you see out there. So, that is how that exponential term ends up arriving. So, we find that Id is related to, the current in the diode is related to the voltage of this diode using this equation that you have here, where you have an e power some constant. So, you can call you to know q by gamma kT is all constant. All these are constant once you set the temperature, once you set the temperature to be something then q by gamma kT is a constant. So, you essentially have, you can even write this as Id equals I0, e power some constant let us say A Vd minus 1. ok, minus 1. So, A V subscript d. So, A V d is subscript, V subscript d minus 1. So, this is basically what we have, in our subsequent equations, I will still keep you know q by gamma kT available, but you just have to keep in mind that it is simply it does not, it is not as complicated as it looks on the, when once you write all the terms, but because it is all several of them clubbed together as a constant and so, that is just something that you have to keep in mind. So, this is the relationship of Id to the Vd. So, this relationship we will use to understand how the solar cell behaves as you attach some kind of an external circuit to it. (Refer Slide Time: 10:53) So, if you go here, on this page we have a bunch of equations, I will walk you through them. So, there is nothing to worry about. The primary equation is what you saw here. So, let me just clear some of this. So, it is clear to you. So, the primary equation is what you see out there, which is how the Id relates to Vd. So, just keep that in mind and I am going to show that again the next slide and so, even though there are several terms it is just some simplification of a set of terms, which includes this particular term of Id which is the diode current ok. So, now we saw in our previous class the equivalent circuit. So, I will just walk you through the equivalent circuit and then go through these equations. So, we understand what is the various parameters and how they relate to this equivalent circuit. So, on the equivalent circuit, you see this; this is where your solar cell is sitting and that is creating this photocurrent. So, there is a lot of light falling on its photocurrent is being created. So, this is the direction of conventional current. So, you have positive charges heading off that way and this is the, so, this is the same diode in. So, you have positive this side and you have negative this side, and this it is a diode internally as I said it is a diode and so when you build up more positive charges on the p side, and more negative charges on the n side, you have internally forward bias the diode. So, this is that diode that we are talking of internal; internal to the solar cell. So, this is not an external circuit this is internal to the solar cell right. So, this is a forward-biased diode. And so, some amount of current will flow through the forward bias diode, and internally get consumed. We do not want that to happen, but that is what is going to happen. So, some will always happen that way. So, that is going to happen, then we also saw that you know if you generate all these charge carriers, there is always going to be some recombination that is occurring. So, that is internally again you know sort of an internal shunt resistor that we are putting here, which means this you are getting an opportunity for those electrons and holes to recombine within the solar cell. And when it recombines that is again some current that you cannot get in the external circuit because you have lost the charge carrier, you created the charge carrier and so, it shows up as part of a photocurrent that you generated, but you lose it before you get to the external circuit it is consumed internally.