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Hello, in the past few classes, we have been looking at the semiconductor the p-n junction, various characteristics of the kinds of you know materials that are involved, what happens when you put them together? What parameters we have to be cautious about and so on and we also looked at how the material is even you know manufactured; how do you start with essentially sand and arrive at something that is single crystal silicon or polycrystalline silicon or even amorphous silicon and then the idea that you know you take this and then you make your p-n junction and so that is something that we seem to think was necessary. So, what we would like to do today is to look at this p-n junction a bit more and to see how this junction you know responds to the arrival of radiation. So, in the end, we are going to use a p-n junction as a solar cell. So, what we will see today is how does it function in the context of solar radiation incident on it and therefore, you know how why is it that you know you need that p-n junction for it to work as a solar cell ok. So so, that’s the idea that we will pursue through this class. (Refer Slide Time: 01:26) So, we are going to look at the learning in terms of learning objectives we are going to describe the interaction of a p-n junction with radiation. So, a p-n junction how does it interact with radiation once radiation is incident on it what are the phenomena that are occurring in it and what’s the consequence of that phenomenon and in that context, we would like to explain the functioning of a p-n junction solar cell. So, that’s the basic idea that we would like to pursue through this class ok. (Refer Slide Time: 01:56) So, we did some work on this a p-n junction understanding how it behaves, I will just highlight 1 or 2 key aspects of it specific aspects of it because that is how we will be able to continue with the description we will see in this class. So, we spoke about the idea that once you make the p-n junction, there is a transfer of charge from one side to the other and from the other side to this side and you end up creating this depletion region or the space charge region and then that you can do a forward bias of it. So, once you create this p-n junction, it has certain characteristics in terms when I say characteristics, it in terms of how its current and voltage will change depending on what conditions it is placed in. This is you can think of it as you know information that you can learn independently, but and in often that is how it is taught often that is how you see the p-n junction and its IV characteristics, etcetera, but it is not just an independent you know scientific curiosity kind of thing on what a p-n junction will do, but those characteristics are critical in explaining how it functions as a solar cell and that is why we are you know spending some time trying to understand those characteristics so. You do have this exchange of charges because of how the energy is lined up and you create this space charge region or depletion region which primarily means that on each side of the junction whatever was the majority carrier is missing for a small distance ok. So, it is exaggerated as a little larger distance here and similarly a larger distance here, but you are looking at a very thin region across the junction where the majority carrier. So, in this, in this case, we have the n side here and we have the p side here in keeping with the p-n named p-n junction, I am most of my diagrams are with I am I have been trying to keep it consistent with p on our left side and n on the right side. So, it is easier for you to follow. So, on the n side, the majority carrier would have been an electron on the p side, the majority carrier would have been a hole when you create this junction because the holes don’t see enough holes on the n side, they drift into the; I mean, they diffuse into the n side and the electrons do not see enough electrons on the p side. So, they diffuse into the p side. So, that’s basically what you are seeing and in fact, as I said once in one of our idea classes when we looked at the metal the electron can actually roam all over the metal because you have the same you know ionic core everywhere and therefore, it can roam everywhere, without any restriction. Whereas, in this kind of a situation where you have a p-n junction the electrons as they roam into the p side are seeing a different you know background condition. The holes which are moving to the n side are seeing a different background condition. So, they cannot indefinitely move they are charged. So, the region they move into, it is no longer charge-neutral they are creating they are building up a charge in that area, it’s no longer charge-neutral it was charge-neutral, to begin with, but since they are arriving at that region with the with a different charge. They are changing the charge neutrality of the region and that is why this is called space a space charge region. This entire region is called a space charge region because it is building up a charge there and that’s the reason why you know the holes don’t diffuse all the way across into the n side and the electrons don’t diffuse across to the p side and that is how this differs from; you know; this being a metallic sample or even a junction between 2 metals. So, even there you will have some buildup, but that’s maybe that’s not the that also has some aspects associated with it, but let’s say 2 you know 2 pieces of the same metal which are put together then you can have you know essentially the electrons free be roaming around. So, this is how the buildup is there and having put this together you can attach a battery to it. So, now, clearly, because we have put a charge on either side of it I mean not put it has automatically redistributed, it’s charge and charged and created this space charge region. So, there is an inbuilt potential that has been created you can put a potential outside of the sample which can you know counteract this potential or build on this potential okay. So, this potential that builds inside this sample or the field which would be from the positive to the negative. So, thee field would be this way. So, this potential is preventing further flow of charge right. So, you can put external potential to this sample which either assists this potential in which case, it makes it even more difficult for the charge to get transferred across this junction or it counteracts this potential and makes this potential essentially ineffective or less effective and then eventually charge can go across it. So, we basically can put what are we what we would call as the forward bias which means we are putting the positive side of the battery external battery in contact with the p side of the sample and the negative side of the battery in contact with the n side of the sample right. So, we are pushing more electrons into the n side and we are drawing away electrons from the p side which means effectively like we are pushing more holes into the p side. So, as we discussed what this does is that. (Refer Slide Time: 06:59) It reduces the space charge region. (Refer Slide Time: 07:02) So, it starts pushing more holes this way it starts pushing more electrons this way. So, that therefore, the space charge region begins to decrease and once you cross the potential that corresponds to this space charge region, essentially, you will have current steadily flowing through this p-n junction and in the context that we traditionally associate current the conventional current is associated with a positive charge, this is the direction of flow of the current of conventional current the direction of the flow of the holes is the kind of direction of the flow of the conventional current electrons are flowing the opposite way. So, you can think of it this way; electrons are coming to this site and they are getting consumed by the holes coming from the other side and hole essentially means it means this sample is charge neutral, but the bonds can accept one additional electron right. So, that is what we mean by saying that there is a hole there and so, this electron that is coming from the n side as it crosses across the boundary and goes into the p side it is going into that location where that you know one additional bonding electron was not available. So, it’s readily accepting that electron. So, the electrons are steadily flowing from your right to left and and and and because there are as; it sits in that location one more hole arrives one more electron arrives and it keeps occupying a with locations and therefore, you can think of it as a current that is flowing okay. So, one way they describe it is that they are all coming and getting annihilated at the junction the other ways you can think that there is a steady flow of electrons and which is being compensated by electrons being drawn away there and therefore, being replaced by holes again and again. So, every time you put an electron into the p side, you are also removing an electron from this side, right. So, the electron is entering from the right side and it is exiting out on the left side of our sample you can think of it that way. So, if you remove an electron it is the same as having added a hole there. So, you were short of you know one one bonding electron was missing there and one electron crossed over from the n side and occupied that site and then you took that electron to the left hand and took it off the circuit and therefore, you have essentially reintroduced that hole that place. So, that’s why that’s the description you keep hearing of holes coming from the left electrons coming from the right and they are basically; you know annihilating each other in the junction, it does not mean the matter is being destroyed or some you know some energies some nuclear activity is going on there that are not what is happening it is just that this is the description that captures the activities that are happening there, but you can also think of it you know, if you want to not to confuse yourself you can think of it as an electron that is going through and through and through as it crosses the junction it occupies the location that was available where there was a hole which means that hole now disappeared that’s basically what we mean. So, that hole is no longer there because an electron is now sitting there. But you slowly draw the electron away to your left and there you removed that electron from that region you have again brought back that hole that missing bonding electron is still there. So, you have brought a whole. So, each time the electron hops from one hole to the other hole it is the same as that hole having hopped this way. So, you have one hole; one electron; electron goes this way, it has cleared this location on your right-hand side. So, you have let’s say one hole here which I put us a positive hand I put an electron here e minus. So, if this, switches here then this location now has the electron and this region which it left goes back to being a hole. So, that’s essentially what it means. So, every time an electron moves from left to right it is the same as the hole moving from right to I am sorry from every time an electron moves from our right to left it is the same as the hole moving from our left to right. So, so that’s what we mean and. So, you can think of this circuit that way and also understand what is going on. So, anyway; so, this is what is happening if you forward bias the sample and so, this junction will disappear and you will have a steady flow of current. So, that’s the idea of this p-n junction in forwarding bias, please note that when I said forward bias to show that as an experiment we put this battery here. So, we put this battery in this external circuit and we know deliberately connected the positive to the p side than negative to the n side. So, this is what we did to demonstrate this process to demonstrate this you know the characteristic of this p-n junction. But what has happened, in reality, what has happened is, we have pushed electrons to one side of the p-n junction and we have pushed holes to the other side of the. So, if you want to call it h plus as the hole with that charge and we have pushed that on the p side of the sample. So, or we are drawing electrons out that side. So, therefore, you are pushing holes into this side. So, you can put it that way. So, the point that I am trying to make is that when we say something is in forwarding bias when we say p-n junction is in forwarding bias it means we have electrons additional electrons from an external circuit or anywhere additional electrons appearing on the n side additional holes appearing on the p side okay. So, so anytime you create a situation where you know initially you have a p-n junction which is sitting there and there and because it this is the junction is formed you had the space charge region being developed you had this depletion region being developed and that happened as soon as you made your p-n junction right. So, that is your starting point from this starting point if you do anything to this sample which creates more electrons on the n side and more holes on the p side you have essentially created a situation which is similar to what you are seeing on your screen which is you have created a forward bias okay. So, that’s the point I wanted to keep in mind. So, it doesn’t have to be through a battery in this case we are showing this example by putting a battery outside and doing the connection, but that is not necessary you create a situation where there are more electrons sitting on the n side and more holes sitting on the p side, then I say more concerning what we are present when you initially found the junction when you do more you have created a situation which is similar to a forward bias and therefore, at that point the p-n junction will show you this behaviour that you just saw of what it is going to do during a forward bias okay. So, that is something you keep in mind and we will get back to it. So, as we saw that you know because of the space charge region you will get this negative charge here you will get this positive charge on the I mean the n side of the sample, this is the p side as we said this is charge neutral here. So, charge neutral. So, negative and positive and because of this relationship, we find that e has you know linearly decreasing characteristic from where this region begins and goes to a fairly low value some appropriately low value here and then since the slope suddenly becomes positive here the rho becomes positive here this is rho. So, negative rho becomes suddenly positive rho and therefore, in your equation, the slope is now suddenly positive. This slope is now suddenly positive and therefore, from this lower value, the slope keeps increasing and then you arrive at this neutral value where suddenly again the rho is 0 because then once the rho is 0, the slope rho by e rho by epsilon becomes 0. So, here rho by epsilon is positive, rho by epsilon negative rho by epsilon 0 ok. So, because it is 0 you have a flat line where it is negative, so, you have a negative slope it is positive. So, you have a positive slope it says its 0. So, again you have a flat line here. So, this is the behaviour we see and then a correspondingly if you look at the potential as you go from left to right you find that know the if you look at this relationship here then you see that the slope is essentially related to minus e and e itself is 0 here. So, e is 0 here and then e is decreasing ok. So, if e is decreasing minus e is increasing and minus e is increasing means the slope you v by doux is increasing okay. So, it is continuously increasing that’s what you see the slope is steadily increasing right. So, the slope is continuing to increase and then you cross this origin. So, you suddenly see here e is increasing implies minus e is decreasing okay. So, minus e is decreasing because minus e is decreasing the slope having reached some value now starts decreasing. So, the slope starts decreasing. So, it starts decreasing like this and then once you reach this region again once you reach this flat region corresponding to this point here e has become 0 okay and so, once e is equal to 0 the slope is 0 and you again get a flat line. So, this is you know the behaviour of this junction in its static state as soon as it is being built or once it is in that kind of a stable situation. So, this is the characteristic and we saw what would happen if you stake this and then you put you know forward bias to it. (Refer Slide Time: 16:26) And again if you take the same thing and you do a reverse bias which means you are now taking the negative side and I am sorry the positive side and connecting that to the n side and you are taking the negative potential here and connecting that to the p side okay as supposed to the opposite that you saw here we are doing the opposite here we are taking the positive and connecting to the n side whereas, previously, you had the positive connecting to the p side and here you are taking the and previously, you had negative connecting to the n side you now have the negative connecting to the p side. So, what is happening, you are pushing more electrons in here and you are pulling out electrons from here. So, when you pull out an electron you leave behind a bond that is unsaturated okay. So, if I essentially you have added a whole. So, that’s would basically what happens. So, you are increasing the number of holes in the n side of the sample you are decreasing the number of holes on the p side of the sample because you pushing electrons in you are pushing electrons in it will go it will travel through and through and through and it will reach a point where it till it hits some other electron and it is not able to go forward it will go it will continue to go there and it will because you are pushing it and it will go there and it will occupy that site which was a hole. So, you are increasing the number of electrons on the p side and you are increasing the number of holes on the n side naturally you can expect that the number of you knows this positive region will now increase a little bit and the region that was negative here will increase a little bit. So, that is called reverse bias and. So, that’s essentially what you see here. (Refer Slide Time: 17:51)So, this is what will happen when you have incoming radiation at that point I indicated to you that when you do this you are creating a situation where the electron and hole are in physical proximity. So, in the sense that this hole in the electron is essentially physically in the same location, they are just the electron is simply moved up in energy to a value across the bandgap. So, if you give it enough time the electron will simply decade on and it will come back down and it will occupy that spot that it vacated and it will the material will go back to being its old self before the radiation came to it. So, therefore, when you simply take a semiconductor even though we say you know semiconductor has a band gap and then, therefore, it can absorb some radiation and all that stuff even though we say that if you simply take a sample of a semiconductor and keep it out in the sun you are not going to be able to capture any electricity out of it it will do the transitions, but the transitions will simply reverse and at the end of it, you will not be able to capture any electricity. So, we have to do something about you know ensuring that you are decreasing the chances that the electron can fall back into this hole that it created okay and to do that we essentially have to move the electron to some other location move the hole away to some other location and in that process, you know physically it is not any longer that easy for them to just like that collapse into each other; we don’t drop that to 0 percentage, but it decreases it dramatically. So, this is called charge separation you have to chop a separate the charge and stabilize it. So, it has to get just separated from these locations and only then, it will get stabilized. So, that’s the point we would like to understand with the perspective of this diagram. So, we looked at it as you know again the pain same thing p-n junction. So, this is p side this is n side. So, for the n side; for both these samples assuming that we started with the same semiconducting material their original intrinsic Fermi energy EFi. So, that is what I am calling as E subscript F for Fermi energy and subscript I saying that it is the intrinsic Fermi energy is that is the energy Fermi energy of that material if it had got no dopants was this particular value. So, that is the value that you see here. So, that is the Fermi energy value that you have. Now, because the on the p side you put in some dopants, you created some acceptor levels which were here. So, those acceptor levels were available here which made it easy for electrons to go to those acceptor levels and similarly on the n side, you put in some donor levels. So, donor levels showed up here and. So, that again became easy for the material to you know perform I mean put gate charge carriers into the system. So, now given the way the Fermi energy is defined essentially the Fermi energy of the n side of the sample moves to this donor level and the Fermi energy on the p side of the sample moves to this acceptor okay and so they. So, on the p side the Fermi energy came down on the n side the Fermi energy went up and when you put these samples in I mean we will connect the 2 samples because of equilibrium requirements for equilibrium these 2 energy levels line up they line up with each other okay because there and that becomes the defining you know parameter for that sample the fact that the Fermi energy lines up across that sample you took an n sample and a p sample and you join them together and the 2 of them now understand that they are you know in contact with each other their Fermi energies level off. So, that’s how the energy remains constant. So, it’s just basically got to do with energy minimization. So, it minimizes the energy and this is how they end up minimizing the energy the Fermi energy and the fact that the chemical potential on either side should be the same and this is how it ends up being in contact okay. So, this is the situation we will have. (Refer Slide Time: 24:56) And on this sample; let’s say we have incoming solar radiation. So, we have incoming solar radiation. So, in some ways you can still think of it as you know a transition occurs you create holes and electrons holes on the; you know valence band and electrons on the conduction band. So, that’s basically what I am showing you here there is incoming solar radiation this radiation. So, this is also incoming solar radiation right. So, incoming solar radiation on both sides of this junction and you create these holes down here you create these electrons appear holes down here electrons appear ok. So, in this situation, we have created. Now we see an interesting situation the interesting situation we see is that we have holes sitting a 2 different levels the Fermi energy is what levelled out Fermi energy is flat, but the band structure is not flat Fermi energy is flat across the sample band structure is not flat the conduction energy I mean the conduction band the lowest energy level of the conduction band of the n side is sitting here the lowest energy of the conduction band or the p side is sitting there. So, the lowest energy level of the conduction band is not the same if you go from left to right okay. So, the conduction energy band lowest available energy level is high on the left side it is low on the right side okay. So, that is the idea we have. So, this is called band bending the idea that in the middle you have this is a situation where the band is bending from one level to another level right. So, this is a band bending that has happened. So, these 2 are not on the same level similarly you look at the no valence band energy level. So, the valence band energy level on these. So, this is the highest occupied energy level on the I mean if I set aside you know the impurity levels a concerning the intrinsic material this is the highest occupied energy level on the n side of the sample and this is the highest occupied energy level on the p side of the sample of the valence band. So, they are also not at the same level the highest occupied energy level on the valence band on the p side is high the highest occupied energy level on the way of the valence band on the n side is low and. So, it has to bend down and go it starts off bends down and goes. So, so that is basically what we have now given the nature of the electrons and the holes the electrons are negatively charged and in the context of this energy diagram will tend to go to the lowest negative value lowest energy level that they can find. So, they will naturally slide towards the lowest energy level they can find. So, this they tend to slide down and the holes on the other hand given that they are positive charge and essentially they represent an absence of electrons will try to move to a high level so that the electrons can go to a lower level okay. So, the electrons will like in this diagram is set up concerning electrons fundamentally. So, as the electron and a hole moving up in energy level are essentially equivalent of an electron moving down in energy level right. So, if all the electrons are moving down you can think of the holes as moving up. So, therefore, in this situation when you have created electrons at 2 different energy levels and you also created holes at 2 different energy levels the holes try to consolidate. So, they all the holes try together and consolidate such that they are holding the highest position possible all the electrons tend to consolidate get together and consolidate such that they are holding the lowest position possible. So, what this means is the electrons that are out here will try to come to this site and the elect holes that are out there will tend to try to go that side essentially trying to minimize their energy this is basically what they are trying to do to minimize the energy electrons on which were holding a higher energy level will slide downwards and join electrons which are holding a lower energy level and holes which were holding this lower energy level here they are not necessarily going to a higher energy level, but they are you know analogues to electrons sliding down. So, holes going upwards are the same as electrons coming downwards. So, these electrons will bubble up. So, to speak they will bubble upwards whereas, the holes will bubble upwards electrons will slide downwards. So, this is basically what you are going to see and that is how the sample now behaves okay. So, you initially formed p-n junction and you already had a transfer of charge okay from one side to the other and that is what created your space charge region etcetera now over and above that you put solar radiation on it and you created more electrons and more holes transition occurring on all sides and then these electrons gather together in one location the holes gather together in another location driven by the ideas that I have shown you in this slide. So, once this happens these diagram will evolve. So, if you want to look at it step by step once this is this is the step of the radiation just having come and having created this electron holes pair hole pairs. So, once they consolidate these electrons here would have gone down to this location and the holes here would have gone up. So, once you do that you will have a situation which looks like this. (Refer Slide Time: 30:16) Those electrons which were sitting here moved down and the holes that were sitting here moved up. So, we have this situation where the electrons have gone one side and the holes have gone the other side. So, now, what do we have we have an interesting situation again as I said if you look to go back to what we had previously just put down we had one semiconductor and we had this transition. So, you had a hole here and you had an electron there, right, a hole here and an electron there and this transition occurred electron in the conduction band this is the valence band at that time I told you that you know if you do this there is an equal chance that the hole I mean the electron drop right back because the hole and the electron are sitting right there and they can recombine fine. Now, what do we have we have a situation where you did the transition you created a bunch of electrons in the conduction band and created a bunch of holes in the valence band, but they are no longer in the same location the holes all slid off to this side the electrons all slid off to this side. So, you have greatly dramatically reduced the possibility that these electrons which are now on the n side of the sample will be able to combine with the holes that are sitting on the p side of the sample and annihilate each other okay. So, you have greatly reduced this chance or at least it is not an immediate activity, it is not like immediately this is going to happen you have given them a chance to stabilize okay and so, that is the key function that the p-n junction accomplishes ok. So, that is the key step that the p-n junction accomplishes which an independent semiconductor such as what you see here is not able to accomplish okay.

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