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So, therefore, it is important to understand this, that this p-n junction doesn't need to be you know symmetric or this charged space charge region to be symmetric across the junction, it does not have to be and it often is not. And in fact, we may even find it interesting and useful for us to deliberately create a situation where they are not equal in equal degrees on either side of that sample okay. So, this is something that we should keep in mind, I have just shown you an example where the p side the Dopant concentration is less, and the n side the Dopant concentration is more, you can similarly think of a situation where let’s say on the p side the Dopant concentration is high, whereas, on the n side the Dopant concentration is low. So, again here you are going to a much greater depth then you are going here okay. So, to do this you know to do this transfer. So, this is worth remembering and keeping in mind and as necessary we will utilize it. (Refer Slide Time: 40:59). Now, we will also look a little bit on the energy of this system and the various energy levels that are involved here. So, in both these samples, because you are starting with silicon as our starting point, we have the valence band, the top of the valence band that is sitting here and we have the bottom of the conduction band. So, on both sides, I am just showing you notionally some aside that is the p side and an another which is the n side, and we are looking at a situation where we are just about to bring these 2 together to form the junction okay. So, we are going to see what is happening to the energy levels in the system as we start with these 2 independent materials and bring them together to form the junction. We just now we saw what happens conceptually in terms of charge carriers moving on either side, we would like to also understand what is happening concerning these energy levels. So, we have 2 important levels that I have already drawn your attention to the conduction band and the valence band, there as. If the material were intrinsic then the Fermi energy would be this the intrinsic Fermi energy of this silicon sample. So, that intrinsic value is going to be the same on both sides of this boundary, because that is the original value of that material. But now that you have doped the material that is not the Fermi energy, that is of that is operational. So, to speak in the system the energy that level that is operational is this Fermi energy E f subscript p which is the which means it is the Fermi energy on the p side of the sample, and you have here E F n which is the Fermi energy on the n side of the sample. So, these are the 2 values that are of greater interest as I said, this is now this is closer to the Dopant or donor level energy level. So, this is the donor energy-related Fermi energy and this is from the acceptor level. So, that is basically what we have, of course, the vacuum energy level is sitting up there, and I mean it is something that is that basically sets the 0. So, to speak and everything else is below that okay. So, that is the way we would look at it. (Refer Slide Time: 43:05) So, now, let’s say we bring these materials together and what we will see is that the main concept that happens when you do this bring these materials together is that, the Fermi energies on either side begin to line up with each other. Because they represent the highest energy level that the electrons can have and is essentially they are the chemical potential correspond to the chemical potential of the electrons in the system, and therefore, they cannot you cannot have you cannot at equilibrium have a situation where the chemical potential is different in different locations in the sample. That is the driving force there any difference in chemical potential is the driving force for a process to occur and you end up creating in equilibrium only when the chemical potential becomes even across the sample. So, the 2 samples the energy levels in the 2 samples rearrange themselves. So, that you get the situation, where the Fermi energy now is uniform across the sample whereas, previously this Fermi energy was low, and this Fermi energy was high relatively speaking right the E F n was high E F p was low. So, clearly when you move the entire thing on the left-hand side up, and the entire thing on the right-hand side down till the Fermi energies line up everything else will also shift you all your conduction bands will shift valence bands will shift etcetera. So, if you go back here. So, if you again look in isolation to the left-hand side of your sample, you will see the energy corresponding to the conduction band on the p side of the sample, the energy content corresponding to the valence band on the p side of the sample, and the Fermi energy corresponding to the p side. Independently you can again look at conduction band energy level on the n side, valence band energy level on the n side and the Fermi energy level on the n side. But they have now repositioned themselves, I mean on the n side they are all the same, on the p side they are all the same as you saw in the previous plot, but relative to each other they have repositioned themselves such that, the Fermi energy on both sides is the same value is now at the same level ok. So, this creates a situation where the conduction band energy level is forced to now vary over a region that is that I am marking here. So, the conduction band value is a little high on the left-hand side of our image, as you continue from the left to the right as you move from left to right you find that the conduction band energy level is high, and then it steadily and at some point, as it comes close to this junction, it begins to go down and then it reaches the conduction band energy value of the n side of the sample, the same thing about the valence band. It starts at a high value and then as you go towards the right-hand side, it will reach a point close to the junction where it starts sliding down, and when it reaches the value of the valence band energy level of the n-type sample and then it stays at that value through the sample. So, this in-between region that you have, where you have this band energy value changing from one value to the one level to the other level is referred to as the region where the band is bending okay. So, the band is bending in this region, and it is very interesting for us to keep in mind because this is a very key parameter in deciding how the p-n junction behaves when it is used as a for a solar cell application. And incidentally, if you just for notionally if you follow the value of the Fermi energy of your intrinsic sample, then the region where it crosses the Fermi energy of this you know p-type n-type, a combination, that location is essentially where the p-n junction boundary is okay. So, the p-n junction boundary is at that location and that is how you see it, the and that’s how we determine what the location of that p-n junction boundary is fine. So, this is how you look at the energy values as you combine a p-n junction, I have, of course, done some colour coding here just so, you understand how this system is looking when you go from left to right, there is no other significance to the colour-coding. The conduction band value is one uniform value, which moves from a high value to a low value as you go from left to right, valence band energy value also goes from a high value to a low value as you go from left to right, the Fermi energy level remains flat as you go from left to right. So, that is really the only sign of those lines, the colouring is simply to show you the different regions that exist as you go from left to right. (Refer Slide Time: 47:39). Okay, so just a few more points to keep in mind in this space charged region and this relate to how this sample behaves as you utilize it. On the generally the if you look at the charge density that is created as a function of position, you will see if you start from the left-hand side of this image it is charge neutral and therefore, this is you can set this as the 0 levels. So, this is the 0 zero level. So, it is the charge-neutral material and as you move towards the junction as you arrive at the space charge region relatively sharp transition is there and you get this collection of negative charge right. This is a p-type material the holes have left. So, the and electrons have moved in and. So, you have a negative charge there. So, you have a charge buildup which is negative in charge and then as you cross the boundary you have an abrupt increase of charge to the positive side which relates to the fact that you have an n-type material on your left-hand side from which the electrons have left and some holes have moved. So, given this combination you have the charge being positive here, it is negative here, and then again once you cross this boundary here, which is a relatively sharp boundary it again becomes charge neutral. So, this is again charged neutral value okay. So, this is how the charge density varies as you go from left side of the sample to the right side, which you go from the p sample to the n sample n side of the sample. So, now, from this, we will try to understand how the field looks and how the potential looks for this sample. (Refer Slide Time: 49:05) So, if you look at the field the equation that defines the field is simply that you know you E by doux is simply this charge density that you have they're divided by the permittivity right. So, this is dou E by doux is rho by E is what we have. So, we saw in the previous case that you had a negative charge in this region. So, it simply means the slope of the field is going to be negative. So, it starts again with a neutral field, because there is you know neutral material when you arrive at the boundary. After all, the charge density is negative and it’s a constant negative value, the slope is a constant negative value and then, therefore, the slope goes downwards. Okay so, that’s how the slope goes downwards and so, you see this coming down. As you cross the boundary here the charge suddenly becomes positive and therefore, the slope here this rho by E goes from being a negative value to a positive value rho by epsilon goes from negative value to a positive value. So, from this position onwards the slope is positive and it again goes to this boundary here, where it again becomes a flat value and that is how the field varies as you go from left to right. So, you saw how the charge varies as you go from left to right and we have also seen how the field varies as you go from left to right. (Refer Slide Time: 50:20) If you go to the potential of this sample as a function of position, then it relates to the slope of the potential or the partial derivative of potential concerning position is this minus E okay. So, we saw previously here that the E is actually starting at the boundary value at this boundary and then going to steadily more and more negative values right. So, therefore, minus E is going steadily to more positive values and it is going to higher and higher values. So, it is initially it is minus it is E which is this much and then it E becomes this much E becomes. So, it is becoming more and more negative here. So, therefore, minus E is becoming more and more positive, which means the slope of this potential curve is steadily increasing. So, not only is the slope positive it is also steadily increasing, which is what you see here it is a flat region up to here and then it starts becoming a positive slope which is continuously increasing. So, it is continuously increasing right. So, that is how the slope is increasing; if you go back here now the slope reaches one maximum negative value and then starts decreasing in value in negative value this way till it reaches 0 okay. So, it decreases steadily negative values and heads toward 0 therefore, the slope effectively which is a minus E starts at a high positive value and now decreases in slope. So, that is why the slope is continuously decreasing here and then it decreases off to a flat value and then that’s what you see here. So, that is how you get this curve for the potential as you go from the left side of your sample to the right side of your sample. (Refer Slide Time: 51:59) So, if I put all 3 of them together this is what it is, you can see here the negative charge the positive charge and because the negative charge gives you the slope of the E versus a supposition curve, it’s a constant negative slope here and then a constant positive slope here, and then the value is continuously increasing and then continuously decreasing. So, if you take that with a negative sign you have a value that is going to more and more positive values which is what you see here increasing positive value, and then a slope that again decreases in positive value till it levels off. So, this is the curve. So, I will close this description with just a couple of more points here on what would happen when you took this material and used it in a p-n junction. (Refer Slide Time: 53:43) So, as I said you know this you can connect this to some source of energy, and if you can connect the negative to the n side and the positive to the p side, this would be considered forward bias. So, basically what we are doing is, we are pushing more electrons in here and we are pulling them away from this site. So, that is essentially what we are doing. So, when that happens, you are in a position to push more electrons into the boundary into this charged space charge region or the depletion zone and similarly, as you draw electrons away you are sort of pushing more holes into this region. So, therefore, in the forward bias, this is basically what happens your depletion region decreases in size and if you increase the potential from coming from your battery steadily. So, some value you have used previously you make it more and more a higher value, essentially the charge the space charge region will disappear, and you will have a steady flow of electrons e minus that way, you will have a steady flow of holes this way and so, this direction of the flow of holes would be the positive current and. So, that is how the p-n junction will work in the forward bias. (Refer Slide Time: 54:02) If you use the same thing in the reverse bias, you can again you know put the positive and the negative the positive will now be in contact with this n side and the negative is in contact with the p side and so, what your draw doing is you are pushing electrons in here, and you are trying to draw it away from here. So, then if essentially what you are doing is, you are increasing the positive window here and you are increasing the negative window here. So, you are increasing the depletion region or the space charge region. So, from starting from here, it will look something like this. So, you are increasing this region and this greatly resists the flow of current because it is now we know in opposition to the potential that you are trying to force through the system. (Refer Slide Time: 54:44) And therefore, if you look at the current characteristics it will look like this in the forward bias because the depletion zone is continuously decreasing. Very quickly you reach a point where the depletion zone disappears and you have a steady flow of current. In the reverse bias when you go, you are increasing the depletion zone. So, you keep on increasing it till you reach the extent of the sample, and then you are actually breaking through the sample and going down. So, it’s kind of a breakdown voltage and that is how you end up seeing this. So, you have a very you know asymmetric I versus V characteristic for a p-n junction based on whether it is biased for you know forward direction or in the reverse direction, as necessary in our discussion with solar cell we will revisit this concept, but it is sufficient that you are aware that this is the case. (Refer Slide Time: 55:27) So, I will sum up with these conclusions a p-n junction can be formed using appropriately doped materials that are carefully processed. So, that a particularly as I said the grain boundary is important it needs to be well defined, and you should not have any you know to break in that boundary. The charge field and potential depend on the location in a p-n junction we had very interesting you know features on concerning the charge density concerning how the field was and concerning how the potential was. And the p-n junction has very interesting I-V characteristics based on whether it is biased in the forward direction or the reverse direction. And these are all concepts that we utilize as we use p-n junctions for a variety of applications including in the use of in the formation and use of solar cells. So, with this I will conclude for today we will pick it up in our subsequent classes. Thank you. Hello, in the last couple of classes we have looked at the semiconductor and we have also looked at the p-n junction. In these classes, we have been looking at a series of topics associated with the idea of capturing solar energy in the form of you know directly in the form of electricity and essentially using a photovoltaic process to enable that. So, it is in that context that we looked at the semiconductor as well as the p-n junction. When we looked at the semiconductor as an independent entity we looked at its band diagrams, we looked at the origin of those band diagrams, we tried to you know at least briefly look at how the internal structure of the material impacts the band diagram and the behaviour of the electron concerning that internal structure creates that band diagram. We also looked at those flat band diagrams we looked at thee versus k curve and how those you know interactions between e versus k curve and the periodic structure of the elements creates the band diagram for you. Then in the next class that we looked at the p-n junction where we are looking not just at an individual semiconductor, but at the idea that you can take two different semiconductors one which is p doped and one which is n doped and then bring them together at least conceptually, that’s the way we would look at it. And then we try to understand what are some characteristics that happen that that is there for such a junction and possibly what could happen if you bring such a junction together what would be it's you know operational characteristics so to speak.
We also looked at you know how the energy of the p side will look like concerning the n side and that the idea of this Fermi energy being constant and then that there are some band bending features that appear. So, these are all the things that we looked at the last couple of classes it was a little bit intensive from the science side of it we will get back to that and take that forward from our next class. In this class, I wanted to do something which is a little bit more technology-oriented to get a better sense of how this technology comes together because we. Now, know what the semiconductor is, we understand that there is something called a p-n junction, we understand that we wanted to be we want the junction to be good even at an atomic level. So, for example, I indicated to you that it doesn’t help if we take a separately a p material and an n material and then you press them together the contact between those two surfaces is so bad even though visually we don’t realize that it seems like to polish surfaces have been pressed against each other visually we do not realize it. The contact between those two surfaces is so bad that it would perform extremely poorly as the p-n junction. So, we do why we understand the signs of it we also need to acknowledge the practical aspects of it and create this junction in a way that that would work as predicted based on the characteristics we are expecting. So, in this class, we will look at growing the single crystal and making the p-n junction and some associated aspects although the title is on the single crystal will also look at amorphous silicon and we will look at various characteristics associated with it. So, there is a little bit of a technology orientation for this class. We will get back to the science of it in our upcoming classes. (Refer Slide Time: 03:32) So, our learning objectives for this class are to become familiar with the techniques used to make a single crystal as well as amorphous silicon. So, that is our learning objective the main objective. So, there are some specific techniques it’s a good idea to get a sense of what those techniques are, so you see a chip you see it and you know you go see a solar panel you will see a chip there you can also look at you know semiconductor chip which may be there in various places in electronic devices that we use. But where does that come from and what are some challenges in putting that together. So, we will look at it so. So, techniques used to make those single crystals as well as an amorphous version of it and having understood that we will also briefly look at starting from there how you would make a p-n junction. So, these are two things that we will look at as we go through the contents of this class. (Refer Slide Time: 04:27) Okay so, to do this more specifically we will look at two processes one is called the czochralski process and the other is called float zone process. So, these are two processes that are used to create that single crystal. So, they have some you know details associated with them at least briefly we will consider that. So, that you become familiar with the when you see a single crystal you know what is the effort that has gone in towards making it. We will also look at something called zone refining it’s an idea that is used to purify some material and purity is a very critical thing in the semiconductor industry and we will see some you know parameters associated with purity, what kind of level of purity we are talking about and therefore, how challenging it is and therefore, you know you need some special techniques to do it and zone refining is one of them. So, we will talk about it. We will also look at the cut how wafers are cut because finally, initially we when we go through this contents we will see that what is first created is a pretty big object solid object you know it is not anything like what you see in your computer and therefore, that or on the solar panel and therefore, that has to be cut into very fine slices before can be used anywhere. So, that is something we look at. We look at amorphous silicon how that comes about and finally, we will look at how p-n junctions are manufactured. So, this is what we would do. So, as we go over this I think you what you will find as a common thread that goes through this set of topics that we are going to look at in this class is the fact that there is something associated with crystal structure okay. So, particularly we are talking of terms such as a single crystal, we can also talk in terms of a polycrystal and we can talk of an amorphous material, so amorphous material. So, these are three different kinds of material that we can consider. And that’s the thread that runs through, so the same material essentially the same material. So, in this case, for example, we are talking of silicon. Silicon can be made available to us in all these possibilities as a single crystal as a polycrystal and as amorphous material. So, we look we will start first by understanding what is the difference between these and then from that, we will move towards each of these techniques. (Refer Slide Time: 06:57) So, if you see here what you see on your left top corner is what we would refer to as a single crystal right. So, what does that mean? A single crystal means that if you start from one end of the material. You will see a crystal in order, so you are going to see you know from the start from this end and you move in some direction let’s say you move some distance a and you arrive at one plane a crystallographic plane. Then if you continue another you will get you will again arrive at the plane one more you will arrive at the plane and so on and this process will continue till the end of the crystal. So, you can do this and you arrive at the end right. So, all the way to the end from one end, one point, one starting point in the crystal to the other end of the crystal the atomic planes will be in perfect order. So, when I say from one end to the other I am talking of from one end to the other of an object okay an object that you can hold in your hand. So, some big object that that is sitting in your hand which you can hold and lift with your hand from one end of the object to the other end of the object the atoms are in perfect alignment. So, they are perfectly aligned from one end to the other. So, therefore, if you see one orientation of atoms on one end you will see the same orientation in the other end. So, something like that is referred to as a single crystal and that is not easy to manufacture. It takes a lot of effort to get as that kind of a sample where you can have this big block of materials sitting in your hands where this perfect atomic order from this end to the other end. What we are more likely to see are more along the lines of b and c okay. So, both of these are polycrystalline materials material. So, this is also polycrystalline okay. So, both of these are polycrystalline. So, now, what you see here, for example, are boundaries. So, this is a boundary, this is also a boundary here, you can see some specific boundaries here I am just tracing them out for you. So, it is easy to see. So, these are boundaries. So, now, what it means is if you start from one end of the crystal. So, first of all even the same this end of the crystal itself if you go from the bottom of the crystal to the top of the crystal you don’t see the same order. So, the top of the crystal you see these planes vertically down let’s assume we are looking at the same plane you see those planes vertically down and the top of the crystal, but those planes happen to be at an incline and this end of the crystal bottom end of the crystal which was not true on the in the example that we saw here right. So so, as you start itself when you go from the bottom of that sample to the top of the sample on your left-hand side of the sample let’s say the order is not maintained and further as you move into the crystal as you move away from that end as you approach this end you will find at various locations such as this the orientation will change. So, in this example, for example, it is just changing in one place. So, it changes here as you go from the left to the right following the path on the bottom of your sample, but that can vary from sample to sample you may have had 3 divisions in the middle you might have had 100 divisions in the middle, so on. So, this idea that you have crystalline order only up to a certain location. So, for example, this location and then after that there is a breakdown of order at least at that boundary at this boundary area there is some breakdown of order. So, there is some breakdown of order there and then again order starts in this in this location. So, you see some crystalline order in that location again order breaks down in this region here and then once again you have crystalline order. So, this idea that you have pieces of crystalline order with boundaries in between them is then referred to as a polycrystalline situation okay. So, this sample is polycrystalline. It has many crystals that are why polycrystals which are now, distributed across the sample. So, what’s the difference between these two? The main difference is the crystal size. So, this is a small crystal size this is a large crystal size. So, that’s the difference between these two samples both are polycrystalline. So, in both of them you as you go from one end to the other you see so many boundaries, so many boundaries here. So, for example, this is a boundary that is, so this region is a crystal a neighbouring region has a crystal oriented differently and so on. I mean it’s just a pattern that I have put that, but it could be in any shape it does not have it doesn’t even have to be so uniform in size. So, this happens to be a uniform grain size crystal size sample, but this is not. So, b is not so, where a c happens to be a very uniformly sized crystal sized sample. So, that is just a variation. So, you can have a small crystal size you can have large crystal etcetera and you can notice that the 4 samples that are on screen at least for visual examination are essentially the same size. So, you can think of physically itself samples of the size that you are holding in your hand which are having all these characteristics. The final sample that we have here is what I have marked as d which is a sample which is having the complete disorder as you start from one end of the sample and you approach the other end of the sample. So, as you go from one end of the sample to the other end of the sample there is no sustained crystal to any degree that you can you know seriously measure. So, it is an amorphous sample. So it’s an amorphous sample there is no crystalline order. So, you start from an atom you head off in some direction you may find another atom. If you head continues in the same direction at the same distance there is a chance that you will not find the next atom you have to go a little bit to your right or a little bit to the left to find the third atom then from that again you move forward in that same direction again you may have to go a little to the right or a little to the left to get to the fourth atom and so on. So, it is just in a disordered way those atoms are sitting and so that’s an amorphous sample.