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Module 1: Solar Radiator and Semiconductors

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In the last class, we looked at the semiconductor in a sort of in isolation, in particular, we try to understand quite a bit about the band diagram. In particular, I told you that we have something called the flat band diagram, and on most occasions that is adequate for us, it adequately explains to us how the behaviour of the semiconductor happens and what are you know steps that are involved in that process etcetera; these are all reasonably well captured by the flat band diagram, and that’s the kind of notation that you most commonly see. But at the same time, I also told you that if you go dwell deeper into the subject, you understand that that flat band diagram comes from something more fundamental which is thee versus k diagram, which tells you the kinds of energy that the electron can have as a function of you know wave vectors that it can have, and also we looked at you know how does that e versus k relationship interact with the periodic structure of the material and the fact that you see this band structure appearing because of this interaction of thee versus k of the electrons, with the periodic structure of that material. So, this interaction is what creates a situation where there is diffraction occurring at specific locations, and due to diffraction, there are some standing waves in those locations that creates a situation that is unfavourable and creates a gap in the energy. So, this distortion of thee versus k creates some values of energy, that are not allowed for the electron and that is what shows up as our bandgap that we see. And that is how the band structure develops and that’s how the flat band diagram relates to thee versus k diagram and the periodic structure of the matter. So, this is the background that we had, in this class, we will build on it we will again start a little bit with these isolated semiconductors and then particularly we will focus on the p-n junction which is this particular concept that comes that can be put together when you put together specific type of semiconductors. (Refer Slide Time: 02:20) So, that is the focus of this class. So, in particular, our learning objectives for this class are to describe some material features associated with this p-n junction as well as the characteristics of the p-n junction. So, that is something that we will see running through the class at different points in time you will see references to this, and we will also look at trying to explain the functioning of the p-n junction. So, these are the 2 major points that we will look at, of course, there is going to be a lot of detail as we go along, but this is essentially what we are trying to go over in this class. (Refer Slide Time: 02:53) Okay, so we will begin again with the intrinsic semiconductor because that is it is the right kind of stage for what we are trying to discuss. So, as you can see on your screen there is an empty conduction band, and there is a filled valence band and so, that is the starting point for an intrinsic semiconductor; by definition, an intrinsic semiconductor means that it is pure it doesn’t have any impurity in it, and most specifically it’s conductivity or charge carrier concentration depends only on temperature. What we mean by that is you have to have enough energy in the form of which is being provided in this case in the form of temperature, and at that point, you will have some transitions from the filled valence band to the empty conduction band. And it is only these temperature-induced transitions, that create the charge carriers in the conduction band ok as well as the empty holes that remain in the valence band. So, that combination that gets created happens only as a direct result of the energy being provided into the system in the form of thermal energy. There is nothing else that is contributing to this charge carrier process. So, if you keep it at say 0 Kelvin or very close to 0 Kelvin, there will be no charge carriers and nothing you will not be able to see any significant electrical property from this material. So, charge carrier concentration depends only on temperature and as a result, conductivity which depends first of all on the availability of charge carriers also it depends only on temperature okay. So, if there are no charge carriers there is going to be no conductivity. So, the first requirement for conductivity you have to have something that you can carry the charge, that is the thing that you are measuring and then referring to it as conductivity. So, if there are no charge carriers there is no conductivity, if you increase the number of charge carriers everything else being the same conductivity will go up. So, if the charge carrier concentration depends on temperature, conductivity will also depend on temperature. More specifically if the charge carrier concentration increases with temperature conductivity increases with temperature okay. So in fact, that’s also a very important characteristic of semiconductor material as opposed to say a metallic system. So, we will talk about that very briefly as we proceed forward. So, examples of these intrinsic semiconductors are typically group 4 A elements. So, silicon and germanium are commonly coated as these intrinsic semiconductors. So, they can be you can be intrinsic, the semiconductor can be intrinsic both in the form of an elemental version as well as a compound version. So, the elemental version is this idea that we can use silicon or we can use germanium for example, and they would have these specific band gaps of a 1.1 electron volt or 0.7 electron volts. But you could also have compound semiconductors where you have 2 elements, but they are in equimolar ratio. So, it is not a doping kind of a situation, you have a group 3 A and a group 5 A element. If you combine the 2 of them, again on balance they behave as though they were you know in terms of the number of electrons that are available in the system and so on, it looks somewhat analogous to a group 4 A element alone being present there and so, these are referred to as 3-5 compounds. So, that is the other way in which you can arrive at an intrinsic semiconductor, you could also do group 2 B and group 4 A combinations. So, an example would be cadmium sulfide or zinc telluride, and that would be referred to I mean as a group as a 2 6 compound. Group 2 b and group 6 A. So, this combination is referred to as a 2 6 compound. Notionally you can consider even going further in the periodic table away from group 4 A, but then increasingly you are increasing the chances that the bond formed will be an ionic bond, because there is going to be that much difference in the electron affinity and electronegativity of the 2 elements involved. So, generally, we are looking at only at these group 4 A as elemental semi intrinsic semiconductors or 3 5 compounds or 2 6 compounds as elemental as compound intrinsic semiconductors. So, this is the general set of characteristics associated with an intrinsic semiconductor. Now if you take an intrinsic semiconductor and to that, you do add something called a Dopant. So, that you create something called an extrinsic semiconductor. (Refer Slide Time: 07:15) So, that is what we are discussing here, we can again have that in 2 forms we have something called as a p-type extrinsic semiconductor, in which case you create this is arrived right by you know starting with a group 4 A element. So, for example, silicon, silicon is the most commonly used element in this case, because you already have an industry which is using silicon-based single crystals, which is all the electronic industry that you have and in this you can dope small quantities of group 3 A elements. So, those would be boron, aluminium, gallium, indium, thallium. So, these are all elements in the which are group 3 A elements, and you could dope a little bit of this into the silicon structure. So, what happens is that these are elements that are you know they have one valence electron less, than that of silicon and so, they are potentially in a capable of grabbing onto an electron or in other words releasing that vacant location. So, releasing of that vacant location is referred to as a hole. So so, they have acceptor levels they can accept those electrons very easily, and those acceptor levels are just above the valence band. So, whereas, in an intrinsic semiconductor the Fermi energy level is right in the middle halfway between the valence band and the conduction band. In in the case of a p-type extrinsic semiconductor, it essentially lines up with the acceptor levels because that is where the essentially the action is, and as I said the Fermi energy is indicative of the chemical potential of the electrons in the system, and this is a very representative of that in that case. So, you have this situation where you have these acceptor levels that are very close to the Fermi energy levels. So, this changes the behaviour of the semiconductor quite dramatically. The change appears in the idea that now the charge carrier concentration is not solely dependent on temperature in fact, at room temperature it is not dependent on temperature for a very wide range of temperatures it is not dependent on temperature. It is not it’s not a uniform behaviour, what happens is that extremely low temperatures it is dependent on temperature, but then at even marginally some you know some relatively small amount away from saying 0 Kelvin as you start increasing temperature, it pretty soon levels off the charge carrier concentration levels off and remains flat for a very long range of temperature. So, typically the all these semiconductors at room temperature have a constant charge carrier concentration. If you raise the temperature very significantly high, the charge carrier concentration begins to climb again, and that has got to do exactly with this band structure that you are seeing on your screen, and that is got to do with the fact that you need very little energy to do this jump from the filled valence band to those acceptor levels. So, that happens at an extremely small temperature, that small temperature itself is adequate energy to provide you with this shift. Now once you have done that, and there is only a small number of you are only doing a small amount of doping. So, all those charge carriers and now have now become available for a very small increase in temperature. Beyond that, for you to further increase the charge carrier concentration, you have to go to a much higher temperature before this transition becomes possible. So, as long as you are in the energy level between here and here in that entire intermediate range of energies and the corresponding temperatures, there is no change in charge carrier concentration, all of it comes only from this acceptor level related transition, you don’t see the intrinsic transition this find this transition. This overall transition that you see here would be referred to as the intrinsic transition. So, the intrinsic transition occurs only at much higher temperatures, you don’t see that in this system at the lower temperatures. So, for a significant fraction of temperature range, you find that the charge carrier concentration depends only on the Dopant concentration, it doesn’t depend much on the temperature it is flat concerning the temperature. So, if you increase the Dopant concentration, then for that entire temperature range you will have a higher charge carrier concentration. If you decrease the Dopant concentration for the entire temperature range you will have lower charge carrier concentration. And again conductivity depends on the Dopant concentration because it depends on the charge carrier concentration. I told you in the earlier also fundamentally for conductivity to occur you need the charge carriers and so, charge carrier concentration directly reflects on the conductivity of the material, and since the charge carrier concentration is now independent of temperature and only dependent on Dopant concentration, the conductivity also follows the same trend and depends only on Dopant concentration. So, this is the p-type extensive semiconductor, and as I said it is simply consisting of group 4 A elements with the small group 3 A elements doped into it, small amounts of group 3 A elements doped with. You can think of an analogue a situation where you have the group 5 A elements being doped into the system, and that would create your n-type extrinsic semiconductor. (Refer Slide Time: 11:59) So, the n-type extrinsic semiconductor has conceptually is many similarities to the p-type except fundamentally the charge carrier is different here. Here you are essentially taking again the group 4 A element, that’s a good starting point for us again silicon is a very good starting point for us and in that we dope small quantities of group 5 A elements; those are things like nitrogen, phosphorus, arsenic, antimony and bismuth. So, those are the kinds of elements that we have available to us in group 5 A, which we can dope into silicon and create a situation where you have n-type extrinsic semiconductor. Now, these elements have essentially one additional valence electron available to them, and so that valence electron is available for more free movement within the system and therefore, at very marginal availability of energy this electron begins to run around the system. And that is captured in the band diagram by this donor level, which stays very close to the conduction empty conduction band. So, at a very small amount of energy, you can get this donor electrons to get into the conduction band, and then carry out the conduction processes. So, the electrical properties then get defined by this transition, which is occurring at extremely small energy. Once again you can still have an intrinsic transition, but that will occur at much higher levels of temperature because you have to have corresponding energy to enable this huge transition huge gap has to be jumped. So, here again, the Fermi energy now is lined up with this donor level and so that is characteristic of this structure of the n-type extrinsic semiconductor. So, and again you know this is again consistent with the fact that that’s where the energy level of the electrons is and therefore, effectively the chemical potential of those electrons is right. (Refer Slide Time: 13:48). So, now if you step back and again look at the intrinsic semiconductor for a moment, we will use this for just to understand one important concept as to why we need in this class we are going to look at p-n junctions, we would like to first understand why we need to look at p-n junctions okay. So, in general, we see that if you take a semiconductor in this case I am taking an intrinsic semiconductor to you know for the sake of clarity so that we are not you know having too many parameters to keep in mind. So, in an intrinsic semiconductor where you have a bandgap of Eg, and a Fermi energy level E f okay. So, for this bandgap, if you do Eg equals h nu. So, you have some incoming radiation right if this has a nu and the frequency of that radiation is such that h nu corresponding to this radiation is equal to the bandgap E g, then you can do this transition, and that’s what I have shown you here an electron caught transition from the valence band to the conduction band. So, now, you have an electron sitting in the conduction band, and since its transition from the valence band, you have a hole sitting in the valence band okay. So, this is what we have. So, in principle if you are if the idea of this use or this particular use of the semiconductor is simply to capture solar energy, in principle we are already said you have an intrinsic semiconductor you put it out in the sun you will have transitions, you will have transitions. So, solar energy has been captured by this material now so so, we should essentially stop our discussion with this, there is nothing more to look at if this is all there is, but we end up having to look at some additional parameters and particularly that leads us to a p-n junction specifically because of one particular issue. The issue is that when you do this kind of a transition, the electron and the hole are pretty much right there they are in great proximity to each other. So, if you give them even a fraction of time, they will just collapse right back. So, the electron will fall right back because it is not sitting at the lowest energy level that it can sit at. So, even though you send in the radiation and lifted it to a higher energy level, if you give it some chance it will go back to it is lower energy level and close that valence close the hole in the valence band. So, it will recombine with that hole, and it will go back to its original location in the valence band. So, what happens here? When you do this or when this happens in the material, you are not capturing the electricity; you are not the when this happens you no longer have that electron to go to the external circuit to do some job and therefore, effectively you have not generated electricity you did a transition, but you did not generate electricity. You did not capture the electricity in any manner that you could use for some particular application. So, what has happened is you created this electron-hole pair and they recombined. So, they recombined. So, recombination is an event that happens in semiconductors, it is not something that you can eliminate it will happen, but we would like the semiconductor and devices based on the semiconductor to be made such that, despite the recombination, you can continue to do something useful with it right. So, when you have single semiconductor sitting like this, that option becomes difficult for you; you are not really in a position to completely utilize this electron-hole pair that you generated, it simply recombines and therefore, you have an issue effectively of this electron-hole pair. So, the idea of not just stopping with this kind of a semiconductor, but creating a device based on it, in this case, a p-n junction, is at least one of the reasons for it in from the perspective of solar energy capture. It is used p-n junctions are used for a variety of different things, from the perspective of solar energy capture one of the reasons we look at this is that the p-n junction will do something that will stabilize the electron-hole pair. So, that part we will see as we go ahead in an in a little later, but now we will look at the p-n junction, we will try to understand what how it comes together what are some specific aspects associated with it. (Refer Slide Time: 17:50) To get into this diagram that I am going to show you about a p-n junction, I would like to first start with a diagram that relates to a metal. So, in metal, we one image that we have of a metal a model that we have for metal is that you have all these positive ionic cores positively charged ionic cores, which are in a crystalline position they are holding some crystalline locations inside a crystal structure and then you have a sea of electrons. So, you have electrons roaming around. So, when it when this happens the overall material is charged neutral. So, the overall material is charged neutral. So, the material is charged neutral. So, there is no specific charge that it has built up, the electrons are free to roam around and the ionic cores are fixed. So, we have this idea of fixed ionic cores and a sea of electrons. So, that is an image that we have of a metallic system, but to keep in mind the entire metallic sample from one end to the other, is charge neutral. And therefore, even though the electrons are free to roam around the entire structure the overall structure continues to remain to charge neutral. And to the extent that you are not putting a potential on this or a doing any such thing, it and that it’s only sitting as out there as and experiencing the temperature of the system of the surroundings. Then these electrons are roughly equally distributed throughout the metallic sample, okay, and that’s how the overall charge neutrality is maintained and relatively you know even section by section if you look at various locations in the metal, by and large, the charge neutrality is going to be maintained. So, that is how a metallic system behaves. So, we will keep this in mind we are now going to look at a semiconducting system we will have some diagrams relative to the semiconductors, and I will at least alert you to specific aspects which may have some similarity to this, but will be in many ways different. (Refer Slide Time: 19:50)