 We'll wait for others to join, just one or two minutes. Still people are joining in, we'll wait for some time. Good morning sir. Good morning. All of you are able to hear me right? Sir, why the exclamation points in the polls? Sir, why exclamation points after everything in the poll option? So you guys are able to hear me. All of you have selected yes. Some of the people haven't joined yet. As in, Paras is not there. So what do we need to choose? Nothing, nothing. You joined late, so 100%. I can put an objective question also like a poll. I can ask what is the answer and then you can pick ABCD. If there are multiple students, it's a good way to select Konbaniya Karpati. So I think we should start now. I'll share my screen and suppose if you have to answer anything, you have to speak up, okay? Chat, although I can access the chat, but to access the chat, I need to close everything and then see what is the chat message, okay? Or if you really want to just text me on WhatsApp, don't text me on the Zoom on this interface. Although I will be accessing it, it may become delayed response, okay? Fine. So I'll share my screen. You can see my screen, right? Yes, sir. Yeah. So today we are going to start this chapter and this is the last chapter of your class two and syllabus, right? All of you? Sir, EMWaves. Semiconductor. Okay, we'll do it. See, what we'll do is that we'll have one session in which EMWaves and the communication system, they are very small chapters. Both can be done in a single session, so we'll complete that. So then our syllabus will be over, right? Any confusion? Once we do these two chapters also, then our syllabus will be over, right? Yes, sir. Yeah. Yes, sir. Then you'll be scoring full. The chapter is over. Assuming we have a good accuracy rate. Oh, is that the only thing that is stopping you Barat? No. Okay. No, but then, yeah, if you, if you improve your accuracy rate, probably that, that is the first and the easiest step you can take. Okay. Yesterday I was reviewing one of the paper and this guy wrote further maths. I don't know whether you know further maths. It is an advanced level maths paper people write to get into US University. So this guy got C. Okay. And the only reason he got C, not a was that in every question, he made silly error every question. I'll just give you kind of silly error that I have noticed. So there was this SHM question. Okay. He got acceleration also everything he got. He has got acceleration, something like this expression was equal to minus of some constant times X. Okay. Then in a hurry, he has taken Omega as one by root C. And then time period was asked. So he has written two pi by Omega, which was two pi root C. So he's got zero. Nobody can teach you how to avoid this kind of error. Omega is root C. But he is just for some reason, he was in a hurry probably to get the answer in his mind. It was like time period is inverse of Omega. So he has, he has first taken inverse to find Omega and then again took the inverse. So like that, there's several errors. This guy has done. Okay. So it is, it will be really sad that you know how to get the answer. Okay. And you, you are treated at par with those who don't know how to approach also. Okay. So at the end of the day, you don't want to see your marks to be equal to that guy who doesn't even know how to solve and silly rare is going to bring you down there. This is not only for Bharat, but I'm sure everyone of you make a lot of silly errors. So please take care of it. Fine. So today we are going to start this chapter semiconductor. Today will not, we may not be able to complete this chapter, but substantial portion will be covering. Okay. And one more thing, semiconductor is a huge topic. Okay. It's a, it's a very big topic and people spend around an year or so in engineering to understand completely about semiconductor and its devices. Okay. So we can spend couple of years just understanding the devices made up of semiconductor, what it is, how it works and several other things. Okay. But in our curriculum, they're just basic introduction of semiconductor. Fine. We are not getting into too much of, let's say, complicated stuff. So we'll, when we talk about devices made up of semiconductor, we'll not discuss how to make the chips and how to make the ICs and so on and so forth. We are just going to get introduced to semiconductors and the basic devices that can be made out of semiconductor and on what principle these devices work. We are not all, we are not going to get into how to fabricate deep devices also. So for example, I'll be talking about diodes, but I'll not get into how to exactly construct a diode. Fine. So just basic working principle will be there. Right. Now semiconductor is basically a technology topic. It is not a science topic. You can say that it is technology. It is not science because the technology is what application of science. So every now and then you keep on hearing a new semiconductor device coming in. Okay. The microprocessor are becoming faster and faster. So technology keeps on changing. But since semiconductor is an extremely important component of all the electronics that we are using. So that is the reason why a basic introduction of semiconductor is there in class 12. Semiconductor has become so integral part of our life is that we cannot imagine the kind of luxury we are living into without semiconductors. You'll not have mobile phones. You'll not have LCD televisions. You'll not have LED TVs. You'll not have LED lights. Okay. You'll not have computers. And will not be able to have this class also. So if semiconductor would not have been there, I would not have been taking an online session with you right now. So it is an extremely important part of our day to day life. Now, just like, you know, before we understand anything for, you know, like for example, before you start understanding in chemistry, let us say if you have to understand about the elements. First, what you do, you categorize the elements based on their behavior, the physical and chemical property or the behavior. Similarly, before we even get into the details of semiconductor and it's working, we are going to first categorize that. Okay, fine. How many different kinds of semiconductors are there? Once I know the categories, then I can study them one by one. Okay. For example, if, if I have to study the behavior of the people in this world, I'll not be collectively studying them. Right. I'll be segregating them. For example, I'll talk about the behavior of people who live in India in a city like Bangalore. More or less similar behavior could be there. Then I'll be studying the behavior of people in India in a typical village. Then I'll be studying the behavior of the people in a city like Paris or New York. So there will be a difference. Right. So that is why the category creating a category or a bucket is important before you even start studying about the semiconductors. Okay. So there are different ways you can categorize the semiconductor. Okay. And you, like for example, you can categorize the people on the earth based on their gender. Okay. Then you can categorize the people on the earth based on their age, age group. Then you can categorize based on their locations. Right. So different types of categories are possible. Similarly, semiconductor can be also categorized in a couple of types, two or three types. So the first type of category is on the basis. Please write down. We are trying to categorize on the basis of conductivity. Do you know what is conductivity? Anyone? How little resistant something offers to the flow of charge. What is the mathematically quantification of conductivity? One over resistivity. One over resistivity. Right. So resistivity is row. Row is called resistivity. More is row, more is a resistance, you can say. And conductivity is given by Sigma. Sigma is one by row. Okay. This is conductivity. Okay. So we are going to just find out typically what is the conductivity or the resistivity of different kinds of matter on the earth. When I say I am categorizing them based on their conductivity, clearly there can be three types of matter that can be seen. First is conductor. Second is insulator and third one will be semiconductor. So entire matter on the earth can be categorized into these three segments. Okay. Conductors are loosely referred as metals also. So in your textbook, it is referred as metals. So please write down. By the way, the kind of questions that will come in J mains from this chapter, there's a high chance that it will be a theoretical question. Okay. So you need to pay very good attention to the theoretical concept. And if you look at the actual J mains paper, 20% of physics paper will be theoretical. Okay. It is not all numerical. So the moment you keep your eyes off from the theory, you lose 20% of the marks. Okay. So don't just completely focus on mathematics of the physics. All right. So metals, metals have low resistivity and because of that conductivity is very high. All right. So the kind of values that I'm talking about for resistivity is lying between 10 is power minus two to 10 is power minus eight ohm meter. Actually, they should have written 10 is power minus eight to 10 is power minus two, but it is all right. So the range is from higher to lower sides. Okay. This is the approximate resistivity value. Conductivity value will be inverse of this. It will be 10 is power two to 10 is power eight and one by ohm is s. Fine. So these are the typical values of metal, but it doesn't mean that if the resistivity or conductivity values are beyond these values, it cannot be a metal. Okay. These values do not define. Understand. These values do not define. They just explain. So these are like in general, the conductivities and resistivities are metals. Yes. Semiconductor. You'll, you'll understand when we, when you see the range of everything there, there is an overlap of the range also. Write down semi conductors. The resistivity and conductivity of the semi conductors will be between metals and non metals. Or you can say metals or metals and insulator. Since we are using insulator. So the, I mean, they are not exactly in between. So roughly they are in between. The resistivity will be from 10 is power minus five to 10 is power six ohm meter. Do you see an overlap for the resistivity of metal and semi conductor? So there's a big overlap. This is 10 is for five to 10 is a power minus six. There's a huge range for the semiconductor. And then you have insulator insulators have the value of resistivity from 10 is for 11 to 10 is upon 19, which is very high resistivity and the conductivity will be inverse of this 10 is for minus 11 to 10 is for minus 19. So again, I am reemphasizing that these values do not define what is metal, what is semiconductor, what is insulator. These are just typical values. Okay. Now you might be wondering why we are. What is so special about these material? I mean, is it because of the resistivity or conductivity? They are showing that property so that we can use it in in a microprocessor or something like that. Or there should be something else. So the answer to that is the semiconductor is an intelligent device semiconductor itself is a device. Let's say if you have a piece of object like this, this, this is an object. Now, suppose it is metal. Okay. Then if you create a potential difference current can flow like this current can flow like that current can flow like this. Okay. Current can flow in any which way. So the piece of metal is just a path for the free electrons to move depending on which is higher potential and which is lower potential current will just move. It will allow any current to move in any direction. All right. So it doesn't put its own intelligence. So we call metal as even loosely call it a dumb device. They don't put any intelligence on whatever is happening to them. So this blindly supports whatever current flow you want. Yes. Now semiconductor does something interesting. I'm not telling, I'm not saying all semiconductor do that. I'm just giving you an example of what semiconductor does so that you appreciate the beauty of semiconductor semiconductor will if this is a piece of semiconductor, it may allow current in this direction, but no matter how much high potential difference you apply, it is not going to supply. You is not going to support the current in that direction current. If it has to flow only it can flow from left to right. Okay. So now this is the material which can apply some brain on which current it should apply of which current it should support. Okay. Another example could be this. Suppose this is a device and current is flowing like this. Now the moment the current starts flowing in this direction, this current stops. Fine. So there is an if then else statement. If then else. So what is if then else statement over here? If the left portion is at higher potential than the right portion, then the current will flow. Else current will not flow. If this is if then else statement of this device here, if the current from top to bottom is not present, then it will allow the current from left to right. Else it will not allow the current from left to right. So basically a semiconductor is giving you if then else statement and entire computer program, whichever code you write, however long you write, ultimately it is nothing but if then else only. Okay. So you can hard code your entire computer program in a semiconductor. Right. So it basically gives you way to play with the logic. Right. So that this makes the semiconductor the the useful device and not the values of resistivity and conductivity. The values of resistivity and conductivity happens to be that. Okay. For the devices who who who showcase these properties. Is it clear to all of you? Yes, sir. Okay. Now we are going to talk about classification based on something which is more meaningful or something which can attempt to describe or attempt to put logic behind why it is showing the property which it is showing. So please write down the classification based on the energy bands classification of the matter. Now before we understand this, we need to first understand what is energy band. Okay. So basically energy band is nothing but someone is joining. Okay. It is nothing but if you plot a diagram, let's say if this is the line which tells you the energy of a particular electron in a matter. Okay. And then if you start plotting the values of the electron in the matter, then you'll see that some electrons have less energy. So they will lie in this band. Let's say every dot represent the energy of a particular electron. So these are the electron which have energy from this point to that point. Okay. And if if the electron is free to move, then only it will conduct electricity. Okay. Let's say the energy required for electron to free minimum energy is this. So if there is an electron whose energy is more than this energy level, then only it can conduct electricity. Right. So in a metal, there will be a certain electrons which might be here. Okay. So basically you need to just see how many electrons are there in this zone to check the conductivity of a certain matter. All right. So these electrons are basically called valence electron. It is just a name. Okay. These write down valence band electrons. This is this looks like a band. So they're naming it as a band. Okay. And this is this band is called conduction band. So basically valence band electrons have very less energy. So how the how the electron, which is in the valence shell, how can their energy be less or how can they decrease their energy? Anyone to decrease the energy of valence electrons. Don't they emit light and jump down to a lower energy level? No, that is when they are excited and when they are allowed to do so. If they if at the room temperature, they have the sufficient energy to be in the valence band only, then I'm saying that how else can they decrease their energy? Forming a bond. Forming a bond. Correct. So basically these valence band electrons, they are creating a bond. They are not the free electrons. Okay. Whereas the conduction band electrons, they are free electrons. Okay. So we are going to see how how this diagram looks for for a conductor for an insulator and for a semiconductor. All right. So first we will draw for metals for metals. A metal have a lot of free electrons and they don't need any energy from outside to become free. Okay. So what happens is that the valence band energy, let's say this is the valence band, the energy of the valence band and energy of the conduction band. They overlap. Okay. So even if there are electrons. Okay. So this is the this is the valence band and this one is the conduction band. So you can see that there is an overlap. So this is an overlap and you can see that a lot of free electrons are there even though they are in the valence band, they are free to conduct electricity. Okay. This is this happens for the metal and for the non metal is right down. If this is the conduction band. So this is the valence band and that is the conduction band. Then there are no electrons in the conduction band and all the electrons are there in the valence band. Okay. And if electron has to go to the conduction band or if electron has to conduct electricity, they need to at least absorb this much energy. Okay. And in case of non metal, this energy gap EG has to be greater than three electron volt. Fine. So this energy is very high for an electron to jump from this level to that level. So non metal, they practically do not get any electron in the conduction band for a non metal. And the energy gap is the is the lowest energy gap between the conduction band and the valence band that has to be greater than three electron volt. Fine. Now, if we talk about semiconductors, what will be the difference between semiconductor and non metals? The band gap is less than three electron volt. Yeah. Okay. So this band gap EG is less than three electron volt. Okay. There is no hard and fast rule that three electron volt is a sacrosan figure. You cannot ask me that what if energy gap is equal to three electron volt, whether it is metal, whether it is non metal, metal or semiconductor. Okay. So this is just an assumed value. It is seen that if energy gap is less than three electron volt, then this material can behave like a semiconductor. The semiconductor can absorb energy which is less than three electron volt by just absorbing a photon from outside. Okay. And electron can jump to the conduction band and then a material of semiconductor can conduct electricity. Otherwise, if there are no electron in the conduction band, it cannot conduct the electricity. Is it clear? So this is called, this is the classification of the or this is the classification of the semiconductor based on the conductivity and the bay and on the basis of their energy banks. No doubts, right? Then another classification that is there in our syllabus is based on what type of semiconductor it is. Please write down type. The semiconductor can be elemental. It can be compound. And compound can further be of three times. The first one is inorganic. Hence, whoever that is, can you mute yourself please? Yeah, a lot of noise is coming from your side. I muted you. So inorganic, organic and organic actually, organic polymers, they are referred separately. So this is organic polymer. Don't text, okay? How many times I have to say? You can text me on WhatsApp if you really want. Or you can speak up. All right. So the elemental semiconductors are the pure semiconductors as in the entire semiconductor is made up of a pure element. The example of the pure semiconductor or the elemental semiconductor is silicon and germanium. So SI and GE. Fine. And the inorganic, the example of that is this cadium sulfide, right? CDS and gallium. What do I say this? Gallium arsenide. Arsenide. Okay. Organic polymer, sorry, not polymer, organic. One example I'll just write anthracene and organic polymers, polyperol. I'm just writing a few examples only. Okay. So we are not going to study the compound semiconductor. Our focus is elemental semiconductor in this chapter. Okay. So our focus is more elemental and we are not getting into the compound semiconductors. Right. So we have learned about the classification of the semiconductor different types than based on the energy levels and also based on their conductivity and resistivity. Is there any doubt? Quickly tell me. No, sir. No, sir. No, sir. The chapter is full of theory. Okay. It's like inorganic chemistry of physics. Fine. So basically now we're talking about the elemental semiconductor. The elemental semiconductor itself can be divided into two types. Okay. Since this entire chapter is devoted to elemental semiconductor only. So let's get into the deeper study of elemental semiconductor. So elemental semiconductor, please write down, can be divided into the first one is intrinsic semiconductor. And the other one is extrinsic semiconductor. But we'll get into extrinsic one little later. Right now let's talk about intrinsic semiconductor for a while. Okay. So we know that the example of the elemental semiconductor is silicon or germanium. So we are going to restrict ourselves with only those two examples going forward. So if you look into the silicon, if you look into the silicon, then it will have these valence shell electrons. Okay. So these valence shell electrons are going to just rotate around silicon. Okay. And there is another neighboring silicon over here. So this also has the valence shell electron, which is rotating about the silicon atom. And suppose there is another silicon atom here. This also has valence shell electron rotating like this. So basically what happens is that if silicon is not conducting, the electrons of the silicon will just rotate around the silicon atom only. But suppose you give the atom enough energy, then this atom, sorry, then this electron, the valence electron will just rotate around silicon. And if you give it certain energy, it will jump to the next atom. Okay. Like this. And then further energy you give, it will start jumping here and there. And the direction of the motion of this electron that is jumping from one atom to another atom can be controlled by creating an external electric field. Or if you create a potential difference that will direct the motion of this free electron. So this electron, which is jumping from one atom to the other atom, this electron, you can say it is a conduction band electron. You have increased its energy and this electron came out from the, let's say, lattice of the silicon. And it is now freely going from one point to the other point. Okay. So if we just draw the lattice of the silicon or germanium, it will look like this. Suppose this is a nucleus of the silicon or germanium. So plus four. Okay. And then another nucleus plus four. So I'll draw the four, five nucleus. All of you draw with me. So this is the way we are showing the bonds. One silicon will be surrounded by how many silicon? Anyone? It'll be surrounded by six, right? Six. No, I'm not. Immediate neighbors four only, right? No, 3d because there's one in front of you. So single layer or in a, in a. Already tetrahedral, I think. Oh, oh, wait. Tetrahedral arrangement, right? Okay. One is you answer it mathematically. Other is you can use a logic. From chemistry that how many electrons are already in one of the silicon atom for balance. It needs to have four more to complete its octet. So one electron is off of its own. The other electron is shared. So like this, it immediate neighbors will be only four. Okay. These dots are represented as the shared electrons between the two silicon atoms. Okay. So there it is a single bond or a double bond between two silicon. Single bond. Single bond only, right? Two electrons are shared, but still that together is one bond. Correct. So it is one silicon is making four bonds total. Now what happens is that if you give energy to let us say this electron, this electron, if you give energy, then this electron can just leave this bond and move away. And because of its movement, what would remain wherever it was earlier? There will be a, let us say a hole that gets created. Okay. And this electron is now free to move. So conduction will be because of this electron. And what about this whole? If you consider this whole to be part of the silicon atom itself, this whole is basically positively charged. Net net that atom become positively charged because it has more number of electron and less number of electron. Now this whole will attract the neighboring electrons as well. So this whole will probably attract electron from this. So this electron will go and fill the whole. But in that process, a whole get created here itself. So this may be filled, but there will be a whole over here now. So when this process is happening. Can I say the positive charge is moving indirectly? Yes. Okay. So the current is because of the whole movement as well as because of the electron movement. Both are contributing to the current. Okay. Although electron, you can see it as a particle, but the positive charge is also moving. Whether it is a particle or not, that is immaterial. You need to only worry about whether positive charge is moving or not. Positive charge is moving in terms of whole. And because of that, then if the direction of the electron movement is this way, the whole movement will be typically in opposite direction. Net net. So their currents will get added up or subtracted. This is whole current and this is let us say electron current. What do you think? Paras. You're there. Paras is not there. Aditya. What do you think? Their current will get added up or subtracted? That should get added. No, because the because positive charge flowing in one direction same as negative charge flowing in opposite direction. No, I think you have to just consider one of them. Right. I was asking Aditya. Aditya, speak up. You want to hear your voice. You have muted me. I have unmuted also. Okay. Say it. I think they'll get added up. Okay. See what happens is that net net the movement of whole will be in opposite direction of the movement of electron. Fine. So we know that direction of movement of positive charge is the direction of current and opposite direction of movement of electron is the direction of current. So the movement of electron on right hand side creates the current in the left hand side. So basically the current will get added up. So it will be whole current plus. Electron current like this. So, but the electron current will kind of create the whole current. So like I thought they're not independent. So what? The number of holes and number of electrons need not be different. There might be three electrons missing about and that might be just holes getting filled up. The number of electrons need not be equal number of holes. Okay. Number of. Okay. So let's write down the at equilibrium, the rate of generation, rate of generation of electron is equal to the rate of recombination of charge carriers. Okay. Because number of electrons, the number of electron that are free will be equal to the number of holes that are getting created. Isn't it? Because the electron will come out from the bond only. So every electron that is free will create one whole. Fine. So at equilibrium, the rate of generation of the electron is equal to the rate of recombination of charge carriers. When I say rate of recombination, it means that electron getting getting inside the hole. So it neutralizes it. Okay. So in intrinsic semiconductor, number of holes will be equal to number of electrons. Is there any doubt till now? No doubt. No doubt, sir. No doubt. Fine. Now tell me a question here. The lattice structure of carbon, silicon and germanium is similar. They are basically same. But why silicon and germanium can be utilized as semiconductor and not carbon. Smaller size and higher electronegativity of carbon. So the bonds are less likely to break and give free electrons and holes. Yeah. They talk in terms of whatever we have discussed till now. I'm not saying you're wrong. You're correct only, but you're not using the language of physics. So probably the energy gap between energy band and valence band is very high for carbon. Yes. That is what I wanted to discuss. Okay. So the energy gap between the valence band and the conduction band is very large because the electrons are getting attracted to the nucleus of carbon in a stronger way. So you need a lot of energy to make it free. Okay. Now I can access the chat also. You can put your messages on chat as well. I think Shreya's microphone is not working properly. Shreya, you're there? Shreya, Shreya, Shreya. Shreya is there. You can chat. Okay. Don't worry. All right. So basically we have just learned about the intrinsic semiconductors behavior. But the problem with intrinsic semiconductors, although they are pure, the problem is that the energy gap is still large. Okay. You will have to have extremely high potential difference to be applied across a semiconductor to create some meaningful current. Okay. Because it takes a bond to be broken. So because of that, practically still this intrinsic semiconductor is not so useful. So that is the reason why we need to modify the semiconductor intrinsic semiconductor in such a way so that its conductivity increases multifold. Okay. And that is what exactly happens in the extrinsic semiconductor. So please write down extrinsic semiconductor. Is this chapter coming in your midterms? Yes. So for YPR it's not. Wait. How is, how are the papers different? Paper of YPR will be different. Sir, it's usually a common paper. So it's usually a common paper for all NPS is like HSRI and all that have the same paper. Does that mean they won't ask us any questions from you? All right. Please write down extrinsic semiconductor. So what happens is the conductivity of the semiconductor only depends conductivity of the intrinsic semiconductor depends on its temperature. Okay. If you increase the temperature, then only the, then only the valence shell electron will absorb the energy and go to the conduction band. Okay. But at room temperature, they don't get that much amount of energy so that they start conducting. Okay. So at room temperature, the conductivity of intrinsic semiconductor is very less and practically it is like an insulator. All right. So the way what we do in extrinsic semiconductor is that we put some impurity and because of that impurity, the conductivity of the intrinsic semiconductor increases multiple. Let's say, let's see exactly what happens. So adding impurity is right down intrinsic semiconductor creates extrinsic. Okay. The, this process of adding impurity is also referred as doping. Now adding impurity doesn't mean that you can add any garbage. All right. So, although it is called impurity, but you need to be very selective about it. So basically it's like actual doping. What do you mean by actual doping? It is getting recorded, but tell me. So I prefer not to say that. Okay. See Sukrit is so innocent. He doesn't know anything. Anyways, listen here. We are talking about adding impurity to intrinsic semiconductor to create extrinsic semiconductor. So, so there are two kinds of impurity that we add. There are two kinds of impurity that we add to the intrinsic semiconductor. The first one is pentavalent. Pentavalent elements can be treated like an impurity. Why are they treated like an impurity? Because mainly it is the pure semiconductor only. Only silicon is there, but just a little bit of pentavalent element is there. Like for example, you can say one pentavalent element out of one billion silicon atom. So one part per billion. So you can say that is impurity. Okay. That is the reason why they are called impurity. So one is pentavalent element and other is trivalent. Okay. So it is seen that if you add pentavalent or trivalent element in the silicon or germanium, then their conductivity increases tremendously. Okay. Let's see how it happens. Can you give me quickly the example of pentavalent element? Phosphorus. Phosphorus is there. Arsenic. Arsenic, antimony. Is bismuth also used? It's too big, isn't it? That's what I'm asking if it's used. Similar, I mean it should be like what Bharat said. It cannot be very big. It will disturb the lattice itself. So it should just mix up with the lattice. But it won't be that as big. Like it won't be really big. It'll be about the same size as antimony because of f-block contraction. Okay. That's my contraction. Yeah, that's what I'm saying. Okay. I might have forgotten all that. It is 20 years now. But see, still I'm not saying that suddenly the conductivity, if you add such pentavalent element as bismuth, conductivity will suddenly go down and it will start like an insulator. I am talking about the best fit here. Okay. There's no right or wrong exactly. So trivalent element could be indium. Aluminum, gallium. Boron and aluminum. Okay. Gallium also you can put. Similarly, bismuth also you can put as a pentavalent element. But these are the examples typically. Okay. Now let's see what happens to the lattice when we add a pentavalent element. So pentavalent element, let us see, let us say that this is the nucleus of pentavalent element, which is plus five. Okay. Now this pentavalent element, when you add, they are so less in number as in one part per billion or one part per million that the probability is almost one that this pentavalent element will be surrounded by the tetravalent element only, which is silicon. Okay. The probability is close to one that it is surrounded by silicon only. Please draw the silicon lattice. There's plus four, which is silicon, nucleus, silicon or germanium you can say. How I draw this quickly. Hmm. So pentavalent element have how many electrons in the valence shell? Five. Okay. But silicon require only four. So four electrons of the pentavalent element create bonds with the neighboring silicon. What happens to the fifth one? The fifth one is free. This is not creating bond. So energy of this, this is, this is not free. Okay. This is not free. Still it is bounded to the nucleus of the pentavalent element. But relatively it is free. The electron that has participated in the bond formation, the energy of that electron is reduced. But the electron that is not participating in bond formation, the energy of that electron is higher than the electron that is participating in the bond formation. Relatively it is free, but still it is in the influence of pentavalent nucleus itself. But if you give energy to this electron, this electron can become free and start conducting electricity. Now I am talking about the electron from one of the atom. There can be billions of such atoms inside matter. So you don't need infinite electrons to conduct electricity. Okay. So even if there are certain good number of free electrons that are generated because of adding pentavalent element, that is sufficient. Okay. Now if you have to create the energy band diagram. Okay. Please create this. If suppose the y-axis is the energy, can you draw the energy bands quickly? Have you drawn? Actually you can scribble on my board also, right? So you can click annotate and can you draw on the board itself? Let's see whether it works. Bharat is drawing. Okay. What do these three lines correspond to Bharat? Wait, everyone can see those lines. Oh God. Okay. So sir, is it that basically the first line corresponds to the four bound electrons? Then between the first and the second line corresponds to the fifth electron, slightly higher energy and closer to the conduction band. And that yellow line corresponds to the lowest level of conduction band. Logically correct, but you're drawing to improve. Okay. Please erase this. So basically what happens is that this will be my tea like that. You mute yourself and then drink tea. So this is the valence band. Okay. And similarly, there will be a conduction band which will start from here. So this is, these are the bands when the, when the, when it is only silicon or when it is intrinsic semiconductor. Okay. Now, when you put the impurity, this is this band correspond to the electron that has participated in the lattice bonds. Okay. And this is, this correspond to the electron that are free. So when lattice is getting created, there are no electrons that are free. So all the electrons are participating in the bond. So they are all in the valence band. But when you put the impurity, when you put the impurity, then there will be these electrons who have slightly higher energy but lesser than the conduction band. Why lesser than the conduction band? Because they are still bounded to a particular nucleus. Okay. Now can anyone tell me why the conductivity has suddenly increased? There are more number of electrons that are closer to the conduction band. So there are few electrons that are not participating in bonding. So, so this takes a little bit of energy just to kick them in that little bit into the conduction band. So there are more electrons that are very close to conduction band. Correct. So now you don't need these electrons to jump to the conduction band. You just need these electrons to jump to the conduction band. Okay. And this energy gap is 0.01 electron volt. You just need this much energy for these electrons to start conducting electricity. Fine. So that is the reason why if you add a pentavalent element you just require such low energy which is possible by just giving let us say 0.7 or 0.8 volts of battery can create a push of 0.01 electron volt and your semiconductor will start behaving like a metal. You start conducting. Okay. Now here when you add impurity the number of charge carriers I'm talking about I'm not talking about number of electrons. Okay. So basically number of charge carriers number of electron will be very high compared to number of holes. When I say small n this is density of the charge carrier. So number of electrons per unit volume is much higher than number of holes per unit volume. Okay. For this type of extrinsic semiconductor so when you dope the pentavalent element we name it as n type. Okay. This extrinsic semiconductor is called n type. When you dope pentavalent element on the intrinsic semiconductor now let us see what happens when you dope a trivalent element can you draw a similar kind of crystal lattice for a trivalent element. So let's say at the center you have a nucleus of boron let's say that is plus three and it is surrounded by silicon. Four silicons are there. So the neighboring ones are plus four plus four like this. Now can anyone tell me what happens be like a free hole or something. He has a little bit. One of the bonds will only involve the sharing of one electron and then there will be a hole. There will be a hole here like this. Why there is a hole anyone? It only has three electrons to share. It only has three electrons to share but the neighboring silicon they require four electrons. Okay. So what happens is that this hole will attract the neighboring electrons so it will jump like this create a hole like that. Fine. So you can see that the hole attracts the neighboring electron. Now can anyone tell me how exactly this increases the conductivity? A lot of holes will be created so they'll be able to move again freely. Electrons basically move in the opposite direction as the holes basically an electron just jumps so net positive charge gets transferred. Still I'm not convinced. See the conductivity increases because how easily the charge carrier can move. Okay. It is a ease with which charge will move not the movement. So how is the easiness of the charge carrier improves? See the previous case it was easy. In previous case it was like the electron did not participated in the bond itself so it was relatively free. So that is why that electron which hasn't participated in bond can freely move. The electrons surrounding the hole are relatively free because they can jump from one bond to another because of the fact that there's a hole so that is basically increasing their energy so they're relatively free. The electron which has already participated in the bond has a fixed energy. It has nothing to do with what is nearby. So it's not influenced by anything outside the bond? It gets influenced but when you talk about the energy of an electron which has participated in the bond that is fixed. See what happens is that the energy of the hole if there is some energy associated with the hole and there is some energy associated with the electron that is participated in the bond. Whose energy will be higher? Hole or the electron that has participated in the bond? The hole. The hole because there is nothing there as such. Now if the electron has to jump to the hole how much energy it is requiring? Energy of the hole minus energy of the electron in the bond. Does the electron need to be free to move? Does it need to be completely free? No, it doesn't need to be completely free. It can be still in the bond only. From one bond it has jumped to the other bond. So energy required will be difference in the energy levels of these two. Energy required will not be the difference in energy between a free electron and the electron in the bond. Energy required will be energy of a hole minus energy of a bond electron. Are you getting it? Not clear, is it clear? Could you explain it again? I will explain it after I will draw the energy diagram. So let's say this is the energy diagram. You will understand more with the energy diagram. So let's say that this is the valence band and let's say this is my conduction band. There will be some energy corresponding to the hole. So the holes will have energy which is close to the bonded electrons or the bond's energy but still it will be higher. So this much will be the difference. So the electron which is there in the bond will just need this much energy, this much energy difference for electron to move from one place to the other. Electron doesn't need to jump from here to there for its movement. So it provides an alternate path for conduction. Yes. So now the energy... What did you say? Anyone understood? Shravan can you message me? I can't hear you clearly. Alright, so now the electron if it has to move it requires just 0.01 to 0.05 electron volt. Shravan that is not required. For conduction movement of charge particle is required. Simple. But charge particle movement will happen only when either it becomes completely free and just move randomly or there is a place to go to. Earlier there was no place to go for an electron. So it has to become completely free. Now there is a place to go to and that place to go to is a hole. So electron will jump from its actual place to the hole. So that movement itself creates a current. Movement of electron from its original place to the hole creates a movement and that is a current only. So when electron moves again there will be a hole created. So this hole will create a current further. So because of that the hole which is positive charge is moving. So the current is because of the movement of the hole and you can control the movement of hole by creating external electric field or you can create a potential difference that will direct the movement of hole in a particular direction. So in this case the number of holes will be very large in terms of charge carriers compared to number of electrons. And this type of semiconductor which is doped with trivalent element, so intrinsic semiconductor doped with trivalent element is called P type of the semiconductor. And there is another equation. They are very, very less. In fact there are just couple of them, couple of mathematical equations are there and here is one more equation at thermal equilibrium. We are not getting into the derivation of this. At thermal equilibrium of extrinsic semiconductor number of holes multiplied with number of electron per unit volume of hole multiplied by per unit volume of electron charge carriers I am calculating should be equal to Ni square. Ni is number of charge carriers of intrinsic semiconductor. It will be given. It is like a constant. Number of charge carriers per unit volume. So NH and NE multiplication of that should be equal to Ni square. This is the condition for thermal equilibrium. Any doubts now? Where does that come from? Where is that NH times NE equal to Ni square? Is that like an empirical relation or is it derived from something? It is derived. So when will we learn that? You learn when you take electronics and communication as your engineer. Which brands you plan to take? I am not really sure as of now. Suppose you get computer science in IT Bombay. Will you choose computer science or electronics? Sir it depends. I was not going to do computers initially but I might change later. Not fully fixed. Bharat? Sir I don't know if I even wanted to be engineering in the first place. Okay. Anyways all others you see the thing is that be very careful with what you are planning to do next after class 12. At times we get if you are really passionate about something you don't need to worry about anything. But if you have not found your real passion then don't force into some glamorous thing. Okay. Look at what the world demands. What the market demands. Because at times we think that computer science is something which is very boring or mechanical engineering is something which is very interesting. Something like that we create notion in our head and all these branches are so big that there will always be something which will be of great interest to you. So there are couple of examples like one of my friends who is on lot of disturbance on your side. I muted you. So one of my friends have done PhD on the when electron get trapped inside the diamond how it behaves. Okay. So it was very interesting study for four or five years he did that study only that focus study but when he came out nobody was giving a job to him. And practically he was jobless and he did not get any let's say he was not interested to become a professor also. So he has to you know at the age of 29 or 30 when he has done couple of postdocs and PhD as well he has to spend his entire life on doing a job which was completely out of his interest. So he was just reading documents and creating somebody out of that. Okay. So from 30 years to the 70 years of the age 40 years he'll be doing just that just for couple of years of his hobby kind of things. So you need to look further ahead than just going with. Okay. So it is good that some people are not yet decided so for clear than all and everybody who is not yet decided is perfectly fine. My worry would be that if your heart bent on doing something like suppose you say that I think that I want to become a hacker or I want to become a nuclear scientist. Then it will be a cause of worry being confused is fine. At least get some good ranks in the exam so that you have choice. Otherwise you'll not even get a choice as well. So if you make a lot of silly errors, you may end up doing civil engineering from some unknown college. I'm not demeaning civil engineering but typically lower ranks take civil engineering. Okay. So let us take a numerical now. Let me read it from your textbook. Part one is a conductor right? Part two sir. Part two last chapter. Where in the middle? Middle. Second last. So all this. Sir is the answer 5 to 10 part 23 and 4.5 to 10 part 8. Wait I got 5 into 10 part of 22 and 4.5 into 10 part of 9. Yeah that is correct. Wasn't planning on it sir. Did you get the answer? Yeah I did. 8 minus 6 is 3. Nice. Yes I got it. Fine so clearly here it is a pure silicon crystal doped by pentavalent arsenic and we know that for pentavalent arsenic a number of electron per unit volume is much greater than number of holes. In fact I can say that number of electron is same as number of arsenic. Concentration of arsenic. Fine. So the concentration of arsenic is how much it is for the silicon has this much atoms per meter cube one part per million. So 10 is power 6 silicon atom will have one arsenic. Atom. Okay. So 5 into 10 is a part 28 silicon will have 5 into 10 is a part 22. Okay. So this is my number of electrons the free electrons. So number of hole into number of electron is ni square. So 1.5 into 10 is power 16 whole square. You can substitute the value of any to get the number of holes per unit volume that will come out to be 4.5 into 10 is power 9 per meter cube. Okay. So you can see that number of electron per meter cube is of the order of 10s for 22 number of holes per meter cube is of the rough tens for 9. So there is a tremendous difference. Right. So we have learned about the intrinsic semiconductors and extrinsic semiconductors but still we might be wondering as a new might be wondering as such why we are studying all of this. What is the usefulness of all of that apart from getting marks in your exam. Okay. So for example, suppose I take take n type semiconductor like this and if I connect it to a potential difference of five words like this, what will happen is n type. Tell me what will happen. Anyone will it create a current. Yeah, there should be a current right because there's a potential difference across it and it's moderately conducting so it should pass a current through it. But some amount of voltage is required for the electron to jump to the conduction band. Yes. Yes. Yes, there is. So n type is only 0.01 it has five volt here sir it will be fine. 0.01 electron volt. Electron volt energy is required and there's five volts potential. Right. So basically there will be some opposition so it will behave like a battery of point you can say point zero one volt this entire object will be like a point zero one volt battery. And this is a five voltage. Okay. And then after that opposition behaves like a metal. Okay, so five volt minus point zero one volt will be the potential difference across this material which is practically behaving like a metal now. Fine. So, apart from this opposition of incoming voltage, there is nothing great about the p type or n type semiconductor, they will behave like a metal only. All right. So n type and p type in isolation, they are not showing any intelligent behavior. But when you look at when you combine p and n type together, then they start to show some of the amazing property that you cannot hope to get in piece of metal. Okay. So that is what the next topic is. We are not, we are now getting into the devices that are made up of semiconductor basic devices. So the first basic device itself is a PN junction is right down PN junction. It is also called junction diode or PN junction diode. Okay, let's see what happens at the PN junction. So suppose this is a semiconductor, which has one side as P, the other side is n. Okay, so there is a way to combine P and n. You can't just use Feveq or Feveq to connect P and n like this. There is enough technology that is going through, which go through to combine P and n and create a junction out of it. Okay. Now there is some special property of the junction, which makes PN junction a useful device. Okay. So before we get into what will happen when you put a battery outside it. First, let us see what happens at the junction. Okay. So here number of electron per volume is very high and here number of holes per volume is very high. So at the interface, can there be a diffusion current? Will there be a diffusion? Yes, at first there will be a diffusion current. Yes, some electrons will occupy the holes this way. Okay. So the number of the diffusion happens from higher concentration to lower concentration. So because of that, the electron will jump or it will go inside a little bit and it will combine with the holes which are here and it is going to make it negative charge net net. So there will be a net net negative charge over here and similarly the holes will go that side to combine with the excess electrons it has. And it will create net net positive charge like this. Okay. Now, what will happen is here tell me one thing that this diffusion will keep on happening till infinity or will it ever stop? It will stop because there will be a net electric field which is developed which will prevent further transfer of holes in electrons. Correct. Now, see there is a negative charge over here and a positive charge over there. So what will happen is that it will prevent the next electron that will try to jump from this side to that side. Fine. So this electron will ripple it and positive charge will attract it towards the inside. So what will happen is that because of this electric field, let us say that because of this electric field, I can say that positive charge will try to move this side. Okay. So this is a current which I can name it as drift current drift current arises because of the electric field. Okay. This is drift and there will be a diffusion current as well. This is diffusion current. Diffusion current happens when it is going from higher to lower concentration. Is it clear till now? Yes, sir. Okay. So when the drift current becomes equal to the diffusion current, equilibrium is attained. Okay. And at that equilibrium, this will have some charge separation. So at equilibrium, there is some charge separation. Can I say that there is a potential difference between these two lines? Will there be a potential difference? There is positive charge and there is negative charge because of charge separation, there has to be a potential difference. So let us say that potential difference is V0. Are you getting it? Yes, sir. Yes, sir. All of you. Okay. Now, let us study this further. By the way, this is called depletion layer. There is another layer. There is another name to it. This is called depletion layer or depletion zone. Okay. There are several names to it. Depletion region also it is called, let me write down completely depletion zone or layer. This is depletion zone. So let's talk about the property of the depletion zone. Can you tell me a few things about depletion zone? Just one thing. Just tell me one thing. This is only an electron hole recombination takes place. Okay. What else? What is unique about it, which makes it different? I mean, can I say that depletion zone belongs to half of it belongs to P and half of it belongs to N. Can I say something like that? Or the property of depletion zone is completely different from P and N type. Symmetrical distribution of the depletion zone about the center between P and N regions. What if one is more heavily doped than the other? You're talking about ideal PN junction. I mean, same doping level. Tell me one thing. Property of the depletion zone. Is there any correlation between property of the depletion zone and P or N type? Or what is unique about depletion zone? So as in what? Tell me what is N type? In the N type, lot of free electrons. Not exactly free, but yeah, you can say that a lot of charge carriers are there in N type. And in P type, lot of holes are there. So basically it's just like an intrinsic semiconductor in this case, the depletion region. Very few holes, very few charge carriers. What happens in the depletion zone? There are no free holes or free electron. If it there is, it will recombine and create and it will eliminate all of that. So depletion zone has no free electrons or holes. But does it have electrons in the depletion zone? Sir, the electrons are there in the bonds. Electrons are there in the bonds. Now, can I say that depletion zone therefore acts like an insulator or it is like, yeah. Can I say depletion zone is like an insulator? N type can be a good conductor. P type can be a good conductor. But depletion zone is acting as if there is a gap between the two conductors. It is like wire is coming till here, till there. And you're connecting a potential difference. But there is a gap and this is a depletion zone. There are no charge carriers. So electron has to jump if it, electron has to conduct electricity. Yes or no? Yes, sir. Okay. Fine. So can I say that bigger is a depletion zone, more will the problem for production of electricity? Because then electron has to jump from this side to that side for electricity to get conducted. There are no charge carriers over here. When electrons are moving in a conductor, what happens is that electron from one end need not go to the other end. All the electrons together starts moving because everywhere there are charge carriers. But suppose there is a gap in the conductor, then electron has to jump. Similarly here also. So if depletion zone is larger in size, then the problem will be that electron has to jump the larger distance. So more and more problem will be there to conduct the electricity. Okay. So this makes the depletion zone very interesting to study. So at times it is seen that the zone, the depletion zone shrinks. And sometimes depletion zone will expand. So this expansion and contraction will actually increase or decrease the conductivity. So if the depletion zone contracts, conductivity of PN-gension increases. And the depletion zone expands, conductivity of depletion zone, conductivity of PN-gension increases. Okay. And PN-gension in a, let's say in a circuit diagram is referred like this. This is a symbol of PN-gension. So this side is P, that side is N. Okay. This is PN-gension diode. Okay. All right. So we'll take a small break and meet after that. Fine. So right now it is 11-25. We will meet at 11-35. Okay. Fine. So this is a break time. All of you please eat something and come back. All right. So break is over now. Yes, sir. Fine. So we have just introduced a junction diode, a PN-gension. And we were talking about the property of this junction to expand and contract. And because of which the conductivity can increase or decrease. So let's see when it will expand and when it will contract. Okay. So suppose you have a PN-gension like this. This is P. This is N. This side will be net net negative. This side will be positive. Fine. Now suppose you are applying a negative potential here and positive potential that side. Then what will happen? Negative potential is going to attract the holes this side and positive potential is going to attract the electrons, the free electrons from the N side towards the right. Because of that, the depletion zone will widen up. Okay. Why depletion zone actually is created because hole from here jumps to this side to combine. Now if holes are going this way, then the electron will further penetrate. Because of that, the zone, the depletion zone, the width of that increases. Okay. And it makes it an insulator. Okay. So this is called reverse bias. So but it doesn't like fully compensate or so there is a point where it like normal current will flow or it will always be like this, like where no current fully flows. See if you increase potential difference, it will further widen the gap. So your increasing of the potential has actually increasing the, let's say, resistance itself. So it is having a reverse effect. So there will be a point where like the depletion region can no longer widen up so it normal current will slow. Let me finish now first. When you keep on increasing the potential difference, then there will be a point when the electrons that are bounded inside the depletion zone. They will get enough energy to break the bonds itself. Okay. And suddenly a lot of free electron will appear out of nowhere in the depletion zone and then it will start behaving like a conductor. And that is called a breakdown of the PN Genshin itself. But till breakdown happens, the depletion zone, which is void of free electrons becomes wider and wider if you increase the potential difference. And because of that, you can say that almost zero current flows, almost nil. The only current that you can say is available is because of the drift or diffusion. It will be, right? Yeah. So where was I? Right. So this is the reverse bias. Whereas if I connect the P side with the higher potential and N side with the lower potential. If I connect it like this, the holes get pushed this side and electron get pushed that side. Because of that, the size of the diffusion zone shrinks. And now if electron has to conduct electricity from N side, it has to jump a very small distance. Fine. And that is the reason why a forward bias will start conducting electricity very easily. In fact, you just require a potential of around 0.7 volt to break this barrier and electrons will jump from N to P side. So this is called forward bias. So if I connect P side with higher potential and N side with lower potential, it will act like a conductor with an opposing voltage of around 0.7 volt. But if I connect P with lower voltage and N with higher voltage, it will behave like an insulator, almost no current flows. So now you can see that this is an if then else statement. So if P is at higher potential, current will flow. If P is at lower potential, current will not flow. Now, clearly I cannot apply Ohm's law in this device. Ohm's law is not valid because, just one second. Okay. So Ohm's law is not valid. And hence I cannot, who is sending me what's happening? Just close it. So Ohm's law is not valid. But then I want to know how current behaves when I increase or decrease the voltage. So since there is no formula as such, I will create a chart or I will create a graph between voltage and current. So in this entire chapter, most of devices, in fact, none of the semiconductor device follow Ohm's law. So there is no direct correlation between V and I. So that is the reason why you keep on drawing characteristic curves between voltage and current. Okay. So for every device, we will draw a plot between voltage and current. So that is what we're going to do next. All of you please plot this graph. Try plotting it. The axis is you should draw first like this. If voltage is positive, you can treat it as a forward bias. And if voltage is negative, take it as negative bias. The positive Y axis current is a forward bias current. It is measured in milli amperes. And the negative current is when it is reverse bias, it is extremely less. So I'm measuring it micro ampere. And forward bias voltage required will be very less to have higher amount of current because at the forward bias, it actually start acting like a metal very soon. So the divisions, positive divisions are increasing at a lesser rate 0.2, 0.4, 0.6, 0.8, 1, 1.2 like that. Whereas in the reverse bias, it is acting like an insulator. So I will increase the voltage at a much faster rate. This 20 volt, let's say this is 40, 60, 80, 100. Similarly, on the positive axis, the scale is milli ampere. On negative axis, it is micro ampere because current in the reverse bias is very less. Can you try plotting it? Can you guess what should be the plot? First do it yourself quickly. Yes sir. So when voltage is in the forward bias, it will require 0.7 volt approximately to start behaving like a conductor. And as soon as it starts behaving like a conductor, the current will just shoot up after 0.7 volt. Till 0.7 volt, it practically acts like an insulator because that is what the junction barrier is. And in the reverse bias, the current will be very less because it is acting like an insulator. And there will be a point, let's say around 90 volt when the bonds of the junction will break and it will create a surge of the charge carriers. So sudden increase in the current, you will see beyond let's say a couple of voltage in the reverse bias. This is called a breakdown voltage, voltage breakdown. And this one, this voltage, sorry not that, this voltage where it shoots up is called knee voltage. Just a term. No doubts, right? All right, so the threshold voltage in case of germanium, it is 0.2 and in case of silicon, it is 0.7. So this is basically for the silicon or silicon knee voltages 0.7 volt. And for germanium knee voltages 0.2 volt. If nothing is said in a question, you can assume that it is a silicon diode. Now we need to define terms like resistance also over here. Now the way we define resistance is not simply a ratio between voltage and current because it was a straight line passing through origin in the case of most of the metal. But when it comes to semiconductor, it's no longer a straight line passing through origin. So basically a ratio between voltage and current, physically it doesn't mean too many, I mean it doesn't give you any proper indication of what is going on. So rather than calculating a ratio of voltage and current, I will basically calculate a ratio between change of voltage and change of current. This will give me an indication of at that point actually what is happening. For example, if I calculate change of voltage divided by change of current at this point over here, it will come out to be almost infinite. Because voltage is changing but current is not changing. Similarly, if I calculate the change of voltage divided by change of current over here, it will come out to be almost 0. Over here it is close to 0. So that is the reason why delta V by delta I keeps on changing everywhere along the curve and it will give you some indication of what is going on. So if delta V by delta I is close to infinite, it means that you are talking about a zone which is here or there. If delta V by delta I is almost 0, you are talking about zones after breakdown or after the new voltage. There is a physical meaning of delta V by delta I, we also call it dynamic resistance. This is called dynamic resistance. Basically the derivative of that characteristic curve at any given point is dynamic resistance. Basically that is. It must be inverse of a derivative, like one by derivative. Inverse, one by derivative of that curve. So it gives me some indication of how easily it is to create the, sorry, how difficult it is to create the current from that change of voltage. So that is the reason why it is called resistance and since we're talking about change and hence it is called dynamic resistance. Alright, so let's take a small numerical based on this. All of you attempt this numerical. Sorry, sorry, sorry, last connection. What happened numerical in front of you. What do you talk about daily online sessions will be their problem practice make sure you have a decent internet connection by then. So that 0.5 and that voltage axis is it corresponding to the dotted line the first dotted line. So, yeah, I'm looking at it. Not exactly. No, roughly you can say that dotted line is 0.7. This one is 0.7. This dotted line correspond to 0.7. And this dotted line, it is around 0.8. So then is the first one 10. Yeah, it'll be 10. Yeah, we saw me and don't speak before I ask. Others also please try. So I'm getting 0.03 and infinity. Alright, so let's talk about how to solve this. We need to find out the resistance when ID is 15 million pairs. Okay, so over here. I need to find out what is the resistance and since the current is changing there very quickly, I will find out the dynamic resistance for that which is more meaningful as in how fast it is changing. Delta V by Delta I I find out there and to find out Delta V by Delta I I can take any two points near 15. But better point will be one below 15 and one above 15 and which are marked very neatly one is 10 milliampere other is 15 million. So is the one corresponding to 10 milliampere 0.5 volts or Let me do it you will understand. Delta V will be 0.8 minus 0.7 divided by changing current will be how much 20 minus 10 and 10 is for minus three. Alright, this is going to give you 10 ohms of dynamic resistance specify that this is a dynamic resistance. Okay, and then we need to find resistance over here. Clearly dynamic resistance is close to infinity there. Okay, RD tends to infinity. Okay, but you can also you know in in our textbook they have referred as a ratio of voltage divided by the current at that point and that is not a dynamic resistance. Okay, that is just a ratio between the voltage and the voltage and the current at that point. So that also gives us a fair bit of indication of some sort of resistance. Okay, that I can call it as static resistance. So at this point, the voltage is 10 and the current is 10 is for minus six. So this is coming out to be around 10 is about five ohms. Fine. Any doubt? No, sir. So how are we supposed to know that the other line was 0.7 just by looking at the graph? Yeah, actually, you can say that this is this is 0.5 over here. This is 0.8. Then this would be 0.7. They should be 0.6. Then only this is 0.5 equal divisions if you take it. So then it could be something like 0.68 or something. Yes, so your answer will be close only right. Okay. All right. And if they're very particular about the accurate answer, they will clearly write down that it is 0.7. Otherwise an approximate answer is fine. Assuming there is no other doubt, others. So should the second also be 10 per second? Second, did I make some cellular? I've done a cellular like what Bharat does. This is 10 is power seven. Bharat, I'm catching your habit. What should I do? Bharat is gone. Sir, I'm still here. What should I do to remove cellular? Sir, I don't know. Okay. All right. So next we are talking about see the right now we have just introduced PN junction. We have not created a device made up of PN junction. Okay. Now we're going to talk about the devices. Which can be made out of PN junction diode. And first such device is the rectifier. Okay. Please write down junction diode rectifier. Do you know what is rectifier? What does it mean? It converts AC to DC, I guess. It doesn't allow like a backward flow of current like only one direction. And also just prevents any huge spikes in the voltage. Wait rectifier doesn't do that. All right. Junction diode as a rectifier. So like what Sukit said junction diode. Sorry rectifier basically helps to convert the alternating current into direct current. So you can use the junction diodes to convert AC into DC. In fact, you have the laptop charges right laptop charger is there mobile charger is there. So the adapter has a rectifier inside which when you connect to alternative current it converts AC into DC and then it is fed to your laptop or to your mobile phone. Okay. So in fact any device let's say LCD television now nowadays I think almost every device runs on DC only. Because there are a lot of electronics inside and electronics typically work on DC only. So there has to be a rectifier. So rectifier has a very great importance when it comes to running electronic appliances. Okay. So after this like can you tell us how to make an AND gate and OR gate with diodes. That is at the end of the chapter. Wait it's in the chapter. Yeah. Okay. It will actually take another two hours after today's class to finish the chapter. Okay. It's not a small chapter and I'm not going very fast also I'm going slowly. Because it is not numerical right it is more of concept on theory. So I should go slow so that you grasp as much as. Yes sir. Anyways. So this is what the construction of the rectifier looks like. I'm talking about a very, very basic rectifier and I'm going to talk about just let's say this is a representation of how the block diagram is. Okay. This is not exactly how rectifier looks. Please draw this with me first draw it and then we'll discuss why it is the way it is. Have you seen transformers. Yes sir. Not the movie. The transformers. Yeah those transformers. Have you seen transformers? Have you ever broken up let's say an adapter, a laptop adapter or your mobile charger adapter? Not yet. So inside the adapter also there is a transformer. Okay. So what do you might have seen that in an adapter the ratings are typically given like five volts. So input voltage is very high and you want to create five volt out of it. So there has to be a transformer inside the adapter itself. So that is what I'm making here. So I'm talking about the block diagram of the full adapter itself inside the adapter. There is this transformer. This is how you draw a transformer in a diagram. This is primary. This is secondary. Let's say this is point A and that is point B and this is your load. What do you mean by load? Between X to Y there is a load with load resistance RL. Load could be any device. It could be your mobile phone, television, your laptop could be anything. Okay. It is not a useless thing. For load only you are having all this setup. Load can be your electronic device. And here is a PN junction diode. Now let's see what happens. I will draw the input voltage and then I'll draw the output one. All of you draw with me. During the positive cycle I'm assuming voltage of A is more than voltage of B. Okay. And this is how the input voltage is. Let us say. Okay. So what happens is during this positive cycle voltage of A is more than B and negative cycle voltage of B is more than A. Now what happens in the negative cycle? Anyone will diode conduct? No, it won't. Assuming that it doesn't break down. Yes, it will not conduct current is very less and voltage applied is lesser because of the transformer. If you directly connect without transformer, then your diode could break down, but you are decreasing the voltage and then connecting to the circuit. So the diode will not break down and it will not conduct anything during the negative cycle because the negative cycle is a reverse bias cycle and reverse bias the current is zero. So potential difference across a load X to Y will be zero. So what this load will observe is this. Okay. Load is going to see only positive cycle of the voltage. Negative cycle is vanished. So basically you're not letting current reverse its direction or voltage reverse its direction across the load. All right. And hence this is a crude example of how to convert AC into DC. But the problem is half the energy is lost. Almost half of energy is lost. And where it goes, it gets converted into heat and other things. Because of that, the diode could heat up and many other losses will happen. And it is not a good scenario to have. And on top of it, the DC voltage, although it is not changing direction, but its magnitude keeps on changing. That is also not a, let's say a good scenario. This is output and this is input voltage. Any doubt till now? No, sir. Okay. So this is this rectifier is called half wave rectifier. We are going to discuss about full wave rectifier also. This is called half wave rectifier. Okay. Now please write down full wave rectifier in full wave rectifier. I will not have so much loss of energy. So let's first draw the circuit diagram. All of you please draw with me. It is, if you draw with me, you'll understand more about it. So I'll talk while drawing. So the first thing you draw like earlier is a transformer. Now I'll not draw the full transformer. Just part of it is understood. There will be a transformer. This is the transformer and the transformer, the two ends are connected to two diodes. It is like this. And then there is a link that is coming from here. This is the first link. And then you have a center tap center tap is a voltage supply from the center of the secondary side of the transformer. So you have taken a connection from the center of the transformer here. Okay. This you can say it is connected to ground, although it is not required though. And you extend it like this and then you connect a load resistance between these two. So your laptop or a mobile is connected as a load resistance between point X and point Y like that. Okay. And this transformer, which allows you to take the voltage from the center of the secondary is this is a special kind of transformer. It is called center tap transformer. And this please name this as a this is B. This is diode one and that is diode two. Okay. Between X and Y, whatever voltage you get is the output voltage and input voltage will be the voltage supplied. Many of these adapter don't have a third ground terminal. So how they do it? Yeah. So like I said, the ground is not required as such. So no all the like no fluxes like properly lost to the ground or like how it is like all the fluxes going there. So grounding is done so that you don't get a shock. Okay. Not for anything else like what are you saying? Grounding also is done so that there is a reference voltage. Like if you want to compare the voltage with respect to something, you when you said to old to will compare to what? Yeah, you connect all the ends of all the points. All the ends of what I'm saying to connect all the ends of a circuit at a single point and then start comparing all other points voltage with respect to that. And you start calling that common point as ground. Okay. There's nothing called zero voltage. Okay. It is just assumption. You can assume zero voltage anything. So this is the input voltage. Now I'm going to draw the input voltage for both a and b. How can I drop both a and b? I'm comparing the voltage with respect to this ground. Okay. I'm comparing the voltage of a with respect to ground and then voltage of B with respect to ground. Are you getting it? And then plotting the voltage at a and voltage at B. Okay. So the waveform at a and waveform at B. So during the positive cycle when this voltage at a is more than voltage at B. It'll be like this. And it goes like that. Yes or no. I'll extend it. It will like this. Let us say now what kind of waveform the B will have when we a is more than ground then we B will be more than ground or less than ground. Tell me less than ground. It should be less. Suppose this voltage is VC. Okay. I'm saying that VC. I'm assuming to be zero VC is assumed to be zero. Okay. And I know for the fact that VB is less than we a and we B is also less than VC because VC is in between. So if I assume VC to be zero VB will be negative. Yeah. All of you understand this is very critical. Yeah. Yes, sir. Okay. So the waveform at B compared to the ground will be reverse of it will be 180 degree out of phase. If these two waves meet, they'll disappear. I mean, if they are light waves anyways, this is the output. I'm now plotting the output voltage extended down. Let's talk about our output. So during the positive cycle, this is positive B has a negative cycle. When this is negative B has a positive cycle when a is positive B is negative like that. So if a has a positive cycle, D1 will conduct electricity, right? But D1 can conduct electricity only when it gets a loop. So it can't go like that. This is not possible from P to N current will not flow across D2. So that is discarded. So what it will do is that the current will travel like this. It is going to be X going to go through X like this. It goes like that. And this is how it completes the loop. During the positive cycle, okay? And during the negative cycle when a is negative, a stops to conduct, but when a is negative, B is positive. So that is the reason why now what will happen B will conduct. So red lily thing. Okay. So now it will go like this. It will go like that. It flows like this. Then it goes through this and it is going to go like that. So in both ways, whether a conducts or B conducts, both the ways it is getting a loop. Yes or no? Yes, sir. Okay. And in both the ways the current is going from X to Y only. The direction of current is not reversed across the load. So voltage of X will always be greater than voltage of Y. No matter which diode is conducting. Current direction is same. Because of that, you're going to get this voltage across the load. So you're not losing much of power. You're going to get the, this side. This is due to D1. This cycle is due to D2. And this cycle is due to D1. So like that, D1, D2, D1, D2, like you'll get. Okay. One more thing you can see that if frequency of input voltage is F, frequency of output voltage will be how much? Two F. Two F. This cycle will repeat two times. Okay. When one complete cycle of input voltage is repeated. So we have actually got rid of that problem that a lot of power loss was happening. But still the problem of not having a constant voltage is still there. So how to correct that is what we are going to discuss next. capacitor inductor. So I'm assuming no doubts. If you have any doubts, please pick up or type in. So I'm not going to draw the entire circuit of rectifier again. I'll just draw a box and I say that that rectifier is inside this box. Fine. Because that is a fixed circuit. I'm not going to modify anything inside it. So this is your input AC. This is your rectifier. F, I, E, R. Did not. Let me try again rectifier. So this is rectifier. And then you're having the two branches like that. Which are these two branches? These two branches are these. One is this. The other one is that in between the load should be connected, but I'm not connecting the load immediately right now. What I'm doing is I'm connecting a capacitor first like this. And then I'm connecting a load. This capacitor is called filter. Okay. This is called filter capacitor. This is the load resistance. Fine. This is let's say point X and this is let's say point Y. So what happens is that if there is no filter capacitor, you are going to get the output like this that we have just learned. But if there is a filter capacitor during the first cycle, the capacitor will charge up to this voltage. And then when the voltage is trying to decrease, what will happen? Voltage across capacitor should also decrease because Q is equal to CV. If you decrease the voltage of the capacitor, charge in the capacitor should decrease where the excess charge will go. Excess charge will just flow through the load from the capacitor. When you decrease the voltage, when you try to decrease the voltage, the charge will flow towards the resistance. And it will resist the change of voltage across the resistance. So basically the current got compensated because of the capacitor. So voltage across the load tries to drop, but almost remains constant like this. Okay. So I can draw it like this. So this is dotted now. Any doubt guys, how it is done? We're not getting into a mathematical expression of exactly what has happened, how it has happened. But this is what happened in principle. Any doubt with respect to concept here? Anyone? Yes sir, could you just explain the graph again? See, when the voltage across a capacitor tries to decrease, the charge from the capacitor will flow. And it will compensate any decrease in voltage across the load. So it will not let the voltage across the load decrease. So the load resistance is getting the current not only from the source directly, but also from the capacitor. So the capacitor won't discharge quickly. Like it's able to charge quickly, but it won't discharge quickly. Capacitor will discharge only that much which the voltage will allow it to. So but then, sir, it's able to quickly like charge to a maximum. And then when the voltage is not there, it's taking long time to like... No, it is not taking long time. I am calculating potential difference across RL. I am not calculating potential difference across capacitor. Okay, sir. Because a load, it is like a charging, discharging circuit, right? Yeah. So the charge across the load, we have done this, right? Charging and discharging of capacitor. Time constant is R into C. Yeah. So typically load resistances are higher. Time constant is high. Yes, sir. But then... On the left-hand side, it is almost like zero resistance. But then in the beginning, it's like fully able to charge quickly, right? Though it has a very high time constant. So how is it like charging quickly? That's the thing. No, it is getting charged from that side and it will charge with the voltage which is... I have unnecessarily discussed about the charging basically. Alright. So I should have discussed it from the point where it is already charged. Okay. Still, if you talk about its charging, let us say it takes time for charging. Okay. Let's say it takes time. So what? Okay. So it will be trying to charge at the maximum for several cycles and then it will require a pretty high charge and then it will follow the graph which you have drawn. No, no, no. It will follow the graph only during the charging. Okay. And it will have the maximum charge. Alright. What capacitor will... See, capacitor typically they want to resist any change in current. Yes or no? Yes, sir. The inductor tries to resist any change in voltage. The capacitor tries to resist any change in current. So the moment the current through the capacitor tries to decrease, it will increase the current. Yes, sir. Got it. Charging itself. Okay. That is like inertia against the change of current because of capacitor. Inertia against change of voltage is because of inductor. Why that happens? It comes out mathematically. Okay. Yeah. All right. So how much time do I have? I have around 10 minutes. So next is a special purpose PN Genshin diode. Okay. You might have heard about Zener diode. Zener, Zener. Go on. Sir, we've done experiments with Zener diode. We have made the voltage stabilizer. No, we just had to make that characteristic curve. Okay. Great. Head on PN Genshin special purpose. Now what makes a Zener diode special compared to the other diode is that even if it breaks down, you can use it again and again. Whereas a normal diode, once it breaks down, you know what is breaking down means you create huge amount of reverse bias voltage and your bonds will break and tremendous amount of current will flow because huge amount of current flows through the diode. The amount of heat energy that get generated is very high and hence your diode will just burn out. Okay. Whereas Zener diode has a special diode which doesn't burn out and you can use it again and again even if breakdown happens. Okay. So the way we are using Zener diode is that we are trying to use it at a zone where the breakdown of a Zener diode happens. What is so special about that breakdown zone? Let us first discuss that. So if we notice typically a diode's characteristic curve looks like this. This is what we have plotted. It was like this and then this was a typical characteristic curve. I am saying that I am going to operate Zener diode when breakdown happens after this voltage. Okay. Now you see that something very interesting happens at the breakdown. The breakdown no matter what is the value of current, this current could be infinite also. Corresponding to that current, if you try to find out what is the voltage, voltage remains fixed. Fine. So after a point, voltage across the Zener diode or any diode, if breakdown happens, then potential difference across the diode will become fixed. Okay. So I can use this property like a voltage stabilizer. Suppose breakdown happens at 80 volt and I don't want my television to get exposed to potential of more than 80 volt. So I will connect my television across the Zener diode. So whatever happens to the Zener diode, Zener diode will never let voltage across itself to be more than 80 volts. So my television is secured now. Even if outside voltage is 1000 volt, then also the voltage across the Zener diode remains 80 only. So this property is very useful. And Zener diode can be used again and again for this purposes. And since it is used very widely, that is why we are having a special symbol to differentiate Zener diode from the other kinds of diodes. So this is how I represent a Zener diode. So please write down the voltage stabilizer. I'll first talk about the circuit diagram of voltage stabilizer or voltage regulator. Then we'll discuss it. Please write down Zener diode as a voltage. First we'll draw the circuit. Please all of you draw this across the Zener diode as expected will be the load resistance. So this is the load which could be television, mobile phone, AC, anything. There should be some resistance RS connected like this. And this is the input voltage which is unregulated. Input voltage is this. And this is regulated voltage or you can say stabilized voltage across a load. So this is regulated voltage VZ. Okay. What happens is that if input voltage is very high, then breakdown of this Zener diode will happen. So suppose this is let's say Zener diode, please write down works under reverse bias. So this will be negative potential. This will be positive one. No, sorry, reverse of that. So this is P type. So this has to be negative. That has to be positive. So a large amount of voltage is applied. Breakdown happens and the voltage of the Zener or across a Zener, the voltage becomes fixed. And hence the voltage is stabilized across a Zener. And that is what is called regulated voltage. Okay. Any doubt? Anything? No, sir. Sir, speak up. Most of you are keeping quiet. No doubt sir. Sir, what's the purpose of RS? What is what? What's the use of RS? If you have input voltage of 1000, RS is not there and Zener diode across should be 80 only. It will create huge amount of current. Zener diode could have a resistance of let's say just one ohm. So potential difference across one ohm plus potential difference across one ohm plus potential difference of Zener could be 80 volt. So across one ohm plus 80 ohm, 80 volt should be equal to the input voltage 1000. So voltage across one ohm should be 1000 minus 80. So current should be huge and such amount of current is not very safe. Even though Zener diode could be used again and again, but still it cannot be exposed to a huge amount of current. It will just burn it. Okay. So how large is RS? It's somewhat large. RS is somewhat large so that the current over here is reduced. Otherwise this current will be very high. Understood. You will understand more when you solve a numerical. So can this be used even when the voltage drops like really low? Why you want a regulatory voltage is very low. It is not going to increase the voltage. It is not a source. It can't generate power. Okay. It can just let the voltage to be regulated, but if input voltage is less, it can't increase it. So just puts an upper cap on the voltage. Yes. I'm talking about only this circuit, but nowadays there are some devices that can stabilize the voltage. Voltage stabilizer and voltage regulator are two different things. All right. So there is a safety criteria, which you should remember. Please write down safety criteria. The safety criteria is that the Zener current, the current across Zener should be roughly five times the current in the load. Okay. It cannot be more than five times. Otherwise Zener diode will start burning out. This is just a rough, this thing, safety criteria, which people normally follow. Okay. So this you can treat as an equation itself. Fine. Now let us take a numerical. Okay. Here is a numerical and put it on the screen. Solve this numerical. So is it 500 ohm? Others. So I'm getting 166.66666. I'm getting 41.6 is probably wrong. Oh my God 416 416.6. It's probably wrong though. Okay. You said something someone said. I said two hundred. 200. One second. One second please. So 166 is right. Okay, I'll do it now. Yes, sir. Yes, sir. What? How is it 166? I'm going to show you how it is. So input voltage is 10 volt. Xenobreak down happens at six volt. So voltage across RS will be four volt. Yeah. Okay. The load current should be four milliampere. So load current should be four into 10 is power minus three ampere. Yeah, Xenocurrent should be five times of that should be two into 10 is power minus two ampere. Okay. What should the values of series resistance RS. So this is IZ This is IZ. So this current will be what? Some of these two So I will be equal to IZ plus IL, which is 24 into 10 is power minus three ampere. Okay. And this current into the RS resistance should be equal to four. So RS will become 1000 divided by six. That's 166. 0.6167 ohms understood. So numericals are straightforward in this chapter, but they're counter intuitive because you have never seen such scenarios. So and on top of it, there are a lack of questions from this chapter. So you get a source of good questions from this chapter. Please give it. I mean, please solve a lot of questions from that because there are not many good books available, which gives you a set of questions on this chapter. Okay. I'll try to send you a set of questions on whatever topics you have done today. And that's it for today. Meet the next class. Okay. Yes, sir. All right, then we'll Bye bye. Thank you. Thank you, sir.