 Our next lecture is about about the p-n junction right. So, somebody asked you know why can we use only p-type or n-type semiconductor? Answer is no, we have to use p-n junction in order to make a solar cell ok. So, let me start the next thing continuity equation and p-n junction solar cell. In the last lecture we have discussed about the carrier generation recombination, direct and indirect band gap semiconductor, absorption coefficient, length recombination mechanism, carrier lifetime and so on. Here we are actually going to discuss continuity equation. Continuity equation is one equation which is which if you solve that equation you can get the performance of your device or basically continuity equation is the starting point of your solution in order to get the equation for your device right. Somebody knows the equation for the p-n junction diode. What is the equation for p-n junction diode? i equal to i 0 e raise power qv by kt minus 1. So, that is equation for p-n junction diode and that equation actually the starting point of derivation of that equation is nothing but the continuity equation. So, continuity equation we will discuss and the most important thing is p-n junction because my p-n junction acts as a solar cell and see we started from the very fundamental we looked at the solar radiation, we looked at the various parameters of a semiconductor mainly the 4 events charge creation charge transport generation recombination. Now, we will all put all this together in the form of continuity equation so that we can now how solar cell is going to perform. So, this is what we discussed minority carrier lifetime and then we have discussed that you know the excess carrier concentration will decrease exponentially with respect to time and the characteristic of the exponential decay will be minority carrier lifetime that we have seen this is just revision. We have also seen that the change in the majority carrier concentration is not significant, but the change in the minority carrier concentration with respect to time is significant. So, we have seen this with respect to time we have to also see the what happens with respect to distance right. So, continuity equation is actually the equation which takes all kind of actions taking place on a carrier right. So, in a device the p-n junction you can consider as a box and when light falls on it carrier generates there is a thermal generation taking place there is a carrier drift taking place there is a carrier diffusion taking place and when you connect the when you connect the solar cell to external load the current is flowing outside and some current is inside. So, basically within a p-n junction lot of things are taking place and once we actually combine put all this behavior together in some equation form. Then we can solve that equation with the proper boundary condition and once we solve this with the proper boundary condition we get the current voltage behavior of a device and in this case what is our interest our interest is to find out the current voltage behavior of a solar cell. So, continuity equation is this you look at the black box here there is some box. So, some current is going in where J p J is by the way current density and p is for the hole. So, some hole current is going in this box some hole current is coming out some generation is taking place some recombination is taking place. So, these are all the events that is taking place and within this because current is going in and out what else is taking place, drift is taking place and diffusion is also taking place, drift is taking place and diffusion is also taking If I want to summarize this, whatever is taking place in this box, if I want to summarize this, I can put it like this, that the rate of change of whole concentration with respect to time within this box. The whole concentration, first of all some current is coming inside the box, which means, which is increasing the current, whole concentration. Some current is going out of the box, which is decreasing the whole concentration. Some generation is taking place inside the box, which is again increasing the whole concentration and some recombination is taking place, which is reducing the whole concentration. So, that is I want to put here, that so this part is actually taking care of the current, which is coming in, current which is going out within, this is taking within the distance x plus x plus del dx. So, within the dx delta x, this is taking place. What is this term? X s carrier concentration divided by the minority carrier lifetime, what is this? Rate of recombination and G is a generation rate. Now, by my differential, this thing, I have to put minus here, because my final current, initial current divided by delta. So, I have to change this term here and that is why minus will come here. So, basically the rate of change of whole concentration with respect to time and distance x and t. Now, we are talking about change in the concentration both x and t can be governed by this equation and this is called the continuity. It takes care of the generation, it takes care of the recombination, it takes care of the current which is leaving, it takes care of the current which is coming. So, basically drift, diffusion, recombination, generation everything is taken care in this equation and if you solve this equation, I get the solution for my device continuity equation. Continuity equation can be simplified in various ways and we will come back to that why need to simplify. Current as I said discuss can be because of the drift and it can be because of the diffusion. Current because of the drift depends on the electric field, current because of the diffusion depends on the concentration gradient. If the electric field is 0, drift current is 0. If the electric field is 0, drift current is 0. So, in many case, what happens in your semiconductor? There is no electric field and therefore, what is possible? If the electric field is 0, then the current will only because of the diffusion. So, the drift current component will become 0, it is only because of diffusion and in that case, I am going to put here this current and this current will only be diffusion current. So, if I do that, then my continuity equation becomes a diffusion equation, simple equation. The drift current component part is not there. So, assumption is that your zeta equal to 0, which means electric field is equal to 0 and that is actually true for the many parts of the device will come back to that. So, when I solve the diffusion equation for the various solutions. So, let us how the diffusion equation has come now? Same thing here, j is this and when I put j here. So, this is the diffusion assumption is zeta equal to 0, electric field is 0. So, my current is only because of the concentration gradient, which is a diffusion current component. If I put this into this, if I put this into this here, I get this equation. This is called my minority carrier diffusion equation. So, minority carrier diffusion equation can have a many simple solution and that is what we will discuss here. So, remember this is your minority carrier diffusion equation. So, rate of change of delta n with respect to time, so second order differential with respect to x. So, it takes care of the change with respect to time, it takes care of the change with respect to distance and this is what is the rate, the combination rate, generation rate. So, what is my situation? I am talking about study state. What is study state? Study state means, study state means no change with time, no change with time. So, when there is no change with time, what will happen to this term? It will become 0. This is called study state. What is the other possible situation? The concentration, no change in the concentration, no change in concentration. When there is no change in concentration, what will happen to this term and second order? I am writing for the whole, but same thing can be written for the electron also. When there is no change in concentration, this will become 0. When no change with respect to time, this is 0. When no change with respect to concentration, this becomes 0. When there is no generation, no generation due to light, then what term is 0? G equal to 0. No generation will light, G equal to 0. And then, when there is no recombination, when there is no recombination, then your delta P by tau P, that is recombination rate, this is equal to 0. So, these are the four situations in which four different terms that appears in diffusion equation can be 0. Study state, no change with time, this is 0. No change in concentration, this is 0. No generation rate, G equal to 0. No recombination, this is equal to 0. So, what is the study state? This is 0. So, what is study state and no light? No light means no generation, so G is also 0. So, this is your simplified equation now, simplified diffusion equation. And if you solve this, this is the second order differential equation with 0, right hand side is 0. You will get this kind of solution. You get this kind of solution and let me put again this kind of solution. So, your solution is change in the delta with respect to x, because with respect to time, there is no change. So, this term is anyway 0. So, what is changing is only with respect to it. So, delta P with respect is equal to some constant e raised to minus x over L P plus B plus. And notice, what is already, when you solve is there, L n and L P is. So, here I am talking about L P is equal to square root of D P and tau P. Diffusion length, this comes from this solving this equation again due to the shortage of time. I am sorry, I am not going there, but when you solve that equation, when you solve that equation, you will find that when you file that one of the factor that comes is square root term of this, which has a unit of length. And the square root of D and tau, what is the unit of this? So, unit of D diffusion coefficient is centimeter square per second, tau is the lifetime has the unit of second. So, square root of centimeter is centimeter. So, it is nothing but a unit of length. And that is why this factor L P equal to square root of D P or tau P is called the, as I am having length and it is called the diffusion length. It is called the diffusion length, diffusion length of minority carriers. Again, we are talking about minority carrier, why? Because we are talking about diffusion and diffusion, the concentration gradient for majority carriers is not there. It is a minority carrier that results in a significant concentration gradient and therefore diffusion. Again, in this term, this will component will become, B will become 0 because this is positive term. So, your carrier concentration cannot increase. It is only going to decrease and therefore, which means the B term has to be 0. So, basically your excess whole concentration, minority whole concentration will have some term, some constant A which is e rest of minus x over L P. So, with respect to distance, what happens there? Earlier we have seen with respect to time, there is a recombination taking place. What happens? With respect to time, there is a exponential del k. Same thing we are seeing here. Now, with respect to distance, your delta P excess whole concentration will decay exponentially and this is x distance and this characteristic slope will be e minus x over L P. So, two important thing to learn, if there is excess carrier concentration, the excess carrier concentration decreases exponentially with respect to time due to the recombination. Also, excess carrier concentration decreases exponentially with respect to distance due to recombination. So, an earlier case, if the time variation is there, if things are varying with the time, this is by the way the previous case not here. This is the previous case not here. So, there we have say delta P with respect to time is varying exponentially and the characteristic was t over tau P and if the change is occurring with respect to distance, the decay will be exponential again and the characteristic here is L P diffusion length. Lifetime tau P is a lifetime, L P is a diffusion length. Again, very two important material parameters for solar cells. Other two important parameter I talked about is mobility and diffusion coefficient and the next two parameters is carrier lifetime, minority carrier lifetime and diffusion length. Minority carrier lifetime is what is the minority carrier lifetime. So, let me put those parameter so that you remember. So, mobility is important, D is important, tau is important, L is important. Diffusion length is the average length travelled by a charge carrier before it recombines. What is happening here? With respect to x, so carriers will actually diffuse and eventually reduce and they will recombining. This is due to the recombination, the average length that is travelled. Similarly, for the when you are talking about the with respect to time, with respect to time when the carrier constant decreases, when it decreases to certain level, we say it is the carrier lifetime. Mobility is the ease with which the carrier flow in a semiconductor, diffusion coefficient is ease with which the carrier diffuse in the semiconductor. So, these are the four most important parameters a scientist working in a solar PV is worried always. Whether you are developing cadmium telleride solar cell or amorphous silicon solar cell or silicon solar cell or gallium arsenate, any solar cell that you develop in the world, mobility diffusion coefficient carrier lifetime diffusion length. For the let me give the units again this is the unit of length typically given in micrometer unit of time it is given in microsecond. Mobility unit is centimeter square volt per second per volt second, diffusion coefficient is centimeter square per second. Typical diffusion length of the carrier I am talking about silicon now. Let me take the example of silicon. Typical diffusion length of the carrier that is the average length the carrier travel before the recombine is about 100, 200 micrometer. Typical lifetime of a silicon that is the carrier spend in the excited state before the recombine is about 1 to 10 microsecond. Typical mobility now this now both of these are for both holes and electron. You have to look at the holes and electrons. Mobility for holes is an electrons normally higher about 1400, 200 and for the holes it is lower. Diffusion coefficient is 35 for electron I will give the summary of this. So, do not worry about this. So, this is for electron and you get about 400 for the hole. These are the typical number please remember these are the four first of all four important parameter you must understand the significance of each of them because they are very important for the solar cell operation. You should know the rough value of mobility diffusion coefficient, lifetime and diffusion length and these are important when it comes to the diffusion. And in this we are trying to look at the diffusion equation where only the diffusion is taking place. Remember in the previous slide we already assume that electric field is 0. So, we are not considering the drift and in the later slide I will tell you why this decision is correct that we do not have to worry about the drift most of the time in the solar cell you have to worry about the diffusion. So, under this condition steady state and no light you will get this solution under this condition no concentration gradient means this term is 0 right. No concentration gradient means this term is 0 no light means g is equal to 0. So, you get this which is the variation of excess carrier with respect to time you have seen already the solution right very nice. So, this is shows the variation with respect to distance due to the recombination term is non-zero here. Here also recombination term is non-zero. So, change in the concentration with respect to time when the recombination is taking place and that is also exponential decay with respect to time. Study state and no concentration gradient study state means this term is 0 concentration gradient no concentration gradient means this term is 0 both this terms are 0. So, what is left is this. So, what is it means the excess carrier concentration is the function of lifetime and generation rate unit of generation rate is per unit volume per unit time. So, when you multiply with the time you get the excess carrier concentration. So, when you are putting some light how much is the excess carrier concentration and you can find out from this. So, this is the way simple solution you can get. So, this is an example which shows that let me explain you this is in your tutorial this problem is in your tutorial. So, I have semiconductor like this x equal to 0 here x equal to 0 and this is x equal to L. So, L is the thickness of the silicon light is falling on it from this side what we have discussed in the absorption we discussed when we discuss absorption that if the high energy photon it will absorb very close to the surface. If it is a low energy photon or a low absorption coefficient photon it will go deeper. So, assume that I am talking about high energy photon. So, absorption is taking place only here absorption is taking place only here. So, as a result of that what is happening here close to the surface you are creating excess holes. Let us say this is my n type semiconductor. So, my minority carriers are holes. So, I am talking about excess holes. So, because you are using high energy photons your absorption coefficient of high energy photons is high and therefore most of the photon get absorbed very close to the surface may be 15 nanometer 100 nanometer depending on the wavelength. So, this excess carrier concentration is and this is continuously happening your light is not off it is continuously on continuously on what will happen now. So, if I plot the p equal to 0 scenario your situation was in a equilibrium. So, you have this this is your p 0 equilibrium carrier concentration because of the light falling your sum of the carriers are generated here this is also p 0 this is p now right carriers are generated here. So, what is what you see here this is x this is a concentration axis what you see the difference here concentration difference. So, because of this concentration difference this carrier will diffuse in this direction carrier will diffuse how they will diffuse how they will diffuse look at the solution of my minority carrier diffusion equation how they will diffuse exponentially. What is the exponential factor diffusion length they will diffuse with the diffused characteristic figure of diffusion length. So, this carrier will excess carrier will diffuse and this exponential curve shape of the exponential curve will depend on the diffusion length l p as long as you are putting the light this will take place as long as you are putting the light your carrier will keep on diffusing and the profile will become almost a stable. And this is what also happen in solar cell as because when you are putting the light continuously continuous generation is taking place some place then you are diffusing. So, this is what we have and use please solve this problem this problem is nothing very simple. So, what is given is the doping level is given excess carrier concentration is given at the surface and then it will diffuse. So, basically you need to plot at various depth what is the remaining carrier concentration it is nothing, but a simple exponential decay function. So, do this in a tutorial quasi Fermi level we do not bother about again shortage of the time, but basically what happens your Fermi level changes when you are putting light, but because of the light you are actually creating extra electron and hole and electron and hole result in the shift in the Fermi level that we have discussed. Because of the doping you actually create more electron or more hole and because of that your Fermi level shifts either closer to the conduction band or away from the conduction band. Similarly, either closer to the valence band or away from the valence band. Similarly, when you put a light on it you both electron and hole is changing concentration is changing and therefore, you will change the Fermi level position. So, now, so the again so the continuity equation and what happens under the specific condition when the there is no change in the time when there is no change in the concentration gradient when there is no recombination or no generation. So, now the most important thing is now the p n junction which acts as a solar cell. How to make a p n junction? Take a p type and take a n type put them together make a p n junction. By the way, can a simple semiconductor be used to generate the power? That is more important question. Somebody has asked this, can I use a only n type semiconductor or p type semiconductor to generate power? Who will give me the answer? You will give me the answer. So, let me give this example that if I keep my pen here, if I keep my pen here this is my table here. Where is the pen going? No, it is not going anywhere. Why it is not going anywhere? Because it is a equipotential surface. A potential energy of each heat point is equal. So, pen is not going here. In the instead of these if I have a if I create a difference in the level. So, I take another thing now you created a difference in energy level. So, at this point potential energy is higher and at this point potential energy is lower. If I keep my pen here now what will happen? See what is happening? My pen is always going from low energy to high energy. My pen is always going to low energy to high energy. So, the automatic moment of an object will occur when there is a different energy level. So, now coming back now coming back here to the white board that this is what is what is my this axis? Potential energy and this is distance. What do I see? Potential energy this is a flat line. This is my conduction band H. This is my valence band H. The line is flat which means potential energy at this point at this point at this point at this point at every point is same. Potential energy at every point is same. What does it mean? If I put a light on it and if I create a electron and a hole here in which direction the electron will go? If it is not recombining which direction will electron will go here here or here? It can go either direction because energy levels are same energy levels are same. So, conduction band when it is a flat it is a constant potential energy level. So, once electron is generated it can go either here it can go either here also. So, half of the electron is moving one side half of the electron is moving one side the net motion of the charge is 0 and the net motion of the charge is 0 means no current. So, basically which means if you have only flat energy bands electron current conduction is not possible it is not possible right. So, what you need to do? You have to create a difference in the potential energy right. What does it mean? If I somehow have a level like this and a level like this what do you see now here? This point potential energy higher this point it is lower this point even lower this point even lower this point even lower ok. Now, if my generation takes place here what will happen to this electron? What will happen to this electron? Will it go left hand side or it will go right hand side? Answer is it always go right hand side right because it is going down in energy this electron will always go down in energy right. So, I need to create that energy level difference so that my electron goes one side my holes go one side I create positive charge one side negative charge other side and I generate that voltage and therefore, my direction of current should be u 1 ok. Electron should not be confused some electron go this side some at go other side and no current close got it very I have this point should be clear to all of you that potential energy. So, single semiconductor either it is a p type or n type can never act as a solar cell you require two semiconductor one is p and one is n. So, that you can create this kind of n potential energy difference and that is important ok. So, you make a p n junction take a p type and n type I will give a separate lecture on actually how in industry we make solar cells. So, we will not spend time on this. So, this is what happens ok when you take a p type. So, this is your p type semiconductor look at here Fermi level is close to the valence band this is your n type semiconductor Fermi level is close to the conduction band when you put them together one thing happens that again due to the shortage of time I have not discussed with you one thing happens is the Fermi level aligns ok. Fermi level of materials in contact with each other remains same at equilibrium ok whatever you do right whatever you do Fermi level of two materials in contact with each other at equilibrium always remains same. So, what does it mean if I have a p type semiconductor with Fermi level here I have n type semiconductor with Fermi level here in equilibrium even if I put 5 semiconductors together Fermi level is always going to be constant for all those 5 ok. And this is a very important theory behind it that if Fermi level is not constant some energy will automatically flow from one semiconductor to other semiconductor and that is not possible that is not possible right otherwise you will have immediately some voltage generated that is not possible. And therefore, that requires that Fermi level should be same. So, when when you want to draw the band diagram of p and n together right this is a band diagram this is the band diagram or energy band diagram to be more precise energy band diagram for the p type and this is energy band diagram for the n type ok. I want to draw the energy band diagram of p n junction together how to draw it energy band diagram of p n junction how to draw it. So, because my Fermi level is constant throughout the material whether it is a 1 or 2 or 3 or 4 or 5 whatever number of materials I need to draw first of all a constant line and this line is now my Fermi level ok. Now, with respect to my Fermi level I can draw other energy level right. So, in p type semiconductor my valence band is close to the Fermi level and my conduction band is here. So, this is my p type now side in the n type my conduction band is close to the Fermi level and then this gap is equal to the band gap then I have the conduction band and this gap is equal to the band gap what happens in between in between you have to have the smooth connection ok. So, this is the way you can actually draw the band diagram of p n junction any material right you can now. So, this is your n type now. So, this band gap should match this band gap should match equal to your silicon. So, both p type is silicon n type is silicon you have to make 1.1 ok sometime p type can be silicon n type can be germanium is that possible yes that is possible in cadmium tellerite solar cell for example, cadmium tellerite itself is a p type and it makes a junction with the cadmium sulphide. So, actual cadmium tellerite solar cell is nothing but a. So, cadmium tellerite solar cell is cadmium sulphide and cadmium tellerite. So, this is how the junction is make this is p type and this is n type. In crystalline silicon solar cell both p type is crystalline silicon n type is also crystalline silicon, but in cadmium tellerite this is like this same thing is C i g. Since C i g is also you have the n type cadmium sulphide and C i g s is p type. So, this is your p type this is your n type. So, easy to plot a band diagram draw the Fermi level constant and then with respect to Fermi level you draw your valence band and conduction band both for both p type and n. So, this is what I have done here with respect to Fermi level you draw your valence band and conduction band look at this thin dotted line this is the Fermi level which remains constant and that is the theory that we have to follow that under equilibrium condition any materials putting together Fermi level remains same everywhere ok. Now, we are coming closer to the operation of a p n junction and then we look at the solar cell. So, in p n junction in the p type n n type semiconductor you have lot many electrons and there are many. So, electrons are the mobile carriers right electrons one which is donated, but after donating the electron the phosphorus atom becomes positive charge right that we have seen phosphorus atom become positive charge in p type boron is there boron takes electron taking electron becomes negative the, but there is a hole which is there which is positive right. So, that is why now this phosphorus atom itself cannot move in a lattice, but this electron which is donated can move around. Similarly, boron after taking electron the boron atom is fixed, but the hole which is created is moving right. So, the that is I mean here the charge carrier which is shown by the circle is actually mobile carriers and the fixed charges the charges which are shown by the rectangle are actually charges due to the atom and this is true right the charge neutral it has to maintain the total positive charge is equal to total negative charge ok. So, in p n junction we have this kind of situation at equal to 0 now look at this mobile electrons which are there many mobile electron at the n site and there are many mobile holes at the p site right there are many mobile electrons at the n site there are many mobile holes at the p site. So, this when this electron. So, basically when you connect them together what should happen there is a concentrating difference of electron at one side and less electron at the other side right more electrons at the n side less electrons of the p side. So, there is a concentration difference of electrons. So, electron actually must diffuse from n side to p side right. Similarly, holes holes are mobile in the p side. There are lot many holes in the p side, but less holes in the n side. So, lot of holes should actually move from p side to n side. And this why they should move, they should move because of the difference in concentration. Therefore, it is called diffusion. Diffusion should take place. It does take place indeed, indeed it does take place. After this electron here, it goes there, this hole comes here and they recombine with each other. As I said, when diffusion takes place, the carrier moves and they recombine. Minority carries the move and they recombine with exponential decay that we have seen. So, how long the diffusion should take place? All the carriers should actually merge with each other and die out or what will happen? So, when the electron is leaving behind a fixed positive atom, phosphorous atom, you create a layer of positive charges. And this when the hole is moving, it leaves behind a fixed negative charges. And what this fixed charges are? So, earlier there was a phosphorous atom which was positive charge and there was electron. And this is my junction, phosphorous atom and electron, phosphorous atom and electron. Then I have boron minus and a hole, boron minus and a hole, boron minus and a hole. This is a time t equal to 0, when you just brought them together. Now, you are allowing them to move. So, this electron will go and recombine with here or this vice versa. So, this will recombine with this, this will recombine with this. There are many, many others. There are many electrons here and there are many holes at this side also. We are not taking. We are just looking at the interface. So, after that what you will have? You will have the positive charge. There are the positive charges which is left behind. These are the negative charges which is because of the boron atom. These are the positive charges because of the phosphorous atom. They are fixed. They cannot move. Atom cannot move. So, what do you see now? One side of the line, one side of the line there is positive charge, other side of the line there is a negative charge. So, positive charge separated by negative charge you have a electric field. There is an electric field now, electric field set up. Electric field is set up because of this with this direction. So, this electric field will do what? This electric field will do what? Now, because of the electric field, remember this is the p side and this is n side. There are lot many holes here. There are lot many holes. This electric field in this direction and force on the holes is also in this direction. So, this electric field will not allow hole to come in this direction because the electric field will repel it. Similarly, force on electron is in the opposite direction of electric field and therefore, it will not. This electric field may not allow electron to come again, more electron to come. Therefore, after sometime this electric field that will set up, it will stop the flow of majority carrier from n side to p side and it will also stop the flow of majority holes from p side to n side. And therefore, the electric field is generated at the junction and corresponding to electric field there is a built-in voltage. So, electric field is generated and corresponding to that there is a built-in voltage. So, this slide is a good summary of what is happening at the p-n junction under equilibrium condition. What is happening at the p-n junction under equilibrium condition? All this expression can be derived, but again we are running out of time. So, we will not have that, all the derivation I am leaving for you only, this is for you homework, all the homework you do after the course is over or whenever you get time. All this derivation, all this are given in my book, you can read that and do it, I am just giving you the concepts. So, there is electric field that exists and look at here, this is the p-n junction diagram now. So, here the band is flat. So, no electric field, here the band is flat, no electric field. In the junction, near the junction band is not flat means potential energy is different at different point, which means there is electric field. Similarly, potential energy different, different point there is electric field. West side is this side, Fermi level is close to the conduction band. So, it is n type or you can see there are lot of electrons sitting here. So, it is n type, west side is this side, p type lot of holes are here or we can say Fermi level is close to the valence band, very nice. What is this electron here? Remember in the p side, if your doping is 10 for 16, still there are 10s for 4 electrons are there, is not it? n 0 p c is equal to n i square. So, even if there are lot of holes, there are some electrons. Similarly, in n type, there are lot of electrons, but there are some holes. What is happening with this electron and hole? What is happening with this electron and hole? Now, once you have the carrier, what will happen? Carrier will move. How the carriers move? Either drift or diffusion, two things can happen. For the n type, for the electron, this carrier cannot move this side. There are lot many electrons here and less electrons here. So, diffusion should occur in principle because of the concentration gradient, but it will not occur because this electron will have to rise in terms of the energy. Remember what is this axis? So, I have this energy band diagram. There are lot many electrons here. There are lot many electrons are here. This electron cannot go there. They should, they want to go because of the concentration is different, but because the energy, this is the energy level. Energy at this side is high, but possibly this electron can go. So, the motion of this electron will be what? This electron is going here because of the diffusion. So, this is the diffusion reaction of electron. Now, there are many holes here. This is the p side. This is the p side and this is n side. There are many holes here, but there are some electrons here. Can this electron come down? Yes, it is going down in energy. Anything which is going down can happen automatically. Like my pen comes down automatically. So, this electron can come automatically and also it experience electric field. What is the direction of electric field? Direction of electric field is always uphill. Take a thumbnail. Direction of electric field is uphill and therefore, force on electron is in this direction. Force on electron is in this direction. Therefore, this electron will come under the force of this electric field and therefore, this electron will move here under the force. It is called the drift. So, diffusion of electron will take place. Drift of electron will take place. Similarly, this hole cannot go there because by the way, whole energy increases this time. So, this is energy of electron and this is whole energy. Whole energy increases downwards. So, this hole cannot go there, but this hole can go there. This hole will go there because of the concentration difference. So, this is the diffusion of hole. Now, similar to this, there are lot many n side, there are lot many electron, but there are some holes also there. This hole will have the force on this direction. So, this hole will actually come and this motion of the hole will be drift. So, in this condition, everything is happening. Drift of electron, diffusion of electron, diffusion of holes, drift of holes, everything will happen and that is what I have shown here. Everything is happening. It is thermal equilibrium means the situation is not disturbed. No light is falling, no applied is, no bias is applied, no magnetic field, nothing is there. It is all equilibrium, but it is a p-n junction. Because nothing is happening, no contact is made for net current has to be 0, is not it? In your p-n junction device, net current has to be 0. So, it is 0, but the individual current components are not 0. There is an electron drift taking place, there is an electron hole, a diffusion taking place, there is a hole drift taking place, there is a hole diffusion taking place, all this event taking place in a semiconductor, all the time such that the net motion of charge is 0 and that is what is the situation of a p-n junction diode when no light is applied, no bias is applied. In the next lecture, we will see what will happen if you put light on it. Before that, we will see what will happen if you put bias on it. So, this is actually your p-n junction and by understanding this graph, by understanding this graph, you can actually understand what is happening to the operation of your p-n junction. So, far so clear. So, we have discussed lot of thing about semiconductor, we have come to the p-n junction theory and we have, we are utilizing what you have learned, we are utilizing why diffusion occurs, we are utilizing why drift occurs, we are utilizing about what is, what is the meaning when the flat band is there, what is the meaning when the band is killed, when the difference in the potential energy is basically electric field. So, we are utilizing our knowledge whatever we have discussed and with this, we are coming closer to learning how solar cells results in a generation of voltage when light falls on. JHM Rajendra College. Sir, do we get sufficient energy, I mean power generation when we keep our solar panels under artificial lighting during nights? Well, first if you have to define what is sufficient for you, if you define sufficient level, then yes, I mean if you want micro watt power, yes it is possible, but otherwise the intensity is low that it is not going to be useful. Can we light up one light at least? What type of power generation is possible? No, again what light you want to light up? If you want to light up you know 0.1 milli watt LED, yes possible, but otherwise not and remember what is the energy of the photon has to be higher than the band gap of the material, so that is important. There is a question from COIP, direction of drift current due to electron and hole is the same direction, then how it is opposite direction in partial flow you shown in the slide junction at thermal equilibrium. Think about it yourself and when we discussed about why the direction of drift current, by the direction of drift current for electron and hole is again in the same direction, where the particle flow is different because of the different energy level. So, think about yourself which are, so normally the way to look for the direction of the current is first find out what is the driving force. So, driving force is, I will show you for those who are not clear. So, whenever you want to find out the direction of current, first look at the driving force. So, driving force is the electric field, draw electric field, this electric field exert a force on a particle, electron and hole in a different direction. So, the force on electron is in this direction, force on electron, the force on hole in this direction, so that is the next step. So, this is the driving force, this is the motion, it is acting and due to this motion when electron is going in this direction, our convention is that the current flows in this direction. So, this is the electron current and therefore, my hole is also going in the direction, that convention is that the hole flow is in the same direction as the current flow. So, this is my both the direction the current. So, in the P N junction also that I have shown, actually electron is moving in this direction due to the drift, but the electron current is flowing in the opposite direction. Similarly, hole drift is flowing in this direction and the hole drift current is in the same direction. So, again direction of electron drift current and direction of hole drift current is same, not different. What I have shown here is the direction of the particle only, not this, this is not the direction of current, direction of currents is here. Look at the hole drift yellow line and the electron drift yellow line, both are in the same direction, hole diffusion and electron diffusion, both are in the same direction. So, this is the current flow, this is the particle flow which means electron and hole. How does the P N junction produce the potential difference? You have already said that P type and N type are individually neutral. So, that is I shown when the carrier flows, when the carrier flows here, the sum of the carriers recombine at the interface ok. So, at some portion of the interface, there is only positive charge and some portion of the interface there is only negative charge. So, only at the interface you have the electric field, rest of the place is still neutral ok. This portion of the semiconductor is still neutral, this portion of the semiconductor is still neutral, in between there is electric field for a very small portion ok, this may be in a less than half micron. If your material is 180 micron thick, only about a half a micron of the silicon will have the electric field ok. Does the P type and N type material should have the same band gap? Answer is yes, crystalline silicon, if the material is same, the P band gap of the P type and N type remains the same. Staple college? Sir, actually we have performed one of the experiments like tracking of sun and in that we have plotted V I characteristic and for every time duration, we have noted that maximum power is continuously decreasing in nature. So, could you please elaborate why it is happening, what is the reason behind it and what is the advantage if such kind of solar system is synchronized with the power system. If I understand correctly you are measuring the I V characteristic in a tracking mode, but every time you do the measurement, your power peak power is going down right. Yes sir. Ok, so how much time you have taken to perform this experiment? Sir, we have taken 15 minutes for every reading. So now, so one possible reason could be that you know this point of the time you are in Jaipur you know. So, it is the sun may be setting down very fast, so the intensity of the radiation is decreasing fast and therefore, you know what happens when you actually doing your experiment, if the intensity is maintained constant. So, what you should do actually is that if you normalize your power. So, for each experiment are you measuring the power also solid solar radiation also or not. So, what you should do for each experiment you should measure your peak power and you should measure the solar intensity right and if you actually normalize these two, if you normalize these two, if you normalize peak power per solar intensity, then I think that problem will not be there because I guess that at this time of the hour your sun is setting fast and therefore, your though you are making with the tracking you are trying to get the best possible output, but because your input intensity itself is going down and therefore, your peak power is also going down. So, if my general question is like so whether it is like in practical system where we are doing this kind of system tracking system whether this maximum power is decreasing or not or it will be remain constant. No, it definitely will decrease. So, maximum power see what is the point is like this that normally this is the I V curve of the solar cell or module right. So, this is your current axis this is your voltage axis. So, this point of if cell is operating at this point or module is operating this point your power is 0 because voltage is 0. If the module is operating at this point your power is 0 because your voltage is 0 your current is 0 and there may be some other operating points and we when you plot the power also voltage you will find that there is only one point where the you get the peak power. Now, this peak power is not constant it is a function of a intensity it is a function of intensity or if I explain you know other way that if you plot the efficiency it is what peak power output divided by power input. Now, I am worrying about the power output. So, I can write power output is equal to efficiency times power input. Now, my efficiency of the module is not changing right once you make your module efficiency is fixed. So, what is changing your input power is changing. So, when your input power intensity will go down your output power will also go down even though you are tracking. Yes sir. So, whether some advantages or disadvantages are attached to such kind of system. Now, so when you are doing the tracking. When we synchronize such kind of system with a power system. So, when you are doing the tracking actually you are trying to get collect more radiation. So, if you are not taking if you are not doing the sun tracking your actual output will be lower than the case when you are doing the tracking for the same condition. So, you do actually get a example and you collect more energy by doing the tracking and that your experiment should show that. Thank you sir. Okay, Amal Jyothi college Karala. Sir, our doubt is actually the reduction efficiency it is mainly due to recombination. Is there any any other reason for the reduction in efficiency or reduction absorption of the photons by the material. So, when the solar cell is fabricated the recombination takes takes place always right. So, it is the design of the solar cell the material of the solar cell the processing of a solar cell that determines the recombination right. Now, once you made your solar cell and put into the field in the form of module, but when your module is going down the you know day and night at temperatures changing there is a humidity change and so on. So, the so contact between the semiconductor and metal also eroded gets degrades over a period of time, but that time is a longer you know years and years and years. So, there are other mechanism also that results in a decrease in the efficiency. Sir, for fresh sort of old type cell it want to have the efficiency is less the reason is the main reason is what you called recombination. Well, the reason could be the other reason could be and there may be a reflection there may be a reflection from the cell there may be transmission from the cell the junction of the cell is not optimized. So, these are the same we will see two lectures later. When we look at the design of the solar cell we will see what are the other parameters that affects the efficiency of a solar cell. One more doubt regarding that absorption length that is the physical length of the material which is required is it so sir. Yes, that is the physical length yeah physical thickness of the material that is required to absorb a given photon or given wavelength of the photon. Length of the material which one is this? It is the thickness. So, it is the thickness perpendicular to the surface from where light is entering. So, if you are talking so if my cell if I am talking about this is the material and my light is coming from this direction then this is the thickness this is the absorption length I am talking about before a given ok. So, if this is the surface perpendicular to the light so in this direction I am talking about. Sir, one more it is not exactly related to the photovoltaic theory. Actually can we learn something from the what what you call sun flower sun flower tracking? Yeah, definitely you can learn from many many things in the nature sun flower is one example and that is what is the sun trekking is all about right. You actually keep your module perpendicular to the sun rays so that the amount of light going inside the semiconductor is higher. If your light is coming at some angle then you know some of the light may also get reflected that is the problem. So, if you are fixing your module in the afternoon it is fine, but in the morning and in the evening your light will come and get reflected also because of the small angle with respect to the plane of the glass, but if it is perpendicular then fine. So, if you take your module then actually your module is intercepting more radiation. Yes, sir, but if you go for tracking we have to consider for energy used for that tracking also regarding typically yeah typically typically the energy used for the trekking is very small. Now, because you are actually you know remember how much is the your DC motor AC motor they runs at the 2000 rpm 1500 rpm right rounds per minute. In a solar module trekking you have to trek only half a round per day. So, actually your energy requirement is not much. The total generation is given 1 megawatt solar radiation is 2000 kilowatt hour per meter square per year efficiency 10 percent and we have to calculate the area and circum approximately so and so ok. So, by the way that question was there to confuse you little bit when we want when you want to calculate the area of your module you do not need the information about basically you want to you are equating for the what peak power right. So, when you want to calculate the module area. So, solar radiation requirement information about solar radiation is not required very simple you know when when you have when you have for example, efficiency of the module is 10 percent. What does it mean? Under the standard test condition you get the solar radiation of 1000 watt per meter square that is the standard test condition ok. Under this condition you you know manufacturer's defines the rating of their module. So, when you when you define the rating of module what I said it is not the watt rating it is watt peak rating right. So, P as a subscript is what peak what does it mean? So, if I my module is 10 percent and if it is rated at standard test condition which always should be it means that out of this 10 percent radiation can be converted ok. So, out of 1000 watt per meter square 10 percent of the solar radiation will be converted into the electrical power ok. So, this becomes how much? This becomes 100 watt per meter square 100 watt peak actually not watt 100 watt peak per meter square. Now, what in my question I told you not 1 megawatt I have not given 1 megawatt what I told you 1 megawatt peak 1 megawatt peak remember. So, now, if I divide 1 megawatt peak by this amount which is 100 watt peak per meter square I get my answer in meter square which is 10000 meter square ok. So, my module layer requirement is 10000 meter square there is no need of using any solar radiation information and remember we are talking about not 1 megawatt I am talking about 1 megawatt peak and therefore, using this rated condition I will get this information. I hope it is clear. Next question how can we recycle the solar cell if there any recycling plant why because it is bring garbage after 25 years good that you are worrying about the environment so much. By the way I told you in the introduction also that silicon panel is consist of a glass aluminum and silicon itself and all these materials are completely recyclable. Remember I will tell you in the lecture when we will discuss the manufacturing of silicon that silicon is manufactured from very kind of raw material silicon oxide which is mainly available in the form of sand etcetera. So, from the sand actually we can extract silicon in the form of ingot and wafer and make solar cell. So, I am sure I am sure when there is a pure silicon available in the module and in the glass and in the aluminum the frame it definitely we can be able we can recycle it. So, I do not think recycling will be an issue in the energy band diagram what does the space represent on x axis yeah space is basically I am talking about distance x axis in the energy band diagram y axis is energy potential energy of electrons and x axis is a distance x what is the significance of x axis it is simple the distance right when I am talking about let me go to the whiteboard again and you still could not sort your problem. So, when I am talking so for example, this is my solar it is my semiconductor right. So, this is my x thickness or let us say length right. So, when I when I am seeing that what is the energy level of electron at this point at this point at this point at this point at this point and maybe when I make my solar cell I will actually get a p n junction right. So, p n n so this is a physical space physical distance I am talking about. So, when we draw the energy band diagram like conduction band and valence band I am actually talking about physical distance only. So, this x axis is my physical distance. So, this is my conduction band this is my valence band and this is my potential energy and this is representing this x this x here you can say it is x also. So, this x here represents this x same physical distance we are talking about. Amarjyothi why the mobility of electron and photons at the holes are different. Yeah the question why is the mobility of electrons at holes are different basically. So, you have to consider the you know what is the hole it is absence of electron right. So, suppose in a in a matrix when there are when there are many electrons there are many electrons are sitting there and suppose this is the empty place which is available this is empty place which is available. The mobility is different because of what is called the effective mass of the electron is different from the effective mass of the hole. So, basically the hole appears it to be a heavier particle why it is like that because once this electron is going from this space to this space once electron goes from this space to this space there are various this electron will have a binded by many other electrons. So, there are other forces that is working on electrons it has to break that forces and then get yourself itself free and then go there. So, it is equivalent to that the hole moving from that side to this side electron going from here to here is equivalent to hole moving from here. So, the difference in the effective mass of the electron in hole comes from the fact that the forces that acts upon an electron before it actually can you know unbind itself from one location and go to the other location that is different for both the cases that results in a difference in the effective mass and that results in the difference in the mobility of the carrier and diffusion also of the carrier. So, normally electrons move faster than the hole. There is any question? Yes, go ahead. Is there a particle called phonon? We searched in the internet, but we did not find anything about phonon related to photovoltaics. Are you sure that? Ok. So, phonon is a particle which is described or which is used to describe the lattice vibration. So, energy within the semiconductor can also flow from vibration to vibration and phonon similar to a photon is a particle. The difference between the photon and phonon is that the phonon is considered a high mass and less energy particle and therefore, you know when I showed you that if I go back, if I go to the white board. So, if I showed you that if you have the indirect band gap semiconductor, you have the momentum axis here, you have the energy axis here. So, we have the valence band of semiconductor which is not aligned with the conduction band. And this momentum comes from the theory of the atoms itself. So, now, if I want to excite a electron from my valence band to a conduction band. So, this electron requires a change in energy and it requires change in momentum also. Now, the photon is a very light particle. The mass of the photon is like transfer minus 31 or so. So, therefore, if my electron absorbs a photon, it can only result in change in energy. The momentum change cannot occur. So, where does this momentum change then it will occur? It occurs because of what is called the phonon. And this phonon is in a broadly is associated with the it is a particle which is which you can use in reference to the lattice vibration. So, you can understand it is a kind of physical let vibration of the bonds that you are talking about. So, some of the energy that can be taken or given to the bonds in terms of the phonon. And this is considered as a heavy particle, but having less energy. So, this transition which be caused by the phonon and this transition will be caused by photon. So, when you are having indirect band gap material, you will have the photon and phonon transition. But I am sure if you search on the net, you will find lot of material on phonon also. Particularly in the books of semiconductor physics quantum theory, if you go you can find the details. Sir, thank you. Thank you very much. All the best.