 So, good morning once again all remote centers. In the last thing that we have discussed is about the carrier concentration and about the doping particularly how to increase the electron concentration and hole concentration and that is by doping. The doping level normally increases from let us say lower side 10 for 13 it goes to about 10 for 18, 19 and how much to dope is actually determined by the function that we want from our semiconductor do. One very important parameter in operation of any device is the temperature ok. One very important function of a parameter in operation of any device is the temperature. So, let me go back and tell you something about what we discussed when you are talking about intrinsic material ok, we are talking about intrinsic material. What did we discuss that because of the temperature at room temperature at room temperature because of the thermal energy of the room temperature some of the electron will actually get energy in go and it will create a electron hole pair some other electron will go and create a electron hole pair ok. We create a electron hole pair and the number is at room temperature we call n i equal to P i equal to transfer 10 per centimeter cube that is what we know fine. This we are talking about at room temperature right now what will happen if your temperature increases what will happen if your temperature increases ok. So, fine if you increase the temperature more and more electrons will get enough energy to go ok. So, there will be more electron more hole more electron more hole and this this process is happening because of what this process is happening because of the temperature ok. Light has not come into picture we are still only talking about temperatures. As a result when you increase the temperature what will happen this n i equal to P i equal to transfer 10 per centimeter cube is at room temperature. So, if the temperature is higher what do you expect n i is n i 2 also increase you also expect P i to increase and temperature is higher you want you expect that n i will also increase P i will also increase because more and more electrons get enough energy to get excited and go to the conduction band ok. But in what way it affects the performance of solar cell and many people were asking that what happens to the efficiency of the solar cell when you increase the temperature and the answer is that efficiency of the solar cell decreases because of the increase in temperature and that happens because of exactly because of this reason. Because of increase in temperature your intrinsic carrier concentration that is electron and hole concentration increases and that result in decrease in efficiency how we will see later ok. But the main culprit of decrease in efficiency is this the main culprit for decrease in efficiency of solar cell due to increase in the temperature is increase in this and why it increases because the more temperature and more energy is available for electron so that they can actually increase the number ok. And this is the graph that shows that look at the silicon n i this axis is n i actually intrinsic carrier concentration per centimeter cube when you go from low temperature this side right hand side right most side is the low temperature and this is high temperature when you increase your temperature you can see the intrinsic carrier concentration increases and in some point it can become as good as what is the 10 for 14 to 15 doping level ok and some point it becomes as good as your doping level and that is where the problem starts ok. In reality the doping the at room temperature the concentration for intrinsic carrier in silicon is 10 for 10 1.5 10s 10s for 10 as we discussed germanium has a lower band gap and therefore, it will have higher concentration gallium arsenide has a higher band gap higher band gap means more energy is required therefore, the concentration of electron is and holds in the room temperature because of the thermal excitations lower. One other important thing to understand is when you are doing the doping of your semiconductor and when you are making it p type is the semiconductor become positively charged that is the question or when you are doping your semiconductor by phosphorus and when you are making it n type is the semiconductor becomes negatively charged positively charged means p type doping if there is a p type doping you touch the semiconductor if it is positively you will get a shock will that happen or if it is a n type semiconductor you touch it you will get a shock will that happen answer is no it will not happen why it will not happen. So, why it not happens it it says that there is a always phase charged neutrality and compensation what does it mean it means that if here. So, because of this if you are getting a electron here extra electron because of the hole sorry because of the phosphorus you are getting extra electron because it had 5 electron and you wanted only 4 electron to share. So, it gave extra electron donated extra electron. So, this electron it becomes free when electron leaves the atom the phosphorus becomes positively charged. So, it will become positively charged. So, as a result you will create one positive charge here and there is corresponding negative charge here. So, the what is the net effect net charge in the semiconductor is 0 that is called the charge neutrality. So, the charge neutrality is maintained. So, by doping of the semiconductor it does not become positive charge or negative charge it remains neutral and this neutrality can be explained here n 0 is the charge on electron number of electrons and all negatively charged n a is accepted. So, when hole like boron atom can accept electron and after accepting it becomes a negatively charged. So, the net negative charge is equal to the net positive charge and this p 0 is whole concentration and d is the donor atoms after donating electron it becomes positively charged. So, after giving away electron it becomes positive. So, in a semiconductor net positive charge is always equal to net negative charge it is called the space charge neutrality is always maintained. So, whenever you do the doping your semiconductor does not become either positive or negative charge. So, so far we have learned about how the carriers are generated in semiconductor. So, one way to increase one way to get electron hole pair is doping. So, you can put boron phosphorous and you can board electron and hole. What is the other way you can increase the electron and hole pair we already discussed. What is the other way in which increase the electron concentration and hole concentration thermal energy right you put more temperature your electron generation is more. So, there are two ways we already learned in which electron and hole can be generated or can be increased or decreased in a semiconductor. There is one more important way that is that comes in picture that is because of the light falling on your solar cell that will come later when we discuss the solar cell operation right now we are just discussing a plane semiconductor. So, in the last lecture the job was to find out how many carriers are there how many electrons are there how many holes are there how we change them. In this lecture we will find out how these carriers move how they go from one place in semiconductor to other place how they go from one place in semiconductor to other place. Because the whole operation of a device is motion of carriers right when your BJT works when your transistor works when your diode works or when your solar cell works what happens inside the carriers move from one place to other place. So, we should understand how these carriers are moving from one place to other place and corresponding to the moment and the moment of carriers is what what is the moment of charge carrier the moment of charge carrier is current ok. So, once we know how the carriers move we should try to define corresponding current that is what we should do in this lecture. So, in the last lecture we have seen charge carriers their numbers and their distribution in energy levels that is what we have seen in last lecture. In this lecture we will see how the carriers move motion of carriers very simple there are only two ways carriers can move they can move by the drift motion and they can move by diffusion ok two important thing and then we will we will quickly see ok. But remember there are two ways carriers can move in a semiconductor drift of the carriers which happens because of the electric field diffusion of the carriers which happens because of the concentration difference in the carriers ok. Let us look at it in a semiconductor when there is no electric field apply equal to 0 by the I am sorry this this symbol E is not the E potential energy that we draw right when you draw the energy band diagram or let me clarify this here. So, this symbol E is actually this E I am talking about this zeta let me clarify here. So, when we draw this energy band diagram this is the energy level and here we say E and this is a distance x. This energy level E here what is this it is a potential energy we are drawing. Now, I am going to use another symbol called zeta and this is the electric field ok. So, do not get confused between the two I am going to draw electric field ok. So, this is here is the potential energy and the motion of carrier when you discuss the motion of carrier we talk about the electric field ok. Coming back here so, when so sorry this is not E this is zeta here. So, please correct it E zeta equal to 0. So, when electric field is 0 what will happen to the electron in a semiconductor will it be sitting nicely at one place like you at your chair or it will be moving. The answer is even when there is electric field is 0 in semiconductor because semiconductor is not at 0 Kelvin it is at some temperature and that temperature is good enough to provide you provide the electron some energy and with that energy electron can move. But because the guidance to the electron there is no guidance where it will move it will go in all direction it will go randomly in all direction and if you watch that electron after some time the net motion of the electron will be 0 ok. So, in the absence of electric field the net motion is 0, but look at here when electric field is non-zero it is positive what will happen electron will start it motion here it will still have some random direction. So, this change of the direction that basically what is the electron is moving in where it is moving in all the atoms. So, it will actually have the collision it will go in other direction then it will go in other direction that will change the direction, but because there is electric field there in net motion electron will actually grow from here to here because the electric field is in this direction. By the way the force on electron the force on electron is given by minus q times zeta electric field and the charge of electron the minus represent the opposite direction. So, this is the direction of electric field this will be the direction of force the force applied on electron due to the electric field is in the opposite direction keep that in mind. So, therefore, when force is in this direction right to left the electron is moving from left to right this motion of electron in electric field is called the drift motion drift motion. What is the velocity of this electron? Now, we will say electron is going in this direction and then it goes in this direction then it goes here here here here here. So, electron is moving in one direction, but still it is random. So, we cannot talk about the velocity as such we can talk only about the average velocity. We will talk about the average velocity and this average velocity is called the drift velocity of electron. This average velocity of the electron under electric field is called drift velocity. Similarly, hole is also positive charge and because it is a charge it will also experience a electric field. So, this is for electron what will happen for the hole the force on hole is plus q zeta plus q charge because of the positive and if this is my direction of electric field this is my direction of force. So, the motion of electron is in the opposite direction of electric field the motion of the hole is in the same direction as that of electric field very important to understand it will be useful. The motion of electron is in the opposite direction to that of electric field because the force is opposite. The motion of hole is in the same direction as that of electric field. The thing here is that the electron moves with the velocity average velocity called the drift velocity under electric field which means once you apply electric field electron is moving with the net velocity when the electron is moving with the net velocity there is a charge transfer taking place the charge flow taking place and the flow of charge is what rate flow of charge is current the net flow of charge is current. So, once we know the electrons are moving we can actually find out the current right how we will find out the current you can actually you can do this the current is is given by this expression here. So, this is the drift velocity expression do not will not go into the details of that, but basically the drift velocity is a function of electric field. Let me go back here the velocity attained by electron will depend on what it will depend on the electric field the electric field is very strong the velocity will be higher ok. Very important thing here is the velocity attained by electron will also depend by the structure of the material right if your structure is very defected amorphous material ok. So, if it is very defected when there are lot of hindrances that will occur in the path and because lot of hindrances the velocity that will gain is 0, but if your material is smooth smooth means monochrist line very well ordered material if your material is very smooth the electron will flow with a faster velocity ok it will attain higher velocity. So, the velocity the drift velocity will depend on the electric field and it will also depend on the structure of the material and we will know how to quantify that. But before coming here if you have the carriers if you are carriers which are moving if you are the carriers electrons let us say I am talking about electrons if you are the electrons which are having n in the number what is n? n is the density number of electrons per centimeter cube n is the number and if they are moving and each n is the number and if I multiply with the cube what I get the charge density charge per unit volume. So, n is the number per centimeter cube n cube is charge fine or coulomb if I multiply n cube with the drift velocity the velocity which they are moving velocity with which you are moving what is unit of velocity centimeter per second. So, what is the unit of n cube and v d unit of n cube and v d is that the unit of n cube v d is that is the. So, this centimeter will get cancelled with the 3. So, now, you will have 2. So, you have coulomb per second and per centimeter square coulomb per second per centimeter what is coulomb per second? Current charge flow rate of flow of charge. So, coulomb per second is current and current per unit area right. So, here it is this area right. So, n k d is nothing but j that is your current density it is nothing the expression is coulomb per second is a ampere. So, you have the expression in ampere per centimeter square or j is the current density right. So, if you know the carrier concentration electron if you know the charge and if you know the velocity with which they are moving. So, you will find out this product will give you that the coulomb the total coulomb that is moving per unit area and that is nothing but your per unit area per unit time by the way rate of flow of charge per unit area per unit time. So, that will actually give the current density is it very clear. So, that is current density if I want to find the current then I should multiply the area. So, my current is nothing but j into a we will use this symbol throughout that j represents current density per unit area I represents the current if I multiply with the cross section area of my semiconductor I get the current. This is the current density due to the electrons right. Now, in my semiconductor there are electrons and there are also holes. So, holes will also move right holes will also move. So, can I write. So, this is let me write this is the current density of electron I will write a subscript a n. Can I write expression for the J p or let you people write the expression for the J p. Let us say the drift velocity of hole is v d drift velocity of hole is v d write the expression for the drift current density due to the holes. Same thing will exactly do similar n is electron concentration let us say p is hole concentration q is the charge of electron in the charge of electron and hole is equals I will have the q also and the drift velocity that is it. This is the expression and I am talking about what I am talking about the drift current. This is the drift current drift current of electron and drift current of hole. So, under the electric field electron will contribute to the current hole will contribute to the current. What will be the total current? Total current will because in a semiconductor you have electron as well as holes. So, both electron and both hole will contribute to the current. What will be the total current? Total current will be total drift current will be ok. So, total drift current will be sum of electron plus whole current right both carriers are contributing and therefore, you will have the expression as this is N Q V D plus this is P Q V D right. So, this is the expression and this is the drift current ok. So, I will say J drift is sum of the electron drift and sum of the and the whole drift very easy you can find out that right. And this is the current density by the way J is current density if you multiply with the area if you multiply with the area. So, your I will be nothing but A area times N Q V D plus P Q V D where V D is the drift velocity ok. So, this is the expression for the drift current this is the expression for the drift current. Now, from the drift current we actually find out. So, this is what you will get, but we can define a very interesting parameter ok. The velocity attained by a carrier is dependent on the on certain parameter. So, how much velocity it attains per unit electric field is called the mobility right. Remember what I told you that if your material is amorphous the velocity that your carrier will attain under a same electric field will be lower why because because of the amorphous a lot of defects and there will be lot of collision that will take place. And because of a lot of collision the velocity attained will be lower right. Same thing if you are asked to run on a plane highway or the plane road you will run faster, but if you are asked to run on a crowded street then you will not be able to run faster. Same thing will happen to the electron. So, when you are talking about a perfectly ordered crystal you are talking about a highway ok. So, for that electron will run faster when we are talking about a defected material like amorphous silicon because of the defects the hindrance in the path of electrons higher and therefore, the drift velocity attained is lower. And therefore, that brings me to a very important parameter called mobility mu. Mobility of a electron will depend on how much is the velocity it is attaining per unit electric field. So, mobility is a very very important function or very very important parameter of the material for a solar cell ok. A material with good mobility means good a material with a bad mobility or lower mobility is not good. So, always a scientist all over the world try to achieve highest mobility as much as we can. What is the unit of mobility you can find out? What is the unit of velocity it is centimeter per second and what is unit of electric field? Old per centimeter. So, old per centimeter. So, unit becomes centimeter square per volt second. Unit of mobility is centimeter square old per second. You have the mobility of electron similarly you will have the mu P mobility of holes right holes will also move and will also have the similar process. So, then your expression can be simpler. So, Q and V D instead of V D you can say mu N and zeta electric field. So, your current density due to the electric field is Q and mu zeta. Your current drift current for the holes is Q and mu P zeta and mu is the mobility and very important parameters for the semiconductor very very important parameter for the solar cell very very important parameter for the solar cell operation. So, coming back to the mobility we can actually have the drift current density given for the electrons and drift current density given for the holes which are given here, here right and this is the number and also the centimeter square per volt second is the mobility. So, if you look at the silicon the mobility of electrons is higher than the mobility of holes. Mobility of electrons is 1350 and mobility of holes is 480 centimeter square per volt second. In Germany mobilities are higher as you go from monochrist line material to multicrist line to polychrist line to amorphous what will happen to the mobility I will not answer talk to your friends ok. As you go from monochrist line to multicrist line to polychrist line to amorphous silicon what will happen to the mobility will it decrease and increase you discuss with your friend among yourself ok. So, as you increase your doping as you increase your doping your mobility actually decreases right why because you are disturbing your lattice too much you are disturbing you are putting external impurities you are putting more boron more phosphorus you are disturbing your silicon and because you are creating the disturbance the hindrance you are creating more put the path of electron in hole and because of that hindrance is created your mobility is decreases. At higher temperature also your mobility decreases right because at higher temperature the there is a lattice vibration and because of the lattice vibration there is a more chance that electron moving around will actually collide with the atom and because of the increased probability of the collision as a increase in temperature your mobility also decreases ok. Mobility can be measured using the the hall effect you can measure the your carrier concentration using the hall effect I am not going to discuss here these are the extra slides for those who want. So, but using the hall effect you can actually check your mobility there are hall effect measurement devices which can help you to check your mobility. Once you know your mobility you can find out the current you can find out the doping level also ok. So, there are equipments available which can help you if you give the semiconductor they will tell this semiconductor is doped with tens of 15 electron concentration or tens of 16 electron concentration or whatever it is or it is a hole concentration or electron everything is possible you can measure that ok. Now, that brings me to the second important mechanism of charge transport and that is the diffusion of carriers. So, carriers can diffuse so, one transport mechanism is electric field. So, when you have electric field carriers moves and other is the diffusion of the carriers. What is diffusion? Diffusion is basically a motion of carriers from high concentration level to a low concentration level ok from high concentration level to low concentration level. Have you ever experienced such motion of the particles? An answer should be yes you might have done that already because when you let us say the classical example is the perfume ok. So, when somebody spreads a perfume in one corner of the room, immediately smell of the perfume spreads all over the room and that is the example of how. So, when the perfume spread in one corner there is a high density of that particles of the perfume in the other corner there is low density and there is a concentration difference. So, particles will move from high concentration to low concentration. Exactly same thing also happens to the electron and holds in a semi conductor ok. By some by any reason if there is a concentration difference at one point as compared to the other point carriers will move ok by some reason if there is a by some reason if I have let us say this is my concentration. So, number per centimeter cube and this is my x distance if I have two reason of semi conductor where let us say this is electron concentration n. So, this is the reason where you have high concentration and this is the reason where you have low concentration ok. What will happen the electrons will move from high concentration to low concentration ok. So, what is the direction of the current? By the electrons are moving means there is a current flowing whenever there is a net flow of charge of either electrons and holds there is a net flow of current. So, when electrons are moving in this direction what is the direction of the current flow? The direction of the current flow is always as a convention is opposite direction of the electron. So, this is the electron flow and the direction of the current will be in this. So, this will be a current flow current flow is happening in the opposite direction of the electron flow and this current flow is happening why what because of what not because of the electric field it is happening because of the concentration difference. Because one reason is having higher concentration as compared to the other reason and because of this concentration difference there will be a current flow. And therefore, this current is called the diffusion current this current is called diffusion current. What was the term earlier for the electric field current? Electric field current the term was the drift current this current is called the diffusion current ok. So, the diffusion occurs I mean I will not explain in the detail why diffusion occurs it is very clear that the carrier will move from high concentration to the low concentration. So, diffusion occurs this is the mathematical expression why for the flow of the electrons due to the concentration gradient. So, this is n x n is the concentration in per centimeter cube this is the distance. When there is a electron profile or the concentration changes from high concentration to low concentration carrier will move carrier will move from other side. And again I will not go into the detail, but let me come directly here there is a flux of the electron flow that is the number of electrons per centimeter square per unit time because this is a flux per unit time is depends on what? It depends on what is the concentration gradient. So, higher is the concentration gradient higher will be the flow. So, if I have two scenario in one scenario in one scenario the concentration is changing like this in other scenario concentration is changing like this. So, here the gradient is higher in this case d n over d x that is the concentration gradient is higher as compared to this case because of the higher slope this is higher as compared to this case. And therefore, the current will be higher in this case whenever the concentration gradient is higher current will be higher. So, the flux of the carriers because of the concentration gradient depends on the proportional to the concentration gradient. And in the electric field when the motion of carriers were described in electric field we talked about the mobility here we are talking about the diffusion coefficient d here we are talking about the diffusion coefficient. So, flux is proportional to the diffusion coefficient and the carrier concentration. So, that is flux and the unit of the flux is number per unit area per unit time number per centimeter square per second. So, that is the flux. What we want to find out we are not interested with the flux of the electrons or flux of the holes we are interested in the current due to the electrons and current due to the holes ok. So, this is number per unit area per unit time what should I multiply here to get the current? What should I multiply here? What is the current charge per unit area per unit time? Current density is a charge per unit area per unit time. So, if I multiply with Q then if I multiply by the q then I will get the flux if I multiply q into the I am sorry the current density is q into the flux. Current density is the q into the flux you will find the same thing here. So, this is the flux of the electrons and similarly you can actually draw the flux of the holes and you can find out the flux of the electrons, flux of the holes and the current density due to the diffusion is q times dn and the concentration gradient and current density due to the holes is q times dp and the concentration gradient of holes. Important thing is why there is a negative sign here, let us understand that. This is electric field direction, if this is electric field direction the force on electron is in opposite direction e and the force on hole is in this direction h. What is the current direction? Because electron is in moving in this direction the current is in the opposite direction of electron flow. So, the current due to the electron in this direction and hole is moving in this direction the current is also moving in the same direction. So, hole current is in the same direction. Eventually, what is happening? The electron current, direction of the electron current is in the same direction as electric field. Direction of the whole current, direction of the whole current is in the same direction as electric field. So, both electron current and hole current moves in the same direction as the direction of electric field. Clear? Look at the diffusion current. So, these are the drift. This is the case for drift and this is very important. Let us look at the diffusion and because in electric field the electron current and hole current is the same direction electric field, in the expression there is no negative sign. There is no negative sign in the expression. What happens in diffusion? Suppose I have this profile of a N x, electron concentration N for electron. If I have this profile of electron, what is the direction in which the electrons will move? High concentration to low concentration. So, electron will move in this direction, moment. Here we talked about the force. Here we are talking about moment. So, moment of electron due because of this kind of profile is this direction and when the electron is moving this the current is always opposite. The current is in this direction. So, this is electron diffusion current. This current is electron diffusion current direction. Now, dN over d. So, which direction dN over dx is positive? If I go from low concentration to high concentration here. So, my dN over dx is positive in this direction. How the dN is final minus initial divided by final minus initial? So, my gradient of a electron concentration is positive in this direction. So, my positive gradient direction is my current direction. My positive gradient direction is my current direction and therefore, there is a positive sign in the carrier. Current density. So, electron current there is a positive sign here. J N diffusion, diffusion current due to the electron is q dN dN over dx. Here is a negative sign and I will understand immediately why. Now, suppose I have a whole profile that is px whole concentration profile is like this because carrier will move from high concentration to low concentration. So, whole will also move in this direction moment of whole will be in this high to low go from here to here right and because whole the direction of current for the whole is same as the direction of the whole motion. So, therefore, the whole current is in the same direction right. Now, what is the direction my gradient dP or dx? My dP or dx is again positive in this direction. Gradient is defined as final minus initial, final minus initial. So, my gradient for the whole concentration is positive in the this direction opposite right to left. But, my whole current is moving in the other direction left to right. This is here and that is you can see the directions are opposite and because of that direction opposite you should have the negative sign in the expression and that that is why you have the diffusion current for the whole as having a negative sign got it. So, for electron there are two components electron drift and electron diffusion for the whole there are two component electron drift and electron diffusion in total 2 plus 2 there are four current component in a semiconductor. How many current components? Four current electron drift, electron diffusion, whole drift, whole diffusion and the total current is sum of all ok. So, this expression here and you have a look at whenever you have time look at in the detail total electron current, total whole current and this is the total current of a semiconductor which will flow under the electric field and under the diffusion or under the concentration gradient. This is what we explain already this is already in your slide. The diffusion coefficient is also given the value of diffusion coefficient you can find out from the expression ok. You can work out from this expression the unit of diffusion coefficient is centimeter square per second ok. So, let me write here again. So, unit of mobility is centimeter square per whole second unit of diffusion coefficient is centimeter square per second ok. Normally this two very interesting ok. So, D is related to the diffusion which is concentration gradient mu is related to the mobility which is electric field phenomena ok. This is coming from the electric field motion ok. This is coming from the concentration gradient motion right, but a scientist Einstein found that both of them are related ok. So, mu by D is actually k T by Q is that correct? No opposite I am sorry D by mu is equal to k T by Q D by mu is equal to k T by Q and you can see the units ok D is centimeter square per second and centimeter square per whole second. So, you get cancelled and k T by Q has always a unit of volt k T by Q has a unit of volt and only k T has a unit of electron volt k T by Q has a unit of volt and this is the mobility centimeter square per volt second diffusion coefficient 17 to square per second. Mobility is therefore, electron in holes diffusion coefficient is therefore, electron in holes and you have the this expression it is called Einstein relationship k T by Q is equal to D by mu or D by mu and this are the value of mobilities are normally higher diffusion coefficient values are lower and you can see yourself k T by Q equal to D by mu works or not. This is the expression that I was talking about k T by Q equal to D by mu again we do not have time to discuss it. So, in summary very important thing to understand that the two current the two forces which causes current to flow in a semiconductor drift of the carriers which happens because of the electric field diffusion of carriers which happens because of the concentration gradient under the electric field electron can move hole can move and both will contribute to the current. So, there is a electron drift current and there is a hole drift current under the concentration gradient both electron will move and hole will move and both will contribute to the current. So, there is a hole diffusion current and there is a electron diffusion current and the total current is the sum of all the four current component in the semiconductor. So, there are four current component and we have discussed how to write the direction of the electric field and based on the direction how to check the motion of the current and electric field and electron and hold drift current is the same direction as the field electric field. Similarly, we can actually if you know the concentration gradient profile then we can find out the motion of the electrons and once you know the motion of electron we can find out the motion of direction of electron current and hold diffusion current also. Let me take a few questions very quickly ok, Gandhinagar, I am Rajesh Tripathi speaking from Gandhinagar. How albedo effect affects the efficiency of PV module? Albedo is the current it is a component of the solar radiation that come from the reflection from the ground and surrounding area and because of the reflection the efficiency will not get affected ok. Because of the reflection basically you are getting more radiation and more conversion will take place but the efficiency will not be dependent on albedo. Sir your previous lecture you have said that in extrinsic semiconductor they are stable because one silicon is connected with the four silicon but in extrinsic semiconductor when you are doping then due to these doping there will be instability. So this instability will not create a problem in doping because the stable condition is disturbed. Yeah, so in the when you when you make extrinsic semiconductor when you do the doping remember the atomic density of silicon is 10 to the power 22 atoms per centimeter cube ok, 10 to the power 22 and you do the doping of 10 to the power 15, 16, 17 ok. So, still you are making 1 atom into 10 1 billion atom or 1 million atom ok. So, because your doping level is so small it does not affect normally the stability of the material. So, my question is sir easily it is allowed the other atom, other atom is allowed in the semiconductor in pure semiconductor. Yes, yes, yes you can actually you can actually force other atom to go into the semiconductor and there is one lecture that I will take about how the silicon is fabricated ok. So, in that lecture we will discuss in detail how the doping is done in practice. Jaipur college. Sir, my question is sir we all know that a semiconductor behaves an insulator at 0 Kelvin and as we increase as we increase the temperature the electron acquired the thermal energy and they migrate into the conduction band from valence band. So, my question is at room temperature the thermal energy is about 0.025 electron volt whereas the minimum amount of a band gap say for germanium is about 0.6 electron volt. So, I want to know how that can they can cross the state amounts of energy which is almost 24 times larger than the band gap. Ok, yes very good question, so question is very nice that you know band gap of a silicon is let us say 1.12 electron volt, the thermal energy is very small ok it is in the milli electron volt. How it is possible that with a room temperature electron can excited? The thing is in semiconductor everything is statistical in nature right, you remember when you study the class the quantum mechanics even in the classical mechanics you know if you take a bottle and if you you know take a marble inside the bottle what is the probability that the marble is outside available outside the bottle 0 right, but when you look at the quantum mechanics you look at the quantum well and you put a particle in the quantum well and if I ask you question what is the probability that the particle is available outside the well and the answer is it is a non-zero probability right, there is some possibility that the electron even it does not have enough energy to come out of the well it still is available outside. And considering the same thing because of the statistical nature out of the trillions and trillions of electrons, some electrons will always have the probability that it gets enough energy and go to the conduction band engineering college Pune question is is it essential to use trivalent or pentavalent impurities in order to doping ok. The question is I will repeat the question is is it essential to use trivalent or pentavalent impurities for the doping answer is yes because you want to create a hole, but it is not necessary that you have only trivalent or pentavalent you can also have the doping of a bivalent ok. So, for example, when the doping is done for the let us say 3 5 metal gallium arsenide. So, it is very interesting to see how the doping is done right. So, you can do the doping. So, basically you have to somehow create a shortage of electron ok or you have to create some of the shortage of the electrons for making the enough number of covalent bonds. So, whenever that shortage is created you actually can have the doping done. So, the answer is it is not necessary that you only have the trivalent or pentavalent to make it p-tapper in type. There are other ways you can also create the doping levels. Karnataka, yeah go ahead sir instead of having a flat solar PV module why cannot we have dome shaped structure. So, that any one of the PV module will be exposed to direct radiation that is normal to the plane. So, that you can avoid the solar tracking. So, if I understand your question correctly instead of a flat module why cannot we have cylindrical module right ok. So, the problem with the spherical module is that yes you can actually if you use a spherical module you can avoid the tracking, but the problem will be that only some part of the module will be operational at a given time right. So, for example, if I go if I go to the white board. So, what will happen? What will happen if your module is like this in the afternoon you will get the rays like this in the in the evening you will get the rays like this, but what will happen when sun sun is setting in the evening this part of the module will not be operational right. So, this will not be active part of the module and because of that there will be loss of power you are using a solar sail, but it is not working because light is not falling or the worst case is this part this side of the module which will not receive any light and therefore, it will not work. So, yes it is good that you can actually get the radiation all over the day without tracking, but it will be a problem definitely and to to give an example there is a company there was a company called Solyndra the name comes from the fact that the modules of that company was cylindrical ok, but unfortunately just last month they have got the bankrupt ok. So, the technology actually did not work. So, so it is not a good idea to have a not a good idea to have a cylindrical modules. Sir, one more question why is carbon not used as a semiconductor? Why is carbon not used as a semiconductor? Well carbon I mean depending on the arrangement for example, the carbon is also you know tetravalent like silicon, but if you look at but if you look at the if you look at the band bonding between the carbon to carbon atom if there is a perfect band then you get the diamond structure right and you know the diamond structure you know the diamond very hard non conducting or you can get a graphite structure. If you get the graphite then it is a very soft material, but it can be conducting. So, depending on the depending on the kind of bonding between the carbon it is difficult to get a material who which is brittle which can self-stained and which can still be conductive like silicon. So, diamond it can be very hard like a like a diamond or it can be like a graphite and therefore, some people are trying to convert carbon into carbon nanotubes and people have shown that by controlling the bond arrangement one can actually try to get the semiconducting properties from the nanotubes, but carbon it is not easy to make in terms of the wafer and use that as a is a semiconductor because of the conductivity, brittleness are other factors. Sir, we have one more question. Yeah. Characteristics of the panel the input power should be kept constant. Yes. So, if the input is changing then the I V curve that we plot may not be all right. So, it is better to include an emitter across the calibrated solar cell and take only those points corresponding to constant value of current which is generated by the solar cell. Am I correct or wrong? No, Professor Murthy, you are very much correct that when we are plotting the I V curve during the entire data points that we measure the input radiation should be constant. Now, because we are plotting and it takes only a couple of minutes to take all the data points. So, it is you know safe to assume that your input radiation is constant, but in a very changing scenario when the light is changing very fast or when there is a cloud conditions and all, in that case you are correct that we should only take the data points where the input intensity is constant, but normally because we are doing it very fast and 20 data points can be taken in a couple of minutes it is safe to assume that the intensity is constant. Professor Murthy, go ahead. How the input power can be measured using the calibrated solar cell? Okay, I will explain how we do that. Actually what we have given the solar the solar cell has two parameters. The solar cell current and voltage. The current of a solar cell is proportional to the input power almost linear and this linearity is valid almost from very low power density like let us say about 200 watt per meter square all the way till 1000 watt per meter square. So, basically if I measure the current and this current is a short circuit current. This current is a short circuit current. So, if I basically measure the solar cell short circuit current and if I know, if I calibrate it that at, if I calibrate with respect to pyrronometer. So, what we have done is we have taken a pyrronometer with the dome. We have measured the solar, we have measured the intensity by the pyrronometer for a long hours. So, we started our measurement in the morning and till the evening and at the same time we have measured, we have made a table. So, that once column we have the pyrronometer reading and other column we have the current of a solar cell short circuit current ISC. So, when we get the large number of data for the pyrronometer reading and short circuit current we can plot it and once we plot it we will find that they are all comes in a linear fashion. So, you can find a slope of this curve and therefore, your reading will be that. So, i is proportional to p in or you can say i is equal to some constant k times p in or we can say your input power is equal to some constant another constant k dash i. So, if you know if you if you know your constant if you multiply with the current and you take your constant multiply with the current. So, you can get the input power. The advantage of this is that the good thing about this is that actually if you measure your solar cell in this plane you are measuring your radiation in this plane. If you are measure your solar cell in this plane you are measuring your radiation in this plane. So, by changing the angle of the solar cell you can actually get the solar radiation in that particular plane. Now, this is a approximate way of doing it, but it is a very low cost and very simple way of doing it. So, more than 90 percent it is correct there may be 5 percent error in doing that, but I think most of the applications like many engineering college, many students studying using solar cell as a input power density measurement, input radiation density measurement is a good tool. Now, when we measure power the solar cell should be in the same plane as that of the solar panel. Right. Baramati please go ahead. Sir, my question is regarding efficiency of solar cell, solar cell efficiency material then absorption coefficient and actually sir in one article I have gone through an article. It is also reported that it also depends on the texture and orientation of the film, but orientation one can understand in terms of monocrystalline and polycrystalline, but sir what about texture of the film? Okay, so madam I would request you just wait for couple of lectures when we will look at the technology for fabrication of a solar cell. You will get an idea how does the texture and the orientation as other thing determines the efficiency, but you are very correct. There are many parameters which determines the efficiency of the solar cell and once we finish the physics part we will go to the technology part and there we will discuss how we fabricate and how we actually achieve or try to achieve the higher efficiency. One question is regarding the solar water heater, sir if we want the temperature that is higher temperature as well as steam is it possible for the same water heater? A water heater that you get for the domestic application, the temperature you can get is only about 60 to 80 degree centigrade. So basically with this you cannot get a steam you know because there are lot of losses that occurs, but if you go for the concentrator type of water heater or concentrated type of you know collector like a parabolic concentrator then definitely you can generate steam also. In fact many power plants which are at a very large scale, mega out scale they try to generate steam directly using the concentrator solar power and use it. Okay there is a question from NIT's Calicut how to measure the diffuse radiation using pyronometer? Okay let me explain you how to measure the diffuse radiation using pyronometer. So once you have this, so this is the sensor of a pyronometer and there are domes. Okay now this pyronometer actually gets a radiation from all the direction, right? It gets radiation from here, it gets radiation from here, gets radiation from here, it gets radiation from all the direction, okay all the hemisphere. Now you want to only, you want to only get the diffuse radiation from your pyronometer. So what you can do, so what you can do basically if this is your pyronom, this is the sensor okay and this is your pyronometer and if the sun is here, okay let us say your sun is here, when your sun is here the direct light is coming from this direction, okay this is the direct light which is coming and all other direction you are getting the diffuse light, right? All other direction you are getting the diffuse light, so this direction, this direction, this direction you are getting the diffuse light. So somehow if I can block the direct light, okay, somehow if I can block the direct light then whatever light that is falling on sensor of the pyronometer will be only the diffuse light and therefore one ring is available normally or if you actually some kind of ring is available with the pyronometer and if you block that direct light then whatever light you are going to get is only diffuse light. In that way, in that way the diffuse light can be used, I am sorry in that way the pyronometer can be used to measure the diffuse solar radiation also, okay Calicut. Sir now calculate the efficiency of the solar. So first I have measured IM and Vm values then I directly calculated solar radiation from using a pyronometer then multiplied with area of the module, can I get the solar electrically behind the PV module? No, there is one more parameter that you need that is called the fill factor. Yeah, no you are correct that if you are using IM, Vm you can also get it. So let me tell you that here the efficiency will be power output divided by power input, right. Power output is IM times Vm, power input is whatever you measure the inward pyronometer square and you divide multiply by area. If you do that you can actually get the efficiency. Thank you.