 Good morning all of you. So, before I start a quick recap that we did last time, I will just put on the whiteboard that we have discussed about the intrinsic and extrinsic semiconductors. So, we discussed about the N i, N p i, intrinsic carrier concentration, we have discussed about the doping N 0 and P 0, electron and hole concentration. N 0 is actually equal to the doping concentration right. So, if you put whatever doping concentration of donor atom like, so we can refer it as a capital N D donor atom concentration, the atomic concentration. And similarly P 0 is the acceptor atom. So, this will be a phosphorous and N A is the acceptor atom concentration. So, P 0 equal to N A that we have seen, then we will we have also seen N i as a function of E f per mi level or E i, we have also seen N i as well as N 0's function of E f and E i and E c. We have also seen P 0 and P i as a function of E f, E v and E i. Then we have also seen that N 0 into P 0 equal to N i square. Then we have looked at the drift of the carrier motion that carrier motion under the electric field. And then we have looked at the diffusion of the carrier, motion of the carrier under the concentration gradient E n over dx or D p over dx. So, these are the driving force electric field is a driving force to move the carriers from one point to other point. And in one case diffusion is a driving force to move the carriers from one point to other point. Corresponding to this we can we have find out the drift current for the electrons and drift current for the holes. So, we have found out the J n drift due to electron J p drift due to holes. Similarly, we have found out J n diffusion due to electron and J p diffusion for the holes. And eventually current is sum of all these four components that we have seen. Also we have come to the very important material parameters called the mobility which is the coming from the drift and the diffusion coefficient which is coming from the diffusion. Mobility as a unit of centimeter square per whole second and diffusion coefficient as unit of centimeter per second. And we have also seen that Einstein by Einstein relationship the mobility and diffusion coefficient are connected with each other. Mobility and diffusion coefficient are the material parameter and as I said very very very important for the operation of a solar. So, basically what we also seen that d by mu is equal to k t by q k t by q. So, these are the things that we have discussed yesterday. And now today we will actually start discussing the two other things that happened. So, our philosophy so far is what are the carriers electron holes? How we can make how we can increase the number of carriers by doping? How the carriers move from one place to other place by drift and diffusion? Now when it comes to the solar cell two important events take place. What is the light that falls in your solar cell? So, generation of carriers and recombination of carriers are the two other important event that take place. So, then in this lecture now we will look at the generation of carriers and recombination. So, how this carrier get generated and recombined using because of the light? Carrier concentration is affected by many things. What are the many things? One is doping. By increasing the doping you can increase the hole concentration electron concentration. What else? Thermal energy right because of the temperature your carrier concentration in can increase. And as I said the intrinsic carrier concentration is defined at room temperature. But if increase your temperature more and more electrons and hole is enough enough energy to go from valence going to conduction band and therefore, your carrier concentration increases. So, temperature is important role. The third important function which can result in the carrier concentration change is we are talking about change is the light generation due to light. And the reverse reaction also take place and the recombination can also occur. So, this is what we are going to discuss in this lecture carrier generation and recombination. So, what we have discussed yesterday is again transport of carriers in semiconductor drift of motion of electronic electric field diffusion drift velocity mobility of carriers. Diffusion motion of carriers under concentration gradient diffusion coefficient direction of current due to the drift and diffusion very important. If you know the direction of electric field we should be able to find out the direction of current. If you know the gradient concentration gradient profile we should be able to find out the direction of current due to the diffusion. This is all thing we have learned yesterday. So, let us continue. So, today we will look at the carrier generation and carrier recombination. And this is very important for the solar cell. It is not important for the diode right, because diode is a encapsulated material there is a capping on it. So, light does not go in it. So, you do not worry about the carrier generation due to light, but here we are talking about the solar cell and therefore, we are also worried about the carrier generation due to light, ok fine. So, carrier can be generated because of the thermal excitation as I said because of optical excitation which we want to discuss. This we already discussed that if the energy of the photon is equal to or greater than the band gap energy then that photon can give its energy to the electron and electron gets its energy from lower level and goes to the higher energy level, ok. This y axis is a potential energy, fine. If this is not the case, ok. If photon energy is less than the band gap energy then material is transparent, ok. What does it mean? For example, typical example is the glass of our window. In the glass window most of the light comes inside. Why? Because the band gap of the glass, glass is a silicon oxide one of the dielectric material and because it is dielectric the band gap is very high and what is the highest energy of photon in our spectrum? As we discussed the highest energy the photon energy in our solar spectrum varies from highest energy about 3.5 electron volt to lower side about 0.3 electron volt. In this 3.5 electron volt is not enough to excite electron silicon oxide which is a glass and therefore, all the photons gets transmitted. This should give you a very important signal immediately. What is that important signal? Important signal is that the incoming photon should have a energy h nu equal to or greater than e g. My solar spectrum, solar spectrum has a photon which is as high as 3.5 electron volt at higher ultraviolet photon and lower side about 0.3 electron volt, ok. This is what is available in solar spectrum. Now, the band gap of silicon which is the commonly used material for silicon it is 1.12 electron volt, right. Now, connect this two number, ok. This is one number and this is another number range of the numbers. What you can derive from this? That because the band gap of silicon is 1.12 electron volt and the photons in the solar spectrum range from 3.5 electron volt at higher side to 0.3 electron lower side which means not all the photons in our solar spectrum is absorbed in silicon also, ok. Silicon is also transparent to infrared light and because we our eyes cannot see the infrared and therefore, we do not notice it, but even silicon is transparent to some part of the light, ok. So, silicon does not absorb silicon also does not absorb 100 percent light. If it does not absorb 100 percent light means its efficiency definitely has to be lower and that is one of the reason why solar cells have lower efficiency that no material because it is a band gap, it is a semiconductor, there is a band gap. So, all the photons which are lower than the band gap cannot get absorbed and therefore, that material also becomes transparent to some portion of the spectrum and therefore, we do not have 100 percent. Very important to note before we go further I will already tell you that the ideal band gap of a semiconductor for solar cell, for solar cell is 1.45 electron volt, this is ideal, ok. We want a semiconductor which is having 1.45 electron volt. Now, go back to your spectrum, the sun spectrum and you will see that lot, lot many photons are there which is having energy less than 1.45 electron. So, whatever solar cell you get, whatever the best solar cell you get, none of the solar cells actually absorb 100 percent photon that is the important message I wanted, ok. None of the solar cell absorb 100 percent photons that are falling on it and that is important and that is one reason why efficiency is low, ok. So, let us move further, energy has to be greater than equal to the band gap energy fine. So, now, how do we know how much how much absorption takes place? Like yesterday we discussed that the absorption probability depends on whether the material is a direct band gap or a indirect band gap semiconductor, right. Whether it is a material is direct band gap or indirect band gap, this is an example of, ok. So, how much is the absorption probability is given by a factor called absorption coefficient, ok. Absorption coefficient is given by alpha and alpha is a unit of inverse of length, ok 1 over centimeter that is in a absorption coefficient. If you can see it clearly look at the value of the absorption coefficient transfer 5, transfer 4, transfer 3, transfer 2, 10 and 1. What do we want? Do we want absorption coefficient value to be higher or lower? We want absorption coefficient value to be as high as possible so that, so that the light can strongly be absorbed and if light is strongly getting absorbed, we can use only thin material to absorb the whole spectrum, ok. So, higher is the absorption coefficient, stronger is the absorption, higher is the absorption coefficient, stronger is the absorption coefficient. So, if absorption coefficient is transfer 5 or even transfer 6, it is very good. If absorption coefficient is transfer 2, what is the unit per centimeter? So, if absorption coefficient is only transfer 2 per centimeter then it is not good. Why it is not good? I will tell you. So, we have absorption coefficient, right and this is given by alpha and unit of alpha is 1 over centimeter that is what normally given, ok. If I take the universe of alpha, absorption coefficient, if I take universe of alpha, what you get? Unit of length and therefore, it is called absorption length. Then we can define absorption length is an average length which is 1 over alpha is 1 over alpha and its unit will be centimeter, absorption length is 1 over alpha and its unit will be centimeter. If I can find out the value of absorption coefficient, I can find out absorption length. Absorption length is the average length of the material or you can say average thickness of the material that would be required to absorb the spectrum or a given photon, ok. By the all this is a function of a wavelength, ok. This is a function of lambda, this is also function of lambda, it is a function of wavelength. So, let me take an example. If I have a absorption coefficient, if my alpha is transfer 4 per centimeter, what is my absorption length? Absorption length is 1 over alpha which means 1 over transfer 4, this is now in centimeter. So, basically transfer minus 4 centimeter, how much is the transfer minus 4 centimeter in terms of micrometer? 1, transfer minus 4 centimeter is equal to 1 micron, 1 micron, 1 micrometer, ok. Transfer minus 6 centimeter is 1 micrometer, sorry transfer minus 6 meter is 1 micrometer, transfer minus 4 centimeter is 1 micrometer, ok. What does it mean? If you have the absorption coefficient of transfer 4, you need, you need 1 micron material to absorb the, the photon, all the photons of that energy. On the other hand, if your absorption coefficient of let us say 10 per centimeter, what is the absorption length? 1 over 10, basically 0.1 centimeter, 0.1 centimeter is 1 millimeter, ok. So, if your absorption coefficient is only 10 per centimeter, then your absorption length is 1 millimeter. So, remember you need 1 millimeter thick material. Now, 1 millimeter is extremely, extremely thick and because the cost of silicon is high, using a 1 millimeter thick silicon is going to be very, very expensive, ok. So, all these lights which is having low absorption coefficient, remember the light is a function of wavelength, the absorption coefficient is function of wavelength. So, for this kind of photon, you require 1 micrometer material, for this kind of photon you require 1 millimeter material and 1 millimeter is too much thick. Remember what I talked about the thin film solar cell? Thin film solar cells are either a micron or couple of micron or less than a micron, ok, which means in all the material which is based on the thin film solar cell must have an absorption coefficient higher than transfer 4 or that is what is desirable. If you have the absorption coefficient of transfer 4 per centimeter, then it is good, otherwise you require thicker material. So, coming back to this slide, look at the absorption coefficient, transfer 5, transfer 4, ok, but look at silicon, ok, this is the graph for silicon. Silicon absorption coefficient falls very sharply and near the band gap, ok, near the band gap, this is the wavelength, but if you look at the energy, it will also come near 1.1. So, near the band gap, absorption coefficient is very small and therefore, you require very thick material for silicon and we do not use that thick material, which means you lose some part of the spectrum because it is not getting absorbed, ok. So, this is the generation rate, alpha is the absorption coefficient. So, as the light falls in your solar cell, as the light falls on your any material, if I have this material as light falls here, if I draw what happens, it actually decreases exponentially. Intensity of the light decreases exponentially and this can be given by I 0 e raise to the power minus alpha x, alpha is your absorption coefficient. So, that is once a light enters, everything falls exponentially. Now, this exponential decay depending on the absorption coefficient can be very sharp, ok, it can fall like this. So, if absorption coefficient is high, it will absorb in a very small length, which is the absorption length. If look at this graph here, if the absorption coefficient is high, then the absorption length is this much or if the absorption coefficient is even smaller, absorption takes place like this, then your absorption length is this much, right. So, depending on your absorption coefficient, your absorption length increases. Smaller absorption coefficient means higher absorption length, higher absorption length means higher thickness of the material that you need to have and higher thickness means more cost, because you require you are using more material, fine. So, these are the various band gap and I told any photon which is having less than the band gap does not get absorbed, which means amorphous silicon actually use lot of spectrum. All the photons having energy less than 1.7 electron old do not get absorbed. In crystalline silicon, all the photons having energy less than 1.12 electron old do not get absorbed and this is already a significant loss. This we have discussed already that, you know, absorption coefficient is high when your absorption coefficient is high. Absorption coefficient is high when you are neither direct band gap semiconductor like this. No change in the momentum is required. Sorry, I think you cannot see it, but if you look at the indirect band gap semiconductor, then there are two steps change in energy and change in momentum. Absorption coefficient is low here, because of the low absorption process. So, indirect band gap semiconductor requires thicker material, because absorption coefficient is low. Direct band gap semiconductor like in thin film require less material. This we have discussed already flight falls from here, x equal to 0 as the light goes deeper and deeper, its intensity decreases and absorption length is given as 1 over alpha. Inverse of the absorption coefficient is absorption length. So, which means the light forms here, at the surface you get the highest generation and as you go deeper, your intensity of the light decreases and corresponding generation of electron hole pair will also decrease and this can actually be given by this. The generation rate is the power in, if you divide by the energy of the photon alpha is the absorption coefficient, this is 1 over q. So, you get the number of generation rate we are talking about. So, generation of generation rate is given as number of carriers per unit volume per unit time. The unit of generation rate would be the generation rate, normally given by G will have the number of electron hole pair per unit volume per unit time per second. So, this is per second. So, that is the generation rate. Remember it is rate, so per unit volume per unit time. So, there is a generation rate you can find out and calculate. Observation coefficient is also given here for the various silicon material. Now, important thing is silicon, the amorphous silicon acts as a direct band gap silicon, a very thin amount of layer is required, very thin layer is required for amorphous silicon, but crystalline silicon acts as a indirect band gap silicon. So, for crystalline silicon, the cell thickness is commercially is 180 micron, but for amorphous silicon, cell thickness is 1 micron or even less. So, because amorphous silicon is so disordered material, there are so many defects are available, there are lot of scattering of the light take place and because of the scattering, the absorption is stronger and therefore, the absorption coefficient in amorphous silicon is higher than the absorption coefficient in crystalline silicon. And that is what is shown here in the graph, if you look at the graph carefully that the stop curve here is absorption coefficient for amorphous silicon, the bottom curve is absorption coefficient for mono crystalline silicon. And penetration depth basically absorption lengths are also given, this is micrometer. So, look at very low absorption coefficient here alpha value, your penetration depth can be 10 to the power 4 micrometer, transfer 4 micrometer. So, almost kind of millimeter or more than millimeter and if you go to the higher absorption coefficient, you actually require for example, this wavelength you require only 10 to the power minus 2 micrometer 0.01 micrometer, 10 to the power minus 2 0.01 micrometer means 10 nanometer. So, for very high energy photons, high absorption coefficient, absorption coefficient means very smaller absorption length. So, that is the case for a different silicon material, crystalline silicon, polycrystalline and monochrystalline and this is the graph which shows the various thin film material. So, gallium arsenide, cadmium sulphide, amorphous silicon, germanium and cadmium tellerite, this graph here is a cadmium tellerite. So, lot of you can see that most of this material the absorption coefficient is high more than 10 to the power 4 that is what is required. Absorption coefficient of more than 10 to the power 4 is required for thin film. So, that your absorption length is only 1 micron or around that order and therefore, you can make thin film solar cell. This is just a graph that I have plotted as per the previous equation, you can have a look at it just to give the feeling what happens. So, if you have incident photon energy of 2 electron volt having a. So, 2 electron volt what is the wavelength of the 2 electron photon? How to find out it? The wavelength of 2 electron photon is 1.24 divided by 2 electron volts. So, you will find lambda in micrometer. So, that that gives me that gives me about 620 nanometers 0.6 micrometers. If my standard power 0.1 watt per centimeter square 0.1 watt per centimeter is equal to 1000 watt per meter square. So, if that is falling then what happens here if your absorption coefficient is high that is for the black curve it absorbs like this very close to the surface this scale is a nanometer. So, only 200 nanometer it almost gets absorbed and this is the generation rate. Typically, the generation rate at the surface will be in the range of 10 to the power 22 numbers per centimeter cube per second. Look at the green light which is having absorption coefficient of transfer 4 in gallium arsenide it absorbs like this. And this with the very low absorption coefficient transfer 3 in crystalline silicon the dark blue light it almost does not get absorbed or all on the other end absorption is uniform. So, look at it is given in the larger scale here it is up to 200 nanometer it is 3000 nanometers you can see all the high absorption coefficient light absorbed very close to the surface that is the important point to note. Please note this because we will use this in a solar cell operation that high absorption coefficient light gets absorbed very close to the surface. This surface from where light is entering you know from where light is entering from where light is entering. And this this information is useful when we design a solar cell how to design a solar cell right that is useful. This is another way of representing the same that low absorption coefficient light this is given in terms of the normalized. So, most absorption takes place here, but the high absorption coefficient light gets absorbed close to the surface low absorption coefficient light it absorbs more or less uniform almost everywhere. So, note this point and this is again the table just you can also find out this, but I have kind of summarize what happens here. So, if I have 400 nanometer light 400 nanometer is corresponding to 3.18 3.1 electron volt light a photon of 3.1 electron volt. If it is a crystalline silicon you require 0.15 micron material to absorb it. If it is amorphous silicon you require only 0.05 micron to absorb it 0.05 micron 15 nanometer only. If you CIGS again you require only 15 nanometer, gallium arsenide you require about 19 nanometers. If you have 600 nanometer. So, higher wavelength remember what we have observed in this graph as the wavelength increases x axis as the wavelength increases absorption coefficient decreases as the wavelength increases absorption coefficient decreases. So, that is why in this table 400 nanometer light absorb very close or requires very thin material to get absorbed 600 nanometer light for crystalline silicon it requires 1.8 micron for amorphous silicon 0.1 micron 0.14 micron for CIGS 0.06 micron 16 nanometer only. Gallium arsenide 0.18 micron 800 nanometer light which is having a band gap of 1.55 electron volt or sorry the photon energy of 1.5 electron volt. In crystalline silicon it requires 9.3 micron in amorphous silicon it will not get absorbed why 800 nanometer light will not get absorbed in the amorphous silicon why? Question to you all I will not give the answer you discuss I will not give the answer you discuss and find out the answer why 1.8 nanometer I am sorry 800 nanometer light will not get absorbed in silicon. Look at the energy 1.55 electron volt because this energy is the less than the band gap energy of amorphous silicon which is about 1.7 electron volt therefore it will not get absorbed here 1000 nanometer 1000 nanometer photon or 1.24 electron volt will require 180 micron look at the thickness how it is increasing why? Because 1000 nanometer photon have lower absorption coefficient and obviously this 1.24 electron volt is lower than the absorption lower than the band gap energy of amorphous silicon it will not get absorbed here in CIGC require 0.25 micron even see what is the difference here it requires in crystalline silicon 180 micrometer in CIGC it only require 0.25 micron and gallium arsenide will not get absorbed because the band gap of gallium arsenide is also 1.45 electron volt. I hope this is clear to all this we have already discussed high absorption probability in direct semiconductor low absorption probability in direct semiconductor fine. So, that was all about the absorption in the semiconductor absorption does what? It results in a generation of extra electron hole pair it results in generation of extra electron here, but everything which goes high in energy can also come down right everything which goes high in energy can come down. For example, this is my pen if I drop it it comes down why it comes down because it is a higher energy level it wants to come down to the lower energy level. So, this my excited electron which is going to higher energy level by getting the energy from a photon can also come down to the lower energy level and it give away its energy that is also possible right. In fact, the recombination is something we do not want if your recombination is taking place in a solar cell or if lot of recombination is taking place in a solar cell then the solar cell efficiency will be low. So, this process that electron comes down from the high energy level to low energy level that is it from conduction band to valence band this process is called recombination and we do not want recombination why we do not want to commencing because the photon has done its job photon has actually given energy and excited a carrier. Now, this carrier actually should be useful to do our work and what is the work we want this electron to do we want this electron to run a light for us should go through the fan it should go through the light it should go through the computer and do the work rather than coming down here directly right that is what want. So, what we want that normally what happens in a power plant for example, what happens in a power plant in a power plant this you are actually run your turbine you run your generator. So, that electron energy you increase its potential you increase potential to let us say 440 k v or some number then it goes to the substations and it decrease the potential it goes to another substation it decrease the potential finally, it goes to your house it goes to your house at 230 volt and here it goes through house and it goes via bulb and comes down to the potential it comes here. So, that is the journey of electron at a power plant you are increasing its potential then it is going to the transmission distribution at various substation it is resulting in the drop in voltage drop in voltage eventually it goes through the bulb or fridge or the fan of the motor of your fan it gives the energy. So, here it is dropping in voltage basically it is doing the work and that work may result in a light that work may result in a motion of fan that work may result in any other function by doing this work it come back to the same level and then again. So, this is the cycle of a electron in a power plant and the same thing should also happen in a photovoltaic right. So, if I draw the band diagrams in a photovoltaic if I draw the band diagram. So, when you are putting a photon here actually you want this electron to get excited and go here create a hole you do not want this process to happen right because the this if this happens then no work is done you want this electron to go outside the circuit may be go via bulb and then come here. So, that should the process that you want that is the process you want. So, this process of recombination is is not a good process and we do not want recombination to happen and all the scientist around the world always try to minimize the recombination, but it happens it happens. So, lower is the recombination higher is the efficiency of your solar cell. Now, there are various ways the recombination take place one is the band to band recombination. So, photon the electron comes directly from the conduction band to valence band and give away in energy in the terms of light. This other recombination called the Auger recombination in which the electron come here recombine, but it give energy to some other electron which goes to the some higher energy level. This process is discovered by scientist called Auger and refers to Auger recombination, but the most important of all in a solar cell is this kind of recombination. It is called the TREP assisted recombination in this recombination the energy of this electron the electron does not come directly to the valence band it actually comes down gives its energy it come down to some energy level in between and then come down. Now, so far what we have discuss is that between the conduction band and valence band there are no energy levels. This is what we have discussed so far that I have conduction band I have valence band and this is energy gap this is energy gap there is nothing in between, but in practice when you manufacture your solar cell or when you manufacture a material there are lot of defects that are there in material there are lot of impurities that are there in material and this impurities suppose in for example, in silicon the common impurities could be some part of the copper some iron some very small quantities parts per billion kind of thing one atom in one billion atom of silicon. So, this those kind of impurities there, but because it is a different material it will have its different energy levels and because they are different energy level this energy level sometime appear in the middle of the band gap and remember because the concentration of this impurities are not that high or defects is not that high and therefore, this energy levels are isolated they are not continuous in nature. So, this in between the energy level appears and this the recombination of electron take place via this energy levels recombination of electron take place via this energy levels and this is called the trap assisted recombination. This is called trap assisted recombination and this is the most common recombination that occurs in solar cell. This is the most common recombination that occurs in a solar cell and we scientists worry all the time about this. So, there is a band to band recombination we will not go into the detail there is a archer recombination that that takes place in a solar cell. Now, one important thing is we will go we have to go back again and see what is the this generation, but it is important, but another important thing we have to discuss now is what is called the excess carrier density. Let me take the case of silicon again. So, you have N i which is equal to P i which is equal to 10 for 10 fine. Let us say I am talking about the P type semiconductor I am talking of P type. So, you dope with a boron with the acceptor donor acceptor concentration of 10 for 16 atoms per centimeter cube of boron which is means which means what what is the whole concentration 10 for 16. So, then your P 0 is also 10 for 16. So, this was a starting point you dope with the boron you get P 0 10 for 16. What is your N 0? So, then you have to apply P 0 into N 0 equal to N i square and N 0 is equal to N i square by P 0 sometime you also write N i square by what is P 0 P 0 is equal to N a. So, you can also write N a. So, this is 10 for 20 coming from here and this is 10 for 16 here that we have done the the solution we have done yesterday, but I am just repeating again for your sake. So, we get electron concentration of 10 for 4 per centimeter fine. So, what has happened? So, at the end of the story we have N 0 equal to 10 for 4 and we have P 0 of 10 for 16 fine very nice that is the situation. Now, let us goes to the next page and now let me put a light on my semiconductor. So, what is this scenario I will repeat? So, my scenario is that I have semiconductor in that semiconductor my N 0 which is the minority carrier I am sorry electron is 10 for 4 per centimeter cube and I have majority carrier which is whole is 10 for 16 percent. Now, this is the condition at T equal to 0 time T equal to 0 I have this condition time T equal to 0 I have this condition. Now, I am putting light when I put light on it what happens? When I put light on it what happens? The carriers are generated because of the light light is getting absorbed if the and energy of the photon is higher than the band gate light is getting absorbed and then when the light is getting absorbed carrier generation is taking place. So, because of the light new type of electron whole pair is generated. Suppose, my generation is suppose due to the generation I am creating 10 power 14 electron whole pair per unit volume I have created 10 transfer 14 electron whole pair what does it mean? It means that I have 10 power 14 electrons as well as 10 power 14 holes right I have 10 power 14 electron and I have 10 power 14 holes. This number here N 0 represent equilibrium right 0 represent equilibrium. Equilibrium means no disturbance, but now I am putting the light my semiconductor got disturbed a semiconductor got disturbed, but if I look at the new electron concentration let us say N the disturbed condition is N and disturbed that is equilibrium is N 0. So, my new electron concentration should be N 0 plus N due to the generation right. Similarly, my P new hole concentration should be P 0 plus P due to the generation and this is N generation equal to P generation right what happens to my new what is the electron in this case this is a P type right. So, electron is a minority. So, N equal to 10 power 4 plus what is the new generation electron 10 power 14 my god. So, from N what up at the P it is 10 power 16 plus 10 power 14 what happened to the minority carrier and what happened to the majority carriers. 10 power 4 plus 10 power 14 is almost equal to 10 power 14 10 power 16 plus 10 power 14 is almost equal to 10 power 16 what do you see here because of the light following on your semiconductor such that the electron hole pair generated is 10 power 14 per centimeter cube electron hole pair by the. So, both electron concentration and hole concentration due to the generation is 10 power 14. Therefore, new minority carrier concentration is much higher than the 10 power 4 initially it was 10 power 4. Now, it is 10 power 14 the electron concentration which are in minority for P type has increased by 10 orders of magnitude what happened to the majority carrier concentration hole nothing it was earlier 10 power 16. Now, the new generation is 10 power 14 which is 0.00, 0.01 times tensor. So, this is hardly any increase in the majority carrier concentration, but minority carrier concentration has changed significantly. This is a very important point to note that in solar cell minority carrier concentration changes drastically because of the light following on it and because of this drastic change in minority carrier lot of behavior of a solar cell is also determined by minority carrier concentration and change in minority carrier concentration got it very important point to note I will also show you some graph why it is important. So, this change in the minority. So, delta n this delta n is the excess carrier concentration and the delta P is the excess carrier concentration excess carrier as compared to the equilibrium. So, I can say it this delta n or the excess carrier is nu n value which is the disturbed condition minus undisturbed condition n minus n 0 n 0 is the disturbed condition non equilibrium minus equilibrium that is delta n and we referred as excess carrier concentration. Similar delta P is disturbed condition that is P minus undisturbed condition that is P 0 that is delta P. So, that is the slide is showing delta n is n minus n 0 division of the carrier concentration from equilibrium similar delta P is P minus P 0 division of the carrier concentration from equilibrium. Low level injection tells me that what is this situation now after I put the light on it this was a P type semiconductor if I put a light on it such that there are 10 for 14 electron hole pair are generated my whole concentration remains unchanged 10 for 16 my electron concentration which are minority is 10 for 14. 10 for 14 is still much smaller than the 10 for 16. So, my P type semiconductor remains P type only right my P type semiconductor remains P type the behavior does not change, but if I create a condition when there are 10 for 17 electron hole pair are generated then my both electron and hole concentration will almost become equivalent semiconductor and then my P type semiconductor will lose its behavior and it will almost behave like intrinsic then that is referred as the high level injection. So, normally your device is operated in a low level injection such that the majority is other. So, means P type remains P type n type remains n type the material behavior does not change what is it required that the minority carrier concentration should always be less than the majority carrier concentration even in the excited condition. So, that is called the low level injection. So, P type should remain P type n type should remain n type that is called the low level injection. I hope it is clear to all or otherwise let me repeat the this thing again let me repeat a not a condition of a low level injection. So, I have a initial P type my P 0 is 10 for 16 n 0 is 10 for 4 I have light falling light generation due to light generation the EHP that I am creating is 10 for 18 per centimeter here. So, my new P 0 is 10 for 16 plus 10 for 18 my I am sorry not P 0 P this is a condition my new n is 10 for 4 plus 10 for 18. So, P becomes almost equal to 10 for 18 is 2 order magnitude higher. So, it is almost equal to 10 for 18 n 10 for 18 is much higher than this it is already 10 for 18. So, my both n and P is almost equal and therefore, it is not anymore a P type semiconductor it has changed its behavior. And therefore, this is called the high level injection high level injection normally we do not design our material or solar cell to work under high level injection, but sometime you require that and that requires a different altogether different approach. So, normally we work with low level injection and I hope it will be clear to all the rate of recombination. So, now we so we have talked the generation rate number per unit volume per in time then there should be rate of recombination also. I will actually skip this and the rate of recombination is excess charge carriers divided by the carrier life time. The average carrier life time or the minority carrier life time is the average time a carrier spends in a excited state. What does it mean? If I have the material light is falling on it, electron get excited and after sometime it may recombine it may recombine. The time it spends in the conduction band at excited state, average time it spends in excited state is called the carrier life time. So, this carrier life time for semiconductor depends on the type of material. What do you expect? Which material will have the higher life time monochrist line or amorphous silicon? Monochrist line will have higher life time because it is less defect material is very ordered, but in amorphous silicon the large number of defects are there. Large number of defects means large number of extra energy levels in between and therefore, larger path for the recombination and therefore, smaller carrier life time. So, carrier life time normally can be as low as nanoseconds or it can be as high as millisecond. So, carrier life time can vary from millisecond to nanoseconds. So, we want higher carrier life time. Again note down this point in solar cell for in order to get good efficiency your carrier life time should be as high as possible. So, this carrier life time actually comes from this that there is a recombination taking place in all this. So, we are skipping in interest of the time, but I think the main concept is you have to define the rate of recombination which is excess carrier concentration per unit time. So, what is the unit excess the delta p will have the unit of per centimeter cube and time is per second. So, the rate of recombination is also number per unit volume per unit time similar to the rate of generation per unit volume per unit time. This will depend on excess carrier concentration and the life time. By the life time has a symbol of tau this is the life time and this can be tau n that is for the electron and tau p is for the whole carrier life time for the electron and carrier life time of the whole. Now, we will also very soon you will also come to the term what is called the minority carrier life time and majority carrier life time. But just note down this that excess the rate of recombination depends on the delta p that is the excess carrier concentration under the disturb condition divided by the life time. Remember what we are talking about n type semiconductor we are talking about whole life time which is when it is n type semiconductor we say it is the minority carrier life time we are interested in. When the p type semiconductor we say we talk about electron life time. So, we talk about the minority carrier why we talk about minority carrier I will show you some example this. So, look here first of all this is the p type semiconductor and this graph higher graph is the majority carrier this is the minority carrier look at the change. Because of the light falling in the change in the majority carrier concentration with respect to normal condition is almost negligible look at the change in the minority carrier concentration. Change in the minority carrier concentration is very strong and that we have I have told you by the numbers. Now when you excite the carrier because the light putting at the majority carrier concentration slightly increases and then almost decreases and come to that level because the low level injection the majority carrier concentration does not change. But look at the change in the minority carrier concentration with respect to time within the time of 15 nanoseconds the minority carrier concentration changes significantly. So, that is why we will see that in solar cell it is the minority carrier concentration change that is very important for the functioning of the device. And that is why we will that is why the there is importance of the minority carrier concentration then the majority carrier concentration. And that is why we more we are interested more in the minority carrier life time. So, when we are talking about p type semiconductor we are interested in the electron life time when we are talking about n type semiconductor what is the minority in n type hole. So, in n type semiconductor we are interested in the hole life time. So, minority carrier life time is also important one more reason. So, you look at this graph look what you are seeing the change in the majority carrier with respect to time is not much, but the change in the minority carrier with respect to time is significant. Similarly, we will find that the change in the minority carrier concentration with respect to distance is also much, but the change in the majority carrier concentration with respect to distance is also not much. So, what? So, it means that you know our diffusion current. So, let me put here it may take some time, but let me finish this it is very important. So, our drift current drift current is proportional to the electric field and diffusion current whether this is drift current and the diffusion current is proportional to what concentration gradient. And for the minority carrier concentration gradient can be significant as we are seeing right here this can be significant with respect to time and with respect to distance also. So, because here the gradient is very small here the gradient is very large change in the concentration with respect to time and distance is very large. And therefore, the diffusion current can be very large because of the minority carriers right. Diffusion current can be large because of the minority carrier and therefore, we are more interested in the minority carrier lifetime. I hope everybody got this we are more interested in minority carrier lifetime because again let me repeat in solar cell operation because of the various reason that I am giving now and we will discuss later that the minority carriers plays very very important role and that is why minority carrier lifetime. So, that is why here the change in the minority the rate of recombination is for the n type solar it depend on the minority carrier lifetime. So, delta p by delta tau p for the n type semiconductor. Let me tell you one other reason one other way why minority carriers are important right. So, suppose you have p type semiconductor n type semiconductor there are many many electrons here many many many electrons right because it is a majority and you have few holes here right it is minority this electron if you want to recombine it requires a hole here is not it it requires a location in the valence when to come then only it can come down and occupy. So, therefore the rate of recombination will not depend on the electron concentration, but it will depend on the minority got it another way of explaining that the rate of recombination will not depend on this carrier concentration because they are already in the number, but in order to recombine they need a hole electron need a hole then only it can recombine and therefore therefore the recombination rate. Therefore, the recombination rate is controlled by minority carriers recombination is controlled by minority carriers, and that recombination rate is given excess-aeroconsentering excess minority carrier concentration divided by the lifetime excess minority carrier concentration for p type electron is the minority. So, p type excess minority carrier divided by the life time of the carriers. And I told you life time is in the range of millisecond to nanoseconds, higher is the life time better it is. So, once we know this, this is the differential equation and we can solve this differential equation and obviously, the solution is very simple. The once you have the excess carrier concentration, the decrease in the excess carrier concentration is exponential. First order differential equation if you solve this, you will find the solution is this. So, the this is the recombination rate and the solution of this is going to be like this. What does it mean that if I am going to, so at time t equal to 0, if my excess carrier concentration delta p is this, excess minority carrier by the way, excess minority carrier is this. With respect to time, my carrier concentration will decrease exponentially and this will be exponential minus t over tau of p over tau of p and tau p is a minority carrier life time. So, the characteristic decay coefficient will be tau p and this is what will happen and this is the excess, this is given in terms of time. Is it clear? The excess minority carrier concentration, so once you excite electron hole pairs and you switch off your light, the recombination is taking place and the excess carrier concentration will decrease exponentially with the minority carrier life time. And it will decrease till what level? Till this level reaches to equilibrium level. What is equilibrium concentration p 0? So, this will decrease to a equilibrium carrier concentration. This is the, how the minority carrier behave, a minority carrier behaves as a function of time, exponential decay of excited carriers as a function of time due to the recombination. Why the decay is happening because of the recombination? Fine and that I have shown you already, so that brings me to the end. We will not again discuss, in general the theory of recombination can be actually much more, can be more sophisticated and we can actually get lot of information out of it, but in brief. So, this equation if you actually take some approximate values, this equation the rate of recombination actually results in the same equation as this. So, this is a simpler equation and this is more complicated equation takes more into account, how many defects are there, how many energy levels are there, how many electrons are there and so on. But the this is simple enough for us to understand and it is good enough for you to. So, you should be actually using this, what is the rate of recombination if you know the excess carrier concentration of minority and their life time. So, with this let me summarize what we have learned in this lecture is, how the carriers are generated as a function of light and how the carriers are recombining through the interface through the defect level and what is the carrier life time and if you know the carrier life time, how the excess carrier concentration decreases. We also discussed that it is a minority carrier that plays a very important role in the operation of solar cell and I have shown you by various example. So, we can calculate what is the excess carrier concentration with respect to the equilibrium condition, excess carrier concentration decreases exponentially and eventually if the disturbance is removed, light falling on a semiconductor is removed eventually you will get the same equilibrium condition after some time. I will take some question. Pandit, Deen Dayal, University. I would like to suggest that can we have this workshop for solar thermal. Yes, we can. Thank you very much. One question is there sir. See the mother earth is covered by water for more than 75 percent. So, can we use that water surface for photovoltaic cells to keep photovoltaic cells and get more energy because land is very costly. We can do that also. Now, you can start the research on that and use all the land all the waterfront available. That is possible. NIT Varangal. When you fix the position of the panel, if continuous tracking is not the, let us say if it is per day tracking, per day you are fixing the panel position. So, instead of taking the noon, it will be better if you take somewhere between the center and the noon because moon time will be very lesser time whereas, in between time will come two times. Yeah, first of all the noon time as per the, as per our local watch should not be taken as a noon time. You know because our noon time is as per the longitude which is 82.5 degree. But the actual noon at a different place occurs in a different time. So, what we should take is what is called the local apparent noon time. That is the time we should take. But noon, taking anything other than noon is not going to help you. The noon time is the best time. NIT Trichy? Sir, my question is like you said solar energy spectrum varies from 3.5 electron volt to around 0.3 electron volt. But you said that the ideal band gap of the materials semiconductor material is around 1.45 electron volt. Why it is so, sir? Because can we, can we reduce even up to 0.3, I mean 4.3 electron volt? So, answer to this question will come in the lecture number 11. So, wait for that. So, basically we have to optimize you know we are interested in the maximum power. And power is a function of current and voltage. So, we have to, we have to optimize both current as well as voltage. And therefore, when we come to the solar cell itself we will discuss why 1.45 is more optimum than 0.3. But good question. MNIT Bhopal? Sir, my question is that you told about the trap assistant recombination. And this is due to the impurities that is one in billions. But somewhere it also gives it that trap assistant recombination, the recombination take place between the energy gap. So, can't this be a beneficial or advantages to get absorption of absorption from those spectrum part that is basically the infrared reason. There again the electron can get excited and get to the valence band and we can use those electrons for the conduction means somewhere it is increasing the efficiency of the solar cell or not. Okay, very good question. So, if the middle energy level middle of the band gap, if they are helping in the recombination why can't the same energy level help us in generation also. So, when the photon energy is low which is not enough equal to the band gap, but let us say half of it then 2 photon can be used to excite one electron from the first of all valence band to the middle energy level in the trap level and then from the trap level to the conduction band. That is possible, but you require that extra trap energy level in a very large density. So, sometime people are actually done lot of theoretical work in what is called impurity photovoltaic. Sometime people intentionally put lot of impurities to increase the trap level such that this traps are actually helping you to generate more carriers than the recombination. But the problem is same trap can also be helping you to recombine. So, in practice there is not a good demonstration of this concept, but yes there is some theoretical work which is available where people are trying to use lower energy photon using such energy traps. Thank you sir. R.C. Patel, Shirpur. Sir, can there are little bit possibility though when electron is recombined with the hole that have generated the energy that generator energy can further utilize for the excitation of the electron. Good question. So, when the electron recombine with the hole it results the energy of that electron must be given off. In LED for example, LED works on the recombination LED survives because there is a recombination. So, LED recombination is taking place and in LED that recombin energy of the recombining photon electron is given in terms of the light. In solar cell the energy of the electron which is recombining is given as a heat and that heat energy cannot be utilized because the kind of energy is low and it just heats up the material. But yes in some kind of direct band gap semiconductor when the recombination takes place and the light comes out the same light can again get absorbed in the material and that it can be useful. But if the light escapes the material then it is not useful. So, normally it is very difficult to use the energy of the electron which is recombining. Amrita, University Co-M tour. Why some semiconductor materials? For example, titanium dioxide exhibit both direct and indirect band gap. Why some semiconductor material exhibit both direct and indirect band gap? Basically it also. So, one thing like silicon like silicon when it is a mono crystalline form it is a indirect band gap semiconductor. But when silicon is a amorphous silicon form or a nano crystalline silicon form because of the increased scattering that is taking place in the semiconductor and because of this increased scattering the light absorption probability is much higher and therefore, it behaves as if it is a direct band gap semiconductor. So, the behavior of the semiconductor whether it is a direct or indirect also depends on the structure of the material. I will take a last question. Which type of semiconductor material that is more suitable for producing more solar power? Either it may be N type or P type? I will again in my next lecture tell you that it is neither N type nor P type it is a combination of N and P together. Only N type alone or P type alone cannot be used to produce any power. You require a junction between P and N only N type alone or P type alone cannot be utilized can be utilized. There is a question on chat from GSITS. Why on increasing wavelength absorption coefficient decreases? So, basically the absorption behavior or the absorption behavior of a given photon is all depends on the kind of the interaction of the wave within the semiconductor and it will depend on the arrangement of electron and energy levels of the electron within this the binding of electron within the semiconductor. So, you have to go to really a kind of quantum physics in order to understand why it increases. But basically it is the interaction of the waves or the photons of a given wavelength or energy with respect with material that determines the absorption behavior. One more question on chat. We can increase the absorption capacity by coating solar cell with black paint. Coating the solar cell with black paint can we increase the absorption capacity? The answer is we can increase the absorption capacity but absorption will occur in the black paint. We do not want absorption to occur in a black paint. Absorption should be occurring inside the semiconductor and therefore, that is not useful. The absorption in the black paint is not useful. So, in principle we cannot do that. Our absorption should be increased inside the semiconductor. So, that we will learn in the next lecture that the carriers are kind of generated in semiconductors. So, that it contributes to the solar cell or the voltage that is generated. Rajpur University. What absorption rate direct band gap semiconductor is higher than the indirect band gap semiconductor sir? Well I told you that in direct band gap semiconductor in order to excite electron from valence band to conduction band you require one event and that event is only change in energy of the electron. But in indirect band gap semiconductor if you want to excite electron from valence band to conduction band you require two events. First it has to change its energy and it has to change its momentum also. And whenever events take place in series the chances that it happens successfully reduces and therefore, the probability also reduces. So, it is a question of one event versus two event. In the indirect band gap semiconductor because two event take place the change in energy and change in momentum and therefore, the probability is lower fine. Thank you very much. All the best.