 You can follow along with this presentation by going to nanohub.org and downloading the corresponding slides. Enjoy the show. The previous lectures of mine and the stuff that we did, the easy part, we talked about the high-quality critical results, and a lot of the research that we do is the lower cost materials, the lower cost of solar energy production, in which the cell designs are a little different, there are many more of the effects, and there are a whole different set of considerations, and we're really lucky to have Professor DeLong, who's going to give us two different lectures on thin film solar cells and tell us about the issues. So with that, I'll turn it over to Professor DeLong. Alright, you can hear in the back, right? Yeah? Alright. So, what I'm going to talk about today is thin film solar, as you just heard, and if you think about the summer school, then it has covered a lot of topics, right? You must be tired by now, but essentially it had two broad groups of things. One is for transistors, spin tronics, memory elements. These were for information processing. That is, if you learn those things, you can get a job at Intel. On the other hand, the other topic, set of topics, were the grand challenges of today, which is not information processing necessarily. This has to do with energy conversion. So you have heard about thermoelectronics and PV, the photovoltaics. And of photovoltaics, there were five lectures. And these five lectures had to do with the basics of solar cell. And by now you know that. What this all about? That if you have a semiconductor and light comes in and shines on it, it may come from the sun or it may come from some other source, essentially a photoelectric effect. Then you essentially have electron hole pair generated. Professor Lundstrom explained that. And when you connect a load to it, or a light bulb to it, the light bulb lights up without having to sort of connect to your power socket. That's what the, fundamentally, what PV is all about. And then once that was done, the very basics, you learned a lot about crystalline solar cell. And you learned about how thick this radian has to be. So because it doesn't absorb very well, you remember that. And you also remember perhaps that 80% of the market today is due to crystalline silicon. So this is the dominant technology, that's for sure. Now if that was all there is to it, of course we could go home and that would be nice. But unfortunately it looks like that there are in fact very interesting additional trends. And that counts mainly because of the cost. Because at the end of the day, when somebody says that your iPhone costs $300, you say okay, here is the $300, you buy it. But for solar, for energy, cost is very cost sensitive. Because in one hand you have oil and gas, which are very inexpensive. And the other hand, if the PV people say that it costs twice as much, but look, this is very environmentally friendly, you'd say no thank you, I don't want it. So therefore, it's very cost sensitive and this is the cost aspect of it that makes this thin film organic solar cells, plastic solar cells so interesting. But also the physics is very beautiful and I'm going to explain to you how that's going to work. So to talk, this talk is about thin film solar, organic photovoltaics, will be the next lecture. Now here is a brief outline, I'm going to talk a little bit about the background information, give you some background information. But I'm going to talk a lot about photo current and this aspect you might find a little bit interesting because Professor Lundstrom, one thing of all the things he said, one thing you might remember, he said that when he was a student he used to go home and explain to his wife that why he doesn't work on the photo generated carriers for the solar cells because it was flat and so therefore he could focus on the dark characteristics. So if you remember one thing from this lecture that is what you should remember is that he cannot give this explanation to his wife for thin film solar. So I like to then explain a lot, explain that how this is done but I'm not going to do it by using any differential equation. I'm going to use very simple things that just counting, counting electrons going left and right, that's all you need in order to find how this electrons move around and how these photo currents are generated. Very simple, if you just don't fall asleep then you'll be able to understand them all. And then I'm going to talk about dark current but very briefly, Professor Lundstrom has already explained to you, Professor Gray, a lot about dark current so I'll not really do much about it. Instead what I want to tell you about is that once you put these cells in a module or connect them up so that you can use them, variability and reliability becomes fundamentally important and this is an aspect that you didn't really hear about much. But at the end of the day it matters a big deal if your solar technology lasts for 20 years versus 40 years because it's free energy. You bought your panel for $1,000 let's say from Sunpower and that's your initial investment. If it gives you free energy for 40 years versus free energy for 2 months it makes a huge difference in terms of cost per kilowatt hour, the amount of energy. So reliability is very important and I'm going to explain to you how that works. So very briefly there are different types of solar cells. You have heard about this crystalline solar cells and you may remember that the green n-plus region is very thin. You remember that we cannot make it any thinner because otherwise there will be a big resistance drop when you want to collect it to the electrodes on the top, this plug-like structure on the top. But the main problem is that the crystalline silicon, the P-region, the P-base is very thick, 200 micron and why is it 200 micron is because it's a very weak absorber, indirect band gap, that's what crystalline silicon is and so therefore it takes many, many bounces on the order of 10,000 micron before everything is absorbed, 50 bounces maybe before it's absorbed. So it's a thick material compared to what you could do with gallium arsenide or any other thin film technology. For example, you could take a PIN structure, for example based on amorphous silicon where you have a P-region that's the yellow and the intrinsic I-region that's in the middle 250 nanometer. You see on one side you have 200 micrometer, in another case you have 250 nanometer and then you have an N-region on the bottom which is green and the top and bottom you have the two electrodes. You see you could put the whole thing just almost inside the N-plus region, it is that thin so maybe just the device itself without the encapsulation or anything maybe a factor of 500 smaller thinner compared to the other one. So you can immediately see that if this material, the two things cost the same then this would be way less expensive compared to the silicon. Of course there are, this is not the only version, the other version involves metal insulator metal and that will be the next lecture and that has to do with flexible organic solar cells so we'll talk about that. Now you might ask why is it PIN here and PIN over there? In this case in both cases you have a given electric field and once you have that electric field the electrons can be pulled out on the both from the both contacts so you can have either type of the technology depending on your need. So what I'm going to tell you about is this basically the middle one PIN structure, thin film amorphous silicon and explain the physics of it and how it differs from the crystalline silicon. It's actually very different but of course you will see how this comes about. But of course this is not all great news if the thin film was so good why is the market 80% crystalline silicon is because many times the material may not be abundant in the earth you know silicon is everywhere. So silicon in various forms it may not be many of the things may be very rare so once lots of people start buying it then you they mean the suppliers may not be able to sell it some of them are toxic so there are other problems and generally the substrate may be more expensive so although you are using far fewer material, far smaller amount of material it may be more expensive per unit and so therefore you may not end up really saving a lot of money. So if you make a quick comparison and this is by the way I take no responsibility for these numbers the numbers are very sensitive but my main point is to show that for crystalline silicon the material is about like say $200 per meter square the process cost $100 and when you put them all together it is cost per watt without installation is about close to $1.75 and compared to that other thin film technologies generally typically have lower cost but in addition there is another problem that generally crystalline silicon is heavy because you have to put it on top of some substrate a truck has to come to your home and then put it up you cannot go to Walmart and buy in a plastic or cheap wafer and bring it on yourself and put it on the top of your roof not that you should try but in principle that would make things much more expensive it turns out one-third of the cost of PV is the installation cost half or one-third so therefore this silicon technology generally is very expensive so a lower so a thin film PV might actually be much better. So let me explain to you then what the physics is you see it's thin so when things are very thin lots of trouble can happen because things can short from one side to another thin is not always necessarily a good thing so for example this region I do you remember in the middle region this I region this we said this is on the order of 2 to 250 or 300 nanometer right very thin then doping regions the dope regions are on the order of 10 20 nanometer so again very very thin this material often are grown in low temperature and so therefore there can be a lots of other problems also for example one problem it could be that since these regions are very thin the contact might diffuse inside that device now you might say well a little contact diffusing inside of what harm is it going to do it's a very big a little bit but what I am going to show this is like impact crater that it may enter small but its impact will be huge a micron size hole can essentially drain away carriers from a millimeter size region so we are going to talk about that and then of course many of these materials have horrendous grain boundaries nothing beautiful like silicon where all the atoms are like an army right all regimented and all every atom in their right place instead here you have grain boundaries going from left and right and the question you ask yourself how in my life I'm going to actually solve this problem of course there is a simple answer is that we can close our eyes forget about the defects and put some effective parameters in the silicon simulators and whatever result we get we don't tell anybody else and go home now this is the four things I'm going to talk about but the fifth thing is equally important then that has to do with series connection solar cells are always series connected because each cell is like one volt battery just like in a toy many times you have to put three four batteries in order to get the right voltage in the solar cell many times you have to connect let's say as much as a hundred of them in series so that you get can get hundred volt out if it's one voltage and the way people do it that if you have an a glass substrate if you put the mirror TCO is type of a electrode highly conducting electrode then you put the material that you want to put in this is your solar cell material amorphous silicon cadmium telleride whatever and then you do the laser stripe open up this holes and then put the second contact on top of now do you see what it just did instead of having a simple PIN junction this successive layers of things now currents are going to do this that it will enter through one end go up through this contact come down so this is one solar cell then go down come up and again come down that's another solar cell and so although initially you had thin planar structure you have just by striving and connecting it up properly you have just made it a series of solar cells which are connected in series now this is very important many times you will see if you Google I hope nobody is doing it now but if Google then you would see many of this lines in here and essentially these are scribe lines essentially that are showing you that that's how you cut it up so that when you string them together it gives you a bigger voltage so these five things we are going to think about as we go through the rest of the talk so now let me remind you let's go back take a step back that what did we learn from professor Lundstrom talk I was sitting in the back so this is what I learned essentially what he talked about that when a photon comes in a light particle comes in if it has energy larger than the band gap then a electron whole pair will be generated the red electron will go to the left contact the the white hole will go to the right contact and they will eventually go through the load and therefore whatever is delivered the power there and you remember what we talked about also in that lecture that there is something called a dark current on the right hand plot this is something called a dark current which is essentially the diode and you can see on the bottom that we have a symbol for this diode and that is ID we have written ID next to it so that was the dark current and he essentially explained to you that the photo current is essentially a constant in the graph it's a photo IPH that's a constant so therefore it's like a current source and when you combine them together the total current essentially is a dark current and the photo current together right and that's why what you get and so the voltage at which there's no current is called open circuit voltage and the point where you want to operate is the maximum power point how do you find that point well if you remember from your circuit days that if you have one element that has this particular IV characteristics and if you have a load line then wherever that one intersects that rate point that is where the power would be now what is the maximum power maximum power would be whatever corresponds to the rate point with a voltage that is little less than VOC and photo current which is a little less than the ideal photo current the short circuit current now solar cell people are lazy so instead of really calculating what they do is that they say okay this is my original box VOC multiplied by I photo but of course that box is too big what I should really have calculated is green box now I don't know really what this green box to this one ratio is so I'll call that field factor and so that is what they will this is how they will write this formula that this IPH multiplied by VOC is the bigger box and the field factor is the factor that you multiply so that you get the green box which is the power that you really want now this is ideal solar cell because in this case you can take that current I'm sorry you can take you can take essentially this current and add it up to this dark current to see at what point the VOC so you can calculate a VOC you can get a power maximum power and you will be done but it turns out for solar cell this is not really for thin film solar that's not really the full model or the full story what you need is two more things one is this extra current source that only occurs when there is light in there so instead of having a voltage independent current source as you heard before now I have this combination which depends on voltage and I'm going to explain to you very simple there's nothing funny about this whole thing and then there is another thing in solar in particular call this shunt now somebody asked professor Lansstrom the other day that what is shunt and he mentioned that there could be pinholes and other things didn't really go into the details I want to explain to you that this can be understood very simply as well so we'll talk about that so let's the main point I want to make is that super position doesn't hold so therefore if you see a thin film solar most of the time you shouldn't try to use copy textbook formula from your undergraduate textbook and try to apply it because you may not get right result okay so let's get started on in terms of photo current now before I get started let me tell you something simple and this is something you understood will understand very easily no differential equation or anything just look at how the what the electrons go assume that I have a semiconductor and then two metal contacts and assume that I have six photons coming in and that has generated the six red electrons and six white holes now for some reason and we'll understand that reason later four of the electrons are going to the left and two of them going to the right and similarly two of the holes are going to the left and four of the holes are going to the right how much how many currents how much current do you have now you have no differential equation to hide behind so therefore you must be able to answer this clearly the answer obviously is not 4q because you could look at this electron and you could say four of the electrons coming out so I'll say it's 4q not really because the two of the holes are coming out through the wrong contact so as soon as this four comes out they will recombine and only two can go to the load and so therefore the current will always be the current at any given junction the electron current to the left contact minus the hole current to the left contact and when you sum them up that's the total current and so in this case I have only 2q v0 v0 is the velocity at which electrons are going now of course you could write it slightly differently you could say that these four are really out of the six because six photon came in so four over six so it's really the fraction of the total that is going to the left contact and these are the ratio of the probability that you will escape to the left contact right if I have two doors then the probability that I'll escape through that one versus the probability that I'll escape through this one so it's normalized so that's it so you have so I'll write a formula which is something like this which is generation rate probability that you the electrons escape through the right contact the proper contact and minus the probability that the holes keep through the wrong contact and that gives me the total current now what happens if you have recombination remember if you have defects and all you might have recombination we don't have to worry too much about it because that's really again very simple see here I have three coming out two electrons two holes coming out through the wrong contact so the total current is just one electron that's going around the circuit right now what happened all through all this recombination and all why did I forget them not really I didn't really forget them because if you think about it that if I wanted to write what fraction of the total electrons are getting out then I would write three divided by six three actually went out through here and six were generated and so when I write the ratio my recombination is sitting right here because the total rate had the recombination in there of that only a fraction escaped and so therefore these two formulas if you sort of remember that sort of makes sense then you will see how very complicated things will get very very simple as you will see now before I get there let me tell you about this semi classical probability of escaping through the context so for example if you have a barrier and this is something professor Lundstrom also mentioned of a certain height and if you wanted to know what is the probability that the electron will escape there you will say that is probability is proportional to the height right proportional to the height of the barrier if the barrier is big nobody is escaping and if the barrier is very low everybody is will go away very quickly so that there's something you know and this Katie is tells you the temperature so the more the thermal vibration is easier is it is for it to jump over the barrier now you can of course make the same argument if you had a left contact if you have a device in the middle I'm trying to see whether how can I get to the left and how can I get to the right because then I can do something called the partitioning so in general therefore what I do that if I have two barriers then essentially depending on the barrier height the left and the right I'll escape with two different probabilities now this turns out to be very important as we try to understand why thin film solar is different from crystalline silicon as you'll see next so assume this very simple case you remember this simple formula from before that this is if I injected a particle here a photon has just come in generated two electron whole pair a one electron one whole pair and I want to know the fate of this electron what is it going to do based on this formula well it has a probability that it will escape through the left contact but it has also some probability that it will escape to the right contact and so you can see this ln and rn are the probabilities for the electrons keeping to the left contact and the right contact and similarly for the holes you also have the same probability it can go to the left or it can go to the right now if I ask you what is the probability of electrons going to the left well in that case there is no barrier it's just fall is like water flowing down a hill and in that case I wear it will there's no barrier so whatever is the flux it will just get out from there on the other hand if it wants to go through the other contact let's say this is a very this electron likes torture so it wants to go out to the wrong contact now if it wants to of course it can if the electric field is e and if this distance is x and whole thing is w then the barrier it has to climb is e w minus x over kt that's the barrier right electric field multiplied by the distance and so that's the barrier I all you have to do is to insert these few quantities in here because you see I have everything gamma l gamma r I'll just put it in here by the way why do I do this integration because of course sunlight is going to come at every point right it's going to generate at every point and so therefore when I want to know the fate of all the electrons that are in there I'll have to integrate them up now if I do that I'll put this formula you recognize this one is here this V naught is here you put them in and very soon you get a formula which looks something like this now you this integration exponentian on all you if you don't remember you can Google it the integration formula but this is something that is that will get and in fact it turns out that this formula it is originally derived in 1981 it probably takes eight pages six to eight pages with a lots of differential equation left and right and boundary condition at the end you get this but you do not know what happened to the electrons in between you are so lost in differential equation that the electrons you have forgotten about the electron but you can see very simply what these electrons are doing in here what this is all about is essentially that if you are close to this region where electrons can skip in that case there'll be a loss of certain number of electrons will not come out through the right contact and so therefore you'll have a reduction in current your current cannot be voltage independent because you see as I am pushing this voltage up and up right biasing it as I'm pushing it up and up the fraction that will begin to go through the other contact the wrong contact their fraction will increase and eventually there may be a point and as it'll show in the next slide there may be a point where this is flat half going the wrong contact half going the right contact and essentially you have zero current voltage independence cannot hold in this particular case right it's simple so you know why it is voltage independent requires a lot of discussion but why it's voltage dependent should be simple to understand so you think that well this is a simple formula may not be very good who knows so you have this formula and here is this green line and I'm going to talk about this red and the this is the dark current the blue one is the dark current red is the total current this is photo current this is not only not constant it is going through zero and going to the other side flipping its sign right photo current is not only constant but it is changing its sign and you can if you'd put it in a numerical simulator like adept or any other device simulated that professor gray talked about yesterday at the results will be right on top of it and so therefore you can trust this result and you can easily see the physics what happens here is that you have in the right at low voltages this partitioning occurs so most of the current is going in the right way the way you want it to be when the voltage is VBI the built-in voltage the partition equally the current is zero right so this point is current is zero and if you flip it on the other side then of course the currents are going to go to the wrong way instead of electron flowing this way now the electron is going to flow to the right side and so the current is going to flip that's it so voltage independence doesn't really hold in this case now how do you want to make it if you really wanted to make it voltage independent then what you could do you could put a big barrier here and I put a big barrier here so that nobody is allowed to go through the wrong way right you close one door if you close one door then even if I try I cannot escape through the wrong contact so in that case of course this formula immediately knows that that has to be voltage independent why because the right contact this would be zero now because right contact you cannot escape anymore that has been blocked and similarly this holds this this cannot also escape and so therefore this will become one and when you this is very happy integration zero to W DX multiplied by one gives you W and that means every photon that has been every electron that has been created will come out through the right contact independent of voltage now under these circumstances for sure you are going to have a voltage independent voltage independent photo current okay so blocking layer is very good yesterday you heard about this electron mirrors and other things right in the lecture if you remember and so this blocking layer is therefore very important now only if there's low recombination as I'm going to tell you sure now one thing I haven't been telling you so far is that this material is full of defects right remember low temperature deposition all those grains sort of crisscrossing full of defects now when you have things full of defects then life is a little bit more complicated because even in that case what I want to show that even if you put a blocking layer it is not going to help you in terms of making the current voltage independent you know I'm very trying very hard to make it voltage independent it doesn't want to stay that way why not what happens in this case why can I can I not have make it happen because as soon as an electron whole pair is generated this electron whole pair is going to randomly walk around it is very soon going to find a hole that has also been generated it's going to recombine how far is it going to go before it recombines well you'd say this time to recombination that depends on how many defects I have and the velocity of it and the electrons movement will be new multiplied by the electric field that will be the velocity mobility multiplied by the electric field and it's going to stay alive for tau so that is the amount of distance over which it is going to recombine and if it recombines and if it doesn't come out is it as if it were never never generated right because I do not really know whether it was generated and then recombine or essentially it generated it it sort of no it's not generated to begin with okay again this formula would this formula work well generally it should work because you can see how this formula should work gamma lp the whole zero because I have put a blocking layer this is zero gamma rn is also zero because I have put a blocking layer so that's not going to go anywhere now the fraction of electrons that is injected at a given point and comes out because just going through this recombination processes is this ratio gamma ln gamma ln divided by plus gamma r you know you let's say the chances of going from here to over there there are a lot of sharks between here and over there and if I have to swim through this my chances of getting out on the other side is exponentially suppressed that ratio and so what I am going to put is zero to w dx and this ratio is e to the power x over lc lc is that distance because that is how far I can go before I am eaten up so I can integrate this simple thing up and again I can write the photo current again if you look at this paper the original paper which is which derives this that will be another six page but this is essentially a sense of it is just this that you cannot get out without getting through this recombination processes so therefore you can rewrite it a little bit q gw was my total generation voltage independent right independent because if I could collect everything independent of voltage that would be the thing but of course this green blue one is telling me what fraction of it is recombining inside the device before getting out and so therefore this whole quantity is essentially this voltage dependent current source again in the presence of recombination in this region the current will be voltage dependent now if we understood so much now it's good to go back and ask the question that what happened to the crystalline cell then in that case things were much nicer so what happened in that case well you can easily see what happened in this case and why if the quality of the material is bad or poor many of the crystalline silicon if you want to pay less money then not the champion cells of martin green but if you want to do a commercial cells their quality is generally lower because that's less expensive so in that case many times this barrier may do you no good very counterintuitive why barrier wouldn't do any good again this formula will tell you that why the barrier doesn't do any good look at this formula simply says that all you have to keep track of is the number of electrons that are going getting out through a junction so I have the electron current moving to the left and the whole current moving to the left but I have a potential barrier here it's a p-n junction so my whole current is essentially zero the amount of electron that can get out through that contact so if that is the case from the previous slide you remember so it is as if these electrons are getting out through this region and that is what I showed in the last slide and when you put this thing in put this same formula copy this same formula you find that only the electrons within a diffusion length away from this region only those will be collected rest of them will essentially recombine here now you may say that let's take out this potential barrier but this barrier must be doing me some some good because after all here it's sort of reflecting all the carriers electron mirror this should be doing me some good but actually it doesn't do any good because you can see the for the following reason because if you remove it of course these electrons will be coming out to the wrong contact but because the electron number is a little bit less now the recombination of the holes that are coming out here will also be a little less and so therefore what's going to happen more holes are going to come out here and when this current is added to that current it will show there is no difference whatsoever between these two cases because who cares whether you recombine right here or you recombine two nanometers into the contact there's no difference a wrong contact wrong recombination so it makes no difference and you can this seems very counter intuitive the blocking layer in one case whether it makes no difference so in one case you see this is the electron current the red one and the blue one is the hole current in the other case this is the electron current through the right contact this is through the wrong contact it's going the wrong way but what will happen the hole will also escape in a larger number and the total current will remain exactly the same so this sounds as I said counter intuitive but it will turn out that this exactly consistent with numerical simulation you can see that this is the current electron current going out through here the hole current is very small and then if you remove this blocking layer there'll be a spike in the in the hole current I'm sorry this is spike in the hole current but there'll be a little bit negative electron current and when you sum them up the total current will be absolutely flat total sum of the current will be absolutely flat okay so again as I'm saying that this view I haven't solved a single differential equation but you can see most of the things that would be intuitive non non intuitive will come out if you just think about which contacts or which doors are the electrons are coming out through differential equations are good capabilities but not necessary and if you combine I don't want to go through this point too much but if you combine if you have both recombination and electric field if you have this don't put a blocking layer don't want you if you want to complicate your life without putting the blocking layer the life would be a little bit more complicated but once you have done this your numerical simulations and this simpler form most of the time will give you good results I'm glossing over this point a little bit but it requires a little bit more discussion so long you get the basic idea I think that should be fine these numerical simulations are these symbols and then the analytical formula is essentially this green line so you can see that how accurate this simple formula okay so that's all I had to say about photocurrent and the bottom line is that you cannot tell that someone that current is flat and therefore you're working on dark current all right now the dark current and very quickly the dark current I'll just show you two slides this has some math just want to show you that if you do this partitioning argument the dark current will also come out right and all the features will come out right but I don't want to go through too much detail because I want to show you a few more things so if you wanted to know the dark current no photo no light generation then again you will do the same thing in order you'll calculate the electron current by taking looking at how many electrons you have on the left side and how many of them can go to the right hand side and similarly you will see how many electrons on the right hand side and that I should have put a r here so gamma r and gamma l and then correspondingly how many electrons are going to the opposite side so divided highway or at least two-lane highway that professor that talked about remember that there was these two fluxes and you want to subtract them essentially to get the total flux now at zero bias this current must be zero and if this current is zero you can get a ratio of gamma l to gamma r because that's the only unknown and if you do that you remember the probability of going from the left to the right is exponentially suppressed because there is a big barrier here right big barrier p-n junction barrier and so that is exponentially suppressed and correspondingly this one on the other hand if somebody is trying to come from here and go to this side of course there's no barrier so that's one and you can just insert this in in this formula okay so oh by the way so if you have this gamma l and gamma r put it in this equation that will tell you this concentration on the left hand side how is it related to the concentration on the right hand side now do you remember what this relationship is this just turns out to be the law of the junction essentially telling you the two sides the electron concentration are exponentially off and equal to this vbi or whatever the barrier is barrier height is now once you insert these equations again gamma r and gamma l is the same you insert this equation under bias condition in that case this will remain the same the gamma l0 nl0 so you take this expression n and the gamma l now the barrier is a little smaller because you have applied a bias and it is smaller by v minus v vbi minus v because you by applying a voltage v this has been suppressed so you do a few lines of algebra and you get an expression here and that expression tells you essentially that what is the dark current for a p-in structure like this and if you want to get the total current you can just sum up the electron current and the whole current and you can get it all so again no differential equation but you can see that the final result comes out reasonably okay and this i0 you have seen many times that's the pre-factor that we just use it as a constant so now the question is my dark current should look like this i have a beautiful formula on when i'm applying a voltage on the positive side it should go up exponentially and you remember why this is saturating off because of that series resistance and other effects right that's why it saturates off now when v is positive it goes up exponentially when v is negative what should it do it should be minus qv over kt and that will go to zero very rapidly and so if i plot the absolute value this would this height will be equal to i0 this is what a textbook will tell you what is supposed to happen but if you go and make a measurement like show rough dead then you're going to get something which doesn't look like a a solar cell or a diode at all and this is how it looks like now i do not know whether you have made enough measurements when we were younger in the college we had to make a lot of diode measurements it used to have this two pins or three three legs transistors we made a lot of measurements and i have never seen in my life that the measurement a p and jung a diode characteristics looks like this first of all look at this this is supposed to go down exponentially it hasn't then it has these two wings which looks like a butterfly wing completely symmetric with respect to each other now if you slow do that theory which i do it so beautifully partitioning and all and then try to compare with experiment you'll see that you are in for a big surprise and because this doesn't really look like a ideal diode characteristics at all so what is this so this is something i want to talk to you about next and this has to do with this contact diffusion what the contact diffusion will essentially do in in a in a summary that originally i had a p i n structure the contact diffusion in this place localized it will make this region p type because aluminum when it diffuses in that will make this convert this region to p type and therefore this region will become a p i p structure it will not remain a junction anymore and in that case those butterfly wings will come out of this immediately let's see how it works and in fact there are experiments in which you can find out this dark spot this light spots correlating to this shunt regions so how does it work well if you had a p region which sort of diffused through this do through this n layer then you can see you do not have a diode anymore what you have is a p i p a shunt region where the current can leak through at low voltages what's going to happen most of the current is going to flow through this low resistance structure at high voltages of course the diode will turn on and then it's everything is fine so at low voltages this is the butterfly wing associated with this region and at high voltages of course the finally the diode behaves like a diode and its value generally comes up the reason being this is a much larger larger diode these are tiny few tiny regions so therefore it can be higher only up to a certain point beyond that certain point of course this larger structure will show up now this is a good theory but of course how do you know this theory is at all correct or are you daydreaming that if i had this type of thing that will be very good to have but you can go and explain try to explain that how this walkers what the current transport through this structure if it's a p i n p structure then i'll not go through the details but you can again calculate the current through a structure like this and that current i should have a p here because whole prime but this is equally well or works for electrons so if you had just an electron current or if you had the whole current then this would be proportional to the electric field majority carrier region and once you solve for this and i'm not going to go through the details but this is something in the north so you can go through essentially if you combine this transport through this region with the Poisson equation associated with these charges and then solve what you're going to see is that the current in these tiny structures is going to have a very special property it is going to go as square of the voltage and be inversely proportional to the thickness of this region i'm sorry thickness to this region to the power cube that is how this particular current is going to behave the butterfly wing is going to have this property so if this theory is correct this is how this component of the current is going to behave in general of course if you do generally this exponent is between two and three and this could be on the order of three to four so essentially that is what we'll be looking for so there are more general theories but essentially we're looking for whether the exponent is between two and three and now and this is the butterfly wing this all things are about butterfly wings because you can see that if you take this two points take a point here and take a point here and take its ratio if it really was that conduction then it will ratio it be absolutely equal to one so you can see it's a exponential curve and there you are taking two linear quantities on top of each other and dividing them and when they become one you can realize that how close to perfect these butterfly wings are these shunt conductions are then you can also look at the temperature dependence but most interestingly you can look at the non-linearity of this shunt between two and three you can see and this is about close to 60 devices so it's not just one or two accidental happening 60 devices all showing essentially the same characteristics and here is the one over lq i believe this is also 60 devices right or is it 400 devices 280 devices so this is based on 2 e t devices with different eye layer thickness this is the region in here again you can get it approximately a one over lq type dependence showing that this type of shunt conduction is parasitic but at the same time can be accurately and quantitatively described okay so i'm coming to towards the end a few more slides so we saw voltage dependent photo current which is good we understood the shunt which people say oh well i really do not know what it is but essentially say it could be a linear thing it could be a non-linear conductance but you can clearly see how to think about the physics in a consistent way now let's talk about the final piece and then will be done the final piece has to do with grain boundaries and how current these grain boundaries affect essentially the response of it and it'll be very brief assume and what i want to show you here that a small defect a micron size defect can make take away a big region and make them ineffective so sort of take them out of the circuit and how it does so it's like a the example would be like a sink you know in a faucet or in a tub you have the sink and the sink or the the opening in the bottom and that may be a very small space but the amount of region it affects is significantly larger so that is what i'm trying to do through all this equation that's that's that's the goal i have assume that you have a solar cell and i have divided the solar cell into many pieces and one of them has a grain now that means all the solar cells have the same characteristics except i have this black ship oh i should have put i'm sorry this is a diode so this line is missing but i have a black ship diode meaning that that diode has a high recombination so i marked it black and so you can easily see that if you have a current i total current is i this is the dark current and this is the photo current and i v says that it's a voltage dependent photo current then i can say that if the at the voc point when there's no current flowing in the external circuit then at that point i is zero and so therefore i can solve for voc because i can put the voc in here i can put the voc here and i can solve for the voc now what you can do is you can write this i not in terms of this voc you see because this i photo and if you say this is big compared to minus one you can bring this up exponentially on top here and then can rewrite the whole diode equation solely in terms of the photo current do you see here here i had the dark current and the dark current of course depends on the recombination all i did was to convert it in terms of voc so that i could write everything in terms of the photo current now think about what will happen what will happen if there's one diode that has a lot of recombination or because you have a lot of recombination low voc if you have a low voc then what's going to happen that it is going to sink instead of this current going to the useful load to your battery or to your light bulb these are all going to supply current and sink in here right all of them and so the number of those diodes that have been affected that has been affected is this number they have all voc one and this black one has voc two lower and if you solve for it what you find that the number of diodes that have been affected by it is exponentially dependent on the voc difference and if you have a defective region it will take away a whole set of region around it and so therefore this if you had all had the same voc you didn't have any one that is defective of course you there will not be any penalty but if you have one of them bad that will really cause a huge amount of trouble okay so now towards this end let me come to this final final thing you know many times you have seen these beautiful pictures where a satellite is gradually rising and many times there you can see the boom of that satellite casting a long shadow on its wing on the solar cell wings and you may not really worry about it that well that looks beautiful and many times the solar cars are going next to trees with a shadow on it and there may be other sources of shadow some bird droppings and other things and other bad things may happen and you may not think or a leaf maybe that's a better example that may fall on top of it and you may not really think much about it but it turns out that that is inside the solar cell when things are in shadow there's a havoc inside happening inside and that's because of this serious connectedness of solar cells so I told you in the beginning right that was the fifth topic that the solar cells like this dolphins coming up and going down coming up and going down and these are of course the diode and the current sources each sort of facing opposite and the continuous current is flowing around it right beautiful no problem but think about for a second what will happen when this long shadow of the boom is on the solar cell wing then all in a sudden one of them has just lost his power because that doesn't have any photon and so therefore just lost his power now of course everybody else doesn't like it they have their current and they want to supply their current series connected cells you like it or not you have to play with this this diode has to supply current now in order for this diode to supply current what is going to do it's going to go in the reverse bias break itself down and then supply its current go in date and then essentially make sure everybody is satisfied very simply I can show you through this diagram think about this this yellow this is this blue line blue dashed line a single single diode and then this blue solid line being a set up diodes these are in series so therefore your VOC has gotten multiplied by that number all on a sudden the middle one loses power if it loses power then it must go down it doesn't have any photo generation anymore it must go down and get in the reverse bias break down and supply the current that the circuit dictates that it must have and therefore the remaining two must now give up a little bit of voltage to help it break down even more so that it can give some current in through the in the reverse bias and your total output will be dramatically reduced it's like this analogy is like this let's say somebody you are you are in a battlefield five of you are going in somewhere when one person gets hit it is not that just one person get hit and the four can run you have to carry that person around with you so essentially with one person getting hit essentially may take out the five person and you may be in a very bad situation so this is the same issue with the series connected thing and this is called shadow degradation shadow on a solar cell is a very bad thing and you can show that as a function of time if you put things in shadow that this is going to degrade significantly the dark current is going to degrade significantly because more and it's one of them in the reverse bias and not only the output power will temporarily go down but the whole power that that shadowed one which you are thinking of just resting that one will essentially be in the reverse bias and a significant amount of defect will be generated very counter intuitive right shadow you think good it can rest but not when you just take one of them and don't give everybody else rest as well my final two slides are on something that is called light induced degradation very important for amorphous silicon everybody in the field knows it so therefore you should too what light induced degradation is that solar cell when you put it in operation you don't even have to put it in operation if you go to many companies what you will see many times they have a test set up right in front and what they're trying to do is trying to show that as soon as you put a solar cell which is especially amorphous silicon solar cell in light it begins to degrade and people knew it from 1977 almost from the very early days the solar cell degrades very quickly so the champion solar cells you hear about in the newspaper or in various journals well if you asked about them about two months later what the efficiency is the efficiency would have been might have been significantly lower so this is light induced degradation and it has a very beautiful physics because if you look at the efficiency of those solar cells they drop as a function of time but the most interesting thing is that if you put it as a function of time on a log log plot then you will see this as an exponent of t to the power one-third time to the power one-third and this is very strange we know exponential degradation we know from circuit and other things but a time the degradation that's going as power law is actually very unusual right so we want to know a little bit about how that happens and with that we'll be able to end the basic idea is this you know amorphous silicon is a random it's not crystalline it's a random structure and many of the bonds are essentially not saturated and so therefore what happens that you need to passivate them by hydrogen if you bring it hydrogen that sort of ties up and then therefore you can have good performance but as soon as you put them on the light inside in light then these bonds begin to break and therefore something that you make easy also breaks easy right cheap things and so therefore what happens that this defects begins to come up and as you have more and more recombination centers your shorts are this dark current begins to increase and so you can write a very simple equation you can say the number of broken bonds is proportional to the light amount of light you have and but of course once they are broken some of them can come back and repassivate so that pre-passivation probability is a number of hydrogen that has been liberated and the number of broken bonds so you can write one equation like that and you can write another equation that accounts for the diffusion of hydrogen within this region and the dimerization of it so just two little equations and if you solve this remarkably it will tell you that this thing should degrade as t to the power one-third it will go as t to the power one-third and most more importantly it will also tell you it goes as light intensity to the power two-third that's also been shown in experiment that it goes as light intensity in a particular way so what I'm trying to tell you although recombination and reliability this type of thing seems very esoteric but fundamental there are good fundamental theories that can account for it okay let me skip this one and then in the final one so let me tell you that what I told you so far about is all intrinsic degradation this is light induced degradation shunt leakage shadow degradation wig diodes I just told you all about material degradation but of course solar cells are not something that you carry in your pocket you may but generally it's not like your iPod where you protect it very nicely if there's water falls on it you clean it up you don't treat solar cells so nicely you hang it out there and you get the power out of it and when things are left to its elements then of course a whole lot of other things can happen there can be corrosion there can be moisture coming in and there can be and the most important delamination the layers can peel off and so that can air if you are in the middle list then there is sandstorms and it can be coated with sand and essentially no power output so there are a whole lot of extrinsic reliability issues that people also have to worry about and the most important reliability concern these days when people say they cannot have a 25 year reliable solar cell is the inverter reliability because you have to put an inverter in order to make the DC output make it to AC so that you can connect to the grid and most of them don't have more than five years of reliability so here is a 25 year cell which you have gone away home hoping that this will be reliable and no problem five years down the road inverter breaks and your solar cell is out and so you have to go send someone to fix that inverter and there is that's the huge cost so the one of the most important reliability is not with solar cell at all it has to do with power electronics and power conditioning okay so very briefly then uh these are my conclusions economic incentives right we want chip solar cells so that we can have uh good economic performance I told you about thin film PV and its unique features right no voltage dependent voltage independent current let's say important thing I said weak diodes shadow degradation all sorts of things I told you about and extrinsic reliability is of course important but the intrinsic reliability people are spending a lot of time on because this is something a good understanding of physics can help you really make a lot of progress the things that are outside your control or the control of mechanical engineers they will think about it but we as electrical engineers the equations that are in our control we address those and turns out shadow degradation light induced degradation those we can contribute a lot and this reliability and variability are key concerns and this is something anytime you have a new advertisement let's say that I have such and such solar cell and big news release and all let's say in technology MIT technology reviewers and the most important thing is not to read that part the most important thing is to read the comments underneath because in the comments they the real experts in the field they make most interesting comments about the technology and most of the time what people show is their best highest performance as soon as you put it in a module four to five percent of the efficiency is gone because of the variability and so therefore things that look really very impressive on paper right or in the first laboratory demonstration not always good but it turns out that this type of variability until they are addressed is very little hope that this type of skin fame solar will actually be commercially viable okay so that's it thank you for your attention so you mentioned lighting new difficulties so is this characteristic of crystalline solar cells? the one slide I skipped is the one slide you're asking the question about so maybe I go go back in order to respond to this let me go back to this one in principle the way I described light induced degradation right do you remember random network you have to tie them up with hydrogen and therefore when light comes in the light dissociates them and all the bonds are again broken something that you sort of patched up with duct tape you know as soon as light comes in those are again broken and so again you have problem for long people thought that amorphous silicon are most susceptible and which is true that everybody knows that but it turns out that if you have this boron drop a low quality chakraski crystals that also show light induced degradation but here the boron essentially diffuses around it's not to do with dangling hydrogen bond boron diffuses around and form complexes which acts like trap so therefore in order to get rid of this if you can show that this is really related to light by replacing this boron with gallium in that case you see all in a sudden the light induced degradation disappears or you can do float zone float zone is a essentially is a much purifier version and in that case if you use that one that also suppresses light into degree but it adds to cost so generally light induced degradation is there also it's just the rate is slower and in crystalline silicon industry is amorphous how much is the first one yes so the quite yeah so quite you know these numbers I cannot be exact but let me give you a general idea that crystalline silicon is steel the dominant technology I'd say 80 percent probably is crystalline silicon in part because for long the price of silicon was high and especially in the last prices around 2008 or so or 2009 there's a spike in price spike in silicon price so there was a lot of thin film solar cell company jumped in at that time but now it's really dropping very fast especially from the Chinese companies they have very high quality quality silicon at relatively lower price so but in terms of thin film the most successful company is first solar and that is the only company that can supply now power that is below one dollar per watt it is more like 70 74 cents and they have consistently done so so when the middle list I have seen also when China decided to have this two gigawatt plant in the Gobi desert I guess so in that case when they decided when they were to think about this which technologies to choose they chose actually this cadmium terrarium based technology over silicon in part because of price but there was always a persistent question that will it be reliable for 25 years and in many places in the middle list already the things are running for 12 years or so no problem 10 12 years no problem so thin film has hope but crystalline silicon you know price keeps going down so it will be a strong strong competition always so you will give me a nice derivation of the ag characteristic in terms of the transmission to the left and the right right so when you measure the dial factors and you get out of the shunt regime what's the end factor for the dial is it one tell me one more time you know you when you measure the dark any characteristics and you show this the shunt but when you get the higher voltages where you just have the junction current but what's the diet factor so that diet factor I would assume between one and two and very robustly about 1.5 1.5 to 1.8 in that so it's in between one and two nothing not perfect one and neither perfect two especially for this with this structure yeah I think if you if you do numerical simulation many features of it will probably because it's not really like where you can separate out the recombination and the injection over barrier into separate components and add them because at every point just like the transmission picture shows that at every point you have a probability of recombination and probability of going up in the barrier or down in the barrier so at every point so when you add them up unlike a pn junction where it's very sharp and small when you add them up you expect more complicated n n values let's see let me let me see whether you can you can immediately tell which one it is because they look different do you see a difference in these two pictures which one do you think is crystalline of course the answer is given the ones that you have a wafer found like this because you got that structure and then you cut it into slices and so this would be crystalline crystalline silicon in many cases the thin film will look like this because it's a roll to roll or essentially vacuum deposited so it will look continuous you cannot see it here but there are striplines which allows them to connected in series so if it looks beautiful blue then you know that's the silicon solar cells that you have if you have it like this then continuous then you know that this is that right generally that's the more thin film thin film like structures yes and you said that the reason why we are doing these things is because of cost but I was wondering I mean we've seen I mean we've seen some dissipation it hasn't because of these thin silicon so when you compare the current and you have to power things out of these sort I mean does it does it really save that much money yeah and the other question I had is also you know you've also learned that you know silicon is basically you know most of the solar cell is based on silicon right so why not use like an infrastructure where you did essentially harness much of the life from the sun you know at the cost really is it that big that you know we have to do certain because they're cheap and not you know although you can have a structure would be like that I mean the main reason here for thin film as Professor Lundstrom also mentioned that it can absorb light within a very short distance right so gallium arsenide will be few microns will be all that you need in order to get 90 percent of the 1995 percent of the light in now remember the 50 bounces that I told you about it's not on all wavelength the wavelength that are close to band gap those are the most difficult to absorb and they don't want to get absorbed you keep bouncing and you have to wait a long time before before they get fully absorbed so the main thing is that you really require smaller amount of material in part because you have easier absorption is the direct band gap material most of them thin films are in direct band gap material so therefore it absorbs things easily now in terms of cost if you go to one of this company websites and ask them that what is the install cost for some of these companies it will be as high as five dollars because although in specific numbers you get in various industry positions one thing but essentially 200 watt per module will cost you about nine hundred dollars when you when you buy this thing so silicon is already very expensive now the price is coming down that's true and the thin film is in that especially for cadmium to ride significantly cheaper now whether all thin film can go there whether you can have a reliability problem or not that will sort of balance the cost that's the second issue that aqua I think I'm not sure that question can be definitely answered today that which one was the ultimate winner but very difficult to count out silicon silicon despite all sorts of problems has very resilient we hear a lot about grid badly can you comment on number one on that number two solar is a very important so anytime people talk about solar energy they talk about the cost issue is a very important one I mean if you have gas based power power generation stations it's about what do they call it maybe four or five cents per kilowatt hour something like that one tenth of that okay so it's very inexpensive dart chip because in some way god has already put the solar cell prefabricated the energy and put it in the gas so you don't pay anything for the for the equipment to generate the gas so therefore you are just bringing it up and using it so the question is that whether you can get below 10 cents that's that's the goal per kilowatt hour in terms of energy use and it's very difficult very difficult people are trying all sorts of ways to get the cost down but even the best effort it's not really without incentive from the government that you have tax breaks and other things it's very difficult to see that how it can be directly competitive in even next two three four years so great parity is important question and the reactive power in terms of variability how do you do load balancing all those things are very important questions but what people from sun power what they argue that this variability because there is sometimes there's sun like now and sometimes there is no sun in the night and then whether the question is whether that would be a significant variation and if you have that level of variation generating power is very very difficult what they show that if you connect a lot of solar cells as solar power generating units into a grid the variability is essentially essentially all eliminated because different regions have different time pattern for the solar cells and then they show if you combine with the wind power and this is all these things about smart grid technology then essentially you can have a very stable power source so there's a lot of work going on in terms of this circuit or the power transmission system aspect of it exactly that's right so the cost includes so this is the power electronics cost so this is already included when um when sun power or somebody will sell you a module the module has everything all the inverters everything it has all those pieces in you have to come in when the person comes with a truck all they do essentially these are contractors they don't know anything about solar cell no shadow degradation nothing so they just essentially they should be able to hook it up without asking too many other questions so when you buy that system that thousand dollar has all those pieces in you don't have to buy them separately and install them right yes if i heard correctly that right now the water length is the inverter part of it not the solar cell no no inverter is very inexpensive how much did you say 22 cents yeah i know that you're in my leg so yeah i was like 20 percent of the total yeah right you see very inexpensive those are silicon normal silicon technology i mean those can you don't really have to national semiconductor produces those parts many companies produce the part that's not the problem the problem is it fails after three four five years it fails so you put it on the back side and but because you cannot and you try to encapsulate it but still if you leave something like this over a period of time in the exposed air think about it what would happen if you lost your cell phone and the cell phone was sitting in front of park then it was not going to survive very long right so that is what we are asking that park and what to do very cheap but very problematic so yeah i think so thanks