 You can follow along with this presentation by going to nano hub.org and downloading the corresponding slides. Enjoy the show. Okay, so we'll get started on this very last lecture. It looks like you have still survived. At least your eyes are open, so that's good. So this very last lecture is also the most colorful one because it has to do with plastic and organic solar cells. Sounds very interesting. And what I'd like to tell you is that although it's at the end just a solar cell, you know, PN junctions, electron holes coming out in respective contacts, but the idea and the innovation that lies under this technology is something that is very beautiful and I hope that you will appreciate it. It's not just something that could come, it requires a very sort of deep insight about how electrons and holes flow in a system. So let me get started. So I'm going to talk about a little bit about that why organic solar cells, but by now you know that we want to reduce cost and what could be less costly than going into sort of a hardware store and buying two cans of paints. If you could buy it, mix them up and can make a solar cell by painting on something. Now that would be great. That would be cheap. You can buy it in Walmart. So that is what the sort of the argument is that it will be a very, very cheap technology. In practice, of course, nothing is simple and it turns out that if you go and try to make a cost estimate for organic solar cells, it is higher than crystalline silicon. So actually we are not there yet and I want to tell you that how one might get there and what the physics is. Actually very, very simple and very elegant. Hopefully you will see that. I'm going to talk about three things. One is the planar heterojunction organic photovoltaic. That's the word OPV mean. Organic, some people will call instead of organic, they will call it plastic. Plastic photovoltaic. Now then I'll talk about checker box heterojunction and the most important one is something called a bulk heterojunction devices. Now the word heterojunction as you might realize that this will involve in some form two materials that are going to do something special for this device. You don't see any word homojunction floating around here. So that must mean that you need two materials at least. Silicon is a homojunction. There's no hetero in there. So we'll be seeing there's something called two materials play a very important role in here. And then I'm going to connect it with percolation, fluctuation and efficiency limits and then conclude. So again this picture you have seen and the basic argument is that PN junction crystalline cell is very important. 80% of the market may be more, but it's relatively thick, very weak light absorber. So we are looking for thinner structures and the thinner structures of course the one I talked about in the previous lecture had to do with this PIN structure. You remember electron hole partitioning, electron going at the right contact or falling off through the wrong contact and the partitioning and how you sum them up and understand why the current is not independent of voltage. We will discuss that. Now I'm going to talk about this, but first of all look at this. This looks horrible to begin with. There's these two plastics inside one another and I don't even know how to even begin thinking about this structure. At least this looks reasonable. This doesn't look reasonable. And so how would you do a theory on unreasonable things? And moreover look at this structure. This is not even flat. It's carved on something and also colorful and the question is then how are you going to think about this structure that doesn't really look reasonable. So very quickly in terms of the efficiency limit this is what people say. Generally steel probably $1.36 for the OPV and this is not by any means cheap currently. And the reason it is not cheap is because although the material you will see is very cheap. It's like a $6 per kilogram. That is how cheap it is. But it turns out that by the time you put in the glass and capsulation the mirrors, the ITOs, the other things, encapsulation and all those things price goes up very quickly. And most important reason why the price goes up is because the reliability is horrible. You'll be lucky if it survives a year. And then so therefore the hope is that if we can do something that will have 15% efficiency and will last for 15 years now that will be an unbeatable technology. This is where this is not a current technology. This is something, it's a hope for the future but we'll see why people are so excited about it. So let's talk about planar heterojunction. But before I do that I'll have to tell you something about something called an exciton. Now you might not have heard this term before but you can immediately see that when Professor Lundstrom talked about solar cells there was something that was a little fishy. It was correct but it was a little fishy. And the fishy thing is this that when you have an electron hole pair generated due to an incident photon we immediately thought that if you apply an electric field the red electron goes to the left the white holes go to the right and I have a photocard. But if you step back one second you can immediately realize that that doesn't sound right because this electron, this electron is negative this hole is positive. Is it possible that they should immediately go apart from each other? I mean this is, if you think about hydrogen atom you wouldn't really say that they will simply fly out from one side to another because you would say no, no, in this case there's a coulombic attraction between them this red electron and white hole and they'll be circling each other. That's why you have a hydrogen atom. So in that case why didn't you ask that question in here because that should have been circling each other also a positive and a negative thing. Now it turns out that you can easily answer that question. By the way so if they begin to circle each other this electron and holes if they begin to circle each other this entity is called exciton. So exciton you could say that electron plus hole instead of writing that big thing is called exciton. Now if you look at this bound level for the hydrogen atom you may have seen in your first course in physics that the buffers bound level is given by a bunch of constants and that has one over kappa square. Kappa square is a dielectric constant. Now in air where the hydrogen, the electron is moving around the proton, kappa is one. So that gives you about 36.13.6EV and they are bound tight. And what is the radius of the hydrogen atom? Of course you know that because the Bohr radius also you could calculate and if you calculate that you will find this is proportional to the dielectric constant if you put the dielectric constant is equal to one then this is about half a angstrom 1.53 angstrom. So that's why this electron moves around the proton. Now if you now think about this and apply it to this electron and hole you will see Professor Lundstrom was right because in silicon the effective mass let's say in the order of 0.1 I'm just making up some numbers kappa is on the order of 10 it's about 12 or so but let's make it 10 and if you put these numbers in here you can see immediately the binding energy will be divided by 100 here multiplied by 0.1 so it will be 1000 so I will have only 13.6 millilektron volt now kt in room temperature is 25 millilektron volts so yes they want to go around each other but their binding is 13.6 a phonon comes in, kicks them and they are immediately apart they are not strongly bound so therefore the electron went in their respective contact now if you on the other hand think about a polymer for example the polymer would be the grocery bag that you get from Walmart in the polymer the dielectric constant unfortunately is very low on the order of 3 to 4 so in that case same formula same everything you put it in here now and I'll explain this in a second if you put it in here 151 millilektron volts many many kt, 6kt now this is not going to go anywhere they are going to circle each other and the radius is 15 angstrom and so what is going to happen all this pair of electrons and holes like a little droplet they will be moving around charge neutral, negative and positive they will not scare about electric field they are not going anywhere so this is exciting and after a while they will recombine each other and you don't have any light coming out or any energy coming out so this is my problem with organic solar cells something special in order to get the electron and hole out because as electron and as electrical engineers we don't like excitons that they stay together like this and then they recombine without giving us free electron and hole so this is the problem so long you understand the problem by the way I have assumed this is to be 0.1 in the polymer along the polymer chain this number is correct in the pi pi stack the other direction about 1.75 much higher because you see hopping is involved but when you put them the effective mass by averaging them you will get some number something like this so this is not unreasonable so this is the trick you see instead of having a single polymer which is a homo junction you can say if I somehow and nobody is going anywhere they are diffusing around and not giving me so I want to break them up well I put a separate material in there instead of having one I put now two now it is going to break why because although this material so this is the band diagram for this side this material you can see that this one has a particular work function material A this one has a different work function and that is the material so this is B this is A and in here I have an atomically sharp junction sharper than this 15.3 angstrom because 15.3 is like six seven atoms so now if a if a exciton comes in and gets to this junction this feel like a knife will get inside it and pull them apart if it is any gentler like a p-i-n junction or a p-i-n junction it is not going to do anything to the exciton that's why we need a hetero junction right now of course if you put it in a hetero junction like this this thing will diffuse and when it hits this junction this electric field will pull them out and the electron will go this way the hole will do the other way and there will be a light output which is very good which is what we like but you see if I these regions interface regions are very defective generally if I don't do something special these electrons will be moving around and a fraction of them will be recombining in here because this is a lot of traps here and that I don't like so then what do I do what I do that instead of keeping these two metals the same work function what I can do I can make one aluminum and another Iq let's say in that case the work function aren't the same so therefore this one doesn't care that you have two metals this one is charged neutral so this will diffuse without knowing that there is an electric field but as soon as it comes in here this one is pulled out through this electric field this one is pulled out through the electric field and now we have good current so this is what how an organic solar cell works so if you understood this far hopefully then the rest of the story you'll be able to appreciate because without really knowing that the other pieces doesn't really make sense so I have this beautiful sun here and this two material three dimension I'm showing here two material stack this is a planar hetero junction because the two materials are sitting and sharing one plane across them so the junction is a big plane on them and so when the light came in it generated this droplet of electron and hole it was diffusing around until it saw this junction it saw that junction this went this way the other one the hole went this way and the output circuit in the output circuit I had the light bulb light up so this is how a planar hetero junction works now the question is how am I going to make understand a structure like this cartoon is good power point can do this very quickly but the thing is that if I now have to think about this structure can I use what I just told you in the last class last lecture and can I use that partitioning going left going right of course otherwise I wouldn't tell you that it can be done so let's think about it how to do it so what I'm thinking about you remember this for thin film we have this complicated slightly complicated equivalent circuit I'll be talking about this one and this one now a little bit later about this one and not very much on this one because this is very similar to what we had in the last lecture so even then we have shunt resistance non-linear shunt conductance and all I'll not be discussing that so let's get started on the photo current which is supposed to be a constant for silicon solar source now one thing you can see that how this has a little bit of complicated that if a exciton is generated here away from the diffusion length of this junction then all of them who have been diffused here they will also recombine because before they find this junction which will pull them apart they essentially they are very close together they will recombine give up the photon or give up the energy and that exciton is gone that photon has no purpose whatsoever in this discussion so the exciton diffusion length square root of d tau x and why am I talking about just diffusion because charge neutral plus and minus in the droplet charge neutral so I should only have to think about diffusion no drift is necessary now do you remember that I gave a example of silicon solar cells where half of it is diffusion half of it is going to the left junction and half of it is going to the right junction with a blocking layer and all I wanted to explain how that works I have rotated the diagram 90 degrees so what I am trying to show here that any exciton this is the exciton profile any exciton that is generated in this region they go and get dissociated in here the right contact because that's where I wanted to go on the other hand a bunch of them can go and recombine this get dissociated in this contact which is also a junction but that's a wrong contact to get out of so the only one that will be useful for me is the flux associated with this one so let's calculate how much flux this is this is how many excitons will produce electron and holes so again I am using the same formula that I have you may remember this W I put 4 Lx if it's thin then W is the whole thing W over 2 is this and if it is very thin then it will be W over 2 which can be collected from this side because the other half will be essentially collected from the other side then it will be completely useless now think about how I can do the partitioning argument so my electrons and holes have just been created these electrons have two options they can go or they can loiter around a little bit and if they find a hole close to the interface they can recombine through the holes so how will I do the partitioning very simple you remember this formula how many electrons are going flux that is going to the left contact gamma ln and I have this recombination that's telling me what is the recombination with this quantity with the holes and I have gamma Rn any flux that can jump over the barrier now most of the time the barrier is so big I am going to ignore it so therefore most of the time I shouldn't have to worry about that term so I drop that term now what about the holes should I not have to worry about this term well you can see this barrier is so big the holes cannot come out here and so I get rid of this it is 0 so the whole term goes to 0 that's simple now when this one comes out what is the flux mu times E0 E0 is the electric field here that is the flux is going to come out no barrier in front of it if you use the electric field it's just going to slide down the hill and essentially be collected on the other hand if you have gamma recombination this is a simpler expression it simply says it depends on the recombination time constant associated with it if you have a lot of trap the time constant will be low and so that will be your recombination rate you can put it in if you put it in then mu E0 and mu E0 plus S S is the recombination interface recombination and that immediately tells you that this current cannot be voltage independent do you see why this electric field E0 is the electric field here that electric field is Vbi minus V is the applied voltage divided by Wn this is the Wn and as I am changing V my E0 is changing if my E0 is changing this ratio is changing and this J exciton is independent of field but J photon cannot be independent of field if the field is high they are rapidly getting pulled out no recombination very little recombination if the field is low they are sort of loitering around next to the dangerous junction and this huge fraction of is recombining so therefore this current photo current in the beginning will be high gradually it will be low and eventually it will be essentially equal to 0 if you have this process continue now in general of course instead of just shockly read hole type recombination if you have a bimolecular recombination you have to work a little harder you have to say write one more line of algebra you have to say that the exciton current that is coming in is equal to the recombination flux at x equals 0 plus any shockly read hole type recombination multiplied by this drift flux and if you add them you can see this is a quadratic equation of N0 and even I can solve quadratic equation and so therefore the photon current will be related to the exciton one and you can put it in again this will not be voltage independent why? because the voltage is sitting in this VT it has mu times E0 the electric field and the E is changing with voltage V and therefore the photo current is absolutely dependent on voltage so that's the important piece so this interface and we'll come back to this this interface recombination is a big problem because think about it if I didn't have this interface recombination if this were 0 then this would be 1 and I could get every exciton that has been generated I could collect them all as output current and this interface recombination is causing me the problem and that's what we'll need to work on to reduce okay so that's all I had about photo current you see very simple that a fraction of this electron the whole exciton that are here gets dissociated and only a fraction can get out depending on this how many recombine at the interface now if you wanted to look at dark current dark current is very important again here is very simple calculation why? because dark current remember I don't have any do I have any exciton I didn't shine light so therefore no electron hole pair were generated close to each other and if there is no electron hole pair generated close to each other of course I cannot have any exciton and therefore there is no exciton in the dark dark condition now in this case again if this is the only recombination mechanism how would you calculate this total dark current because there is no other place to go it cannot go over the barrier the barrier is too high and therefore all you need to do is to find out how many electrons you have at x equals 0 and how many holes you have x equals 0 multiplied the gamma that is the recombination rate you can easily calculate how many can climb up over this barrier and how many this is the voltage Q electric multiplied by W n exponentially suppressing the number of electrons that are on the left contact so only a few can climb up climbing up is difficult and similarly for the holes a few can climb up because the hole doesn't want to go down so they want to climb up and essentially you can get an expression and where did this V B I minus V come from well again from the electric field you remember the electric field had this V B I minus V divided by the distance so that's where it came from anyway so once you plot this current and this simple local expression and you do exact numerical simulation they will be very close we don't really care about this region because what I am going to show that essentially this region is sufficient to explain the IV characteristics of your organic solar cell now before I go any further and compare it maybe I step want to step one step back one thing I want to make sure that you understand that this is a very special solar cell in the sense because the electrons didn't go here they cannot climb up and go here right because they didn't go here each region has just hole or just electron we cannot have both this is very different than other solar cells remember the silicon solar cells the electron was going this way the holes were coming this way if you took a microscope and wanted to look at one point you would find both electrons and holes sitting there right they are going in different directions not in here because look these holes are electrons are coming out here but there is no electron here very and on the other no holes here I am sorry no electrons no holes here similarly this band gap is big no electron came up here so essentially I don't have any electron over there I just one type of carrier in respective regions this is very important that's why even if this region is highly defective you will not have any recombination all recombinations will only occur at the interface right so low quality material that will still not have any recombination or you can you know you can take this equation that I already told you excitant flux two slides ago four ton flux from the excitant flux one slide ago and then this is the dark current I told you about to put them all in and this is the total current and this is the approximation the blue current and the red one you do it by if you solve big complicated differential equations second order and all they will be almost correct they will be almost correct so that says that we have caught most of the physics except that if you go in and solve for numerical simulator you will see like a debt that professor Gray talked about yesterday you will see that this is what the thing is saying that it should be all whereas I am saying that this should be the flux based on this so what is it that went wrong you can immediately see the horrible field factor right field factor is remember because the analysis people are lazy so there is this green small box that you set in with respect to the big box and so here the field factor is actually pretty low 0.5 maybe even 0.5 or 0.6 pretty low and what happened then so you can easily understand what happened and that's why why you should not be using planar junction most of the time what happened is the following if this is the band diagram remember this is this version that I wrote draw and a cartoon and a power point cartoon but if you do really a numerical simulation what you will see this is the band diagram this is v equals 0 lot of high field and as you push the up voltage up then gradually this this curve gradually goes up and the field is reduced yes the field is reduced but you can see the field is not constant and why is the field constant because I assumed the field is to be constant look here I have constant the cartoon diagram has constant potential that means a constant field it's not a constant because of that issue that only one type of carrier is in respective materials so as soon as the electrons are trying to get out from this region all the pre-existing electrons in here they are saying don't come this is a self-consistency problem because they have all been piled up in here they are saying they are trying to as a result the electric field is low so it's not getting collected as efficiently so you're putting a voltage but the voltage is not reaching the junction and therefore now the field is low electrons moving around and it loses a huge fraction of those electrons by recombination in this here because you're not supposed to stay here you're supposed to get away from this region as quickly as possible alright so this is how a planar heterojunction work but of course that is not why I said that this is beautiful because it's not so far doesn't look very beautiful to me but we want to do more but one thing you realize that if we could sweep the electrons out quickly in that case they wouldn't build up to such a high value will not be able to screen the electric field this way and as a result in that case if I had high mobility then my approximate formula should become better and better because then the constant electric field assumption will be correct and that is indeed the case because if you do the numerical simulation just with a little bit high mobility this mobility is 10 to the power minus 4 this mobility is 10 to the power minus 3 in that case you can see immediately approaches the analytical solution because the approximations are now better done see how low the mobility is the silicon mobility would be hundreds of times or thousand times more than this right look at how this is 10 to the power minus 3 10 to the power minus 4 cheap material has low mobility so that is expected so what's wrong with this planar heterojunction why it looks like we can do this things the main thing that is wrong is that only a fraction of these excitons can be collected and all these excitons that were generated they essentially self recombine as if they were never born to begin with so it doesn't really matter so all them are lost so that's not a very good condition so what can you do so what you can do is you can say well I am an electrical engineer so what I am going to do why not make this region comparable to this right so that is just square root of d tau x and this is then it will be like 15 to 20 nanometer and in that case I will collect everything but of course you realize if you try to do that then this heterojunction is also close it will take away half of your half of your carriers wrong contact wrong recombination and so you cannot really do that you have to do something more clever so what can you do more clever a little bit more clever well this is what you can do what you can do is to realize that excitons don't care about electric field only thing they care about is diffusion and the only thing they care about is finding a junction so that they can be dissociated on the other hand electron and hole they care a lot about electric field so why don't I make them orthogonal because if I make them orthogonal then probably I don't have to keep the considerations coupled so I can make them orthogonal this way what I can make is material A and material A these two heterojunctions here and the white region is material B now no matter where the exciton is generated it will quickly find the junction but it will not go and touch this wrong context it will essentially just be dissociated in here and once it is dissociated then the electrons and holes can be pulled apart so this is let's say this is electron highway so they will remain in electrons in an electronic material and this one is a hole so they will stay with the whole material so this is like a really divided highway sort of a semi-classic analog of this mean effect where the k and minus k gets really specially separated this would be the semi-classical analog of it because now the electrons and holes they are going in the opposite direction and not talking to each other except they will recombine when they meet at the interface which we don't like so you can people are already making such cells you may say how do I make this checkerboard structure people are making it there are many many schemes so you can have a bunch of nanowires or nanopillars of one material and coat it with the other material so that in between the second phase comes in and if you shine light on it then essentially if it's the organic structure in that case the holes these pillars will carry only electrons the other one will carry only holes and then they will get separated in their respective context and the excitons will be dissociated because look at the surface area huge amount of surface area associated with it they will quickly find a surface nearby and they will be dissociated very good now of course this will be costly to make you can make Sardar is going to be cost effective with silicon solar cell maybe not but the idea look at the idea what they did they make the exciton and the electron go in orthogonal direction that is the trick here so you can do some analysis and this is my checkerboard in 3D power point is very good I see so you can calculate quickly calculate number of fingers you have fingers are this red fingers and this is 1 over 2 S squared the number of fingers because you see half the volume is blue and half of them are red so you have to do a half and then a S squared in order to know the number of fingers you have per centimeter squared because the rate is half of the total volume and the volume of each one of them is this red volume which is WS square is the volume of each finger if the electron whole pairs excitons are generated here only the ones which are within square root of DT within this junction they will be separated and the rest which are sitting in the middle they will self recombine they are not coming out so I don't have to care about them so if you want to know what fraction of the charges are going to be collected power finger well you have 4S you know 4 sides but of course it's being shared and so you have a factor of 2 here and S squared because you want to know the fraction S squared is the area and only this fraction is getting collected this is the diffusion length so 4S is the perimeter multiplied by distance this is the area of this white region remember if you want to put a garden next to your backyard and you want to calculate what fraction of the area you just multiply things like this and then once you do that you can see how much the total charge collected will be this is how many excitons you will collect and you can see that it can scale with the number of fingers or how small you make the individual finger so your efficiency can really go very high that's why you should do nanostructuring here and without nanostructuring actually organic solar cell is not going to work and again these things you can easily do electron in one highway holes in another highway you write down the formula let me not go through it you can go through the dark current analysis and essentially make an approximate calculation of how many electrons and how many holes are you going to collect here I have to account for the recombination as the electrons are coming out through their highway and the holes are going in the opposite direction if they meet in the interface they are going to annihilate each other and not going to come out of the structure and so you have to account for this for this recombination but other than that you can essentially use the very similar partitioning argument and very similar expression for current so now comes the last part and the last part hopefully is what people actually do which is much more interesting than what I told you so far about what they do is that they don't have these pillars they don't have this type of planarized function what they have is two materials they'll put it in somewhere mix it up put it in an oven and out comes the solar cell this is what this look at this green is one phase the other one the other material is other color another phase and they are inside each other tangled bundled and you cannot tell one phase from the other and the question is how are you going to think about that and it turns out hopefully you will understand that it's easy to think about because you can think about what it did what this one does this random structure does is exactly what this one did because the structure is so random no matter where the exciton is generated it is quickly find a junction if it finds a junction it will be pulled out here and it will be pulled out in the whole carrying region and they will be separated and you'll have a photocardom look at the area this area was a planar area in many of the jails and in other things the area per centimeter cube if you mix it very well and each domain is a micron size the area could be two football field size per centimeter cube volume that is how big this surface area has become every exciton essentially close to 100% of them the light that came in everybody will be dissociated this is how efficient organic solar cell these days are exciton part of course we have to pull them bring them out that's the second question but at least getting them dissociated no problem so let's talk about bulk heterojunction now what is this word bulk the word bulk comes from the fact that this heterojunction is distributed within the bulk it's not on the surface or not on the planar not on the checkerboard it is distributed within the whole volume and that makes it bulk heterojunction solar cell so let's think about it how should I think about a solar cell which is so complicated so this is my chemist bowl of solar cell I mixed polymer A and a polymer B put some sort of solvent and then presumably this blue is one phase I said it will be colorful presentation so this is the color and then you put it in an oven 125 degrees C 15 minutes later out comes the solar cell now the way it works interesting what happens is the phase desegregation most of the time if you put salt and water and put it in your microwave they get homogenized they don't get phase segregated but these polymers are such and their surface tensions are such that if you put it in here they like spoiled milk they get phase segregated so this is called spinodal decomposition and here is a cartoon that we made and look at how as a function of time how these two structures get phase segregated in the beginning completely mixed up you cannot say which is region A which is region B yellow and red cannot say really this is not, if you shine a light on it excitons wouldn't really laugh at this structure because the hetero junction is not really there nobody is going to get separated but after a little bit to anneal it this is what's going to happen so this is going to get phase segregated did you notice two things one is that as the time progressed the black and the white the phase volume didn't change if you started with 1 kilogram of polymer A and 1 kilogram of polymer B none of them evaporated so you still at the end you have 1 kilogram of polymer A and 1 kilogram of polymer B nothing changed that's a very important statement because nothing evaporated the second is that these regions are gradually getting thicker so they are bringing their like kind and if you waited long enough long enough then this might even become segregated like a planar hetero junction if you use a long enough if you didn't have any boundary effect because they want to stay bring their own kind together so now how are you going to describe such a system I am going to very quickly tell you what equation was used but not going to explain it very much the equation that was used was sort of a diffusion equation of some sort here is the surface tension and here is the mobility of the polymers how they can diffuse across one another so you can solve this equation and then once you do that I think many there are recent experiments in nature materials where they use that high Z contrast so this is not really two polymers it's two polymers but one has not for PV one has very high number of protons nucleus is very high so that when you do electron tomography you can get the Z contrast out of it so that is how this picture was taken very popular anytime you want to do three dimensional complicated structure this electron tomography I see it used all the time so this is how the picture was taken suggesting that this way of thinking about the material is okay that's fine and I will very quickly tell you a little bit because that's not the sense of the story that if you start with a completely homogenized structure and then increase the temperature and then there is a stable point here and in the phase and then stable point here so that in the black region there is a little bit mixed up and also in the white region there is a little bit of black mixed up but on the whole these junctions are reasonably sharp and so when you put your exciton in here they will be separated so it's not a pure phase it is sort of a little bit of mixture of the other but it's like 90% white or 90% black so we shouldn't complain because the junction is a maybe a little bit lower than the pure phases but still it will dissociate things now what I want to tell you about this is interesting because I think okay let me go and see what happened so the question is that if things look so complicated then can you do any physics with it and the answer is that actually you can do a lot of physics with it first of all look at this these regions as a function of an yield time in the oven how long you have put it in your microwave that as a function of that these are getting phase segregated and people know and you can do it from simulation also that this grain size average width of this region goes as an yield time to the power 1 third now that is an yield time so within a thousand seconds which is a couple of minutes then essentially your grain sizes will grow to a certain distance but it will continue to grow phase segregate as a function of time in the beginning it is a log plot so in the beginning very fast but then gradually it will roll out it will slow down because phase segregation has already occurred now you can use this information to do something which you might not have thought possible think about it so the phase is this width of this blue region is W if I know the width of this blue region can I calculate the interface area of this blue to red I should be able to right because if I know the width if I knew the original volume if I divide one by the other I know how the interface is going to evolve as a function of time so let me show you how those excitons and I'll come back and show you how to calculate those things but this is a movie that shows how the excitons are generated in the complex structure and how they get gradually phase segregated they get dissociated at the context so let me show you one more time so what is happening is that light pulse came in they generated excitons in one of the phases let's say in the later this like a raindrops it is coming and getting collected on the red phase and then they are finding the junctions and getting dissociated since I had one pulse they will either self recombine or they get dissociated at the junctions and so that is how this pulse comes in what happened there is something wrong here so let me move on and see whether how I calculate how the interfacial area is do you understand why we are thinking about the interfacial area remember that the recombination can only occur at the interface so if I could calculate how the interfacial area is changing as a function of time then I could stop in the right moment where the recombination is the lowest so that is why I am spending so much time trying to calculate the interfacial area of this complex structures and which is very easy to calculate as you see you see although this one looks very complicated you can think of it is like two threads like my daughter sometimes will take two threads and then mix them up all together then you have to unspool it now if you can easily unspool it let's say but the volume of the red and volume of the blue they will remain the same a little bit later again if you unspool it because these things have gotten wider this interfacial area will become smaller and if you unspool it further of course getting wider interfacial area is getting smaller so in this sense you would wait till it is the it is very small that way of course you can dissociate them interfacial recombination will be very good very small so now think about it what is the interfacial area of this complicated structure you know the area original area divided by two because it is one to one blue and red was one to one so area divided by two Wt this width evolved as a function of any time as t to the power one third so without doing anything else despite this complexity of the structure you can immediately find out what how the interfacial area of this one will evolve as a function of any time you don't have to do anything else now how does it help me I can calculate exciton current based on this in the following way remember that only a fraction of the electrons exciton that are generated can be dissociated and those has to be within square root of d tau x that gets dissociated the rest of them essentially recombines and they cannot be collected so I can easily collect calculate what this Q is this is the square root of dT this is how much it gets collected and L is the interfacial area so this will be the total charge that's collected and if you wanted to collect calculate the exciton current you do Q divided by tau x that will be the total charge collected and the time it took to generate the charge and from there you would say the exciton current would fall as any time to the power one third and then you will do a complicated calculation and if you can then do a simple analytical expression both will give you the same answer and one thing is you can run the computer for a certain period of time shining light letting the excitons go in various places and then collect them and another is two line of algebra and essentially you get the same thing now you can ask yourself why do you really get the same answer and the reason is this exciton which is generated here doesn't really care that this structure is complicated and the example analogy I gave is the analogy of a fly a fly which sort of is born here dies within 30 feet of where it was born there is no it's not necessary for the fly to know that the Himalayas exist because the local topography the only thing it cares about is the local topography it lives and dies within a very small distance and therefore the complexity of the morphology has nothing to do with its life or how the excitons are generated and how it dies so therefore you can catch this essence very complicated transport argument in essentially a simple equation very nicely now here is a problem you can immediately see if it is so great the exciton current in the beginning it has a lot of area if it is so great then why should I anneal in the beginning I had a lot of surface area excitons will get dissociated very nicely I should not anneal but it turns out that you should anneal experimentally this would be wasting their time so they have been they have known by empirical methods that you should anneal so what's the trick what am I missing here now the trick is the thing is the following that actually if you really look at the short circuit current that is coming out of the cell out of a complex cell that really doesn't go from a high value to a low value rather it starts with 0 now you wonder why would it start with 0 and then it goes up goes through a peak and this is why the chemist and engineers who do not care about theory they stop by using a lot of grad students this can be empirically found the trick is the following the trick is that of course if this structure is thick then there is a connected highway that will allow you to go to the proper contact if the structure is on the other hand so this allows you to get out the holes get out let's say but if the structure if there are islands like this which will trap the electrons or holes then they cannot get out and what happens in these structures yes excitons can get out very easily but the electrons and holes may not be able to come out through this complicated maze so you collect increase exciton dissociation but you lose out on electron and hole collection and because you lose out on this that is why there is an optimum so this is a percolation problem for electron and holes and so you get a lot of exciton dissociation but as the electrons are trying to find its way to the other side lots of holes are also trying to find its way to the other side lot of recombination and as a result you really do not get much out to begin with by the time you come about here it sort of nicely balances the exciton dissociation with the electron hole transport you have a maximum efficiency a maximum short circuit current and then if you stay too long then these regions get so thick then they get out very nicely but they don't get dissociated very very effectively because these regions are thick you are losing a lot of excitons so this is a trade-off between resistance and current collection versus exciton dissociation that defines the maximum so if you want to compare these various structures you can see that the bi-layer or the planar is the least efficient this structure is somewhere in between and the ordered structure if you could make them cheaply then that will be in some way most efficient but in general this random structure is essentially pretty close to optimum if you can process it correctly so let me then end with a few slides and this is sort of the essence of the point remember what the problem I said in the beginning was that this looks all very nice nice physics you can write a PhD thesis and all but of course you cannot sell a single one of them in the market because these are too expensive the question is too expensive low efficiency few percent, 7-8 percent efficiency these days and horrible lifetime so one year you would be lucky so the question is how what can you do to solve that problem that's the goal at the end we are engineers physics is good on the side the real reason we do this is because we want to solve problems so what can you do one is use low polymers with low bandgap because as professor Lundstrom mentioned professor Gray mentioned also that if you have silicon it's almost optimum bandgap or gallium arsenide this has too higher bandgap sometimes close to too heavy of course these are inefficient because lots of photons are just going through so you can ask what are all these chemists doing the problem is that as soon as you try to synthesize new polymers with a lower bandgap not that you cannot make it but remember you have to mix it solubility is very important and so far people haven't found a way in which they can have a low bandgap 1.7, 1.6 EV and at the same time soluble with respect to each other that pair does not exist so that is the problem in this technology and people are trying very hard if you have any idea or can come up with something you will be very happy that it could be done some people might say why not change the ratio of the blue and the red you know 1 to 1 is good but maybe the red one if it absorbs all the light generates all the excitons then maybe I should make it 3 to 1 so that I can catch a lot of lot of light and lot of excitons and that will be good but it turns out that the percolation theory suggests that you are beyond 1 to 1 it doesn't really matter what you do it's a geometry problem physics you can beat geometry is very difficult to beat you can say I will optimize an ill time not very much you can do and then you can do regularized morphology but as I said random maybe in some cases close to optimal so you are in a tight box why percolation why 1 to 1 is very good this is one of those organic material P3HT and then there is something called the other phase is called PCBM this name of two chemists don't ask me what does acronyms mean I do not know the thing is that what you see that the connected volume of the percolating structure of course when it's 1 to 1 both phases can percolate because they have to each individually connect to their respective contacts if they don't then of course they are not going to one phase is trying to get the electron out holes are not coming out you have zero current so that's not going to work and since in 3D the percolation threshold is 33% at 33% they begin to percolate it will turn out that close to 33% the efficiency of the connected volume begins to fall very very rapidly so you cannot really go away from 1 to 1 there is no way the connected volume will arise so in one phase in one condition all the blue will be trapped within this red and they can dissociate exciton they are not going to contribute to current on the other phase the red will be trapped in the blue and again you have no current and in between you have a connected volume and the holes are coming out from their respective contacts and the other thing is that you cannot even get here because as you get close to this region there is huge fluctuation from one device to the next sometimes it gets connected sometimes it doesn't and so remember we have to connect them in series so if one of them has lower efficiency and lower output voltage it is going to kill the whole thing it's like the shadow degradation problem you have a lower current in one and then of course that is going to sort of drag down everybody else connected in series so therefore going away from this type of thing is very difficult now one time I gave a talk in Columbia and one of the chemistry students came up and said that if I knew this argument I could get to my advisor and it would have saved me two years sort of work because they had been trying to map out the whole thing and he didn't have an argument to go and argue with his professor not that's a good idea go and argue with his professor that why he didn't work, he didn't work but why he didn't work, he didn't have a simple argument so this was his argument and he was very happy with it the other thing is fluctuation that is what I just mentioned that organic solar cells if you have a random structure you have huge variability in the efficiency in the short circuit current in the field factor in the VOC why? because every structure is slightly different and so therefore you will have huge variability so for example this one this is WD is a function of the anneal time the longer you anneal the coarser it gets all those regions are getting thicker and so you can see that this whole trajectory is evolving and each point is for one of the cells now if you are interested in publishing in nature and science or the important journals you can try a lot of them and pick this one and publish that will be fine because that shows that how much you could get in principle but when you are going to connect a bunch of them in series and going to have a technology where you want to have huge volume in that case the efficiency you are likely to get is the average of them if not lower so in that sense ordered structures because in the ordered structure very little fluctuation and this is always connected to the right context so therefore very little fluctuation and you can get very high efficiency relatively high efficiency and not suffer from this variability problem so this is one of the challenges of organic solar cells the fundamental nature of how an organic solar cell works that makes this variability an inherent part of this but of course if your area is very big your variability is going to go down but your average is going to gravitate towards this average so therefore it really doesn't help you to have one data point in here and say that this is the potential of organic solar cells so the last thing about reliability and that's where I end so one thing is when I said that you process it in microwave oven or in your oven but you have found recently that walking out in the open is no different than being in the oven because these both temperatures are not so far but different in the oven it may be 125 degrees outside 100 degrees so for a solar cell when you place it out in the sun it doesn't know whether it's in the oven or in Arizona sun let's say it still continues to think that is in the oven now if it continues to think as an oven what is going to do? it is going to continue phase segregate yes you stopped it and you said that don't go any further this is my optimum point all these phases and all these are good but then you put it there and it begins to phase segregate because it thinks that you have accidentally put it in the oven so what's going to happen is that depending on the temperature if you have 80 degrees these are test temperatures 100 degrees or 120 degrees these are test temperatures the phase segregation will continue and if the phase segregation continues what's going to happen the width of these regions are going to get wider exciton collection is going to get poorer and poorer and in one year for sure the cell is not going to work this is the cluster size remember this T to the power of one third I told you about if you made the temperature high 120 degrees then this is going to get faster and on the other hand if it is lower so in Alaska maybe things are better for the organic solar cells but Arizona may not be so good now so therefore what you can do is to look at when you ship the product to the consumer then what the W was the width of this region was at that time you put the short circuit current L exciton that is scales with D to the power N but now remember this is the operating temperature hence the word T0 and this is the effect of the initial when you ship the product this is how long you annealed it so when you put them together you can get a simple equation that tells you that if you have soft material that can go through each other very quickly which is the activation energy if you put in the Arizona sun then this whole thing is going to degrade very very quickly with the exponent of N is one third so this is to extend you can actually predict how this is going to behave you know one thing you can say this is degrading I will just measure it and plot a few points and send it out in a report but here you can see you can essentially say exactly that how this thing is going to behave as a function of time and so what's going to happen your short circuit current is going to fall and these are experimental data and this is the theory that says that generally the trend is pretty well reproduced and how much is this this is in seconds so this is couple of hours and most things die within a month so this is the reason why this happens and you can calculate the lifetime you will be lucky if you get a one two years so that's how this thing works now of course this is not the end of the story people are very clever what they have done is that right after processing there are photo cross linkers in here which essentially just before the ship it they zap it with X-ray so that this photo cross linkers create a container sort of a network which puts them binds them in place now they cannot face segregate when they are in Arizona sun they want to but this trap network of traps then keeps them in place that is how they have recently gotten three to four years projected lifetime so this is my summary then bulk hetero junction is good checkerboard is better checkerboard is better because you can essentially is always above the percolation threshold electrons go in their divided highways they can recombine and you can optimize it but of course it's going to be expensive if you want to do it it's a stop down method it's not like putting two things together and then the structure like this which professor Agrawal's group have also worked on this type of double gyrate structures is good not because it's a solar cell it can bit VOC or short circuit current or field factor anyway because it cannot you can mathematically show that the VOC of these three structures will essentially be the same but what it does is that it puts things traps the phase so that it cannot face aggregate now many times of course the width is not really what you need which is too small so it doesn't collect excitons very efficiently that's the problem with this structure but other than that if you could make it this self-trapped structure would be the best because this is above the percolation threshold all connected and then at the same time highly reliable it will be highly reliable ok so this is sort of the end of the story so we said that the main reason we work on organic solar cell and by the way now if you go out most of the universities and many universities you will see very exciting work going on the reason is not that this is a technology yet but it promises to be a technology that is unbeatable if you could do it there will be few things that will be better this is and the most important thing is it's going to be very lightweight and it will be very easy to install you can install it rather than having a company come in and install it now I explain to you very simply that how percolation plays a role how the reliability and the solubility the same physics that governs phase segregation makes it easy to work with is the same one that makes it less reliable so reliability and performance are flip sides of the same coin and so therefore should be considered as such and this variability I told you about that when you have a series connectedness is a fundamental aspect of our solar cells and if the series connectedness because the series connectedness you cannot have cells that have huge variability because if you have that you lose several percent of your efficiency by the time you connect them all up together and that's not really very good so the base solar cell that you might say for organics is how much maybe 8.1 percent or so but by the time when the company wants to sell it they cannot sell it to anyone they sell it for bus stand and nice covers on the automatic because it's not commercially viable so in that case they only get about maybe 3 to 4 percent efficiency very very poor no one near what it needs to be okay but I suggested a few ways by which we can get to this 15 percent efficiency and hopefully if we can do it you'll one day buy your organic solar cells on your own thank you so it needs to be one of us and then we need them and they do this kind of thing so is it on a substrate some what is the substrate the substrate is very important but most of the work that I have seen done this is on a small petri dish type thing and the role of the substrate is not very clear because what they say because the physics is so where sort of not well understood and the nature of the phase segregation and all what they generally do is they get a postdoc from a group that already knows how to do it and then they exactly follow the recipe but in general people have been talking long about texturing the substrate so that you can grow these structures monitor this so this is there is a lot of work going on in locally templating the structure nucleus on that and then then that will also improve reliability yeah but so far I haven't seen any result that we call promising the previous lecture I think you didn't mention about axiotones and certainly you introduced that and it seems like it's very important for organic work why is it so important for 24 organic for this one right so I tried to probably I went too fast in the very early part of the lecture should I go back to this one I mean I think maybe that's a very important point because on no other solar cell we talk about exciton and all of a sudden you're talking about exciton going this way that way that's very important to understand to highlight the importance I made a joke about Prof. Lundstrom that you should have considered his lecture fishy and the idea was the following the when you think about the main point I wanted to make was exciton is the most natural thing to to happen because anytime you have a photon coming in electron hole pair generated they are in the same atom where electron just got bumped up now you have this hole within a few angstrom and this Q and minus Q is like a hydrogen atom they should be circling around each other why should they go away so going away is abnormal exciton is normal now the argument I made was that if you look at the binding energy of how strongly they are bound in the case of a hydrogen atom it's in the vacuum so your relative dielectric constant was 1 so you had 13.6 eV and so if you didn't put a X-ray or something in it nobody is going anywhere very strongly bound on the other hand when you think about silicon silicon dielectric constant is 12 or so so look at this goes kappa squared so it will divide it by 144 let's say in that case effective mass is 0.1 so what's going to happen 13.6 eV it is 13.6 millilectron volt now 25 millilectron volt is KT so yes they want to circle each other if one arm comes in and kicks one of the electron they forget about that they were excitons ever they get out through their respective contacts not true for organic materials because organic polymer have low dielectric constant and because they have low dielectric constant on the order of 3 and 4 this factor is not as big and therefore the value that you get normal temperature cannot kick them out right and so therefore and also that this radius is such that unless you use a hetero junction you cannot even pull them apart because they are just close together and they are moving like together all this time and then if you apply a p-n junction field they don't care because the p-l junction field is a factor of 100 smaller than what you need to get into that's the problem is that clear yes please can you use like a 4 in the 2 fluids there is a problem of the trade-off to do connectivity in the green space we go for a 4 fluid with like 2 sort of like rather big fluids which would together form you can have 4 fluids so if you image 2 fluids form the correct length in the next 2 fluids is that an interactive problem first of all I am not a chemist so I am always a little worried about saying something so the question is essentially that can you decouple this exciton problem and dissociation problem and the connectivity problem but whether it is to the 0th order and I will have to think more about it to the 0th order the percolation problem is very fundamental but it has to connect to the respective contacts so if you have 4 then let's say it has to be less than half and half right because other 2 phases will take care of let's say you have 0.4 0.4 and 0.1 0.1 4 phase now because this 0.4 individually have to connect so they may not be able to percolate 0.1 is doing the percolation yeah 0.4 0.1 you need in 3D you need at least 33% for the total volume in order to percolate on the average so you cannot go below in some cases you may be able to percolate but most of the cases you will not be it will be trapped within these pockets okay