 This is where we stopped 7 excitons at the cost of 1 and now we want to know how did they even know that they have done it. Well they knew it from transient absorption data and to understand what they did it is instructive to follow this schematic that they had presented in their paper. What they say is this as we saw earlier in 200 picosecond or so the hot excitons have cooled down. So whatever we have beyond 200 picosecond is has got to do with exciton and here we are talking about transient absorption right. So transient absorption beyond that initial decay is quite long lived and that is entirely due to well if I may call it mono exciton not by exciton not anything else. So what they said did is this delta A or what as they have written delta alpha they designated this as B and here this Nx equal to 1. Nx equal to 1 basically means it is a regular exciton not by exciton or anything and then what do you get after this instantaneous excitation you get this hot electron well hot exciton then by exciton so on and so forth. So what they said is that this instantaneous excitation is designated as A and this Nx equal to A by B this is what they call well that multiplied by 100 that is a percent quantum efficiency for formation of exciton. So this is what happens when everything is a regular exciton this is in the initial stage you have got exciton and then you have your biswater and so on and so forth. So what they say is that this is a measure of quantum efficiency and then once again what they did is they tail matched and the tail matched at 1 why because Nx equal to 1 at long times and then when after tail matching in fact you see the tail matching has done at longer times here it is not even 200 because second it is 1200 or more as we have discussed earlier excitons can actually have a long component of lifetime. So here if you go from bottom to up you actually go from 2.4 times Cg to 3.9 times Cg 4.9 times Cg 6.7 times Cg 7.8 times Cg are superimposed and at 0 time they are superimposed at a value of 7 remember normalization has been done to 1 at long time. So basically this one is B so whatever we get from the Y intercept if I may call it well it is Y intercept it is just that Y is delta alpha that is your efficiency that multiplied by 100. So this is how they arrive at 700% efficiency 700% efficiency might sound strange to people working in fluorescence spectroscopy let us not forget that more than 100% efficiency is quite common in photochemistry right number of molecules produced per photon absorbed that can be more than 100% the only reason why we cannot have quantum yield more than 100 fluorescence quantum yield more than 100% is that you use one photon you cannot get more than one will always get less actually. So this is different here whatever extra energy has been so we are using a photon of higher energy and the excess energy is being used to generate more excitons that is why we get this 200 300 500 700% quantum efficiency this quantum efficiency is for formation of excitons not fluorescence is this the efficiency of formation of charge carriers actually no that will come later and what they have in the inset is that they have superimposed for every case the clock time constant obtained by regular fitting and by this NX normalization and they have shown that it is just the consistent. So what we have arrived at is that there is a difference between bulk materials and nanomaterials and there are many differences between bulk material and nanomaterials in this context the difference is that for a bulk material what happens is when you excite at EG you have one photon absorption and generation of one exciton so efficiency is 100% yeah if you excite at 2 EG or 3 EG or wherever this efficiency does not change one photon is absorbed and an exciton is generated that is what happens most of the time in bulk and the inset here is the actual efficiency of charge carrier generation and that efficiency has been worked out already it turns out that it can be maximum of 0.44 sorry 0.44 as you see you excite at very high EG value you get nothing you excite at 0 which means you do not excite then of course you get nothing when you excite at EG that is when you get the maximum efficiency because you have excite at more than EG then non radiative processes take over seen all the discussion so far in the previous module and this one we are not for once talked about other kinds of dissipation well we have in a way because they talked about cooling but we really did not think about it so much we kept thinking that we generate one excite on somehow that excite on will give us one charge carrier it is not necessary they can recombine they will recombine right so the competition always is between recombination of electron and hole by themselves and their separation by applying and potential difference so 0.44 is the best one can do I am talking about efficiency of charge carrier generation efficiency of charge carrier generation can at best be 0.44 in bulk in nanoparticles however what one can think is that if you use smaller EG nanoparticle so this plot is I understand it in a different way if you use photons of higher and higher and higher energy so compared to that this EG is smaller and smaller and smaller what one what we are saying is that as you use material with bandgap that is much smaller than the energy of the photons that you use efficiency can in principle go up what which efficiency efficiency of charge carrier generation can in principle go up to 100% that is the ideal scenario this is the reality in these two modules we are going to take the names of certain people who have really made advances in this field over last few years you must have heard of Nozick because he one of his works actually made it to the newspaper I think last year or year before. So what Nozick's group showed was that this is what you expect a stepwise increase in efficiency of charge carrier generation and well efficient quantum yield and then efficiency of charge carrier generation is written this is what they get for VBC quantum dots this is what they get for bulk PBC so see bulk PBC also it is not flat right what is the expectation quantum yield should be just the same that is not correct and if you look at the efficiency of charge carrier generation in bulk it is 0.2 in nanoparticles it is 0.4 it is definitely more but the picture is really not as rosy as we might have thought it is it gets double it does not get hundred times but nevertheless the efficiency of charge carrier generation does go up if one goes from bulk material to its nanoparticles and that is what has made this quantum dot solar cells very attractive these are two kinds of quantum dot solar cells that are commonly studied commonly made Schottky barrier and PN hetero junction in Schottky barrier what you have is you have glass ITO ITO is a transparent electrode so light has to get it right and but at the same time there has to be an electrode inside that you have this semiconductor nanoparticle film and then you have the other electrode well calcium aluminium that is what it is that is what gives you the Schottky barrier and in the other one you have a PN junction so you have a P quantum dot layer you have an N quantum dot layer and rest of it is pretty much the same there has been a lot of study of not only efficiency but also ultrafast dynamics of charge carrier formation in quantum dot solar cells this in itself is has become a very hot field of research over the last ten years or so before quantum dot solar cells people used to talk more about dye sensitize solar cells well again let me digress a little bit why is it that we need all this and solar cells are there all around we can see solar cells and from here if you go to look at the roof of almost any building you see solar cells what is the need of further research in solar cells the problem is the solar cells are actually very expensive solar energy works because of huge amount of government subsidy it is really not a commercially viable proposition even and then it is very easy to break those cells also somebody gets unhappy with solar energy and go with the stick and mash up the cells and it is very expensive. So one approach that had been taken was we will use a dye excite the dye and that dye is going to transfer its energy into things like titanium dioxide nanoparticle and then charge carrier generation would take place and there has been a lot of work in from late nineties well of course people started working with things like porphyrins and other dye molecules it was found out that your dye molecule has to have a COH functionality otherwise it cannot anchor itself on a titanium dioxide nanoparticles. So people tried other things like vegetable dyes somebody proposed goat blood that contains a lot of dyes and so on and so forth. But there is a problem with dye sensitized solar cells dye sensitized solar cell can actually be bought for I think few hundred rupees or maybe a few couple of thousand rupees you can buy it everything will come you assemble and you are done it is very nice thing to demonstrate the problem is this the whole idea of this your dye sensitized solar cell comes from photosynthesis in photosynthesis you have light harvesting you have a reaction center where charge separation takes place and that is how it works. So if one can mimic photosynthesis before the step of production on glucose then one can harvest sunlight and all these processes are ultra fast right absorption of light of course and then there is always this freight that takes place and electron transfer everything is ultra fast that is why the ultra fast community got into this field. Now the problem is this that even chlorophyll by the way is something that degrades in sun but the advantage of a plant is that it is a living thing so it can grow more leaves it can produce more chlorophyll dye sensitized solar cell cannot grow cannot produce more dye and it will be really messy if you have to change that dye all the time that is why whatever dye is used in dye sensitized solar cell so far is found to be not not stable to the point of satisfaction in sunlight. So the cell would work maybe for one hour or two hours or maybe two days five days and not anymore so it is once again not a very practical thing that is why focus move to solid state solar cells and quantum dot solar cells have been explored for a long time because quantum dots are more stable than dyes and secondly what we saw is being nanoparticles there is an advantage of formation of multi excitons. So ideally this module should have ended here but let me just for the sake of completion also go ahead and say that quantum dot solar cells as many of us would know already are slowly making way or not maybe not even slowly for another kind of material solar cell with another kind of material and that is perovskites again the problem of perovskites is stability so far two problems one is that perovskites contain lead so one major focus has been to make perovskite without lead the other issue is stability stability to water moisture stability to light and so on and so forth. But quantum dots perovskites have turned out to be very very promising so once again let me just show you a piece of data not really going into the detail of perovskite but there is another reason why I want to show it Moser and coworkers and this is a paper that has been published this month 2020. So again perovskite quantum dots have been made you can see the images here and generally when you have perovskite quantum dots you see squares nice squares they are very good looking only last week there has been a paper from the group of Narayan Pradhan where they have made perovskite quantum dots of shapes other than square that itself is a an interesting advance but here since it is a nano crystal anyway you have similar absorption and PL spectra that you expect for nano crystals. So what Moser and coworkers have done is that they have studied ultrafast dynamics in this perovskite nano crystals using transient absorption as well as fluorescence of conversion but the fluorescence of conversion conversion data here actually looks like transient absorption doesn't it? I talk about the top panel there are 2 axis actually 3 axis third axis is pointing towards you intensity and the 2 axis are time and wavelength okay. So the way it has been done I think I mentioned it in the passing when we talked about fluorescence of conversion is that they have used they have used a different kind of crystal in some frequency generation crystal that they have the optic axis is horizontal and that makes it possible for some frequency generation over a broadband. So what you can get is that you can get the fluorescence spectrum entire fluorescence spectrum at whatever delay you want rest of the instrument is same there is a delay which delays the gate pulse there is an excitation pulse the only difference is the fluorescence is focused onto a some frequency crystal along with the gate pulse where the some frequency crystal allows phase matching independent of frequency. So for a given delay you can get the entire fluorescence spectrum that as we understand makes life much simpler makes data acquisition maybe 100 times or 1000 times faster. So that is what they have done and what is of interest here is that if you look at the transient absorption time evolution and fluorescence of conversion time evolution they are more or less the same once again as you go higher in energy of pump or excitation wavelength you get this ultrafast component which is missing when a lower energy pump or excitation is used. So once again very similar hot exciton dynamics is observed here and what they have been able to do here is that they have been able to show what is the spectrum of the bi exciton and this also tells us that whatever we have discussed earlier that is not complete because here even bi excitons emit it does not have to wait to get to exciton level if bi excitons emit that means what they have recombined they are not there anymore. So not all bi excitons are going to produce excitons that we had expected right the light will be emitted so they have been able to separate these two and they have been able to propose a interestingly the model they have proposed is very much like a model that we would encounter for molecules but that is because we are using a particle in a box model here anyway to close this discussion what I want to say is this there is more to life than even bi excitons you talked about excitons you have talked about bi excitons you can have things where that balance is not there in excitons as well as in bi excitons what do we have number of holes is equal to number of electrons but there are other particles at these these are actually known it is not as if this is new discovery bi excitons have been known for many decades similarly what is also known for many decades is try on try on means one hole two electron or one electron two hole you have a bi exciton somehow an electron has been lost to a defect or something like that and in this paper published last year by Professor Hiren Gorsh's group what they have done is that now they have worked with 2D material MOS2 monolayer and it is not even homogeneous this is MOS2 monolayer with gold nanoparticles and what they have been able to show using transient absorption very elegantly is what is it that happens they have shown that in 500 femtoseconds you get the exciton then 600 femtoseconds the exciton can actually transfer the energy to gold nanoparticles or you can get try on in 1.2 picosecond how they got try on for that we will have to read the paper we are not going to discuss this is quite a loaded paper this is this cartoon is only a summary of what is there and then from try on it takes 3.7 picosecond to transfer the energy to gold nanoparticle well when I say takes 3.7 picosecond perhaps I am not really being exact the time constant is 3.7 picosecond so let me just say that this scope of study of ultrafast dynamics in nanomaterial we have talked about plasmonic nanomaterial we have talked about semiconductor nanomaterial we have talked about perovskite well we have shown you the data on perovskite nanocrystals and here we see 2D material this scope is infinite at the moment a lot of new things are there that have not been explored earlier and using ultrafast techniques one can explore them and learn things that are interesting definitely from the fundamental research point of view and possibly also to devise newer applications like what we saw application in quantum dot solar cell so that is where we close the discussion of systems as such we will have maybe 3 more modules in which we are going to talk about other kinds of ultrafast spectroscopy because in so many lectures you might have given the impression that ultrafast spectroscopy means transient absorption and femtosecond upconversion is definitely not there are many other techniques we will not be able to go into all of them fortunately if you understand how transient absorption works then you can understand most of the other things so we will talk about only two kinds of experiments one is two dimensional spectroscopy and the other is surface sum frequency generation that is what we will do over the next maybe 2 or 3 modules for now this is it.