 Today we close our discussion on ultrafast dynamics in semiconductor nanoparticles. So far we have been talking about excitons and how they evolve, we have talked about exciton trapping, we have talked about the ultra short and ultra long life time constants and we have seen an elegant example where a rather complicated decay has been handled and useful time constants and rate constants have been extracted from there. Today we move on to another phenomenon that is very peculiar and is observed in nanoparticles and that is of multi excitons. As we have discussed already and it is common knowledge nowadays that nanoparticles have band bands like in bulk but then within the bands they also have this discrete energy levels and we have talked about how they are named. This sort of NL kind of nomenclature this one is well it is easier to go by L, S stands for the angular momentum of the exciton if it is 0 then the level is designated S. If it is 1 then it is designated P, if it is 2 then it is designated D and so on and so forth and the reason why the lower ones are designated H is that after excitation these lower energy levels are occupied by holes and higher ones are occupied by electrons and the one that is there that is N that denotes the number of levels of particular kind of angular momentum. For example this is 1S because this is the first level with angular momentum 0, 1P first level with angular momentum 1 and so on and so forth and this review by the way by VI Klimov is very instructive what we will do today is that we will really gloss over several papers it is not possible to discuss the vast body of literature that exists in this field but it is important that we individually actually read those papers cover to cover then only we will understand the field right. So we have also said that the absorption spectrum in semiconductor nanocrystals shows several features due to different kinds of transitions. The lowest energy one is called the band H transition because it involves the energy levels at the edge of the conduction and the valence bands however you can have a promotion from a lower level so after promotion the hole can be left in a lower level and the electron can be in a higher level and so on and so forth. One thing that may be noted is this see we have drawn this arrow here from 1S H to 1S E we have not drawn a line from here well we actually have drawn from here to here as well but well the point I am trying to make is that selection rules do hold here as well. And if you do a good experiment if you have uniform nanoparticles and if the absorption spectrum is recorded properly then one can see features like this which are very easy to miss because in any case there is a scattering background that is there but different excitations can take place at energies higher than the band gap as well. So what we talk about today really is what happens when excitation is performed at energies greater than band gap and in this discussion it is conventional to write the x-axis as E by EG how much above one what by what factor above band gap are we exciting that is what is typically used and results are also discussed in these terms that is what we are going to do. So you can say this is the band gap so this is EG this is 2EG 3EG 4EG and so on and so forth. What happens is for that kind of an excitation the electron reaches a higher energy level and the hole in the general case would also reside at a lower level hole residing at a lower level remember means that electron has been promoted from a lower level and so energy is more. So to start with what we produce is called a hot exciton after hot exciton means an exciton that has more energy than the band gap a cooled exciton has energy equal to band gap. So in this phenomenal work by beard and co-workers what they have done is that they have tried to explain what happens when hot excitons are formed in other words they have studied hot exciton dynamics and a very interesting thing that happens if one uses an excitation energy of more than 2EG is that when this electron comes down to 1 SE and the hole floats to 1SH the energy that is involved can be utilized to cause another electron hole separation to lead to what is called a bixiton. So bixiton remember is within a single nanoparticle within a single nanoparticle you have 2 electron hole pairs instead of 1 and when one wants to study this phenomenon one has to be very careful about something if you use too much of pump fluence then also you can actually generate bixitons by the excitation itself because every nanocrystal is subjected to a lot of photons one photon will cause only one transition. But if a single nanoparticle is bombarded with millions of photons then it is possible to have more than one electron hole pair formation in a single nanoparticle directly even if one uses pump energy of not more than 2EG that is a different ball game altogether in fact there has been a lot of study in that as well we are not getting into that for the paucity of time. So what they also proposed is that after the bixiton formation there is an auxiliary combination which leads to formation of single exciton. So how would this show up and what is the time scale involved it would show up in transient absorption data like this. Now this transient absorption data are again we have encountered tail matching again and again in this course these transient absorption data are also tail matched at long times well tail is at long time so that is I am saying tail matching at long times is sort of saying the same thing twice. But when they are tail matched what one sees is if you look at the transient absorption decays this transient absorption not downstate bleach now state bleach is once again a little different story. So what one sees is as you go from 1.9EG to say 4.66EG excitation energy then we see the emergence of an ultrafast component that gets over by 200 or 300 picosecond that is the time involved in cooling of hot excitons formation of bixiton so on and so forth. But again this is rather complicated dynamics because it is not as if hot electrons are formed and then they cool down and form single excitons hot excitons are formed and then they cool down to form single excitons the intermediacy of bixiton is always there. So to understand that one needs to analyze the data very very carefully and in this this seminal paper of Nozick comes handy. So what Nozick had discussed in this paper this review annual review of physical chemistry published in 2001 is what happens after what is called impact ionization. Impact ionization means what we have said earlier formation of a hot exciton and he said the first step is always bixiton generation. In your clue from there Klimov and well Scheller and Klimov did more elaborate study few years later and these are all very interesting papers and these are really papers that have pushed the frontier it is absolutely new novelty is one thing that is not in question in the papers that we discussed today. So what the said is that okay you have impact ionization and then you have auxiliary combination and then you can have formation of exciton like this. So their model the model that they used was immediately following photo excitation and what they did is they did photo excitation at more than thrice band gap to ensure the formation of hot excitons. So this is the model that you have hot excitons that are formed and of course the reality is not this homogeneous also because do not forget we are working with femtosecond pulse there is always a width there is always heterogeneity. So whatever we talk about here is really an idealized situation and a manifestation of that will also show up in a result that we are going to see in a couple of slides. So what they said is that 50% of this population undergoes impact ionization and formation of bixiton remaining 50% undergo cooling cooling means the energy is given to the lattice no further exciton formation is there and then these bixitons also undergo auxiliary combination and cool down this is the model they used to fit the data we are not going into fitting of the data as such because if we do then to discuss this one paper again we are going to need 3 modules like we did last time and now we are almost at the end of the course everybody is sufficiently familiar with the phenomena. So we should be able to read this and understand ourselves but it is time consuming and I strongly encourage everybody to read this alright now while doing experiments like this couple of things need to be kept in mind first of all what we discussed already we should use a low pump fluence low intensity of pump light so what happens in ground state bleach is that you see a rise time in ground state bleach so rise time in ground state bleach is something that we may not expect at first thought why would there be ground state bleach you perform an excitation population in the ground state gets depleted so the bleach is supposed to be instantaneous and then it recovers that is associated with the decay when can there be a rise time in a ground state bleach when post excitation further depletion of the ground state population takes place and that is what is happening here isn't it. Well formation of bixiton when the bixiton is formed this generation of another electron whole pair and this another electron whole pair means that comes at the cost of excited state population unexcited so if you think of how many unexcited nanoparticles are there that number would go down that is why one sees a rise in ground state bleach and if I may digress a little bit this is a phenomenon that is once again definitely not expected in molecules we have talked a lot about molecules in molecules one does not expect it but even in molecules this can be seen and it can be seen in a in something that has attracted a lot of contemporary interest I am digressing from nanoparticles for a moment I am talking about molecules now recently there has been lot of interest in what is called singlet fission singlet fission means okay we have this S0 state we have S1 state we have S2 S3 whatever we perform excitation to a higher singlet state and this is something that we have seen already when we talked about the Haraj work there we could actually see the emission from S2 state in ultrafast time scales singlet fission means in case the energy of a triplet state is approximately half of the energy of some excited singlet state of course I am talking about relative energies here in case this happens then this molecule can undergo what is called singlet fission means they can be further excitation to the triplet state okay this will cool down right but while cooling down that energy can be utilized by another molecule to get excited to triplet state and in this molecule intersystem crossing would take place in another molecule the triplet state would get populated right so you start with a situation like this if I draw simply this is your ground state ground state configuration this is excitation to some singlet state which has energy that is double that of your triplet state and then what you have is you take another molecule which is in ground state this combination becomes something like this even in this case one can see a rise in ground state I missed out on this while talking about molecules so I thought that since there is a very similar situation in materials it is a good idea to just at least mention it once right but now let us come back to the topic that we were discussing what we have learned so far is that one can generate a hot excite on y promotion of the electron to a higher energy state and when the hole is in a lower level per se that hot electron cooling can generate by excite on and then the by excite on can undergo or say the combination to form regular excite on and this would show up in a fast decay in the transient absorption when pumped at high energies when I say energy I basically mean when a pump when pumped at more at shorter wavelengths I am not talking about pump fluence let us not confuse pump energy and pump fluency here when excitation is performed at lower wavelengths higher energies then this phenomenon can be seen that is when you see a fast decay in the transient absorption that is when you see perhaps a rise time in the ground state at lower wavelengths this observation is not there so the question one can ask at this point is so what this happens great so what is the need of getting excited about this well this multi-excitron generation actually has a rather elegant application and that application is I am going to excite using one light one photon and I am going to generate not one excite on but several excite on and in fact that is what was shown by Klimov and coworkers in this nano liters paper that has really made an impact in the field the title itself is such that you have to read the paper if you read the title 7 excitons at the cost of one redefining the limits for conversion efficiency of photons into charge carrier okay what use is it why should I get excited if I can produce more exciton per photon well I should get excited because one very major application of semiconductor nanoparticles is in solar cells light harvesting so the idea is that your solar cell should be able to absorb the light from sun and it should be able to generate charge carriers so more excitons means we are going to get eventually more charge carriers in the ideal case scenario from each electron we should get an electron and we should get a hole. So if it is possible to harvest the blue part of solar energy spectrum and then if it is possible to generate more charge carriers per photon per blue photon I am saying blue in a very qualitative manner here all I mean is higher energy or if it is possible to generate not 2 but 3 or 4 as they have shown here they have generated 7 excitons so if I can generate 7 pairs of charge carriers then it is great so that is why this is a rather important problem but how did this people know that they have generated 7 excitons at the cost of 1 that is what we are going to discuss in the next module.