 So, now in the last module we have started talking about semiconductor nanocrystals. We have discussed Rosenthal's work where they had obtained a bi-exponential decay for cadmium selenide nanoparticles and the important thing that we learned from that study was that the every time constant has a contribution from a radiative part and a non-radiative part. Of course there can be special cases when one of the amplitudes can be 0. I mean one of the rate constants may not contribute that is a different issue but the general scenario we should not forget is that every time constant is associated not only just one radiative process. And we had also said that very often you have ultra long-lived trap states not always you can try and make nanoparticles where this trap states are almost not there. But in most of the cases you have long-lived trap states which is usually a hindrance because that would steal from the bandage emission intensity but in some cases trap state emission has been used effectively to make things like white light emitting nanoparticles or red emitting nanoparticles which have different kinds of use. So what is established in this work of Karki and Polaris and others is that for cadmium selenide there are two types of radiative traps so it is not a single exponential decay. And secondly if you pump with higher energies there is more efficient trapping will not go very deep into this right now but when we talk about multi excitons and all we will talk about the effect of pump energy as well. Now let us move on to another piece of work by V's and co-workers and here we will not complete the discussion in this module what we will do is we will discuss the philosophy of what they have done and then we will come back in the next module and then discuss the mathematical detail that they have used in the data analysis. So this is the system that they worked with cadmium selenide nanocrystals once again rather small and now we are familiar with this absorption spectrum you can see the bandage absorption you know what it is which electron level which whole level is involved and you can see the other structure very nicely that we had shown earlier in the previous module and this is the emission spectrum the point to note is that these are nanoparticles where not much of trap emission is there but the emission quantum yield is as low as 5% not great. As low as 5% because if you look at the decays of photo luminescence here you might notice that V's and co-workers do not use the term fluorescence and phosphorescence they are in deviation with Rosenthal's assignment so you see almost all the PL has decayed within the first nanosecond. However if you look more carefully so this is the decay that you get using a femtosecond optical gating of conversion and this inset shows the decay of PL using TCSPC and that goes on for hundreds of nanosecond. So this is the interesting as well as problematic aspect of working with this kind of nanoparticles you have ultrafast decays you have ultra slow decays and everything means something it is not easy to separate the components and say which one means what and that is why this paper in ACS Nano 2011 is very useful because it gives you a good idea about what to do with this many time constants that you get in most of the papers they are dealt with rather slowly but this is one paper where they had done a thorough analysis of course whenever you do something like this many of the models are phenomenological many of the models are just empirical and can be debated and that is why so much of work is going on even now because the last word is not really out alright. So let us show you some of the time constants that they got so when they looked at the time resolved PL peak at 580 nanometer they got 6 exponentials 3 from up conversion 3 from TCSPC so you see 4.5 picosecond and 48 picosecond these are in agreement with Rosenthal's work remember Rosenthal had got by exponential decays for her PL decays femtosecond time regime picosecond time regime they get that what they get in addition is this 730 femtosecond timescale so this is something that one can miss very easily if the resolution of the instrument is not good enough and the other thing that they have got and Rosenthal did not most likely because Rosenthal did not try to do a TCSPC experiment and they did is that they got these 3 time constants 1.4 nanosecond 13 nanosecond 45 nanosecond. Now there are papers where the ultrafast component is not even considered and these 3 lifetimes obtaining being obtained in TCSPC is quite common and remember this is not trap emission here we are not talking about very redshifted emission if trap emission component is there then the trap emission is hidden within the bandage emission itself. So the energy of the trap is very close to the bandage so this is an experiment which is more carefully done and more thorough in which the ultrafast as well as these slow components everything have been considered but now the question is what will we do with so many components how does one make sense of this one way of making sense of complicated systems is to do more than one kind of experiment and they did they did transient absorption experiments and compared the results with the time-resolved photo luminescence experiments. So this is the transient absorption that you can see again what is this feature the strong negative feature naturally ground state bleach here you would see some kind of a transient absorption and here again ground state bleach and of course this signal in this entire range is a complete mix because do not forget the absorption is not just here it keeps on going up. So whatever plus signal that you see is really a net signal there is a minus component as well okay what is the most notable thing in this spectrum I would say the quality it looks like a steady state spectrum it is absolutely smooth right so it is beautiful. Now so then they looked at the ground state bleach recovery not only in picosecond but also in nanosecond so they did flash photolysis as well so as you can see the ground state bleach is not recovered completely within even after one nanosecond and this is a major difference between the transient absorption data and time-resolved PL data time-resolved PL remember was gone in 100s of nanosecond 100s of picosecond well not 100s of picosecond if you go beyond one nanosecond you can see that time-resolved PL is almost gone okay. But here you can actually see that the ground state bleach recovery is not complete that means that you do have states that are that do not radiate which are holding either the electron or the hole keeping them separated and not allowing complete recombination and regeneration of the ground state within one nanosecond and you get this long component in ground state bleach recovery. So first of all what is vindicated here is that the nanosecond signal that you get in time-resolved PL is not rubbish okay as you know whenever we talk about fluorescence or photolysis we are very picky we always think that there may be some impurity and whatever long life time is there is perhaps because of a small amount of impurity that can happen here also. But what transient absorption looks at is the bulk it is looking at absorption right so if there is very small quantity of some impurity it will not show up in transient absorption. So from here first thing we learnt is that that long component that was seen in transient in time-resolved PL was genuine. Now if you compare the time constants something interesting happens first of all that 0.73 picosecond component does not show up so where is it gone. Similarly you see 4.5 picosecond in TRPL 4.5 picosecond in transient absorption 48, 13 and 12, 45 and 46 amazing beautiful match the only thing that is not matching is instead of 1.4 nanosecond you are getting 0.7 nanosecond which may be okay. When you do a 6 exponential fit in all and when you stitch together two kinds of experiments one out of six components going over is fine right. So this is what they have got. Now the problem is where is that 7.30 picosecond component why is it that you do not see it in transient absorption. Actually it is seen in transient absorption but not in the visible range of probe. So the other experiment that was done is transient absorption but using NIR probe and already there was literature which said that this transient absorption in NIR is due to bandage to higher energy states. In fact one can even guess that you are getting a positive signal. So from bandage it must you must be probing transition from bandage to higher it is just that those energy levels are much closer than the band gap that is inherently there that is why it is NIR and not visible. Now the literature that existed had established and again for the positive of time will not go into how they established is actually an interesting thing to know but it was established that of this transient absorption spectrum the higher energy part is dominated by electrons the lower energy part is dominated by holes very interesting papers one should read them okay. And then when you look at transients across the transient absorption band when you plot delta OD versus time this is what you get at 900 nanometer you get this kind of a decay at 1400 nanometer once again remember this TAHARA's work that we are shown tails were matched and at the blue edge of the emission spectrum we could see the ultrafast component nicely this plot is similar long components are there everywhere but the short components gradually emerges as you go from higher energy side to lower energy side what does that mean short component is not there in the higher energy side that is dominated by electron relaxation but it is there in the lower energy side which is dominated by hole relaxation what does it mean it means that the ultrafast component that is there is associated with hole relaxation it is as simple as that the problem is when they just fit the data simply they did not see that 730 picosecond component 730 femtosecond component they got something like this first two if you remember were very nice 4.5 4.5 48 48 what they see is when you go into NIR 4.5 becomes 4.7 to start with which is we can say within acceptable limits and then it becomes 2.5 I have not shown the data in between if you read the paper all the data is given and you can see the gradual this decay become faster and faster and faster as you go from 900 to 1400 nanometer here we show you only the 1400 nanometer data here this component is 2.5 and then even tau 3 instead of 43 48 43 they are similar it has become 26 tau 4 is actually something like 0.39 nanosecond and tau 5 could not be determined very nicely because in the NIR experiment they did not have flash photolysis so this is not a very good fit so what appears from this is that this analysis is not quite right the NIR UV pump visible pump NIR probe experiment analysis is not quite right because we expect to see that 730 femtosecond component because it has to be somewhere in some range it has to be there because it is there in time result PLA that is not showing up and this 4 picosecond component that is sort of sacrosanity in our minds that is becoming 2.5 when does that happen you know very well that there are 2 components you miss the faster one but the component that you see which should not have become faster appears to become faster and that does that happen when you actually have the slow component what you are not looking for it you understand what I am saying your it is a multi exponential decay right you are fitting to 4 exponential functions so it is not very difficult to lose one of the components but then it is there so what it will do is it will show up in some other component remember average lifetime sum over i ai tau i so suppose I fit instead of a bi exponential decay I fit to a single exponential decay what will happen I have a bi exponential decay of course it will not even fit but let us say just to understand the situation that I have a 4 nano second decay and I have a 2 nano second decay or let us make it more realistic 2 nano second 4 nano second 8 nano second 3 components are there I fit it to a bi exponential function and usually it will fit maybe i square will be a little bad I fit it to a bi exponential function what will happen I will not get 2 4 6 I will not even get 4 and 6 perhaps I will get a 3 and 5 or something like that so because I am not accounting for the genuine short component that is there the other components will also appear to be shorter than they are same is true for longer component okay so here is the issue here the important thing that comes is what we have discussed while talking about data analysis data analysis cannot be done blindly you cannot just take whatever comes out of the program you have to think that what should be the situation in your system and you have to use an appropriate model okay so the appropriate model they used was first of all they did what we have discussed towards the beginning of this course they did global analysis global analysis across this transient absorption in IR band so they took 21 decays so here the good thing is that you are recording the spectrum right so in principle you can take very large number it is because you have many pixels there so it took 21 decays and the fit to actually 6 components 5 components I think is wrong 6 components why 6 components because you expect that there are 5 components that you see from transient absorption and a 6th one from your fluorescence photo luminescence the fit to 6 components this is a mistake 6 components and also what they did is they fixed the lifetimes and this is where this can be contested one can say why are you fixing the lifetime you vary it globally but they did not do that instead of so they call it global analysis but what they have really done is that they have fixed the lifetimes whereas because transient absorption data as we know is not as nice as TCSPC data it may not be so easy to do proper global analysis using it especially in NIR but this is what they did they fixed the lifetimes 6 lifetimes and they did an analysis so what would change what are the variables here the amplitudes yeah the amplitudes are the variables so they got the amplitudes for different wavelengths and they plotted this is the plot of amplitudes versus wavelength we will focus only on the on C1 and C5 this is C1 right what is C1 associated with 0.73 picoseconds 735 second so as you see in the higher energy side from 900 to 1100 nanometer that amplitude is actually 0 then it rises to some value in the lower energy side remember lower energy side is dominated by holes okay we do not even have to go into the rest lower energy side dominated by holes so from there what they did is they assigned this 0.73 picosecond component 735 second component to ultrafast hole relaxation okay and that is only the beginning of the story. So what we have learned in this module is that handling data in this kind of situations is the most difficult part of the game recording itself is a challenge because you need good data without good data useless and that is why it helped that they had such a smooth absorption spectrum but what you do with the data that is actually what takes maybe 75% of time when you do experiments like this not recording data not preparing the sample so what they have done so far what we have discussed is that they have fitted their NIR data to 6 components coming from the visible probe transient absorption and PL and from here they have been able to get that earlier elusive 735 second component is assigned to ultrafast hole relaxation. And the next step is a closer look at the components themselves and that is what we are going to take up in the next module.