 Hello everyone, in today's class on advanced characterization techniques, we are going to study low energy electron diffraction. Now an electron diffraction is something that we have encountered in earlier section of our course, wherein we studied diffraction in a transmission electron microscope as well as in a scanning electron microscope for a technique known as electron backscatter diffraction. However, in today's class we are going to focus on a completely new technique or a rather a completely different technique known as low energy electron diffraction which is used to characterize the surfaces of crystalline materials. So talking about leads, low energy electron diffraction is essentially used for atomic structure of surfaces and the first experimental observation of low energy electron diffraction was given by an experiment carried out by Davison and Gremer way back in 1927. However, the evolution of the field took quite a few decades and it was not until 1970s that leads was used as a surface characterization tool in laboratories over the world. So as we already know as the name suggests rather this essentially corresponds to diffraction from electrons with low energy in the range of 20 to 500 electron volt. We are aware that once the electrons interact with matter that leads to elastic as well as inelastic scattering. The inelastically scattered electrons get lost if the penetration depth is higher within the sample. However, if the penetration depth is only few surface layer then the electrons that are getting diffracted do carry a lot of surface information that can be utilized to get an idea about the structure of the surfaces. We will try to see how essentially it works out in the next few slides. But before that let us first compare X-ray crystallography which we had covered in the last 3 or 4 glasses with lead crystallography. So as we all are aware of X-ray crystallography essentially deals with bulk structures right while lead crystallography essentially deals with surface structures. I would like to emphasize that X-ray crystallography can be used even to get information about the surfaces. However, the major focus of X-ray crystallography is on bulk structures. Another important thing is that we do not need a particular sample preparation technique or rather a particular sample preparation condition for carrying out X-ray crystallography at the same time any arbitrary sample shape can be used in X-ray crystallography while we need extremely flat and oriented surfaces for carrying out lead crystallography. Surface impurities generally do not play an important role in X-ray crystallography while they are very very important in lead crystallography. Generally, X-ray diffraction experiments are carried out at ambient temperatures and conditions. However, we need ultra high vacuum for carrying out lead crystallography. You are also aware that for X-ray crystallography the diffraction condition is satisfied for a particular wavelength or a particular angle depending on the condition of Bragg's diffraction. However, the diffraction conditions are pretty much relaxed and they get satisfied at almost all energies and angles when it comes to low energy electron diffraction. We had seen that in normal X-ray crystallography kinematic theory of diffraction generally works out and at the same time we can generally neglect the absorption with the exception of grazing incidence small angle X-ray scattering. However, when we come to low energy electron diffraction we have to deal with dynamical theory of diffraction and which also accounts for huge amount of absorption in case of low energy electron diffraction. And the basic difference between say something like say X-ray crystallography is that it gives us 3D information while a lead crystallography gives us 2 dimensional information of the lattice. Having talked about it, let us go back and try to revise how actually diffraction takes place and this is something that we had covered in the very first class wherein we saw that we have for every lattice we have a corresponding reciprocal lattice associated with it. During diffraction we use a particular wavelength which decides the diameter of the evald sphere and all X-ray diffraction or for that matter all diffraction techniques are based on orienting either the crystal or the evald sphere in such a manner so that the diffraction condition is satisfied. However, as you can easily visualize from this image which we had seen earlier diffraction is essentially a 3D phenomena. However, since we are dealing with surface structures if we jump from 3 dimensions to 2D we do see the same construction in 2D and this figure also we had again seen and here in we see the evald sphere and the limiting sphere which is a larger sphere and the condition for a diffraction in 2 dimensions. However, the situation is not as simple and a real picture of this is given through taking a view of the reciprocal space. So, in this case we have taken a section of AG 111 surface that is the section of the 111 surface illustrating accessible range of XRD in grazing incidence mode which shows the red part. Here in this is our evald sphere and you can imagine that you can always draw a sphere comprising of consist with diameter twice that of the diameter of the evald sphere which comprises of the limiting sphere. However, what lead essentially offers us is this dotted view or rather the dotted circle essentially shows the region which can be viewed the region of the reciprocal space that can be viewed with low energy electron diffraction. So, we can see that part of the region which is not accessible through grazing incidence XRD diffraction is essentially available through low energy electron diffraction and this is what is the USB of this particular characterization technique. So, as we can see with the change in wavelength with the increase in energy there is a decreasing wavelength and therefore an increase in the diameter of the evald sphere. So here in this figure we can clearly see that the information given by lead is completely different it is shown here by the green arrows or the green lines over here. So, this is this part or this view of reciprocal space is provided by lead while the red part the red region shown red lines shown over here is essentially provided by normal grazing incidence XRD diffraction. There is another technique which is known as spot profile analysis low energy electron diffraction or what is known as SPA lead which gives us information about exactly perpendicular to the plane and here in we can get a lot of information about the dimensions of the features on the surface along the z axis. We will talk more about it in the next few slides. Let us try to understand how exactly two dimensional diffraction works. So, you can imagine that once you move from 3D structures to 2D surfaces the reciprocal space essentially transforms to something like a reciprocal plane. So, instead of having a space group we do have a plane group we are aware that there are 32 point groups in 3D and there are 10 point groups in 2D. When you talk about space groups we have something like 230 space groups in 3D and 17 plane groups in 2D right. So, the obvious question arises is that when we are looking at say 2D patterns of films or islands which are on the surface are we seeing the 2D structure well the answer is not really true because we are not seeing the existing 2D planes. Instead we have to keep in mind that lead is a two dimensional projection of 3D lattice and therefore, we are not restricted to the 17 plane groups or 10 point groups in 2D instead we are left with 80 dipyrolic space groups. However, the good news is most of them or rather all of them have been accounted for and there are tables like we have tables for all these 32 point groups and 230 space groups even the crystallography community is quite aware of the 80 dipyrolic space groups which are existing and this information can be used to characterize or rather to index the obtained diffraction pattern. Talking about how exactly the diffraction occurs in 2D this is just the extension from the figure which we had shown a couple of slides ago. So, here we can have two cases or rather two conditions when it comes to low energy electron diffraction we can have a normal incidence wherein you can see that your incidence wave is perpendicular to the lattice over here at 000 at the same time in one case we can have incidence which is not normal which can be seen over here in this particular slide. So, here we can see that if the incidence is not normal we can we do get a diffraction however this diffraction component can then be classified into a parallel component the component which is parallel to the surface and a component which is perpendicular to the surface. So, this way you can imagine that there are two implications or rather two conditions wherein we can have either normal incidence or we can have non-normal incidence in low energy electron diffraction. Now, this is very similar to what we have in case of x-ray diffraction so the concept remains the same only thing the implications are slightly different. So, talking about how exactly diffraction occurs let us go back and look at the diffraction in three dimensions. Now, this we are this equation we have come across plenty of times in the last few classes. So, the Bragg's law we know that you know n lambda is equal to 2 d sin theta having said that we know that how do we derive to this formula we get and calculate we go and calculate the extra path length that the light that x-rays have travelled. In this case it is ab plus bc and we know that if the extra path length or the path difference if it is an integral multiple of lambda we do get constructive interference and we essentially we end up getting diffraction therefore we have n lambda is equal to 2 d sin theta. However, when we come to 2 d we see that the diffraction occurs in this way having said that we see that this is restricted only to the plane only diffraction occurs only in one plane. There is no diffraction in the third dimension and therefore the Bragg's law gets modified into the 2 d form as a sin theta is equal to n lambda. In this particular figure we have given we have shown the actual thing the projection of the Ewald sphere. So here again we can see that instead of having a complete space group we are having a plane group and therefore instead of getting a criteria for diffraction or deriving the structure factor in terms of hkl we are just restricted to h and k depending on the geometry of the figure you can see that you can derive the Bragg's law for 2 d plane condition in such a with this particular equation. So this is very similar to our normal n lambda is equal to 2 d sin theta stuff because you can imagine that this particular term 2 sin theta cos theta plus phi essentially accounts for the incident angle and once taken on this side this particular tel h square plus square root of h square plus k square essentially tells us the distance something which is very similar or analogous to the interplanar distance between the two atoms in case of Bragg's law. So we are all aware and I hope we have understood by now that essentially what we are seeing or what we expect to see in low energy electron diffraction is nothing but the actual reciprocal space corresponding to the 2 d lattice under consideration. So this is again the slide which we had covered that any crystal structure comprises of crystal lattice and unit cell content and the diffraction pattern associated with it has a reciprocal lattice and a structure factor. So if we have a particular crystal structure with the you know the unit cell and the atoms sitting over it we do get a diffraction pattern which is related in a particular way. So what we are going to actually see in low energy electron diffraction is actually the same thing. Now the beauty of low energy electron diffraction is that we are essentially looking at 2 d structures. So we can really look at a 2 d structure in real space and visualize it in 3 in 2 d reciprocal space. So I will just give an example. So something like 111 plane in FCC which has been shown over here. So you can literally calculate it how we can do that. So I hope you remember the formula for calculating reciprocal vectors like A star is equal to B cross C divided by A dot B cross C. So you can extend a similar formula and calculate the entire reciprocal space. Now what actually happens in low energy electron diffraction is that you actually see this and this is what I have shown. So this is what we calculated and this is what you can see over here. So in this case we see a low energy electron diffraction pattern of silicon 111 7 x 7 deconstructed surface. So you can see the symmetry gets directly reflected in the reciprocal space. Having said that up till now I have just focused and showed you like what all we can do on the surfaces like looking at the structure of the surfaces and all. But there are other important things for the entire branch of surface chemistry that deals with absorption and desorption of various chemical entities on the surfaces. So low energy electron diffraction can be used not only to study the structure of the surface but also to study the structure of the adsorbate as well as the substrate. So here I have shown you a classical example wherein we have a substrate which can be characterized by basis vectors of A1 and A2 and adsorbate. Now the adsorbate are sitting at a particular location and if you draw the adsorbate lattice you end up getting a basis vector of B1 and B2. So this is what is actually existing in the real space. Now how what can you expect in the reciprocal space? So again we go about and construct the reciprocal lattice of the substrate and then construct the reciprocal lattice of the adsorbate and then we know that you know what diffraction pattern we are going to get is going to be essentially a superposition of these two reciprocal lattices and this is what we get as a result of this existing structure. Having said that what actually happens in an experiment is that we get we do start from something like this the diffraction pattern and then we kind of go back and essentially derive the structure but the point that I want to emphasize is that we can do a lot of surface chemistry related studies using low energy electron diffraction. However an important point that needs to be noted that what all we are talking about till now has gives us is only essentially qualitative information that we have obtained. There are quantitative results that can be obtained through leads through by lead but we will talk about it later. Let us now talk about the instrumentation aspect. So talking about lead one of the most striking feature about low energy electron diffraction is the simplicity of the instrument. We talked about small angle x-ray scattering and grazing incidence small angle x-ray scattering in the last two classes and we saw that they involved a lot of instrumentation right and hardware. However low energy electron diffraction as such is very very easy and this can be seen over here. So all you need is a nice electron gun which gives you electrons with the energy in the range of 20 to 500 electron volts. Now this is much lower than what we have you know say a TM or even a scanning electron microscope. So we need a small electron gun and a vacuum chamber wherein we keep the sample. The vacuum chamber also comprises of G1, G2, G3 which are nothing but the grids at different potentials and the screen to obtain the signal of electrons after diffraction. So essentially the electron gun releases electrons on the samples, the electrons get diffracted partly G1 is the grid which is essentially grounded while G2 and G3 are kept at a negative potential to ward off the inelastically scattered electrons and only diffracted electrons go back and hit the screen and this electrons what we are getting we do observe them using a external detector. So as I had already mentioned we need the instrumentation part is very very easy and all we need is electron gun, hemispherical grids, a screen and a detector. Now the electron beam has to have energy of about 20 to 500 electron volt with current of 10 nanoamperes to 10 microamps. Another important point is we do need a very strong magnetic shield to expel residual magnetic fields and the sample has to be focused for hemispherical grids. The elastically scattered electrons which carry all the diffraction information have to reach the screen while the inelastically scattered electron constitute the background and they have to be kind of reflected off this is achieved by giving the lens G1 ground while lens G2 and G3 are kept at a negative potential. Now what all pattern is forming on the screen can be obtained on a photographic film or a video camera. Now one of the important condition for getting for carrying out successful low energy electron diffraction is that the sample surface has to be extremely clean at the same time lead uses information only for crystalline materials which undergo diffraction. We can use lead to detect various adsorbate at the same time you can appreciate that if at all there are some defects like steps or kings on the surface or for that matter if there is some kind of relaxation occurring on the surface we do can capture this information using low energy electron diffraction. Therefore electron diffraction certain features like irregular steps lead to blurred or streaky pattern while kinged surfaces lead to additional spot or spots in different direction of the step direction. So I would like to emphasize that when you talk about irregular steps or kinged surfaces essentially we are talking about atomic level of irregularity or kinking. So this kind of ability to really study the structure at atomic level is provided by low energy electron diffraction only. So we have seen the kind of result we get with low energy electron diffraction wherein we see nice spots now there lies a wealth of information in the shape and distribution of diffraction spots obtained in low energy electron diffraction. The spot intensity and position correspond to the structure factor well this is what we had agreed that actually what we see in low energy electron diffraction is the reciprocal space. At the same time this spot profile can give us a lot of information about the defect structure this is what we saw that the irregular steps lead to blurring and streaky pattern. Therefore we can see that the spot position as well as the spot intensity and profile carries a lot of information about the surface structure of the material under consideration. We can see that low energy electron diffraction offers us qualitative information about symmetry of surface structures. It also gives us information about size and orientation of adsorbate with respect to substrate it gives us quantitative information of the atomic positions on the surface from IV plots. This aspect we are going to cover in the next few slides I would like to mention that this is a very involved topic and we are going to just touch upon this aspect and see that what all we can do with IV plots rather than knowing how we can do surface structure analysis using IV plots. Another technique that I had mentioned earlier which was the spot profile analysis low energy electron diffraction it gives us information about the lateral and vertical lattice constants of surf of say islands on the substrate. It also gives us complete island dimensions and reduced however it has a problem that the screen size offered by SPA lead is much lower compared to conventional low energy electron diffraction. Therefore depending on our need we can choose either the lead option or the SPA lead option. I would also like to mention that one thing that we should keep in mind that since we are using electrons for diffraction we can always use the same electrons for imaging purpose and just use our simple low energy electron diffraction setup as a electron microscope and to get some image to get an electron image and go to the region of our interest and then try to get diffraction from that particular region. Another important point that needs to be discussed is we talked about just single or diffraction event occurring which leads to formation of the reciprocal space. However as we had mentioned earlier that low energy electron diffraction comprises of dynamic scattering from various layers of atoms. Now this makes it necessary to account for intensity of the spots it is therefore necessary to determine the amplitude and phase of the diffracted beam. However we know that the phase of the beam cannot be determined using a detector. However the intensity still gives us a lot of information and this is achieved by using a CCD camera in the low energy electron diffraction setup. So just to illustrate how does dynamic diffraction occurs. This is the classical 2D diffraction that we had seen in the earlier slide. However when we go and have a dynamic event we do see that the diffraction occurs not only from the surface but also from another level or the another plane. Now depending on the kind of things we are having that if you have adsorbate on the substrate so we can get diffraction not only from the adsorbate atom on the substrate but also and substrate atom which is below the adsorbate. So you can imagine that these multiple scattering events are similar to what we talked about in grazing incidence small angle x-ray scattering. So this essentially ensures that our bar approximation of single diffraction is no longer valid and we need to modify it extensively. Now this dynamical scattering can be caused because of ion core scattering because of multiple scattering as we had already seen in elastic events like the ones that I had mentioned earlier and at the same time it can occur because of surface vibrations due to temperature. We will come to it and we won't go in details and try to find out how exactly this all happens but all this carries important information on the interlayer spacing in terms of like what is the adsorbate and the substrate interlayer spacing the height of the adsorbate atoms as well as relaxation phenomena like how relaxation is occurring on a free surface. Now this can be obtained as I had already mentioned by measuring the intensity as a function of incidence angle and incidence energy we know that if the incidence angle and the incidence energy changes there is a change in intensity. So by systematically studying the variation of intensity as a function of incidence angle or incidence energy we do can get different conditions of dynamic diffraction and then derive back the structure in details. So here in this image I have just given you a glimpse of how actually we can compare kinetic versus dynamic low energy electron diffraction. So here in we see that if at all we are getting kinetic diffraction we see a nice periodic variation of intensity. Now this essentially occurs I hope you occurs because of only single scattering event. Now all these peaks that you are seeing essentially corresponds to spot right all the diffraction spots and if you plot the intensity of it and get intensity versus your energy peak versus energy curve you see that we get a nice periodic pattern. However if there is dynamic diffraction you see that there is a lot of noise in the diffraction pattern. Now the trouble is it is much easier for us to kind of you know assume a particular structure and reproduce the diffraction pattern using single diffraction single scattering event. However when you talk about dynamic scattering event I hope you can see that each peak over here corresponds to a different scattering event something what we had noted down over here and all these events have to be accounted for in order to reproduce this kind of a diffraction curve. And I hope you appreciate that once we are in the dynamic low energy electron diffraction regime getting information about the structure is very very difficult. Having said that one thing that cannot be disputed is that the dynamic lead carries a lot more information than a kinematic lead or lead occurring due to kinematic diffraction. Therefore it is very important to see what is the effect of theta as well as that of energy on the intensity. So here in I have just shown the effect of energy on the beam intensity. So this is for copper 1 0 0 1 0 0 surface and here in we can see that all the peaks that we are having over here did not only change their position but also their profile. So look at this peak which is at around 100 we see that with the change in our incidence angle which is shown over here you see that not only the peak position is shifting you can see here the peak position is shifting. In fact even the peak profile is changing now this essentially indicates that as we change our incidence angle we are not only getting a change in the kind of in the intensity of diffraction or just the structure factor in fact we are getting additional scattering events. Now all these scattering events are to be accounted for when we try to back calculate the structure from the low energy electron diffraction data. So again to go back all these kind of electron rather scattering events the multiple scattering events that are likely to occur they have been tabulated and are well known. So actually once we get this kind of a pattern our job is to essentially assume a structure and then consider all these diffraction events and try to reproduce this diffraction pattern. However this is much easier said than done and as we had already seen that we use borne approximation of single scattering for kinematic lead. However for dynamic scattering if we start looking at all the events that are occurring it becomes very difficult and therefore we follow a particular strategy wherein we consider the hierarchy of diffraction. So at the lowest level we have the atomic scattering wherein we get scattering from the substrate from the adsorbate atoms right so that is the atomic scattering or for that matter diffraction from the first atomic layer so that corresponds to atomic scattering. The second level of hierarchy is the layer scattering right so if you have an adsorbate on a substrate the diffraction occurring from the entire adsorbate that corresponds to your layer diffraction. However depending on your energy or your angle of incidence you can also get diffraction from the crystal itself or the substrate itself. So again going back you can see here that is what seems to be happening that as your incidence angle is increasing we see that you know there is merging of these peaks you have a peak which essentially first disappears and then again it reappears. So what exactly is happening so you can understand we can try to understand it in terms of hierarchy of diffraction and get some idea on it. Now when we actually get the low energy electron diffraction data we account for all these events to model that data. Now our entire job once you get this your spectra is to obtain or rather a simulated spectra which shows a good match with the experimental spectra. However having said that it is very difficult to kind of compare to spectra and therefore we use what are known as r factors to quantitatively compare the spectra and there have been two strategies which have been used till date they include mean square deviation and penderi r factor. So I need not emphasize much on mean square deviation where we see that you know that the mean square deviation is minimum in the simulated and the experimental pattern while in penderi r factor approach we see that the location of maximum is more important. I won't go in details but I would just like to emphasize that what we are trying to do is we assume different diffraction events at corresponding to different hierarchies and try to simulate the diffraction pattern or the diffraction spectra. However we do see that there are lots of parameters that have to be used to fit the spectra and to know how good our fit is we do use these two strategies. Now our r is a function the r factor which I showed is a function of many of many parameters and deciphering the exact structure though is possible is very very complicated. However there are some advances made in data analysis and one of the latest advantage or one of the latest advancement is what is known as tensor lead wherein the computational effort required is reduced drastically. Now in case of tensor lead what essentially we end up doing is that we start with a reference structure and perturbate it to get exact IV curves the intensity versus voltage curves. So this essentially ensures that we start with a structure and perturbate it and to get some idea about the IV curve and once we get an exact match according to the r factor we are we get sufficient information about the structure of the surface. I am not touching upon and going in details of data analysis in this part because it is too involved and is beyond the scope of this particular lecture. However I want to emphasize that essentially we can get a lot of information regarding not only the condition of the surface but also a lot of information about the adsorbate on it not only the kind of adsorbate but also the orientation of adsorbate using low energy electron diffraction. So there is to do all this data analysis there are dedicated softwares which are available so I have just listed down one of the lead calculation home page wherein you can go and take your data and do the calculation. But calculation of your structure from low energy electron diffraction is a field in itself and it requires a lot of analysis and understanding of the diffraction processes occurring in two dimensions in various materials. So just to summarize I would like to emphasize that low energy electron diffraction provides surface and adsorbate size and symmetry. It is very good or a very sophisticated tool to study in situ processes like temperature effect and reconstruction and relaxation phenomena in crystalline materials. It provides information from the top 1 to 10 atomic layers and can account for all the surface reactions which are occurring in different materials. However the presence of defects like kinks and ledges can complicate the simple diffraction pattern that we had calculate that we had envisioned from the derivation of the reciprocal space. The IV and I theta curves which gives us the variation of intensity with the voltage or the incidence angle have a lot of information about the not only the structure and orient but also the orientation of the adsorbate and the surface but they are very complicated and need a much careful analysis to get to derive any important information. Thank you.