 In today's class on advanced characterization techniques, we are going to touch upon reflection high energy electron diffraction. In the last class, we had studied how does low energy electron diffraction works. I would like to mention that reflection high energy electron diffraction is a sister technique of low energy electron diffraction and shares a lot of principles in common with low energy diffraction. So as I had already mentioned reflection high energy electron diffraction is very similar to low energy electron diffraction. However, unlike low energy electron diffraction which essentially comprised of back reflection if you remember we had a source coming over here for x-rays and the sample position over here and we had this entire grid along with our screen position somewhere over here. So essentially it comprised of back reflection unlike low energy electron diffraction we are now going to talk about reflection high energy electron diffraction wherein we talk more about or rather we talk only about forward scattered electrons. As I had already mentioned if at all the electrons are going to scatter in the forward direction we have to ensure that the geometry of the electron beam that we are using is essentially grazing incidence geometry. Now the geometry that we are going to talk in reflection high energy electron diffraction is very similar to or rather same as that of what we used in grazing incidence small angle x-rays scattering. By now I hope you must have you know developed an understanding about how we play with the geometry of say x-rays or electrons or for that matter say even neutrons which we are going to talk about in a couple of lectures from now on to get relevant information or to achieve relevant diffraction condition. Talking about forward scattered electrons the major advantage that it offers is that it gives us a large elastic cross section at the same time it gives us excellent surface sensitivity that was precisely the reason why we had opted for grazing incidence small angle x-ray scattering over simple small angle x-ray scattering. So I hope you understand the geometries now we are going to use the geometry of you know grazing incidence for our own advantage in reflection high energy electron diffraction. Now as we had seen any technique that works with grazing incidence provides us important information about the surface crystal structure the orientation as well as the roughness of the surface as well as any adsorbate or any entity say thin film or quantum dots which are mean grown on the substrate. So we had seen earlier that you know the output of low energy electron diffraction was nice diffraction spots we could actually envision the reciprocal lattice in low energy electron diffraction. Similarly in reflection high energy electron diffraction we also see the reciprocal lattice however I hope you appreciate that the diffraction condition is relaxed in a particular direction and this precisely happens because the thickness of the film or the entity that we are talking about is very less. Now once we go to the reciprocal space the lesser distance in real space gets transformed into higher distance in the reciprocal space and therefore instead of getting diffraction spots we end up getting diffraction streaks in reflection high energy electron diffraction. Now similar to low energy electron diffraction where we had used the position of the spots the position as well as the spacing of the spots to decipher the structure we can use the position as well as the distribution of the streaks to find out the crystal structure of the entity under consideration. At the same time I should mention that the theory for reflection high energy electron diffraction is not very well developed though I am going to show at the very end of this lecture a couple of examples where we use you know the theory and carry out simulations for reflection high energy electron diffraction on a routine basis the theory is not as well developed as that for low energy electron diffraction and therefore generally we do not account for the intensity variation that occurs during occurs in the spots obtained in low or rather streaks obtained in reflection high energy electron diffraction. Another basic advantage that reflection high energy electron diffraction offers is that it can be coupled with any thin film growth technique for that matter with a technique like say molecular beam epitaxy to monitor the growth of the epitaxial layer in situ so wherein we can play with the deposition parameters at the same time by seeing how the thin film is growing. So this is one of the biggest advantage that reflection high energy electron diffraction offers in the processing as far as semiconductor industry is considered. So let us look at the geometry of reflection high energy electron diffraction as you can see over here the source is shown over here and here is our sample you can see that the electrons are incident at a very small angle I would like to mention that this figure is a bit exaggerated and this angle what I am showing with the normal is very close to 90 meaning this angle the angle with the surface is very very small. So once the electrons which are incident on the sample get diffracted from the surface we put a grid over here and give a negative voltage so that it repels all the inelastically scattered electrons and only the elastically scattered electrons are able to travel and hit the screen and give rise to the diffraction pattern. Another important thing that differentiates reflection high energy electron diffraction from low energy electron diffraction is the energy of the electrons. I hope you remember from our last class that we had used the energy electrons with energy of 20 to 500 electron volt in case of low energy electron diffraction. However when we go to reflection high energy electron diffraction we use energies in the kilo electron volt range. So we start with energies of the order of 5 kilo electron volt to a 100 kilo electron volt. I would just like to draw your attention to the fact and particularly at the energy levels that we are talking about. If you recollect we can use these energies in the kilo electron volt regime in a simple scanning electron microscope. At the same time the higher spectrum is for a very low kv transmission electron microscope. So I hope you appreciate that the essential thing or essential difference between reflection high energy electron diffraction and low energy electron diffraction is not just the geometry but also the energy of electron beam that we are using. As we had seen the incident electrons are directed at an angle which is almost normal to the surface that is the electrons are incident at grazing angle. These high energy electrons are restricted to the surface due to this very grazing incidence geometry. Now as I had already mentioned these electrons which are getting diffracted or scattered can undergo elastic as well as inelastic scattering. So we do not like the inelastic scattering because they contribute to background and therefore we put a grid and like similar to what we had in low energy electron diffraction give it a negative bias so that we get rid of all the inelastically scattered electrons and the diffraction or the elastically scattered electrons that are able to reach the screen they contribute to diffraction which is occurring from a very small thickness of the order of few atomic layers from the surface. So because of this relaxed diffraction condition that I had mentioned earlier the reciprocal points are replaced with reciprocal rods or rel rods. This essentially happens due to relaxation of diffraction condition in one particular direction. Now what are the consequences of the geometry we have already seen that you know everything is restricted only to a few atomic layers however another important difference that we had mentioned was the tremendous difference in the energy levels. So what does the energy level contribute to when we compare low energy or for the compare low energy electron diffraction and reflection high energy electron diffraction well the high energy used in reflection high energy electron diffraction leads to a very small wavelength of the electrons. I hope you appreciate that electrons at such a high energy can be easily considered as a wave. Now the basic importance that or the basic consequence that it has is in determining the evolved sphere radius. If you remember we had talked about this even in x-ray diffraction and during low energy electron diffraction that the radius of the evolved sphere is nothing but 1 over lambda or for that matter it is 2 by lambda. You can imagine that if the wavelength is very small the evolved sphere will be very very large. Now you can also imagine that if the evolved sphere is very very large the circumferential part of the evolved sphere can be as good can be considered as good as a straight line and that is what essentially happens say in a transmission electron microscope and similar things happen in reflection high energy electron diffraction. Now what does this you know flat nature or planar nature of the evolved sphere uses well it leads to diffraction at multiple points. This is essentially because the diffraction condition is satisfied we have more and more you know diffraction or reciprocal spots or for that matter in reflection high energy electron diffraction the rail rods or reciprocal rods lying on your evolved sphere and this leads to many diffraction spots separated by small angles in case of reflection high energy electron diffraction. So the image showing the actual you know geometry of the process is shown over here I hope you remember this is what corresponds to our you know planar reciprocal space where you have the 0 0 bar 1 0 bar 2 0 over here and 1 0 2 0 3 0 and so on. So here as you can see the evolved sphere which is shown over here having wavelength of 2 pi over lambda we see that the Bragg's condition is satisfied not at a particular point but at multiple number of rail rods not only that we get diffraction condition not only for the 0 0 but also for the 1 bar 0 spot we do not get either of them but most of the time we do get diffraction from the 0 0 or 1 bar 0. Now as you can imagine for such from such a figure that the diffraction condition is very very poorly defined and therefore it is very difficult if not impossible to do any quantitative estimate of diffraction from such a diffraction condition. Having said that these diffraction pattern obtained from reflection high energy electron diffraction comprises of streaks and not reciprocal spots. Now what information we get from this diffraction pattern that we are getting in reflection high energy electron diffraction well we get the periodicity of orthogonal to the diffraction plane using this the diffraction pattern that we get in reflection high energy electron diffraction. Now this information is essentially obtained by measuring the separation between the streaks and it can be easily for very small angles you know we can always determine it using the similar formula like your tan theta is equal to sin theta which is equal to s where s represents essentially your distance between the two streaks and l represents the distance between your sample and the screen a better figure is given over here and here you can clearly see what exactly I meant. So we have a situation where we have incident beam which is coming at a very small angle right from the surface of the sample and you see how we get diffraction you see the 0 0 spot the 0 bar 1 spot and the 0 1 plot you can see that in this plane of diffraction you do see a lot of streaks which are seen over here also now the distance between the streaks sorry for that the distance between the streaks is s which is given over here and what we figured out was that the angle what we are having in the plane is essentially proportional to s and the distance between the sample normal and the screen. So going back again we can clearly see that for information in normal direction eval sphere must intersect several red rods and that is what essentially happens now for a fixed wavelength if we increase theta you can ensure that the streaks will be replaced with a row of blurred spots now this essentially happens because over a diffraction condition itself is changing. So if you go back to the this figure you can see that this particular angle over here which is shown or you can say that the phi angle which is shown over here is changing and if the phi changes we can see that these diffraction spots are essentially changing and from this we can get information about the kind of symmetry we are having in the normal direction. So this is what we mean by changing the angle phi you see that instead of getting streaks we do get these blurred spots having said that this is a bit of an exaggeration and you can consider that you get only one of the lines over here so you end up getting only one such set now this therefore by varying this angle it is possible to obtain intensity as a function of this angle now this is very similar to rocking curve now I would like to remember we did not touch upon rocking curve essentially but what we do in rocking curve again we have to go back to x-ray diffraction and if you go back and if you remember in rocking curve all we end up doing is we go at a particular 2 theta we fix the 2 theta get a peak and now we vary omega right just to ensure that what all how is what is the quality of the crystal or thin film that we have grown. Similarly here also by changing the phi angle all we are trying to see is what is the quality of the crystal or the thin film that we have grown on the surface. However there is a considerable effect of dynamical diffraction is that that is what was happening when we talked about getting rocking curve in case of thin films using x-ray diffraction. However as we see again that as rather I had mentioned earlier the theory of reflection high energy electron diffraction is not very well developed. In fact there are some groups who claim and rather it is I will show at the end of the lecture some calculations which account for dynamical diffraction but having said that this is more of a qualitative technique rather than you know getting quantitative information from reflection high energy electron diffraction and therefore the results are slightly difficult to elaborate. So as I had mentioned and the entire focus of going for reflection high energy electron diffraction is that the technique is highly surface sensitive and as I had already mentioned the theory is not as well developed as low energy electron diffraction and does not account for multiple scattering events. Having said that it is also characterized by plenty of inelastic scattering events and therefore quantitative estimate from reflection high energy electron diffraction has not achieved as widespread use as that for low energy electron diffraction. As I had already mentioned that one of the biggest USB that reflection high energy electron diffraction has is concerned with its ability to be incorporated in thin film deposition techniques. So the biggest advantage that reflection high energy electron diffraction offers is that we can actually monitor in situ during deformation the kind of layer or rather the kind of film that we are growing not only the kind but also the quality of the film that we are growing. Now this gives us a lot of advantage particularly for industries for semiconductor industry where they are very interested in growing the thin films of very high quality. Here in Reed offers a very robust tool where you can do in service monitoring of the quality of the thin film which gives us a very handy tool to play with the processing parameters. Now this also ensures that there is no need of doing post processing characterization. Now this makes life much easier for process engineer. So as I had mentioned the biggest advantage of reflection high energy electron diffraction is in thin film deposition setup. Now the basic advantage of reflection high energy electron diffraction is that it can be incorporated in any thin film deposition setup for say something for various deposition techniques like MOCVD or molecular beam epitaxy. The biggest advantage that it gives to semiconductor industry is that you can really monitor in situ the quality of the film that we are trying to grow. This gives the process engineers a wonderful tool to play with. Therefore they do not have to do process optimization after the processing has been done. Instead we can monitor the evolution of the thin film under consideration while the thin film is growing and we can control the quality of the thin film which we are going to get. Therefore this is the case where reflection high energy electron diffraction gets the maximum importance. A schematic showing the actual assembly having a thin film deposition technique as well as reflection high energy electron diffraction is shown over here. As you can visualize generally reflection high energy electron diffraction is used only as a qualitative tool to determine the kind of films that we are getting. And therefore you can understand that during the processing of thin films there is no way we are going to stop and do entire analysis from the reflection high energy diffraction pattern that we are going to get. And hence generally in most of the practical applications reflection high energy electron diffraction data is essentially used to get qualitative information about the quality of the thin film. A brief comparison between low energy electron diffraction and reflection high energy electron diffraction is presented over here. As we had seen reflection high energy electron diffraction offers much better access to sample while collecting the diffraction data that aids in observation during growth. This is the biggest USB of this technique. Having said that the we have the ability to monitor layer by layer deposition of epitaxial films using reflection high energy electron diffraction. I am going to show you some data at the end wherein we see how we can go as small as you know 4 or 5 mono layers and obtain precise data, precise qualitative data from reflection high energy electron diffraction. And as we had seen earlier it is integrated with thin film deposition techniques like molecular beam epitaxy and used on a routine scale in semiconductor industry. However there are some disadvantages that reflection high energy electron diffraction has over low energy electron diffraction and that include the quality of the diffraction pattern that we get is not as good in case of reflection high energy electron diffraction. Having said that in order to obtain complete information about the film in the plane or the symmetry and the structure of the film in the entire plane we need to rotate the sample because if you remember we had got information only in one direction. In order to get complete information in two direction we also need to rotate the sample. However this will give us a lot of information about how exactly the quality of the film is in the plane. Another important thing regarding the geometry of reflection high energy electron diffraction is enumerated over here in this figure. So this is very similar to the earlier figure that we had seen but this clearly shows that how exactly we get diffraction from different spots and on the real screen each and every spot over here corresponds to a particular you know any diffraction spot corresponds to a reciprocal spot in the which in turn is again related to a real lattice point in the diffraction pattern. So here we see the zeroth law is on of the film under consideration and how it gets reflected or rather manifested on the read screen. Again similar to what we had seen earlier the distance between the two spots as I have shown over here is proportional to a star which is nothing but the reciprocal lattice parameter and L where L is nothing but the distance between the screen and the law way zone. I would like to remind you that this entity that we have shown over here is essentially in the reciprocal space. So let us not get confused if you remember we had got parameter S by L and that is what was equal to R. So the same equation that we had got only differences in this case I have represented everything in terms of the reciprocal lattice vectors. And this is why do we do that do the you know aforementioned exercise is to essentially simulate the read pattern that we are likely to get. So here in you can see the kind of read pattern that we would obtain for a silicon 001 peak in 100 or rather this is the silicon 001 crystal in 100 direction. So you can see depending on the different you know zone access you get these all spots which you are getting over here and these can be indexed. Now below is given an experimental read pattern. So just by qualitatively comparing these two patterns we can see that what are the diffractions that we are getting in the silicon film and from this we can comment about the quality of the film. I would also like to mention that here you can see there is only one spot and there is a bit of streaking but here you see there are two spots and this is what I had shown you earlier. Now this is one of the aspect that happens over here right. So you see instead of having just one spot you are having two spots. So this is what happens essentially because in experimental condition the diffraction criteria is relaxed in one dimension. Having said that I have just showed you how we can get a qualitative estimate. Now let us go ahead and see what all we can do using reflection high energy electron diffraction. But before we do that if you remember in low energy electron diffraction we had seen we had considered different you know unit cells and we had seen how they will look like in the reciprocal space. We can do a similar exercise for reflection high energy electron diffraction. But what differentiates read from low energy electron diffraction is that instead of having diffraction spots we do get diffraction streaks and this is what is shown over here. So you see different lattices and how they will look again this time also there in the reciprocal space. But because of the geometry of reflection high energy electron diffraction how do they get modulated. So mind you this is your real space which is shown over here. This is your reciprocal space right and this is how the pattern will look in reflection high energy electron diffraction. So let us go back and this is why I had shown you this figure where actually I showed that you know how your reciprocal lattice which is shown over here gets modulated into your read pattern which is shown over here. So the same concept which when you can extend see this is something that we had covered in the last class. And we saw that what actually happens is since here B is greater than A your B star is lower than A star which are the reciprocal vectors. But what we get in reflection high energy electron diffraction is not actually this means in low energy electron diffraction we got all the spots right over here. But here no because of the grazing incidence we do get a streak pattern and this is how the pattern looks like. Now similar example for different unit cell configurations is shown over here and these can be easily computed. Now let us go and look at some real examples. So just to show you the read sensitivity or I have given an example of growth of gallium arsenide by molecular beam epitaxy on a silicon substrate. So here you see this oscillatory pattern right you have this oscillations which are dying off. And you see here you see that the gallium shutter is open and after the particular amount of time you switch off the gallium shutter or you close the gallium shutter and you see as a function of time you see that the there is damping of the oscillations. Now what does these oscillations correspond to? Well these oscillations actually give us information about the surface disorder. Another important thing that I had mentioned that each oscillation this each oscillation corresponds to each high intensity you see over here the intensity each oscillation or each high intensity actually corresponds to one single atomic layer. So you can imagine the sensitivity of reflection high energy electron diffraction. So here in we have a very simple technique which gives us information about deposition of single atomic layer mind you single atomic layer and here another thing that we can see that the intensity is gradually reducing. So now when does the intensity of diffraction reduce? Well when most of the material that is being deposited is not satisfying the diffraction condition and therefore we can conclude that with increasing time there is a decrease in intensity which essentially indicates that the defects which are incorporated or which are getting incorporated in our gallium arsenide films are increasing with the deposition time. Now this may affect the quality of the film and we may not get finally good quality epitaxial films. So here in we have a situation or wherein we can monitor in situ the quality of the film and control it and use this information that we are obtaining to control the process parameters. Another important example is for deposition of germanium on silicon. Now this is a classical example where we are going to look at a case wherein we are going to use simulations also. So there are certain groups who have developed you know something similar to what the simulation tools that we had seen in the last class for low energy electron diffraction for reflection high energy electron diffraction also. So in this case we are depositing germanium by evaporation on a silicon 111 7 x 7 substrate. I would like to remind you that the 7 x 7 substrate is essentially you know a substrate on which there is restructuring of the first 7 atomic layers because of the dangling bonds. Having said that the read or reflection high energy electron diffraction was carried out on the germanium deposition at 18 kilo electron volts and here in also you see that how the oscillatory nature is seen experimentally. Now what all things we can do actually you see it is silicon 111 and you see the incident electron beam is at 112 direction and at an angle of 1.2 degree to 112 what essentially happens in the actual experiment is shown over here where the angle was varied to 7 degree and here we see that there was damping of oscillations after 10 monolayers of germanium and what we could do was actually incorporate these things in the simulation and obtain a good match using between the simulations and the experiment using a particular parameter. I will not go in details of how exactly it is done because that is beyond the scope of this class but I want to just impress upon you that there are certain groups who claim that we can do not just qualitative but rather a semi quantitative analysis using reflection high energy electron diffraction. Now this is again another classic example from a paper by Chen Etten. So in this case there was growth of a epitaxial gold crystal on titanium that is TiO2 substrate. So that is where read is of very very great use to us because read offers us not just information from the thin film or a quantum dot that we are growing but also from the surface under consideration. So here you see nice specular pattern as well as normal diffraction from the titanium. Now as we grow you see that some additional spots appear. Once we try to index it we do see that these corresponds to FCCAU. Not only that if you look at the pattern in detail which is shown over here you can go back and assume a particular shape of your particle that is being grown and back calculate the diffraction pattern from it and if you see that there is a good match between the simulated diffraction pattern and the obtained diffraction pattern we can believe that the not only the shape but also the size of the epitaxial gold particle that has grown on the titanium substrate. So this is how you know I talked about you know getting qualitative information from read and here in I am presenting how we can get a lot of quantitative estimate not only about the shape but also the size of a single particle using reflection high energy electron diffraction. So this is one technique which is you know growing very fast. So as I had mentioned we always end up getting some diffraction from the substrate. So this may be used in a very advantageous way as I showed you in the last example. However having said that in most cases it contributes to reduction in intensity it also leads to additional spots in the diffraction pattern and it is best suited for monitoring thin film just a simple qualitative way and other simple qualitative way rather to get more quantitative information things are a bit involved. But having said that there is no technique which comes even closer to reflection high energy electron diffraction when it comes to semiconductor industry where it is used on a routine basis for growing epitaxial films using metal organic chemical vapor deposition or molecular beam epitaxy. Another important thing now that we saw in case of low energy electron diffraction that at the end of the day we are having a electron beam and if you remember we had also used low energy electron diffraction to get some images. But having said that the energy of electrons in low energy electron diffraction was very small 20 to 500 electron volt. Now we have energy as high as a low kv transmission electron microscope. So what we can do essentially is actually use this high energy electron beam to get convergent beam electron diffraction. So here again I have shown you different geometry. So you see what kind of geometry we are having over here when we are doing normal reflection high energy electron diffraction beam is not at all converged. However if we want to do convergent beam electron diffraction as we do in a TM what do we do we take the electron beam and using the voltage of the lenses we actually converge it. Now what are the advantage that we get well we do get a smaller probe not only that this is equivalent to getting a rocking curve information and you see unlike the read pattern that I had shown up till now here you can see these nice lines. Now these lines are in fact the same thing that we get in a convergent beam electron diffraction and carry information about the symmetry that is existing in the entity under consideration. And here in we can clearly see for a silicon 0 0 1 2 cross 1 substrate that there is a mirror symmetry and what actually we are seeing in this particular slide is actually the higher order Laue zones and what we see here in this particular example is the half order Laue zone that represent the super lattice discs from 2 cross 1 domains of silicon 0 0 1 which clearly indicates that there indeed is a mirror symmetry for this reconstructed surface. So you see we started from normal reflection high energy electron diffraction and understood that we are not going to get much of quantitative information and at the end of the lecture I have contradicted myself and presented to you what all quantitative information that we can get from reflection high energy electron diffraction however it is to be mentioned that one needs to take a lot of care before extracting so you know such in depth information from reflection high energy electron diffraction. So to summarize we have seen that reflection high energy electron diffraction offers excellent in situ monitoring tool it is very simple and inexpensive however it provides information only in one dimension. If you want to get information in say the entire plane of the paper or rather in the plane of the sample we need to rotate the sample. We have also seen that how it can be embedded in thin film deposition techniques like MBE and MOCVD and can be used on a routine basis it gives us a rapid simple qualitative analysis we have also seen that we can get information not only about CBED bus but also rocking course however these things as I had already mentioned are very difficult to analyze but it is something that can be done using reflection high energy electron diffraction. Having said that I should also mention that one of the biggest disadvantage of reflection high energy electron diffraction is that it is very sensitive to the surface roughness and therefore it is very important to see what kind of sample we are using and therefore it is very very useful only for in situ growth. Having said that I hope that I have been able to present you how does electron how can we use electron diffraction to get similar and at times even better information than what you obtained using x-ray diffraction. In the next class we are going to just change slightly the course of our training and go from diffraction and scattering we touch upon scattering but we leave aside diffraction for some time and for one lecture we go and study about spectroscopy then we again come back and do neutron diffraction till then have a good time thank you.