 Welcome to this material characterization course. In the last class, we just looked at the concept of scanning electron microscopy functions and this basic instrumentation and its controls and operator controls and so on. We will continue this discussion and then we will look at much more details about the electron beam specimen interactions and what is that is going to affect your ultimate resolution and its effect on image in general imaging. So, if you look at the controls which I talked about yesterday, we will just quickly review this. We just started looking at the operator control in SEM of lenses. We have three primary parameters, one of them is the aperture. So, this schematic clearly shows that if the final aperture which basically controls the probe diameter which finally impinged on the sample by controlling this objective lens and this is what we just summarized here. The optimum aperture angle that minimizes the aberration on the final probe size. The final convergent angle controls the image depth of focus. The aperture determines the current in the final probe because only a fraction of the current sprayed out to the angles alpha 1 passes within the aperture angle alpha a. So, if you look at this, the initial spread of current, this is what it is mentioned here, the current sprayed in alpha 1 eventually its controls by this aperture and then it makes alpha a, this aperture angle and eventually it controls the probe size. This is one of the primary parameters which is in control of the operator and then we can see the next one the working distance. We also define this, what is the working distance? It is the distance between the final aperture and the specimen surface and you can clearly see this effect of working distance from these two schematics. It is quite evident that if you increase the working distance you are increasing the the probe size. You carefully look at it, you can see that the probe size is increased now and obviously it will have some significant effect on the resolution. So, we summarize this, increase in working distance produces a large spot size at the specimen and which will cause the degradation of the image resolution and also you see that convergent angle decreases which will result in improved depth of focus and increasing working distance will also cause weakening the objective to focus at a long working distance W which eventually increases both the focal length and the aberration of the lenses. So, which is very clearly shown in the schematic and which also increases the scanned length and which will cause reduction in the magnification as well. So, this is again a very important parameter which an operator can have a control on this and then take an appropriate decision depending upon what we are looking at, what information we are looking at on this specimen surface. The third one is the condenser length strength which operator can control which is also is nicely shown in the schematic. If you increase the condenser length strength which increases the demagnification of each lens which will cause again the reduction in the probe size. So, you can see that effect very clearly from the schematic. So, this is the first schematic is for a given field strength if you increase it further you can see that the final probe size is completely reduced. You can see this, this is the initial probe size with for a given field strength, but if you increases from that and you see that there is a control of the probe diameter. So, the final probe size can only be reduced at the expense of decreasing the probe current and a conscious choice between minimizing the probe size or maximizing the probe current must be made for each imaging situation. So, this is exactly I was just mentioning that all these parameter controls has to be done as per the requirement for the appropriate information we are looking at from the specimen and it is completely in the user control. So, now we will move on to the probe diameter which we yesterday we quickly reviewed I just want to give an emphasize on the probe diameter again because whatever we have just seen before ultimately the parameters controls a probe diameter which results in the complete resolution as well as and its effects on the imaging process. So, to fully understand how the probe size varies with the probe current we need to calculate the minimum probe size and the maximum probe current. Say in idealized situation the aberration free Gaussian probe diameter Dg which is the full width at half maximum height of the intensity distribution of Dg is given by Dg is equal to square root of 4ip divided by beta pi square alpha p square. The current in the final probe can be estimated as ip is equal to square root of beta pi square alpha p square and Dg square divided by 4. If there were no aberrations in the system it would only be necessary to increase the convergent angle to increase the probe current at a constant probe diameter. See why we talked about this Gaussian probe diameter because this is the one which we will start with to mathematically quantify assuming there is no aberration at all but eventually that is not going to be the case. You are going to have the effect of each aberrations which we talked about in an electron optical system and then we can see how this Gaussian probe diameter is modified because of this aberrations that is what we are looking at finally is a real probe diameter. So, if you look at the minimum probe size involving all this aberrations calculations of the probe size assume that Dp is quadrature sum of the diameters of Gaussian and other aberration discs. You look at this expressions there was a little bit of typo which was there in the yesterday's presentation I have made the corrections. You see that Dp is equal to Dg where Dg is Gaussian probe diameter and Ds square spherical aberration diameter plus Dd square this is a diffraction disc plus DC which is chromatic aberration whole to the power half. At normal voltages sorry I just did a mistake this is not whole to the power half it is square. So, Dp is equal to Dg square plus Ds square plus Dd square plus DC square whole to the power square. At normal voltage of 10 to 30 kilo volt the relationship between the probe size and the probe current can be calculated at alpha optimum which is D minimum is equal to k Cs to the power half lambda to the power 3 by 4 times Ip by beta lambda square plus 1 whole to the power 3 by 8 where Cs is the spherical aberration coefficient. Here only considering this aberration this expression is valid the it is assumed that other aberrations do not have a significant influence on that circumstances this expression is valid. Maximum probe current at 10 to 30 kilo volt you have the I max equal to 3 pi square by 16 times beta into Dp to the power 8 by 3 divided by Cs to the power 2 by 3. So, it is a kind of a maximum resolution one can obtain in the presence of other aberration effects. Now we will look at the plots where the relationship between the probe current and the probe diameter using a tungsten thermionic source. You see in the beginning we just looked at all the the electron gun sources I just mentioned there are two types one is thermionic source another is field emission source. So, this how this probe current and probe diameter varies with the tungsten thermionic source versus the field emission source is shown in all these four plots. You can carefully look at it this the probe diameter which is varying from 1 to 100 nanometers versus probe current which is a normal imaging condition and you can see that you have these thermionic field I mean thermionic source and as well as you have the field emission source. Obviously, you can see that field emission source exhibit a superior probe diameter for at the given 30 kilo volt which is a normal imaging and then you have another low kv imaging you can see that similar plots are obtained and the plot C shows very low voltage imaging where you can see that how the probe current varies with the probe diameter and this is kind of a plot where mostly this kind of situation is used for the chemical analysis and you can see most of this plots shows that the field emission gun source exhibit superior diameter compared to the thermionic source and then it also varies with the as a function of operating voltage just to give you an idea how this electron sources controls the probe diameter as a function of operating voltage. We will look at this aspect in the imaging and its resolution and so on in the due course. So, now we will look at the much more detail about this the probing current and so on it is usual to define the primary beam current I0 the backscattered electron current IBSE the SE current is ISC and the sample current transmitted through the specimen to the ground is ISC such that the Kirchhoff current law holds. So, the primary beam current can be S can be represented as a summation of IBSE plus ISC and we are interested in the signals which is coming out of the samples. So, basically how they are quantified we know that a secondary electron signal and the backscattered electron signals are going to come out from the sample and how they are quantified this is what is about we will see. So, these signals can be used to form a complementary images as the beam current is increased each of this currents will also increase the backscattered electron yield eta and the secondary electron yield delta which referred to the number of backscattered and secondary electrons emitted per incident electron respectively are defined by the relationship where eta is equal to IBSE that is the backscattered electron current divided by I0 similarly the secondary electron yield delta is ISE divided by I0 both the secondary and backscattered electron yields increase with decreasing glancing angle of the incidence because more scattering occurs closer to the surface because more scattering occurs closer to the surface. This is one of the major reasons why the ACM provides an excellent topographical contrast in the AC mode. As the surface changes its slope the number of secondary electrons produced changes as well. This point we just discussed in the introduction of the ACM class as well. I just mentioned why only these two signals BSE and SE for widely used in ACM that is because only these two signals vary as a surface modulation or surface slope changes very sensitive to the surface unevenness with the backscattered electrons this effect is not as prominent since to fully realize it the backscattered electron detector would have to be repositioned to realize realize it the backscattered detector would have to be repositioned to measure the forward scattering. This is an operation detailed for detecting this signal we will see how it is being actually done in the lab. See another important aspect of this ACM we mentioned is a depth of focus and this set of micrograph clearly illustrated that aspect. So, what you see here is A this is a machine screw viewed at under the optical microscope and this is under scanning electron microscope. You can see that in an optical microscope you do not see any of this detail when you look at the screw from the top you can see the all the other the circular details of the screw and C and D are taken with the sides of the screw you can see that the much more clear details are obtained using scanning electron microscope this is just to illustrate that effect you have a very high depth of focus and you by now you know that why we get very good depth of focus the another set of micrographs illustrates the effect of both secondary electrons as well as backscattered electrons. What you are seeing is it is a let in alloy surface is some what we are seeing as bright as an eutectic let in eutectic people who do not understand this metallurgy of this you can assume that there are two phases and you can clearly see that this particular micrograph is obtained at 25 kV and this micrograph of the same region is obtained at 5 kV and these two are obtained using secondary electrons and the same region was imaged using backscattered electron in this image C. So, I would like you to look at this three images little more carefully and what is the difference you are seeing and if you are able to figure out the differences then that means you have clearly understood the previous information what we have discussed and if you are not able to catch that differences I will help you you look at this the scratch here scratch mark here and look at this scratch mark here. So, you see that these two are up even though they are obtained using the secondary electron signals there is a small difference and also you see that this scratch is not at all visible as clearly as in the micrographs obtained by secondary electron signals. So, that clearly indicates that your secondary electrons are much more sensitive to the surface unevenness and the difference between this A and B is because of further complications because of the electron specimen interaction what is that you see that this micrograph is obtained at lower kV 5 kV and this is obtained at 25 kV. So, if you recall we just discussed in the beginning of this lecture probably yesterday or day for yesterday I had mentioned that the higher the operating voltage the severe will be the beam specimen interaction and then you also produce Se1 Se2 and Se3 and these signals will get produced more if the electron beam specimen interaction is intense and when this Se2 and Se3 signals they are not going to promote the topological details in fact when they come out of this specimen they are going to interfere and reduce the resolution that is what is happening here you can see that the scratch details are not as clear as what you see in the image B. So, it is not that if you keep on increasing the operating voltage you are not you are going to obtain much more a clear image there is an optimum voltage and other parameters under which circumstances you get the much more clear picture. So, this is just to explain that phenomenon and what you see in other images I mean this figure D is a EDS spectrum and E and F are maps elemental analysis maps and these particular about the spectroscopic details we will discuss later in a separate lecture series right now my focus is only on the SEM imaging we will talk about this elemental analysis and how it is done and what are the limitations with existing spectrometer and so on we will discuss in a separate lecture series. Now we will just summarize what we have just looked at in the previous slide the spatial resolution of the SEM due to Se1 usually improves with increasing energy of the primary beam because the beam can be focused into a smaller spot but at higher energies the increased penetration of the electron beam into the sample will increase the interaction volume we will quickly see in few minutes what is this interaction volume about which may cause some degradation of the image resolution due to Se2 and Se3 this is shown in image figure B which is a secondary electron image taken at only 5 kilo electron volt in this case the reduced electron penetration brings out more surface detail in the micrograph and if you look at the method of producing the backscattered electron image there are two ways to produce BSE image one is to put a grid between the sample and the secondary electron detector with a negative voltage that is minus 50 volt bias applied to it if you recall when I just introduced the instrumentation schematic where I said that if you put positive voltage it will collect both BSE and SE if you put negative voltage it will ripple and then it will collect only one so similar thing so that is the bias this will ripple the SEs since only the BSEs will have sufficient energy to penetrate the last electric field of the grid this type of detector is not very effective for the detection of BSEs because of its small solid angle of the collection we will look at the detector system and its details little more as we go along and this right now we are just discussing about how this signals are collected and how what are the immediate effect of these two individual signals on its image formation a much larger solid angle of collection is obtained by placing the detector immediately above the sample to collect the BSE two types of detectors are commonly used here one type uses partially depleted n-type silicon diodes coated with the layer of gold which convert the incident BSEs into electron hole pairs at the rate of 1 pair per 3.8 electron volt using a pair of silicon detectors makes it possible to separate the atomic number contrast from topographic contrast the other detector type the so-called Sinclair photo multiply detector uses some material that will fluoresce under the bombardment of the high energy BSEs to the produce a light signal that can further amplified so these are all some of the specific operations of the type of detectors which eventually give the image in CRT we will look at this detectors separately and we will talk about all the functions much more detailed in the view course the photo multiply detector was used to produce BSE micrograph in figure C what we have just seen in two slides before since no secondary electrons are present the surface topography of the scratch is no longer evident and only an atomic number contrast appears atomic number contrast can be used to estimate the concentrations in binary alloys because the actual BSE signal increases somewhat predictably with the concentration of the heavier element of the pair so this point is about the material detail and what do you have to understand is BSE is sensitive to atomic number that we will anyway we will talk about much more detail when we discuss the image contrast and contrast mechanisms and so on now we will divert our focus to very important aspect of imaging that is electron beam specimen interaction in it involves lot of physics as scattering physics we need to understand this clearly then only you will be able to interpret all the images which we are going to see so I would like to request all of you to pay much more attention to look at this particular section this is more fundamental it may be very difficult to understand in the beginning but if you look at them again and again and if you are finding it difficult to follow this I request you to go through some of the basic physics book about the scattering phenomenon and then come back to this section then things will be all right so as the beam of electron enter the specimen they interact as negatively charged particles with the electrical fields of the specimen atoms the positive charge of the protons is highly concentrated on the nucleus while the negative charge of electrons is much more dispersed in a shell structure the beam electron specimen atom interaction can deflect the beam electrons along the along a new trajectory which is considered elastic scattering causing them to spread spread out laterally from the incident footprint I am going to show you some of the schematic regarding this to understand the point 3 what we are now talking about so the elastic scattering after numerous events actually result in beam electrons leaving the specimen process called back scattering it gives a kind of a definition for back scattering that is the elastic scattering after numerous events actually result in a beam electrons leaving the specimen a mathematical description of elastic scattering process at angle greater than a specified phi naught as the form q which is greater than phi naught is equal to 1.62 into 10 to the power minus 20 times z square by e square cot square phi naught by 2 so this is events scattering events greater than phi naught divided by the electron which is atoms per centimeter square where q is called the cross section which is in centimeter squared for elastic scattering that is probability of elastic scattering which is given in this form the distance between scattering events is known as the mean free path lambda is calculated from the cross section and the density of the atoms along the path where lambda is equal to a divided by n naught rho q which is in centimeter a beam electrons lose energy and transfer this energy in various ways to the specimen atoms which is nothing but inelastic scattering see you see in an SEM we get a characteristic x-rays for chemical analysis like we discussed in the beginning the basic fundamental physics of that event is what we are now discussing this the beam of electron lose energy and transfer this energy in various ways so one of the ways is like you know you are getting a characteristic x-rays and you have SCEs BSEs and all the signals solve basically inelastic scattering this transfer takes place gradually so that the beam electrons propagate through many atom layers into the specimen before losing all their energy so this the loss of energy of the electron beam is not going to be a instantaneous so it will be more I mean the you can see that how some of the models are being made for this how the electron beam is losing energy which I will show you in few minutes will from that you will get an idea how the electron beam after impinging on the specimen surface loses energy gradually as a function of interaction volume inelastic scattering gives rise to useful imaging signals such as secondary electrons and analytical signals such as such as x-rays Bethe described in 1930 the rate of energy loss DE with the distance traveled DS as DE by DS the energy is given in kilo electron volt and the distance is in centimeter which is equal to 2 pi E square n naught into z rho divided by AEI ln 1.66 EI by J where J is equal to 9.76 z plus 58.5 z to the power minus 0.1 into 9 into 10 to the power minus 3 where n naught is equal to Avogadro number the rho is the density z is the atomic number A is the atomic weight EI is the electron energy at any point of the specimen J is the average loss in energy per event it is just this expression simply tells you how this energy loss takes place and how we can visualize quantitatively with all this variables I just want you to appreciate that point rather than getting into the details at this mode. So you can see that two plots which are based on this Bethe equation how the energy loss due to inelastic scattering is calculated you can see that plot A is energy loss due to inelastic scattering calculated with the Bethe equation at intermediate and high beam energies for all these elements and the plot B is the comparison of energy loss at low energy as calculated for silicon with Bethe expression and others. So how this energy loss occurs as the function of electron volt. Now what you are going to see is we will look at what is this interaction volume and the electron beam comes and interacts with the specimen surface and what you are now seeing is the simulation is the interaction volume for a 20 kilo electron volt beam striking the silicon as calculated with a Monte Carlo electron trajectory simulation it is a numerical simulation and what you see is you see that there are thick black line and then very light black lines which just getting inside this specimen to the order of volt few microns. So this is happening in a three dimensional so let us try to understand how this happens this is you can see that this is another schematic showing that this kind of interaction volume is interpreted through an etching experiment in terms of contours of the energy deposited in the specimen as calculated with the Monte Carlo simulation. So the left hand side is how the energy varies as a function of depth using an etching experiment. What is this etching experiment? People have taken some of the low atomic number of materials like poly methyl methacrylate kind of specimen and then they just do an etching experiment within a bombardment of electron how it just I mean damage this molecular and polymeric molecules and then how it that intensity of the damage decreases from the surface to the core and that is done with that model that is called etching experiment and then the left hand side is the experimental measurement how the energy varies from the surface to the core in a three dimension and the right hand side is the same thing is done numerically through Monte Carlo simulation and then you get some kind of very close agreement with this. So the important point to appreciate here is you get a kind of an idea what is an interaction volume is and how it occurs three dimensionally and what are its dimensions. So it gives you a kind of a basic outline about an interaction volume and please remember whatever we are just showing is not it is only a static images and actually it is happening dynamically between the interaction between electron beam and the surface and I will just show you few more schematic which you have the excuse me. So I would like to show this as a function of electron beam energy versus interaction volume you actually what you will see that the as the electron energy increases the interaction volume also will increase and somehow this simulation is not working right now. So you can see that the same effect of atomic number also you can see influence of atomic number on the interaction volume you can see it for different material here it is a carbon and this is for a carbon K shell and then you have the iron and then you have the iron K shell. You can also see that as the atomic number increases the linear dimension decreases that is very much understandable because the that is because your scattering cross section varies as the atomic number increases. So you can see that the linear dimension also decreases in accordance with that number and you can see that a similar another systems same effect for a silver silver L shell and then you have uranium and uranium M shell and so on. So what I try to tell here is depending upon the atomic number as well as the the energy of the electron beam which is impinging on this sample your interaction volume is going to change and the scattering physics involved is little more complicated and this has got a significant influence on your image resolution and the kind of details one can get from the specimen surface that is all I just want to emphasize here and then we will look at the the scanning action how how this the electron beam is scanning the surface and how exactly the image is formed all those details we will see it in the next class. Thank you.