16. The SUPREM IV Process Simulator

Key Takeaways

Get started. Just a couple of reminders. Um homework number four is due today up up front. You can bring that up at the end of the hour. Um homework number three is going back. I've got it in the back there in that orange folder. So, you can pick up your homework before the uh before you leave today. And there are a couple people who haven't picked up prior homeworks, and they're in the back of that orange folder. Um we've got one hand handout for today. That's handout 27. Um today we're going to be talking about the Supreme 4 process simulator. This is where we are, November 2nd here on election day. And you're handing in homework number four. Uh the solutions to homework number three are you're getting your graded homework number threes back. The solutions will be on the web later today. And I'll bring hard copies um next time. They They didn't get printed um or Xerox uh in time. Okay. So, let's go on to handout number 27, which is today's handout for today's lecture. The uh this this handout or this lecture is on so-called the {quote} {unquote} introduction to the Supreme 4 process simulator. Now, you've already really been introduced to it. Uh fortunately, you've been using it uh for the last couple of homeworks in your homework sets. And And your TA uh introduced it uh in in sort of a practical sense uh number of weeks ago when she gave she gave a lecture when you had your first Supreme homework. But, I want to talk about it in a little more um detail and maybe give you some some examples of what it can do to give you give you an idea. Um So, um the first In the very first lecture lecture, we discussed an example of a CMOS process flow. And we drew a series of cartoons, you know, sort of PowerPoint uh artist's conception of what things would look like. At this point in the class, at this point in in in the class, we've covered some of the fundamentals and the modeling of a lot of the key processes in that CMOS flow. We've talked about thermal oxidation, diffusion of dopants. We've just had four lectures on ion implantation and transient enhanced diffusion. And we've talked a little bit about how these processes fit together. So, today I want to review some of these concepts and some CMOS process modules and CMOS flows. Now, in the context of what we know about models and in the context of using the Supreme Force simulator. This is just an example of an n-MOS FET and a p-MOS FET fabricated on a wafer. This was the cartoon that we showed earlier in the in this course in the very first lecture. And what we can do today is we don't need to use cartoons anymore. As you know, you can use the Supreme Force simulator to generate this this type of information reasonably accurately. So, let's go on to slide number two. And I have a series of examples I wanted to go through. Now, some of these things since you've already run the simulator, you may be familiar with, but we'll go into some some things you may not have seen. The first three are 1D. Supreme um Supreme 4 is can be run is a two-dimensional simulator, but it can be run in a one-dimensional mode where you're primarily interested in what happens in depth. But in general, you'll run it in 2D mode, but to run things quickly, to understand basic physics concepts, it's it's often easier to to run the simulator in 1D mode and then later on run a two-dimensional example. Obviously, when you do it in 2D mode, you have a lot more calculations to do and it's a lot slower. So, first I'm going to talk a little bit about boron segregation at at a gate oxide silicon interface and and compare a couple issues. And And using this as an example for you to understand a little bit about gridding issues that can take place when you use the simulator. It's a very prac- practical issue of um uh keeping an eye on on the the um how fine your grid is. The second example we'll talk about um comparing some arsenic and phosphorus implant profiles uh the different types of profiles um to actual SIMS data. We'll see which ones do a better job at actually um simulating uh or or reproducing what the data looks like. And then we'll talk about diffusion models. Introduce the different types of diffusion models that are uh that are available. And these are again, these are three uh 1D. The last example, I hope we have time, is a 2D example of um kind of an older technology. It's a It's a 200 nm gate length N MOSFET. Just to go through um uh some of the uh processing of that. So, let's go on to slide number three. This is an example and I if you've already done the homeworks, you've probably seen this. This is an example of what's called the mesh or the grid. And um Supreme 4 uses a a triangular grid, triangular mesh. So, it's a series of non-overlapping triangular elements. You see each one of these, if you look at it carefully, it can be uh drawn as a triangle. Uh the mesh is very important um because what we do in the mesh or the grid is that we Supreme 4 tracks the values of all parameters numerically. Um along a moving adjustable grid. So, at these nodes, at these grid points, it's tracking the values of all important parameters. Um the uh interface, what the material is, the interface between two materials, it tracks um the dopant concentration value. A lot of different things are are each are tracked at each grid point. Uh if you look at this grid, so this is a grid that that belongs to uh a device structure. Let me see if I have uh in the next slide. Uh that's a blowup. Yeah, let's just go a little bit of a blowup on on slide number four. You can see the grid a little bit better. Um this this belongs to a device structure where uh over here on the on the left-hand side, there's actually a gate. There's a polysilicon gate. There's a spacer, and if you can see, here's a gate oxide. And there's some metal up here, and this is the silicon. This is an ion implanted and diffused junction. And you say, "Why does the grid look like it does?" Why would it look like this? You see, in this region here, near the channel and near the surface, um you see a fairly fine grid. The mesh is very is very um fine. The spacing between the grid points is very small. Whereas, you get down here in the silicon substrate, and the mesh is very coarse. The spacing between points on which you do the solution is very is very large. So, why would that be? Does anybody have any idea why up here I would use a fine I would have a fine grid, and down here I have a coarse grid? Because the current density is changing rapidly. Right. Because it up here at this at the junction, you probably have some doping profiles that are changing very rapidly in depth. So, you need a lot of grid points to maintain good accuracy and and good fidelity in reproducing those uh those those profiles. Down here, there's really not much action. Probably just constant doping of boron. So, there's no need to have very fine mesh. The computer even today's computers are only so powerful. So, Supreme tries to do intelligent gridding and not waste and put in a lot of grid points where you don't need it. If you use a very fine mesh everywhere, you'd say, "Well, that's the best, right? Make it fine everywhere." Problem with that is you'll never be able to um it it would take too long to do the solutions, and it's it's a really a waste of time. Um so, just going back to slide three, this is exactly what we just said. The grid needs to be fine near the active device region, near the interface, or where anything any quantity of interest is changing very rapidly depending on what you're interested in knowing about doping profiles, interstitials, vacancies, wherever they they change rapidly, you need um a fine grid. Um for diffusion uh very often supreme does a finite difference solution for oxidation. It uses a finite element type of technique. Again, both on on this grid. Okay, uh let's go on to slide number five. Actually, I probably should have shown this first. This is the actual of that um that mesh that we just showed, this is the actual device structure. Uh it's half of an N-MOSFET. And now it becomes pretty obvious what you were looking at in terms of the grid. The yellow here is the silicon. This is the polysilicon gate. Um the blue is the gate oxide. This is the an oxide a spacer a sidewall spacer on right next to it. Um there's a metal contact here to the silicon. And this is the uh sort of LOCOS region or the isolation region uh in between devices. This is either the source or the drain and you can see contours here corresponding to arsenic um arsenic doping. So, this is the actual um structure. Very often in supreme um things are symmetrical. So, another way besides doing intelligent gridding, uh if you have a symmetrical device, you can often only simulate half of it and then just project that uh uh about the center about the center line here because the device the MOSFETs are very often um symmetrical in the way they're fabricated. So, sometimes that that helps you save save time in the simulations. Again, once you start it we haven't had may had you do very many two-dimensional simulations, but once you start doing them, you'll see how much time it can take to uh to simulate all these diffusions, especially if you're doing the most sophisticated models. So, you have to take advantage of uh sort of intelligent uh gridding. I want to start on slide number six. Uh the first example uh now, which is a simple one-dimensional um example at that looks at the behavior of boron and how it it behaves and segregates at a an oxide silicon interface. And this this is a supreme four input file. As you know, you all of you who've done your homework, supreme four takes text files as input. You can write the text in any text editor you want as long as it doesn't leave a lot of spurious characters that confuse uh the program. And the program has a parser that reads in the text and interprets the text in terms of the commands that are that are that supreme four knows about. Um whenever you see dollar sign, of course, that's just a comment. So, supreme ignores that. So, this is only for your own notation. So, the first um the first command here is called the mesh command, and it it tells you that a parameter called grid.fact equals .04. And the grid factor has to do with the fineness of the grid. The smaller the number, uh the finer the mesh. Um and um so, we're defining in this one statement uh what we want to make uh the default uh sort of mesh size uh in in a uniform sense. Uh .04, it's not uh in units. Um I think it it's a multiplier. So, I think it can be anything from one to 10 to maybe .01. Um if you look up in the supreme manual, it'll tell you. I I don't remember the exact definition of grid.fact, but um when grid.fact equals one, it gives you a certain grid spacing. My experience has been that for most modern devices, a grid.fact of one is it's a pretty large spacing, larger than we would would probably want to have. I think I have some examples where we've varied this in here, so we can look for the different grid.facts, and you'll see how how it comes out. The next thing is pretty simple. It says an initialize statement. This is just create the silicon substrate. That's all it does. It tells you the orientation in the Z axis is 100. Um so, that's the the the the orientation of the wafer and that's boron doped and it's 1E17 uh per cubic centimeter. And again, if you need to know um things like boron equals 1E17, you wonder what the units are, if you go into the supreme manual, it'll it'll tell you what the default units are for any variable. This is an implant statement. You you just did a homework um on ion implantation uh where we're implanting boron. So this is the species. This is the dose, number of atoms per square centimeter, the energy, uh and uh that you're specifying a tilt angle of 7°. Um depending on the dopants, there will be different default models. Uh a lot of the dopants default to the Pearson 4 model. Um if you don't know the words, if you don't say what model to use, it automatically uses default Pearson 4. Uh I think arsenic uh defaults to dual Pearson. It You have to look up in the supreme manual and figure out what the default is if you don't specify. So remember, just because you didn't say a model, supreme has to assume one of the models. And so that's the default model and you need to become familiar with what that is. Um this is uh this statement here is depositing is a deposition statement. So it's not a growth. It's not thermal oxidation. It's literally depositing oxide uh just by plunking it on the surface. You're not consuming any silicon. And we haven't talked about this type of process before, but it's called chemical vapor deposition. The next several lectures we'll talk about that. So this is not thermal oxidation. We're just plunking an oxide down at a at a certain temperature, 600, and we're telling it the thickness in microns, 0.005 uh micron. So it's very thin. It's it's 50 angstroms. DY If you look in the supreme manual um under the deposition statement for oxide, DY tells it the thickness the uh the grid spacing in the Y direction that you want to use in the oxide. So DY is the grid spacing specific to the oxide. And look how small it is. It's 0.0001. Well, the reason it's so small is because the thickness is so small. You don't want one grid point in the oxide. You'd like to have several. So, we're telling it what what what the gridding to use just in the oxide. So, after and then there's a simple statement in which you select what variable you want to plot. In this case, you want to plot the log 10 of boron. You can do some fancy, you know, put in titles and all that stuff. The save file command uh saves the file in a format that SUPREM can then later use, read in, and use later on. It's not necessarily a format that you would find very useful, but SUPREM uh uses it. So, save file into an out.file is uh defines which file you want it to write to, and this is picking a name we chose, b1.inp. You can put it wherever you want. Here, you're simulating uh the diffusion. So, this is um uh simulating diffusion uh for a time of 17 minutes at a temperature of 850. And if I specify an inner ambient, it's just like a diffusion like in argon or nitrogen. If I specify dry O2, then you're actually doing an oxidizing. So, oxidation is done, as you know now, by using the diffusion statement and specifying what type of ambient, wet O2, dry O2, whichever. And then the then uh after this amount of diffusion, 850 for 17 minutes, you're going to plot what the profile looks like of the boron after that. So, we have an as-implanted plot. Um and we have a certain line type and and color. Here, color number one. And we have after diffusion at uh 17 minutes at 850. This is a simple file. It's the type of file that you've been uh using that your TA has been creating for you and you've been running them. Now, we want you to start to understand what those files do so you can create them and modify them yourself. And remember, you can always go to the SUPREM IV manual to look up any of these commands. Deposition, select, save file, all those are are explained in the manual. So, this is the output of that file on slide number seven. Uh this is what it it looks like. Of course, I've doctored it up. I've added a little color and things to make it look a little better, but it's the basic output. What it that file plots out is a plot on the Y axis is the boron concentration. Um the X axis is distance. And Supreme assumes that zero it puts zero at the original silicon interface or surface, I should say. So, if you deposit um layers on top of that, they will they will be sort of on the negative X axis. Uh remember we deposited 50 angstroms of oxide. That's what I'm showing in the yellow here. If you go back 1 minute and you look at deposition oxide thickness is 0.005 microns, that's 50 angstroms. Um so, that's what this is from here to here in this yellow region. And there are two um profiles uh that are shown here. The the the black one, the dark one is Supreme plot of the boron profile immediately after ion implantation. So, that's the as implanted. Um and the red one is the boron profile um after that anneal that we did, 17 minutes the inert at 850. Of course, it's diffused. It the peak is gone down a little. It's broadened out and there has been a little bit of segregation at the um oxide silicon interface. Uh the diffusion of boron in oxide is relatively slow. It's about a factor of 2,000, roughly factor of a thousand slower than diffusion in silicon. So, you see a fair amount of motion of the boron in silicon, but when it hits that wall, hits that oxide, it doesn't diffuse very fast. So, you're not going to get you you see in the in the silicon there's very little boron after a 17 minutes has actually um diffused in. If you want to know the segregation coefficient, you can look it up in the appendix. They have an appendix in supreme 4 for each of the dopants um for boron segregation, which is the ratio of the concentration of boron in the silicon to that in the oxide at 850. Supreme calculates it from this formula. Uh you can modify either one of these constants, by the way, if you want to. And uh I calculated out about a factor of uh 10 to 1 or 0.1. Um so that will be this peak value to the value in the oxide. So that's that's sort of what that simple file puts out. Now let's look at um uh a couple of other uh special cases. So we're going to now do uh something similar, but instead of depositing the oxide straight down by deposition uh from chemical vapor deposition, we're going to form the oxide by thermal oxidation. Uh this is the type of model that we've talked about uh before, and we're going to display the output here on on slide number um eight, I'm showing a a new supreme um input file or command file. And this time, instead of saying deposition, we're going to say to do a diffusion time equals five, that's five minutes, at temperature of 850 in dry O2. So it's it's going to grow five minutes worth of oxide at 850 in dry O2. And then we're going to plot it using color number two. Then we're going to do another five minutes and plot it again. So we can do sequential, so that'll be after after 10 minutes. Um so you can look at it and see how the oxide grows and see what happens to the boron profile as the oxide grows. So we're going to display it at five, 10, and 17 minutes. We're going to display the boron profile in the oxide. So this is after on slide number nine, this is after five minutes of now thermal oxidation. Uh we have uh an initial oxide that's formed. And um this this is what the um uh the boron looks like. And you notice the boron near the surface has been depleted again because of that segregation and the Now you're oxidizing, so you're consuming silicon. So you're moving moving into the silicon. Uh this interface is moving towards the right. And um same segregation as the previous case and now we have a little bit of um boron that's been incorporated in the silicon. Not so much by diffusion cuz again, but by consumption. Cuz you remember we initially implanted with boron and then you start oxidizing. If you go back to the command file, um uh reading the as-implanted structure. So, remember um what we we did a save file of the in uh of b1.imp. How did I get that? Well, that save file So, this is a way to just keep save time. After we did the as-implanted, um we saved the file in something called b1.inp. And then we're going to call it back later that same file in uh a subsequent uh uh supreme run. So, here I'm loading in a file called b1.imp. If you didn't want to do that, you could repeat the simulation of the implant. It's not going to take very many minutes, but if you have a a complex two-dimensional simulation, you might as well save it. You know, it takes an hour to run, save it and you can always use it again as the input to another supreme simulation, another diffusion and or oxidation. Um okay, so we are going to in this here on back on um slide number eight, uh we're going to uh load that in, take whatever oxide was on there off just to make sure it's not there, and and diffuse it at 850 uh for 5 minutes in dry O2. We're going to grow uh grow a couple different um thicknesses of oxide. So, I've consumed this and that's how long the boron has gotten in there and you see the segregation from this point from here to here. That ratio is about a factor of 10. That's what we expect. Uh because we said K not per segregation of boron in supreme four is about a factor of 10. Go to the next slide, slide number 10, after another five minutes, so we have total of 10 minutes of oxidation. Um, again, you you see now you're you've you've grown a little more oxide, the yellow is thicker, and you've consumed more of the boron, and the segregation is causing this effect. Uh, so this is not really diffusion because the diffusion, look how rapidly the boron drops. If it were diffusing fa- it were diffusing, this would go straight through the oxide, but it's not. Cuz there is slow boron diffusion in this assumption, um, in the oxide. You can see the boron profile in oxide. If we finally go um, to the last, which is after the full 17 minutes, we have grown now uh, 50 angstroms of gate oxide at at 850 in 17 minutes. Um, and the red is what it looks like the boron looks like due to thermal oxidation. You see a lot of the boron has been incorporated into the oxide because of segregation effects and consumption. Um, the black is as implanted, so that was how it was as implanted. If I thermally oxidize it, I get the red curve. You can see it's depleted at the surface, and it's piled up in the oxide. If I instead of thermally oxidizing, let's say I didn't want to grow my gate oxide, I just deposit it. 50 angstroms at 850, the boron profile is quite different. It's the blue. So, why is that? What? So, there's two different cases here. In the case of if I do an implant and I thermally oxidize it, I consume silicon, and I suck some of that boron into the oxide, and then it segregates by segregation. So, you see the boron, uh, concentration is relatively low at the surface. If instead of thermally oxidizing, I just implant the boron, place an oxide down there by, um, a chemical vapor deposition process, um, then I get, uh, I don't consume any of the silicon, so the boron stays a lot higher. So, I have about a factor of two more boron at the surface. So, you can imagine you would get different device characteristics due to these slightly different ways of forming this oxide and it has cuz it has an impact on the boron profile by different diffusion uh diffusion coefficient is the same, but it's really different segregation and the fact that we're in one case we're consuming silicon, in the other case we're not. Okay, that's just a simple example. I had to use You see all these little points. So, I had to use a really fine grid in order for you to see this uh this effect. So, look So, let me talk a little bit about that grid.fac uh and the gridding. Uh for when you have very shallow profiles, which is mostly what will what you're doing these days and for CMOS and thin oxides. Oh, okay. Here here we go. This gives us the answer. Uh use if you use the default grid um then um it it the grid spacing is about 0.1 micron. So, there's about 0.1 micron That's That's actually uh bigger than a lot of devices. So, it's it's it's much too uh much too crude. So, um uh we can multiply that by a small number like the grid.fac and make that grid spacing much much smaller. So, um in this particular example, I'm showing you where we did that same implant of boron uh and then 850 70-minute oxidation with a grid.fac of 0.4. Um it's still very coarse. You can see this doesn't look really have much of a shape to it. There's a point here where we solved. There's a point here. There's a point here. But, it is it is it's just very um very jagged looking because the grid is too coarse. And in fact, in the oxide you're getting almost no detail or information at all because you really don't have any grid points in the oxide. You got one at the interface and one at the surface. Uh so, for this particular example, a grid.fac of 0.4 is way too crude. So, this This something you always want to check by doing a quick test. Well, what kind of a grid do I want? If you go on to the next slide, slide number 13, here's a factor of 10, finer grid. Grid.fac of .04. Um, still it looks pretty good. Now it's starting to look like a smooth curve. It's not all jagged looking and it has a shape that you would imagine could be associated with diffusion and ion implantation and diffusion. But the oxide grid in the oxide is still too coarse because the oxide is thin. It's only on the order of 10 to 50 angstroms during this oxidation. So I'm only getting what one point in the oxide. I have one at the interface, one in the oxide and one here. That's still not enough. Um, so if we go down to go to the next slide, slide number 14, and as I'd mentioned before, we use this particular statement to make a very fine grid and just inside the oxide. We don't want to make it that fine everywhere. Uh, then we use this You can you can insert um, a statement called method.dy.oxide equals .0005. That puts in a five angstrom grid in the oxide, which kind of makes sense. You have a 50 angstrom oxide you're growing. Um, you'd like to have something like a five angstrom grid uh, in that oxide. And now you can start to see what it really looks like. Remember before I had one point here, one point here, one here. It's a solution look completely different. This is what it what it looked like if you just hadn't bothered to to put in a special grid in the oxide. You'd think it was a triangular sort of profile. It's not triangular at all. The boron actually looks sort of flat topped in the oxide and then goes down very rapidly. So you really need to keep an eye on your grid and um, you know, you typically want to run problems or solutions for a number of different grid spacings to a feel for what grid is appropriate and what grid, you know, uh uh what grid gives you physically a realistic uh results. Okay, so that's a a little bit of a trivial example on oxidation, but just wanted to make the point of of how important uh knowing your grid is cuz you can get a solution, you look at it, and you think it shows you something, and in fact, it could be physically not meaningful if you haven't used the right grid. So, what's going to slide number 15 and an example number two, I want to talk about uh implant modeling. Remember, there's a number of different analytic models that we talked about. Um we said you can use a Gaussian, you can use a Pearson four, you can use dual Pearson. Um and that that there are tables in the literature that give the first three moments, the RP, the delta RP, and the skewness. Those tables have been uh tabulated since the 1970s or so, and they've been updated over time. Uh of the implant distributions, and they've been produced by theory and also by fitting to experiment. This is the most common analytic formulation that you will see in in in simulators. It's called the Pearson four. We talked about that uh distribution, and we said it does a pretty good job of replicating um uh profiles into amorphous case. It does not model channeling all that well. Channeling requires use of more parameters, uh generally by uh curve fitting. Um so, that the Pearson four is a single Pearson distribution. If you want to do channeling, you'll often see dual Pearson, meaning two different Pearson four profiles are added together. Uh you and and look up tables are used. One of the things you need to be aware of uh are inaccuracies in stopping powers, particularly the electronic stopping at low energies. Um and and even nuclear stopping powers at at very low energies, a lot lot not powers are not known that well. So, if you're trying to simulate energies below say 10 kV, 20 kV, depending on the dopant, uh you may not get very good results. Uh dopants that are widely used in silicon technology, they're constantly updating these tables to try to make them a little better, more accurately represent reality and experiments. But, some dopants that are not used that often at low energies, you'll simulating you won't get a very good simulation uh compared to the actual data. So, let's go on to slide number 16. And this is an example of a supreme input file where we're using tabulated moments. So, supreme has in its in its database uh tables of all these moments. And he's using tabulated moments to evaluate and to plot for you an implant distribution. So, here's an example of ion implanted phosphorus. Um so, we define our mesh. Here's a grid fact equal 0.1. So, it's not all that fine of a mesh. Um the substrate is boron. We're going to implant phosphorus at a particular dose, 80 14. Energy not all that low, about 30 kV, but you know, somewhat low. 7° tilt. And we're saying to use a Gaussian model. Very, very simple model. Save it in a file called gaussian.saved. And then plot it. Um and then we're going to plot it in addition to plotting um the phosphorus that it calculated, uh supreme has a nice um way of you can in we're using a command called profile, you can input into supreme XY data, a matrix of concentration versus depth. And that's called the profile statement. It reads in phosphorus and the name of the file, this is the particular name, it's kind of ugly, but you can call it whatever you want. Um and use that to replace to to to plot uh the phosphorus. Um so, we can not only plot the supreme simulation, we can also plot the actual Sims data. So, this happens to be an implant for which I have actual Sims data that I have entered into this. We're going to compare that data to the to the Gaussian solution. So, if you go on to slide number 17, you'll see this is for that relatively low energy phosphorus implant. The Sims data here is shown in red. This is actual data obtained from a company called Charles Evans. I think we've talked about Evans Associates in this class. They use the cesium beam with a primary beam energy of 2 keV to profile. And this is what they got. And the black line is what supreme says it should look at look like using a Gaussian simulation. And these are default values that are tabulated inside the supreme 4 simulator. Using the standard LSS range primers, RP and delta RP. Remember you only get two for Gaussian. So, compared to the Sims, it's not all that great. Not all the the uh the simulation does not do a very good job. It's too simplified uh too simplified of a model. The stopping power is apparently too small. Uh and the range is overestimated by the by the theoretical calculation compared to what was experimentally observed. Well, we can try another model. Um same Sims data. This time we try the black model which is um the dual Pearson. Okay? Dual Pearson uses more parameters. Um It simulates this sort of channel tail a little bit better, but again the range and the skewness are both overestimated. Way too much skewness. Um so, what does this tell us? Well, this this basically tells us that these tabulated um moments are not perfect. For all dopants, so take them with a grain of of salt, especially phosphorus. Phos- use that much in CMOS technology, right? Shallow junctions for N-type are typically made by arsenic because phosphorus diffuses too fast. So, not a whole lot of energy and and and manpower has gone into you know, improving the moment tables for phos- for shallow phosphorus. So, if you happen to be using phosphorus in your experiments, um take take it with a grain of salt if you're using these tabulated values. According to my data, it doesn't fit that well. And of course, there might be something wrong with my data. That's another possibility. So, you know, exactly what's what's reality what's not always clear. But interestingly, on the next slide, exact same data this time compared to Monte Carlo simulation. Now, these Monte Carlo simulations take a lot longer. It's not an analytic. It's a numerical solution. You have to follow each ion into the silicon and see where it lands up and then statistically create a profile. And that's what the black is. Okay? And you can see the black looks kind of jaggedy because again, you're statistically creating this profile. Uh but interestingly, the the black does a very a reasonably good job um of agreeing with the Sims. Doesn't mean they're right, but but it kind of gives me some confidence that, you know, when I see a simulation agrees pretty well with the Sims data at least in terms of its range and its um delta RP, it's broad it's width here, that's probably a pretty good sign. Um so, that that the there's enough physics in this Monte Carlo simulation to reproduce the data um pretty well. But notice, this is how um how you uh you tell SUPREM to do a Monte Carlo implant. You give it the implant statement. You tell it the species, the dose, the energy. Now, here you tell it how you want to do it. You see, in prior, I had said Gaussian or dual Pearson or or if you say nothing, it defaults to to probably to to Pearson 4. Here you said Monte Carlo. Now, an important thing when you do Monte Carlo is to specify the number of ions you want it to shoot into the sample and to follow. So, this is 25,000 ions. Not very many. And tilt and rotation. You need at least 10,000 uh to get good accuracy. Probably 100,000 is better cuz you can see here after I'm two decades beyond the peak, I start to get a lot of noise. So, the noise comes in. So, I'm really only getting two get decades of smooth data. That's with 25,000 ions. In a one-dimensional simulation, this isn't too bad. It might only take 5 10 minutes. No big deal. But now, this is just 1D. If I'm doing this in 2D across the channel of a MOSFET, that minutes goes to be three or four hours or more. So, you have to really compromise to a certain extent. So, what people will do sometimes is fit the 1D profile using Monte Carlo and then fit to it an analytic solution by changing some of the default parameters and then use that analytic in the two-dimensional simulation as a way of getting around spending so much time. So, that's just an example of how actual supreme outputs compared to to data, real data. Let's take another case. So, that was that was phosphorus. As I said, phosphorus is not all that widely used. Here's the case for 30 kilovolt, same energy, but this time arsenic using the dual Pearson analytic. Again, the SIMS data is the red the red line and the calculated is the black. And this time with the dual Pearson, it does a pretty good job. You got the range almost just right. And even the the broadening, not quite, but pretty close. The shape are are much more accurate than for phosphorus. I don't know why, but my I'm guessing it's because shallow arsenic junctions are the way people make junctions these days. And so, people have updated in supreme these tables, these tables of moments to fit better the experimental data. Arsenic is also heavier, dominated by nuclear stopping, which is a little better understood than uh electronic stopping. Remember we said electronic stopping powers always have a little bit of fuzziness about them. Phosphorus is going to be lighter, it has more electronic stopping, maybe that's why. But again, take take the profiles you get with a grain of salt unless you've checked them out experimentally. Uh slide 21, that same data this time with Monte Carlo. Excellent job. Uh this looks even better. It's got the broadening a little better. Um uh so it it looks uh looks quite good uh using Monte Carlo. Of course Monte Carlo took longer uh longer to generate, longer to simulate. What's another advantage of the Monte Carlo besides the fact that it seems to be pretty accurate, has pretty good comparison to data? Um you can generate profiles of silicon interstitials and vacancies. And we need those profiles if you if you want to use those profiles, you can use them in in subsequent diffusion simulations in order to get uh to to simulate TED. If you do an implant and you don't tell the simulator to use a damage model, it's not going to be able to simulate TED cuz it needs to it needs to have some damage model. So Monte Carlo is also uh very useful for that purpose. Okay. So let's go on to slide 22. So those were a couple of examples of um simple oxidation, simple ion implantation. Now we get to the more um uh more a little more exciting models, a little more complicated. There are three major diffusion models in SUPREM 4. And these are what they they're called. The way you invoke a different model in SUPREM 4 is you use the method statement. And there are three methods for solving the differential equations associated with diffusion in SUPREM 4. There's PD, that's partial differential equation, PD.Fermi um is a method that takes into account the impact of the Fermi level just like the name would would suggest on the dopant diffusion coefficient. For example, this is a equation that supreme uses uh for n type dopants you're very familiar with this it has an n over n i and it may be an n over n i squared depending on the dopant. And it has stored in it values for d naught d minus d double minus for all the dopants. It models concentration dependent diffusion but it does not model TED or OED. So it's it's quite simple. It's very fast and the nice thing is there's only there's relatively few parameters. Just a few d parameters and you can get your answer. So that's the nice thing about it and it does model concentration dependent. So this is the first thing you would use because it's relatively fast. The next method the next level of complication is pd.trans. And and it takes into account the the Fermi level so it already has this model built in the Fermi model as well as the impact of non-equilibrium interstitial and vacancy profiles on the diffusion. But not the other way around. It will not show you the impact of dopant diffusion on the the the on the motion of interstitials and vacancies. So it's not fully coupled but it does take into account the impact of the INV on on the dopant diffusion. It's very useful for OED. So people tend to use it for oxidation enhanced diffusion or you can use it for transient diffusion with relatively low dopant concentrations. Um If you have higher dopant concentrations then the the coupled diffusion of the of the pair of the dopant plus the point defect actually affects the point defect profile and so you need something more sophisticated than pd.trans. And this is the model it uses the basic concept that that that you should be familiar with now if you've done your homework is that the diffusivity is the unperturbed diffusivity times some something in parentheses where it depends on F sub I. So, it takes into account the enhancement in CI over CI star that can happen when you do an oxidation or the enhancement in CV over CV star if you do a nitridation or if you do an implant and these things get get enlarged or suppressed. It'll take that into account. The last method you can use takes the longest in terms of it it can be very long simulation times pd.full. The name comes from the fact that it is fully coupled diffusion and what does that mean? It means that the interstitials and vacancy vacancies impact the flux of a dopants and vice versa. The flux of the dopants impact the interstitials and vacancy diffusion. This should be used most of the time if you are interested in in transient enhanced diffusion and in high concentration in general for instance the emitter push effect we talked about how phosphorus can pair with interstitials and by diffusion drag the interstitials into the substrate. When when it goes substitutional it releases those interstitials. Those interstitials then cause the boron base to broaden. That was the emitter push effect. You'll never be able to get that out of the Fermi model. There's no pay and even the trans model won't have that. So, in you to simulate the things like emitter push effect those types of fully coupled cases you need this pd.full. So, those are three different statements and you can sort of compare the results from all three statements for a given situation. Now, one thing I should say as you go from here to here to here you're invoking more physics, more chemistry and also more parameters. That's one problem with this. Sure, you can you can do it. You can model the emitter push effect but there's a lot of parameters you need to know. The diffusion rates of the of the vacancies and the interstitials, their recombination interfaces. If those parameters are in supreme, they always have default parameters, but they may not be accurate. So, again, take everything you simulate with a grain of salt. If somebody has input something in there to the best of their knowledge, that might be the inefficient the interstitial diffusion diffusivity, but maybe it wasn't well characterized at the temperature under the conditions that you're using. So, you can get lots of different profiles, but how accurate they represent experiment is something that that you need to um to uh to determine for yourself. So, here's an example. Let's look at a couple of examples of of different diffusion profiles. Um Here's uh on page 23, this is a simple 1D arsenic implant. And then we're going to do a long-time diffusion. So, the simplest thing you can imagine is implant arsenic at 30 keV, the certain dose, intermediate dose, 2.6014. And diffuse it in a furnace at 1,000° for 30 minutes. Um before we did the diffusion, we put down an oxide cap, not by oxidation, but by deposition. And so, that oxide cap helps prevent the arsenic from evaporating out of the wafer. So, um this is the actual um this is the actual command that was used that specifies the point defect model. Method pd.fermi, so we're using the Fermi diffusion model. And this is the diffusion statement, 1,000° for 30 minutes inert. Uh I have some Sims data here, which is shown in the red. And then the black dots or the black circles are the simulation using a Gaussian model. Here's a Gaussian. And a Fermi, and you can see it actually reproduces the data amazingly well. That means that somebody calibrated supreme pretty accurately to this particular furnace. Um Fermi model's good enough. And you say, "Well, how about all that? Why didn't you use PD trans or fully coupled? How'd you get away with such a simple 30-second simulation? Well, the anneal is long. So, there's there's not going to be any big damage or TED effects, right? After normal diffusion is going to dominate this. You need concentration dependence. See how blocks like it is. So, you need to use the Fermi model for Fermi level effects, but you don't need to go and invoking necessarily TED or anything. So, if you know you have a case where TED effects are not that prevalent, you might as well use the Fermi model. It'll go a lot faster and in a two-dimensional simulation, um that could save you a lot of time. Here's that same simulation here on slide 24, but um this time I used the fully coupled model. Um so, when we did the simulation instead of method pd.fermi, we said method pd.full. Um and the simulation that is the black line, it agrees still very well with the data. Maybe not quite as well, but I mean within all the experimental uh uncertainties, it it really does a good job. So, the fully coupled model doesn't make much difference. Uh that should say difference, not different. Difference. Uh because 30 minutes again is much longer than the time scale for TED at 1,000° with this dose. I'm guessing TED time scale is probably uh you know, less than a second or so. And in fact, if you go on to slide um 25, we can even figure out uh roughly what it is. And at 1,000°, this was for uh 2014 phosphorus at 40 kV, TED is less than a second. Um so, for 2.6 E 14, it it's again, it's 2.6 times that. Almost the same uh range, not much different. So, we're talking on the order of a few seconds. So, a 30-minute anneal, clearly TED is not going to be very important. That's why you get the same results, but this is a sanity check you can do with Supreme. Make sure you get the same result for that 30-minute anneal with pd.fermi and pd.full. If you don't, then you then there's something missing in your in your in your understanding of what Supreme's doing. So, there's a there's a simple example. Um now, let's do something different. On slide 26, instead of 1,000° for 30 minutes, I'm going to do 10 seconds. 1,000° for 10 seconds. Okay. Now, you're you're in a range where you can imagine there might be some TED effects. Um and this is the simulation um we're getting. The as-implanted here is shown in the black. Um and I believe this was implanted with a Monte Carlo. In fact, you can tell it's Monte Carlo because see all this jaggedness in the as-implanted? You'd never get that out of an analytic solution, right? The jaggedness comes from the statistical nature of Monte Carlo. So, that's the Monte Carlo as-implanted in black. pd.fermi, which does no TED, shows not very much motion of the arsenic for a 10-second RTA. Um pd.full, you get quite a fair amount of broadening. So, that's that's got the TED built into it. Now, exactly which one is more accurate? I really can't say. In fact, my experience with arsenic has been on our rapid thermal anneals, the Supreme tends to overestimate a little bit the amount of motion compared to what we see by SIMS. If you actually do a SIMS profile of a 1,000° 10 second. Of course, there's always the question of how well is your RTA calibrated. Rapid thermal annealing machines are extremely difficult to cal calibrate. Um they are non-equilibrium environments, right? It's not like a hot furnace where everything's same temperature. The wafer is the only thing that get gets hot, and measuring its temperature is is kind of an art. So, it's hard to say. So, so you you have to be careful when you typically when you're doing rapid thermal annealing and and simulating TED, you want to compare it to a couple of experimental results uh just to make sure that it makes sense. Now, I can make this pd.full look like whatever I want by changing some of the internal parameters in the Supreme Force simulator. If I change um things like um the diffusivity of the of the vacant of the interstitials and vacancies, I can I can change the what this profile looks like. Um so, you have some latitude there. This is using default um default parameters that are built into Supreme 4. Let me go on on slide 27 uh to another related example. We we're going to talk about how we talked last time about some clever experiments that have been done at the IEDM where the order of the anneals Okay, the exact same anneals, but we're going to reverse the order which we do them makes a difference uh because that's going to that's going to dissolve a lot of 311 defects. We're going to show how Supreme can actually simulate that. And in first, I'm going to just remind you what the usual order of making a MOSFET is just from last time. Usually, you start with a wafer, you do your isolation. This could be your shallow trench isolation. We talk about as oxide. Whoop, that didn't come out very well. I'm going to implant um the uh the uh boron profile. This is an N MOSFET. I'm going to implant that early on. Uh super steep retrograde. Uh grow the gate oxide. So, we're growing the gate oxide. Form the uh polysilicon gate by uh deposition and etching. Um do the shallow the source drain extensions are now implanted. Now, those source drain extensions bring with them when when we talk about the um reverse short channel aspect, they're going to introduce a certain number of uh 311 defects that are going to cause TED of the boron that's underneath here. Put in the spacers. Now, the spacers, if they're nitride, a lot of people today are using nitride and not oxide. If they're nitride and they're LPCVD nitride, that's a pretty high temperature process, about 800°. One of the worst temperatures you can possibly use for TED. Why is that? Well, we saw that the time the TED lasts at 800, it can be quite long. Um and and the uh CI over CI star can be quite large. So, uh an hour at 800 can cause a lot of transient enhanced diffusion. And then after that, uh typically after you make the spacers, you do this deep source drain implant here to to to get the for the contact regions. And then you do a final rapid thermal anneal, usually 1,000 to 1050, uh maybe 10 to 30 seconds, something in that range. So, the important thermal steps are this nitride at 900, this nitride uh thermal budget at 800, and then a a rapid thermal anneal at around 1,000. And now we're going to compare with Supreme how Supreme thinks in a 1D sense um this would go. Um so, we're going to just look at the uh effect of TED just on the arsenic diffusion itself. I'm not going to look at the effect on the on the boron diffusivity, that would require a two-dimensional simulation. So, this is a simulation of an arsenic source drain extension implant and diffusing it using the usual order, which is 800° C uh step for the nitride deposition, followed by um deep source drain, and then um uh followed by a 1,000° C 5-second RTA to activate everything. So, here's the arsenic Monte Carlo implant, and you can see on this scale, this is the distance in microns and the the um didn't use a very fine grid. Um good enough to get this to get this profile, but for the as implanted, you can see it's kind of ugly looking, and that's part of the reason is the the grid was a little bit too coarse, but again, with Monte Carlo, we were trying to um you know, speed up the processing a little. So, here's 2 keV, very shallow peaks uh at 1 1e15, um and then uh the the blue line is 800° 30 minutes anneal. Uh, and then the red line is 800° 30 minutes followed by a rapid thermal anneal at 1,000 for 5 seconds. It's a 1D simulation. So, almost all of the diffusion really takes place at the 800° 30 minutes. And that's because of TED. That's not ordinary 800° C. So, in order to model this, this must be a pd.full. So, it must be taking into account the transient enhanced diffusion. Well, this is trans. I'm sorry, this is pd.trans. You can either use trans or full. This particular one is is pd.trans. Uh, okay, so that's what it looks like. Very little contribution of the RTA. And your junction depth here is about 0.1 micron. That's what this predicts. Um, so well, why is that? If you look on slide 29, um, this is a plot in Supreme. In addition to the dopants, you can output the the interstitials and vacancies. So, here's a normalized concentration um, versus depth. And the blue line here is for CI over CI star at 800°. And so, you can see CI over CI star, um, after this anneal, um, it's at the 800° anneal, that is, it's pretty large. It's somewhere between 20 and 40 and near the surface. It's it's pretty big. Uh, that's the blue line. The red line, which I apologize you can't see, you'll have to write it in on your It's it's the same as your x-axis, basically. The red line is just about one. You can't even see it on the scale. So, CI over CI star at 1,000° for after 5 seconds is one. Which there isn't much enhancement left. And we saw that. Remember the enhancement time, the amount of time, uh, that it lasts is is relatively short. So, this is after after 5 seconds. Uh, so TED is already the the the interstitial concentration, the 311s have all dissolved, and the interstitial concentration has gone back to CI star. So, after 5 seconds, we still have a lot of enhancement at 800 degrees, and that's why we get all that TED in the 800 degrees C profile. So now this on on slide 30, we're going to do something a little different. Um we're going to activate the source drain extension implant prior to the nitride spacer at 800. So what we're going to do instead of doing the usual put the nitride down right after implanting, we're going to do a 5-second rapid thermal anneal after implanting. So we send it out for implant, we bring it back, we do a 5-second RTA first, and then we do another 5 seconds and then we do 800 degrees plus 30 minutes. We do that second. So we're changing the order. And you can see the red line now is the after the the implant plus 5 seconds at 1,000. You diffuse this far, and then if you add the 830 minutes, it only goes that far. It doesn't go very far because 5 seconds at 1,000 is really enough to dissolve all the 311s, right? The enhancement the the the TED time at at 1,000 degrees is only a couple seconds. So I dissolve all the 311s, then you put it back in the furnace at 800, and you don't get this is just normal 800 degrees C diffusion. There's not money CI over CI star is now been reduced cuz I got rid of all those 311s. So the junction depth now here, instead of being out here at 0.1, it's only 0.07. So the exact same amount of time that the wafer spent in the RTA and in the furnace is just that the order of the operations was changed. And this has reduced the junction depth reduced because CI over CI star is reduced by about 3x during the 1,000 degrees C step. So this is something now this is these are all simulations. Supreme can simulate the the fact that 311s are generated by the damage and that they dissolve at different temperatures at different rates, and then so it can take into account these um uh these types of effects. Again, it's using the trans model. Uh the accuracy, of course, you always take with a grain of salt, whether the junction depth is really 0.06, 0.04. I wouldn't put my life on it, to be honest, cuz there's a lot of parameters in SUPREM, but the point is you can fit your data. Assuming you get some data, you can fit data that shows the effect of the order of of the different implants. There's enough physics built into it. You just have to get the right parameters. Uh so, the final process, just simulate just to show um that what what what we did is the extension implant followed by 5-second RTA at 1,000 high temperature nitride spacer at 800, and then another 5-second RTA. The reason I needed to add the last RTA is to activate the deep source drain. Remember, the deep source drain goes in last, after the nitride spacer. So, this is 5 seconds at 1,000, 800, 5 seconds at 1,000. This is what it would look like. The final 5 seconds at 1,000 really doesn't contribute much to further motion. It's already done most of its motion um because TED at that point has been is is completely over. And if you done it the or the usual order, 800 degrees 30 minutes spacer plus 5 seconds to anneal everything, you get this junction depth. So, uh this the SUPREM predicts that revising the reversing the order of the anneals makes a difference. Again, it's something you'd have to check experimentally uh just to be sure. Okay, so that was a TED example. And then uh for the fourth example, this will be the only example I'll do where we do two-dimensional uh uh a two-dimensional simulation. And this I took this right from the SUPREM manual, so you can run this yourself. This particular example is not one that I made up. I took it out of the um example file that and this is on the computer. This example is uh one of the canned examples that comes with SUPREM 4. It's a it's a 20 200 nanometer gate length, so that's 0.2 micron gate length and MOSFET. It's kind of old-fashioned now. But, it uses something called self-aligned silicide, and we're going to talk about silicides in the next few lectures, so you get an idea. And I I put the um input file in columns, so this is the first uh part of the file and this is the second part. Again, if you want to see the active file, it's in the SUPREM uh 4 um directory. Uh so, this is Tsuprem4. So, example, here's the mesh using a fairly grid grid.fac of 0.9. Um you can also define the mesh in different uh directions uh in in the in the Y direction and the X direction. Um so, a little more sophisticated um definition of the grid. We start out by growing the gate oxide. So, here's 850 25 minutes, and it's in dry O2 plus a little bit of HCl. So, there's an HCl oxidation. And then you can plot the structure to see what it looks like after gate oxidation. Um and this says, whenever you see the word source, what that says is and then you need have a file name that says, "Take all the commands from that file name and run them now." So, Tsuprem4, in order to If you go Let's say you do the same operation in SUPREM over and over again, like you always do a plot. You want to do several different plots. Rather than putting all those plot commands in the main file over and over again, you create sub files. And this this file called S4EX10P.input is just a series of commands that defines the colors and things like that. So, it enables you to call this file whenever you want it to create a plot. So, it's a way of cleaning up uh your SUPREM input file. So, if you want to know what this particular file does, you have to go look at that command file. Uh then you deposit uh some materials. You're depositing polysilicon. You tell it the thickness. You're etching the polysilicon to the right and to the left. This is to make a gate. Um And here you're calling that file again, that plotting file. Okay. Uh now you one of your homework problems that you just handed in was on or we just handed back to you a homework three was different methods. This is using the compressed method as far as solving for the oxidation rate goes. Uh here's 850 oxidation in dry O2 and HCL again. So this is what we'd call reox. So you formed the gate now. Um So the initial gate oxidation is just to grow a very thin gate oxide. You formed the gate and you etched it. And then in in the course of etching sometimes you introduce damage right near the corners of where the channel is going to be. Remember this is going to be my channel. So you often introduce some plasma damage down here. You thin up the oxide there. You do things that are not necessarily good for the gate oxide. So people often at this point will in this technology say 0.18 micron technology would take the wafer at this point, put it back in the oxidation furnace and do what's called a gate reox. And this looks like we're doing a reox here at 850 for 25 minutes. So that reox is going to help if you thinned the oxide at all in the course of your etching, it's going to help boost that back up and it's going to it's going to grow a little oxide along the edge here of of the polysilicon. So it's a way of dealing it was introduced for reliability considerations. Reox as it says, take the gate, put it back in and do another oxidation. Um then you form the sidewall spacer. Here we're depositing oxide. It's using an oxidation deposition process. Um and then the thing you do is the deep source drain implant. This is 1e 15 energy of 60 kV. Fairly deep. Um then you're going to deposit some titanium. I won't go through the details of this, but once in the next few lectures we'll talk about the fact that um when we get to the silicide lecture, you can take metals, put them on silicon, and react them at a certain temperature and form a metallic phase. It's called a silicide. This is titanium disilicide, which forms um uh a good contact. And then we look at the final structure. So, that's the file and you can go ahead and run that. Let me show you some examples of what comes out of that. Oh, the actually the slide number 33. This is uh remember I was saying you wanted to repeat this over and over again, these commands? This was that file s4ex10p.input. This is just a plotting sequence file that you you use over and over again that tells it what colors to use and and how to um label things according to what material is. So, you rather than type this in every time in your Supreme 4, you can put it in a separate file. It's just for your reference. So, let's go to slide 34. This is from running that example after gate oxidation. What does it look like? Well, you have an XY structure, so Y is in depth and there's a there's a certain gate oxide grown everywhere across on the structure. That's relatively simple. After gate patterning, you have deposited this green layer everywhere and then etched it off everywhere to the right of this one line. So, now that's what the polysilicon gate looks like with a gate oxide underneath it after gate patterning. Okay. And notice it doesn't model etching in any sophisticated way. You just tell it where to cut it off. So, it's not modeling any shape effects of the etch or anything like that. It's not That's not that type of a program. We'll talk more about that when we talk about how to model etching. After gate reacts, remember I said we're going to put it back in the furnace and subject it to a step of 850 for 25 minutes to oxidize all around and to beef up this oxide. But interestingly, look what it's done to the gate oxide. You see what it's done? There's like a bird speaking effect. Some of the oxidant has diffused underneath the polysilicon and diffused it, and you've got a little thicker oxide now here on this part of underneath the gate compared to the center of the gate. That's not necessarily a good thing if it's too thick here, because what do we know about the gate oxide thickness determines the threshold voltage of the device. So, if I have a thicker gate oxide here than here, I'm going to turn on my channel uh at um um at different uh you know, different places differently. So, that's that's not necessarily a good thing. We want a uniform gate oxide. Here of that same structure now after I've formed um a spacer, here's the oxide spacer, and we did um we did a um a source drain extension. I'm sorry, first did the 5E13 source drain extension, and you formed the spacer, and then you did the deep source drain. Um these contours by the way um correspond to uh arsenic in the substrate. Each one is a different arsenic concentration. You can see how it's shaped. This this region here corresponds to the extension, this region to the deep source drain. Uh this particular uh simulation uses PD.Fermi. So, the Fermi model, very simple. And then after silicidation, Supreme doesn't necessarily do a very good model of siliciding, but you see it's reacted. We'll talk in in subsequent lectures about what silicidation's all about. I mostly want you to get a feel for how a two-dimensional simulation um of such a structure actually looks. Here's the final structure um here on on slide 39, the showing you the arsenic concentration contours. So, here this region in between is your channel. Um uh here's the polysilicon gate in green, and this is your gate oxide. And because of the reoxidation, we have a little bit of the smile effect. You see the way the device seems to be smiling? Has a little smile here. That's actually a very happy device, but um but it's not actually all that good. The smiling is not very good. In fact, you want a gate oxide that's perfectly flat, has the same concentra- the same thickness as much as possible all the way across it. It got unflat because we did the reox, and a little bit of oxidation took place from the corners. So, these days for the very shallow of the very um shortest channel devices, reoxidation is not such a popular thing to do. Uh because it does create this non-uniformity in the oxide thickness. In fact, you can go back What What I did was I go went back here on page 40 and said, "Oh, okay. Is there some way we can deal with this and and and maybe make the reox um have a little bit less effect um on on the a little less of this extra oxidation right at the corner." Um so, this is this is really what we're talking about, just to give you a zoom in on slide 40. Here actually here's a zoom in of what it is, this non-uniform oxide thickness uh took place under the gate. And the the real origin is the lateral oxidation under the poly during the gate reox step. This is when the gate reox was done at 850 for 25 minutes. Um So, this is um in fact from the very first lecture of class, this is this is a real TEM of a real device to show you this effect is real. See the way this device is smiling also? Um so, Supreme didn't just make that up. The accident did get under here and oxidize in this region. So, the the the the VT is going to be non-uniform sort of across this device. So, you have to actually watch out for this. This does really happen. Just to show you that Supreme is based in reality with respect to some of these things. Um On slide 43, actually um did a a little example um of of how we can change the amount of, uh, the amount of this effect that happens. So, the, the amount of this non-uniformity. Now, it may not be very clear from looking at this, but on, on the left-hand side, what was done was, um, when we did the, um, the etch, we etched all the way down. Okay? Um, and then did, did a, re-ox. So, on the left-hand side, you're etching like this, and, uh, here's your gate oxide, uh, like this, and we're basically etching in, in the example where we should told Supreme, we, we act as as if we etched all the way down. So, the oxide the prior to re-ox. So, when we put it in the furnace on the left-hand side, uh, sorry, when we put it in the furnace for oxidation, um, this oxide was gone, uh, at that corner. Uh, so, that's the, and that's what you end up with on the left-hand side. So, you can imagine when that oxide is gone, then you can get a fair amount of, you know, sort of attack in here laterally, uh, of the, the oxidant, uh, getting underneath there. So, what, what was done here? On the right-hand side, instead, um, 50 of the 70 angstroms were etched. So, we left a lot of the oxide on there, um, and then just, um, oxidized at, uh, re-ox was done at a lower temperature, 825 for for a short time, 12 minutes. Um, so, you get some of the benefits of the re-ox without some of that extra. So, in this, in this example, when we did the, the, the etching, um, it didn't remove it all. Sort of it looked like this when it went into the oxidation furnace. Kind of looked like that, and then got oxidized. So, by sort of refining the etch process, we didn't etch all the way down. Um, and if you look carefully, I think on the next slide, it'll be maybe a little more obvious. Um, Um this is uh the the the lateral non-uniformity is a is is quite a bit reduced. This uh oxide thickness is much more uniform going across here. There's still a little bit of it, but 825 for 12 minutes um uh there's a lot less of that lateral non-uniformity. So, it's an example of a process you can use SUPREM IV to optimize reasonably efficiently uh and and reasonably accurately uh in this two-dimensional model. Okay, so let me let me go on summarize uh this The uh simulators like SUPREM IV, which by the way, I didn't tell you, but SUPREM IV was originally um written at Stanford. Um and uh sometimes it's called S-SUPREM. That's where it came out of originally in the 1980s. It was then commercialized in a small company called TMA. That company was bought out by another company called Avant! And Avant! was later later sold uh sold the um technology to a company called Synopsys. Synopsys is a big design house. They make a lot of CAD software for designing uh chips, but they also support TSUPREM IV. So, if you want to uh have questions about the simulator, you need to contact people at this company called Synopsys. There are other simulators out there. Um TSUPREM IV is one of the most uh popular, but there's another company called Silvaco, which makes a competing product which is called Athena. In any case, these simulators like this um they've been developed over the years to enable what we call physically uh accurate or robust or correct simulations of complex processes. However, I've tried to tell you to take everything with a grain of salt. Don't believe it just because you simulate it in SUPREM and it looks like that. One thing you might have done it wrong. You might have used the wrong grid factor. Um you might have SUPREM itself has parameters in it that are unknown um that somebody just stuck in there. Some graduate student writing the program said, "Oh, I don't know exactly what this parameter is. I'll put this number in and it's rough." Well, you need to find out what parameter is in there. And if you go to the appendix in the manual, it'll tell you in general what all the numbers are that it's using. And you can decide whether those numbers whether you like them or not. Uh, the nice thing about these simulations from Supreme 4 or Athena, you can feed them into a device simulator, such as Medici or whatever, and then predict IV and CV characteristics, the actual electrical characteristics of the device. So, they are designed to be coupled that with the the the um, process simulator and the um, device simulator. Uh, that's a very nice feature. Um, there's a lot of new understanding that's being developed uh, and issues related to TED and OED and other anomalous effects. Low energy ion implants, I showed you some low energy phosphorus where Supreme doesn't do a very good job of modeling the data. Um, highly tilted implants with shadowing, um, oxidation of trenches. Supreme can handle a lot of most of these situations because it has the physics built in. Exactly the accuracy that's always the question mark. Um, uh, whenever you're running these simulators, keep in mind the basic physical models. Uh, there are a lot of parameters that must be known accurately. Um, and we don't know them all accurately. So, keep your eyes open. Uh, a big uh, caveat is keep the mesh or the grid in mind. Um, when your grid is fine enough, you should be able to get the exact same solution with minor changes to the grid. So, I run it for a certain grid, I cut the grid spacing in half, the solution should look identical. If all of a sudden the solution looks much smoother when I cut the grid in half, the the spacing, or much finer, then obviously the original solution didn't have a fine enough grid. So, you've got to do these sanity checks. Run it once with a certain grid, then use twice the grid points. Does it look a lot smoother? Well, that means you probably didn't do a good enough job the first time. And then do it again. And eventually it'll sort of converge. It has about the same smoothness regardless of of your grid, in which case your grid is probably fine enough. Your solution should be independent of the grid. Otherwise, you know, uh that can't that's not physically realistic. Um there's a lot of different process integration schemes. I just showed you one just changing the order uh of of the device uh of the anneals. The simulators help us to understand these interaction between the various steps and and how to overall optimize the overall technology in ways that you could never do if you just did this by hand. So, you've used Supreme four now. You're going to use it again in in homework number five. So, I think gives you some idea of uh the how powerful this tool is. But, if you are going to really use it in your research, make sure you read the manual. It is very important cuz there's a lot of little things in there you you need to know about. Okay, that's it for today. Um homework number four, please bring up front. Homework number three is in the orange folder in the back by the TA. And um I guess that's it. We'll meet on Oh, the uh somebody have the um the sign-up sheet for your final project? Oh, great. Thanks. Make sure you sign up.