WEBVTT 1 00:00:00.330 --> 00:00:08.060 Mark Kushner: Brought his laptop. 2 00:00:09.130 --> 00:00:35.009 Mark Kushner: Good afternoon. Welcome to the 1st Mepsi seminar of the fall. 2,024 semester. Well, folks remind me when it's December and semester is over is my pleasure to introduce today's Mempsi Speaker, Dr. Laurel Filippovitch, Professor of Micro Nanoelectronics at Vienna, University, Technology 3 00:00:35.050 --> 00:00:42.239 Mark Kushner: and the Director of the Christian and Goldwood Laboratory for moping cell process. Modeling of sending injector devices. 4 00:00:42.780 --> 00:00:54.019 Mark Kushner: Professor Philipovitch is principal investigator of research projects related to both the basic science of semiconductor fabrication and the Institute Relevant Research. 5 00:00:54.390 --> 00:01:05.710 Mark Kushner: The primary interests are on the fabrication, operation and reliability of novel semiconductor devices and sensors using advanced process and device modeling. 6 00:01:07.490 --> 00:01:25.269 Mark Kushner: Professor Phyllispovic is also investigating efficient integration of machine learning with process tcab to merge abanechio, metrodynamic simulations to aid material design and discovery. Then you combine feature, scale and metro scale models. 7 00:01:25.270 --> 00:01:37.850 Mark Kushner: His team had released several open source software tools to model semiconductor device fabrication. These are known as the Vienna Ps. And Vienna Emc. Platforms. 8 00:01:37.920 --> 00:01:46.329 Mark Kushner: The title of Professor Philip Public Seminar is multi-scale process Tcad at the Institute for Microelectronics tu Vienna. 9 00:01:47.040 --> 00:02:03.539 Mark Kushner: Before we start I'd like to thank you, Lino, very much for making the trek here to give the seminar and acknowledge that we present you with the Nipsey mug. 10 00:02:04.190 --> 00:02:11.169 Mark Kushner: I should show I should show this side right with the, with the proper side facing forward. 11 00:02:14.461 --> 00:02:27.399 Mark Kushner: Very nice. Thank you very much. Thank you, Mark, and thank you for having me here. It's my pleasure to to come visit this beautiful campus my 1st time here. So it's really really nice to see everything. 12 00:02:27.460 --> 00:02:42.909 Mark Kushner: And yeah, so, as Mark already mentioned, I will be talking about some things that we're doing in my group for multi scale process. Tcad. I mainly will concentrate on the topography simulation. So what we're doing with etching and deposition. 13 00:02:42.910 --> 00:02:58.060 Mark Kushner: We also have a branch. Let's say they're doing that where we're doing iron implantation and doping simulations. And this is more. Let's say, at the mystic level, because we have a lot of problems with novel materials like 3, 5 14 00:02:58.160 --> 00:03:01.309 Mark Kushner: wide band gap materials and how to actually dope them. 15 00:03:01.647 --> 00:03:09.649 Mark Kushner: But yeah, so we'll get started with the with the talk. Oh, by the way, now, the official English name of our university is the 16 00:03:09.910 --> 00:03:19.239 Mark Kushner: yeah. They changed it as a few years ago, because in in German it's technical university, and it used to be Vienna University of Technology, the English version. And now they just said, you know what 17 00:03:19.410 --> 00:03:22.139 Mark Kushner: the English name is. Tain. 18 00:03:23.250 --> 00:03:27.550 Mark Kushner: So so first, st who actually knows what Tcad is. 19 00:03:31.560 --> 00:03:41.179 Mark Kushner: Oh, this is good and bad news, good cause you won't be bored for the next few slides bad, because I want more people to know about it. But I guess also good, because then you'll know about it after 20 00:03:41.818 --> 00:03:49.699 Mark Kushner: technology computer aided design. So basically, what it means is, you want to design a certain circuit. You want to design a certain chip. 21 00:03:49.870 --> 00:04:12.310 Mark Kushner: but you don't want to gain all the knowledge you need just by going into the lab and testing everything constantly. So you want to do something through simulations that helps you decide either how to make a circuit, how to design a device or anything in between, or how to fabricate it. So basically, there's a set of simulation tools that are used to model semiconductor fabrication and operation. 22 00:04:12.320 --> 00:04:22.469 Mark Kushner: So typically, what you would do when you design a circuit is you first, st you design it just by, you know, putting in your your transistors, resistors, capacitors, whatever you need. Then you do a layout 23 00:04:22.760 --> 00:04:24.650 Mark Kushner: where you actually 24 00:04:24.890 --> 00:04:43.910 Mark Kushner: show how the how these devices will be built on a chip. And how does that actually then become something usable and useful. And how can you be sure that? Let's say, every every device you've put in there is actually going to look like what you want it to look like, and that it's actually going to operate how you want it to operate. 25 00:04:43.920 --> 00:04:46.780 Mark Kushner: But what's in here are a whole bunch of 26 00:04:47.228 --> 00:05:15.330 Mark Kushner: small signal models or or compact models for the transistors and for the resistors and capacitors that are inside. And you also have to do. Rc. Extraction, which means that for all the parasitic resistors and capacitors, especially at the back end of line, you need to extract those so that you can have an idea of what the actual circuit here will do. But how can you be sure that the devices in there, or the models, the spice model that represent the device in a very simplistic way that they're actually accurate. 27 00:05:15.370 --> 00:05:29.440 Mark Kushner: So this is done through device, Dcad, and how do you know that the device you build is actually looking like you want it to look right because there's also some variation in the process. So if you are etching away and trying to design this feature here with this, this gate 28 00:05:29.470 --> 00:05:52.660 Mark Kushner: or this channel here? How do you know that the gate is exactly as thick as you want it to be. How do you know that you don't have any tapering along the side walls, that you have unwanted surface roughnesses that are going to cause some problems or limitations in the electron transport and as well as doping. So you have to dope certain regions of your of your device for it to operate properly. So how do you know that the doping levels 29 00:05:52.690 --> 00:05:56.849 Mark Kushner: are what you told them here to be? So? This is then done through process tcap. 30 00:05:57.280 --> 00:06:26.879 Mark Kushner: Now, traditionally, when you build the circuit. And when you these, these spice model cards were basically provided by extra experiments. So you basically do perform a few experiments with the new scale the devices, and then you can do some tests with this, some test circuits, and you can get your spice, model cards or these pdk, the pdk, which is then provided to your your layout designer or your your circuit designer, too. 31 00:06:27.210 --> 00:06:42.909 Mark Kushner: Now the problem here becomes that as we continue to scale silicon. I don't know how aware you are what transistors look like nowadays. They're no longer. They're completely different, right? They don't look like these Planar architectures that we had before. 32 00:06:43.300 --> 00:06:44.730 Mark Kushner: Sorry. Here we go. 33 00:06:45.839 --> 00:07:13.899 Mark Kushner: So they used to look like this. Basically, right? You have the source chain on either side, and a gate on top of it, and your channel is in here. So you have transport through here now, so the current, probably most of your your laptops and and the phones have a finfets inside, and finfets mean that this is your channel. Now, instead of being planar like this, the current here goes from, let's say, outside of the screen, to inside the screen. And the reason for this is when, as this shrinks, you have whole 34 00:07:13.990 --> 00:07:36.580 Mark Kushner: bunch of problems that arise. So with the electron transport, you have small signal of the the length scaling issues. You have any problems with with potential defects in that in that channel become exacerbated because of the scale, and you have less control over it. You let less electrostatic control over that feature because it gets much smaller. So the contacts that 35 00:07:36.580 --> 00:07:50.069 Mark Kushner: that channel gets much smaller. So that's why we kind of went up, let's say, starting to build skyscrapers. After this, the plans are these kind of floating cities or these gate all around transistors. So there's been really a lot of innovation. 36 00:07:50.070 --> 00:08:08.289 Mark Kushner: And the problem is, you can't test every possible variation that you might want to have and every possible material that could play a significant role in there and every geometry. You can't test all of that in the lab, right? So you need to have some support from from simulations, at least simulations you can trust that are based on some physics. 37 00:08:08.450 --> 00:08:14.799 Mark Kushner: Right? So this is where, then, this comes in. What processes do we need in order to actually fabricate such 38 00:08:15.270 --> 00:08:18.130 Mark Kushner: strange and different geometries? 39 00:08:18.260 --> 00:08:26.330 Mark Kushner: And how did the devices that we envision actually perform, and, in fact, the the 1st finfets 40 00:08:26.330 --> 00:08:51.009 Mark Kushner: they initially the idea was to basically have as vertical of a finfet as possible, and through Tcad it was found that they found out that actually the optimal geometry of a Finfet is not vertical, but rather slightly slightly Connal, so slightly triangular because it it had. Then you have better electrostatic control and more room for electron transport. So so Tcad has basically entered the space of development. That is 41 00:08:51.644 --> 00:09:20.110 Mark Kushner: hardly any development done nowadays for new semiconducted devices without Tcad support, and it, of course, increases the speed with which you can then actually get get your chip out to market or develop a new technology. Right? So here there was a rough estimate that if you do an in silicon device, new technology development you need anywhere between 3 to 6 months. Whereas if you do, Tcad supported, it's optimistically, one to 5 days. 42 00:09:20.812 --> 00:09:30.979 Mark Kushner: Right? And then so the Itrs also estimates that the use of Tcad has improved time to market and the the budget. 43 00:09:31.310 --> 00:09:38.288 Mark Kushner: So the the cost of technology development by about 30%. 44 00:09:38.970 --> 00:10:02.449 Mark Kushner: Right? The other thing is, it allows you to see inside the device. Right? So if you measure something, you go to the lab, you check your device, you measure it. You can see what happens under certain conditions. But you don't necessarily know why. So Tcad is basically there to also answer that question. So why are we seeing certain behaviors in when when we measure these? And we can visualize the valid information which is otherwise impossible to measure. 45 00:10:03.320 --> 00:10:12.294 Mark Kushner: And so there's also. Now this this idea to use Tcad in for your development of the new new technologies. A new 46 00:10:13.300 --> 00:10:14.340 Mark Kushner: nodes 47 00:10:14.910 --> 00:10:38.200 Mark Kushner: is called Dtco. So this this means that you're it's the design technology called optimization. So the idea is what we know and what we want to have is a certain design, a certain circuit that gives us a certain performance that does what we want it to do. Now, if we want to optimize this, we need to understand what technology is being used to develop it. So 48 00:10:38.200 --> 00:11:03.179 Mark Kushner: processes that are required there and out of the devices that are used in that design actually work. So now, instead of again, instead of doing all of this, using experiments and measurements and fabrications which are extremely expensive and time consuming the idea is, we can do a lot of this just by doing simulations. And Tcad. So this is where we come in. So we have a bunch of different tools for for device simulations. 49 00:11:03.180 --> 00:11:03.880 Mark Kushner: Nations. 50 00:11:04.260 --> 00:11:12.239 Mark Kushner: In my group, we work a lot on on process dcat. So the simulations required to actually Fab generate the devices 51 00:11:13.932 --> 00:11:25.210 Mark Kushner: at our Institute. There's a history of of Tcad. And it was actually the 1st 2 dimensional Mosfet simulator was actually from our Institute. So this is the paper from back 52 00:11:25.210 --> 00:11:52.939 Mark Kushner: in 1980, 1979, 1980. So the idea was, you can kind of develop. Set up what your semiconductor looks like you have your source dray and your gate and your bulk. You set it up just by simple commands where you say, Okay, this is what the thickness of my oxide, the width and length of my device, the doping levels that you can identify you can put in there. And it's and it kind of it gives you a reasonable estimate of what the structure should could look like. 53 00:11:52.940 --> 00:12:09.070 Mark Kushner: And then you can look at what the doping concentration inside is, what the electrical potential distribution inside your Channel region is. And then ultimately, you can get your Idvg curve. So how much current are you getting when you apply a certain bias at the gate. 54 00:12:09.270 --> 00:12:26.489 Mark Kushner: Now. The the before, like. I said, the devices were quite simple, quite straightforward, and you could, even just from simple commands and simple estimates still get a reasonable iv curve that fits what you've measured, simulated what you've measured in the lab 55 00:12:26.530 --> 00:12:28.629 Mark Kushner: nowadays. This is very difficult. 56 00:12:28.740 --> 00:12:40.949 Mark Kushner: Devices are changing drastically, and there's more and more need to also understand the processes that get you there. So what? How can you optimize the fabrication steps as well in order to generate these devices. 57 00:12:41.470 --> 00:12:58.800 Mark Kushner: So this is where we come up. We've come into multi scale process modeling. Right? Ultimately, you want to have a certain design, and you need to also be able to simulate what that design does. So when you have something like this, you need to do. Prem Rc extraction, and you can then model it. 58 00:12:59.221 --> 00:13:08.489 Mark Kushner: But to generate these structures you need to have a continuum model. Typically, right? You, you need to have some model that describes how the surfaces are moving. 59 00:13:08.840 --> 00:13:30.599 Mark Kushner: but how to get there? If you're using new materials, then you have to think about okay, well, how does this new material even behave so if you know silicon carbide and gallium nitride, these are materials that are starting to replace silicon for for high power and high temperature operation. But we don't know very much about how they actually can, how they can be manipulated 60 00:13:30.600 --> 00:13:43.569 Mark Kushner: with silicon. We have about 60, 70 years of experience with these new materials. We simply don't have that, and we don't have the time to to investigate everything. So if we want to do something like doping of a silicon carbide or gallium nitride. 61 00:13:43.570 --> 00:14:03.779 Mark Kushner: We can do some experiments, and we can extrapolate some information from an experience, and we can create some very simplistic models. But we won't know what exactly is going on in there until unless we start looking at the optimistic picture. So we're doing this now with silicon carbide and and gaudium nitride as well, trying to do molecular dynamic studies of of what's actually going on with the doping 62 00:14:05.985 --> 00:14:16.279 Mark Kushner: so this brings me to the Vienna Ps framework. The Vienna Ps Ps stands for process simulator. So here's the the Github link, or 63 00:14:16.590 --> 00:14:24.699 Mark Kushner: this is the link to the the documentation. Basically, there are 3 major parts of this. One is the level set 64 00:14:24.820 --> 00:14:36.560 Mark Kushner: storage and manipulation. One is the cell set, which basically is a a voxel based approach to to set up the geometries, and one is the ray tracer. 65 00:14:37.580 --> 00:14:39.870 Mark Kushner: The Vienna ls, so 66 00:14:39.970 --> 00:14:43.169 Mark Kushner: the level set method is is how we 67 00:14:43.680 --> 00:15:12.619 Mark Kushner: how we store our geometries, so instead of explicitly storing the geometries with the where nodes and edges or triangles or tetrahedras represent the material, we store interfaces so interfaces between materials and surfaces, and we store that also not explicitly. So we don't actually store points along that surface. We store a, we set up a grid, and we store values on that grid which tell us how far we are from the interface. 68 00:15:12.620 --> 00:15:35.790 Mark Kushner: So the further we get from the interface. The higher this signed distance function gets, and the further into the material that we get, the lower the number gets and the and the surface. If you are directly at the way. If one of your nodes from your grid is directly on the surface, then it is assigned a value of 0. So this is basically the level set method. And it's how we store the store our materials. 69 00:15:35.790 --> 00:15:58.539 Mark Kushner: The reason we do this is if you are having interfaces that move a lot which would have, which is what happens when you're doing etching in deposition. So, for example, if you have 2 edges and you're depositing, you're doing some Cvd process in a trench, and you end up the 2 sides end up coming together, and you have a void underneath in order to mesh that this becomes very, very difficult with with explicit 70 00:15:58.540 --> 00:16:13.260 Mark Kushner: mesh representation. So that and because you can have nodes that cross into the materials, and then you have to figure out what to do with that, and you have to do constant remeshing and cleaning up of of the mesh itself. So this allows us to kind of treat this implicitly. 71 00:16:14.505 --> 00:16:41.120 Mark Kushner: Now, of course, we don't want to store the entire domain. That's that's a waste of storage resources. So we do. A narrow band method, where we only store a few layers around the surface or sparse field where we only store one layer around the surface. And we store the Manhattan distances to that. So the the distance to this is also not Euclidean. It is so. We only go along the the grid spacings and stuff. So that's saves a bit in in the computation time. 72 00:16:41.990 --> 00:16:50.929 Mark Kushner: Right? And so we only store these active green points. And we also have level set values here so that we can still store we can solve the gradients along the surface. 73 00:16:51.180 --> 00:17:18.639 Mark Kushner: Okay, in the Vienna, Ella, Vienna, Cs. Which means that we can now also store the so voxel. So we can store the material information as well. So each corner of each of these cells has a representative level set value, and then the cell can also have some material value or any value that represents either the material or some doping level, or any anything else could be relevant to our our system. 74 00:17:20.670 --> 00:17:32.039 Mark Kushner: And then we have the ray tracer. So via an array. And what what we do here is we basically assume ballistic transport, which means that everything moves in a straight line. So right above our 75 00:17:32.150 --> 00:18:01.640 Mark Kushner: particular features, where we're doing our etching or deposition simulations, we accelerate particles from this plane that's above, and that those particles are accelerated towards the surface. So we have to treat boundaries properly which can be reflective or periodic. And then the particles basically hit off of the walls, and they will either stick cause the position or etching, or they will be reflected to stick, or to deposit or etch elsewhere. So these, this is the the whole 76 00:18:01.910 --> 00:18:19.929 Mark Kushner: core of the framework that we have, and we've done some, let's say, accelerations with the Vn array. So we can use also Gpu Ray tracing, which causes which makes it a lot quicker because for our for our systems and typical. So problems that we're solving, it's this 77 00:18:19.930 --> 00:18:46.980 Mark Kushner: flux calculation that takes the most time. Right? So this, basically what we have here is what we need as as input, we have the flux or the number of each type of particle that is arriving at the source plane at right above our features. And we redistribute that, or then we calculate the flux or the arriving particles all along the feature, and that takes the most time with this ray tracing approach. 78 00:18:48.502 --> 00:19:15.350 Mark Kushner: And so with this framework, we've done many different types of simulations. So we can do the position. So this is a typical kind of deposition in a trench plasma, etching deep reactive iron etching, wet etching. We do some ald as well. And and this process here is we could be. We. We can do this now, because we have both the cell set and the level and the level set. So even though the level set, the surfaces here are defined by a level set. What we are doing is here etching 79 00:19:15.788 --> 00:19:24.549 Mark Kushner: the silicon oxide, silicon nitride stacks. This is for 3D nand memory, and you etch away the silicon nitride 80 00:19:24.670 --> 00:19:52.360 Mark Kushner: where the silicon oxide should stay. And then these areas that were etched away are refilled with a metal. So this is where you get your nand gates that are stacked, and they serve as storage. But what happens sometimes is that a precursor that is is removed from that surface can redeposit onto your oxide pillars here, and then you can get something like these these bone structures. So we can simulate that now. 81 00:19:52.731 --> 00:20:22.040 Mark Kushner: With the fact that our framework allows for both level set and and cell set representations. So in this talk I will mainly concentrate on deposition and and plasmashing, and some some recent works that that we're doing. So start with. It's the yeah plasma enhanced chemical vapor deposition. So what what the typical flow that we have is that the radical so neutral, radical and ion transport inside the chamber is something that 82 00:20:22.040 --> 00:20:38.659 Mark Kushner: we don't solve explicitly. This is so some. What's done in Mark's group here. So what we need to find is what kind of what transport, so flux and angular distribution and energy distribution 83 00:20:38.660 --> 00:20:56.789 Mark Kushner: of the ions and radicals do we have here at the source point, so that we can then apply ray tracing and find how that flux redistributes along the surface. So what we need typically is the flat wafer rates which are analogous to the flux and ion directionality. So this is how 84 00:20:56.970 --> 00:21:17.880 Mark Kushner: companies or how, let's say, Tcad vendors often develop these these models is the flat wafer rates. That's basically the rates of the the position that are really what it says, on a flat wafer, so not without any any different features. And then how does how that redistributes along the features is what is being sold with the model. 85 00:21:17.930 --> 00:21:44.849 Mark Kushner: So from those rates and the isotropy in the ion distribution. So we already kind of show it here. The radicals, the neutral radicals, have a relatively even distribution along the source plane, while the ions have a are accelerated vertically in the in the plasma sheath. So that means that there's some vertical acceleration, but they're not perfectly vertical, so that we treat these angular distribution using a power cosine. So 86 00:21:44.850 --> 00:21:56.789 Mark Kushner: what power the cosine has, the higher, the power of the cosine, the more vertical it is. So these are the 2 things that we can get that we basically need in order to start our model. So as inputs. 87 00:21:56.970 --> 00:22:22.230 Mark Kushner: then when we do ray tracing. So we do this ballistic transport, and we count how many rays or how many rays, particles of each type hit the surfaces at each location. So we store that and that becomes the particle flux along that material surface. And then from that particle flux. The combination of the ion and radical contribution contributes to the the position rate 88 00:22:22.230 --> 00:22:27.828 Mark Kushner: B, so just by looking at the the rate 89 00:22:29.140 --> 00:22:39.459 Mark Kushner: of incoming the the fluxes of the radicals, fluxes of the ions, and the ratio between those 2. So understanding how much impact each one of them has. 90 00:22:40.090 --> 00:22:58.472 Mark Kushner: And then, when we have that rate or the velocity of the surface, we solve the level set equation, which means we adjust the values of the sign distance functions to move the surface. So the surface isn't moved by moving the nodes. It's moved by solving this level set equation and changing the values of the sign distance function in all of the 91 00:22:59.250 --> 00:23:23.840 Mark Kushner: in the whole grid. So this is what the kind of model looks like. So if you go here, you can look at the the different models that we have that are pre prepared. So essentially, we need to find. So when we're trying to calibrate to some some process that let's say, if we have a an industry partner or somebody who uses a Pcvd process, and they give us some 92 00:23:23.870 --> 00:23:31.720 Mark Kushner: 10 images or some images of of what the position happened. These are the, let's say, parameter space that we 93 00:23:31.800 --> 00:23:43.289 Mark Kushner: play in. So we have to have, of course, have some understanding of what they mean. But essentially, what we need to do is find which parameters of here best represent their process. 94 00:23:43.320 --> 00:23:47.219 Mark Kushner: So we've done this with one example here. 95 00:23:47.310 --> 00:23:53.139 Mark Kushner: So we have this recipe of what the the company did in order to fabricate these devices. So the idea for us is. 96 00:23:53.420 --> 00:23:54.800 Mark Kushner: we have 97 00:23:55.780 --> 00:24:20.839 Mark Kushner: the initial topography. So this is what the initial topography is, and we wanted to find what parameters will get us to this deposited oxide. So this is the deposition after Pacvd. So what we did is use the global optimizer to find the parameter space so that all the parameters that should get us there for the neutral radical and ions. 98 00:24:20.870 --> 00:24:22.210 Mark Kushner: Now. 99 00:24:23.580 --> 00:24:52.299 Mark Kushner: how do we do this? So first, st we have to identify something that we call geometric descriptors. So what is it that defines this particular deposited geometry? And there's a bunch of things you can use. What we ended up just looking at as an initial guess, was the side wall thickness at around the halfway point. Here the thickness at the bottom of our trench, and the thickness at the nearest kind of pinch off region. And we tried to now 100 00:24:52.300 --> 00:25:00.929 Mark Kushner: vary those parameters in order to vary those input parameters in order to get as close as possible to these values. 101 00:25:01.310 --> 00:25:05.289 Mark Kushner: So this global optimizer is basically saying that our error is 102 00:25:05.550 --> 00:25:21.189 Mark Kushner: so defined by the difference between the simulated thicknesses here and the optimal ones that were calculated that were measured. Right? So the optimizer basically looks for different parameter sets. 103 00:25:21.540 --> 00:25:41.700 Mark Kushner: We simulate using the Vienna Ps tool, the process extract these values and then return an error. And so we do this in a loop. After some 500 or so iteration runs with this particular with this optimizer, then we get the optimized set of parameters. 104 00:25:41.750 --> 00:25:48.450 Mark Kushner: And when we when we use the optimized set of parameters, we got a services 105 00:25:49.140 --> 00:25:58.569 Mark Kushner: that's still this one. So we got this profile, which is very close to what we initially had. But at least these values are very close 106 00:25:58.993 --> 00:26:06.330 Mark Kushner: but we're now working on. Of course there are certain parts that are not so not so perfect. I won't have it here. But 107 00:26:06.480 --> 00:26:14.019 Mark Kushner: so if we, for example, if we look at this there's much more. These corners are much more pointed. There's a thickness difference here. 108 00:26:14.100 --> 00:26:36.039 Mark Kushner: So the idea was, now we either start introducing more and more geometric descriptors. In order to describe this geometry and try to improve our optimizer, or the other idea is to use the level set values directly. So the idea here is, if we already know what the optimal surface looks like, we can simply make a level set out of the difference between 109 00:26:36.040 --> 00:26:51.579 Mark Kushner: the simulated structure and the the expected structure. And we use the level set values of that difference as the as the error estimate, right? So we know that it should be 0. But if anything above 0 could be the error. So this is what we're we're working on now 110 00:26:52.980 --> 00:27:22.179 Mark Kushner: right and then, when we when we found those Prem, those particular values. We wanted to test them on a different structure. Because that's the whole point, right? We want to have a model that's predictive so this. So we then used this structure where the initial geometry is is so here and has a basically just the the main difference is that it's further apart. So the trench has a a longer distance here along a critical dimension. So here it's 799 nanometers. The previous one was around 600 nanometers. 111 00:27:22.180 --> 00:27:29.130 Mark Kushner: And when we ran the model we actually got very close. The values were very close to also what the experiment values showed, so 112 00:27:29.180 --> 00:27:37.530 Mark Kushner: the thickness is matched reasonably, reasonably well, even with this very simple descriptor of the geometry itself. 113 00:27:39.760 --> 00:28:01.209 Mark Kushner: For plasma etching the the flow or the thought process for us is very similar. So we still need to know the flux at the source plane of all the different particles that are involved. So here we'll look at sf, 6 0, 2 plasma etching. So we need to know. We we look at oxygen, a neutral which typically is the fluorine 114 00:28:01.210 --> 00:28:12.209 Mark Kushner: and ions are bulked as a single type of particle. So we need to know those distribution of the fluxes and the ion energy and angular distribution. 115 00:28:12.840 --> 00:28:41.069 Mark Kushner: Then we perform the ray tracing again. And now in this time we don't directly take the incoming flux and say, Okay, this is now directly related to the rate, like we did with plasma enhanced. Cbd, because the process is a bit more complex, right? Because you have a simultaneous oxidation of the surface where oxygen comes in and adsorbs which then inhibits chemical etching, and at the same time you have ions that are coming in and causing physical etching. 116 00:28:41.070 --> 00:29:08.200 Mark Kushner: and you also have the combined ion enhanced etching whereby let's say an ion can modify the surface, so that chemical etching it can more readily happen, or chemical etching, or a chemical modification of the surface, can cause the can cause lower energy ions to to increase the etching. So what we have is these, these multiple processes that are taking place 117 00:29:08.250 --> 00:29:17.059 Mark Kushner: that cannot be simply or or linearly defined by a function that just follows the fluxes. So we need the coverages. 118 00:29:17.580 --> 00:29:41.079 Mark Kushner: And so what we have is a surface coverage of the fluorine and surface coverage of the oxygens. And then ions are tracked with their flux. So basically, when an ion comes in, if it has sufficient energy, it will remove part of the surface. So that builds the the etch rate that we have. So here we have the chemical etching, which means fluorine interacting with the silicon. 119 00:29:41.080 --> 00:30:06.369 Mark Kushner: Here we have the sputtering, which means that the ion is basically physically hitting the surface, bombarding a piece of the way. And then here's the ion enhanced etching, which means that that, this 2 combined systems can actually cause a higher etch rate than just each one individually. And here the we use these equations in order to follow or see the coverages. So basically, if a fluorine comes in 120 00:30:07.034 --> 00:30:21.909 Mark Kushner: it can only stick to a location where we don't already have a fluorine or an oxygen, and we also have some desorption, and and ion removal of this of the previously covered piece of the. So the surface. 121 00:30:22.050 --> 00:30:25.269 Mark Kushner: So once we have those coverages, then we can get the edge rate. 122 00:30:25.330 --> 00:30:40.260 Mark Kushner: and for the ions we need to track the energy. So the ion energy distribution we assume a Gaussian distribution which is incorrect, but it's often done also with with commercial deca tools, because it's easier. 123 00:30:40.638 --> 00:31:05.400 Mark Kushner: And then it's the difference between that energy of an incoming ion and the threshold energy for etching of a particular material that basically determines how much etching takes place as well as a yield function. This yield function depends on an incident angle. So if you think about etching some crystal, of course, depending on how the ion hits that crystal, you're going to have a different different 124 00:31:05.470 --> 00:31:10.150 Mark Kushner: potential or probability of an atom being removed. 125 00:31:10.160 --> 00:31:19.799 Mark Kushner: So we also take that into consideration, and then finally, from the that combination and that edge rate, we can then again solve the level set equation 126 00:31:19.820 --> 00:31:24.259 Mark Kushner: and do this in every time step and have the service move after each time. Step. 127 00:31:25.420 --> 00:31:27.539 Mark Kushner: Okay. So then the sum of 128 00:31:27.760 --> 00:31:30.219 Mark Kushner: the parameters, which, let's say. 129 00:31:30.380 --> 00:31:50.740 Mark Kushner: can be, or or should be, modified for to to calibrate to a particular process are given here. There are many other parameters in the background that have been, let's say, optimized. They're already pre calibrated to the, to the system. But these are the ones that you can then use. So 130 00:31:50.960 --> 00:31:56.779 Mark Kushner: the different fluxes for the ions, for the main agent, oxygen, ion energy, and so on. 131 00:31:58.183 --> 00:32:07.080 Mark Kushner: So yeah, the the calibrated model. So the model is calibrated to some experiments. These are from a previous publication. 132 00:32:07.080 --> 00:32:31.989 Mark Kushner: And yeah, they relatively, they match this relatively well. And what this allows us now to do is to say, Okay, well, the model can relatively well describe the what what the physical behavior is or what we anticipate would happen under different conditions. So now, if we, for example, have some a mask with a different angle or a different thickness, we can actually 133 00:32:31.990 --> 00:32:39.100 Mark Kushner: predict what the what the topography should be with the different 134 00:32:39.360 --> 00:32:40.650 Mark Kushner: mask shapes. 135 00:32:42.369 --> 00:32:54.860 Mark Kushner: We applied the plasma etching model to edge and silicon Germanium inner spaces. So this is again for devices like that are 136 00:32:55.360 --> 00:33:12.850 Mark Kushner: let's say, coming now after the finfet, which is this gate all around device. So the way you fabricate those because you you need to get somehow. These floating, floating silicon pillars is by stacking silicon silicon germanium, and then etching away the the silicon germanium layer 137 00:33:13.319 --> 00:33:24.739 Mark Kushner: and the so that means that you need a process which can etch away silicon Germanium away and laterally while keeping the silicon still there. So 138 00:33:26.610 --> 00:33:29.290 Mark Kushner: so we have some experiments here 139 00:33:29.350 --> 00:33:50.389 Mark Kushner: which did this using? Cf, 4, 0, 2 plasma. And so this is the recipe that we use with the the plasma power, the different flow rates and they varied. We varied the pressure between 10 and 40 millitor, and we see how, let's say, the silicon Germanium is being etched away from the sides here on the single pillar, while the silicon is remaining relatively stable. 140 00:33:50.390 --> 00:34:04.699 Mark Kushner: So we try to. So here are the average edge depths. We also don't see too much variation between l. 1 and L. 6 here. So if you look along this pillar as long as there's not much else 141 00:34:04.740 --> 00:34:27.379 Mark Kushner: that's interrupting it on the side here they have a relatively similar well, flux of particles that are arriving there, so that this flux from a source plan or from the chamber that's coming here is is relatively the same up here as it is down here, unless there's something interrupting it there. So it's it's it's a relatively linear average 142 00:34:27.889 --> 00:34:30.219 Mark Kushner: edge depth also in time. 143 00:34:30.429 --> 00:34:47.600 Mark Kushner: And here we have varied when we vary the pressure. We see also that it's there's a there's a relatively linear description between the edge depth and the pressure. And but we do see some variation and some perhaps saturation and variation here at higher, at higher pressures. 144 00:34:48.927 --> 00:34:58.782 Mark Kushner: So why is etching isotropic and selective against silicon? So where does the selectivity come from? We try to investigate this 145 00:34:59.230 --> 00:35:20.630 Mark Kushner: from the atomistic level. So we know that the bond strengths. So the dissoci energy, dissociation, energy of the Germanium, Germanium and silicon Germanium bonds are lower than the silicon silicon bond, so that are more readily so that you don't need as much energy to remove them. And the Germanium oxygen bond is also slightly lower than silicon oxide. 146 00:35:20.670 --> 00:35:45.519 Mark Kushner: but there's probably a bit more to it. So what we looked at here is the presence of oxygen in this space. So here's a mask that's silicon dioxide. So you have quite a lot of oxygen. But we see oxygen basically at the surface of all of these layers so that that definitely plays a significant role. So when we look at the how to model this, we can track the the 147 00:35:45.610 --> 00:35:49.200 Mark Kushner: agent and oxygen coverages. 148 00:35:50.550 --> 00:36:14.350 Mark Kushner: and we know from this from previous studies, that some native oxide on silicon Germanium will not prevent etching as much as it will from silicon. So silicon dioxide will not be etched as much as silicon. Germanium just require a very high difference in the x rate here. 149 00:36:14.730 --> 00:36:17.939 Mark Kushner: so the oxygen will hinder the etching of the silicon. 150 00:36:19.550 --> 00:36:31.100 Mark Kushner: Now, the problems that we can have is we don't necessarily just want a single pillar sitting somewhere. We want to place as many devices next to each other as possible. So we need to find out 151 00:36:31.450 --> 00:36:55.649 Mark Kushner: how dense can this structure get and what impact that will then have on the actual etching, but having structures close to each other and having different kind of aspect, ratios can cause microloading. And so this is what we typically think of with microloading, that if your opening here of a trench is wider, you're gonna have more etching than if it's narrower even for the same 152 00:36:56.130 --> 00:36:58.040 Mark Kushner: for the same process and the same depth. 153 00:36:58.890 --> 00:36:59.660 Mark Kushner: Okay. 154 00:36:59.780 --> 00:37:27.480 Mark Kushner: so we can capture this in our model. So we have this here, we if you look at this etched structure we see on the side here of the pillar. That's that has nothing, let's say hindering particles coming towards it, because this just keeps going for, for I think several several millimeters. Then this side gets etched similar to how about a single pillar was was etched here we see less etching even at the top 155 00:37:27.480 --> 00:37:33.749 Mark Kushner: pillar here. So at this top silicon Germanium layer, there's less etching on the left side than on the right side. 156 00:37:33.880 --> 00:37:48.629 Mark Kushner: and as we go from the top to bottom we see that the top pillar is being etched more than the bottom, so that there's definitely the lateral. Rather etching is that is hindered by these nearby pillars and also by the high aspect ratios. 157 00:37:49.310 --> 00:38:09.180 Mark Kushner: Okay, so these are some other experiments which show so how it evolves over time. So we do see that I mean this, this is a we can. We can track it, how it changes over time. And here it's we see it even more clearly that the left side here the the inner pillars here are being etched much less than the other pillars. 158 00:38:09.660 --> 00:38:24.899 Mark Kushner: Here we also look at different pressures. And what kind of impact they have. So we see again, that the behavior is quite, quite similar that the outside pillars get etched more, but the increased pressure will 159 00:38:25.510 --> 00:38:32.540 Mark Kushner: will etch more, but it still has that same behavior as we had previously with the with the 160 00:38:32.960 --> 00:38:34.120 Mark Kushner: lower pressure. 161 00:38:35.040 --> 00:38:58.850 Mark Kushner: And so if we look at the average edge depths of the different pillars from the inner and the other side. It's if we're press changing the pressure, or if we're varying the the time, it's the outer side always has a higher average edge depth than the inner side, and it doesn't seem to be too much, let's say, benefit here from from reduction or an increase in pressure. 162 00:39:00.180 --> 00:39:02.510 Mark Kushner: So when we then apply our model to this. 163 00:39:03.188 --> 00:39:28.810 Mark Kushner: What we're trying to get then, is the fluxes that are basically coming in here and etching that silicon dominium. So we want to calculate this these velocities. So what we do is we calibrated our model similar to what I mentioned before. So we calibrate our model on this 5 pillar structure with 100 nanometer critical dimension. So the initial initial layer was just 164 00:39:28.910 --> 00:39:30.260 Mark Kushner: the pillar itself. 165 00:39:30.600 --> 00:39:38.862 Mark Kushner: so we did not do the plasma etching through the different layer stacks with our tool. We only did the lateral etching so. And then we 166 00:39:39.440 --> 00:39:44.530 Mark Kushner: tried to calibrate this model. So we played it with the basically the flux and the sticking coefficients 167 00:39:44.710 --> 00:39:55.030 Mark Kushner: to get well, just the flux and the sticking coefficient, because there's only we only looked at the the Radicals here there was no added bias, so there's no ions involved. 168 00:39:55.520 --> 00:40:06.879 Mark Kushner: and we saw that we could generate this pick the sticking point. Coefficient here was about point 2 something like this, and we could generate exactly the structure that they actually saw in the in the lab. 169 00:40:07.660 --> 00:40:24.299 Mark Kushner: And then, when we applied our model to the diff to different structures they had. So this was now so, using the model that was calibrated with the previous slide, we now did us another geometry, and this one has a critical dimension of 50 nanometers. So that means that the mask here and the width 170 00:40:24.340 --> 00:40:32.519 Mark Kushner: between the 2 between the pillars should be about 15 nanometers. We do see quite extreme variation, and this is in these 171 00:40:32.540 --> 00:40:50.389 Mark Kushner: pillars, so not all the pillars have the same width. And this is a problem from the previous step. But but our model seems to reproduce the structures quite well, and also the single pillars, which isn't too surprising, because they basically behave the same way as this kind of outside pillar over here. 172 00:40:51.681 --> 00:40:59.490 Mark Kushner: We also did the same thing for the 40 millilito pressure. So it's also able to reproduce the structures 173 00:40:59.670 --> 00:41:00.830 Mark Kushner: that were 174 00:41:01.470 --> 00:41:02.939 Mark Kushner: measured in the lab as well. 175 00:41:04.870 --> 00:41:06.016 Mark Kushner: Okay? And 176 00:41:06.680 --> 00:41:35.069 Mark Kushner: we are now using a global optimizer to now find the the parameters to see whether we can to apply this more generally, so that when we vary other conditions in the Chamber, and if we have any other images, then we can, let's say very quickly find the optimal set of parameters, which in this case was simply the flux or rate, or the flat wafer rate h rate and the sticking coefficient. But 177 00:41:35.542 --> 00:41:39.920 Mark Kushner: so this is what we're working on now. So what we do here is 178 00:41:40.160 --> 00:42:01.720 Mark Kushner: for these, for example, we run the optimizer. We, we run the optimizer based on the total edged depth in each of these these pillars. So we create basically extract this depth matrix which gives us the the simulated values of the depths of each of these pillars. So we get this, and we can then use that matrix to 179 00:42:01.750 --> 00:42:04.590 Mark Kushner: define our optimization target. 180 00:42:07.130 --> 00:42:32.119 Mark Kushner: Okay? So now, what's what's missing here is what you've probably noticed. And this is not atypical of process. Dcat is that there's not really a link to the equipment itself. Right? So we have. The models themselves. Look more at at rates, at fluxes, and and assume a lot of things about the the different distributions rather of of ions and neutral particles. So 181 00:42:32.782 --> 00:42:34.529 Mark Kushner: so there is. 182 00:42:35.020 --> 00:42:40.609 Mark Kushner: Depend. I mean, there are not many process Tcad vendors out there. 183 00:42:41.240 --> 00:42:47.409 Mark Kushner: 2 that I know of, Salaco. I'm I'm working with them on these projects and synopsis 184 00:42:47.891 --> 00:43:13.760 Mark Kushner: and so Vacco does not have any link to equipment settings, for this synopsis has a very simplified, as far as I know, and from what I've spoke with them simplified model, which at least the companies I work with are not too happy with. So they need. They want to have some improved model there. So I'm working together with also with synopsis a little bit in order to try to try to make that connection. 185 00:43:14.533 --> 00:43:43.069 Mark Kushner: So here we we can visualize kind of what kind of scales we're dealing with in general. So we have the reactor scale where we, the particles behave, and differently than they do with this feature scale. So here the if you just look at gas flow the particles. Diffusion depends on the interparticle collisions. So the mean, free path of the of each of these particles. 186 00:43:43.130 --> 00:44:02.779 Mark Kushner: The mean free path is much higher than the scale at which we deal with here. Right? So this here the trench here is, I don't know, 100 nanometers, 50 nanometers, but the mean free path is on the order of of micrometers, or more so, 100 micrometers, or more so. So that means that the particles in this scale here will 187 00:44:02.850 --> 00:44:14.209 Mark Kushner: much more likely hit against the surface or a wall than they will against another particle. So this is why, at this scale we can we do this ballistic transport, and we ignore the interparticle scattering. 188 00:44:14.840 --> 00:44:18.690 Mark Kushner: But in order to understand what's happening at this 189 00:44:19.200 --> 00:44:45.760 Mark Kushner: this plane here, the source plane, where we then begin our feature scale simulation. It would be good to have a link to some kind of reactor simulation. So we've done some simple simulations where we for for the Co. 2 AR plasma. So we vary the coil power, the gas flow rate pressure, the ratio of fluorine to argon temperature and the and the bias voltage 190 00:44:46.150 --> 00:44:51.110 Mark Kushner: and ran some reactor simulations. And then we can link that to Vnps 191 00:44:52.750 --> 00:45:07.650 Mark Kushner: in here we include some typical systems. So so plasma behavior. So ionization, dissociation excitations and and so on in order to try to just extract the 192 00:45:08.141 --> 00:45:16.160 Mark Kushner: yeah. So with the with the certain electron cross sections. And the idea is to extract the behavior here at this 193 00:45:16.220 --> 00:45:41.189 Mark Kushner: location, where our wafer typically would be. So what we want to extract there are, let's say in this case, what we did is the fluxes. So the flux of the the chlorine chlorine atom, which is involved in the etching and the ions as well. So we got here some fluxes, and we see the cross wafer fluxes here as you go from the center of the wafer to the edge. 194 00:45:41.260 --> 00:45:44.320 Mark Kushner: And so this is what we get from our reactor simulation. 195 00:45:44.810 --> 00:45:57.419 Mark Kushner: So we can then use this. So we say, okay, if we're near the center, then we'd use a value that's somewhere, maybe around here, and then we can plug that into the our source plane, and then we can run our features. Get simulation. 196 00:45:57.500 --> 00:46:02.370 Mark Kushner: However, we don't want to do this every single time we want to run a simulation. 197 00:46:02.470 --> 00:46:08.020 Mark Kushner: So the idea was we if we vary all these parameters within a certain. 198 00:46:08.040 --> 00:46:29.910 Mark Kushner: let's say, feasible range and generate a whole bunch of results from that, a whole bunch of values for the fluxes. Then we could use different computational methods. So whether it's machine learning or some interpolative tools in order to provide essentially a surrogate model for Vienna. Ps, so we did this for this 199 00:46:30.288 --> 00:46:39.759 Mark Kushner: simple system. And this is what we varied here with the power flow pressure. And so on. Okay and created about 19,000 combinations. 200 00:46:39.860 --> 00:46:55.999 Mark Kushner: And then, develop a multi variable spline interpolation model. And now this model is basically connected to Vienna. Ps, so when we run this particular simulation, we can provide equipment inputs to Vienna, Ps. It will 201 00:46:56.570 --> 00:47:08.029 Mark Kushner: look up the this from this table and extrapolate the values based on this multivariable spline interpolation and then run the actual hedging itself. 202 00:47:10.430 --> 00:47:35.049 Mark Kushner: the other things we're doing is with some with some machine learning. So the idea here is to have reactor conditions, whether they come from simulations, or from experiments to train a model. So whether the model can then have, either from flux, extraction and feature simulations where we run semi empirical or physical models like what I showed before. 203 00:47:35.210 --> 00:47:44.709 Mark Kushner: From that we can then develop a machine learning model which links the reactor conditions to how the what the the feature. 204 00:47:45.030 --> 00:48:07.500 Mark Kushner: the feature, scale model should be, or the other option. And the other thing that we're investigating with with other with some industry partners is to, not even to simply try to predict the what types of geometric features we expect to get from certain equipment inputs. So if they already have a database with a a lot of information, for example, for this. 205 00:48:08.260 --> 00:48:30.710 Mark Kushner: trench fillings, for example, and they know already what kind of geometric descriptors you get from certain dimensions. Then we could train a machine learning model to let's say, either optimize the system or to predict if you have these particular reactor conditions, then you can expect that your geometric features will have such and such dimensions. 206 00:48:30.710 --> 00:48:43.269 Mark Kushner: So this is the the core idea here, and then we can get a feature geometry which we either model if we use the feature simulations, modeling, or which we simply quasi, draw or emulate. 207 00:48:43.530 --> 00:48:47.680 Mark Kushner: If we use the geometric descriptors instead. 208 00:48:49.070 --> 00:49:12.019 Mark Kushner: Okay, so we did this on some simple data. So this is an Sf, 6 0, 2 model that's based on some published experimental data where they vary the pressure somewhat the combination of O, 2 with sf, 6 the bias voltage. And then so these are our inputs. And then the outputs are the the. 209 00:49:12.060 --> 00:49:20.700 Mark Kushner: the flux of the fluorine, the oxygen flux, and the ion flux. And then there's a a parameter for the effective 210 00:49:21.148 --> 00:49:24.550 Mark Kushner: so for the yield function of the oxygen itself. 211 00:49:24.810 --> 00:49:25.980 Mark Kushner: So we 212 00:49:26.190 --> 00:49:44.279 Mark Kushner: use this data to calibrate the model. So we basically then then try to use different machine learning approaches to try to basically with this data and have a machine learning infused semi, empirical or physics based model for the Nfps. 213 00:49:44.780 --> 00:49:50.480 Mark Kushner: what we? Then we tried first, st the Gaussian process regression. And 214 00:49:50.650 --> 00:49:53.629 Mark Kushner: what it does is it basically takes. 215 00:49:53.790 --> 00:50:04.880 Mark Kushner: let's say, around around, I think, 50 50 to 100 functions and tries to fit the data. You give it with these functions, and it tries to then find the I'd say the best fit. 216 00:50:05.390 --> 00:50:14.881 Mark Kushner: What's good about it is that it tells you an error estimate. So it tells you how confident it is, gives you some confidence interval at certain regions. 217 00:50:15.390 --> 00:50:30.010 Mark Kushner: so. But if you take the mean to be the the correct answer, then you will be very disappointed, because, for example, here, if we're looking at how the oxygen flux at the surface is impacted by the O 2 fraction and feed. 218 00:50:30.170 --> 00:50:51.459 Mark Kushner: This bump is completely not physical, right? And or if you look at the Ao constant. This bump here is probably not something that you'd want to see. So it but at the same time, what's good about it is, it tells us, well, my, my my certainty or uncertainty is quite high. So that means that we we can at least say, Okay, well, we need more data points 219 00:50:51.460 --> 00:51:13.920 Mark Kushner: here. So if we add a data point there, so if we do another experiment and add a data point there, then we can at least get to something that's a bit better. However, we again see if you're trying to fit Gaussians is the same issue when you try to fit something like splines you get, you get overfitting. You get these curvature between points that is simply not not realistic. 220 00:51:16.102 --> 00:51:39.699 Mark Kushner: We also tried a a neural network. So we played around with different number of of hidden layers. But the main point is right. Your pressure bias, voltage and auto concentration are the inputs and our outputs are the fluorine fluxes. And then ion yield proportionality constant for oxygen. And then this one so the neural network basically gives us more of a linear fit. 221 00:51:40.110 --> 00:51:45.140 Mark Kushner: So this is just looking at a 2D image. So a part of this only the flux. 222 00:51:46.250 --> 00:51:49.729 Mark Kushner: yeah, the flux, just by varying the O 2 fraction 223 00:51:50.258 --> 00:51:54.109 Mark Kushner: and so we didn't vary the the bias fortitude. 224 00:51:54.400 --> 00:52:11.480 Mark Kushner: But we see that. Okay. So at least it gives us some kind of a linear prediction between the points. So at least, if you say if you try to somewhat, not interpolate. But if you go between, if you're looking for an answer, for between these points, then you will get at least something that's a little more 225 00:52:11.590 --> 00:52:37.880 Mark Kushner: more probably close to being realistic. However, extrapolation. This changes drastically depending on. Let's say what run you make, how many nodes you put in every time you run. There's some some stochastic, some randomization that's done in there, and you can get the extrapolation is is really really poor here. So we need to have more. Let's say, physics informed information there, or a larger data set in order to trust what we're getting out here. 226 00:52:38.290 --> 00:52:40.949 Mark Kushner: Right? So because when we run a simple test 227 00:52:40.990 --> 00:53:02.529 Mark Kushner: using the the Gaussian process regression in neural network here, with the same parameters, same inputs, except here, we have point 3 0 2, and here we have point 7 0, 2. As a concentration, we see again stressly, different geometries that end up, even though when you look at this, you would say, Okay, well, I mean, it's not horrible. 228 00:53:02.540 --> 00:53:23.450 Mark Kushner: It's seems at least somewhat reasonable. And here you can also say, Well, it seems to be a reasonable fit. But the trend how that translates to the actual topography is is really a very, very large difference. So before we can really trust any kind of as a machine learning methods to describe a topography. There's still a lot of work to do there. 229 00:53:24.730 --> 00:53:41.530 Mark Kushner: Okay, so that I'll I'll leave you with this. We also have just to kind of advertise a bit to be in a Ps. We recently put it, released it uploaded to Pipi, so you can also install it with Pip install Vnps, and if you want to play around with it. There are some examples, and I can. You can just 230 00:53:41.830 --> 00:53:49.870 Mark Kushner: play with it at your leisure, and if you find something that's wrong. Let me know that we always want. We want negative feedback. So we can fix it. 231 00:53:50.100 --> 00:53:52.551 Mark Kushner: Okay, yeah, thank you very much. 232 00:53:56.040 --> 00:53:58.930 Mark Kushner: Thank you so much. Are there questions? 233 00:53:59.500 --> 00:54:00.260 Mark Kushner: Yeah. 234 00:54:00.993 --> 00:54:08.230 Mark Kushner: In the global fit parameter fitting section. What are? Why does 235 00:54:08.380 --> 00:54:11.320 Mark Kushner: the simulations show a lot 236 00:54:11.700 --> 00:54:18.629 Mark Kushner: less or less? Forget less or more. Horizontal deposition of the experiment. 237 00:54:19.100 --> 00:54:26.319 Mark Kushner: What are the best explanations for that? Yes, you mean, yeah, that one. Okay, let me let me put the one that's 238 00:54:29.170 --> 00:54:31.355 Mark Kushner: Let's say this one or yeah. 239 00:54:32.610 --> 00:54:34.010 Mark Kushner: So where? Where do you mean? 240 00:54:34.120 --> 00:54:38.850 Mark Kushner: Or like in the the gray? They're touching. But the red aren't touching. 241 00:54:39.973 --> 00:54:42.273 Mark Kushner: Oh, no sorry. Sorry this is 242 00:54:43.130 --> 00:54:47.140 Mark Kushner: the I guess you can't see it. Very well. There are 2 materials here. 243 00:54:47.390 --> 00:54:49.419 Mark Kushner: so if you see where the cursor is. 244 00:54:49.430 --> 00:54:54.239 Mark Kushner: This is the way this is where the material ends here. Oh, I see. And here. 245 00:54:55.440 --> 00:55:13.880 Mark Kushner: yeah, it's it's i i should have. It's just a poor some image. I I guess I should have drawn this. But this is the distance here. Yeah, that looks a lot better. Yeah, it's still, it's still not perfect, and and even if it was not perfect, my answer to your question would be because. 246 00:55:14.175 --> 00:55:30.450 Mark Kushner: it is not sufficient to describe this geometry with just 3 parameters. It's simply not enough. And this is why we're now we're now doing the what we're doing is basically at subtracting one level set from the other, or we do Boolean operations. So if you say if you have an overlay here 247 00:55:30.720 --> 00:55:50.699 Mark Kushner: where your surface goes something like this, let's say, and there's an opposite overlay up there versus here. Then you do something like you. Invert one of the level set and and them, and invert the other level set and them, and then some those 2, and when you do that, what you will hand up is a level set description of the material which is wrong 248 00:55:50.780 --> 00:55:53.730 Mark Kushner: right? And you want that to be 0. 249 00:55:53.770 --> 00:56:13.490 Mark Kushner: We want that to be flat to nonexistent. So you. So we are now doing that by basically summing the the differences. If you look at the difference in the sign distance function between the 2 materials that'll give you ideally, you want a 0 so that should give you the the a good error value or optimization target. 250 00:56:15.160 --> 00:56:18.529 Mark Kushner: Because this, yeah, it's just not sufficient to have just a single value. 251 00:56:20.960 --> 00:56:21.750 Mark Kushner: Yeah. 252 00:56:22.340 --> 00:56:32.360 Mark Kushner: yeah, great talk. Thank you, I I might have missed this. But could you explain to me again why you said that the neural network and the the Gaussian regression are not quite matching the same. 253 00:56:32.760 --> 00:56:36.461 Mark Kushner: I mean, if you look, the the reason they're not matching is 254 00:56:39.810 --> 00:56:41.300 Mark Kushner: If you look at this. 255 00:56:41.440 --> 00:56:46.669 Mark Kushner: So from from the Gaussian one. I use the median. That's right, or the main mean value. 256 00:56:47.407 --> 00:56:51.662 Mark Kushner: So if you look at the oxygen flux here, what we have is 257 00:56:53.110 --> 00:56:56.350 Mark Kushner: you have this, this fictitious bump 258 00:56:56.420 --> 00:57:02.260 Mark Kushner: where the flux increases, even though, let's say, this would, this is a physical physical value. 259 00:57:02.290 --> 00:57:11.749 Mark Kushner: this at point 2 5. Now, this should never go between 0 and point 2 5. You should never have. You should not have a higher oxygen flux 260 00:57:11.820 --> 00:57:35.970 Mark Kushner: than what you have here at point 2 5. This doesn't make sense. Now, if you keep going, it now dips down. You should never have less oxygen flux at the source at the source plane than you do as than you do in the in the chamber. But you still have that dip. So if I now check at point 3. I have a lower oxygen content there right now, what does oxygen do? 261 00:57:39.113 --> 00:57:39.976 Mark Kushner: Right. 262 00:57:41.990 --> 00:57:43.870 Mark Kushner: Does this make sense? Then wait? 263 00:57:43.950 --> 00:57:50.880 Mark Kushner: No, maybe I'm concentrating on the wrong one. Let's let's look at the Ion flux or the 264 00:57:52.510 --> 00:57:55.219 Mark Kushner: the Ao constant could also be part of the issue. 265 00:57:55.520 --> 00:57:58.470 Mark Kushner: Yeah, but it's the same here with the fluorine flux. Right? 266 00:57:58.935 --> 00:58:09.349 Mark Kushner: You have a this dip here which is not physical and doesn't make any sense, and you have an increase here a bump here. That's also not physical. It doesn't make any sense 267 00:58:09.710 --> 00:58:12.281 Mark Kushner: for that one for this 268 00:58:13.590 --> 00:58:28.000 Mark Kushner: neural network. It's a linear extra, basically almost linear extrapolation. So you go from 0 to this known value of point 4 sum for one for 2, and it just will linearly give, interpolate that value between them. So 269 00:58:28.450 --> 00:58:35.340 Mark Kushner: if I was to bet which one would be, let's say more accurate in this case, I would say, probably this one. But 270 00:58:35.540 --> 00:58:45.159 Mark Kushner: yeah, it's it's still uncertain. So then you you will have. Then here you probably have probably higher, higher ion and less oxygen. 271 00:58:45.630 --> 00:58:47.002 Mark Kushner: Then you would 272 00:58:47.950 --> 00:58:48.840 Mark Kushner: Here. 273 00:58:49.960 --> 00:58:52.050 Mark Kushner: here you have a lower ion flux. 274 00:58:56.140 --> 00:58:57.329 Mark Kushner: Yeah, it's just 275 00:58:57.340 --> 00:59:03.219 Mark Kushner: the the way that it's not interpolating. But the way it's extracting values is 276 00:59:03.390 --> 00:59:05.369 Mark Kushner: is simply wrong. 277 00:59:05.440 --> 00:59:06.600 Mark Kushner: It's overfitting. 278 00:59:07.890 --> 00:59:21.850 Mark Kushner: Okay? When you were talking about your surface reactions, you mentioned that you only allow for a single chemical species to react with the silicon site so like a floor 279 00:59:21.980 --> 00:59:26.799 Mark Kushner: fluoridating the surface site and not allowing any further fluorine 280 00:59:27.060 --> 00:59:28.990 Mark Kushner: to react. But 281 00:59:29.646 --> 00:59:54.789 Mark Kushner: wouldn't it still be able to further react to reduce the threshold energy for sputter. No, I I maybe it's a it was a misunderstanding. Yeah we for the plasma etching. We track. The adsorption of any number of species that we physically know are there. So for the Sf, 6 0, 2, we track 282 00:59:54.860 --> 01:00:04.183 Mark Kushner: the the fluorine adsorption, oxygen adsorption and ion is not adsorbed. But we track the flux of the ions so 283 01:00:04.930 --> 01:00:11.419 Mark Kushner: in that. So you typically, you need 4 fluorines to remove a silicon. Right so. But so. But 284 01:00:12.270 --> 01:00:16.089 Mark Kushner: so this, this comes into play for us when it's fully covered. 285 01:00:16.140 --> 01:00:24.780 Mark Kushner: then you have an etching. So the etching rate is a quarter of it has that relationship which is one quarter of the 286 01:00:25.800 --> 01:00:28.408 Mark Kushner: of the flux and 287 01:00:31.990 --> 01:00:35.359 Mark Kushner: flux and etso and and coverage combination. Right? 288 01:00:37.580 --> 01:00:43.069 Mark Kushner: So you have a absorption here. So if you have a full, fully absorbed, fully fluorinated surface. 289 01:00:43.140 --> 01:00:53.280 Mark Kushner: the rate, the effective rate will be a quarter. But if you have other species that are also etching, you can track their absorption as well. So there's there's no. 290 01:00:53.520 --> 01:00:58.619 Mark Kushner: there's no limit. As long as you physically know that that's what's happening. You can put in more 291 01:00:59.080 --> 01:01:06.499 Mark Kushner: and there's a let's say, a more complex model. Is that the fluorocarbon? So there's a where you have 292 01:01:06.993 --> 01:01:14.619 Mark Kushner: simultaneously some polymer that's actually causing deposition, and another species that other species that are causing etching. So you could have 293 01:01:14.750 --> 01:01:26.200 Mark Kushner: deposition in one location and etching at another location. So this we also have to treat as well. And follow up. How do you track the etches that 294 01:01:27.476 --> 01:01:39.210 Mark Kushner: do? Do you just allow them to harmlessly flow outside of the feature profile? Or you mean well, you mean when they reflect if they stick right. So what we do is 295 01:01:39.656 --> 01:01:41.359 Mark Kushner: it's it's a stochastic 296 01:01:41.520 --> 01:01:50.259 Mark Kushner: simulation, right? So, Monte Carlo. So that means that when we have a particle that hits the surface you can deal with it one of 3 ways right? You can then roll the dice. 297 01:01:50.280 --> 01:02:12.009 Mark Kushner: find a random number, and decide whether that particle will contribute to the etching, or, if it will be reflected, you can generate multiple particles and have some of them reflect, some of them stick and and cause etching, or you can weigh that particle. So what we do is we basically assign a weight to the particle if it comes from the source directly it has a weight one 298 01:02:12.080 --> 01:02:13.819 Mark Kushner: when it hits the surface. 299 01:02:13.880 --> 01:02:39.530 Mark Kushner: If the sticking coefficient is point 2, then point 2 of that particle causes a deposition or absorbs. So then the adsorption is point 2 effectively, and then point 8 of that. So it's a part of the particle is reflected, but it carries a weight of point 8, it's reflected, and we keep tracking it. If it hits another location on the surface, the same thing happens. Then we say, okay, point 2 times point 8 sticks 300 01:02:39.550 --> 01:02:54.969 Mark Kushner: point 8 times point 8 reflects. And it keeps basically doing this until we reach some threshold of I don't know point 0 0 1 weight of a particle. If the particle happens to leave our simulation domain during this, then for us it's gone. 301 01:02:55.270 --> 01:02:57.049 Mark Kushner: and we don't get it back. 302 01:02:57.550 --> 01:03:01.609 Mark Kushner: And how does that weight coincide with the energy of the particle. 303 01:03:01.959 --> 01:03:20.790 Mark Kushner: This is this is only for the neutral particles. Only neutral particles have a weight. Ions, they have energy, so they are assigned. An energy based on the energy distribution, which, as I said, is, is a raw, is A is a horrible estimate. But it's it's this we got when it hits the surface it can either 304 01:03:21.140 --> 01:03:44.219 Mark Kushner: it it will. It can etch, or it can reflect. If it etches, then the rate or the let's say, the effective edge, the etching etching rate that it creates is based on its energy. So the difference in energy between the particle and the threshold energy of the material and its angle of incidence, which has this, this for which we have this yield function 305 01:03:44.420 --> 01:04:11.789 Mark Kushner: when it's reflected, then a new energy for that particle randomly. So you find a random number, and the new energy of that part that that Ion gets is between what it initially had, and the minimum or the threshold energy of the material. And then it's reflected with that. So that we kind of say, Okay, well, part of that energy is lost to the interaction, so lost to the the heating, and then reflecting. So how would you handle a hot neutral. 306 01:04:12.190 --> 01:04:16.639 Mark Kushner: or do you? We don't handle it. No, we don't have it in here. 307 01:04:17.730 --> 01:04:28.449 Mark Kushner: I mean, you could right, but you can put in particles all you want. You can add part of more particles and more behaviors, but we know we don't have that in any of our models now. 308 01:04:31.476 --> 01:04:40.279 Mark Kushner: So for when when you're talking about the pillars, and you're calibrating the flux when it hit the when there's a lot of pillars. 309 01:04:40.390 --> 01:04:42.781 Mark Kushner: Are you doing that 310 01:04:43.540 --> 01:04:54.830 Mark Kushner: calibration based on physics? Or are you just carefully adjusting the flux, and maybe some of the coefficients, so that you match the experimental results. For this 311 01:04:54.920 --> 01:04:58.460 Mark Kushner: it was this particular case. Here 312 01:04:59.000 --> 01:05:02.560 Mark Kushner: was is just essentially what you need to. 313 01:05:02.680 --> 01:05:03.830 Mark Kushner: So the 314 01:05:04.260 --> 01:05:08.873 Mark Kushner: the combination of flux or rate and and 315 01:05:09.740 --> 01:05:12.390 Mark Kushner: and time is for me. 316 01:05:12.490 --> 01:05:26.140 Mark Kushner: This is the same thing, time and rate for me. It doesn't matter if you set the time to one. Then you adjust the rates to get there. If you have a set your rate to one then you have you? You just have enough time to get that particular etching etching done. 317 01:05:26.560 --> 01:05:30.930 Mark Kushner: So this was done just by eyeballing and trying out different values. 318 01:05:31.120 --> 01:05:40.109 Mark Kushner: But I wanted to get away from that. So this is why I wanted to use the optimizer. So it's kind of it's not really. The optimization itself is is computational. 319 01:05:40.340 --> 01:05:44.640 Mark Kushner: It's not. There's no, there's no physically meaningful model behind it other than 320 01:05:44.720 --> 01:06:01.040 Mark Kushner: I'm modeling it using this, these equations, in order to get etching to take place, and then, based on what kind of etching you get out of it. You know whether you can trust your sticking coefficients here. That's pretty much it. 321 01:06:03.099 --> 01:06:12.080 Mark Kushner: So if the feature is taller or there's more dense of them, you can't use the same color you can. That that's the idea that you can use the same. Yeah. 322 01:06:13.500 --> 01:06:24.250 Mark Kushner: right? Because what we're what we're trying to optimize is the set of parameters that you didn't use in this semi empirical kind of approach, and not not just the geometry itself. 323 01:06:27.060 --> 01:06:28.500 Mark Kushner: Any other questions. 324 01:06:29.990 --> 01:06:41.109 Mark Kushner: When you etched these finfets, were you applying a bias voltage between those different binding energies? No, you just really no. This is just the plasma. There's no bias. 325 01:06:41.580 --> 01:06:54.120 Mark Kushner: which is why I ignore the ions. There might be a bit of a ion involvement. But typically the the ions don't have such a high energy, so their their impact will be minimal if you don't apply any bias. 326 01:06:54.760 --> 01:07:00.299 Mark Kushner: So maybe there could be some directionality difference that's caused by them. But 327 01:07:00.480 --> 01:07:02.050 Mark Kushner: it wasn't sufficient 328 01:07:02.210 --> 01:07:04.680 Mark Kushner: that we felt that we needed to include. 329 01:07:08.310 --> 01:07:11.959 Mark Kushner: If there are no more questions. Thank you very much. 330 01:07:25.222 --> 01:07:30.239 Mark Kushner: Very interesting. Yeah.