WEBVTT 00:00:00.000 --> 00:00:02.029 align:middle line:84% JUDY HOYT: Doing right now is hopefully, 00:00:02.029 --> 00:00:05.030 align:middle line:84% you're all reading chapter 6, which 00:00:05.030 --> 00:00:08.360 align:middle line:84% covers the process of thermal oxidation. 00:00:08.360 --> 00:00:11.330 align:middle line:84% Last time, we talked about general introduction 00:00:11.330 --> 00:00:13.970 align:middle line:84% to thermal oxides in silicon CMOS. 00:00:13.970 --> 00:00:18.080 align:middle line:84% And we also talked about the metal oxide silicon 00:00:18.080 --> 00:00:22.940 align:middle line:84% or semiconductor capacitor and how electrical simple CD 00:00:22.940 --> 00:00:24.843 align:middle line:84% measurements can be used to understand 00:00:24.843 --> 00:00:26.510 align:middle line:84% the quality of the oxide and the charges 00:00:26.510 --> 00:00:28.980 align:middle line:90% that exist in that structure. 00:00:28.980 --> 00:00:32.060 align:middle line:84% This time, we're going to cover a basic model called 00:00:32.060 --> 00:00:32.840 align:middle line:90% the Deal-Grove. 00:00:32.840 --> 00:00:35.390 align:middle line:84% This is after the two people, that's Bruce Deal and Andy 00:00:35.390 --> 00:00:39.890 align:middle line:84% Grove, who came up with this linear parabolic oxidation 00:00:39.890 --> 00:00:40.400 align:middle line:90% model. 00:00:40.400 --> 00:00:44.120 align:middle line:84% It really remains the basic model used today. 00:00:44.120 --> 00:00:46.920 align:middle line:84% And then we'll talk about examples on how to use it. 00:00:46.920 --> 00:00:50.060 align:middle line:84% And we'll finish up with other models of planar oxidation 00:00:50.060 --> 00:00:53.450 align:middle line:84% that are very useful in the very thin oxide regime. 00:00:53.450 --> 00:00:54.950 align:middle line:84% So I'm just curious, how many people 00:00:54.950 --> 00:00:57.140 align:middle line:84% here have known or not known but have 00:00:57.140 --> 00:01:02.160 align:middle line:84% heard about the Deal-Grove oxidation model? 00:01:02.160 --> 00:01:05.600 align:middle line:84% So about maybe a little less than half or so. 00:01:05.600 --> 00:01:07.830 align:middle line:84% OK, so that works reasonably well. 00:01:07.830 --> 00:01:09.888 align:middle line:84% We go through it because it's the basic model. 00:01:09.888 --> 00:01:11.430 align:middle line:84% And then everything after that, a lot 00:01:11.430 --> 00:01:13.222 align:middle line:84% of things after that tend to be corrections 00:01:13.222 --> 00:01:15.760 align:middle line:90% to the Deal-Grove model. 00:01:15.760 --> 00:01:17.310 align:middle line:84% So let's go on to slide number 2. 00:01:17.310 --> 00:01:21.420 align:middle line:84% And that shows the basic schematic setup 00:01:21.420 --> 00:01:24.540 align:middle line:84% for how Deal and Grove derived their model. 00:01:24.540 --> 00:01:26.730 align:middle line:84% What it shows you is turned sideways 00:01:26.730 --> 00:01:29.940 align:middle line:84% is you have a gas stream here on the left that's 00:01:29.940 --> 00:01:31.840 align:middle line:90% on top of the wafer. 00:01:31.840 --> 00:01:35.460 align:middle line:84% There is a thermal oxide being grown here 00:01:35.460 --> 00:01:37.770 align:middle line:84% in this white region, the silicon dioxide. 00:01:37.770 --> 00:01:39.810 align:middle line:84% And the pink on the right shows this meant 00:01:39.810 --> 00:01:41.758 align:middle line:90% to represent the silicon wafer. 00:01:41.758 --> 00:01:43.800 align:middle line:84% And just to give you an order of magnitude scale. 00:01:43.800 --> 00:01:44.940 align:middle line:90% The silicon wafer is thick. 00:01:44.940 --> 00:01:46.830 align:middle line:84% Of course, it's hundreds of microns. 00:01:46.830 --> 00:01:49.260 align:middle line:84% This oxide that we're talking about growing 00:01:49.260 --> 00:01:51.960 align:middle line:84% is on the order of 0.01, 0.01 micron being 00:01:51.960 --> 00:01:54.330 align:middle line:84% about 100 angstroms or 10 nanometers 00:01:54.330 --> 00:01:55.500 align:middle line:90% up to maybe a micron. 00:01:55.500 --> 00:01:58.260 align:middle line:84% That would be the range of reasonable thicknesses 00:01:58.260 --> 00:01:59.310 align:middle line:90% of which you would grow. 00:01:59.310 --> 00:02:01.620 align:middle line:84% Once you start growing more than a micron, 00:02:01.620 --> 00:02:05.340 align:middle line:84% as you'll see today, if you want to grow one or two or three 00:02:05.340 --> 00:02:09.470 align:middle line:84% microns by a thermal process, it gets pretty darn slow. 00:02:09.470 --> 00:02:11.720 align:middle line:84% The kinetics are such that it becomes really not 00:02:11.720 --> 00:02:12.972 align:middle line:90% very practical. 00:02:12.972 --> 00:02:14.930 align:middle line:84% So you don't see too many people growing oxides 00:02:14.930 --> 00:02:17.780 align:middle line:84% that much thicker than a couple of microns. 00:02:17.780 --> 00:02:19.790 align:middle line:84% If they need oxides that thick, they 00:02:19.790 --> 00:02:23.150 align:middle line:84% do a different process called chemical vapor deposition. 00:02:23.150 --> 00:02:25.063 align:middle line:84% So the basic idea of this model, though, 00:02:25.063 --> 00:02:26.480 align:middle line:84% is that we have a gas stream here. 00:02:26.480 --> 00:02:29.810 align:middle line:84% And there's a concentration C sub G of the oxidant. 00:02:29.810 --> 00:02:32.880 align:middle line:84% Let's say it's oxygen. Could be oxygen, could be water vapor. 00:02:32.880 --> 00:02:36.560 align:middle line:84% But there's some concentration in the main gas flow , 00:02:36.560 --> 00:02:37.820 align:middle line:90% in the main gas stream. 00:02:37.820 --> 00:02:41.720 align:middle line:84% As you get closer to the surface of the wafer, which 00:02:41.720 --> 00:02:44.885 align:middle line:84% has oxide on it, it has some concentration C sub 00:02:44.885 --> 00:02:47.490 align:middle line:84% S that's right at the surface of the wafer. 00:02:47.490 --> 00:02:50.390 align:middle line:84% There may be some boundary layer or whatever that causes 00:02:50.390 --> 00:02:51.500 align:middle line:90% a gradient to cross here. 00:02:51.500 --> 00:02:53.083 align:middle line:84% But right at the surface of the wafer, 00:02:53.083 --> 00:02:55.730 align:middle line:84% it's at C sub S in the gap but in the gas phase. 00:02:55.730 --> 00:03:00.080 align:middle line:84% In the solid, right inside at the very surface 00:03:00.080 --> 00:03:04.010 align:middle line:84% in the solid oxide, this oxidant has some concentration C sub 00:03:04.010 --> 00:03:08.520 align:middle line:84% O right at the surface, or C 0 if you would like. 00:03:08.520 --> 00:03:11.520 align:middle line:84% And then there is some gradient of the oxidant, 00:03:11.520 --> 00:03:12.973 align:middle line:90% say of the oxygen molecule. 00:03:12.973 --> 00:03:14.640 align:middle line:84% There's a gradient throughout the oxide. 00:03:14.640 --> 00:03:16.920 align:middle line:84% And at the interface, it has C sub I, the I standing 00:03:16.920 --> 00:03:17.670 align:middle line:90% for the interface. 00:03:17.670 --> 00:03:20.700 align:middle line:90% It has that concentration. 00:03:20.700 --> 00:03:24.180 align:middle line:84% And the basic chemical reactions that 00:03:24.180 --> 00:03:25.650 align:middle line:84% are happening now at the interface, 00:03:25.650 --> 00:03:27.358 align:middle line:84% not at the oxide surface, are shown here. 00:03:27.358 --> 00:03:32.250 align:middle line:84% Silicon plus oxygen going to SiO2 or silicon plus moisture, 00:03:32.250 --> 00:03:35.460 align:middle line:90% H2O, going to SiO2. 00:03:35.460 --> 00:03:37.793 align:middle line:84% And there in the equations that we're 00:03:37.793 --> 00:03:39.210 align:middle line:84% going to derive, the simple model, 00:03:39.210 --> 00:03:41.460 align:middle line:90% there are three fluxes involved. 00:03:41.460 --> 00:03:44.940 align:middle line:84% There's a flux F1 of oxidant that 00:03:44.940 --> 00:03:47.820 align:middle line:84% has to be transported in the gas phase 00:03:47.820 --> 00:03:50.330 align:middle line:84% from the major portion of the gas 00:03:50.330 --> 00:03:52.830 align:middle line:84% phase in the center of the tube to the surface of the wafer. 00:03:52.830 --> 00:03:54.310 align:middle line:90% That's one flux. 00:03:54.310 --> 00:03:56.710 align:middle line:90% There's a flux F2 in the oxide. 00:03:56.710 --> 00:03:59.700 align:middle line:84% This is the diffusion of the oxidant through the oxide. 00:03:59.700 --> 00:04:02.430 align:middle line:84% And there's finally a flux F3, which 00:04:02.430 --> 00:04:04.470 align:middle line:84% is what's happening right at the interface 00:04:04.470 --> 00:04:10.710 align:middle line:84% as the oxygen is incorporated into the growing oxide. 00:04:10.710 --> 00:04:13.490 align:middle line:90% So let's go on to slide 3. 00:04:13.490 --> 00:04:16.790 align:middle line:84% Again, on the upper diagram is exactly what 00:04:16.790 --> 00:04:18.320 align:middle line:90% I've just shown you. 00:04:18.320 --> 00:04:20.930 align:middle line:84% For those of you who have forgotten, on the upper right, 00:04:20.930 --> 00:04:23.210 align:middle line:84% I'm reminding you what the definition of flux is. 00:04:23.210 --> 00:04:24.360 align:middle line:90% What is a flux? 00:04:24.360 --> 00:04:25.830 align:middle line:90% It's the number of particles. 00:04:25.830 --> 00:04:27.240 align:middle line:84% Doesn't have to be, in this case, 00:04:27.240 --> 00:04:29.390 align:middle line:84% I'm talking about oxygen molecules or water vapor 00:04:29.390 --> 00:04:30.110 align:middle line:90% molecules. 00:04:30.110 --> 00:04:32.790 align:middle line:84% But it's the number of particles crossing a unit area-- 00:04:32.790 --> 00:04:36.290 align:middle line:84% so a unit area in this direction here-- 00:04:36.290 --> 00:04:37.680 align:middle line:90% per unit time. 00:04:37.680 --> 00:04:40.520 align:middle line:84% So there's a flux, in this case, going from the left 00:04:40.520 --> 00:04:41.840 align:middle line:90% to the right. 00:04:41.840 --> 00:04:43.800 align:middle line:84% In fact, there's three different of them. 00:04:43.800 --> 00:04:47.000 align:middle line:84% So what Deal and Grove did was write down 00:04:47.000 --> 00:04:51.530 align:middle line:84% three very simple equations, first order flux equations, 00:04:51.530 --> 00:04:55.635 align:middle line:84% which show these three series parts of the process. 00:04:55.635 --> 00:04:57.260 align:middle line:84% Again, they're all happening in series. 00:04:57.260 --> 00:04:59.840 align:middle line:90% So there's a flux, F1. 00:04:59.840 --> 00:05:01.430 align:middle line:84% They wrote down using Henry's law. 00:05:01.430 --> 00:05:04.610 align:middle line:84% So Henry's law just says, in the gas phase transport, 00:05:04.610 --> 00:05:08.810 align:middle line:84% if you have a concentration difference or a gradient 00:05:08.810 --> 00:05:11.990 align:middle line:84% here from this point here in the center of where the gas flow is 00:05:11.990 --> 00:05:16.910 align:middle line:84% to the surface, C sub S, that you can write the flux as just 00:05:16.910 --> 00:05:20.992 align:middle line:84% some constant, some Henry's constant, a constant number 00:05:20.992 --> 00:05:22.700 align:middle line:84% times the difference in the concentration 00:05:22.700 --> 00:05:27.920 align:middle line:84% between the surface and the where the concentration is CG. 00:05:27.920 --> 00:05:31.465 align:middle line:84% So that's a simple equation from Henry's law. 00:05:31.465 --> 00:05:32.840 align:middle line:84% A second equation they wrote down 00:05:32.840 --> 00:05:34.173 align:middle line:90% was diffusion through the oxide. 00:05:34.173 --> 00:05:36.480 align:middle line:84% And this comes from Fick's law, Fick's first law. 00:05:36.480 --> 00:05:38.480 align:middle line:84% Hopefully, some of you have seen this, maybe not 00:05:38.480 --> 00:05:39.710 align:middle line:90% in this particular form. 00:05:39.710 --> 00:05:43.130 align:middle line:84% When we talk about diffusion, it'll become very obvious. 00:05:43.130 --> 00:05:46.550 align:middle line:84% But this is Fick's first law for diffusion through the oxide. 00:05:46.550 --> 00:05:49.650 align:middle line:84% The flux F2 is just a constant number, 00:05:49.650 --> 00:05:53.120 align:middle line:84% which we call the diffusivity, D, times the gradient 00:05:53.120 --> 00:05:56.750 align:middle line:84% of the diffusion, DN by DX, where n is generally 00:05:56.750 --> 00:05:59.790 align:middle line:84% just the concentration of whatever is diffusing. 00:05:59.790 --> 00:06:00.810 align:middle line:90% And you can write that. 00:06:00.810 --> 00:06:02.550 align:middle line:84% If this is a straight line, writing 00:06:02.550 --> 00:06:04.810 align:middle line:84% the gradient of a straight line is very simple. 00:06:04.810 --> 00:06:08.930 align:middle line:84% It's just C at the surface, C 0 minus C interface divided 00:06:08.930 --> 00:06:10.180 align:middle line:90% by the thickness of the oxide. 00:06:10.180 --> 00:06:13.350 align:middle line:84% So it's a simple equation to write diffusion 00:06:13.350 --> 00:06:15.690 align:middle line:90% through the oxide. 00:06:15.690 --> 00:06:19.590 align:middle line:84% And finally, F3 is the flux at the interface. 00:06:19.590 --> 00:06:22.030 align:middle line:84% And this is just a surface reaction rate. 00:06:22.030 --> 00:06:25.960 align:middle line:84% So we write this final flux as K sub S, a constant, 00:06:25.960 --> 00:06:29.100 align:middle line:84% which has to do with how rapidly the reaction is taking 00:06:29.100 --> 00:06:31.950 align:middle line:84% place at the interface, times the concentration of oxygen 00:06:31.950 --> 00:06:34.060 align:middle line:84% or water vapor right at the interface. 00:06:34.060 --> 00:06:36.735 align:middle line:84% So three equations for each of these fluxes. 00:06:36.735 --> 00:06:40.450 align:middle line:90% 00:06:40.450 --> 00:06:41.520 align:middle line:90% So we go on to slide 3. 00:06:41.520 --> 00:06:45.250 align:middle line:84% And what they're assuming is steady-state condition. 00:06:45.250 --> 00:06:47.370 align:middle line:84% And what we mean by steady state is 00:06:47.370 --> 00:06:50.660 align:middle line:84% things are not changing with time, these profiles. 00:06:50.660 --> 00:06:54.150 align:middle line:84% So if I just go back one second to slide 3, 00:06:54.150 --> 00:06:57.540 align:middle line:84% is that this profile is, we're not in the transient phase. 00:06:57.540 --> 00:07:00.390 align:middle line:84% This profile has now been established as a linear profile 00:07:00.390 --> 00:07:01.200 align:middle line:90% in a steady state. 00:07:01.200 --> 00:07:04.860 align:middle line:90% It's not changing with time. 00:07:04.860 --> 00:07:07.030 align:middle line:84% You've established a constant profile. 00:07:07.030 --> 00:07:10.860 align:middle line:84% So in those conditions, then, we can write down 00:07:10.860 --> 00:07:13.740 align:middle line:84% that the three fluxes in series are all equal to each other. 00:07:13.740 --> 00:07:17.430 align:middle line:84% We don't have any buildup or any sync. 00:07:17.430 --> 00:07:21.360 align:middle line:84% So F1, the flux throwing through the gas, has to be equal to F2, 00:07:21.360 --> 00:07:23.250 align:middle line:84% the flux diffusing through has to be 00:07:23.250 --> 00:07:26.020 align:middle line:90% equal to the reactive flux. 00:07:26.020 --> 00:07:29.950 align:middle line:84% So in that case, then, it's relatively simple. 00:07:29.950 --> 00:07:32.490 align:middle line:84% If you sit down and you equate those three equations, 00:07:32.490 --> 00:07:36.600 align:middle line:84% you can derive this formula here, equation number 4, 00:07:36.600 --> 00:07:39.910 align:middle line:84% for the concentration of the oxygen molecules of the water 00:07:39.910 --> 00:07:42.610 align:middle line:90% vapor C sub I at the interface. 00:07:42.610 --> 00:07:45.430 align:middle line:84% You can write it as some constant, C star, which we'll 00:07:45.430 --> 00:07:50.620 align:middle line:84% talk about, where C star is the solubility of the oxidant 00:07:50.620 --> 00:07:54.790 align:middle line:84% in the oxide divided by a three-term expression, 1 00:07:54.790 --> 00:07:58.330 align:middle line:90% plus the ratio of K sub S to H. 00:07:58.330 --> 00:08:01.090 align:middle line:84% So that tells us something about the ratio of the surface 00:08:01.090 --> 00:08:07.526 align:middle line:84% reaction coefficient to Henry's coefficient H, plus k sub S X 00:08:07.526 --> 00:08:12.010 align:middle line:84% node over D. This is involving a diffusivity term. 00:08:12.010 --> 00:08:14.490 align:middle line:84% And so what we are generally going to do in this, 00:08:14.490 --> 00:08:16.620 align:middle line:84% we can actually simplify this equation 00:08:16.620 --> 00:08:22.080 align:middle line:84% by recognizing that we actually can neglect F1, the gas phase 00:08:22.080 --> 00:08:25.050 align:middle line:84% transport, which is usually a very good approximation. 00:08:25.050 --> 00:08:25.920 align:middle line:90% It's very fast. 00:08:25.920 --> 00:08:30.120 align:middle line:84% So if I go back to this slide number 3 briefly, this flux, 00:08:30.120 --> 00:08:32.760 align:middle line:84% this is happening much, much faster than these two 00:08:32.760 --> 00:08:36.851 align:middle line:84% processes, than the diffusion through the solid or then 00:08:36.851 --> 00:08:39.059 align:middle line:84% the reaction, as it happens to turn out in this case. 00:08:39.059 --> 00:08:41.820 align:middle line:84% That won't always be the case for other processes. 00:08:41.820 --> 00:08:44.910 align:middle line:84% When we talk about epitaxial growth or chemical vapor 00:08:44.910 --> 00:08:47.160 align:middle line:84% deposition, it won't always be this case 00:08:47.160 --> 00:08:49.350 align:middle line:84% that you can ignore the gas phase transport. 00:08:49.350 --> 00:08:52.602 align:middle line:84% But as it turns out, the surface reaction is slow enough, 00:08:52.602 --> 00:08:54.060 align:middle line:84% and the diffusion through the oxide 00:08:54.060 --> 00:08:59.200 align:middle line:84% is slow enough that this is always very fast. 00:08:59.200 --> 00:09:01.740 align:middle line:84% And so the beautiful thing about oxidation 00:09:01.740 --> 00:09:03.810 align:middle line:84% is you can ignore gas phase transport. 00:09:03.810 --> 00:09:06.190 align:middle line:84% And that's why you can design oxidation tubes 00:09:06.190 --> 00:09:06.940 align:middle line:90% to be very simple. 00:09:06.940 --> 00:09:09.780 align:middle line:84% You just stand all the wafers up and flow the oxygen through. 00:09:09.780 --> 00:09:12.580 align:middle line:84% And you don't have to care about exactly how the gas flows. 00:09:12.580 --> 00:09:15.160 align:middle line:84% When we talk about other processes 00:09:15.160 --> 00:09:18.700 align:middle line:84% like epitaxial growth, no such luxury by any means. 00:09:18.700 --> 00:09:21.440 align:middle line:84% In that case, this flux is extremely important. 00:09:21.440 --> 00:09:24.160 align:middle line:84% And in fact, it controls the process many times. 00:09:24.160 --> 00:09:26.350 align:middle line:84% So but we're very lucky in oxide growth 00:09:26.350 --> 00:09:29.350 align:middle line:84% that these two processes F2 and F3 are slow. 00:09:29.350 --> 00:09:31.990 align:middle line:90% So we can ignore F1. 00:09:31.990 --> 00:09:34.480 align:middle line:84% And that just ends up simplifying the equations 00:09:34.480 --> 00:09:37.280 align:middle line:90% to a certain extent. 00:09:37.280 --> 00:09:40.870 align:middle line:84% And so if I rearrange this a little bit, 00:09:40.870 --> 00:09:44.680 align:middle line:84% we get equation number 5 here for the-- 00:09:44.680 --> 00:09:46.270 align:middle line:84% we're really interested in C sub O 00:09:46.270 --> 00:09:52.790 align:middle line:84% here, the concentration at the surface of the oxidant. 00:09:52.790 --> 00:09:55.600 align:middle line:84% So let me combine now this equation number 00:09:55.600 --> 00:09:58.720 align:middle line:84% 4, which tells me what the concentration of water 00:09:58.720 --> 00:10:04.180 align:middle line:84% or oxygen is at the interface with-- 00:10:04.180 --> 00:10:06.910 align:middle line:84% I'm going to combine this equation with equation 3, 00:10:06.910 --> 00:10:10.390 align:middle line:84% just going back again, which just tells me that the surface 00:10:10.390 --> 00:10:13.640 align:middle line:90% reaction rate flux. 00:10:13.640 --> 00:10:18.230 align:middle line:84% And we get something like this that says that DX by DT-- 00:10:18.230 --> 00:10:22.020 align:middle line:84% so that's the rate of change of the thickness of the oxide-- 00:10:22.020 --> 00:10:25.010 align:middle line:84% DX by DT, we know we can write it 00:10:25.010 --> 00:10:27.170 align:middle line:84% as a flux divided by a concentration. 00:10:27.170 --> 00:10:29.940 align:middle line:84% So N1 here, does what anybody have 00:10:29.940 --> 00:10:33.120 align:middle line:84% an idea of what N1 is, just from dimensional arguments? 00:10:33.120 --> 00:10:36.830 align:middle line:90% 00:10:36.830 --> 00:10:38.750 align:middle line:90% I want to get DX by DT. 00:10:38.750 --> 00:10:43.590 align:middle line:84% Flux tells you the number of atoms per square centimeter 00:10:43.590 --> 00:10:45.480 align:middle line:90% per unit time. 00:10:45.480 --> 00:10:48.030 align:middle line:84% So N1 has to have the units of the concentration 00:10:48.030 --> 00:10:52.140 align:middle line:84% per cubic centimeter, basically, so that it works out, 00:10:52.140 --> 00:10:53.640 align:middle line:84% even just to work out dimensionally. 00:10:53.640 --> 00:10:54.540 align:middle line:84% Of course, I don't have any chalk. 00:10:54.540 --> 00:10:55.548 align:middle line:90% But that's what happens. 00:10:55.548 --> 00:10:57.090 align:middle line:84% But if you work it out dimensionally, 00:10:57.090 --> 00:10:59.190 align:middle line:84% flux has a number of atoms per unit 00:10:59.190 --> 00:11:00.850 align:middle line:90% time per square centimeter. 00:11:00.850 --> 00:11:03.120 align:middle line:84% This is the number of atoms in the oxide. 00:11:03.120 --> 00:11:05.250 align:middle line:84% Per cubic centimeter, you end up with something 00:11:05.250 --> 00:11:08.140 align:middle line:84% like looks like centimeters per unit time, 00:11:08.140 --> 00:11:09.870 align:middle line:90% or length per unit time. 00:11:09.870 --> 00:11:13.682 align:middle line:84% So this is how quickly the oxide is growing, the growth 00:11:13.682 --> 00:11:15.390 align:middle line:84% rate or the velocity, which is what we're 00:11:15.390 --> 00:11:16.682 align:middle line:90% interested in, the growth rate. 00:11:16.682 --> 00:11:19.050 align:middle line:90% Can be written like this. 00:11:19.050 --> 00:11:21.690 align:middle line:84% It's the product of K sub S, the surface reaction rate, 00:11:21.690 --> 00:11:23.700 align:middle line:90% times the C star. 00:11:23.700 --> 00:11:26.590 align:middle line:84% C star is the solubility of the oxidant in the oxide. 00:11:26.590 --> 00:11:31.590 align:middle line:84% So that's as much as you can put in at that temperature, OK? 00:11:31.590 --> 00:11:33.840 align:middle line:84% You might have more in the gas phase than that. 00:11:33.840 --> 00:11:36.270 align:middle line:84% But that's how much will go in at that temperature. 00:11:36.270 --> 00:11:39.660 align:middle line:84% C star divided by this denominator, 1 plus K sub 00:11:39.660 --> 00:11:44.380 align:middle line:84% over H plus K sub S X naught over D. 00:11:44.380 --> 00:11:47.770 align:middle line:84% So that's telling us the rate of growth of the oxide. 00:11:47.770 --> 00:11:50.710 align:middle line:84% Now, we have it, in terms of certain fundamental physical 00:11:50.710 --> 00:11:53.610 align:middle line:90% parameters. 00:11:53.610 --> 00:11:58.070 align:middle line:90% So let's go on to slide 5. 00:11:58.070 --> 00:12:01.010 align:middle line:84% That was a simple, if you want, differential equation, 00:12:01.010 --> 00:12:04.160 align:middle line:84% DX by DT, just says how rapidly it's-- 00:12:04.160 --> 00:12:06.440 align:middle line:84% what is the velocity of the growth. 00:12:06.440 --> 00:12:07.790 align:middle line:90% And we integrate that. 00:12:07.790 --> 00:12:10.895 align:middle line:84% If you look in the text, it has a little bit 00:12:10.895 --> 00:12:12.770 align:middle line:84% of more detail on how you do the integration. 00:12:12.770 --> 00:12:16.070 align:middle line:84% But you integrate it between 0 and some time 00:12:16.070 --> 00:12:19.490 align:middle line:84% and between some initial thickness X sub 00:12:19.490 --> 00:12:22.460 align:middle line:84% I. And your final thickness or the thickness 00:12:22.460 --> 00:12:24.380 align:middle line:90% at any point in time, X0. 00:12:24.380 --> 00:12:28.010 align:middle line:84% So here, X0 is the thickness of the oxide right at the time, 00:12:28.010 --> 00:12:30.860 align:middle line:84% T. And XI is whatever thickness you started. 00:12:30.860 --> 00:12:33.230 align:middle line:84% With could be 0, whatever you thickness 00:12:33.230 --> 00:12:36.150 align:middle line:84% you started with at the start of the oxidation process. 00:12:36.150 --> 00:12:38.630 align:middle line:84% So by doing that integration, you 00:12:38.630 --> 00:12:44.252 align:middle line:84% end up with that time, if this can solve for time, 00:12:44.252 --> 00:12:45.710 align:middle line:84% is a two-term expression, something 00:12:45.710 --> 00:12:48.770 align:middle line:84% that involves X squared, thickness squared, 00:12:48.770 --> 00:12:51.350 align:middle line:84% and something that involves a linear term, thickness 00:12:51.350 --> 00:12:52.890 align:middle line:90% to the first power. 00:12:52.890 --> 00:12:54.510 align:middle line:90% So this is the origin. 00:12:54.510 --> 00:12:56.730 align:middle line:84% The origin of this parabolic/linear model. 00:12:56.730 --> 00:12:57.882 align:middle line:90% Here's a parabolic term. 00:12:57.882 --> 00:12:59.340 align:middle line:84% It goes like the thickness squared. 00:12:59.340 --> 00:13:00.800 align:middle line:90% Here's a linear term. 00:13:00.800 --> 00:13:04.700 align:middle line:84% And the multipliers are B. Here, this 00:13:04.700 --> 00:13:09.080 align:middle line:84% is the multiplier of the X0 the parabolic term. 00:13:09.080 --> 00:13:10.170 align:middle line:90% Looks like this. 00:13:10.170 --> 00:13:12.710 align:middle line:84% It's it looks like the diffusion coefficient 00:13:12.710 --> 00:13:15.200 align:middle line:84% through the oxide times the solubility in the oxide, C 00:13:15.200 --> 00:13:17.550 align:middle line:90% star, divided by N1. 00:13:17.550 --> 00:13:20.490 align:middle line:84% So the parabolic process has to do with diffusion 00:13:20.490 --> 00:13:21.510 align:middle line:90% through the oxide. 00:13:21.510 --> 00:13:25.980 align:middle line:84% The linear term, the term that multiplies X0, 00:13:25.980 --> 00:13:29.490 align:middle line:84% can be simplified here to something that looks 00:13:29.490 --> 00:13:32.220 align:middle line:90% like C star K sub over N1. 00:13:32.220 --> 00:13:34.080 align:middle line:84% And again, I'm ignoring this 1 over H 00:13:34.080 --> 00:13:36.340 align:middle line:84% because this is going very rapidly. 00:13:36.340 --> 00:13:41.140 align:middle line:84% So H is very large compared to K. So I can ignore this term. 00:13:41.140 --> 00:13:42.640 align:middle line:84% So this is the linear rate constant, 00:13:42.640 --> 00:13:45.970 align:middle line:84% which tells you something about the surface reaction rate. 00:13:45.970 --> 00:13:48.390 align:middle line:84% So linear rate constant has to do with the reaction. 00:13:48.390 --> 00:13:50.790 align:middle line:84% Parabolic has to do with the diffusion. 00:13:50.790 --> 00:13:52.560 align:middle line:84% Notice that they both depend, however, 00:13:52.560 --> 00:13:57.210 align:middle line:84% on C star, which is the solubility of either the oxygen 00:13:57.210 --> 00:14:00.850 align:middle line:90% or the water in the oxide. 00:14:00.850 --> 00:14:02.460 align:middle line:84% So let's go on to slide number 6. 00:14:02.460 --> 00:14:04.515 align:middle line:84% These rate constants, B and B over A, 00:14:04.515 --> 00:14:05.640 align:middle line:90% have some physical meaning. 00:14:05.640 --> 00:14:08.190 align:middle line:84% We just talked about that, diffusion 00:14:08.190 --> 00:14:10.380 align:middle line:84% of the oxidant and interface reaction. 00:14:10.380 --> 00:14:14.490 align:middle line:84% And we find experimentally that we can write them 00:14:14.490 --> 00:14:15.960 align:middle line:90% as Arrhenius relationships. 00:14:15.960 --> 00:14:18.160 align:middle line:84% They're exponentially dependent on E 00:14:18.160 --> 00:14:22.840 align:middle line:84% to some activation energy, E to the minus E1 over KT or E 00:14:22.840 --> 00:14:26.500 align:middle line:84% to the minus E2 over KT times a prefactor. 00:14:26.500 --> 00:14:28.810 align:middle line:90% The prefactor here is C1. 00:14:28.810 --> 00:14:32.020 align:middle line:90% For B and B over A is C2. 00:14:32.020 --> 00:14:34.550 align:middle line:84% And these rate constants have been studied for many years. 00:14:34.550 --> 00:14:35.980 align:middle line:84% People have measured them or tried 00:14:35.980 --> 00:14:37.570 align:middle line:90% to extract them experimentally. 00:14:37.570 --> 00:14:40.600 align:middle line:84% And this is a chart, a table, I took directly 00:14:40.600 --> 00:14:43.070 align:middle line:84% out of your text, which shows the ambient. 00:14:43.070 --> 00:14:47.380 align:middle line:84% So that's the type of gases environment 00:14:47.380 --> 00:14:50.230 align:middle line:84% that you are in, the wafer is in, and the rate 00:14:50.230 --> 00:14:52.610 align:middle line:84% constants, B and B over A, and how to calculate them. 00:14:52.610 --> 00:14:56.020 align:middle line:84% So in dry oxygen, so you're flowing O2 in the tube. 00:14:56.020 --> 00:14:58.090 align:middle line:90% But there's no moisture around. 00:14:58.090 --> 00:15:01.300 align:middle line:84% To calculate the B rate constant, you need to know C1. 00:15:01.300 --> 00:15:08.500 align:middle line:84% And you need to know E1, the activation energies, wet O2 00:15:08.500 --> 00:15:12.620 align:middle line:84% and H2O and moisture environment. 00:15:12.620 --> 00:15:14.665 align:middle line:84% So, by the way, just be careful when you're 00:15:14.665 --> 00:15:15.790 align:middle line:90% going to use these numbers. 00:15:15.790 --> 00:15:18.400 align:middle line:84% These are for 111 silicon oxidation. 00:15:18.400 --> 00:15:20.230 align:middle line:84% So that's the oxidation of a wafer 00:15:20.230 --> 00:15:24.670 align:middle line:84% with orientation surface of 111 at one atmospheric pressure. 00:15:24.670 --> 00:15:28.300 align:middle line:84% If you want to know the values for 100 silicon, 00:15:28.300 --> 00:15:31.045 align:middle line:84% then you take the C2 values, these B over A, 00:15:31.045 --> 00:15:34.520 align:middle line:84% the rate constants, and you divide by 1.68. 00:15:34.520 --> 00:15:39.560 align:middle line:84% So it's slower for a 100 interface. 00:15:39.560 --> 00:15:42.080 align:middle line:84% And if you go back and look at your crystallography 00:15:42.080 --> 00:15:44.630 align:middle line:84% and look at the number of atoms per square centimeter, 00:15:44.630 --> 00:15:48.290 align:middle line:84% it actually makes some sense because on a 111 interface, 00:15:48.290 --> 00:15:51.170 align:middle line:84% we have the largest number of atoms per square centimeter 00:15:51.170 --> 00:15:54.207 align:middle line:90% available for the oxidation. 00:15:54.207 --> 00:15:55.790 align:middle line:84% So it's going to be the rate constants 00:15:55.790 --> 00:15:57.560 align:middle line:90% are going to be faster. 00:15:57.560 --> 00:15:59.780 align:middle line:84% But notice, the activation energy 00:15:59.780 --> 00:16:02.270 align:middle line:84% doesn't change as you change orientations. 00:16:02.270 --> 00:16:05.930 align:middle line:84% It's all for the rate constant B over A, the surface reaction 00:16:05.930 --> 00:16:09.060 align:middle line:84% rate, it all has an activation energy of close to 2EV. 00:16:09.060 --> 00:16:12.000 align:middle line:90% 00:16:12.000 --> 00:16:15.900 align:middle line:84% So the activation energy for B over A is roughly constant. 00:16:15.900 --> 00:16:18.480 align:middle line:84% It just depends on the surface reaction rate. 00:16:18.480 --> 00:16:22.920 align:middle line:84% For B, interestingly, the activation energy for B 00:16:22.920 --> 00:16:24.370 align:middle line:90% varies with the process. 00:16:24.370 --> 00:16:27.780 align:middle line:84% So depending on whether you're in a dry O2 here, 00:16:27.780 --> 00:16:29.970 align:middle line:90% you get 1.23 EV. 00:16:29.970 --> 00:16:31.560 align:middle line:90% Here, this is 0.7 EV. 00:16:31.560 --> 00:16:34.530 align:middle line:84% And for moisture and for water, it's 0.78 EV. 00:16:34.530 --> 00:16:36.637 align:middle line:84% So it actually varies with the process. 00:16:36.637 --> 00:16:38.220 align:middle line:84% And that makes some sense because what 00:16:38.220 --> 00:16:39.670 align:middle line:90% did we say B depends on? 00:16:39.670 --> 00:16:42.660 align:middle line:84% It depends on the diffusion of this species through the oxide. 00:16:42.660 --> 00:16:44.550 align:middle line:84% Well, a water molecule, if that's 00:16:44.550 --> 00:16:46.050 align:middle line:84% what's diffusing the oxide, is going 00:16:46.050 --> 00:16:48.660 align:middle line:84% to diffuse at a different rate or maybe 00:16:48.660 --> 00:16:55.960 align:middle line:84% have a different solubility than just oxygen molecule. 00:16:55.960 --> 00:17:02.660 align:middle line:84% So we do see a difference in the activation energy for B. 00:17:02.660 --> 00:17:05.990 align:middle line:84% And on slide 7, obviously, you can do this yourself. 00:17:05.990 --> 00:17:10.410 align:middle line:84% You just sit down with those equations on a semi-log plot. 00:17:10.410 --> 00:17:12.660 align:middle line:84% So this is a log scale on the y-axis. 00:17:12.660 --> 00:17:15.319 align:middle line:84% And this is 1 over T or a 1,000 over T. 00:17:15.319 --> 00:17:20.390 align:middle line:84% This is a standard Arrhenius plot you've had to make. 00:17:20.390 --> 00:17:25.520 align:middle line:84% So on a semi-log plot, any kind of exponential relationship 00:17:25.520 --> 00:17:29.270 align:middle line:84% will appear as a straight line because it's log paper. 00:17:29.270 --> 00:17:31.640 align:middle line:84% And these are the different constants. 00:17:31.640 --> 00:17:38.870 align:middle line:84% Here we are for water is the B constant, the B over A, rather. 00:17:38.870 --> 00:17:40.370 align:middle line:90% And this is the B constant. 00:17:40.370 --> 00:17:44.330 align:middle line:90% And these are for 111. 00:17:44.330 --> 00:17:47.060 align:middle line:84% So you just literally plot what values are on the table. 00:17:47.060 --> 00:17:48.560 align:middle line:84% One thing you see right off the bat, 00:17:48.560 --> 00:17:52.100 align:middle line:84% just from this plot, these two lines on top that are faster, 00:17:52.100 --> 00:17:56.090 align:middle line:84% that are larger, are for oxidation in water vapor 00:17:56.090 --> 00:17:56.868 align:middle line:90% as opposed to dry. 00:17:56.868 --> 00:17:58.910 align:middle line:84% So right off the bat, you know the rate constants 00:17:58.910 --> 00:18:00.840 align:middle line:90% are higher for water than dry. 00:18:00.840 --> 00:18:03.240 align:middle line:84% So if you want to grow faster in oxide, 00:18:03.240 --> 00:18:07.540 align:middle line:84% you would grow it in a moisture environment, not in dry O2. 00:18:07.540 --> 00:18:08.790 align:middle line:90% And that's typically the case. 00:18:08.790 --> 00:18:12.570 align:middle line:84% People grow thick oxides using a wet environment, thin oxides 00:18:12.570 --> 00:18:14.320 align:middle line:90% using a dry environment. 00:18:14.320 --> 00:18:17.080 align:middle line:90% 00:18:17.080 --> 00:18:20.800 align:middle line:84% OK, let's go just go on to slide number 8 00:18:20.800 --> 00:18:22.720 align:middle line:90% and just reformulate this. 00:18:22.720 --> 00:18:25.150 align:middle line:84% You can do some mathematical manipulations 00:18:25.150 --> 00:18:28.150 align:middle line:84% on the law, the linear parabolic law, as I showed it earlier. 00:18:28.150 --> 00:18:29.740 align:middle line:84% I've just repeated that equation, 00:18:29.740 --> 00:18:31.510 align:middle line:84% where on the right-hand side, we've 00:18:31.510 --> 00:18:36.590 align:middle line:84% solved for T. On the left-hand side is the oxide thickness. 00:18:36.590 --> 00:18:39.910 align:middle line:84% There are alternate ways to express this law. 00:18:39.910 --> 00:18:42.490 align:middle line:84% And in fact, here's a reformulation 00:18:42.490 --> 00:18:45.740 align:middle line:84% of it shown in the second equation on this slide. 00:18:45.740 --> 00:18:48.580 align:middle line:84% What you see is what we've done is now, we've expressing it 00:18:48.580 --> 00:18:52.540 align:middle line:84% as X0 squared over B plus X0 divided by B over A 00:18:52.540 --> 00:18:56.110 align:middle line:84% is equal to T plus tau, where what we've done 00:18:56.110 --> 00:19:01.510 align:middle line:84% is tau now is defined as the time that it would have taken, 00:19:01.510 --> 00:19:04.810 align:middle line:84% the effect of time, to grow the initial oxide thickness X sub 00:19:04.810 --> 00:19:08.590 align:middle line:84% I. So this is just obtained by a mathematical manipulation 00:19:08.590 --> 00:19:10.700 align:middle line:90% of the first equation. 00:19:10.700 --> 00:19:14.410 align:middle line:84% So if you set tau equal to XI, the initial squared, 00:19:14.410 --> 00:19:18.545 align:middle line:84% plus A XI over B, just mathematically, you do that, 00:19:18.545 --> 00:19:20.170 align:middle line:84% then you get a mathematical equivalence 00:19:20.170 --> 00:19:24.280 align:middle line:84% of the second equation to the first equation. 00:19:24.280 --> 00:19:26.590 align:middle line:84% Sometimes, you also want to explicitly 00:19:26.590 --> 00:19:28.840 align:middle line:84% have an equation that shows you what 00:19:28.840 --> 00:19:30.700 align:middle line:90% X0 is, the oxide thickness. 00:19:30.700 --> 00:19:32.200 align:middle line:90% That's not what's shown here. 00:19:32.200 --> 00:19:35.770 align:middle line:84% On the upper two equations, X0 is implicit 00:19:35.770 --> 00:19:38.110 align:middle line:84% because it appears here in two different terms. 00:19:38.110 --> 00:19:41.350 align:middle line:84% If you want to solve explicitly for the oxide thickness, 00:19:41.350 --> 00:19:43.660 align:middle line:84% you can see this middle equation, X0, 00:19:43.660 --> 00:19:44.750 align:middle line:90% it looks like this. 00:19:44.750 --> 00:19:48.790 align:middle line:84% It's got a square root dependence on time. 00:19:48.790 --> 00:19:52.720 align:middle line:84% And where, again, tau has the same definition, 00:19:52.720 --> 00:19:55.810 align:middle line:84% XI squared, it's just that time to grow the initial oxide, 00:19:55.810 --> 00:19:58.015 align:middle line:84% the effect of time in the Deal-Grove model. 00:19:58.015 --> 00:20:01.880 align:middle line:90% 00:20:01.880 --> 00:20:05.460 align:middle line:84% OK, let's go on to slide number 9. 00:20:05.460 --> 00:20:08.362 align:middle line:84% And again, this reformulation, I'm 00:20:08.362 --> 00:20:10.570 align:middle line:84% just repeating the equations from the previous slide. 00:20:10.570 --> 00:20:12.810 align:middle line:84% So you don't have to remember them. 00:20:12.810 --> 00:20:15.690 align:middle line:84% Again, XI and tau account for any oxide 00:20:15.690 --> 00:20:19.050 align:middle line:84% that was present at the start of the process. 00:20:19.050 --> 00:20:21.413 align:middle line:84% When you first push the wafer in, 00:20:21.413 --> 00:20:22.830 align:middle line:84% you might have had other processes 00:20:22.830 --> 00:20:23.970 align:middle line:90% that have taken place. 00:20:23.970 --> 00:20:28.930 align:middle line:84% And they might already have some oxide present there. 00:20:28.930 --> 00:20:30.510 align:middle line:90% So we can take this-- 00:20:30.510 --> 00:20:33.390 align:middle line:84% we can take this equation and differentiate it. 00:20:33.390 --> 00:20:36.030 align:middle line:84% And let's say we're interested in the oxidation 00:20:36.030 --> 00:20:38.530 align:middle line:84% rate, not the absolute thickness versus time. 00:20:38.530 --> 00:20:39.810 align:middle line:90% But how is the rate changing? 00:20:39.810 --> 00:20:42.780 align:middle line:90% How fast is it growing? 00:20:42.780 --> 00:20:44.760 align:middle line:84% Well, this is the oxidation rate. 00:20:44.760 --> 00:20:46.320 align:middle line:84% By differentiating, you can see, it's 00:20:46.320 --> 00:20:50.490 align:middle line:84% given by B divided by this quantity, 00:20:50.490 --> 00:20:53.520 align:middle line:84% 2X0 plus A. So this gives you an idea 00:20:53.520 --> 00:20:57.410 align:middle line:84% of the rate, how rapidly is it growing? 00:20:57.410 --> 00:20:59.860 align:middle line:84% So these equations are very general. 00:20:59.860 --> 00:21:02.760 align:middle line:84% And what they describe as the growth kinetics for oxidation. 00:21:02.760 --> 00:21:04.510 align:middle line:84% When you're in these following conditions, 00:21:04.510 --> 00:21:06.190 align:middle line:84% we have to remind ourselves that it only 00:21:06.190 --> 00:21:08.690 align:middle line:90% applies for certain basic case. 00:21:08.690 --> 00:21:11.080 align:middle line:84% So this means when it's planar oxidation, 00:21:11.080 --> 00:21:14.198 align:middle line:84% so I'm just oxidizing a flat surface, we'll talk next time, 00:21:14.198 --> 00:21:16.240 align:middle line:84% when you have a surface that has structure on it, 00:21:16.240 --> 00:21:18.850 align:middle line:84% the equations need to be modified. 00:21:18.850 --> 00:21:20.740 align:middle line:84% It's planar and it's unpatterned. 00:21:20.740 --> 00:21:22.750 align:middle line:84% So this is just an unpatterned surface. 00:21:22.750 --> 00:21:25.060 align:middle line:84% This assumes that the silicon is lightly doped, 00:21:25.060 --> 00:21:26.500 align:middle line:90% that you can use these numbers. 00:21:26.500 --> 00:21:29.470 align:middle line:84% Heavily doped oxidation, we'll talk about next time. 00:21:29.470 --> 00:21:33.880 align:middle line:84% A simple ambient such as oxygen, dry O2 or water, is assumed. 00:21:33.880 --> 00:21:36.430 align:middle line:84% If you're going to add other gases, nitrous oxide 00:21:36.430 --> 00:21:39.280 align:middle line:84% and other things that people do to grow high K, 00:21:39.280 --> 00:21:42.115 align:middle line:84% these particular equations don't apply exactly. 00:21:42.115 --> 00:21:44.800 align:middle line:90% 00:21:44.800 --> 00:21:47.980 align:middle line:84% And these equations work when the final oxide thickness 00:21:47.980 --> 00:21:50.290 align:middle line:84% is larger than about 20 nanometers, about 00:21:50.290 --> 00:21:52.270 align:middle line:90% 200 angstroms. 00:21:52.270 --> 00:21:53.380 align:middle line:90% They work quite well. 00:21:53.380 --> 00:21:57.010 align:middle line:84% But so that's a certain number of limitations, 00:21:57.010 --> 00:21:59.470 align:middle line:84% still very useful because what we're going to do from here 00:21:59.470 --> 00:22:00.707 align:middle line:90% is now make corrections. 00:22:00.707 --> 00:22:03.040 align:middle line:84% Right off the bat though, when you see this 20 nanometer 00:22:03.040 --> 00:22:04.248 align:middle line:90% number, what do you think of? 00:22:04.248 --> 00:22:06.790 align:middle line:84% I mean, gate oxides today, just from your reading 00:22:06.790 --> 00:22:10.630 align:middle line:84% of the ITRS and high performance devices, what are they? 00:22:10.630 --> 00:22:14.260 align:middle line:84% Are they less than or greater than 20 nanometers? 00:22:14.260 --> 00:22:16.630 align:middle line:84% Less than, significantly less than 00:22:16.630 --> 00:22:18.440 align:middle line:84% for most high performance devices. 00:22:18.440 --> 00:22:20.140 align:middle line:84% So this tells us off the bat, if we 00:22:20.140 --> 00:22:24.760 align:middle line:84% want to use Deal-Grove to model a standard gate oxide thickness 00:22:24.760 --> 00:22:27.280 align:middle line:84% that someone might be growing 100 angstroms or less, 00:22:27.280 --> 00:22:28.610 align:middle line:90% it's not going to be perfect. 00:22:28.610 --> 00:22:30.610 align:middle line:84% We're going to have to make corrections to this. 00:22:30.610 --> 00:22:35.560 align:middle line:84% And we'll talk today about those thin oxidation models. 00:22:35.560 --> 00:22:37.750 align:middle line:90% But let's go on to slide 10. 00:22:37.750 --> 00:22:40.420 align:middle line:84% And again, just to make a different way 00:22:40.420 --> 00:22:41.980 align:middle line:84% of looking at these same equations, 00:22:41.980 --> 00:22:43.900 align:middle line:84% I've repeated them again at the top so we 00:22:43.900 --> 00:22:45.260 align:middle line:90% don't have to memorize them. 00:22:45.260 --> 00:22:49.220 align:middle line:84% But what we can do now is to take two limiting cases. 00:22:49.220 --> 00:22:50.840 align:middle line:84% One limiting case I'm going to say 00:22:50.840 --> 00:22:53.030 align:middle line:84% is when the oxide is relatively thin. 00:22:53.030 --> 00:22:56.180 align:middle line:90% So X0 is relatively small. 00:22:56.180 --> 00:22:59.000 align:middle line:84% But it turns out this term here, the linear term 00:22:59.000 --> 00:23:03.560 align:middle line:84% X0 divided by B over A is going to dominate over this X0 00:23:03.560 --> 00:23:04.100 align:middle line:90% squared. 00:23:04.100 --> 00:23:05.970 align:middle line:84% This is going to become a smaller term. 00:23:05.970 --> 00:23:07.790 align:middle line:84% So we can ignore this first term. 00:23:07.790 --> 00:23:11.750 align:middle line:84% And we end up that X0 is proportional to B over A times 00:23:11.750 --> 00:23:12.810 align:middle line:90% time. 00:23:12.810 --> 00:23:15.110 align:middle line:84% So it's essentially, in thin oxide, 00:23:15.110 --> 00:23:18.390 align:middle line:84% we have the equation is linear in time. 00:23:18.390 --> 00:23:21.400 align:middle line:84% So it's just we have a constant oxidation rate. 00:23:21.400 --> 00:23:23.150 align:middle line:84% And the thickness just increases linearly, 00:23:23.150 --> 00:23:26.200 align:middle line:84% according to this Deal-Grove model. 00:23:26.200 --> 00:23:28.417 align:middle line:84% For thicker oxides-- and we'll define later 00:23:28.417 --> 00:23:30.250 align:middle line:84% what we mean by thicker-- but at some point, 00:23:30.250 --> 00:23:32.800 align:middle line:84% this term, this X0 squared over B, 00:23:32.800 --> 00:23:34.840 align:middle line:84% starts to dominate over the linear term. 00:23:34.840 --> 00:23:36.550 align:middle line:90% We can ignore this linear term. 00:23:36.550 --> 00:23:38.980 align:middle line:84% For long times, where very thick oxides, 00:23:38.980 --> 00:23:42.640 align:middle line:84% it goes like X0 squared is a constant times T. 00:23:42.640 --> 00:23:47.230 align:middle line:84% So it's basically a parabolic term. 00:23:47.230 --> 00:23:49.812 align:middle line:84% So the oxide thickness starts increasing 00:23:49.812 --> 00:23:51.020 align:middle line:90% like the square root of time. 00:23:51.020 --> 00:23:52.562 align:middle line:84% So initially, it's going up linearly. 00:23:52.562 --> 00:23:54.350 align:middle line:84% And then when it becomes thick enough, 00:23:54.350 --> 00:23:57.460 align:middle line:84% it starts increasing more like a square root kind of function. 00:23:57.460 --> 00:23:59.350 align:middle line:84% And at that point, it's thick enough 00:23:59.350 --> 00:24:01.210 align:middle line:84% that diffusion through the oxide is really 00:24:01.210 --> 00:24:03.370 align:middle line:90% starting to limit you. 00:24:03.370 --> 00:24:06.658 align:middle line:84% Mathematically, if you prefer to think mathematically, 00:24:06.658 --> 00:24:08.200 align:middle line:84% you're going to make yourself a plot. 00:24:08.200 --> 00:24:11.950 align:middle line:84% This is actually a log scale, a log plot, log on the Y, 00:24:11.950 --> 00:24:14.380 align:middle line:84% log on the X. And it's kind of normalized. 00:24:14.380 --> 00:24:17.950 align:middle line:84% What is a plot of is X0 divided by A over 2. 00:24:17.950 --> 00:24:25.510 align:middle line:84% So we've sort of normalized the Y-AXIS and T plus tau divided 00:24:25.510 --> 00:24:29.900 align:middle line:84% by this constant, A squared over 4B to make it in unitless. 00:24:29.900 --> 00:24:33.030 align:middle line:84% And what you see, this solid line here 00:24:33.030 --> 00:24:39.330 align:middle line:84% is equal to a plot of X0 squared plus AX0 equals B times 00:24:39.330 --> 00:24:41.260 align:middle line:90% tau time T plus tau. 00:24:41.260 --> 00:24:43.170 align:middle line:84% So that's the exact Deal-Grove model. 00:24:43.170 --> 00:24:46.590 align:middle line:84% At short time, you can see it approaches or low 00:24:46.590 --> 00:24:49.710 align:middle line:84% thicknesses it approaches this linear, rate 00:24:49.710 --> 00:24:51.870 align:middle line:90% constant, this linear equation. 00:24:51.870 --> 00:24:54.930 align:middle line:84% Remember, on a semi-log plot, this has a certain slope. 00:24:54.930 --> 00:24:58.830 align:middle line:84% And then for longer times, much higher thicknesses, 00:24:58.830 --> 00:25:00.900 align:middle line:84% it approaches a straight line, this dashed line 00:25:00.900 --> 00:25:02.130 align:middle line:90% that has half the slope. 00:25:02.130 --> 00:25:06.707 align:middle line:84% Again, linear here versus square root has half the slope. 00:25:06.707 --> 00:25:08.040 align:middle line:90% Different way of looking at it-- 00:25:08.040 --> 00:25:09.810 align:middle line:84% I actually like you to think a little more physically, 00:25:09.810 --> 00:25:12.210 align:middle line:84% not just look at the equations and say, which term is big 00:25:12.210 --> 00:25:13.650 align:middle line:90% and which is small? 00:25:13.650 --> 00:25:16.350 align:middle line:84% In fact, it's much easier to remember the limiting cases 00:25:16.350 --> 00:25:18.030 align:middle line:90% in a physical sense. 00:25:18.030 --> 00:25:21.850 align:middle line:84% And that's what's being shown on slide 11. 00:25:21.850 --> 00:25:24.630 align:middle line:84% So if you look at the case of a thin oxide, 00:25:24.630 --> 00:25:28.770 align:middle line:84% it's relatively thin, what's happening is physically, 00:25:28.770 --> 00:25:29.430 align:middle line:90% is diffusion. 00:25:29.430 --> 00:25:31.410 align:middle line:84% This is so thin, the diffusion process 00:25:31.410 --> 00:25:34.560 align:middle line:84% happens very rapidly compared to the rate at which those atoms 00:25:34.560 --> 00:25:36.130 align:middle line:90% can react at the surface. 00:25:36.130 --> 00:25:39.270 align:middle line:84% So when it's thin, the surface reaction is what limits. 00:25:39.270 --> 00:25:41.430 align:middle line:90% It's the slowest step. 00:25:41.430 --> 00:25:43.260 align:middle line:84% Any of these serial processes always 00:25:43.260 --> 00:25:45.330 align:middle line:84% end up being limited by the rate limiting 00:25:45.330 --> 00:25:46.960 align:middle line:90% step is the slowest step. 00:25:46.960 --> 00:25:49.470 align:middle line:84% So clearly, when you're thin, getting through the oxide 00:25:49.470 --> 00:25:51.060 align:middle line:90% takes no time at all. 00:25:51.060 --> 00:25:54.240 align:middle line:84% What's limiting you is the rate at which you can react. 00:25:54.240 --> 00:25:57.730 align:middle line:84% And we know that is a linear process. 00:25:57.730 --> 00:26:01.820 align:middle line:84% It just depends on K sub S. Now let's 00:26:01.820 --> 00:26:04.730 align:middle line:84% say when you're thick, if you have a thick oxide, 00:26:04.730 --> 00:26:09.380 align:middle line:84% well, then the diffusion process is what's rate limiting you. 00:26:09.380 --> 00:26:12.500 align:middle line:84% The reaction at the surface can be relatively fast 00:26:12.500 --> 00:26:14.960 align:middle line:90% compared to the diffusion rate. 00:26:14.960 --> 00:26:16.740 align:middle line:90% So diffusion is rate limited. 00:26:16.740 --> 00:26:20.960 align:middle line:84% And that process ends up depending-- 00:26:20.960 --> 00:26:25.820 align:middle line:84% has a square root type dependence on time. 00:26:25.820 --> 00:26:30.050 align:middle line:84% So in both cases though, and just for these little diagrams 00:26:30.050 --> 00:26:32.600 align:middle line:84% I drew, C star, remember, is the solubility 00:26:32.600 --> 00:26:33.990 align:middle line:90% of the oxidant and the oxide. 00:26:33.990 --> 00:26:37.310 align:middle line:84% So in the thin case, you diffuse very rapidly through. 00:26:37.310 --> 00:26:41.270 align:middle line:84% You have almost no gradient in the oxide. 00:26:41.270 --> 00:26:43.710 align:middle line:84% You're getting through very rapidly just by virtue of it 00:26:43.710 --> 00:26:44.480 align:middle line:90% so thin. 00:26:44.480 --> 00:26:48.070 align:middle line:84% In a thick case, C star is a solubility. 00:26:48.070 --> 00:26:50.010 align:middle line:84% That's what you have at the surface. 00:26:50.010 --> 00:26:52.743 align:middle line:84% At the interface, it's almost going to 0 00:26:52.743 --> 00:26:54.660 align:middle line:84% because again, you're rate limited by the rate 00:26:54.660 --> 00:26:55.830 align:middle line:90% of diffusion. 00:26:55.830 --> 00:26:57.870 align:middle line:90% You have a large gradient. 00:26:57.870 --> 00:27:00.300 align:middle line:84% So this flux through the oxide is 00:27:00.300 --> 00:27:03.330 align:middle line:90% being driven by this gradient. 00:27:03.330 --> 00:27:04.830 align:middle line:84% So those are the two limiting cases. 00:27:04.830 --> 00:27:06.450 align:middle line:90% One depends on diffusion. 00:27:06.450 --> 00:27:08.385 align:middle line:84% The other is limited by surface reaction. 00:27:08.385 --> 00:27:12.120 align:middle line:90% 00:27:12.120 --> 00:27:13.980 align:middle line:84% Slide 12 is just a little example 00:27:13.980 --> 00:27:16.710 align:middle line:84% of if you're an experimentalist, how do you sit down? 00:27:16.710 --> 00:27:18.850 align:middle line:84% And how do people in the old days used to do this? 00:27:18.850 --> 00:27:20.610 align:middle line:84% Well, it's pretty simple, experimentally. 00:27:20.610 --> 00:27:25.537 align:middle line:84% You just oxidize a bunch of wafers at the same temperature 00:27:25.537 --> 00:27:26.370 align:middle line:90% for different times. 00:27:26.370 --> 00:27:29.288 align:middle line:84% And you plot the oxide thickness measured versus time. 00:27:29.288 --> 00:27:31.080 align:middle line:84% You'll see this linear dependence at first. 00:27:31.080 --> 00:27:33.455 align:middle line:84% And then it'll start to bend over where it's square root. 00:27:33.455 --> 00:27:37.380 align:middle line:84% Easy way to do it is to plot X instead off X0 00:27:37.380 --> 00:27:41.040 align:middle line:84% instead as a function of time, but T time divided by X0. 00:27:41.040 --> 00:27:44.160 align:middle line:84% And you'll find out that the slope, if you just manipulate 00:27:44.160 --> 00:27:47.130 align:middle line:84% those simple linear equations, the slope is the parameter B. 00:27:47.130 --> 00:27:49.620 align:middle line:84% And the y-intercept is the parameter minus A. 00:27:49.620 --> 00:27:52.680 align:middle line:84% So for the Deal-Grove model, it's very simple experimentally 00:27:52.680 --> 00:27:56.610 align:middle line:84% if you do this kind of plot to extract those two parameters. 00:27:56.610 --> 00:27:59.740 align:middle line:90% 00:27:59.740 --> 00:28:02.710 align:middle line:84% These are some actual calculations 00:28:02.710 --> 00:28:06.280 align:middle line:84% of the oxidation rates in dry on slide 13 00:28:06.280 --> 00:28:10.780 align:middle line:84% and dry oxygen using the Deal-Grove model. 00:28:10.780 --> 00:28:12.640 align:middle line:90% This is for 100 silicon now. 00:28:12.640 --> 00:28:14.470 align:middle line:84% So 100 silicon is much more likely 00:28:14.470 --> 00:28:17.860 align:middle line:84% what you're going to be using in a silicon manufacturing process 00:28:17.860 --> 00:28:19.400 align:middle line:90% or probably in your research. 00:28:19.400 --> 00:28:23.350 align:middle line:84% So it's a plot on the left axis linear scale oxide thickness 00:28:23.350 --> 00:28:25.610 align:middle line:90% as a function of time. 00:28:25.610 --> 00:28:28.870 align:middle line:84% And what you do see is a linear regime here, 00:28:28.870 --> 00:28:34.930 align:middle line:84% say, when you're at thin oxide, say below 0.1 microns or maybe 00:28:34.930 --> 00:28:38.660 align:middle line:84% half of that, 500 angstroms, the lines look quite linear. 00:28:38.660 --> 00:28:40.360 align:middle line:84% And then they start bending over. 00:28:40.360 --> 00:28:43.600 align:middle line:84% So they're followed by this sort of parabolic behavior 00:28:43.600 --> 00:28:46.730 align:middle line:90% where they grow less rapidly. 00:28:46.730 --> 00:28:49.270 align:middle line:84% And you can also see, look at the thicknesses, 00:28:49.270 --> 00:28:50.320 align:middle line:90% as we mentioned before. 00:28:50.320 --> 00:28:53.500 align:middle line:84% Dry oxides, even at high temperatures of 1,100, which 00:28:53.500 --> 00:28:55.570 align:middle line:90% is quite high for a furnace. 00:28:55.570 --> 00:28:56.590 align:middle line:90% You're really limited. 00:28:56.590 --> 00:28:58.210 align:middle line:84% For practical times, you don't want 00:28:58.210 --> 00:29:00.010 align:middle line:84% to be leaving the wafers in there 00:29:00.010 --> 00:29:03.298 align:middle line:84% any more than a few hours, four hours, six hours, whatever. 00:29:03.298 --> 00:29:04.840 align:middle line:84% You're limited to things on the order 00:29:04.840 --> 00:29:08.410 align:middle line:84% of 1,000 to 2,000 angstroms, from a practical point of view, 00:29:08.410 --> 00:29:11.080 align:middle line:90% where people grow dry oxides. 00:29:11.080 --> 00:29:13.330 align:middle line:84% Of course, you could leave it in the furnace for days. 00:29:13.330 --> 00:29:15.360 align:middle line:84% But that's not very economical in terms 00:29:15.360 --> 00:29:17.110 align:middle line:84% of use of the furnace, use of electricity, 00:29:17.110 --> 00:29:18.260 align:middle line:90% and all the resources. 00:29:18.260 --> 00:29:21.130 align:middle line:84% So if you want to grow an oxide in this thickness range, 00:29:21.130 --> 00:29:22.030 align:middle line:90% you use a dry oxide. 00:29:22.030 --> 00:29:23.740 align:middle line:84% If you want to go well above that, 00:29:23.740 --> 00:29:25.900 align:middle line:84% you should be going to wet oxidation 00:29:25.900 --> 00:29:30.490 align:middle line:84% because the oxidation rate constants are so much higher. 00:29:30.490 --> 00:29:33.210 align:middle line:84% In fact, on the next slide, slide 14, 00:29:33.210 --> 00:29:40.830 align:middle line:84% you can see the oxide thickness versus time for wet ambient, 00:29:40.830 --> 00:29:43.110 align:middle line:84% for moisture ambient using Deal-Grove. 00:29:43.110 --> 00:29:46.260 align:middle line:84% And now, look at the time of say two or three hours, 00:29:46.260 --> 00:29:49.455 align:middle line:84% instead of growing 1,000 angstroms or so, 00:29:49.455 --> 00:29:53.470 align:middle line:84% at 1,100 degrees, you're growing micron here. 00:29:53.470 --> 00:29:58.240 align:middle line:84% After about two hours at 1,100 degrees in wet ambient, about 00:29:58.240 --> 00:30:01.720 align:middle line:84% a micron, so much faster than dry oxidation, 00:30:01.720 --> 00:30:04.150 align:middle line:90% orders of magnitude faster. 00:30:04.150 --> 00:30:07.750 align:middle line:84% And as it turns out, the physical reason why 00:30:07.750 --> 00:30:12.070 align:middle line:84% is that the solubility, C star, of water vapor 00:30:12.070 --> 00:30:14.950 align:middle line:84% is much higher than the solubility of oxygen, 00:30:14.950 --> 00:30:17.348 align:middle line:84% of the oxygen molecule, for various reasons. 00:30:17.348 --> 00:30:19.390 align:middle line:84% Just because of the configuration of the molecule 00:30:19.390 --> 00:30:21.220 align:middle line:84% and the size of the interstitial spaces, 00:30:21.220 --> 00:30:23.750 align:middle line:84% water vapor is just easier to get in there. 00:30:23.750 --> 00:30:25.430 align:middle line:84% So it has a much higher solubility. 00:30:25.430 --> 00:30:28.900 align:middle line:84% So that whole concentration can be elevated, 00:30:28.900 --> 00:30:32.510 align:middle line:84% and you can oxidize it at a much faster rate. 00:30:32.510 --> 00:30:35.080 align:middle line:84% So if you need a thick oxide, you use moisture. 00:30:35.080 --> 00:30:37.790 align:middle line:90% 00:30:37.790 --> 00:30:38.900 align:middle line:90% Yeah, question. 00:30:38.900 --> 00:30:43.190 align:middle line:84% STUDENT: When B of K is given, so all of the other side, 00:30:43.190 --> 00:30:44.870 align:middle line:84% where is the oxide that doesn't react? 00:30:44.870 --> 00:30:46.820 align:middle line:90% What would it be then? 00:30:46.820 --> 00:30:49.190 align:middle line:84% JUDY HOYT: OK, so the question is going back to, 00:30:49.190 --> 00:30:53.750 align:middle line:84% let's say, slide 11 maybe of these limiting cases. 00:30:53.750 --> 00:30:57.170 align:middle line:84% What happens in a real case, if you have an oxidant diffusing 00:30:57.170 --> 00:30:58.040 align:middle line:90% through the oxide? 00:30:58.040 --> 00:31:00.140 align:middle line:90% And does it all react? 00:31:00.140 --> 00:31:04.040 align:middle line:84% Is there any unreactant species at the interface? 00:31:04.040 --> 00:31:07.310 align:middle line:84% Basically, it does have to react. 00:31:07.310 --> 00:31:12.500 align:middle line:84% And then if the reaction rate is what's limiting you, 00:31:12.500 --> 00:31:14.300 align:middle line:84% then you're sort of in this regime. 00:31:14.300 --> 00:31:17.420 align:middle line:84% But there will be a certain amount of oxidant 00:31:17.420 --> 00:31:19.280 align:middle line:90% that doesn't react. 00:31:19.280 --> 00:31:23.870 align:middle line:84% And that can lead to perhaps excess charges and things 00:31:23.870 --> 00:31:26.750 align:middle line:84% like that, some of the more realistic aspects 00:31:26.750 --> 00:31:30.210 align:middle line:84% of the oxidation process that you're left over. 00:31:30.210 --> 00:31:35.390 align:middle line:84% So it can affect the quality of the oxide, to a certain extent. 00:31:35.390 --> 00:31:39.162 align:middle line:84% And what you generally find is that wet oxides-- 00:31:39.162 --> 00:31:40.620 align:middle line:84% you don't see a whole lot of people 00:31:40.620 --> 00:31:42.060 align:middle line:90% growing gate oxides by wet. 00:31:42.060 --> 00:31:43.530 align:middle line:90% Well, because they want thinner. 00:31:43.530 --> 00:31:46.950 align:middle line:84% But even in the old days, when a gate oxide was thicker, 00:31:46.950 --> 00:31:49.410 align:middle line:84% 500 angstroms or whatever, you didn't see people 00:31:49.410 --> 00:31:51.600 align:middle line:90% growing them in a wet ambient. 00:31:51.600 --> 00:31:54.010 align:middle line:84% And the oxidation rate is a lot faster. 00:31:54.010 --> 00:31:55.650 align:middle line:84% The quality of the oxide, the number 00:31:55.650 --> 00:31:57.358 align:middle line:84% of interface states and things like that, 00:31:57.358 --> 00:31:59.370 align:middle line:84% tends to be higher for a wet oxide. 00:31:59.370 --> 00:32:02.850 align:middle line:84% So typically, what you do if you're 00:32:02.850 --> 00:32:04.860 align:middle line:84% trying to grow a gate oxide, is you grow it dry. 00:32:04.860 --> 00:32:07.920 align:middle line:84% Or if you want to make it thick, and you 00:32:07.920 --> 00:32:10.560 align:middle line:84% have practical limitations, you grow a dry step, a wet step, 00:32:10.560 --> 00:32:11.910 align:middle line:90% and then a dry step at the end. 00:32:11.910 --> 00:32:14.310 align:middle line:84% So the interface was always grown in a dry step 00:32:14.310 --> 00:32:17.800 align:middle line:84% to try to reduce the interface state density. 00:32:17.800 --> 00:32:20.460 align:middle line:84% So if you need a gate oxide that's 1000 angstrom, 00:32:20.460 --> 00:32:23.070 align:middle line:84% you do what they call a dry-wet-dry. 00:32:23.070 --> 00:32:25.620 align:middle line:84% So it does matter if the oxidation rate-- being too high 00:32:25.620 --> 00:32:29.010 align:middle line:84% is not the greatest thing in the world in terms of the device 00:32:29.010 --> 00:32:30.168 align:middle line:90% properties. 00:32:30.168 --> 00:32:31.710 align:middle line:84% I think was there a hand in the back? 00:32:31.710 --> 00:32:33.360 align:middle line:90% Or did I miss a question? 00:32:33.360 --> 00:32:34.990 align:middle line:90% OK. 00:32:34.990 --> 00:32:35.490 align:middle line:90% OK. 00:32:35.490 --> 00:32:37.420 align:middle line:90% Good. 00:32:37.420 --> 00:32:39.120 align:middle line:84% So those are the wet oxide kinetics. 00:32:39.120 --> 00:32:43.560 align:middle line:84% Let's go on to slide number 15 and just show some examples. 00:32:43.560 --> 00:32:46.410 align:middle line:84% Now right off the bat, I'm unfortunately 00:32:46.410 --> 00:32:49.740 align:middle line:84% showing an example to which the Deal-Grove model doesn't 00:32:49.740 --> 00:32:50.490 align:middle line:90% perfectly apply. 00:32:50.490 --> 00:32:51.630 align:middle line:90% But we'll apply it anyway. 00:32:51.630 --> 00:32:54.180 align:middle line:84% And next time, we'll talk about why it's not perfect. 00:32:54.180 --> 00:32:57.345 align:middle line:90% But there is a process called-- 00:32:57.345 --> 00:32:59.220 align:middle line:84% just to make this a little more interesting-- 00:32:59.220 --> 00:33:02.800 align:middle line:84% called recessed LOCOS local oxidation, 00:33:02.800 --> 00:33:05.100 align:middle line:84% which can be used to provide this lateral isolation 00:33:05.100 --> 00:33:08.850 align:middle line:90% between a device A and device B. 00:33:08.850 --> 00:33:11.340 align:middle line:90% We need to grow an oxide here. 00:33:11.340 --> 00:33:15.000 align:middle line:84% And it results in a more planar surface than standard LOCOS. 00:33:15.000 --> 00:33:18.810 align:middle line:84% Remember, standard LOCOS look like this. 00:33:18.810 --> 00:33:21.000 align:middle line:84% When we're done, and you strip off 00:33:21.000 --> 00:33:22.630 align:middle line:84% this nitride up in the upper right, 00:33:22.630 --> 00:33:26.400 align:middle line:84% you have a very non planar surface introduced. 00:33:26.400 --> 00:33:30.480 align:middle line:84% You've got this region up here, where the oxide pushed up. 00:33:30.480 --> 00:33:32.550 align:middle line:84% And so the surface is not very planar. 00:33:32.550 --> 00:33:34.800 align:middle line:84% Recessed LOCOS, so that's the basic idea 00:33:34.800 --> 00:33:36.900 align:middle line:90% is you etch a trench first. 00:33:36.900 --> 00:33:39.720 align:middle line:84% So here, I've etched in the silicon. 00:33:39.720 --> 00:33:42.630 align:middle line:84% Around the silicon nitride, I've etched a half micron 00:33:42.630 --> 00:33:44.550 align:middle line:90% deep trench. 00:33:44.550 --> 00:33:47.520 align:middle line:84% And now, we assume I'm going to subject that wafer 00:33:47.520 --> 00:33:48.730 align:middle line:90% to thermal oxidation. 00:33:48.730 --> 00:33:52.440 align:middle line:84% Well, on the left and the right side of the trench, 00:33:52.440 --> 00:33:54.960 align:middle line:90% that should say silicon nitride. 00:33:54.960 --> 00:33:57.810 align:middle line:84% Sorry, this left and right side should both be silicon nitride. 00:33:57.810 --> 00:34:00.010 align:middle line:84% There's no oxidation taking place. 00:34:00.010 --> 00:34:02.310 align:middle line:84% So maybe correct this handout on the right, where 00:34:02.310 --> 00:34:04.320 align:middle line:84% it's pointing to SiO2, that should 00:34:04.320 --> 00:34:08.790 align:middle line:90% say silicon nitride, Si3N4. 00:34:08.790 --> 00:34:11.250 align:middle line:84% So we're only oxidizing, we're assuming, 00:34:11.250 --> 00:34:13.500 align:middle line:90% in this trench region. 00:34:13.500 --> 00:34:16.080 align:middle line:84% Now, this schematic is highly schematic. 00:34:16.080 --> 00:34:18.010 align:middle line:84% It's not including any bird's beak effects, 00:34:18.010 --> 00:34:20.135 align:middle line:84% which we'll talk about where they originate from, 00:34:20.135 --> 00:34:21.510 align:middle line:84% or any two-dimensional oxidation. 00:34:21.510 --> 00:34:23.802 align:middle line:84% We're going to do a very simple calculation of how long 00:34:23.802 --> 00:34:28.110 align:middle line:84% would it take to fill that to make a planar surface, 00:34:28.110 --> 00:34:30.750 align:middle line:90% assuming I was half micron down. 00:34:30.750 --> 00:34:31.770 align:middle line:90% Yeah. 00:34:31.770 --> 00:34:35.788 align:middle line:84% STUDENT: After doing that, will it [INAUDIBLE] 00:34:35.788 --> 00:34:37.080 align:middle line:90% JUDY HOYT: There is in between. 00:34:37.080 --> 00:34:39.710 align:middle line:84% Yeah, it's just the arrow got displaced. 00:34:39.710 --> 00:34:41.820 align:middle line:84% This arrow is actually pointing to the top region, 00:34:41.820 --> 00:34:43.130 align:middle line:90% which is the silicon nitride. 00:34:43.130 --> 00:34:46.400 align:middle line:84% There is, as was just pointed out by someone in the class 00:34:46.400 --> 00:34:48.860 align:middle line:84% here, this hatched region is meant 00:34:48.860 --> 00:34:53.510 align:middle line:84% to represent the SiO2, what they call the Pad Ox, or the pad 00:34:53.510 --> 00:34:56.880 align:middle line:84% oxide, and if it was stressed, that's induced by the nitride. 00:34:56.880 --> 00:34:58.730 align:middle line:84% So there is, in fact, a thin pad oxide 00:34:58.730 --> 00:35:00.710 align:middle line:90% underneath the silicon nitride. 00:35:00.710 --> 00:35:04.130 align:middle line:84% But what's preventing the oxidation from taking place 00:35:04.130 --> 00:35:06.080 align:middle line:90% is this silicon nitride. 00:35:06.080 --> 00:35:08.270 align:middle line:84% SiO2 itself won't prevent oxidation. 00:35:08.270 --> 00:35:11.100 align:middle line:84% The oxidant will diffuse right through it. 00:35:11.100 --> 00:35:12.650 align:middle line:84% The nice thing about silicon nitride 00:35:12.650 --> 00:35:17.070 align:middle line:84% is that it's hard to get oxygen and moisture to diffuse 00:35:17.070 --> 00:35:17.570 align:middle line:90% through it. 00:35:17.570 --> 00:35:20.660 align:middle line:84% So it can act as a mask or as a blocking layer. 00:35:20.660 --> 00:35:24.125 align:middle line:84% So you don't oxidize underneath it, the first word. 00:35:24.125 --> 00:35:26.000 align:middle line:84% So this oxide that's shown here underneath it 00:35:26.000 --> 00:35:29.360 align:middle line:84% happened before the nitride was put down. 00:35:29.360 --> 00:35:31.680 align:middle line:90% OK, good point. 00:35:31.680 --> 00:35:33.560 align:middle line:90% So let's go on to slide 15. 00:35:33.560 --> 00:35:36.920 align:middle line:84% And here's just an example of a question. 00:35:36.920 --> 00:35:39.640 align:middle line:84% So we're assuming we've etched half micron down into the wafer 00:35:39.640 --> 00:35:43.390 align:middle line:84% below the original surface prior to oxidizing. 00:35:43.390 --> 00:35:46.030 align:middle line:84% And a simple question might be, how long do I 00:35:46.030 --> 00:35:49.120 align:middle line:84% have to put it in the furnace at 1,000 degrees, 00:35:49.120 --> 00:35:55.480 align:middle line:84% assuming water oxidation in H2O to produce a planar surface? 00:35:55.480 --> 00:35:58.060 align:middle line:84% Again, we're going to ignore any of the bird's beak effects 00:35:58.060 --> 00:36:00.190 align:middle line:84% or the stress effects that we know are there. 00:36:00.190 --> 00:36:01.690 align:middle line:84% We'll talk about those next time. 00:36:01.690 --> 00:36:04.180 align:middle line:84% So but just to make it a little more interesting, 00:36:04.180 --> 00:36:07.390 align:middle line:84% we want to fill this up to the surface, the original surface, 00:36:07.390 --> 00:36:10.402 align:middle line:90% and then make it planar. 00:36:10.402 --> 00:36:12.360 align:middle line:84% So we have to be a little careful in doing this 00:36:12.360 --> 00:36:15.900 align:middle line:84% because remember, as I'm growing this oxide right here, 00:36:15.900 --> 00:36:17.640 align:middle line:84% I'm consuming the silicon underneath it. 00:36:17.640 --> 00:36:20.160 align:middle line:84% So you're consuming silicon underneath it. 00:36:20.160 --> 00:36:22.420 align:middle line:84% But the oxide is also growing up at the same time. 00:36:22.420 --> 00:36:24.190 align:middle line:84% So it's kind of starting here, very thin. 00:36:24.190 --> 00:36:25.830 align:middle line:84% And it's kind of going like this. 00:36:25.830 --> 00:36:28.830 align:middle line:84% At some point, it will be just flat or close 00:36:28.830 --> 00:36:32.650 align:middle line:84% to being almost flat with the original surface. 00:36:32.650 --> 00:36:34.090 align:middle line:90% So how do we figure this out? 00:36:34.090 --> 00:36:38.100 align:middle line:84% Well, you make yourself a little schematic diagram 00:36:38.100 --> 00:36:40.740 align:middle line:84% as shown here in color in the lower left. 00:36:40.740 --> 00:36:43.680 align:middle line:84% And in a rough sense, for every micron 00:36:43.680 --> 00:36:46.320 align:middle line:84% of silicon I consume-- so as you start oxidizing, 00:36:46.320 --> 00:36:49.260 align:middle line:84% I'm going to start bringing this trench point lower. 00:36:49.260 --> 00:36:53.310 align:middle line:84% Every micron I go down, 2 and 1/2 microns, 00:36:53.310 --> 00:36:55.770 align:middle line:84% or 2.2., I'm sorry, microns of silicon 00:36:55.770 --> 00:36:59.550 align:middle line:84% is grown, of silicon dioxide, SiO2. 00:36:59.550 --> 00:37:03.540 align:middle line:84% So you can write this mathematically. 00:37:03.540 --> 00:37:06.990 align:middle line:84% If I say Y is the thickness of the silicon that was consumed, 00:37:06.990 --> 00:37:09.730 align:middle line:90% then 2.2 times Y is X0. 00:37:09.730 --> 00:37:12.790 align:middle line:84% That's the thickness of the SiO2. 00:37:12.790 --> 00:37:16.480 align:middle line:84% So that's just due to the volume expansion when you grow oxide. 00:37:16.480 --> 00:37:19.840 align:middle line:84% So we can have that as one equation that 00:37:19.840 --> 00:37:22.890 align:middle line:90% describes what's going on. 00:37:22.890 --> 00:37:26.910 align:middle line:84% Slide 17, so we remember that equation. 00:37:26.910 --> 00:37:31.890 align:middle line:84% But then we also know that the total thickness of oxide grown, 00:37:31.890 --> 00:37:33.720 align:middle line:84% in order to satisfy this requirement 00:37:33.720 --> 00:37:38.400 align:middle line:84% that we fill the trench, well, we want to a specific case 00:37:38.400 --> 00:37:43.200 align:middle line:84% where X0 is equal to 1/2 micron, which is the original trench 00:37:43.200 --> 00:37:46.960 align:middle line:84% depth, plus Y, which is the thickness of silicon consumed. 00:37:46.960 --> 00:37:50.010 align:middle line:84% So by looking at this geometry, so the distance 00:37:50.010 --> 00:37:51.630 align:middle line:84% from here to here is half micron. 00:37:51.630 --> 00:37:52.980 align:middle line:90% That was my original trench. 00:37:52.980 --> 00:37:56.035 align:middle line:84% Plus the silicon is going to get consumed down a little bit. 00:37:56.035 --> 00:37:57.660 align:middle line:84% And that, we're calling the variable Y. 00:37:57.660 --> 00:37:58.950 align:middle line:90% We don't know that number yet. 00:37:58.950 --> 00:38:02.570 align:middle line:90% So we have two equations here. 00:38:02.570 --> 00:38:05.390 align:middle line:84% This X0 equals 0.5 micron plus Y. 00:38:05.390 --> 00:38:09.608 align:middle line:84% And we also have the constraint that 2.2 times Y is X0. 00:38:09.608 --> 00:38:11.900 align:middle line:84% And that's just from the volume expansion that we know. 00:38:11.900 --> 00:38:15.270 align:middle line:84% So if we can simply now just equate these two equations, 00:38:15.270 --> 00:38:16.700 align:middle line:90% we have two equations. 00:38:16.700 --> 00:38:20.330 align:middle line:84% And we're going to set X0 in equation 1 00:38:20.330 --> 00:38:22.280 align:middle line:90% equal to X0 in equation 2. 00:38:22.280 --> 00:38:24.560 align:middle line:84% And then you can simply solve for Y. 00:38:24.560 --> 00:38:26.960 align:middle line:84% So Y turns out to be about 0.4 micron. 00:38:26.960 --> 00:38:29.720 align:middle line:84% So that says, we need to consume about 0.4 microns 00:38:29.720 --> 00:38:33.900 align:middle line:84% in order to just fill the trench up to the original surface. 00:38:33.900 --> 00:38:36.170 align:middle line:84% So I'm going to actually go down here. 00:38:36.170 --> 00:38:37.880 align:middle line:84% From the original trench depth, I'm 00:38:37.880 --> 00:38:41.270 align:middle line:84% actually going to consume 0.4 microns down into the wafer. 00:38:41.270 --> 00:38:45.500 align:middle line:84% So X0, then the oxide thickness must be 2.2 times that. 00:38:45.500 --> 00:38:47.292 align:middle line:90% So it's about 0.9 microns. 00:38:47.292 --> 00:38:48.500 align:middle line:90% So we really have the answer. 00:38:48.500 --> 00:38:53.180 align:middle line:84% We know we need to grow at 1,000 degrees, 0.9 microns. 00:38:53.180 --> 00:38:55.490 align:middle line:84% We were told we can do it in a wet ambient. 00:38:55.490 --> 00:38:58.610 align:middle line:84% So you can calculate B and B over A using the table 00:38:58.610 --> 00:39:02.330 align:middle line:90% in table 6.2 of your text. 00:39:02.330 --> 00:39:05.300 align:middle line:84% So you know this is the Deal-Grove equation. 00:39:05.300 --> 00:39:08.180 align:middle line:84% You can just calculate B and B over A and solve for the time. 00:39:08.180 --> 00:39:10.290 align:middle line:84% Or if you want to go, on the next slide, 00:39:10.290 --> 00:39:13.350 align:middle line:90% I'll show you use the graph. 00:39:13.350 --> 00:39:16.550 align:middle line:84% So on slide 18, these are just the oxidation kinetics or oxide 00:39:16.550 --> 00:39:19.880 align:middle line:84% thickness versus time in a wet ambient. 00:39:19.880 --> 00:39:22.200 align:middle line:84% And I was told we were at 1,000 degrees. 00:39:22.200 --> 00:39:24.870 align:middle line:90% So that's this line right here. 00:39:24.870 --> 00:39:27.390 align:middle line:84% And we know we need to grow a 0.9 microns. 00:39:27.390 --> 00:39:29.960 align:middle line:84% So that's this black line, horizontal line. 00:39:29.960 --> 00:39:31.730 align:middle line:90% And you can get it roughly here. 00:39:31.730 --> 00:39:35.120 align:middle line:84% It's just 3.8 or so hours, depending on how accurately you 00:39:35.120 --> 00:39:36.790 align:middle line:90% can read off the plot. 00:39:36.790 --> 00:39:38.540 align:middle line:84% If you want to get a little more accurate, 00:39:38.540 --> 00:39:40.070 align:middle line:84% you go ahead and calculate B and B 00:39:40.070 --> 00:39:41.743 align:middle line:90% over A and plug in the equation. 00:39:41.743 --> 00:39:43.160 align:middle line:84% But you can always check the plot. 00:39:43.160 --> 00:39:44.870 align:middle line:84% That way, you have a sanity check 00:39:44.870 --> 00:39:47.720 align:middle line:84% that you made didn't make some calculator mistake 00:39:47.720 --> 00:39:50.660 align:middle line:90% or type in the wrong number. 00:39:50.660 --> 00:39:53.810 align:middle line:84% So that seems like a reasonable example 00:39:53.810 --> 00:39:57.550 align:middle line:84% of how you would do a simple calculation. 00:39:57.550 --> 00:39:59.410 align:middle line:90% So let's go on now to slide 19. 00:39:59.410 --> 00:40:01.350 align:middle line:90% So that was a Deal-Grove model. 00:40:01.350 --> 00:40:05.290 align:middle line:84% Immediately, at the same time Deal and Grove published it, 00:40:05.290 --> 00:40:08.130 align:middle line:84% they realized that there was a major problem with the model, 00:40:08.130 --> 00:40:10.560 align:middle line:90% even when it was first proposed. 00:40:10.560 --> 00:40:13.860 align:middle line:84% It doesn't correctly model what they knew to be the thin oxide 00:40:13.860 --> 00:40:15.010 align:middle line:90% growth kinetics. 00:40:15.010 --> 00:40:16.660 align:middle line:84% And you can see that in this plot. 00:40:16.660 --> 00:40:21.060 align:middle line:84% This is a plot I took out of Andy Grove's book published 00:40:21.060 --> 00:40:23.700 align:middle line:84% quite some time ago, but still a famous book, 00:40:23.700 --> 00:40:28.560 align:middle line:84% oxide thickness in microns as a function of time. 00:40:28.560 --> 00:40:33.280 align:middle line:84% This was for dry oxide grown at 700, very low temperature. 00:40:33.280 --> 00:40:36.210 align:middle line:84% And these little bullets or these open symbols 00:40:36.210 --> 00:40:39.360 align:middle line:84% are what they measured as the oxide thickness. 00:40:39.360 --> 00:40:45.360 align:middle line:84% And, in fact, what they noticed is that the model 00:40:45.360 --> 00:40:49.320 align:middle line:84% itself, which would be in this range, 00:40:49.320 --> 00:40:52.920 align:middle line:84% the dry oxides grow much faster for thicknesses 00:40:52.920 --> 00:40:57.670 align:middle line:84% below about 20 nanometers, or 0.02 microns, 00:40:57.670 --> 00:41:02.660 align:middle line:84% than predicted by the linear parabolic model. 00:41:02.660 --> 00:41:05.380 align:middle line:84% So the linear parabolic model would have had them 00:41:05.380 --> 00:41:06.520 align:middle line:90% sort of going like this. 00:41:06.520 --> 00:41:09.470 align:middle line:84% And here, these oxides are already going up much faster. 00:41:09.470 --> 00:41:12.170 align:middle line:84% So there's a rapid initial oxidation phase, 00:41:12.170 --> 00:41:13.780 align:middle line:84% which does not take into account when 00:41:13.780 --> 00:41:15.822 align:middle line:84% you have a linear model in the beginning and then 00:41:15.822 --> 00:41:17.000 align:middle line:90% a parabolic model. 00:41:17.000 --> 00:41:19.660 align:middle line:84% So people knew right off that this really 00:41:19.660 --> 00:41:21.520 align:middle line:84% wasn't going to model the initial oxidation 00:41:21.520 --> 00:41:22.855 align:middle line:90% kinetics very well. 00:41:22.855 --> 00:41:25.930 align:middle line:90% 00:41:25.930 --> 00:41:29.770 align:middle line:84% So if we can go on to slide 20 then, since that time, 00:41:29.770 --> 00:41:33.510 align:middle line:84% there have been a number of people have made suggestions 00:41:33.510 --> 00:41:37.230 align:middle line:84% to explain why the initial kinetics are faster than what 00:41:37.230 --> 00:41:39.870 align:middle line:90% Deal-Grove model would predict. 00:41:39.870 --> 00:41:41.430 align:middle line:84% There isn't really one model that's 00:41:41.430 --> 00:41:44.250 align:middle line:90% widely totally always accepted. 00:41:44.250 --> 00:41:47.590 align:middle line:84% There's a couple of them that are used in simulators today. 00:41:47.590 --> 00:41:49.470 align:middle line:84% So if you go to the Supreme Four Manual, 00:41:49.470 --> 00:41:52.710 align:middle line:84% and you read up about what thin oxide models are 00:41:52.710 --> 00:41:55.170 align:middle line:84% available for you to use in your numerical simulations, 00:41:55.170 --> 00:41:58.430 align:middle line:84% here's an example of three of them. 00:41:58.430 --> 00:42:01.870 align:middle line:84% There's the Reisman model, Han-Helms, and the Massoud 00:42:01.870 --> 00:42:03.322 align:middle line:90% model. 00:42:03.322 --> 00:42:04.780 align:middle line:84% So I want to go through these three 00:42:04.780 --> 00:42:08.890 align:middle line:84% there maybe the most popular or well 00:42:08.890 --> 00:42:10.960 align:middle line:90% known of all the proposals. 00:42:10.960 --> 00:42:13.630 align:middle line:90% 00:42:13.630 --> 00:42:16.860 align:middle line:84% So on slide 21, we have the Reisman model. 00:42:16.860 --> 00:42:22.500 align:middle line:84% And they actually proposed a relatively simple power law. 00:42:22.500 --> 00:42:24.540 align:middle line:84% But it seems and some people regard it 00:42:24.540 --> 00:42:27.360 align:middle line:84% as more of a mathematical fit that quote unquote, 00:42:27.360 --> 00:42:31.830 align:middle line:84% fits the data for dry O2 over a wide range of thicknesses. 00:42:31.830 --> 00:42:33.990 align:middle line:84% And so their power law is actually 00:42:33.990 --> 00:42:35.760 align:middle line:84% looks different from the Deal-Grove model. 00:42:35.760 --> 00:42:38.970 align:middle line:84% They say the oxide thickness X0 is some constant A 00:42:38.970 --> 00:42:40.570 align:middle line:90% times T plus TI. 00:42:40.570 --> 00:42:46.380 align:middle line:84% TI is the initial oxide thickness or time corresponding 00:42:46.380 --> 00:42:50.640 align:middle line:84% to the initial oxide to the B power. 00:42:50.640 --> 00:42:53.520 align:middle line:84% Or you can rearrange it so it looks 00:42:53.520 --> 00:42:56.730 align:middle line:84% something like this in terms of A and B. 00:42:56.730 --> 00:42:58.230 align:middle line:84% Look at this compared to Deal-Grove. 00:42:58.230 --> 00:43:03.285 align:middle line:84% You can see it is actually quite different, although they still 00:43:03.285 --> 00:43:04.410 align:middle line:90% have a couple of constants. 00:43:04.410 --> 00:43:07.050 align:middle line:84% They have a lowercase a and a lowercase 00:43:07.050 --> 00:43:10.060 align:middle line:84% b for a given set of process conditions. 00:43:10.060 --> 00:43:12.960 align:middle line:84% So similar to Deal-Grove, you have two constants. 00:43:12.960 --> 00:43:15.210 align:middle line:90% There are different numbers. 00:43:15.210 --> 00:43:16.380 align:middle line:90% This actually works. 00:43:16.380 --> 00:43:18.300 align:middle line:84% The fit mathematically fits better 00:43:18.300 --> 00:43:20.760 align:middle line:90% in the thin oxide regime. 00:43:20.760 --> 00:43:24.840 align:middle line:84% The problem is it's not as appealing in the sense it's not 00:43:24.840 --> 00:43:27.360 align:middle line:84% as quite as simple as Deal-Grove. 00:43:27.360 --> 00:43:31.110 align:middle line:84% But their physical reasoning was that the interface reaction 00:43:31.110 --> 00:43:33.550 align:middle line:84% controls the oxidation process at all times. 00:43:33.550 --> 00:43:35.320 align:middle line:90% This is what they thought. 00:43:35.320 --> 00:43:38.020 align:middle line:84% But they believed that this volume expansion, 00:43:38.020 --> 00:43:39.420 align:middle line:84% the need for the volume expansion 00:43:39.420 --> 00:43:41.560 align:middle line:84% and the flow of the oxide, the interface, 00:43:41.560 --> 00:43:45.240 align:middle line:84% control the growth kinetics, the rate. 00:43:45.240 --> 00:43:48.630 align:middle line:84% And A and B were believed to be some time-dependent flow 00:43:48.630 --> 00:43:50.260 align:middle line:90% parameters for the oxide. 00:43:50.260 --> 00:43:54.788 align:middle line:84% So not as obvious or as simple as appealing 00:43:54.788 --> 00:43:56.080 align:middle line:90% as the simple Deal-Grove model. 00:43:56.080 --> 00:43:58.450 align:middle line:84% But they also found that mathematically, it 00:43:58.450 --> 00:44:00.370 align:middle line:90% just makes a better fit. 00:44:00.370 --> 00:44:04.270 align:middle line:84% So people do sometimes use this type of model 00:44:04.270 --> 00:44:09.710 align:middle line:84% and then fit their own data with their own A and B constants. 00:44:09.710 --> 00:44:11.470 align:middle line:90% So that's the Riesman model. 00:44:11.470 --> 00:44:16.150 align:middle line:84% Han and Helms came along and got additional data. 00:44:16.150 --> 00:44:18.220 align:middle line:90% And they actually said this. 00:44:18.220 --> 00:44:21.190 align:middle line:84% They actually said that there are two in parallel, 00:44:21.190 --> 00:44:22.990 align:middle line:84% a couple of different oxidation processes 00:44:22.990 --> 00:44:26.240 align:middle line:90% taking place in the model. 00:44:26.240 --> 00:44:29.470 align:middle line:84% So perhaps, they said, not only O2 molecules, 00:44:29.470 --> 00:44:32.770 align:middle line:84% but oxygen atoms can diffuse through the oxide, 00:44:32.770 --> 00:44:34.900 align:middle line:90% and maybe in parallel. 00:44:34.900 --> 00:44:37.790 align:middle line:84% Or maybe there's a diffusion of oxygen vacancies. 00:44:37.790 --> 00:44:39.525 align:middle line:84% And so you have something diffusing in 00:44:39.525 --> 00:44:40.900 align:middle line:84% and something else diffusing out. 00:44:40.900 --> 00:44:43.317 align:middle line:84% And nevertheless, they said there are two species that you 00:44:43.317 --> 00:44:45.380 align:middle line:90% need to take into account. 00:44:45.380 --> 00:44:50.270 align:middle line:84% And they have associated reactions at the interfaces. 00:44:50.270 --> 00:44:53.233 align:middle line:84% So it looks very much like Deal-Grove. 00:44:53.233 --> 00:44:54.400 align:middle line:90% In fact, this is Deal-Grove. 00:44:54.400 --> 00:44:56.050 align:middle line:84% If you express Deal-Grove, remember, 00:44:56.050 --> 00:44:57.940 align:middle line:84% in terms of an oxidation rate, it's 00:44:57.940 --> 00:45:00.640 align:middle line:90% just B divided by 2X0 plus A. 00:45:00.640 --> 00:45:02.980 align:middle line:84% This looks a lot like Deal-Grove. 00:45:02.980 --> 00:45:04.750 align:middle line:90% But they've added a second term. 00:45:04.750 --> 00:45:07.390 align:middle line:84% And this second term here is to correspond 00:45:07.390 --> 00:45:12.700 align:middle line:84% to that second oxidation process happening in parallel. 00:45:12.700 --> 00:45:15.190 align:middle line:84% And they propose that all rate constants 00:45:15.190 --> 00:45:17.830 align:middle line:84% would be of an Arrhenius type nature, based on the data 00:45:17.830 --> 00:45:19.880 align:middle line:90% that they fit. 00:45:19.880 --> 00:45:21.130 align:middle line:90% It's just like Deal-Grove. 00:45:21.130 --> 00:45:23.893 align:middle line:84% But, in fact, so you say, well, you 00:45:23.893 --> 00:45:26.060 align:middle line:84% should double the number of constants in Deal-Grove. 00:45:26.060 --> 00:45:27.840 align:middle line:84% So instead of two, you should have four. 00:45:27.840 --> 00:45:29.350 align:middle line:84% In fact, what they found, they only 00:45:29.350 --> 00:45:31.550 align:middle line:84% really needed three parameters to fit the data. 00:45:31.550 --> 00:45:34.880 align:middle line:84% So they needed a B1 associated with this process 00:45:34.880 --> 00:45:38.860 align:middle line:84% and B2 associated with this process and B2 over A2. 00:45:38.860 --> 00:45:41.920 align:middle line:84% So they found A1 equal to roughly 0. 00:45:41.920 --> 00:45:45.520 align:middle line:84% So those of you who are skeptical in the audience 00:45:45.520 --> 00:45:49.360 align:middle line:84% will say, well, OK, Deal-Grove had two parameters. 00:45:49.360 --> 00:45:50.800 align:middle line:90% And Han and Helms have three. 00:45:50.800 --> 00:45:53.257 align:middle line:84% So if you add more and more parameters to a fit, 00:45:53.257 --> 00:45:55.840 align:middle line:84% you can always do a better job mathematically of fitting data. 00:45:55.840 --> 00:45:57.400 align:middle line:84% Everybody kind of knows that from 00:45:57.400 --> 00:45:58.735 align:middle line:90% your mathematical experience. 00:45:58.735 --> 00:46:00.610 align:middle line:84% So you could be skeptical and say, all right. 00:46:00.610 --> 00:46:01.790 align:middle line:90% They just add another constant. 00:46:01.790 --> 00:46:03.580 align:middle line:84% And perhaps that's true because the truth 00:46:03.580 --> 00:46:08.080 align:middle line:84% is, there isn't really any definitive data 00:46:08.080 --> 00:46:11.140 align:middle line:84% saying what the species that are diffusing through there. 00:46:11.140 --> 00:46:12.860 align:middle line:84% But nevertheless, they did come up 00:46:12.860 --> 00:46:15.350 align:middle line:84% with a model that's reasonably simple that does a better 00:46:15.350 --> 00:46:17.150 align:middle line:90% job in the thin oxide kinetics. 00:46:17.150 --> 00:46:19.750 align:middle line:90% 00:46:19.750 --> 00:46:22.080 align:middle line:84% So actually, let's compare these two models 00:46:22.080 --> 00:46:26.650 align:middle line:84% just on slide 23 with a Deal-Grove model. 00:46:26.650 --> 00:46:30.730 align:middle line:84% So the x-axis here is oxide thickness in microns. 00:46:30.730 --> 00:46:32.322 align:middle line:90% And this is time. 00:46:32.322 --> 00:46:33.780 align:middle line:84% I'm sorry, the y-axis is thickness. 00:46:33.780 --> 00:46:35.070 align:middle line:90% The x-axis is time. 00:46:35.070 --> 00:46:39.600 align:middle line:84% And this is plotted for atmospheric pressure dry O2 00:46:39.600 --> 00:46:41.110 align:middle line:90% at 800 degrees. 00:46:41.110 --> 00:46:43.077 align:middle line:84% And so let's look at the different models. 00:46:43.077 --> 00:46:44.910 align:middle line:84% This line right here, unfortunately, they're 00:46:44.910 --> 00:46:45.702 align:middle line:90% all the same color. 00:46:45.702 --> 00:46:46.260 align:middle line:90% I apologize. 00:46:46.260 --> 00:46:48.000 align:middle line:84% But you can see where the arrow is 00:46:48.000 --> 00:46:51.570 align:middle line:84% pointing to the Reisman model looks something like this. 00:46:51.570 --> 00:46:53.978 align:middle line:84% Han and Helms, amazingly, different mathematical 00:46:53.978 --> 00:46:55.770 align:middle line:84% equations, but they look pretty darn close. 00:46:55.770 --> 00:46:57.540 align:middle line:84% They're not exactly on top of each other 00:46:57.540 --> 00:46:58.950 align:middle line:90% in this thin oxide regime. 00:46:58.950 --> 00:47:00.660 align:middle line:90% But they're pretty darn close. 00:47:00.660 --> 00:47:03.180 align:middle line:84% The Deal-Grove model with tau equals 00:47:03.180 --> 00:47:07.230 align:middle line:84% 0 looks like this and with tau equals 8 looks like that. 00:47:07.230 --> 00:47:09.300 align:middle line:84% Doesn't actually approach either one of them 00:47:09.300 --> 00:47:14.080 align:middle line:84% very well until you get into the thicker regime up here. 00:47:14.080 --> 00:47:17.010 align:middle line:84% But in this thin regime, say below 200 angstroms 00:47:17.010 --> 00:47:20.070 align:middle line:84% or 0.02 microns, Deal-Grove doesn't really 00:47:20.070 --> 00:47:20.910 align:middle line:90% approach either one. 00:47:20.910 --> 00:47:23.340 align:middle line:84% And Han and Helms and Reisman do actually 00:47:23.340 --> 00:47:25.860 align:middle line:90% approach the data quite well. 00:47:25.860 --> 00:47:28.320 align:middle line:84% They will converge though when you get to oxides thicker 00:47:28.320 --> 00:47:32.020 align:middle line:90% than 200 angstroms. 00:47:32.020 --> 00:47:35.380 align:middle line:84% There's one more model that people actually 00:47:35.380 --> 00:47:37.570 align:middle line:90% are very fond of. 00:47:37.570 --> 00:47:39.070 align:middle line:90% And I'll talk about that now. 00:47:39.070 --> 00:47:40.870 align:middle line:90% That's shown on slide 24. 00:47:40.870 --> 00:47:43.517 align:middle line:90% This was the Massoud model. 00:47:43.517 --> 00:47:45.100 align:middle line:84% This was published quite some time ago 00:47:45.100 --> 00:47:46.720 align:middle line:90% at the electrochemical society. 00:47:46.720 --> 00:47:51.220 align:middle line:84% And the neat thing about Massoud's experiment 00:47:51.220 --> 00:47:55.150 align:middle line:84% was they actually measured in situ. 00:47:55.150 --> 00:47:58.090 align:middle line:84% In the furnace, they actually measured the thickness 00:47:58.090 --> 00:48:00.830 align:middle line:84% of the oxide growing as a function of time. 00:48:00.830 --> 00:48:03.250 align:middle line:84% So the other people like Deal-Grove and Han 00:48:03.250 --> 00:48:05.770 align:middle line:84% and Helms, all those people, they put a couple of wafers 00:48:05.770 --> 00:48:08.440 align:middle line:84% in and take them out, put them in for different amounts 00:48:08.440 --> 00:48:09.110 align:middle line:90% of time. 00:48:09.110 --> 00:48:11.800 align:middle line:84% And so they get a few certain data points. 00:48:11.800 --> 00:48:13.150 align:middle line:90% How many wafers can you put in? 00:48:13.150 --> 00:48:15.080 align:middle line:84% Maybe five or 10 in an experiment. 00:48:15.080 --> 00:48:18.633 align:middle line:84% So you can't really measure the kinetics in great detail 00:48:18.633 --> 00:48:20.050 align:middle line:84% if you're just pushing and pulling 00:48:20.050 --> 00:48:22.510 align:middle line:84% wafers out of the furnace and just measuring them outside. 00:48:22.510 --> 00:48:27.040 align:middle line:84% What Massoud decided to do to study the very thin regime 00:48:27.040 --> 00:48:29.140 align:middle line:84% was actually set up-- and it was non-trivial. 00:48:29.140 --> 00:48:30.610 align:middle line:90% He hit a diffusion furnace. 00:48:30.610 --> 00:48:32.740 align:middle line:84% He had special windows placed into it 00:48:32.740 --> 00:48:34.210 align:middle line:90% where he could put laser beam. 00:48:34.210 --> 00:48:35.890 align:middle line:84% So you could put a laser beam coming in, 00:48:35.890 --> 00:48:36.880 align:middle line:90% laser beam coming out. 00:48:36.880 --> 00:48:38.470 align:middle line:84% And he could do in situ measurements 00:48:38.470 --> 00:48:43.930 align:middle line:84% by ellipsometry of the oxide as it was growing in the tube. 00:48:43.930 --> 00:48:45.430 align:middle line:84% It doesn't sound like a big deal. 00:48:45.430 --> 00:48:47.837 align:middle line:84% But it turns out, it's pretty challenging 00:48:47.837 --> 00:48:50.170 align:middle line:84% because there's all kinds of thermal expansion going on. 00:48:50.170 --> 00:48:52.330 align:middle line:84% And the wafer has to sit still and not 00:48:52.330 --> 00:48:54.775 align:middle line:84% move while this laser comes in, hits, and bounces off 00:48:54.775 --> 00:48:56.900 align:middle line:84% because in the ellipsometry, the angle of incidence 00:48:56.900 --> 00:48:58.192 align:middle line:90% is very important and all that. 00:48:58.192 --> 00:49:00.740 align:middle line:84% So designing the equipment was like a huge part 00:49:00.740 --> 00:49:02.390 align:middle line:90% of this PhD thesis. 00:49:02.390 --> 00:49:04.790 align:middle line:84% But the nice thing is, it did produce a lot of data. 00:49:04.790 --> 00:49:06.040 align:middle line:90% Look at all these data points. 00:49:06.040 --> 00:49:08.300 align:middle line:84% They're all basically give you a nice looking curve. 00:49:08.300 --> 00:49:11.330 align:middle line:84% Instead of one point here, one here, and one here, 00:49:11.330 --> 00:49:15.140 align:middle line:84% he published in situ measured oxidation rates. 00:49:15.140 --> 00:49:16.302 align:middle line:90% Now, this is the rate. 00:49:16.302 --> 00:49:17.510 align:middle line:90% So this is not the thickness. 00:49:17.510 --> 00:49:20.810 align:middle line:84% This is angstroms per minute as a function 00:49:20.810 --> 00:49:22.190 align:middle line:90% of the thickness grown. 00:49:22.190 --> 00:49:25.340 align:middle line:84% And indeed, look below 200 angstroms. 00:49:25.340 --> 00:49:27.710 align:middle line:84% All of these rates are much larger 00:49:27.710 --> 00:49:30.320 align:middle line:84% than they are where they reach steady state, 00:49:30.320 --> 00:49:32.059 align:middle line:90% they reach smaller rates. 00:49:32.059 --> 00:49:34.392 align:middle line:84% And these are at three different temperatures, 800, 900, 00:49:34.392 --> 00:49:35.540 align:middle line:90% and 1,000. 00:49:35.540 --> 00:49:37.760 align:middle line:84% And in the thin oxide regime, the rate 00:49:37.760 --> 00:49:40.640 align:middle line:84% itself appears to be going up exponentially 00:49:40.640 --> 00:49:43.070 align:middle line:84% as you get to thinner and thinner or shorter and shorter 00:49:43.070 --> 00:49:43.760 align:middle line:90% times. 00:49:43.760 --> 00:49:45.950 align:middle line:84% So interestingly, initially, it appears 00:49:45.950 --> 00:49:49.500 align:middle line:84% to be, in fact, an exponential process with time. 00:49:49.500 --> 00:49:51.260 align:middle line:90% So it's growing very rapidly. 00:49:51.260 --> 00:49:54.290 align:middle line:84% And then it starts to converge to a process that 00:49:54.290 --> 00:49:57.500 align:middle line:84% looks more linear and then eventually, parabolic. 00:49:57.500 --> 00:49:59.420 align:middle line:84% Only with that kind of special apparatus 00:49:59.420 --> 00:50:01.250 align:middle line:84% could one get enough data point density 00:50:01.250 --> 00:50:03.170 align:middle line:90% to really see that though. 00:50:03.170 --> 00:50:06.710 align:middle line:84% So this is probably the most extensive experimental study 00:50:06.710 --> 00:50:08.900 align:middle line:90% that has been done. 00:50:08.900 --> 00:50:10.940 align:middle line:84% And what he did was he took Deal-Grove, 00:50:10.940 --> 00:50:13.190 align:middle line:84% just as it came, right out of the box, 00:50:13.190 --> 00:50:14.600 align:middle line:90% and added one more term. 00:50:14.600 --> 00:50:18.480 align:middle line:84% But the term was exponential in thickness. 00:50:18.480 --> 00:50:21.050 align:middle line:84% So the oxidation rate had the Deal-Grove B 00:50:21.050 --> 00:50:24.140 align:middle line:84% divided by 2X0 plus A plus a term 00:50:24.140 --> 00:50:28.610 align:middle line:84% that went like C times exponential of minus X0 over L. 00:50:28.610 --> 00:50:29.990 align:middle line:90% So what is this? 00:50:29.990 --> 00:50:32.900 align:middle line:84% Mathematically, this is a decaying exponential. 00:50:32.900 --> 00:50:35.720 align:middle line:84% When L gets very large, L is much greater than 200 00:50:35.720 --> 00:50:38.150 align:middle line:84% angstroms, this number goes away, right? 00:50:38.150 --> 00:50:41.870 align:middle line:84% You can always make it go to be very small compared 00:50:41.870 --> 00:50:42.630 align:middle line:90% to this term. 00:50:42.630 --> 00:50:45.470 align:middle line:84% So he wanted it all converged to Deal-Grove 00:50:45.470 --> 00:50:46.460 align:middle line:90% at thick enough oxides. 00:50:46.460 --> 00:50:51.500 align:middle line:84% But for thin oxides, this is going to dominate, this C term. 00:50:51.500 --> 00:50:53.630 align:middle line:84% And in order to do that, he had to choose 00:50:53.630 --> 00:50:56.660 align:middle line:84% L to be a certain number so that it had the right decay length. 00:50:56.660 --> 00:50:59.090 align:middle line:84% And L, he found experimentally, it 00:50:59.090 --> 00:51:02.090 align:middle line:84% should be about 7 nanometers so that the second term will 00:51:02.090 --> 00:51:08.700 align:middle line:84% decay rapidly enough by the time you get to 20 nanometers or so. 00:51:08.700 --> 00:51:11.510 align:middle line:84% In fact, this model does agree very well mathematically 00:51:11.510 --> 00:51:13.310 align:middle line:90% with experimental data. 00:51:13.310 --> 00:51:14.810 align:middle line:84% It's actually very easy to implement 00:51:14.810 --> 00:51:16.730 align:middle line:90% in simulators like Supreme 4. 00:51:16.730 --> 00:51:20.330 align:middle line:84% And so it has been found to be implemented in Supreme 4. 00:51:20.330 --> 00:51:23.780 align:middle line:84% And in terms of physical explanations, 00:51:23.780 --> 00:51:25.800 align:middle line:84% there's a few that have come out. 00:51:25.800 --> 00:51:28.250 align:middle line:84% But none has really been clearly identified 00:51:28.250 --> 00:51:29.970 align:middle line:90% as being the right reason. 00:51:29.970 --> 00:51:32.630 align:middle line:84% So for now, we use it as sort of a mathematical model 00:51:32.630 --> 00:51:35.070 align:middle line:90% or an empirical relation. 00:51:35.070 --> 00:51:36.110 align:middle line:90% It's very handy. 00:51:36.110 --> 00:51:37.920 align:middle line:84% And it can be reasonably accurate. 00:51:37.920 --> 00:51:39.800 align:middle line:90% So it's appealing in that sense. 00:51:39.800 --> 00:51:41.685 align:middle line:84% In terms of the physics and the chemistry, 00:51:41.685 --> 00:51:42.935 align:middle line:90% it's not a completely obvious. 00:51:42.935 --> 00:51:45.735 align:middle line:90% 00:51:45.735 --> 00:51:47.610 align:middle line:84% OK, so those are the three thin oxide models. 00:51:47.610 --> 00:51:49.153 align:middle line:84% And hopefully, you'll get a chance 00:51:49.153 --> 00:51:50.820 align:middle line:84% to study some of those a little bit more 00:51:50.820 --> 00:51:53.680 align:middle line:84% in one of your homework problems. 00:51:53.680 --> 00:51:55.660 align:middle line:84% So now let's vary something else. 00:51:55.660 --> 00:51:58.000 align:middle line:84% All we varied so far is the following. 00:51:58.000 --> 00:51:59.640 align:middle line:90% We varied the ambient. 00:51:59.640 --> 00:52:02.520 align:middle line:84% We said it could be dry O2 or water and temperature. 00:52:02.520 --> 00:52:03.660 align:middle line:90% What else can you vary? 00:52:03.660 --> 00:52:07.440 align:middle line:84% Well, it turns out, people often do vary the pressure. 00:52:07.440 --> 00:52:10.260 align:middle line:84% That is the partial pressure of the oxidant. 00:52:10.260 --> 00:52:12.268 align:middle line:84% If you want to grow a very thin oxide, 00:52:12.268 --> 00:52:14.310 align:middle line:84% and yet, you want to grow at a higher temperature 00:52:14.310 --> 00:52:16.620 align:middle line:84% because you want to get different electrical quality 00:52:16.620 --> 00:52:18.870 align:middle line:84% of the interface, you can't grow too fast. 00:52:18.870 --> 00:52:21.090 align:middle line:84% So you might want to slow it down by diluting. 00:52:21.090 --> 00:52:24.630 align:middle line:84% You can just take the oxygen and flow mostly nitrogen, 00:52:24.630 --> 00:52:27.760 align:middle line:84% and have oxygen flow be a very small fraction of the gas 00:52:27.760 --> 00:52:28.260 align:middle line:90% stream. 00:52:28.260 --> 00:52:31.590 align:middle line:84% That's a way of diluting the gas stream 00:52:31.590 --> 00:52:35.050 align:middle line:84% and growing at lower partial pressures. 00:52:35.050 --> 00:52:40.440 align:middle line:84% So just as a reminder, Deal-Grove 00:52:40.440 --> 00:52:42.720 align:middle line:84% predicts that the oxide growth rate 00:52:42.720 --> 00:52:45.700 align:middle line:84% should be directly proportional to the pressure of the oxidant. 00:52:45.700 --> 00:52:49.360 align:middle line:84% C star, effectively, if you can think of it, 00:52:49.360 --> 00:52:55.190 align:middle line:84% should depend on PG where PG is the bulk gas pressure. 00:52:55.190 --> 00:53:01.780 align:middle line:84% So basically, if I were to lower the gas pressure, 00:53:01.780 --> 00:53:05.200 align:middle line:84% you would expect that you could lower the oxidation rate. 00:53:05.200 --> 00:53:10.810 align:middle line:84% So just to be a little more specific, we go on to slide 27. 00:53:10.810 --> 00:53:14.620 align:middle line:84% What people have found, though, is it's not completely linear. 00:53:14.620 --> 00:53:17.950 align:middle line:84% Experimentally, if you lower the partial pressure 00:53:17.950 --> 00:53:23.680 align:middle line:84% of the oxidant, in fact, B and B over A do scale like P, 00:53:23.680 --> 00:53:29.230 align:middle line:84% where P would be the partial pressure, for water oxidation. 00:53:29.230 --> 00:53:31.480 align:middle line:84% And the rate constant B does scale 00:53:31.480 --> 00:53:35.620 align:middle line:90% like the pressure for dry O2. 00:53:35.620 --> 00:53:37.633 align:middle line:84% The one rate constant that's anomalous 00:53:37.633 --> 00:53:38.800 align:middle line:90% is the linear rate constant. 00:53:38.800 --> 00:53:44.007 align:middle line:84% The B over A for dry O2 doesn't go quite like exactly 00:53:44.007 --> 00:53:44.590 align:middle line:90% like pressure. 00:53:44.590 --> 00:53:48.070 align:middle line:84% It goes like P to the N, where N is close to 1 but not really 1. 00:53:48.070 --> 00:53:49.700 align:middle line:90% It's somewhere between 0.5. 00:53:49.700 --> 00:53:53.410 align:middle line:84% So it's a power law between 0.5 and 1. 00:53:53.410 --> 00:53:56.920 align:middle line:84% So this suggests that at least for oxygen, the case of S 00:53:56.920 --> 00:54:02.410 align:middle line:84% maybe has some dependence on pressure that's nonlinear. 00:54:02.410 --> 00:54:05.410 align:middle line:84% So these are some empirical models that you'll 00:54:05.410 --> 00:54:07.460 align:middle line:90% find in Supreme 4, for example. 00:54:07.460 --> 00:54:12.550 align:middle line:84% The linear rate constant may go some number B over A 00:54:12.550 --> 00:54:16.450 align:middle line:84% to the I times pressure where I here 00:54:16.450 --> 00:54:20.180 align:middle line:84% refers to the intrinsic values at 1 atmosphere. 00:54:20.180 --> 00:54:22.060 align:middle line:90% N here might be 0.7 to 0.8. 00:54:22.060 --> 00:54:25.120 align:middle line:84% And you notice, you specify the pressure P. 00:54:25.120 --> 00:54:27.490 align:middle line:84% So maybe you say at half an atmosphere 00:54:27.490 --> 00:54:29.790 align:middle line:90% or a tenth of an atmosphere. 00:54:29.790 --> 00:54:31.707 align:middle line:84% But we're not changing-- think of it this way. 00:54:31.707 --> 00:54:33.957 align:middle line:84% You're not actually changing the pressure in the tube. 00:54:33.957 --> 00:54:35.830 align:middle line:84% The pressure of all the gas in the tube 00:54:35.830 --> 00:54:37.180 align:middle line:90% is still an atmosphere. 00:54:37.180 --> 00:54:40.000 align:middle line:84% What we're doing is we're flowing mostly nitrogen. 00:54:40.000 --> 00:54:43.850 align:middle line:84% And we're putting a small amount of oxygen in the gas stream. 00:54:43.850 --> 00:54:47.077 align:middle line:84% So let's say I wanted to oxidize at half an atmosphere. 00:54:47.077 --> 00:54:48.160 align:middle line:90% Well, I just cut the flow. 00:54:48.160 --> 00:54:51.070 align:middle line:84% I use equal flows of nitrogen and oxygen. 00:54:51.070 --> 00:54:55.810 align:middle line:84% So we're diluting the pressure, basically. 00:54:55.810 --> 00:55:00.400 align:middle line:84% We're diluting the oxidant in the gas stream. 00:55:00.400 --> 00:55:01.760 align:middle line:90% So here's an example. 00:55:01.760 --> 00:55:05.180 align:middle line:84% Suppose I dilute it by a factor of 10 to 1. 00:55:05.180 --> 00:55:10.540 align:middle line:84% So I'm flowing 1,000 SECM of inert gas like argon 00:55:10.540 --> 00:55:14.260 align:middle line:84% or nitrogen. And I'm flowing only 100 SECM 00:55:14.260 --> 00:55:16.420 align:middle line:90% of oxygen, dry O2. 00:55:16.420 --> 00:55:21.820 align:middle line:84% This is what we would get as the oxide thickness versus time. 00:55:21.820 --> 00:55:26.740 align:middle line:84% And the solid lines were if you were to do the very brute force 00:55:26.740 --> 00:55:29.650 align:middle line:84% simple idea that it was all scaled like P. 00:55:29.650 --> 00:55:32.950 align:middle line:90% And it's just down. 00:55:32.950 --> 00:55:37.390 align:middle line:84% The rate constants are down by a factor of P, 00:55:37.390 --> 00:55:40.030 align:middle line:84% where p here would be a 1/10 the pressure 00:55:40.030 --> 00:55:41.060 align:middle line:90% of atmospheric pressure. 00:55:41.060 --> 00:55:43.360 align:middle line:84% The dashed line is where you use a little bit 00:55:43.360 --> 00:55:47.345 align:middle line:84% more sophisticated model where, in fact, the B parameter 00:55:47.345 --> 00:55:48.220 align:middle line:90% scales like pressure. 00:55:48.220 --> 00:55:50.213 align:middle line:84% But the B over A parameter scales like pressure 00:55:50.213 --> 00:55:52.070 align:middle line:90% at the 0.8, so just slightly. 00:55:52.070 --> 00:55:55.128 align:middle line:84% So in fact, the kinetics would be slightly faster, 00:55:55.128 --> 00:55:56.920 align:middle line:84% the oxide would be growing slightly faster, 00:55:56.920 --> 00:55:59.680 align:middle line:84% than you would have predicted using very simple dependence 00:55:59.680 --> 00:56:02.410 align:middle line:84% on just saying it depends strictly on P. 00:56:02.410 --> 00:56:04.930 align:middle line:84% So it gives you a little bit more accuracy using some 00:56:04.930 --> 00:56:08.240 align:middle line:90% of these more empirical models. 00:56:08.240 --> 00:56:11.563 align:middle line:84% But again, the idea here is, if for some reason, 00:56:11.563 --> 00:56:13.480 align:middle line:84% you need to control the oxidation rate better, 00:56:13.480 --> 00:56:15.400 align:middle line:84% you want to slow it down, you just dilute 00:56:15.400 --> 00:56:16.690 align:middle line:90% the oxygen in the furnace. 00:56:16.690 --> 00:56:21.440 align:middle line:90% 00:56:21.440 --> 00:56:23.930 align:middle line:84% Oh, I just showed some specific examples here 00:56:23.930 --> 00:56:26.240 align:middle line:84% of trying to read off what the difference would be. 00:56:26.240 --> 00:56:29.180 align:middle line:84% You'd make an error of about a 100 angstroms 00:56:29.180 --> 00:56:31.520 align:middle line:84% if you use the simple assumption compared 00:56:31.520 --> 00:56:40.570 align:middle line:84% to what's a little bit more accurate here at 1,000 degrees. 00:56:40.570 --> 00:56:42.280 align:middle line:90% OK, so let me just get through. 00:56:42.280 --> 00:56:46.772 align:middle line:84% That's the standard kinetics on slide 29. 00:56:46.772 --> 00:56:47.980 align:middle line:90% Let's go on to slide 30 then. 00:56:47.980 --> 00:56:49.438 align:middle line:84% OK, so what I just talked about was 00:56:49.438 --> 00:56:52.900 align:middle line:84% trying to dilute the oxidant so you can grow slower 00:56:52.900 --> 00:56:55.210 align:middle line:90% at a given temperature. 00:56:55.210 --> 00:56:58.030 align:middle line:84% On slide 30, we're doing just the opposite now. 00:56:58.030 --> 00:57:01.780 align:middle line:84% It's not so easy to do from a physical point of view. 00:57:01.780 --> 00:57:05.830 align:middle line:84% But you can imagine growing at higher than 1 pressure. 00:57:05.830 --> 00:57:08.110 align:middle line:84% Let's say the pressure tells you what? 00:57:08.110 --> 00:57:11.680 align:middle line:84% It tells you the number of atoms or molecules, species hitting 00:57:11.680 --> 00:57:13.720 align:middle line:90% the surface per unit time. 00:57:13.720 --> 00:57:16.450 align:middle line:84% So if I double that pressure, I can double the amount 00:57:16.450 --> 00:57:18.148 align:middle line:90% there hitting that surface. 00:57:18.148 --> 00:57:19.690 align:middle line:84% I can double the flux to the surface. 00:57:19.690 --> 00:57:22.850 align:middle line:84% So you expect the growth rate to go up. 00:57:22.850 --> 00:57:26.620 align:middle line:84% It's just not in your intuition is how I could do that. 00:57:26.620 --> 00:57:29.540 align:middle line:84% Here, you have a tube that's made of quartz. 00:57:29.540 --> 00:57:31.810 align:middle line:84% I have it open on both ends to the ambient. 00:57:31.810 --> 00:57:33.160 align:middle line:90% And I'm flowing some gas to it. 00:57:33.160 --> 00:57:34.360 align:middle line:84% How are you going to get a higher pressure? 00:57:34.360 --> 00:57:35.777 align:middle line:84% We're all at atmospheric pressure. 00:57:35.777 --> 00:57:36.443 align:middle line:90% It doesn't work. 00:57:36.443 --> 00:57:37.270 align:middle line:90% But you can do it. 00:57:37.270 --> 00:57:40.160 align:middle line:84% You can build a system where outside that quartz tube, 00:57:40.160 --> 00:57:43.010 align:middle line:84% there's a big envelope made of stainless steel like a diver's 00:57:43.010 --> 00:57:44.450 align:middle line:90% tank. 00:57:44.450 --> 00:57:46.610 align:middle line:84% They have training tanks for deep sea divers. 00:57:46.610 --> 00:57:48.140 align:middle line:84% They put these guys in these tanks. 00:57:48.140 --> 00:57:50.120 align:middle line:84% They seal it up like a submarine. 00:57:50.120 --> 00:57:52.100 align:middle line:84% And they can stuff more and more gas in there, 00:57:52.100 --> 00:57:54.330 align:middle line:84% and you can increase the pressure on the diver. 00:57:54.330 --> 00:57:57.110 align:middle line:84% So that's exactly what people do with high pressure oxidation. 00:57:57.110 --> 00:57:59.073 align:middle line:84% It's a very special type of equipment. 00:57:59.073 --> 00:58:01.490 align:middle line:84% It's not something you're going to find in a standard fab. 00:58:01.490 --> 00:58:02.510 align:middle line:90% They are available though. 00:58:02.510 --> 00:58:03.860 align:middle line:90% They've been commercially made. 00:58:03.860 --> 00:58:08.960 align:middle line:84% And people call it HiPOX, the High Pressure Oxidation System. 00:58:08.960 --> 00:58:11.840 align:middle line:84% So here's an example of how the kinetics would go up. 00:58:11.840 --> 00:58:16.090 align:middle line:84% And this I took from Mayer and Lau's book, 1990. 00:58:16.090 --> 00:58:18.670 align:middle line:84% What they're showing here is on a log plot 00:58:18.670 --> 00:58:21.820 align:middle line:84% here, a semi-log, so it's log on the Y, linearly 00:58:21.820 --> 00:58:24.880 align:middle line:84% on the X, oxide thickness versus time. 00:58:24.880 --> 00:58:27.550 align:middle line:90% And this is 100 in steam. 00:58:27.550 --> 00:58:30.280 align:middle line:84% And they're looking at versus temperature-- 00:58:30.280 --> 00:58:32.483 align:middle line:84% I'm sorry, looking at a couple different curves 00:58:32.483 --> 00:58:33.650 align:middle line:90% here at different pressures. 00:58:33.650 --> 00:58:36.340 align:middle line:84% So at atmospheric pressure, it looks like this. 00:58:36.340 --> 00:58:40.948 align:middle line:84% At 5 atmospheres or 10 atmospheres, 00:58:40.948 --> 00:58:41.740 align:middle line:90% it looks like this. 00:58:41.740 --> 00:58:42.910 align:middle line:90% Here we are 20 atmospheres. 00:58:42.910 --> 00:58:46.130 align:middle line:84% Look how much faster we can grow. 00:58:46.130 --> 00:58:49.570 align:middle line:84% So this can be used to increase the oxidation 00:58:49.570 --> 00:58:50.920 align:middle line:90% rate at low temperatures. 00:58:50.920 --> 00:58:53.105 align:middle line:84% If you need to grow a thick oxide thermally, 00:58:53.105 --> 00:58:55.480 align:middle line:84% you need to have the properties of a thermal oxide, which 00:58:55.480 --> 00:58:56.350 align:middle line:90% are quite unique. 00:58:56.350 --> 00:58:58.870 align:middle line:90% Its density is well defined. 00:58:58.870 --> 00:59:00.820 align:middle line:84% It has much better electrical properties 00:59:00.820 --> 00:59:02.920 align:middle line:84% than you would get by depositing an oxide. 00:59:02.920 --> 00:59:05.470 align:middle line:84% It actually consumes silicon, which is not 00:59:05.470 --> 00:59:07.080 align:middle line:90% true of a deposited oxide. 00:59:07.080 --> 00:59:08.960 align:middle line:84% Then you have to go to a hypoxic process. 00:59:08.960 --> 00:59:11.000 align:middle line:84% Or let's say you have some structure 00:59:11.000 --> 00:59:13.130 align:middle line:84% on the surface like silicon germanium 00:59:13.130 --> 00:59:15.590 align:middle line:84% or some material that can't go to high temperature 00:59:15.590 --> 00:59:18.770 align:middle line:84% because it'll cause the material to diffuse or to relax, 00:59:18.770 --> 00:59:21.470 align:middle line:84% or you're trying to limit the amount of diffusion 00:59:21.470 --> 00:59:22.192 align:middle line:90% in the substrate. 00:59:22.192 --> 00:59:23.900 align:middle line:84% Well, and you need to grow a thick oxide, 00:59:23.900 --> 00:59:27.140 align:middle line:84% you can do it in a hypoxic machine at 800, 00:59:27.140 --> 00:59:30.860 align:middle line:84% where you never would be able to do grow a half a micron at 800. 00:59:30.860 --> 00:59:33.290 align:middle line:84% But you can do it in HiPOX at 20 atmospheres. 00:59:33.290 --> 00:59:36.680 align:middle line:84% So for materials and processes that 00:59:36.680 --> 00:59:38.130 align:middle line:84% are getting limited by temperature 00:59:38.130 --> 00:59:40.255 align:middle line:84% and they have to go lower and lower in temperature, 00:59:40.255 --> 00:59:43.565 align:middle line:84% HiPOX is a way of increasing the oxidation rate. 00:59:43.565 --> 00:59:46.250 align:middle line:90% 00:59:46.250 --> 00:59:51.490 align:middle line:84% So in fact, here are some data shown on slide 31 00:59:51.490 --> 00:59:55.570 align:middle line:84% on HiPOX I took from Simon Z's book. 00:59:55.570 --> 00:59:59.770 align:middle line:84% And what it shows is the measurements on the y-axis, 00:59:59.770 --> 01:00:02.680 align:middle line:84% the parabolic rate constant-- so this is the B parameter-- 01:00:02.680 --> 01:00:06.880 align:middle line:84% as a function of 1,000 over T-- so it's a semi-log kind 01:00:06.880 --> 01:00:09.610 align:middle line:90% of Arrhenius plot-- 01:00:09.610 --> 01:00:11.140 align:middle line:90% in steam. 01:00:11.140 --> 01:00:14.600 align:middle line:84% And this has been measured for a couple 01:00:14.600 --> 01:00:17.260 align:middle line:84% of different orientations of silicon. 01:00:17.260 --> 01:00:20.597 align:middle line:84% And what you see here is this solid line, 01:00:20.597 --> 01:00:22.430 align:middle line:84% which has two different activation energies. 01:00:22.430 --> 01:00:25.360 align:middle line:84% There seemed to be a break point here somewhere around 950 01:00:25.360 --> 01:00:29.110 align:middle line:84% degrees but actual activation energy close to one electron 01:00:29.110 --> 01:00:31.480 align:middle line:90% volt. This is the B parameter. 01:00:31.480 --> 01:00:35.573 align:middle line:84% Here at 5, 10, 15 and 20 atmospheres, 01:00:35.573 --> 01:00:37.240 align:middle line:84% this is what the B parameter goes up by. 01:00:37.240 --> 01:00:41.560 align:middle line:84% And in fact, I marked this blue line, which is at 800 degrees. 01:00:41.560 --> 01:00:44.050 align:middle line:84% And in fact, I'm reading off the chart here, 01:00:44.050 --> 01:00:47.390 align:middle line:84% the B parameter is almost exactly a factor of 20 01:00:47.390 --> 01:00:52.290 align:middle line:84% faster at 20 atmospheres than it is at 1 atmosphere. 01:00:52.290 --> 01:00:56.690 align:middle line:84% So we can go up to 20 times the oxidation rate 01:00:56.690 --> 01:00:58.740 align:middle line:84% at 20 atmospheres at 800 degrees. 01:00:58.740 --> 01:01:02.270 align:middle line:84% So it does scale reasonably well, this parameter does, 01:01:02.270 --> 01:01:04.580 align:middle line:84% with pressure at higher pressures. 01:01:04.580 --> 01:01:07.800 align:middle line:90% 01:01:07.800 --> 01:01:10.110 align:middle line:84% On slide 32, I'm actually showing you-- 01:01:10.110 --> 01:01:13.860 align:middle line:84% remember, I said, you can build this complex diver tank looking 01:01:13.860 --> 01:01:16.410 align:middle line:84% thing with a great big steel vacuum 01:01:16.410 --> 01:01:20.010 align:middle line:84% system that can hold the pressure and pressurization 01:01:20.010 --> 01:01:20.820 align:middle line:90% system. 01:01:20.820 --> 01:01:22.530 align:middle line:84% I've taken this from Simon Z's book. 01:01:22.530 --> 01:01:26.490 align:middle line:84% He actually talks about how you would do a HiPOX 01:01:26.490 --> 01:01:29.120 align:middle line:90% run, if you had such a thing. 01:01:29.120 --> 01:01:31.370 align:middle line:84% Just so you can think about it, what happens 01:01:31.370 --> 01:01:34.640 align:middle line:84% is the wafers get loaded here at atmospheric pressure. 01:01:34.640 --> 01:01:36.618 align:middle line:84% Down here, this solid bar, it means 01:01:36.618 --> 01:01:37.910 align:middle line:90% you're at atmospheric pressure. 01:01:37.910 --> 01:01:40.670 align:middle line:84% Obviously, you can't pump up the diver tank 01:01:40.670 --> 01:01:43.310 align:middle line:90% until the hatch is closed. 01:01:43.310 --> 01:01:45.620 align:middle line:84% So you load them in atmospheric pressure. 01:01:45.620 --> 01:01:47.760 align:middle line:90% And you have a sealing step. 01:01:47.760 --> 01:01:50.810 align:middle line:84% And here, you're starting to increase the pressure, again, 01:01:50.810 --> 01:01:52.610 align:middle line:90% using O2. 01:01:52.610 --> 01:01:53.960 align:middle line:90% You do some purging. 01:01:53.960 --> 01:01:56.180 align:middle line:84% And then at some point, what you do 01:01:56.180 --> 01:02:00.590 align:middle line:84% is you bring this outside steel shell and the tube 01:02:00.590 --> 01:02:01.590 align:middle line:90% up together in pressure. 01:02:01.590 --> 01:02:05.030 align:middle line:84% And you go up to, say 10 atmospheres. 01:02:05.030 --> 01:02:07.445 align:middle line:84% So your pressurizing in moisture. 01:02:07.445 --> 01:02:09.200 align:middle line:90% Then you do your oxidation. 01:02:09.200 --> 01:02:11.720 align:middle line:84% Then you depressurize and bring it 01:02:11.720 --> 01:02:13.400 align:middle line:84% down to atmospheric pressure and unload. 01:02:13.400 --> 01:02:15.108 align:middle line:84% So it's perfectly possible to do this. 01:02:15.108 --> 01:02:17.150 align:middle line:84% Obviously, if you try to do it with a quartz tube 01:02:17.150 --> 01:02:19.380 align:middle line:84% and put end caps on it and pressurize it, of course, 01:02:19.380 --> 01:02:21.252 align:middle line:84% the quartz would explode all over 01:02:21.252 --> 01:02:22.710 align:middle line:84% because it's not a strong material. 01:02:22.710 --> 01:02:26.760 align:middle line:84% But if you have the stainless steel shroud all around it, 01:02:26.760 --> 01:02:29.010 align:middle line:84% then the differential pressure across the quartz 01:02:29.010 --> 01:02:30.360 align:middle line:90% is very close to 0. 01:02:30.360 --> 01:02:32.530 align:middle line:84% Or it can be just maybe one atmosphere. 01:02:32.530 --> 01:02:34.145 align:middle line:84% We know it can withstand 1 atmosphere. 01:02:34.145 --> 01:02:35.520 align:middle line:84% But that way, you keep the quartz 01:02:35.520 --> 01:02:38.470 align:middle line:84% from exploding all over the place. 01:02:38.470 --> 01:02:40.200 align:middle line:84% So it's a special piece of equipment. 01:02:40.200 --> 01:02:42.890 align:middle line:90% 01:02:42.890 --> 01:02:45.770 align:middle line:84% OK, so then let's go on to slide 33, so HiPOX, 01:02:45.770 --> 01:02:46.910 align:middle line:90% we can do low pressures. 01:02:46.910 --> 01:02:50.150 align:middle line:84% You can do high pressures if you have the right equipment. 01:02:50.150 --> 01:02:52.940 align:middle line:84% It turns out, simple oxidation also 01:02:52.940 --> 01:02:58.610 align:middle line:84% isn't always done just with oxygen or water vapor. 01:02:58.610 --> 01:03:01.940 align:middle line:84% Small concentrations of certain other species are often added. 01:03:01.940 --> 01:03:06.680 align:middle line:84% For example, HCl is sometimes added to the O2 01:03:06.680 --> 01:03:08.060 align:middle line:84% because it turns out, people have 01:03:08.060 --> 01:03:12.200 align:middle line:84% found by adding that, they can reduce oxide defect densities 01:03:12.200 --> 01:03:15.020 align:middle line:84% or they can reduce contamination levels. 01:03:15.020 --> 01:03:19.970 align:middle line:84% In the liquid form, HCl is very good at etching off metals 01:03:19.970 --> 01:03:21.180 align:middle line:90% from the surface. 01:03:21.180 --> 01:03:23.420 align:middle line:84% So perhaps, it has a similar role 01:03:23.420 --> 01:03:25.500 align:middle line:90% when it's in the vapor phase. 01:03:25.500 --> 01:03:29.610 align:middle line:84% So sometimes, people add a small amount of HCl to the furnace. 01:03:29.610 --> 01:03:32.600 align:middle line:84% It can produce chlorine, which can react with maybe trace 01:03:32.600 --> 01:03:37.470 align:middle line:84% metals by this kind of process that's shown here. 01:03:37.470 --> 01:03:40.730 align:middle line:84% So it's not unusual to see, in manufacturing processes 01:03:40.730 --> 01:03:45.430 align:middle line:84% oxidation, in not just O2 but HCl, O2 plus HCL. 01:03:45.430 --> 01:03:48.100 align:middle line:84% So these bullets here in the middle of the slide 01:03:48.100 --> 01:03:50.650 align:middle line:84% are just some generic kind of observations 01:03:50.650 --> 01:03:53.620 align:middle line:84% that have been made on these different ambients. 01:03:53.620 --> 01:03:55.930 align:middle line:84% Well, just studied, in the Deal-Grove, 01:03:55.930 --> 01:03:58.750 align:middle line:84% we know in detail that you can get 20 to 50 times 01:03:58.750 --> 01:04:03.910 align:middle line:84% faster than dry O2 just by putting in wet O2 in steam. 01:04:03.910 --> 01:04:05.860 align:middle line:90% So we know that. 01:04:05.860 --> 01:04:09.910 align:middle line:84% 3% chlorine in the ambient can increase the growth rate 01:04:09.910 --> 01:04:11.390 align:middle line:90% by 20% to 30%. 01:04:11.390 --> 01:04:14.083 align:middle line:84% So also, HCl is a way of, at a low temperature, 01:04:14.083 --> 01:04:15.250 align:middle line:90% is boosting the growth rate. 01:04:15.250 --> 01:04:17.470 align:middle line:84% The name of the game these days is keep the dopants 01:04:17.470 --> 01:04:18.010 align:middle line:90% from moving. 01:04:18.010 --> 01:04:19.510 align:middle line:84% But keep the growth rate high enough 01:04:19.510 --> 01:04:22.070 align:middle line:84% to give you a reasonable thickness. 01:04:22.070 --> 01:04:25.430 align:middle line:84% So you can add a little chlorine to speed up the growth rate. 01:04:25.430 --> 01:04:29.283 align:middle line:84% You can also add NF3, another commonly used species. 01:04:29.283 --> 01:04:31.450 align:middle line:84% A small amount of that will increase the growth rate 01:04:31.450 --> 01:04:34.510 align:middle line:90% by two to three times. 01:04:34.510 --> 01:04:37.120 align:middle line:84% Again, this is adding in a lot of new chemistry. 01:04:37.120 --> 01:04:39.182 align:middle line:84% And there's no way in an AB initio, 01:04:39.182 --> 01:04:41.140 align:middle line:84% in a first principle sense, to really calculate 01:04:41.140 --> 01:04:41.848 align:middle line:90% what those rates. 01:04:41.848 --> 01:04:44.440 align:middle line:84% Are so in simulators like Supreme 4, 01:04:44.440 --> 01:04:46.480 align:middle line:84% if you go sit down and tell it, oh, I 01:04:46.480 --> 01:04:49.057 align:middle line:84% want to grow an oxide in chlorine and oxygen. 01:04:49.057 --> 01:04:51.640 align:middle line:84% It doesn't simulate the chemical reaction and all the kinetics 01:04:51.640 --> 01:04:53.020 align:middle line:90% and, come on, spit out a number. 01:04:53.020 --> 01:04:56.348 align:middle line:84% It has a lookup table of B and B over A values that 01:04:56.348 --> 01:04:58.390 align:middle line:84% have been measured in the literature for commonly 01:04:58.390 --> 01:05:02.120 align:middle line:84% used ambients like chlorine and maybe NF3 and a few others. 01:05:02.120 --> 01:05:08.410 align:middle line:84% So it looks up in the table what B over A and B should be. 01:05:08.410 --> 01:05:11.020 align:middle line:84% As a function of the pressure here, this pressure, delta 01:05:11.020 --> 01:05:15.370 align:middle line:84% or chi, these are some functions of the concentration 01:05:15.370 --> 01:05:18.790 align:middle line:84% of this additional species that's in the furnace. 01:05:18.790 --> 01:05:20.765 align:middle line:90% Could it be HCl or whatever. 01:05:20.765 --> 01:05:22.640 align:middle line:84% And they've been determined very empirically. 01:05:22.640 --> 01:05:25.160 align:middle line:84% So don't expect first principles models, 01:05:25.160 --> 01:05:26.990 align:middle line:84% but maybe some mathematical models 01:05:26.990 --> 01:05:28.940 align:middle line:84% would be in Supreme for different ambience. 01:05:28.940 --> 01:05:30.650 align:middle line:84% But again, they've all been calibrated 01:05:30.650 --> 01:05:32.270 align:middle line:90% to somebody's experiment. 01:05:32.270 --> 01:05:34.908 align:middle line:84% So they may not exactly agree with your experiment. 01:05:34.908 --> 01:05:36.575 align:middle line:84% You might have to calibrate it yourself. 01:05:36.575 --> 01:05:39.680 align:middle line:90% 01:05:39.680 --> 01:05:43.580 align:middle line:84% Here's an interesting example on slide 34. 01:05:43.580 --> 01:05:46.100 align:middle line:90% These are some kinetics in-- 01:05:46.100 --> 01:05:47.660 align:middle line:84% HCl has been used for quite a while. 01:05:47.660 --> 01:05:49.250 align:middle line:90% It's even old fashioned now. 01:05:49.250 --> 01:05:50.870 align:middle line:84% Something that's a little bit newer 01:05:50.870 --> 01:05:55.340 align:middle line:84% is people oxidizing an ambience like NO, N2O, 01:05:55.340 --> 01:05:57.050 align:middle line:84% and even implanting nitrogen. Remember, 01:05:57.050 --> 01:06:02.150 align:middle line:84% we talked about oxynitrides are the first form of high K. 01:06:02.150 --> 01:06:05.360 align:middle line:84% Oxynitride, which is a mixture of silicon, oxygen, 01:06:05.360 --> 01:06:07.808 align:middle line:84% and nitrogen, has a higher dielectric constant. 01:06:07.808 --> 01:06:09.350 align:middle line:84% You can make it a little bit thicker. 01:06:09.350 --> 01:06:10.760 align:middle line:84% And so you get less gate leakage. 01:06:10.760 --> 01:06:14.000 align:middle line:84% So gate oxides of oxynitride were 01:06:14.000 --> 01:06:16.190 align:middle line:90% are popular for people to study. 01:06:16.190 --> 01:06:20.750 align:middle line:84% But here's an example of trying to fabricate 01:06:20.750 --> 01:06:24.170 align:middle line:84% an oxynitride where the kinetics are really crazy. 01:06:24.170 --> 01:06:26.000 align:middle line:84% They're not at all linear parabolic. 01:06:26.000 --> 01:06:29.300 align:middle line:84% And in fact, this is a plot here on the y-axis 01:06:29.300 --> 01:06:33.260 align:middle line:84% is oxide thickness or oxynitride thickness, if you want, 01:06:33.260 --> 01:06:37.030 align:middle line:84% as a function of the nitrogen dose. 01:06:37.030 --> 01:06:40.710 align:middle line:84% So here, the substrate was implanted first with nitrogen-- 01:06:40.710 --> 01:06:42.360 align:middle line:84% and we'll talk about ion implantation-- 01:06:42.360 --> 01:06:45.090 align:middle line:84% to a certain number of atoms per square centimeter. 01:06:45.090 --> 01:06:48.540 align:middle line:84% And they're plotting the oxide thickness here 01:06:48.540 --> 01:06:50.790 align:middle line:84% at different times, so say, for 25 minutes 01:06:50.790 --> 01:06:53.620 align:middle line:90% as a function of dose. 01:06:53.620 --> 01:06:56.490 align:middle line:84% And you can see, depending on how much nitrogen you 01:06:56.490 --> 01:06:59.160 align:middle line:84% implanted, the thickness actually can go down. 01:06:59.160 --> 01:07:02.130 align:middle line:84% So the oxidation rate can depend on exactly what 01:07:02.130 --> 01:07:03.090 align:middle line:90% is at that surface. 01:07:03.090 --> 01:07:04.590 align:middle line:90% Was it silicon pure? 01:07:04.590 --> 01:07:07.710 align:middle line:84% Or was it silicon that had been ion implanted with something? 01:07:07.710 --> 01:07:11.700 align:middle line:84% So this needs a qualitatively very different model 01:07:11.700 --> 01:07:15.030 align:middle line:84% from Deal-Grove because you need to specify something 01:07:15.030 --> 01:07:16.740 align:middle line:84% that the Deal-Grove doesn't even treat. 01:07:16.740 --> 01:07:19.230 align:middle line:84% Deal-Grove assumed you had a perfectly pure silicon 01:07:19.230 --> 01:07:22.620 align:middle line:84% wafer that you were oxidizing with just silicon atoms in it. 01:07:22.620 --> 01:07:25.350 align:middle line:84% Once you start implanting nitrogen or some other species, 01:07:25.350 --> 01:07:27.150 align:middle line:90% all bets are off. 01:07:27.150 --> 01:07:30.630 align:middle line:84% You're not going to widely find simulators that 01:07:30.630 --> 01:07:32.040 align:middle line:90% can support this type of model. 01:07:32.040 --> 01:07:33.540 align:middle line:84% If you want to do this, you're going 01:07:33.540 --> 01:07:36.520 align:middle line:84% to have to model it yourself by taking data from the literature 01:07:36.520 --> 01:07:40.150 align:middle line:84% and fitting it or maybe doing your own experiments. 01:07:40.150 --> 01:07:44.570 align:middle line:90% 01:07:44.570 --> 01:07:48.032 align:middle line:90% So let's look at slide 35. 01:07:48.032 --> 01:07:49.990 align:middle line:84% There's another parameter we need to vary here. 01:07:49.990 --> 01:07:51.160 align:middle line:90% You can imagine varying. 01:07:51.160 --> 01:07:52.840 align:middle line:84% And this is a relatively simple one. 01:07:52.840 --> 01:07:54.940 align:middle line:84% And that's the orientation of the crystal, 01:07:54.940 --> 01:07:58.510 align:middle line:84% the face of the crystal that you're oxidizing. 01:07:58.510 --> 01:08:01.480 align:middle line:84% We know that the B parameter, which depends on the diffusion 01:08:01.480 --> 01:08:04.090 align:middle line:84% through the oxide, is independent of orientation. 01:08:04.090 --> 01:08:07.630 align:middle line:84% B over A, which is the reaction rate at the interface, 01:08:07.630 --> 01:08:09.880 align:middle line:84% of course, it's going to depend on the number of atoms 01:08:09.880 --> 01:08:12.820 align:middle line:84% available per square centimeter to react. 01:08:12.820 --> 01:08:14.373 align:middle line:84% So it does depend on orientation. 01:08:14.373 --> 01:08:15.790 align:middle line:84% So and these are the dependencies, 01:08:15.790 --> 01:08:18.460 align:middle line:84% just to give you rough numbers or relationship. 01:08:18.460 --> 01:08:19.870 align:middle line:90% 111 is the fastest. 01:08:19.870 --> 01:08:22.359 align:middle line:84% It has the greatest number of atoms per square centimeter. 01:08:22.359 --> 01:08:23.950 align:middle line:90% 110 is second. 01:08:23.950 --> 01:08:27.130 align:middle line:90% And the slowest is 100. 01:08:27.130 --> 01:08:29.770 align:middle line:84% And in fact, these are the relationships. 01:08:29.770 --> 01:08:35.170 align:middle line:84% If we take the 111 rates and we divide them by 1.68, 01:08:35.170 --> 01:08:37.029 align:middle line:90% we get the 100 rates. 01:08:37.029 --> 01:08:40.700 align:middle line:84% And the relationship between 110 is in between. 01:08:40.700 --> 01:08:43.689 align:middle line:84% And again, it's related to the silicone atomic density, 01:08:43.689 --> 01:08:47.000 align:middle line:84% the number of atoms per square centimeter that are available. 01:08:47.000 --> 01:08:48.729 align:middle line:84% And you can believe that because in order 01:08:48.729 --> 01:08:52.060 align:middle line:84% to have the surface reaction take place, 01:08:52.060 --> 01:08:54.640 align:middle line:84% silicone bonds have to be broken. 01:08:54.640 --> 01:08:56.229 align:middle line:84% So and the number of atoms available 01:08:56.229 --> 01:08:58.390 align:middle line:84% is going to be important in that case. 01:08:58.390 --> 01:09:01.640 align:middle line:90% 01:09:01.640 --> 01:09:05.920 align:middle line:84% Oh, slide 36 is an interesting example 01:09:05.920 --> 01:09:09.069 align:middle line:84% of how even, you might say, well, I only use 100 wafers. 01:09:09.069 --> 01:09:11.319 align:middle line:84% What do I care about oxidation on 110? 01:09:11.319 --> 01:09:15.460 align:middle line:84% Well, you will care because you often etch a trench 01:09:15.460 --> 01:09:17.350 align:middle line:84% and then need to oxidize the trench. 01:09:17.350 --> 01:09:20.319 align:middle line:84% And of course, the trench has different orientations 01:09:20.319 --> 01:09:22.300 align:middle line:90% of its walls. 01:09:22.300 --> 01:09:25.390 align:middle line:84% So this is a Supreme 4 simulation 01:09:25.390 --> 01:09:28.330 align:middle line:84% of a trench that was etched into a 100 wafer. 01:09:28.330 --> 01:09:29.590 align:middle line:90% So 100 means what? 01:09:29.590 --> 01:09:31.960 align:middle line:84% It means the surface of this wafer, 01:09:31.960 --> 01:09:35.290 align:middle line:84% this plane, at the very surface, is 100. 01:09:35.290 --> 01:09:37.819 align:middle line:84% The 100 direction or 01 is pointing up. 01:09:37.819 --> 01:09:41.800 align:middle line:84% But if once I start etching into it, the planes that I expose 01:09:41.800 --> 01:09:43.540 align:middle line:84% will be different orientations, depending 01:09:43.540 --> 01:09:48.020 align:middle line:84% on how I design my trench, if I etch into the crystal. 01:09:48.020 --> 01:09:53.050 align:middle line:84% So for example, I etch a trench here down into the crystal. 01:09:53.050 --> 01:09:56.650 align:middle line:84% The bottom face is 100 because the bottom face 01:09:56.650 --> 01:10:00.070 align:middle line:84% is the same as the top face, the face of the wafer. 01:10:00.070 --> 01:10:03.082 align:middle line:84% But the sidewall, this face right here, 01:10:03.082 --> 01:10:04.790 align:middle line:84% the sidewall that I've exposed, depending 01:10:04.790 --> 01:10:09.200 align:middle line:84% on how I oriented this trench, which is assumed to be square 01:10:09.200 --> 01:10:13.130 align:middle line:84% or rectangular, the sidewall face could be a 110, 01:10:13.130 --> 01:10:15.980 align:middle line:84% depending on how I orient it with respect to the flat. 01:10:15.980 --> 01:10:20.060 align:middle line:84% So you can immediately expect a different oxidation rate 01:10:20.060 --> 01:10:24.720 align:middle line:84% on this face right here from the oxidation on the bottom. 01:10:24.720 --> 01:10:26.540 align:middle line:84% And this is an example of a simulation 01:10:26.540 --> 01:10:31.010 align:middle line:84% that was done 30 minutes in 900 degrees C in water. 01:10:31.010 --> 01:10:34.280 align:middle line:84% And you see the thicker oxide that grew on the sidewall. 01:10:34.280 --> 01:10:36.230 align:middle line:84% That's pretty much-- in this bulk region 01:10:36.230 --> 01:10:37.850 align:middle line:84% of the sidewall-- that's entirely due to the fact 01:10:37.850 --> 01:10:39.330 align:middle line:84% that it's a different orientation. 01:10:39.330 --> 01:10:41.570 align:middle line:84% So this simulator took that into account. 01:10:41.570 --> 01:10:44.840 align:middle line:84% It's a little bit thicker here than it is on the bottom. 01:10:44.840 --> 01:10:48.140 align:middle line:84% What is this, this weird looking corner effect? 01:10:48.140 --> 01:10:50.360 align:middle line:90% That's not orientation so much. 01:10:50.360 --> 01:10:52.442 align:middle line:84% This actually shows a two dimensional effect 01:10:52.442 --> 01:10:54.650 align:middle line:84% we'll talk about next time, which is a stress effect. 01:10:54.650 --> 01:10:58.515 align:middle line:84% When you're oxidizing a corner, again, the oxide has to expand. 01:10:58.515 --> 01:11:00.890 align:middle line:84% In a corner, it's a little bit hard to do some expansion. 01:11:00.890 --> 01:11:02.682 align:middle line:84% We're just going to turn out, the oxidation 01:11:02.682 --> 01:11:04.340 align:middle line:84% rate in these sharp corners, it's 01:11:04.340 --> 01:11:06.360 align:middle line:84% going to end up being slower due to stress. 01:11:06.360 --> 01:11:08.600 align:middle line:84% So that was taken account into the simulation. 01:11:08.600 --> 01:11:11.190 align:middle line:90% 01:11:11.190 --> 01:11:14.450 align:middle line:84% So let me just summarize what we have from today. 01:11:14.450 --> 01:11:17.270 align:middle line:84% The basic growth mechanism is transport 01:11:17.270 --> 01:11:20.330 align:middle line:84% through the oxide by diffusion and then chemical reaction 01:11:20.330 --> 01:11:22.970 align:middle line:84% at the interface as opposed to the silicon 01:11:22.970 --> 01:11:26.270 align:middle line:84% doesn't come out of the lattice and go up to the surface. 01:11:26.270 --> 01:11:29.720 align:middle line:84% We generally have a linear/parabolic law 01:11:29.720 --> 01:11:31.472 align:middle line:90% when we have planar oxidation. 01:11:31.472 --> 01:11:32.930 align:middle line:84% Next time, we're going to see there 01:11:32.930 --> 01:11:35.150 align:middle line:84% are a lot of different cases where it's non planar 01:11:35.150 --> 01:11:39.110 align:middle line:84% and it's not just simple linear parabolic. 01:11:39.110 --> 01:11:42.110 align:middle line:84% The Deal-Grove model isn't completely 01:11:42.110 --> 01:11:43.850 align:middle line:84% accurate in the thin oxide regime. 01:11:43.850 --> 01:11:47.810 align:middle line:84% But it can be corrected by using Han and Helms or Riesman 01:11:47.810 --> 01:11:49.070 align:middle line:90% or you can use Massoud. 01:11:49.070 --> 01:11:52.550 align:middle line:84% And they all can be designed to converge to Deal-Grove for when 01:11:52.550 --> 01:11:55.220 align:middle line:84% you're at thinner and thicker oxides, 01:11:55.220 --> 01:11:57.470 align:middle line:90% say above 200 angstroms. 01:11:57.470 --> 01:11:59.420 align:middle line:84% And the growth rate varies with orientation. 01:11:59.420 --> 01:12:04.297 align:middle line:84% 111 is the fastest and 100 being the slowest. 01:12:04.297 --> 01:12:06.380 align:middle line:84% So that's mostly what I wanted to cover for today. 01:12:06.380 --> 01:12:08.690 align:middle line:84% I have a couple of things for you though. 01:12:08.690 --> 01:12:12.130 align:middle line:90% Your homework is going back. 01:12:12.130 --> 01:12:13.880 align:middle line:84% So you can come up and grab your homework. 01:12:13.880 --> 01:12:16.760 align:middle line:84% It's been graded, up here, homework number one. 01:12:16.760 --> 01:12:19.230 align:middle line:84% And the solutions are also up front. 01:12:19.230 --> 01:12:21.890 align:middle line:84% So if you can come on up and take 01:12:21.890 --> 01:12:24.830 align:middle line:84% the homework and the solutions for homework number one, 01:12:24.830 --> 01:12:25.350 align:middle line:90% that's good. 01:12:25.350 --> 01:12:26.570 align:middle line:84% If you weren't here last time, you 01:12:26.570 --> 01:12:27.987 align:middle line:84% didn't get to see the Intel wafer, 01:12:27.987 --> 01:12:30.230 align:middle line:84% I'm going to hand it back after today. 01:12:30.230 --> 01:12:32.720 align:middle line:84% So you're welcome to take a look at it. 01:12:32.720 --> 01:12:35.320 align:middle line:90% 01:12:35.320 --> 01:12:37.070 align:middle line:84% Oh, these are not in any particular order. 01:12:37.070 --> 01:12:40.130 align:middle line:90% 01:12:40.130 --> 01:12:47.420 align:middle line:90% STUDENT: [INAUDIBLE] 01:12:47.420 --> 01:12:48.350 align:middle line:90% JUDY HOYT: What? 01:12:48.350 --> 01:12:50.420 align:middle line:84% STUDENT: People extracted the strained silicon? 01:12:50.420 --> 01:12:51.860 align:middle line:90% JUDY HOYT: Yeah, people tried. 01:12:51.860 --> 01:12:53.150 align:middle line:90% Jeff tried. 01:12:53.150 --> 01:12:56.930 align:middle line:84% It seems to be pretty darn close, a change 01:12:56.930 --> 01:12:59.900 align:middle line:84% of 1% in the lattice constant because I really 01:12:59.900 --> 01:13:05.180 align:middle line:84% haven't changed the number of atoms per square centimeter. 01:13:05.180 --> 01:13:08.120 align:middle line:84% What does change is as soon as you hit the silicon germanium, 01:13:08.120 --> 01:13:09.410 align:middle line:90% oxidation rate goes way up. 01:13:09.410 --> 01:13:15.890 align:middle line:90% 01:13:15.890 --> 01:13:17.265 align:middle line:90% STUDENT: [INAUDIBLE] 01:13:17.265 --> 01:13:37.000 align:middle line:90%