WEBVTT 00:00:00.000 --> 00:00:03.420 align:middle line:90% JUDY HOYT: This is-- 00:00:03.420 --> 00:00:07.380 align:middle line:84% today's lecture is going to be the final lecture on chapter 7. 00:00:07.380 --> 00:00:09.660 align:middle line:84% It's not the final lecture on diffusion. 00:00:09.660 --> 00:00:13.050 align:middle line:84% We're going to continue talking about diffusion in chapter 8, 00:00:13.050 --> 00:00:15.550 align:middle line:84% once we've talked about ion implantation. 00:00:15.550 --> 00:00:18.480 align:middle line:84% But this will finish up chapter 7. 00:00:18.480 --> 00:00:20.730 align:middle line:84% So hopefully you're finishing reading that chapter 00:00:20.730 --> 00:00:22.740 align:middle line:90% at this point. 00:00:22.740 --> 00:00:25.470 align:middle line:84% Diffusion is probably the biggest topic 00:00:25.470 --> 00:00:29.130 align:middle line:84% we cover in this course in terms of the overall complexity 00:00:29.130 --> 00:00:31.697 align:middle line:90% and the depth of the modeling. 00:00:31.697 --> 00:00:33.780 align:middle line:84% So there's a lot of points I want to cover or just 00:00:33.780 --> 00:00:34.988 align:middle line:90% try to review from last time. 00:00:34.988 --> 00:00:37.680 align:middle line:84% The last lecture was pretty dense. 00:00:37.680 --> 00:00:40.340 align:middle line:84% There was a lot of material to cover. 00:00:40.340 --> 00:00:43.480 align:middle line:84% So what we talked about last time 00:00:43.480 --> 00:00:48.400 align:middle line:84% was that there are these so-called Fermi-level effects, 00:00:48.400 --> 00:00:51.880 align:middle line:84% or high-concentration effects, and electric field effects, 00:00:51.880 --> 00:00:54.040 align:middle line:84% and that both of those become important 00:00:54.040 --> 00:00:56.705 align:middle line:84% when the carrier concentration-- either N over P, 00:00:56.705 --> 00:00:58.330 align:middle line:84% depending on how the material's doped-- 00:00:58.330 --> 00:01:00.640 align:middle line:84% when either of those carrier concentrations 00:01:00.640 --> 00:01:04.930 align:middle line:84% is greater than NI, N sub I, at the diffusion temperature, 00:01:04.930 --> 00:01:08.710 align:middle line:84% then these high concentration effects become important. 00:01:08.710 --> 00:01:11.830 align:middle line:84% The basic idea of the model that we have 00:01:11.830 --> 00:01:16.210 align:middle line:84% is that the Fermi level, as it moves up and down in the bandgap 00:01:16.210 --> 00:01:19.330 align:middle line:84% in response to the doping level, depending on how you have it 00:01:19.330 --> 00:01:22.570 align:middle line:84% doped, as you're doped more heavily, 00:01:22.570 --> 00:01:26.290 align:middle line:84% it tends to increase the point defect concentration 00:01:26.290 --> 00:01:27.995 align:middle line:90% as the doping increases. 00:01:27.995 --> 00:01:30.370 align:middle line:84% We know we've seen that in one of your homework problems. 00:01:30.370 --> 00:01:31.660 align:middle line:90% You had to calculate that. 00:01:31.660 --> 00:01:34.270 align:middle line:84% And the increase in point defect concentration 00:01:34.270 --> 00:01:37.060 align:middle line:84% then increases the diffusivity of a dopant. 00:01:37.060 --> 00:01:41.810 align:middle line:84% And this leads to, or can lead to, generally more box-like 00:01:41.810 --> 00:01:45.650 align:middle line:84% shape profiles because as the dopant diffuses, as you get out 00:01:45.650 --> 00:01:49.460 align:middle line:84% to the edge of that profile, the concentration is dropping. 00:01:49.460 --> 00:01:51.710 align:middle line:84% And as the concentration of the doping is dropping, 00:01:51.710 --> 00:01:53.240 align:middle line:90% the Fermi level is moving. 00:01:53.240 --> 00:01:55.890 align:middle line:84% The total point defect concentration is going down. 00:01:55.890 --> 00:01:58.790 align:middle line:84% So you tend to get these very steep fall-offs 00:01:58.790 --> 00:02:01.850 align:middle line:90% in your profiles. 00:02:01.850 --> 00:02:03.790 align:middle line:84% So in addition to this, this leads 00:02:03.790 --> 00:02:07.420 align:middle line:84% to this concentration-dependent diffusion. 00:02:07.420 --> 00:02:10.970 align:middle line:84% We talked about effects like oxidation-enhanced diffusion, 00:02:10.970 --> 00:02:13.780 align:middle line:84% which is abbreviated OED, oxidation retarded diffusion, 00:02:13.780 --> 00:02:18.070 align:middle line:84% ORD, and the growth or shrinkage of stacking faults. 00:02:18.070 --> 00:02:22.420 align:middle line:84% And these phenomenon can be explained by 00:02:22.420 --> 00:02:25.000 align:middle line:84% not by looking at Fick's law per se or whatever, 00:02:25.000 --> 00:02:28.630 align:middle line:84% but by looking at atomic scale diffusion models. 00:02:28.630 --> 00:02:31.160 align:middle line:90% 00:02:31.160 --> 00:02:34.730 align:middle line:84% And in fact, what we talked about last time is 00:02:34.730 --> 00:02:42.280 align:middle line:84% that based on the impact on stacking faults, that oxidation, 00:02:42.280 --> 00:02:45.100 align:middle line:84% people believe, injects excess silicon interstitials 00:02:45.100 --> 00:02:49.810 align:middle line:84% into the bulk, while thermal nitridation, which, again, you 00:02:49.810 --> 00:02:51.490 align:middle line:84% may not be as familiar with nitridation, 00:02:51.490 --> 00:02:54.730 align:middle line:84% is basically the reaction of the silicon 00:02:54.730 --> 00:02:58.780 align:middle line:84% surface with a gas-like ammonia to create silicon nitride. 00:02:58.780 --> 00:03:03.880 align:middle line:84% That process is believed to inject vacancies into the bulk. 00:03:03.880 --> 00:03:06.460 align:middle line:84% And based on monitoring these processes, 00:03:06.460 --> 00:03:09.670 align:middle line:84% people believe that boron and phosphorus diffuse primarily 00:03:09.670 --> 00:03:10.510 align:middle line:90% with interstitials. 00:03:10.510 --> 00:03:14.740 align:middle line:84% So they have an F sub I number in the fraction interstitial 00:03:14.740 --> 00:03:16.750 align:middle line:90% contribution to diffusion of 1. 00:03:16.750 --> 00:03:20.300 align:middle line:84% And antimony diffuses primarily with vacancies. 00:03:20.300 --> 00:03:25.690 align:middle line:84% So F sub I is pretty close to zero, maybe 0.02. 00:03:25.690 --> 00:03:28.360 align:middle line:84% So today I wanted to review these atomic scale mechanisms 00:03:28.360 --> 00:03:30.350 align:middle line:84% because we kind of breezed through them 00:03:30.350 --> 00:03:32.390 align:middle line:84% at the end of the last lecture pretty fast. 00:03:32.390 --> 00:03:36.050 align:middle line:84% And then I want to go on to some new material 00:03:36.050 --> 00:03:39.980 align:middle line:84% and just give you a brief example, or a brief look at one 00:03:39.980 --> 00:03:43.880 align:middle line:84% example, of how the point defect gradient-- 00:03:43.880 --> 00:03:46.220 align:middle line:84% we talked about this last time-- that not only does 00:03:46.220 --> 00:03:49.910 align:middle line:84% the dopant gradient, D arsenic by DX, 00:03:49.910 --> 00:03:52.200 align:middle line:84% but the point defect gradient, for instance, 00:03:52.200 --> 00:03:53.870 align:middle line:84% the interstitial gradient, can actually 00:03:53.870 --> 00:03:56.450 align:middle line:84% drive diffusion in a way that actually 00:03:56.450 --> 00:03:57.930 align:middle line:90% looks like uphill diffusion. 00:03:57.930 --> 00:04:01.160 align:middle line:84% So it's kind of a nonFickian phenomenon. 00:04:01.160 --> 00:04:05.720 align:middle line:84% And this leads to a phenomenon in MOSFETs 00:04:05.720 --> 00:04:08.163 align:middle line:84% that's called the-- in CMOS [INAUDIBLE] what's 00:04:08.163 --> 00:04:09.830 align:middle line:84% called the reverse short-channel effect. 00:04:09.830 --> 00:04:11.090 align:middle line:90% And I'll just introduce that. 00:04:11.090 --> 00:04:13.700 align:middle line:84% We'll talk about it in subsequent lectures 00:04:13.700 --> 00:04:15.373 align:middle line:90% in more detail. 00:04:15.373 --> 00:04:17.290 align:middle line:84% And then the second half of the lecture, we're 00:04:17.290 --> 00:04:19.415 align:middle line:84% going to talk about profile measurement techniques. 00:04:19.415 --> 00:04:22.029 align:middle line:84% How do we measure all these complex profiles? 00:04:22.029 --> 00:04:24.560 align:middle line:90% What's the best way to do it? 00:04:24.560 --> 00:04:27.370 align:middle line:84% OK, so let's review a little bit on this atomic scale mechanism. 00:04:27.370 --> 00:04:29.120 align:middle line:84% And what I would encourage you in thinking 00:04:29.120 --> 00:04:30.710 align:middle line:84% about the atomic scale mechanisms, 00:04:30.710 --> 00:04:36.440 align:middle line:84% rather than just looking at this particular, very static lattice 00:04:36.440 --> 00:04:39.532 align:middle line:84% and imagining how atoms might move, 00:04:39.532 --> 00:04:41.240 align:middle line:84% maybe you sit down with a piece of paper, 00:04:41.240 --> 00:04:44.660 align:middle line:84% start out and draw yourself a simple two-dimensional lattice. 00:04:44.660 --> 00:04:47.310 align:middle line:84% Draw silicon atoms everywhere except one point, 00:04:47.310 --> 00:04:48.620 align:middle line:90% which you call your vacancy. 00:04:48.620 --> 00:04:52.200 align:middle line:84% Draw a blue atom, or a pink or red or whatever, 00:04:52.200 --> 00:04:54.492 align:middle line:84% which you call your arsenic doping, 00:04:54.492 --> 00:04:55.700 align:middle line:90% or whatever it happens to be. 00:04:55.700 --> 00:04:57.890 align:middle line:84% And draw a couple of time steps for yourself. 00:04:57.890 --> 00:04:59.660 align:middle line:84% And see if you can figure out how 00:04:59.660 --> 00:05:03.110 align:middle line:84% this arsenic atom, this dopant atom, A, and the vacancy 00:05:03.110 --> 00:05:06.590 align:middle line:84% together, by staying in close proximity to each other, 00:05:06.590 --> 00:05:08.528 align:middle line:90% can move throughout the lattice. 00:05:08.528 --> 00:05:10.070 align:middle line:84% Give yourself a couple of time shots. 00:05:10.070 --> 00:05:12.110 align:middle line:84% And I think that will help understand 00:05:12.110 --> 00:05:16.220 align:middle line:90% how these things move together. 00:05:16.220 --> 00:05:20.150 align:middle line:84% So in this vacancy-assisted model or mechanism, 00:05:20.150 --> 00:05:23.360 align:middle line:84% what we do is we say A, where is A dopant-- it could be boron, 00:05:23.360 --> 00:05:25.580 align:middle line:84% phosphorus, arsenic, antimony-- we 00:05:25.580 --> 00:05:29.810 align:middle line:84% combine that with a vacancy, which is pictured here, 00:05:29.810 --> 00:05:31.160 align:middle line:90% an absence of a silicon atom. 00:05:31.160 --> 00:05:33.538 align:middle line:90% And it forms a pair, AV. 00:05:33.538 --> 00:05:35.330 align:middle line:84% OK, so you say, well, that's fairly simple. 00:05:35.330 --> 00:05:37.700 align:middle line:90% What's unique about this? 00:05:37.700 --> 00:05:40.640 align:middle line:84% Well, here A is a substitutional dopant atom. 00:05:40.640 --> 00:05:44.160 align:middle line:90% This pair AV is mobile. 00:05:44.160 --> 00:05:46.990 align:middle line:84% The substitutional dopant atom A is immobile. 00:05:46.990 --> 00:05:50.270 align:middle line:84% So what we're saying is that dopants in silicon do not move. 00:05:50.270 --> 00:05:51.230 align:middle line:90% They do not diffuse. 00:05:51.230 --> 00:05:53.170 align:middle line:84% This is the assumption, unless they 00:05:53.170 --> 00:05:56.080 align:middle line:84% are paired with either a vacancy or interstitial. 00:05:56.080 --> 00:05:57.550 align:middle line:84% But if they're just in the lattice 00:05:57.550 --> 00:06:00.050 align:middle line:84% and there were no vacancies around, no interstitials around, 00:06:00.050 --> 00:06:01.210 align:middle line:90% the dopant won't diffuse. 00:06:01.210 --> 00:06:03.830 align:middle line:84% So this is a hypothesis that we're making. 00:06:03.830 --> 00:06:08.380 align:middle line:84% And we use it to basically model all the diffusion 00:06:08.380 --> 00:06:09.790 align:middle line:90% of dopants in silicon. 00:06:09.790 --> 00:06:12.370 align:middle line:84% So here's the example of being paired with a vacancy. 00:06:12.370 --> 00:06:15.790 align:middle line:84% Obviously the dopant here could hop into this vacant site. 00:06:15.790 --> 00:06:18.340 align:middle line:84% The vacancy can move up here where the dopant was. 00:06:18.340 --> 00:06:19.340 align:middle line:90% Now what happens? 00:06:19.340 --> 00:06:21.370 align:middle line:84% Well, the dopant can stay put for a moment. 00:06:21.370 --> 00:06:23.890 align:middle line:84% The vacancy can move over here to this lattice site. 00:06:23.890 --> 00:06:26.200 align:middle line:84% And a silicon atom can move there. 00:06:26.200 --> 00:06:27.640 align:middle line:90% The vacancy can continue. 00:06:27.640 --> 00:06:28.680 align:middle line:90% It can move right here. 00:06:28.680 --> 00:06:30.430 align:middle line:84% And this silicon atom would move up there. 00:06:30.430 --> 00:06:32.050 align:middle line:84% Now I have the vacancy at this spot 00:06:32.050 --> 00:06:34.960 align:middle line:84% down here at the bottom and the dopant atom next to it. 00:06:34.960 --> 00:06:36.790 align:middle line:84% Well, now they can exchange places. 00:06:36.790 --> 00:06:38.510 align:middle line:84% And the dopant atom has moved here. 00:06:38.510 --> 00:06:40.780 align:middle line:84% So it moved from that point to that point. 00:06:40.780 --> 00:06:44.420 align:middle line:84% And how it got there was just by a couple of steps of the vacancy 00:06:44.420 --> 00:06:47.528 align:middle line:84% hanging around nearby as a pair, essentially. 00:06:47.528 --> 00:06:49.070 align:middle line:84% And that's how the dopant atom moved. 00:06:49.070 --> 00:06:51.230 align:middle line:84% Without that vacancy, it couldn't have. 00:06:51.230 --> 00:06:53.900 align:middle line:84% Similarly, there are interstitial or 00:06:53.900 --> 00:06:56.990 align:middle line:84% interstitial-assisted mechanisms. 00:06:56.990 --> 00:06:59.630 align:middle line:84% And we write this as a chemical equation. 00:06:59.630 --> 00:07:04.070 align:middle line:84% Substitutional atom A, dopant plus silicon interstitial 00:07:04.070 --> 00:07:06.230 align:middle line:90% forms an AI pair. 00:07:06.230 --> 00:07:09.870 align:middle line:84% And it's only this AI pair that can move. 00:07:09.870 --> 00:07:10.980 align:middle line:90% And this is an example. 00:07:10.980 --> 00:07:12.480 align:middle line:84% There are a couple of examples here. 00:07:12.480 --> 00:07:13.980 align:middle line:84% One is called the kick-out mechanism 00:07:13.980 --> 00:07:16.040 align:middle line:84% where you have a pure interstitial, a silicon 00:07:16.040 --> 00:07:18.350 align:middle line:84% atom that's actually in the interstitial spaces. 00:07:18.350 --> 00:07:20.300 align:middle line:84% It's an extra atom in the lattice. 00:07:20.300 --> 00:07:24.920 align:middle line:84% And it can come along and it can kick out that dopant atom. 00:07:24.920 --> 00:07:26.870 align:middle line:90% And then they exist as a pair. 00:07:26.870 --> 00:07:28.950 align:middle line:84% And then the dopant can kick out a silicon atom. 00:07:28.950 --> 00:07:30.580 align:middle line:84% And so they kind of move along, you 00:07:30.580 --> 00:07:33.350 align:middle line:84% can imagine this pair, always one of them-- 00:07:33.350 --> 00:07:37.190 align:middle line:84% either the dopant or the silicon atom-- being off-site, 00:07:37.190 --> 00:07:38.540 align:middle line:90% so to speak. 00:07:38.540 --> 00:07:39.840 align:middle line:90% That's one mechanism. 00:07:39.840 --> 00:07:42.145 align:middle line:84% The other is an interstitial C mechanism. 00:07:42.145 --> 00:07:44.270 align:middle line:84% It's a little bit-- the distinction is a little bit 00:07:44.270 --> 00:07:44.780 align:middle line:90% different. 00:07:44.780 --> 00:07:47.180 align:middle line:84% The interstitial mechanism is this atom that's 00:07:47.180 --> 00:07:49.070 align:middle line:84% here in the interstitial space is 00:07:49.070 --> 00:07:51.980 align:middle line:84% presumed to be not bonded, not covalently bonded in any way. 00:07:51.980 --> 00:07:54.410 align:middle line:84% In the interstitial C mechanism, the idea 00:07:54.410 --> 00:07:57.050 align:middle line:84% is that a dopant and a silicon atom 00:07:57.050 --> 00:07:59.930 align:middle line:84% are kind of both bonded and both sharing partial bonds. 00:07:59.930 --> 00:08:02.730 align:middle line:84% They're sharing a substitutional site, if you want. 00:08:02.730 --> 00:08:04.730 align:middle line:84% There's an extra atom there because there's only 00:08:04.730 --> 00:08:06.897 align:middle line:84% supposed to be one atom at that site in the lattice. 00:08:06.897 --> 00:08:07.820 align:middle line:90% There's two of them. 00:08:07.820 --> 00:08:09.110 align:middle line:84% One of them happens to be silicon. 00:08:09.110 --> 00:08:10.235 align:middle line:90% One happens to be a dopant. 00:08:10.235 --> 00:08:12.470 align:middle line:90% And they can go along sharing. 00:08:12.470 --> 00:08:14.210 align:middle line:84% This can share, and then the dopant atom 00:08:14.210 --> 00:08:17.480 align:middle line:84% can then share with its neighbor and could diffuse perhaps 00:08:17.480 --> 00:08:18.750 align:middle line:90% along bond directions. 00:08:18.750 --> 00:08:21.530 align:middle line:84% So this is an interstitial or interstitial C assisted 00:08:21.530 --> 00:08:22.100 align:middle line:90% mechanism. 00:08:22.100 --> 00:08:24.770 align:middle line:84% Again, unless it's paired with one of the point defects, 00:08:24.770 --> 00:08:28.790 align:middle line:84% we assume that a substitutional dopant atom otherwise cannot 00:08:28.790 --> 00:08:31.280 align:middle line:90% move. 00:08:31.280 --> 00:08:31.780 align:middle line:90% OK. 00:08:31.780 --> 00:08:34.809 align:middle line:84% So last time we also talked about this picture. 00:08:34.809 --> 00:08:37.330 align:middle line:84% I've shown it several times now, but hopefully you 00:08:37.330 --> 00:08:39.640 align:middle line:84% start to become comfortable with it. 00:08:39.640 --> 00:08:42.159 align:middle line:84% What this exemplifies is that how 00:08:42.159 --> 00:08:45.550 align:middle line:84% we use a process going on at the surface in this field 00:08:45.550 --> 00:08:47.680 align:middle line:84% to probe the atomic scale mechanisms. 00:08:47.680 --> 00:08:50.170 align:middle line:84% The problem is nobody can really see interstitials. 00:08:50.170 --> 00:08:51.320 align:middle line:90% They diffuse too fast. 00:08:51.320 --> 00:08:53.920 align:middle line:84% There's no real way of looking at them with a microscope 00:08:53.920 --> 00:08:54.880 align:middle line:90% or something like that. 00:08:54.880 --> 00:08:55.880 align:middle line:90% That's a problem. 00:08:55.880 --> 00:09:00.250 align:middle line:84% So what we do more often is subject the surface 00:09:00.250 --> 00:09:03.010 align:middle line:84% to some kind of a process that we feel either injects 00:09:03.010 --> 00:09:04.810 align:middle line:84% interstitials or injects vacancies. 00:09:04.810 --> 00:09:07.060 align:middle line:84% And then we see what happens somewhere 00:09:07.060 --> 00:09:11.327 align:middle line:84% at a distance in the crystal to infer, or to probe, 00:09:11.327 --> 00:09:12.410 align:middle line:90% what we think is going on. 00:09:12.410 --> 00:09:13.970 align:middle line:90% Admittedly, it's indirect. 00:09:13.970 --> 00:09:16.670 align:middle line:84% But if you build up enough evidence, 00:09:16.670 --> 00:09:18.560 align:middle line:84% people believe they can make a case that this 00:09:18.560 --> 00:09:20.430 align:middle line:90% is what's probably going on. 00:09:20.430 --> 00:09:22.460 align:middle line:84% So there are two service processes 00:09:22.460 --> 00:09:24.110 align:middle line:90% that are very commonly used. 00:09:24.110 --> 00:09:26.330 align:middle line:90% First one is oxidation. 00:09:26.330 --> 00:09:27.860 align:middle line:90% And it's usually done locally. 00:09:27.860 --> 00:09:29.930 align:middle line:84% In order to do an OED experiment, 00:09:29.930 --> 00:09:32.330 align:middle line:84% you typically don't put one wafer in a furnace 00:09:32.330 --> 00:09:34.850 align:middle line:84% and oxidize it and put a second wafer in a furnace 00:09:34.850 --> 00:09:38.060 align:middle line:84% and have it under inert because first of all, the furnace 00:09:38.060 --> 00:09:40.610 align:middle line:84% may not be the exact same temperature every run. 00:09:40.610 --> 00:09:41.967 align:middle line:90% We know they're not perfect. 00:09:41.967 --> 00:09:43.550 align:middle line:84% Temperature may be slightly different. 00:09:43.550 --> 00:09:45.175 align:middle line:84% That'll screw up your whole experiment. 00:09:45.175 --> 00:09:47.480 align:middle line:84% So typically, instead you start with a single wafer 00:09:47.480 --> 00:09:49.940 align:middle line:84% to do an OED experiment, and you coat part 00:09:49.940 --> 00:09:51.920 align:middle line:84% of the wafer-- maybe one dye area 00:09:51.920 --> 00:09:53.810 align:middle line:90% or one small area of the chip. 00:09:53.810 --> 00:09:58.700 align:middle line:84% You coat it with silicon nitride so it won't oxidize, 00:09:58.700 --> 00:10:00.560 align:middle line:84% which is a good barrier to oxidation. 00:10:00.560 --> 00:10:04.160 align:middle line:84% And you have down here a buried layer, some distance-- 00:10:04.160 --> 00:10:06.050 align:middle line:90% maybe half micron or so. 00:10:06.050 --> 00:10:07.730 align:middle line:90% Could be below the surface. 00:10:07.730 --> 00:10:10.237 align:middle line:84% A marker layer of some dopant that's going to diffuse. 00:10:10.237 --> 00:10:12.570 align:middle line:84% And you're going to measure the extent that it diffuses. 00:10:12.570 --> 00:10:15.600 align:middle line:84% So the dark green here is meant to represent the dopant 00:10:15.600 --> 00:10:17.850 align:middle line:84% when it starts out at the beginning of the oxidation. 00:10:17.850 --> 00:10:21.150 align:middle line:84% The light green is the edge or the junction 00:10:21.150 --> 00:10:23.800 align:middle line:84% as it appears after some time of oxidation. 00:10:23.800 --> 00:10:25.800 align:middle line:84% And you can see underneath the region 00:10:25.800 --> 00:10:28.050 align:middle line:84% where you were doing locals, where you were locally 00:10:28.050 --> 00:10:31.830 align:middle line:84% oxidizing the surface, you get a large spread of the boron layer. 00:10:31.830 --> 00:10:34.440 align:middle line:84% And this light green layer is very wide. 00:10:34.440 --> 00:10:37.410 align:middle line:84% Underneath the inert surface-- this is called inert 00:10:37.410 --> 00:10:39.840 align:middle line:84% because there is no oxidation taking place-- 00:10:39.840 --> 00:10:42.280 align:middle line:84% the boron doesn't diffuse nearly as much. 00:10:42.280 --> 00:10:43.620 align:middle line:90% So this is inert diffusion. 00:10:43.620 --> 00:10:46.200 align:middle line:84% This is OED, oxidation enhanced, diffusion. 00:10:46.200 --> 00:10:48.930 align:middle line:84% And also, schematically, in this cartoon, 00:10:48.930 --> 00:10:51.450 align:middle line:84% underneath the area where you're oxidizing, 00:10:51.450 --> 00:10:53.430 align:middle line:84% the stacking faults, these defects, 00:10:53.430 --> 00:10:56.100 align:middle line:84% are growing because they're adding silicon interstitials 00:10:56.100 --> 00:10:57.750 align:middle line:90% to the ends of these defects. 00:10:57.750 --> 00:11:01.290 align:middle line:84% And here they're just staying put or maybe even shrinking, 00:11:01.290 --> 00:11:04.500 align:middle line:84% but they're certainly not growing. 00:11:04.500 --> 00:11:08.340 align:middle line:84% So the key point is that people see the enhancement 00:11:08.340 --> 00:11:11.040 align:middle line:84% of boron diffusion, the oxidation enhancement, 00:11:11.040 --> 00:11:14.520 align:middle line:84% under the same conditions that caused stacking faults to grow. 00:11:14.520 --> 00:11:17.370 align:middle line:84% And stacking fault growth is interpreted 00:11:17.370 --> 00:11:20.220 align:middle line:84% to be injection of interstitials because people from materials 00:11:20.220 --> 00:11:22.140 align:middle line:84% point of view believe that the way you make the stacking fault 00:11:22.140 --> 00:11:23.348 align:middle line:90% grow is to add interstitials. 00:11:23.348 --> 00:11:25.763 align:middle line:84% So that's sort of the key piece of evidence that links. 00:11:25.763 --> 00:11:27.180 align:middle line:84% It's sort of like a criminal case. 00:11:27.180 --> 00:11:28.980 align:middle line:84% You really can never find the fingerprints, 00:11:28.980 --> 00:11:30.940 align:middle line:84% but you have some circumstantial evidence, 00:11:30.940 --> 00:11:35.380 align:middle line:84% and you put it all together, and you convict the person on trial. 00:11:35.380 --> 00:11:36.360 align:middle line:90% It's kind of like that. 00:11:36.360 --> 00:11:37.950 align:middle line:84% The circumstantial evidence-- and it's 00:11:37.950 --> 00:11:39.908 align:middle line:84% reasonably strong-- is that stacking faults are 00:11:39.908 --> 00:11:41.520 align:middle line:90% growing when you're oxidizing. 00:11:41.520 --> 00:11:43.320 align:middle line:90% Boron is also being enhanced. 00:11:43.320 --> 00:11:43.920 align:middle line:90% Aha. 00:11:43.920 --> 00:11:46.188 align:middle line:84% Well, interstitials cause stacking faults to grow. 00:11:46.188 --> 00:11:48.480 align:middle line:84% Therefore, the interstitials are probably causing boron 00:11:48.480 --> 00:11:49.920 align:middle line:90% to diffuse more rapidly. 00:11:49.920 --> 00:11:52.950 align:middle line:84% That's kind of how the logic goes. 00:11:52.950 --> 00:11:55.540 align:middle line:84% Similarly, people have found that nitridation-- 00:11:55.540 --> 00:11:58.500 align:middle line:84% so that's the reaction of silicon with ammonia-- 00:11:58.500 --> 00:12:00.030 align:middle line:90% has exactly the opposite effect. 00:12:00.030 --> 00:12:02.370 align:middle line:84% The boron actually diffuses slower. 00:12:02.370 --> 00:12:04.650 align:middle line:84% It's retarded, as we say in its diffusion. 00:12:04.650 --> 00:12:06.420 align:middle line:84% And the stacking faults actually shrink 00:12:06.420 --> 00:12:11.040 align:middle line:90% relative to inert anneals. 00:12:11.040 --> 00:12:15.060 align:middle line:84% So people feel that nitridation injects vacancies. 00:12:15.060 --> 00:12:19.590 align:middle line:84% And that's how those simple arguments go. 00:12:19.590 --> 00:12:22.653 align:middle line:84% So what we say when we want to get to an atomistic level 00:12:22.653 --> 00:12:24.320 align:middle line:84% modeling-- and this is the type of model 00:12:24.320 --> 00:12:28.010 align:middle line:84% that when you're modeling the diffusion in SUPREM, 00:12:28.010 --> 00:12:32.660 align:middle line:84% we say that the dopants diffuse with a fraction, F sub I. 00:12:32.660 --> 00:12:37.820 align:middle line:84% So F sub I goes from 0 to 1 of interstitial type mechanism. 00:12:37.820 --> 00:12:42.110 align:middle line:84% And a fraction F sub V, which is 1 minus FI, 00:12:42.110 --> 00:12:43.590 align:middle line:90% of vacancy type mechanism. 00:12:43.590 --> 00:12:48.500 align:middle line:84% So we break down its diffusion coefficient into separate terms. 00:12:48.500 --> 00:12:51.800 align:middle line:84% There's one term, which is proportional to F sub I 00:12:51.800 --> 00:12:54.770 align:middle line:90% times CI over CI star. 00:12:54.770 --> 00:12:56.850 align:middle line:84% So again, F sub I, it goes from 0 to 1. 00:12:56.850 --> 00:12:59.690 align:middle line:84% If you believe the dopant only diffuses with interstitials 00:12:59.690 --> 00:13:01.310 align:middle line:84% and vacancies are insignificant, you 00:13:01.310 --> 00:13:03.830 align:middle line:84% would make F sub I equal to 1, like the case of boron 00:13:03.830 --> 00:13:06.410 align:middle line:90% or phosphorus. 00:13:06.410 --> 00:13:08.240 align:middle line:84% And then this term becomes negligible. 00:13:08.240 --> 00:13:10.010 align:middle line:84% If you believe that it only diffuses 00:13:10.010 --> 00:13:13.160 align:middle line:84% with vacancies like antimony, you'd make F sub V close to 1. 00:13:13.160 --> 00:13:16.010 align:middle line:84% If you think it's both, well, then you 00:13:16.010 --> 00:13:17.600 align:middle line:90% apportion it accordingly. 00:13:17.600 --> 00:13:19.130 align:middle line:84% And how do you figure out F sub I 00:13:19.130 --> 00:13:20.570 align:middle line:90% and F sub V, those proportions? 00:13:20.570 --> 00:13:23.450 align:middle line:84% Well, you subject the dopant in the silicon 00:13:23.450 --> 00:13:26.930 align:middle line:84% to different circumstances of injecting vacancies or injecting 00:13:26.930 --> 00:13:30.230 align:middle line:84% interstitials and seeing how much the diffusivity goes up 00:13:30.230 --> 00:13:32.262 align:middle line:90% or down under those conditions. 00:13:32.262 --> 00:13:34.220 align:middle line:84% And that's what people have done over the years 00:13:34.220 --> 00:13:38.380 align:middle line:84% to try to nail down F sub I and F sub V. 00:13:38.380 --> 00:13:41.200 align:middle line:84% So the DA here is the effective diffusivity. 00:13:41.200 --> 00:13:43.480 align:middle line:84% Now, it's being measured under any condition, 00:13:43.480 --> 00:13:44.860 align:middle line:84% but particularly under conditions 00:13:44.860 --> 00:13:47.140 align:middle line:84% where the point defect populations are 00:13:47.140 --> 00:13:48.610 align:middle line:90% disturbed or perturbed. 00:13:48.610 --> 00:13:51.460 align:middle line:84% So this would be during oxidation or nitridation. 00:13:51.460 --> 00:13:52.397 align:middle line:90% DA star. 00:13:52.397 --> 00:13:53.230 align:middle line:90% What does that mean? 00:13:53.230 --> 00:13:56.170 align:middle line:84% That's the normal equilibrium diffusivity 00:13:56.170 --> 00:13:59.720 align:middle line:84% of the dopant, measured under inert conditions. 00:13:59.720 --> 00:14:01.878 align:middle line:84% So again, when we're talking about diffusion 00:14:01.878 --> 00:14:03.670 align:middle line:84% and we're talking about inert, what we mean 00:14:03.670 --> 00:14:06.370 align:middle line:90% is no oxidation, no nitridation. 00:14:06.370 --> 00:14:09.490 align:middle line:84% Inert means nothing that injects excess point 00:14:09.490 --> 00:14:13.670 align:middle line:90% defects into the bulk. 00:14:13.670 --> 00:14:17.840 align:middle line:84% So by using this equation, you can understand how to model OED. 00:14:17.840 --> 00:14:23.530 align:middle line:84% What happens in OED is this term, CI over CI star. 00:14:23.530 --> 00:14:28.078 align:middle line:84% The interstitial equilibrium-- the interstitial population 00:14:28.078 --> 00:14:29.620 align:middle line:84% relative to what it is in equilibrium 00:14:29.620 --> 00:14:31.840 align:middle line:84% goes up by some fraction, some amount. 00:14:31.840 --> 00:14:33.580 align:middle line:90% Could be five, ten times higher. 00:14:33.580 --> 00:14:38.170 align:middle line:84% That causes the diffusivity to be enhanced by 5 to 10 times. 00:14:38.170 --> 00:14:40.930 align:middle line:84% In addition, because of recombination-- interstitials 00:14:40.930 --> 00:14:43.960 align:middle line:84% and vacancies can recombine-- if you pump up the interstitials, 00:14:43.960 --> 00:14:45.380 align:middle line:90% the vacancy is going to go down. 00:14:45.380 --> 00:14:48.640 align:middle line:84% So this term can actually go down to a certain extent. 00:14:48.640 --> 00:14:50.230 align:middle line:84% And that's how the model accounts 00:14:50.230 --> 00:14:54.280 align:middle line:84% for OED or for nitridation retardant diffusion 00:14:54.280 --> 00:14:56.060 align:middle line:84% because nitrogen does just the opposite. 00:14:56.060 --> 00:14:59.890 align:middle line:84% It enhances the CV over CV star and suppresses this term. 00:14:59.890 --> 00:15:03.100 align:middle line:84% And depending on your dopant, your FI and your FV values, 00:15:03.100 --> 00:15:06.040 align:middle line:84% it will have more or less of an effect on diffusivity. 00:15:06.040 --> 00:15:11.440 align:middle line:84% And that gets modeled in the simulations. 00:15:11.440 --> 00:15:14.380 align:middle line:84% I actually pulled out of the literature some data just 00:15:14.380 --> 00:15:18.430 align:middle line:84% to show you some of the classic experiments that took place 00:15:18.430 --> 00:15:21.760 align:middle line:84% quite some time ago on people trying to determine 00:15:21.760 --> 00:15:23.350 align:middle line:90% F sub I and F sub V. 00:15:23.350 --> 00:15:25.720 align:middle line:84% And this is a paper by-- it's a review article. 00:15:25.720 --> 00:15:26.420 align:middle line:90% It's quite long. 00:15:26.420 --> 00:15:28.810 align:middle line:84% It's many pages by Fahey, Griffin, and Plummer. 00:15:28.810 --> 00:15:30.280 align:middle line:90% It's getting older. 00:15:30.280 --> 00:15:34.210 align:middle line:84% It was published back in 1989, but that 00:15:34.210 --> 00:15:36.550 align:middle line:84% was sort of at the height of people 00:15:36.550 --> 00:15:39.100 align:middle line:84% really coalescing all this data on these atomic scale 00:15:39.100 --> 00:15:40.130 align:middle line:90% mechanisms. 00:15:40.130 --> 00:15:42.100 align:middle line:84% So it's a good review article if you 00:15:42.100 --> 00:15:43.840 align:middle line:84% want to understand in more detail 00:15:43.840 --> 00:15:45.820 align:middle line:84% than is given in your text about this. 00:15:45.820 --> 00:15:48.320 align:middle line:84% Since that time, of course, there have been new discoveries, 00:15:48.320 --> 00:15:50.170 align:middle line:84% and we'll talk about those newer discoveries 00:15:50.170 --> 00:15:52.420 align:middle line:90% when we talk about TED. 00:15:52.420 --> 00:15:55.300 align:middle line:84% But what people did was-- this is particular data 00:15:55.300 --> 00:15:56.920 align:middle line:90% I took from Fahey's article. 00:15:56.920 --> 00:15:59.150 align:middle line:84% This is an experiment on nitridation. 00:15:59.150 --> 00:16:02.440 align:middle line:84% So you're flowing ammonia at very high temperatures. 00:16:02.440 --> 00:16:05.530 align:middle line:84% Ammonia doesn't react at as low temperatures 00:16:05.530 --> 00:16:07.340 align:middle line:90% as oxygen does with the surface. 00:16:07.340 --> 00:16:09.590 align:middle line:84% So you kind of have to go to pretty high temperatures. 00:16:09.590 --> 00:16:12.560 align:middle line:84% That's one disadvantage of nitridation. 00:16:12.560 --> 00:16:14.600 align:middle line:84% So you typically see nitrogen experiments-- 00:16:14.600 --> 00:16:19.740 align:middle line:84% 900, 1,000, 1,100-- in order to get reasonable injection. 00:16:19.740 --> 00:16:22.430 align:middle line:84% So under nitridation, 1,100 degrees c and there 00:16:22.430 --> 00:16:24.870 align:middle line:84% are three different dopants studied here-- phosphorus, 00:16:24.870 --> 00:16:26.790 align:middle line:90% arsenic, and antimony. 00:16:26.790 --> 00:16:29.960 align:middle line:84% And this axis here shows the time 00:16:29.960 --> 00:16:32.382 align:middle line:84% averaged because they do diffusion experiments 00:16:32.382 --> 00:16:33.590 align:middle line:90% for a certain amount of time. 00:16:33.590 --> 00:16:36.770 align:middle line:84% Here you could do it for half an hour or five hours, 10 hours, 00:16:36.770 --> 00:16:37.550 align:middle line:90% 20 hours. 00:16:37.550 --> 00:16:40.400 align:middle line:84% And you take the time averaged enhancement, 00:16:40.400 --> 00:16:43.250 align:middle line:84% or time averaged diffusivity, that you get averaged 00:16:43.250 --> 00:16:44.870 align:middle line:90% over that time interval. 00:16:44.870 --> 00:16:49.580 align:middle line:84% And you divide it by DA star, so the equilibrium, 00:16:49.580 --> 00:16:51.800 align:middle line:84% the diffusion coefficient measured right next to it 00:16:51.800 --> 00:16:55.860 align:middle line:84% in the stripe right next to it in the inert case. 00:16:55.860 --> 00:17:01.280 align:middle line:84% So if I go a couple slides back to slide 3, so the DA star 00:17:01.280 --> 00:17:03.740 align:middle line:84% they measured right over here by measuring 00:17:03.740 --> 00:17:05.849 align:middle line:84% the amount of diffusion underneath this region, 00:17:05.849 --> 00:17:07.760 align:middle line:84% the inert region, and the DA time 00:17:07.760 --> 00:17:10.730 align:middle line:84% average they measured over here under either oxidation 00:17:10.730 --> 00:17:11.390 align:middle line:90% or nitridation. 00:17:11.390 --> 00:17:13.819 align:middle line:84% This particular one is nitridation. 00:17:13.819 --> 00:17:17.390 align:middle line:84% And so if you look at these dopants-- 00:17:17.390 --> 00:17:18.890 align:middle line:90% look at antimony here. 00:17:18.890 --> 00:17:23.210 align:middle line:84% What you see pretty much at all times, DA over DA star 00:17:23.210 --> 00:17:25.609 align:middle line:90% is enhanced under nitridation. 00:17:25.609 --> 00:17:30.170 align:middle line:84% So antimony has a strong dependence on the excess vacancy 00:17:30.170 --> 00:17:31.420 align:middle line:90% population. 00:17:31.420 --> 00:17:36.620 align:middle line:84% And that's how people came to eventually give antimony an F 00:17:36.620 --> 00:17:39.140 align:middle line:90% sub V number that's close to 1. 00:17:39.140 --> 00:17:42.950 align:middle line:84% Arsenic has some effect, but not very much. 00:17:42.950 --> 00:17:44.810 align:middle line:84% What happens in the case of phosphorus? 00:17:44.810 --> 00:17:48.440 align:middle line:84% Actually, we do nitridation and we inject vacancies. 00:17:48.440 --> 00:17:51.920 align:middle line:84% Phosphorus diffusion over time is actually slowing down. 00:17:51.920 --> 00:17:54.280 align:middle line:90% It's actually retarded? 00:17:54.280 --> 00:17:55.190 align:middle line:90% Now, how can that be? 00:17:55.190 --> 00:17:57.730 align:middle line:84% Well, let's say phosphorus doesn't diffuse 00:17:57.730 --> 00:18:00.100 align:middle line:84% by vacancy mechanism, but it diffuses almost entirely 00:18:00.100 --> 00:18:01.180 align:middle line:90% by interstitials. 00:18:01.180 --> 00:18:03.850 align:middle line:84% As I inject vacancies you say, well, then it 00:18:03.850 --> 00:18:06.370 align:middle line:84% shouldn't have any effect, but it does via recombination. 00:18:06.370 --> 00:18:08.200 align:middle line:84% Excess vacancies recombine and they 00:18:08.200 --> 00:18:11.560 align:middle line:84% reduce the interstitial population 00:18:11.560 --> 00:18:14.140 align:middle line:84% lower than it would be in equilibrium. 00:18:14.140 --> 00:18:15.970 align:middle line:84% And that lower interstitial population 00:18:15.970 --> 00:18:17.450 align:middle line:84% lowers the diffusion coefficient. 00:18:17.450 --> 00:18:21.220 align:middle line:84% And so for phosphorus, this gives us a hint 00:18:21.220 --> 00:18:24.190 align:middle line:84% that F sub I is probably pretty close to one. 00:18:24.190 --> 00:18:27.250 align:middle line:84% Then you can do the analogous experiment 00:18:27.250 --> 00:18:29.890 align:middle line:84% with these same dopants with oxidation 00:18:29.890 --> 00:18:34.743 align:middle line:84% and see how it reacts during injection of interstitials. 00:18:34.743 --> 00:18:36.160 align:middle line:84% And between those two experiments, 00:18:36.160 --> 00:18:38.118 align:middle line:84% you try to get an estimate of what this F sub I 00:18:38.118 --> 00:18:40.610 align:middle line:90% and F sub V value could be. 00:18:40.610 --> 00:18:44.890 align:middle line:84% So those are some classic experiments people have done. 00:18:44.890 --> 00:18:48.940 align:middle line:84% And in fact, also on the next slide, slide 6, 00:18:48.940 --> 00:18:50.710 align:middle line:84% I've taken a table from that paper 00:18:50.710 --> 00:18:53.380 align:middle line:84% that just summarizes at that time what 00:18:53.380 --> 00:18:55.960 align:middle line:84% was known at the state of the art of the interface 00:18:55.960 --> 00:18:57.730 align:middle line:84% processes at the surface and how they 00:18:57.730 --> 00:19:00.580 align:middle line:84% affect the diffusion of different dopants 00:19:00.580 --> 00:19:02.500 align:middle line:84% under different conditions, and also 00:19:02.500 --> 00:19:05.730 align:middle line:90% how they affect stacking faults. 00:19:05.730 --> 00:19:07.120 align:middle line:90% There are three columns here. 00:19:07.120 --> 00:19:09.330 align:middle line:84% The first and the last, we've already talked about. 00:19:09.330 --> 00:19:12.120 align:middle line:84% Oxidation injects interstitials, causes 00:19:12.120 --> 00:19:15.060 align:middle line:84% vacancies, population to go down, stacking faults grow. 00:19:15.060 --> 00:19:18.720 align:middle line:84% The right column in nitridation, interstitial population 00:19:18.720 --> 00:19:23.040 align:middle line:84% goes down, vacancies go up, and stacking faults shrink. 00:19:23.040 --> 00:19:24.540 align:middle line:84% And for either one of these columns, 00:19:24.540 --> 00:19:27.390 align:middle line:84% you can see what happens, say, to phosphorus and boron 00:19:27.390 --> 00:19:28.830 align:middle line:90% diffusion. 00:19:28.830 --> 00:19:32.100 align:middle line:84% Now he's sort of broken this out to intrinsic diffusion 00:19:32.100 --> 00:19:34.920 align:middle line:84% when n is less than or equal to NI, 00:19:34.920 --> 00:19:36.510 align:middle line:90% or extrinsic when it's higher. 00:19:36.510 --> 00:19:39.450 align:middle line:84% In either case, when you do oxidation, 00:19:39.450 --> 00:19:42.930 align:middle line:84% phosphorus and boron are enhanced. 00:19:42.930 --> 00:19:46.593 align:middle line:84% Antimony is a little tricky, actually. 00:19:46.593 --> 00:19:48.510 align:middle line:84% There's a little bit of enhancement initially. 00:19:48.510 --> 00:19:51.480 align:middle line:84% But overall, the effect is believed to be retarded 00:19:51.480 --> 00:19:54.690 align:middle line:90% or slowed down. 00:19:54.690 --> 00:19:57.210 align:middle line:84% Arsenic is a tough one, because again, its F sub I 00:19:57.210 --> 00:19:59.820 align:middle line:84% value is going to be close to half, it turns out. 00:19:59.820 --> 00:20:03.370 align:middle line:84% It can be enhanced to a certain extent, 00:20:03.370 --> 00:20:05.560 align:middle line:84% depending on if it's intrinsic or extrinsic, 00:20:05.560 --> 00:20:07.270 align:middle line:84% it can be retarded, so it's a little bit 00:20:07.270 --> 00:20:10.570 align:middle line:90% tricky under oxidation. 00:20:10.570 --> 00:20:14.620 align:middle line:84% Arsenic also is enhanced under nitrogen. So it's tough. 00:20:14.620 --> 00:20:17.350 align:middle line:84% That's why we believe that F sub I and F sub 00:20:17.350 --> 00:20:19.142 align:middle line:84% v are somewhat equally weighted, depending 00:20:19.142 --> 00:20:20.350 align:middle line:90% on the amount of enhancement. 00:20:20.350 --> 00:20:21.517 align:middle line:90% It's enhanced in both cases. 00:20:21.517 --> 00:20:24.100 align:middle line:90% 00:20:24.100 --> 00:20:26.490 align:middle line:84% Boron's easier to understand because it's pure. 00:20:26.490 --> 00:20:28.840 align:middle line:84% It's enhanced under oxidation, but it's 00:20:28.840 --> 00:20:30.010 align:middle line:90% retarded under nitridation. 00:20:30.010 --> 00:20:33.610 align:middle line:84% So people have concluded based on a lot of data 00:20:33.610 --> 00:20:35.530 align:middle line:90% that the F sub I is close to 1. 00:20:35.530 --> 00:20:37.450 align:middle line:84% Now, there's one other column in the middle 00:20:37.450 --> 00:20:39.705 align:middle line:84% that we didn't talk about in this class, 00:20:39.705 --> 00:20:41.830 align:middle line:84% and I don't think it's mentioned much in your text. 00:20:41.830 --> 00:20:43.780 align:middle line:84% But Fahey talks about it in this article. 00:20:43.780 --> 00:20:45.650 align:middle line:90% It's called oxynitridation. 00:20:45.650 --> 00:20:47.740 align:middle line:90% It's a little bit trickier. 00:20:47.740 --> 00:20:49.690 align:middle line:84% Oxynitridation refers to the fact 00:20:49.690 --> 00:20:52.920 align:middle line:84% that if you start with a thin oxide-- 00:20:52.920 --> 00:20:54.870 align:middle line:84% so you have a thin oxide on the surface, 00:20:54.870 --> 00:20:56.190 align:middle line:90% and then you nitride that. 00:20:56.190 --> 00:21:00.450 align:middle line:84% You subject it to a high-temperature ammonia. 00:21:00.450 --> 00:21:03.600 align:middle line:84% You are doing something called [INAUDIBLE].. 00:21:03.600 --> 00:21:06.720 align:middle line:84% You're growing something called oxynitride. 00:21:06.720 --> 00:21:08.250 align:middle line:90% It's not pure nitride. 00:21:08.250 --> 00:21:10.450 align:middle line:90% It's not pure silicon dioxide. 00:21:10.450 --> 00:21:12.720 align:middle line:84% It's kind of got both silicon oxygen and nitrogen. 00:21:12.720 --> 00:21:14.550 align:middle line:90% And so people believe-- 00:21:14.550 --> 00:21:16.105 align:middle line:84% because stacking faults, grow people 00:21:16.105 --> 00:21:17.730 align:middle line:84% believe that interstitials are injected 00:21:17.730 --> 00:21:19.740 align:middle line:84% and that vacancy population goes down. 00:21:19.740 --> 00:21:23.310 align:middle line:84% But it's another marker, another process people use. 00:21:23.310 --> 00:21:27.520 align:middle line:84% It's a little bit harder, in some ways, to interpret. 00:21:27.520 --> 00:21:29.685 align:middle line:84% So that's a summary of some of their classic data. 00:21:29.685 --> 00:21:32.440 align:middle line:90% 00:21:32.440 --> 00:21:34.810 align:middle line:84% If I go on to slide 7, now I want 00:21:34.810 --> 00:21:38.290 align:middle line:84% to talk about what I think are some very clever experiments. 00:21:38.290 --> 00:21:40.120 align:middle line:84% What we've talked about so far when 00:21:40.120 --> 00:21:41.808 align:middle line:84% I've been showing this cartoon, I've 00:21:41.808 --> 00:21:43.600 align:middle line:84% been showing talking about one-dimensional. 00:21:43.600 --> 00:21:46.060 align:middle line:84% So I've been assuming I'm very far 00:21:46.060 --> 00:21:50.680 align:middle line:84% from the interface between the neutral or the inert ambient 00:21:50.680 --> 00:21:54.337 align:middle line:90% and the reactive surface. 00:21:54.337 --> 00:21:56.920 align:middle line:84% So far I haven't talked about what happens near the interface. 00:21:56.920 --> 00:21:59.890 align:middle line:84% But you know as you're injecting the interstitials here 00:21:59.890 --> 00:22:02.890 align:middle line:84% due to the oxidation, they don't just diffuse straight down. 00:22:02.890 --> 00:22:05.680 align:middle line:84% They diffuse out in a two-dimensional fashion. 00:22:05.680 --> 00:22:08.410 align:middle line:84% They diffuse down, sideways, over to the edge. 00:22:08.410 --> 00:22:11.570 align:middle line:84% So they're actually diffusing in different directions. 00:22:11.570 --> 00:22:14.050 align:middle line:84% Now, if you're far from this edge, 00:22:14.050 --> 00:22:16.670 align:middle line:84% you don't see much effect of the interstitial. 00:22:16.670 --> 00:22:18.320 align:middle line:90% They primarily go down. 00:22:18.320 --> 00:22:19.900 align:middle line:84% But if you're near the edge here, 00:22:19.900 --> 00:22:21.940 align:middle line:84% you're going to see some edge effects. 00:22:21.940 --> 00:22:27.850 align:middle line:84% And in fact, depending on how far from this stripe 00:22:27.850 --> 00:22:30.925 align:middle line:84% the enhancement of the oxidation occurs 00:22:30.925 --> 00:22:34.390 align:middle line:84% will give you some idea of how rapidly the interstitials are 00:22:34.390 --> 00:22:37.510 align:middle line:84% diffusing in this lateral direction. 00:22:37.510 --> 00:22:39.910 align:middle line:84% But there's another process besides just the fact 00:22:39.910 --> 00:22:41.860 align:middle line:84% that the interstitials are diffusing around. 00:22:41.860 --> 00:22:44.830 align:middle line:84% So they're going vertically and laterally. 00:22:44.830 --> 00:22:46.750 align:middle line:84% One other process is recombination 00:22:46.750 --> 00:22:48.080 align:middle line:90% that we have to consider. 00:22:48.080 --> 00:22:51.610 align:middle line:84% So in fact, the interstitial flux into the surface 00:22:51.610 --> 00:22:54.082 align:middle line:84% is the difference between the generation rate. 00:22:54.082 --> 00:22:55.790 align:middle line:84% There's a certain number of interstitials 00:22:55.790 --> 00:22:57.170 align:middle line:90% being generated per unit time. 00:22:57.170 --> 00:23:00.870 align:middle line:84% That's G. There's a certain number of interstitials 00:23:00.870 --> 00:23:03.720 align:middle line:84% being recombined at the surface per unit time. 00:23:03.720 --> 00:23:04.590 align:middle line:90% That's R. 00:23:04.590 --> 00:23:07.380 align:middle line:84% The net flux of interstitials injected is-- 00:23:07.380 --> 00:23:10.050 align:middle line:84% you can think of the net flux is if G and R are fluxes, 00:23:10.050 --> 00:23:14.250 align:middle line:84% it's G minus R. OK, now, the problem is-- 00:23:14.250 --> 00:23:16.170 align:middle line:84% and we know that the generation rate here 00:23:16.170 --> 00:23:18.450 align:middle line:84% is proportional to the oxidation rate. 00:23:18.450 --> 00:23:21.930 align:middle line:84% But the question is, in your mind, the recombination rate 00:23:21.930 --> 00:23:25.500 align:middle line:84% at this point here at this interface is not necessarily 00:23:25.500 --> 00:23:27.630 align:middle line:84% the same-- at the active oxidizing interface 00:23:27.630 --> 00:23:30.060 align:middle line:84% is not necessarily the same as the recombination 00:23:30.060 --> 00:23:31.640 align:middle line:90% rate at the inert interface. 00:23:31.640 --> 00:23:33.390 align:middle line:84% For one thing, this interface is changing. 00:23:33.390 --> 00:23:35.580 align:middle line:84% It's continuously reacting and oxidizing. 00:23:35.580 --> 00:23:39.718 align:middle line:84% So it's not clear that R should be the same here as it is here 00:23:39.718 --> 00:23:40.260 align:middle line:90% in the inert. 00:23:40.260 --> 00:23:43.440 align:middle line:84% And in fact, it's not necessarily the same. 00:23:43.440 --> 00:23:45.910 align:middle line:84% Depending on the reaction, it can be quite different. 00:23:45.910 --> 00:23:49.170 align:middle line:84% So when in SUPREM, you'll see various parameters. 00:23:49.170 --> 00:23:51.600 align:middle line:84% There'll be a diffusivity for a silicon interstitial. 00:23:51.600 --> 00:23:52.680 align:middle line:90% You need to know that. 00:23:52.680 --> 00:23:54.510 align:middle line:84% There'll also be a recombination rate. 00:23:54.510 --> 00:23:56.880 align:middle line:84% Sometimes they call it K sub S. There'll 00:23:56.880 --> 00:24:00.850 align:middle line:84% be a recombination constant associated with this oxidizing 00:24:00.850 --> 00:24:01.600 align:middle line:90% interface. 00:24:01.600 --> 00:24:04.360 align:middle line:84% And there'll be another recombination constant 00:24:04.360 --> 00:24:07.510 align:middle line:84% associated with the inert interface. 00:24:07.510 --> 00:24:09.760 align:middle line:84% And they'll also be bulk recombination. 00:24:09.760 --> 00:24:12.230 align:middle line:84% We need to know those three parameters if we're really 00:24:12.230 --> 00:24:14.800 align:middle line:84% going to understand what this lateral extent 00:24:14.800 --> 00:24:16.780 align:middle line:84% of the oxidation-enhanced diffusion 00:24:16.780 --> 00:24:19.390 align:middle line:84% looks like because after all, if I'm getting a lot of surface 00:24:19.390 --> 00:24:22.630 align:middle line:84% recombination over here, interstitials injected, 00:24:22.630 --> 00:24:25.490 align:middle line:84% basically, they all get sucked into that surface and recombine. 00:24:25.490 --> 00:24:27.880 align:middle line:84% So the net excess interstitial population 00:24:27.880 --> 00:24:30.810 align:middle line:90% will fall off more rapidly. 00:24:30.810 --> 00:24:33.480 align:middle line:84% And here's an example on the right of a test structure 00:24:33.480 --> 00:24:36.180 align:middle line:84% that people came up with to try to study 00:24:36.180 --> 00:24:37.180 align:middle line:90% two-dimensional effects. 00:24:37.180 --> 00:24:40.920 align:middle line:84% And I think it's kind of a neat test structure. 00:24:40.920 --> 00:24:43.170 align:middle line:84% This is in cross-section now, so it's a little tricky. 00:24:43.170 --> 00:24:45.253 align:middle line:84% But I'm looking at three different cross-sections. 00:24:45.253 --> 00:24:47.220 align:middle line:84% So this is the surface of the sample. 00:24:47.220 --> 00:24:52.610 align:middle line:84% This is a phosphorous junction that was initially diffused in. 00:24:52.610 --> 00:24:55.280 align:middle line:84% So it has a starting junction depth, say of half a micron, 00:24:55.280 --> 00:24:55.850 align:middle line:90% whatever. 00:24:55.850 --> 00:24:57.830 align:middle line:84% Phosphorous diffused into lightly doped boron. 00:24:57.830 --> 00:25:00.620 align:middle line:84% And they put stripes on the sample. 00:25:00.620 --> 00:25:04.640 align:middle line:84% And the stripes are masked such that the open region where 00:25:04.640 --> 00:25:07.880 align:middle line:84% they cut away the nitride, these open regions, 00:25:07.880 --> 00:25:10.263 align:middle line:84% these open stripes, are getting smaller and smaller 00:25:10.263 --> 00:25:11.430 align:middle line:90% as we go from left to right. 00:25:11.430 --> 00:25:15.020 align:middle line:84% So here's a pretty wide open region, narrower, narrower, 00:25:15.020 --> 00:25:19.170 align:middle line:84% until it gets to the point where it's a very narrow open region. 00:25:19.170 --> 00:25:21.500 align:middle line:84% So the nice thing is, what you're doing 00:25:21.500 --> 00:25:25.700 align:middle line:84% is you're sort of changing the region over which 00:25:25.700 --> 00:25:28.860 align:middle line:90% you inject these point defects. 00:25:28.860 --> 00:25:31.028 align:middle line:90% And then they did the oxidation. 00:25:31.028 --> 00:25:32.570 align:middle line:84% They did the oxidation of phosphorus. 00:25:32.570 --> 00:25:34.970 align:middle line:84% And what they see is the junction depth now, 00:25:34.970 --> 00:25:39.290 align:middle line:84% which initially was flat because it was diffused originally 00:25:39.290 --> 00:25:40.940 align:middle line:84% before they put the stripes down, 00:25:40.940 --> 00:25:43.520 align:middle line:84% after they put the stripes down and they do oxidation, 00:25:43.520 --> 00:25:46.797 align:middle line:84% right underneath where the oxidation takes place, of course 00:25:46.797 --> 00:25:48.630 align:middle line:84% you see a big enhancement of the phosphorus. 00:25:48.630 --> 00:25:49.830 align:middle line:90% That's OED. 00:25:49.830 --> 00:25:53.490 align:middle line:84% But interestingly, look at the shape 00:25:53.490 --> 00:25:58.680 align:middle line:84% as you go to different opening widths of these open stripes. 00:25:58.680 --> 00:26:00.960 align:middle line:84% The overall junction depth kind of 00:26:00.960 --> 00:26:04.410 align:middle line:84% reaches the same point here, regardless 00:26:04.410 --> 00:26:07.860 align:middle line:90% of the width of the open area. 00:26:07.860 --> 00:26:10.110 align:middle line:84% It's changing a little bit in shape. 00:26:10.110 --> 00:26:13.980 align:middle line:84% But nevertheless, it reaches the same junction depth. 00:26:13.980 --> 00:26:16.650 align:middle line:84% So what that's saying is that at this point down here, 00:26:16.650 --> 00:26:19.230 align:middle line:84% the interstitial concentration or supersaturation 00:26:19.230 --> 00:26:22.210 align:middle line:84% at the little tip here is about the same as it is here. 00:26:22.210 --> 00:26:24.550 align:middle line:84% It's about the same as it here, as it is here. 00:26:24.550 --> 00:26:26.730 align:middle line:84% And so it's not that much perturbed 00:26:26.730 --> 00:26:30.420 align:middle line:84% by the presence of, all around it, these interfaces, 00:26:30.420 --> 00:26:32.860 align:middle line:90% these inert interfaces. 00:26:32.860 --> 00:26:37.045 align:middle line:84% So the recombination probably at the oxidizing interface 00:26:37.045 --> 00:26:38.670 align:middle line:84% and at the inert interface, those rates 00:26:38.670 --> 00:26:41.253 align:middle line:84% are probably fairly comparable when you're 00:26:41.253 --> 00:26:42.420 align:middle line:90% talking about interstitials. 00:26:42.420 --> 00:26:44.710 align:middle line:84% But let's look at the other case. 00:26:44.710 --> 00:26:45.765 align:middle line:90% Here's another example. 00:26:45.765 --> 00:26:47.140 align:middle line:84% They did an experiment like that, 00:26:47.140 --> 00:26:49.750 align:middle line:84% but instead they started with an antimony junction. 00:26:49.750 --> 00:26:52.800 align:middle line:84% So this initial starting junction depth looks similar, 00:26:52.800 --> 00:26:53.760 align:middle line:90% but it was antimony. 00:26:53.760 --> 00:26:56.490 align:middle line:84% And what do they see as they decrease the opening width? 00:26:56.490 --> 00:26:59.850 align:middle line:84% In fact, the overall junction depth, 00:26:59.850 --> 00:27:02.250 align:middle line:84% even right below the opening, directly below it, 00:27:02.250 --> 00:27:04.630 align:middle line:90% actually goes down. 00:27:04.630 --> 00:27:06.400 align:middle line:84% This is for nitridation of antimony. 00:27:06.400 --> 00:27:08.590 align:middle line:84% Unlike here, where these tips all stay-- 00:27:08.590 --> 00:27:11.620 align:middle line:84% the end of the junction was the same regardless of stripe width. 00:27:11.620 --> 00:27:13.520 align:middle line:90% Here it's actually going down. 00:27:13.520 --> 00:27:14.607 align:middle line:90% So what's that saying? 00:27:14.607 --> 00:27:15.940 align:middle line:90% That's a two-dimensional effect. 00:27:15.940 --> 00:27:18.490 align:middle line:84% That's actually saying that directly below this opening 00:27:18.490 --> 00:27:20.350 align:middle line:84% where the nitridation is taking place, 00:27:20.350 --> 00:27:23.020 align:middle line:84% locally the supersaturation of vacancies 00:27:23.020 --> 00:27:26.810 align:middle line:84% is actually smaller than below an opening that's much wider. 00:27:26.810 --> 00:27:29.380 align:middle line:84% So these supersaturation of vacancies 00:27:29.380 --> 00:27:32.350 align:middle line:84% must be being impacted by recombination 00:27:32.350 --> 00:27:35.020 align:middle line:84% that's taking place on either side of that opening. 00:27:35.020 --> 00:27:38.380 align:middle line:84% And in fact, people believe that the vacancy recombination 00:27:38.380 --> 00:27:41.140 align:middle line:84% rate here at these inert interfaces 00:27:41.140 --> 00:27:44.630 align:middle line:84% is a lot faster than it is at the nitriding interface. 00:27:44.630 --> 00:27:48.310 align:middle line:84% And so the vacancy supersaturation level 00:27:48.310 --> 00:27:50.350 align:middle line:84% is actually impacted at the center point 00:27:50.350 --> 00:27:52.550 align:middle line:84% by what's happening all around it. 00:27:52.550 --> 00:27:55.330 align:middle line:84% So it's a two-dimensional diffusion and recombination 00:27:55.330 --> 00:27:56.050 align:middle line:90% problem. 00:27:56.050 --> 00:27:57.757 align:middle line:84% And there are a number of parameters. 00:27:57.757 --> 00:27:59.590 align:middle line:84% There's the diffusivity of the point defect. 00:27:59.590 --> 00:28:01.540 align:middle line:84% There's recombination at this surface. 00:28:01.540 --> 00:28:05.357 align:middle line:84% There's recombination at the reactant surface. 00:28:05.357 --> 00:28:06.940 align:middle line:84% And there's recombination in the bowl. 00:28:06.940 --> 00:28:09.700 align:middle line:84% So it's kind of a neat way of looking at things, 00:28:09.700 --> 00:28:12.130 align:middle line:84% even with a one-dimensional test structure-- 00:28:12.130 --> 00:28:14.410 align:middle line:84% I mean, all we have is one dimension here 00:28:14.410 --> 00:28:17.820 align:middle line:84% that we can measure, essentially, the junction depth. 00:28:17.820 --> 00:28:19.570 align:middle line:84% But we can get two-dimensional information 00:28:19.570 --> 00:28:23.260 align:middle line:90% by changing the stripe, period. 00:28:23.260 --> 00:28:26.070 align:middle line:84% So actually, if you go on to slide number 8, 00:28:26.070 --> 00:28:28.080 align:middle line:84% I also took this from that same paper 00:28:28.080 --> 00:28:29.760 align:middle line:90% by Fahey, Griffin, and Plummer. 00:28:29.760 --> 00:28:34.590 align:middle line:84% And this is a little more quantitative description 00:28:34.590 --> 00:28:36.690 align:middle line:84% where they've actually done diffusion modeling 00:28:36.690 --> 00:28:38.070 align:middle line:84% of this two-dimensional diffusion 00:28:38.070 --> 00:28:40.362 align:middle line:84% problem, two-dimensional diffusion of the interstitials 00:28:40.362 --> 00:28:43.320 align:middle line:84% being injected and recombining, and what effect they would 00:28:43.320 --> 00:28:46.310 align:middle line:90% have on a dopant diffusion. 00:28:46.310 --> 00:28:48.940 align:middle line:84% So it's a little bit tricky here, but what you're doing 00:28:48.940 --> 00:28:50.440 align:middle line:90% is a local oxidation. 00:28:50.440 --> 00:28:52.460 align:middle line:84% Out here on the wings there's nitride, 00:28:52.460 --> 00:28:53.890 align:middle line:90% which is hatched region. 00:28:53.890 --> 00:28:56.170 align:middle line:84% Underneath the nitride that's inert. 00:28:56.170 --> 00:28:58.120 align:middle line:90% That's an inert interface. 00:28:58.120 --> 00:28:59.788 align:middle line:90% So that's masked. 00:28:59.788 --> 00:29:01.330 align:middle line:84% Now what they did was they're looking 00:29:01.330 --> 00:29:04.600 align:middle line:84% at simulations for case A and B. And case A 00:29:04.600 --> 00:29:07.510 align:middle line:84% is when the mask opening is fairly wide. 00:29:07.510 --> 00:29:10.150 align:middle line:84% So the mask opening in case A goes from here to here. 00:29:10.150 --> 00:29:12.520 align:middle line:84% Case B is you imagine the opening in the mask 00:29:12.520 --> 00:29:13.460 align:middle line:90% to be very small. 00:29:13.460 --> 00:29:17.820 align:middle line:84% So the region that's being oxidized is much narrower. 00:29:17.820 --> 00:29:22.350 align:middle line:84% And they did the simulations for the two cases, A and B. 00:29:22.350 --> 00:29:25.890 align:middle line:84% So A is the case, these two curves for a wide opening, 00:29:25.890 --> 00:29:27.180 align:middle line:90% and B is for a narrow opening. 00:29:27.180 --> 00:29:29.550 align:middle line:84% But there are two different types of curves here. 00:29:29.550 --> 00:29:32.070 align:middle line:84% There's the solid and the dashed. 00:29:32.070 --> 00:29:37.200 align:middle line:84% In the solid curve, what they assumed in their simulations is 00:29:37.200 --> 00:29:40.080 align:middle line:84% that they assumed the case of S value or the point defects 00:29:40.080 --> 00:29:43.530 align:middle line:84% were recombining more slowly at the inert interface compared 00:29:43.530 --> 00:29:44.910 align:middle line:90% to the oxidizing interface. 00:29:44.910 --> 00:29:47.670 align:middle line:84% So they're saying there's not that much recombination 00:29:47.670 --> 00:29:52.320 align:middle line:84% over here at the inert interface compared to the oxidizing. 00:29:52.320 --> 00:29:55.800 align:middle line:84% When they do that, when they adjust those surface 00:29:55.800 --> 00:29:58.170 align:middle line:84% recombination velocities in that way, what they see 00:29:58.170 --> 00:30:01.020 align:middle line:84% is when you change the stripe width from narrow to wide, 00:30:01.020 --> 00:30:04.980 align:middle line:84% the opening, you get profiles that look like the solid lines 00:30:04.980 --> 00:30:07.920 align:middle line:84% where at the very center of the stripe, 00:30:07.920 --> 00:30:13.300 align:middle line:84% the junction depths are almost the same, which is the case, 00:30:13.300 --> 00:30:19.608 align:middle line:84% if we go back, just go one slide back to slide 7, 00:30:19.608 --> 00:30:21.900 align:middle line:84% it almost looks like this phosphorus case in oxidation. 00:30:21.900 --> 00:30:24.720 align:middle line:84% The junction depths, regardless of the width of the opening, 00:30:24.720 --> 00:30:25.750 align:middle line:90% were about the same. 00:30:25.750 --> 00:30:29.380 align:middle line:84% And so you can actually fit this shape, 00:30:29.380 --> 00:30:32.010 align:middle line:84% this shape right here, to the experimentally measured shape 00:30:32.010 --> 00:30:34.710 align:middle line:84% by changing the ratio of the surface recombination velocity 00:30:34.710 --> 00:30:37.660 align:middle line:84% at this oxidizing interface to in inert. 00:30:37.660 --> 00:30:40.350 align:middle line:84% In the dashed lines, what did they assume? 00:30:40.350 --> 00:30:43.380 align:middle line:84% Well, the dashed lines show the case 00:30:43.380 --> 00:30:45.960 align:middle line:84% where the surface recombination velocity of interstitials 00:30:45.960 --> 00:30:47.940 align:middle line:84% at this oxidizing interface is about 00:30:47.940 --> 00:30:49.380 align:middle line:90% the same as the non-oxidizing. 00:30:49.380 --> 00:30:50.920 align:middle line:90% So they made them equally. 00:30:50.920 --> 00:30:54.780 align:middle line:84% So if it recombines equally in this interface 00:30:54.780 --> 00:30:57.720 align:middle line:84% versus that interface-- in fact, what you see for a narrow stripe 00:30:57.720 --> 00:31:02.160 align:middle line:84% is that the overall junction depth is much lower 00:31:02.160 --> 00:31:03.420 align:middle line:90% than it is for a wide stripe. 00:31:03.420 --> 00:31:05.560 align:middle line:90% So the enhancement is much less. 00:31:05.560 --> 00:31:08.160 align:middle line:84% So actually, people use the shapes 00:31:08.160 --> 00:31:11.700 align:middle line:84% of these junctions as a function of stripe width 00:31:11.700 --> 00:31:14.520 align:middle line:84% to say something to infer about the recombination 00:31:14.520 --> 00:31:18.750 align:middle line:84% velocities at this interface versus at the inert interface, 00:31:18.750 --> 00:31:20.560 align:middle line:90% just by changing the duty cycle. 00:31:20.560 --> 00:31:22.152 align:middle line:84% So this is how, in SUPREM IV, if you 00:31:22.152 --> 00:31:23.610 align:middle line:84% look at some of those coefficients, 00:31:23.610 --> 00:31:25.277 align:middle line:84% this is how they were actually measured. 00:31:25.277 --> 00:31:28.040 align:middle line:84% It's kind of a clever experiment. 00:31:28.040 --> 00:31:31.250 align:middle line:84% Slide 9 is actually showing you some experimental data, again, 00:31:31.250 --> 00:31:34.862 align:middle line:84% just to give you a feel maybe from a different vantage point. 00:31:34.862 --> 00:31:36.320 align:middle line:84% It's a little bit hard to see this. 00:31:36.320 --> 00:31:39.380 align:middle line:84% But this is a photograph from a microscope. 00:31:39.380 --> 00:31:41.900 align:middle line:84% And you got to get used to seeing this. 00:31:41.900 --> 00:31:43.220 align:middle line:90% It's been beveled and stained. 00:31:43.220 --> 00:31:45.770 align:middle line:84% So this surface up here that you're looking at 00:31:45.770 --> 00:31:48.380 align:middle line:90% is the top surface of the chip. 00:31:48.380 --> 00:31:50.400 align:middle line:84% This surface down here is the bevel. 00:31:50.400 --> 00:31:53.420 align:middle line:84% So if, actually, I could find a piece of chalk-- 00:31:53.420 --> 00:31:56.000 align:middle line:84% there happens to be one here, which is kind of rare. 00:31:56.000 --> 00:31:59.210 align:middle line:84% So what they do is, this is the top surface. 00:31:59.210 --> 00:32:00.860 align:middle line:84% This region here has been beveled 00:32:00.860 --> 00:32:04.530 align:middle line:90% at some very shallow angle. 00:32:04.530 --> 00:32:10.192 align:middle line:84% And so the top surface here has the stripes on it. 00:32:10.192 --> 00:32:12.400 align:middle line:84% So in the microscope, if you look at the top surface, 00:32:12.400 --> 00:32:13.460 align:middle line:90% it looks like this. 00:32:13.460 --> 00:32:16.450 align:middle line:84% So these are the regions here where 00:32:16.450 --> 00:32:19.070 align:middle line:84% the oxidation-enhanced diffusion took place. 00:32:19.070 --> 00:32:22.210 align:middle line:84% Here's a 50-micron opening, 25, 20, 10, all the way 00:32:22.210 --> 00:32:23.860 align:middle line:90% down to 4-micron opening. 00:32:23.860 --> 00:32:26.200 align:middle line:84% This phosphorus, this region, it turns out 00:32:26.200 --> 00:32:31.000 align:middle line:84% you can chemically etch the silicon surface, and it stains. 00:32:31.000 --> 00:32:33.860 align:middle line:84% So you get a different surface appearance under the microscope 00:32:33.860 --> 00:32:35.050 align:middle line:90% where it's N type. 00:32:35.050 --> 00:32:35.852 align:middle line:90% And so you use. 00:32:35.852 --> 00:32:37.810 align:middle line:84% This is a really old-fashioned way of doing it. 00:32:37.810 --> 00:32:39.760 align:middle line:84% But beveling and staining the silicon 00:32:39.760 --> 00:32:42.190 align:middle line:84% was a way to measure the junction depth because you could 00:32:42.190 --> 00:32:44.260 align:middle line:84% actually measure it-- basically by doing this 00:32:44.260 --> 00:32:46.900 align:middle line:84% at a shallow enough angle, you can spread this out 00:32:46.900 --> 00:32:48.850 align:middle line:84% over a long distance, a distance such 00:32:48.850 --> 00:32:52.670 align:middle line:84% that you can see it in an optical microscope. 00:32:52.670 --> 00:32:55.930 align:middle line:84% So this was just to give you an idea of what the junction 00:32:55.930 --> 00:32:57.010 align:middle line:90% actually looks like. 00:32:57.010 --> 00:32:59.500 align:middle line:84% Under a wide opening, looks like this. 00:32:59.500 --> 00:33:01.180 align:middle line:84% Under a narrow opening at 4 microns, 00:33:01.180 --> 00:33:04.230 align:middle line:90% it's about the same depth. 00:33:04.230 --> 00:33:07.050 align:middle line:84% So this was experimental evidence 00:33:07.050 --> 00:33:10.290 align:middle line:84% that people used and then fit the SUPREM profiles. 00:33:10.290 --> 00:33:12.420 align:middle line:84% We go back one shape, they fit to that shape. 00:33:12.420 --> 00:33:14.128 align:middle line:84% And they found that the model looked more 00:33:14.128 --> 00:33:15.250 align:middle line:90% like the solid line model. 00:33:15.250 --> 00:33:17.700 align:middle line:84% So they could actually fit the recombination coefficients 00:33:17.700 --> 00:33:19.613 align:middle line:90% based on some of this data. 00:33:19.613 --> 00:33:21.780 align:middle line:84% So it was a relatively-- it was a clever experiment, 00:33:21.780 --> 00:33:23.760 align:middle line:90% relatively simple techniques-- 00:33:23.760 --> 00:33:27.750 align:middle line:84% oxidizing, patterning, and beveling and staining 00:33:27.750 --> 00:33:31.170 align:middle line:84% were used in some of these original experiments, 00:33:31.170 --> 00:33:34.230 align:middle line:90% then at high temperatures. 00:33:34.230 --> 00:33:35.670 align:middle line:84% OK, so that's to give you an idea 00:33:35.670 --> 00:33:39.482 align:middle line:84% of how some of these experiments were done originally. 00:33:39.482 --> 00:33:40.440 align:middle line:90% Now, let's talk about-- 00:33:40.440 --> 00:33:42.240 align:middle line:84% I want to talk about a specific example 00:33:42.240 --> 00:33:44.340 align:middle line:84% that we kind of whizzed through last time 00:33:44.340 --> 00:33:47.340 align:middle line:84% when we were doing towards the end of the class notes. 00:33:47.340 --> 00:33:49.920 align:middle line:84% Let's talk about boron diffusion. 00:33:49.920 --> 00:33:52.950 align:middle line:84% And we're going to say that boron diffuses based 00:33:52.950 --> 00:33:56.370 align:middle line:84% on all the data that people have with only two point defects. 00:33:56.370 --> 00:33:58.990 align:middle line:84% Of all the point defects it could have as pairs, 00:33:58.990 --> 00:34:01.050 align:middle line:84% these are the two that it prefers. 00:34:01.050 --> 00:34:04.560 align:middle line:84% It prefers a neutrally charged interstitial, 00:34:04.560 --> 00:34:07.170 align:middle line:84% silicon interstitial, which we write as I0. 00:34:07.170 --> 00:34:08.710 align:middle line:90% And it pairs with that. 00:34:08.710 --> 00:34:10.800 align:middle line:84% And so we have a B, a boron minus. 00:34:10.800 --> 00:34:15.639 align:middle line:84% Again, that boron substitutional in the lattice is an acceptor. 00:34:15.639 --> 00:34:17.643 align:middle line:84% So it has a net negative charge when 00:34:17.643 --> 00:34:18.810 align:middle line:90% it's substitutional lattice. 00:34:18.810 --> 00:34:21.150 align:middle line:84% It combines with a neutral interstitial 00:34:21.150 --> 00:34:25.409 align:middle line:84% and forms a pair, DI super minus. 00:34:25.409 --> 00:34:28.050 align:middle line:84% Minus because the net charge on that pair, if you were 00:34:28.050 --> 00:34:32.530 align:middle line:84% consider it as a pair, is one negative net electron charge. 00:34:32.530 --> 00:34:33.850 align:middle line:90% So it likes to do that. 00:34:33.850 --> 00:34:38.650 align:middle line:84% Or boron might like to pair with a positively charged 00:34:38.650 --> 00:34:44.290 align:middle line:84% interstitial, particularly because the concentration 00:34:44.290 --> 00:34:46.270 align:middle line:84% of these interstitials tends to go up 00:34:46.270 --> 00:34:47.739 align:middle line:90% in high doping concentrations. 00:34:47.739 --> 00:34:49.060 align:middle line:84% But even in low doping concentrations, 00:34:49.060 --> 00:34:51.643 align:middle line:84% you can see there might be some kind of coulombic interaction. 00:34:51.643 --> 00:34:56.170 align:middle line:84% A boron minus might pair with a positively charged interstitial 00:34:56.170 --> 00:34:57.730 align:middle line:90% and form a BI pair. 00:34:57.730 --> 00:34:59.890 align:middle line:84% The pair charge of this particular pair 00:34:59.890 --> 00:35:02.750 align:middle line:84% now is actually neutral as a pair. 00:35:02.750 --> 00:35:05.740 align:middle line:84% So we have two of these simple chemical reactions. 00:35:05.740 --> 00:35:08.623 align:middle line:84% And they give rise to fluxes of mobile species. 00:35:08.623 --> 00:35:10.540 align:middle line:84% So remember originally, on the left-hand side, 00:35:10.540 --> 00:35:11.590 align:middle line:90% the boron is immobile. 00:35:11.590 --> 00:35:14.380 align:middle line:84% One of these guys comes along, pairs with it. 00:35:14.380 --> 00:35:17.200 align:middle line:84% Now it's mobile on the right-hand side. 00:35:17.200 --> 00:35:20.270 align:middle line:84% And we sum these two, the flux of these two. 00:35:20.270 --> 00:35:24.010 align:middle line:84% And we say the total flux of boron in the sample 00:35:24.010 --> 00:35:28.180 align:middle line:84% is going to be the flux of the BI minus pair and the BI 00:35:28.180 --> 00:35:31.420 align:middle line:90% neutral, uncharged, pair. 00:35:31.420 --> 00:35:36.190 align:middle line:84% So that's an example of how SUPREM 00:35:36.190 --> 00:35:38.920 align:middle line:84% might consider this, at least from a chemical equation 00:35:38.920 --> 00:35:40.800 align:middle line:90% point of view. 00:35:40.800 --> 00:35:43.430 align:middle line:84% So given that, those simple two equations, 00:35:43.430 --> 00:35:46.528 align:middle line:84% and all that we know about deviations from Fick's law-- 00:35:46.528 --> 00:35:48.070 align:middle line:84% I showed this last time, but again, I 00:35:48.070 --> 00:35:52.700 align:middle line:84% think we went through it a little too quickly on slide 11. 00:35:52.700 --> 00:35:56.870 align:middle line:84% I just want to show, again, the overall equation that SUPREM IV 00:35:56.870 --> 00:36:01.850 align:middle line:84% is solving for boron, assuming it's diffusing with just two 00:36:01.850 --> 00:36:03.757 align:middle line:84% species with neutral interstitials 00:36:03.757 --> 00:36:05.090 align:middle line:90% and with positive interstitials. 00:36:05.090 --> 00:36:10.650 align:middle line:84% This is the actual flux, so-called diffusion equation, 00:36:10.650 --> 00:36:13.600 align:middle line:90% that SUPREM is solving. 00:36:13.600 --> 00:36:17.490 align:middle line:84% And it's a far cry from what you would think in a simple case. 00:36:17.490 --> 00:36:20.040 align:middle line:84% You would think it would just be DC boron, 00:36:20.040 --> 00:36:24.780 align:middle line:84% or partial T, if you want, is equal to a diffusivity 00:36:24.780 --> 00:36:31.080 align:middle line:84% times partial concentration of boron with respect to X. 00:36:31.080 --> 00:36:32.427 align:middle line:90% This is what you might think. 00:36:32.427 --> 00:36:34.260 align:middle line:84% That's the simple version of boron diffusion 00:36:34.260 --> 00:36:35.940 align:middle line:90% when we started this chapter 7. 00:36:35.940 --> 00:36:39.090 align:middle line:84% It's just regular old Gaussian type diffusion. 00:36:39.090 --> 00:36:40.740 align:middle line:84% That equation looks pretty simple 00:36:40.740 --> 00:36:43.950 align:middle line:84% compared to that one up on slide 11. 00:36:43.950 --> 00:36:47.950 align:middle line:84% And this is actually what SUPREM is solving. 00:36:47.950 --> 00:36:50.198 align:middle line:84% So where do all these terms come from? 00:36:50.198 --> 00:36:51.990 align:middle line:84% Rather than deriving it, let's just sort of 00:36:51.990 --> 00:36:53.760 align:middle line:84% examine and see if we can understand 00:36:53.760 --> 00:36:55.230 align:middle line:84% based on what we've talked about, 00:36:55.230 --> 00:36:57.270 align:middle line:84% what the different effects are that are 00:36:57.270 --> 00:37:01.950 align:middle line:84% causing it to have this large term here in curly brackets. 00:37:01.950 --> 00:37:03.720 align:middle line:84% Well, the first thing you can notice 00:37:03.720 --> 00:37:08.650 align:middle line:84% is the concentration of boron with respect to time 00:37:08.650 --> 00:37:12.240 align:middle line:90% is the D by DX of a flux. 00:37:12.240 --> 00:37:13.420 align:middle line:90% That does hold. 00:37:13.420 --> 00:37:16.870 align:middle line:84% Everything in curly brackets here is represented by a flux. 00:37:16.870 --> 00:37:19.520 align:middle line:84% The question is, why does the flux look so complicated? 00:37:19.520 --> 00:37:21.290 align:middle line:84% Well, the first part of the flux, 00:37:21.290 --> 00:37:26.480 align:middle line:84% there's a term that depends on DBI star. 00:37:26.480 --> 00:37:28.336 align:middle line:90% So what is that? 00:37:28.336 --> 00:37:33.130 align:middle line:84% That is inert, low-concentration diffusion of boron 00:37:33.130 --> 00:37:35.710 align:middle line:84% that's driven by the boron gradient itself. 00:37:35.710 --> 00:37:38.150 align:middle line:84% So that would be equivalent to this D up here. 00:37:38.150 --> 00:37:44.770 align:middle line:84% So that's sort of the simplest part of the equation. 00:37:44.770 --> 00:37:47.620 align:middle line:84% But multiplying DBI star, there is 00:37:47.620 --> 00:37:50.590 align:middle line:84% this interstitial supersaturation coefficient. 00:37:50.590 --> 00:37:55.160 align:middle line:84% CI over CI star appears right here. 00:37:55.160 --> 00:37:58.660 align:middle line:84% And again, that's because we're trying to take into account here 00:37:58.660 --> 00:38:00.320 align:middle line:90% these non-equilibrium effects. 00:38:00.320 --> 00:38:02.380 align:middle line:84% This was sort of an equilibrium diffusion, 00:38:02.380 --> 00:38:05.470 align:middle line:84% but of excess silicon interstitials, 00:38:05.470 --> 00:38:07.550 align:middle line:90% and that we have pair diffusion. 00:38:07.550 --> 00:38:11.920 align:middle line:90% So there's CI over CI star here. 00:38:11.920 --> 00:38:17.600 align:middle line:84% And it's gradient is in here, as well. 00:38:17.600 --> 00:38:19.960 align:middle line:84% There are high concentration effects 00:38:19.960 --> 00:38:21.050 align:middle line:90% on the dopant diffusivity. 00:38:21.050 --> 00:38:24.280 align:middle line:84% So this you recognize this thing in parentheses, 00:38:24.280 --> 00:38:27.550 align:middle line:84% it's 1 plus beta P over NI divided by 1 plus beta. 00:38:27.550 --> 00:38:29.920 align:middle line:84% That whole thing is Fermi-level effect. 00:38:29.920 --> 00:38:31.480 align:middle line:84% That's the high concentration effect. 00:38:31.480 --> 00:38:34.390 align:middle line:84% Remember, beta was the ratio of boron diffusing 00:38:34.390 --> 00:38:38.380 align:middle line:84% with the I star divided by the ratio diffusing 00:38:38.380 --> 00:38:40.810 align:middle line:90% of neutral interstitials. 00:38:40.810 --> 00:38:44.530 align:middle line:84% And so as this kicks in, as P over NI gets large, 00:38:44.530 --> 00:38:46.690 align:middle line:84% it's going to bump up the diffusivity, 00:38:46.690 --> 00:38:49.040 align:middle line:90% the effect of diffusivity. 00:38:49.040 --> 00:38:50.920 align:middle line:84% So if you want, you can think of all these-- 00:38:50.920 --> 00:38:53.770 align:middle line:84% there's a lot of these things here upfront, these three terms, 00:38:53.770 --> 00:38:56.320 align:middle line:84% as all multiplying the inner diffusivity 00:38:56.320 --> 00:38:58.930 align:middle line:84% by some number that's going to pump it up, or maybe pump it 00:38:58.930 --> 00:39:01.510 align:middle line:84% down if the CI over Ci star goes down 00:39:01.510 --> 00:39:03.070 align:middle line:90% under injection of vacancies. 00:39:03.070 --> 00:39:05.740 align:middle line:84% And this last bit here, this partial 00:39:05.740 --> 00:39:08.350 align:middle line:84% x of the lin of everything in parentheses, 00:39:08.350 --> 00:39:12.220 align:middle line:84% that came-- you covered last week when Maggie was lecturing. 00:39:12.220 --> 00:39:15.370 align:middle line:84% That's the electric field effect, just the fact 00:39:15.370 --> 00:39:20.980 align:middle line:84% that besides just the gradient of the concentration gradient 00:39:20.980 --> 00:39:22.300 align:middle line:90% that drives diffusion. 00:39:22.300 --> 00:39:24.070 align:middle line:90% We also know electric fields. 00:39:24.070 --> 00:39:26.780 align:middle line:90% We can have a field-aided term. 00:39:26.780 --> 00:39:29.143 align:middle line:84% So that's where this last term is coming from. 00:39:29.143 --> 00:39:31.810 align:middle line:84% So you can get a feel for where all these terms are coming from. 00:39:31.810 --> 00:39:34.343 align:middle line:84% It's a fairly-- you can't imagine doing this by hand. 00:39:34.343 --> 00:39:36.010 align:middle line:84% To solve this equation, obviously you're 00:39:36.010 --> 00:39:38.343 align:middle line:84% going to have to do something on the computer, something 00:39:38.343 --> 00:39:40.930 align:middle line:90% numerically. 00:39:40.930 --> 00:39:42.830 align:middle line:90% OK, so let's go to slide-- 00:39:42.830 --> 00:39:46.990 align:middle line:84% so that kind of gives you an example of the boron case. 00:39:46.990 --> 00:39:49.990 align:middle line:84% Now I want to give you an example of the case which 00:39:49.990 --> 00:39:53.260 align:middle line:84% is a little bit strange, puzzled people for a long time, 00:39:53.260 --> 00:39:55.450 align:middle line:84% but now is understood as an example 00:39:55.450 --> 00:39:59.380 align:middle line:84% of the impact of the gradient in the point defect. 00:39:59.380 --> 00:40:02.620 align:middle line:84% Not the gradient in the dopant itself, 00:40:02.620 --> 00:40:04.780 align:middle line:84% but a gradient in injected point defects. 00:40:04.780 --> 00:40:08.290 align:middle line:84% How are they going to change the device dopant profiles? 00:40:08.290 --> 00:40:11.020 align:middle line:84% And we're going to talk about this in much more detail 00:40:11.020 --> 00:40:12.640 align:middle line:84% once I talk about ion implant damage. 00:40:12.640 --> 00:40:15.040 align:middle line:84% But just want to introduce it at this point 00:40:15.040 --> 00:40:18.610 align:middle line:84% to make the point that the gradient in the point defects 00:40:18.610 --> 00:40:20.470 align:middle line:90% can drive diffusion, as well. 00:40:20.470 --> 00:40:22.720 align:middle line:84% There is something called the reverse short channel 00:40:22.720 --> 00:40:26.230 align:middle line:84% effect that puzzled people for quite a bit in the early 90s 00:40:26.230 --> 00:40:28.960 align:middle line:84% and ended up being explained, this electrical effect 00:40:28.960 --> 00:40:33.670 align:middle line:84% in devices being explained by this boron pair diffusion, boron 00:40:33.670 --> 00:40:34.970 align:middle line:90% interstitial pair diffusion. 00:40:34.970 --> 00:40:37.270 align:middle line:84% So before we talk about reverse short channel effect, which 00:40:37.270 --> 00:40:38.812 align:middle line:84% sounds really weird, how about what's 00:40:38.812 --> 00:40:41.680 align:middle line:84% the regular or the usual short channel effect? 00:40:41.680 --> 00:40:45.220 align:middle line:84% We talked about it a little bit several lectures ago. 00:40:45.220 --> 00:40:49.030 align:middle line:84% But basically, the usual short channel effect 00:40:49.030 --> 00:40:51.580 align:middle line:84% is for a given process, the threshold voltage 00:40:51.580 --> 00:40:55.630 align:middle line:84% goes down as you decrease the L. So for a given process on chip, 00:40:55.630 --> 00:40:58.880 align:middle line:84% as you look at smaller and smaller devices made on chip 00:40:58.880 --> 00:41:01.430 align:middle line:84% and you plot the threshold voltage, what you'll see 00:41:01.430 --> 00:41:03.200 align:middle line:90% is it rolls off. 00:41:03.200 --> 00:41:04.730 align:middle line:90% Generally the VT goes down. 00:41:04.730 --> 00:41:06.500 align:middle line:84% It becomes easier to turn on the device. 00:41:06.500 --> 00:41:08.780 align:middle line:84% And here's a textbook if you want 00:41:08.780 --> 00:41:11.360 align:middle line:84% to go through in understanding some of the physics. 00:41:11.360 --> 00:41:15.470 align:middle line:84% But basically, what happens is as you bring the source 00:41:15.470 --> 00:41:19.280 align:middle line:84% and drain closer, the potential due to the drain 00:41:19.280 --> 00:41:22.490 align:middle line:84% actually starts interacting with the potential in the channel, 00:41:22.490 --> 00:41:25.400 align:middle line:90% and it starts having an effect. 00:41:25.400 --> 00:41:28.130 align:middle line:84% Ordinarily you'd like that not to be the case. 00:41:28.130 --> 00:41:30.990 align:middle line:84% You'd like to have just the gate have the only effect. 00:41:30.990 --> 00:41:34.700 align:middle line:84% So the lowering of the potential barrier by the drain voltage 00:41:34.700 --> 00:41:42.050 align:middle line:84% is what causes this to go down as you shrink the channel 00:41:42.050 --> 00:41:43.220 align:middle line:90% length. 00:41:43.220 --> 00:41:47.630 align:middle line:84% And how much that potential barrier can be up raised 00:41:47.630 --> 00:41:51.020 align:middle line:84% or lowered is a strong function of the profile of the boron, 00:41:51.020 --> 00:41:54.830 align:middle line:84% say in an NFET, underneath the channel. 00:41:54.830 --> 00:41:56.920 align:middle line:84% So in fact, if we go to slide 13-- 00:41:56.920 --> 00:41:59.980 align:middle line:84% just, again, I took this from Tower and Ning's book 00:41:59.980 --> 00:42:03.272 align:middle line:84% on fundamentals of modern devices for the device physics. 00:42:03.272 --> 00:42:05.230 align:middle line:84% Again, you don't have to understand the detail, 00:42:05.230 --> 00:42:07.600 align:middle line:84% but just gives you an idea of where this comes from. 00:42:07.600 --> 00:42:10.300 align:middle line:84% Imagine here I have-- this is my source, my gate 00:42:10.300 --> 00:42:12.370 align:middle line:84% up here, and the drain over on the right. 00:42:12.370 --> 00:42:16.300 align:middle line:84% And this distance, 0, is right at the source injection point. 00:42:16.300 --> 00:42:17.960 align:middle line:90% And L is the channel length. 00:42:17.960 --> 00:42:19.360 align:middle line:90% So that's right at the drain. 00:42:19.360 --> 00:42:21.430 align:middle line:84% And what he's plotted here in this book 00:42:21.430 --> 00:42:22.940 align:middle line:90% is the surface potential. 00:42:22.940 --> 00:42:25.690 align:middle line:84% So that's the potential at the surface 00:42:25.690 --> 00:42:29.740 align:middle line:84% that a carrier would experience as a function of distance 00:42:29.740 --> 00:42:30.920 align:middle line:90% along the channel. 00:42:30.920 --> 00:42:33.280 align:middle line:84% So here at 0, you're just starting in the source. 00:42:33.280 --> 00:42:34.930 align:middle line:84% And it looks something like this. 00:42:34.930 --> 00:42:37.930 align:middle line:84% Curve A is for the case of a 6-micron device. 00:42:37.930 --> 00:42:42.860 align:middle line:84% Curve B is a 1.25 at, say, half a volt. 00:42:42.860 --> 00:42:49.510 align:middle line:84% And curve C, when I put a drain bias of 5 volts, what happens? 00:42:49.510 --> 00:42:52.573 align:middle line:84% Actually, the potential, even in the center of the channel, 00:42:52.573 --> 00:42:54.740 align:middle line:84% instead of just being the potential of being lowered 00:42:54.740 --> 00:42:56.407 align:middle line:84% in the drain, it's actually because it's 00:42:56.407 --> 00:42:59.820 align:middle line:84% a short channel the potential is actually lowered here. 00:42:59.820 --> 00:43:03.350 align:middle line:84% And so it's that ability of the drain voltage to impact things 00:43:03.350 --> 00:43:06.830 align:middle line:84% that is a short-channel effect, and is partly 00:43:06.830 --> 00:43:09.800 align:middle line:84% responsible for the lowering of the VT. 00:43:09.800 --> 00:43:12.110 align:middle line:84% So the way people-- when you scale devices shorter, 00:43:12.110 --> 00:43:15.200 align:middle line:84% the way people counteract this is they dope 00:43:15.200 --> 00:43:16.370 align:middle line:90% underneath the channel. 00:43:16.370 --> 00:43:17.818 align:middle line:84% They counter-dope it more heavily 00:43:17.818 --> 00:43:18.860 align:middle line:90% with the opposite dopant. 00:43:18.860 --> 00:43:22.737 align:middle line:84% So they add more boron, for example. 00:43:22.737 --> 00:43:24.320 align:middle line:84% If you were to add more boron, there'd 00:43:24.320 --> 00:43:28.490 align:middle line:84% be much less of this effect of this potential being 00:43:28.490 --> 00:43:30.300 align:middle line:90% impacted by the drain. 00:43:30.300 --> 00:43:32.240 align:middle line:84% So there's a tendency, as you scale 00:43:32.240 --> 00:43:33.740 align:middle line:84% devices smaller and smaller, you'll 00:43:33.740 --> 00:43:34.990 align:middle line:90% see the doping in the channel. 00:43:34.990 --> 00:43:38.570 align:middle line:84% If you go on the ITR roadmap, every year it goes up. 00:43:38.570 --> 00:43:41.030 align:middle line:84% mid 10 to the 17th, 20 to the 18th, mid 10 to the 18th 00:43:41.030 --> 00:43:43.080 align:middle line:90% as we shrink devices. 00:43:43.080 --> 00:43:44.930 align:middle line:84% So people counteract this short channel, 00:43:44.930 --> 00:43:48.240 align:middle line:84% the normal short channel effect, by upping the doping 00:43:48.240 --> 00:43:48.945 align:middle line:90% in the channel. 00:43:48.945 --> 00:43:52.060 align:middle line:90% 00:43:52.060 --> 00:43:54.360 align:middle line:84% But what people saw was the reverse short channel 00:43:54.360 --> 00:43:56.370 align:middle line:84% effect, which was confusing people, 00:43:56.370 --> 00:44:00.270 align:middle line:84% is that for short channel lengths on the chip, 00:44:00.270 --> 00:44:03.360 align:middle line:84% it was actually found that the threshold voltage actually 00:44:03.360 --> 00:44:06.420 align:middle line:84% increased in a certain range of channel length. 00:44:06.420 --> 00:44:09.000 align:middle line:84% So as they shrunk the channel length in a certain range, 00:44:09.000 --> 00:44:12.600 align:middle line:84% VT actually went up, almost as if the doping in the channel 00:44:12.600 --> 00:44:14.800 align:middle line:84% was getting higher in that range. 00:44:14.800 --> 00:44:16.440 align:middle line:84% So all these devices are fabricated 00:44:16.440 --> 00:44:19.410 align:middle line:84% on the same chip, subject to the same temperatures 00:44:19.410 --> 00:44:22.710 align:middle line:84% on the same wafer, same iron implants, everything. 00:44:22.710 --> 00:44:24.870 align:middle line:84% Why would it be the doping would be different 00:44:24.870 --> 00:44:27.750 align:middle line:84% in the center of the channel, depending on the channel length? 00:44:27.750 --> 00:44:31.330 align:middle line:84% And people were mystified by this for a while. 00:44:31.330 --> 00:44:33.955 align:middle line:84% So the reverse short channel effect basically 00:44:33.955 --> 00:44:35.080 align:middle line:90% looked something like this. 00:44:35.080 --> 00:44:37.150 align:middle line:84% And this is kind of a backwards plot. 00:44:37.150 --> 00:44:39.750 align:middle line:84% But if you plot threshold voltage-- 00:44:39.750 --> 00:44:41.580 align:middle line:90% now this is on the right axis. 00:44:41.580 --> 00:44:43.720 align:middle line:84% Inverse channel length is increasing this way. 00:44:43.720 --> 00:44:46.590 align:middle line:84% But if you want to look at the upper X-axis, it's helpful. 00:44:46.590 --> 00:44:48.840 align:middle line:84% The channel length is here on the right 00:44:48.840 --> 00:44:51.700 align:middle line:84% going from 0.2 all the way up to 1 micron. 00:44:51.700 --> 00:44:53.710 align:middle line:84% Or if you're shrinking the device, 00:44:53.710 --> 00:44:56.270 align:middle line:90% you're going from here to here. 00:44:56.270 --> 00:45:00.400 align:middle line:84% So as I'm shrinking down here from, say, a 10-micron device 00:45:00.400 --> 00:45:02.980 align:middle line:84% down to 1 micron, what was actually happening 00:45:02.980 --> 00:45:04.840 align:middle line:90% from 10 to 1 micron? 00:45:04.840 --> 00:45:07.960 align:middle line:84% Actually, it's easier to see it if you look at the closed 00:45:07.960 --> 00:45:09.130 align:middle line:90% squares from the experiment. 00:45:09.130 --> 00:45:13.930 align:middle line:84% The VT was actually going up from about 1.1 volts 00:45:13.930 --> 00:45:18.260 align:middle line:84% up to 1.2 or 1.25 volts, which is a significant increase. 00:45:18.260 --> 00:45:22.270 align:middle line:84% So you're shrinking devices from 10 microns 00:45:22.270 --> 00:45:24.580 align:middle line:84% or 5 microns down to the third of a micron. 00:45:24.580 --> 00:45:25.500 align:middle line:90% VT is going up. 00:45:25.500 --> 00:45:27.700 align:middle line:84% That's the opposite of what everyone expected 00:45:27.700 --> 00:45:30.350 align:middle line:84% from the old days from the regular short channel effect. 00:45:30.350 --> 00:45:34.600 align:middle line:84% So people call this the reverse short channel effect. 00:45:34.600 --> 00:45:37.510 align:middle line:84% And in fact, people were able to-- it turns out 00:45:37.510 --> 00:45:40.270 align:middle line:84% there's a paper in 1993 at IEDM from Rafferty. 00:45:40.270 --> 00:45:42.130 align:middle line:84% They were actually able to explain this 00:45:42.130 --> 00:45:46.450 align:middle line:84% based on simulating what they thought the boron profile would 00:45:46.450 --> 00:45:49.112 align:middle line:84% be in this nMOSFET in a case where there was 00:45:49.112 --> 00:45:50.320 align:middle line:90% transient enhanced diffusion. 00:45:50.320 --> 00:45:52.060 align:middle line:84% And we haven't yet talked about TED. 00:45:52.060 --> 00:45:56.200 align:middle line:84% But basically, what they found was that the source drain 00:45:56.200 --> 00:45:58.360 align:middle line:84% implants were injecting excess interstitials 00:45:58.360 --> 00:46:01.090 align:middle line:84% and setting up fluxes of interstitials that were then 00:46:01.090 --> 00:46:03.670 align:middle line:84% driving the boron, which was originally buried, 00:46:03.670 --> 00:46:05.810 align:middle line:84% driving it closer to the surface. 00:46:05.810 --> 00:46:07.960 align:middle line:84% And if you made the channel shorter, 00:46:07.960 --> 00:46:10.840 align:middle line:84% this effect was even greater, basically, 00:46:10.840 --> 00:46:13.610 align:middle line:84% because you're bringing in-- the center of the channel is being 00:46:13.610 --> 00:46:16.490 align:middle line:84% brought closer as you change the channel, closer to the source 00:46:16.490 --> 00:46:19.073 align:middle line:84% drain regions where the excess interstitials were being pumped 00:46:19.073 --> 00:46:20.690 align:middle line:90% in. 00:46:20.690 --> 00:46:23.810 align:middle line:84% But in either case, whether it's OED or TED, 00:46:23.810 --> 00:46:27.200 align:middle line:84% the point was that they were able to explain based 00:46:27.200 --> 00:46:30.470 align:middle line:84% on these diffusion models that more boron, more p-type dopant, 00:46:30.470 --> 00:46:33.230 align:middle line:84% was ending up in the channel region of a short device, 00:46:33.230 --> 00:46:38.240 align:middle line:84% say of 0.3 micron device, than would be in a 1-micron device. 00:46:38.240 --> 00:46:41.540 align:middle line:84% More boron means instead of the short channel effect 00:46:41.540 --> 00:46:44.540 align:middle line:84% and VT rolling off-- actually, there was so much extra boron 00:46:44.540 --> 00:46:46.790 align:middle line:90% that VT was going up. 00:46:46.790 --> 00:46:49.550 align:middle line:84% So the electrical engineers and the circuit people 00:46:49.550 --> 00:46:52.280 align:middle line:84% who would see these weird VT variations with channel length 00:46:52.280 --> 00:46:54.798 align:middle line:84% and didn't know about the processing 00:46:54.798 --> 00:46:56.840 align:middle line:84% were mystified as to how this could be happening. 00:46:56.840 --> 00:46:58.310 align:middle line:84% They just assumed, well, the boron concentration 00:46:58.310 --> 00:47:00.380 align:middle line:84% is the same on a short device and a long device. 00:47:00.380 --> 00:47:02.000 align:middle line:90% Well, actually, it's not. 00:47:02.000 --> 00:47:02.570 align:middle line:90% It can vary. 00:47:02.570 --> 00:47:05.990 align:middle line:84% And of course, that means you need these more complex models 00:47:05.990 --> 00:47:08.240 align:middle line:84% that haven't taken into account point defect injection 00:47:08.240 --> 00:47:11.810 align:middle line:84% from the sides in order to be able to model the boron 00:47:11.810 --> 00:47:14.990 align:middle line:84% profile accurately and to get the device VT right. 00:47:14.990 --> 00:47:17.480 align:middle line:84% So that's sort of a classic example 00:47:17.480 --> 00:47:22.610 align:middle line:84% of how these complex models impact device performance. 00:47:22.610 --> 00:47:24.980 align:middle line:84% And in fact, here's a cartoon explanation 00:47:24.980 --> 00:47:29.560 align:middle line:90% on slide 15 where we-- 00:47:29.560 --> 00:47:32.650 align:middle line:84% this is a two-dimensional SUPREM simulation 00:47:32.650 --> 00:47:35.710 align:middle line:84% of what's going on in the reverse short channel effect. 00:47:35.710 --> 00:47:38.830 align:middle line:84% And what's being shown here is a relatively short device, 00:47:38.830 --> 00:47:39.850 align:middle line:90% short channel length. 00:47:39.850 --> 00:47:44.950 align:middle line:84% And the different colors are the different contours corresponding 00:47:44.950 --> 00:47:46.730 align:middle line:84% to constant doping concentrations. 00:47:46.730 --> 00:47:48.610 align:middle line:84% And if you just for a moment imagine, 00:47:48.610 --> 00:47:50.210 align:middle line:84% this is the drain over on the right, 00:47:50.210 --> 00:47:54.100 align:middle line:84% you see this little region here is the drain extension. 00:47:54.100 --> 00:47:56.480 align:middle line:90% And down here is the deep drain. 00:47:56.480 --> 00:47:59.890 align:middle line:84% Here's the source extension and the deep source extending down 00:47:59.890 --> 00:48:02.500 align:middle line:84% to about this blue-colored region. 00:48:02.500 --> 00:48:05.890 align:middle line:84% These arrows that are emanating from the source and drain, 00:48:05.890 --> 00:48:09.550 align:middle line:84% they are interstitial fluxes coming from the surface 00:48:09.550 --> 00:48:10.660 align:middle line:90% of the source and drain. 00:48:10.660 --> 00:48:12.250 align:middle line:84% These interstitials, people believed 00:48:12.250 --> 00:48:15.192 align:middle line:84% in this particular model, were being injected due to the damage 00:48:15.192 --> 00:48:16.150 align:middle line:90% due to the ion implant. 00:48:16.150 --> 00:48:18.850 align:middle line:84% And we're going to talk in the next few lectures about ion 00:48:18.850 --> 00:48:20.230 align:middle line:90% implantation and how it damages. 00:48:20.230 --> 00:48:22.390 align:middle line:84% But just take that with a grain of salt, 00:48:22.390 --> 00:48:25.360 align:middle line:84% that you believe that there was a process that introduced 00:48:25.360 --> 00:48:28.040 align:middle line:84% a lot of excess interstitials only in these regions, 00:48:28.040 --> 00:48:29.810 align:middle line:90% not where the gate was. 00:48:29.810 --> 00:48:31.820 align:middle line:84% So these interstitials were coming in 00:48:31.820 --> 00:48:33.960 align:middle line:84% and they were diffusing all around. 00:48:33.960 --> 00:48:36.230 align:middle line:84% So these arrows represent interstitial fluxes. 00:48:36.230 --> 00:48:39.388 align:middle line:84% And they're recombining at the various interfaces. 00:48:39.388 --> 00:48:41.930 align:middle line:84% Now, look at this interstitial flux here that goes like this. 00:48:41.930 --> 00:48:44.970 align:middle line:84% This arrow points this direction and goes up towards the surface. 00:48:44.970 --> 00:48:47.967 align:middle line:84% So this interstitial flux, this gradient 00:48:47.967 --> 00:48:50.300 align:middle line:84% of interstitials where there's a high concentration here 00:48:50.300 --> 00:48:52.400 align:middle line:90% and going down at this point. 00:48:52.400 --> 00:48:54.320 align:middle line:84% That gradient of interstitials was actually 00:48:54.320 --> 00:48:56.710 align:middle line:90% dragging the boron with it. 00:48:56.710 --> 00:48:59.450 align:middle line:84% It was actually dragging the boron with it 00:48:59.450 --> 00:49:02.690 align:middle line:84% and moving the peak boron profile from where it originally 00:49:02.690 --> 00:49:04.400 align:middle line:84% was more deep in the sample, moving it up 00:49:04.400 --> 00:49:05.430 align:middle line:90% towards the surface. 00:49:05.430 --> 00:49:07.970 align:middle line:84% So in a short device, it was causing the boron 00:49:07.970 --> 00:49:09.810 align:middle line:90% to be higher at the surface. 00:49:09.810 --> 00:49:12.140 align:middle line:84% And so this is a two-dimensional representation. 00:49:12.140 --> 00:49:14.240 align:middle line:84% If you take a cut straight through the center, 00:49:14.240 --> 00:49:17.960 align:middle line:84% right here at x equals 0 and look along the y direction, 00:49:17.960 --> 00:49:22.250 align:middle line:84% in the vertical direction, you can see three different curves 00:49:22.250 --> 00:49:22.830 align:middle line:90% on this plot. 00:49:22.830 --> 00:49:24.622 align:middle line:84% So this is a plot right through the center, 00:49:24.622 --> 00:49:27.120 align:middle line:84% the concentration of boron versus depth into the device. 00:49:27.120 --> 00:49:30.340 align:middle line:84% So 0 would be right at the surface by the channel. 00:49:30.340 --> 00:49:32.090 align:middle line:84% And there are three different curves here. 00:49:32.090 --> 00:49:34.280 align:middle line:90% The red one is for one micron. 00:49:34.280 --> 00:49:37.880 align:middle line:84% And you can see it peaks here at a certain depth. 00:49:37.880 --> 00:49:39.170 align:middle line:90% 1 micron channel length. 00:49:39.170 --> 00:49:42.230 align:middle line:84% The blue, the dashed blue, is a quarter micron channel length. 00:49:42.230 --> 00:49:47.090 align:middle line:84% And the dashed green is a 0.18, even smaller. 00:49:47.090 --> 00:49:48.800 align:middle line:84% And indeed, what the model is predicting, 00:49:48.800 --> 00:49:51.050 align:middle line:84% as I'm going to shorter and shorter channels, 00:49:51.050 --> 00:49:52.580 align:middle line:84% the amount of boron at the surface 00:49:52.580 --> 00:49:55.310 align:middle line:84% is going up here by a factor of almost 3. 00:49:55.310 --> 00:49:56.370 align:middle line:90% Something like that. 00:49:56.370 --> 00:49:57.420 align:middle line:90% 3 to 4. 00:49:57.420 --> 00:50:00.630 align:middle line:84% So indeed, if you increase the boron concentration 00:50:00.630 --> 00:50:02.760 align:middle line:84% at the surface of a MOSFET by a factor of 3 to 4, 00:50:02.760 --> 00:50:03.940 align:middle line:90% the VT is going to go up. 00:50:03.940 --> 00:50:06.330 align:middle line:90% It's not going to go down. 00:50:06.330 --> 00:50:09.338 align:middle line:84% And how can the channel length impact this? 00:50:09.338 --> 00:50:11.130 align:middle line:84% Well, it's directly through this mechanism. 00:50:11.130 --> 00:50:14.160 align:middle line:84% The normal Fickian diffusion, the simple version 00:50:14.160 --> 00:50:15.785 align:middle line:84% of Fick's law, there was no way people, 00:50:15.785 --> 00:50:17.243 align:middle line:84% when they use a simple models, they 00:50:17.243 --> 00:50:19.620 align:middle line:84% can get that to happen as a function of this channel. 00:50:19.620 --> 00:50:23.550 align:middle line:84% They had to invoke some other thing 00:50:23.550 --> 00:50:26.550 align:middle line:84% to take an original Gaussian-like boron 00:50:26.550 --> 00:50:29.910 align:middle line:84% profile, peaked right here, and then, in fact, 00:50:29.910 --> 00:50:33.190 align:middle line:84% move it in closer to the surface. 00:50:33.190 --> 00:50:35.550 align:middle line:84% In fact, if you just looked at these diffusion profiles 00:50:35.550 --> 00:50:37.717 align:middle line:84% and I didn't say anything about interstitial fluxes, 00:50:37.717 --> 00:50:39.900 align:middle line:84% I just gave you these three profiles and I said, 00:50:39.900 --> 00:50:43.140 align:middle line:84% OK, look, is that normal Gaussian Fickian diffusion? 00:50:43.140 --> 00:50:45.220 align:middle line:90% It can't be. 00:50:45.220 --> 00:50:48.960 align:middle line:84% I mean, for normal Fickian diffusion, 00:50:48.960 --> 00:50:52.260 align:middle line:84% what happens is as the profile gets broader, sure, 00:50:52.260 --> 00:50:54.480 align:middle line:90% it gets broader. 00:50:54.480 --> 00:50:57.060 align:middle line:84% Would you get more diffusion when 00:50:57.060 --> 00:50:59.940 align:middle line:84% it's driven by the flux of the dopant? 00:50:59.940 --> 00:51:01.913 align:middle line:90% But the peak doesn't change. 00:51:01.913 --> 00:51:04.080 align:middle line:84% The position of the peak in normal Fickian diffusion 00:51:04.080 --> 00:51:05.150 align:middle line:90% never changes. 00:51:05.150 --> 00:51:07.650 align:middle line:84% If you did your homework and you did the Gaussian diffusion, 00:51:07.650 --> 00:51:09.487 align:middle line:84% you found, sure, it goes down with time, 00:51:09.487 --> 00:51:11.070 align:middle line:84% but it's not like the peak shifts over 00:51:11.070 --> 00:51:12.112 align:middle line:90% to the left or the right. 00:51:12.112 --> 00:51:13.980 align:middle line:90% It's weird. 00:51:13.980 --> 00:51:16.290 align:middle line:84% If it's driven by its own concentration gradient, 00:51:16.290 --> 00:51:19.140 align:middle line:84% by definition, the peak doesn't shift. 00:51:19.140 --> 00:51:20.610 align:middle line:84% But here's an example of diffusion 00:51:20.610 --> 00:51:22.740 align:middle line:84% where the peak was actually shifting. 00:51:22.740 --> 00:51:25.470 align:middle line:84% The only way to explain that is some non-Fickian sort 00:51:25.470 --> 00:51:26.040 align:middle line:90% of phenomena. 00:51:26.040 --> 00:51:27.613 align:middle line:84% And in fact, people use this pairing, 00:51:27.613 --> 00:51:30.030 align:middle line:84% the fact that boron diffuses as a pair with interstitials, 00:51:30.030 --> 00:51:32.353 align:middle line:84% and the grades of interstitials was dragging the bond, 00:51:32.353 --> 00:51:34.020 align:middle line:84% and so much so that the peak of the barn 00:51:34.020 --> 00:51:36.190 align:middle line:90% was moving towards the surface. 00:51:36.190 --> 00:51:38.190 align:middle line:84% So we're going to talk about this in more detail 00:51:38.190 --> 00:51:41.070 align:middle line:84% when we do ion implant damage and how much interstitials 00:51:41.070 --> 00:51:42.360 align:middle line:90% are injected and all that. 00:51:42.360 --> 00:51:43.770 align:middle line:90% But it just gives you a-- 00:51:43.770 --> 00:51:46.272 align:middle line:84% I think it's a nice example of how the process engineers got 00:51:46.272 --> 00:51:48.480 align:middle line:84% together with a device people who couldn't figure out 00:51:48.480 --> 00:51:52.350 align:middle line:84% what the heck was going on and developed a process model that 00:51:52.350 --> 00:51:55.080 align:middle line:84% actually could explain pretty well the VT 00:51:55.080 --> 00:51:56.520 align:middle line:90% and predict what it should be. 00:51:56.520 --> 00:51:59.770 align:middle line:90% 00:51:59.770 --> 00:52:03.010 align:middle line:84% OK, so that's what I want to say now about this diffusion. 00:52:03.010 --> 00:52:05.020 align:middle line:84% I'm going to go on in slide 16 and talk 00:52:05.020 --> 00:52:07.150 align:middle line:84% about profile measurement techniques. 00:52:07.150 --> 00:52:10.150 align:middle line:84% I showed you some really old photographs 00:52:10.150 --> 00:52:13.480 align:middle line:84% from Plummer and Fahey in the late 80s. 00:52:13.480 --> 00:52:15.850 align:middle line:84% And I talked about beveling and staining. 00:52:15.850 --> 00:52:19.990 align:middle line:84% That's one way, but it was cheap and relatively simple, 00:52:19.990 --> 00:52:23.380 align:middle line:90% but not totally sophisticated. 00:52:23.380 --> 00:52:26.013 align:middle line:84% But let me give you some more examples. 00:52:26.013 --> 00:52:27.430 align:middle line:84% It's really critical-- you can see 00:52:27.430 --> 00:52:28.847 align:middle line:84% from the examples I've given you-- 00:52:28.847 --> 00:52:32.200 align:middle line:84% to have some method of measuring the dopant diffusion profile 00:52:32.200 --> 00:52:35.660 align:middle line:84% as it goes from the surface into depth in one dimension. 00:52:35.660 --> 00:52:37.720 align:middle line:84% And actually, if we're going to explain 00:52:37.720 --> 00:52:39.670 align:middle line:84% the reverse short channel effect like this, 00:52:39.670 --> 00:52:41.470 align:middle line:84% we really need a two-dimensional map 00:52:41.470 --> 00:52:43.180 align:middle line:90% of where all the dopants end up. 00:52:43.180 --> 00:52:45.460 align:middle line:90% That's not trivial. 00:52:45.460 --> 00:52:47.600 align:middle line:84% One dimension is pretty sophisticated. 00:52:47.600 --> 00:52:49.540 align:middle line:90% There are a number of methods. 00:52:49.540 --> 00:52:51.760 align:middle line:84% Probably one of the most sophisticated right 00:52:51.760 --> 00:52:54.130 align:middle line:84% now that you will use in your research or people 00:52:54.130 --> 00:52:58.420 align:middle line:84% use in the fab, or in semiconductor fabrication, 00:52:58.420 --> 00:52:59.972 align:middle line:84% is secondary ion mass spectrometry. 00:52:59.972 --> 00:53:02.180 align:middle line:84% I think we've talked a little bit about SIMS already. 00:53:02.180 --> 00:53:03.710 align:middle line:84% But that's probably the number one technique. 00:53:03.710 --> 00:53:05.047 align:middle line:90% And it continues to improve. 00:53:05.047 --> 00:53:07.130 align:middle line:84% It's improved dramatically over the last 10 years. 00:53:07.130 --> 00:53:10.790 align:middle line:84% As devices have shrunk, as junction depths have become 00:53:10.790 --> 00:53:12.830 align:middle line:84% narrower and narrower, they've found a way 00:53:12.830 --> 00:53:15.710 align:middle line:84% to make SIMS higher and higher resolution. 00:53:15.710 --> 00:53:17.990 align:middle line:84% SIMS only gives you the physical number 00:53:17.990 --> 00:53:20.460 align:middle line:84% of atoms of arsenic or boron per cubic centimeter. 00:53:20.460 --> 00:53:22.010 align:middle line:84% It's the physical chemical amount 00:53:22.010 --> 00:53:25.970 align:middle line:84% of atoms in the sample at any given point in depth. 00:53:25.970 --> 00:53:27.710 align:middle line:84% Sometimes you're interested in knowing 00:53:27.710 --> 00:53:30.800 align:middle line:84% not the number of arsenic atoms, but the number of electrons 00:53:30.800 --> 00:53:32.347 align:middle line:84% at that point per cubic centimeter. 00:53:32.347 --> 00:53:33.180 align:middle line:90% Those are different. 00:53:33.180 --> 00:53:35.750 align:middle line:84% Remember arsenic, you can put a lot of doping in, 00:53:35.750 --> 00:53:37.640 align:middle line:84% but not all of it may be electrically active. 00:53:37.640 --> 00:53:39.380 align:middle line:84% Or it may be compensated by the presence 00:53:39.380 --> 00:53:41.070 align:middle line:90% of boron or another dopant. 00:53:41.070 --> 00:53:43.160 align:middle line:84% So there are electrical techniques 00:53:43.160 --> 00:53:45.120 align:middle line:90% like spreading resistance. 00:53:45.120 --> 00:53:48.680 align:middle line:84% We'll talk about one-dimensional CV and differential vanderpol. 00:53:48.680 --> 00:53:50.420 align:middle line:84% These measure the carrier concentration. 00:53:50.420 --> 00:53:53.630 align:middle line:84% That's not the same as the dopant concentration. 00:53:53.630 --> 00:53:55.400 align:middle line:84% So 1D though, is reasonably sophisticated. 00:53:55.400 --> 00:53:58.047 align:middle line:84% Two dimension is still kind of tough. 00:53:58.047 --> 00:53:59.630 align:middle line:84% The methods are still being developed. 00:53:59.630 --> 00:54:03.410 align:middle line:84% They've certainly gotten beyond the junction staining methods. 00:54:03.410 --> 00:54:05.642 align:middle line:84% But they're generally indirect methods. 00:54:05.642 --> 00:54:07.100 align:middle line:84% They're more difficult. And this is 00:54:07.100 --> 00:54:09.058 align:middle line:84% an area with a lot of research, and development 00:54:09.058 --> 00:54:12.650 align:middle line:84% is taking place just to develop the metrology tools 00:54:12.650 --> 00:54:13.800 align:middle line:90% and techniques. 00:54:13.800 --> 00:54:16.550 align:middle line:84% Here's an example of some 2D techniques I'll show you. 00:54:16.550 --> 00:54:18.380 align:middle line:84% Cross-section transmission electron 00:54:18.380 --> 00:54:21.170 align:middle line:84% microscopy is a way of visualizing junctions 00:54:21.170 --> 00:54:22.310 align:middle line:90% with chemical etching. 00:54:22.310 --> 00:54:25.820 align:middle line:84% It's like the modern analog of the old Paul Fahey days, 00:54:25.820 --> 00:54:28.040 align:middle line:84% look in a microscope after you stain the junction. 00:54:28.040 --> 00:54:32.150 align:middle line:84% But it has resolutions that are a factor of 10 to 100 00:54:32.150 --> 00:54:34.730 align:middle line:90% higher resolution. 00:54:34.730 --> 00:54:37.770 align:middle line:84% The scanning probe microscopy, I'll talk about. 00:54:37.770 --> 00:54:39.380 align:middle line:84% And the last one is inverse modeling. 00:54:39.380 --> 00:54:44.240 align:middle line:84% This is kind of a funny one, but it actually 00:54:44.240 --> 00:54:47.570 align:middle line:84% can be very useful in complicated cases. 00:54:47.570 --> 00:54:49.580 align:middle line:84% What people do is they take a device. 00:54:49.580 --> 00:54:52.280 align:middle line:84% They take all its current voltage characteristics, 00:54:52.280 --> 00:54:54.170 align:middle line:84% its capacitance voltage characteristics. 00:54:54.170 --> 00:54:56.990 align:middle line:84% They put them all in one giant database and think about it 00:54:56.990 --> 00:54:59.960 align:middle line:84% and try to figure out, given all those characteristics, what 00:54:59.960 --> 00:55:02.030 align:middle line:90% must be the doping profiles. 00:55:02.030 --> 00:55:05.090 align:middle line:90% So it's an inverse technique. 00:55:05.090 --> 00:55:07.928 align:middle line:84% Unfortunately it relies on knowing really detailed 00:55:07.928 --> 00:55:10.220 align:middle line:84% electrical models because you're really extracting this 00:55:10.220 --> 00:55:11.595 align:middle line:84% all from electrical measurements. 00:55:11.595 --> 00:55:13.760 align:middle line:84% So it's not the same as doing SIMS or whatever, 00:55:13.760 --> 00:55:17.180 align:middle line:84% but when you get to small dimensions and two dimensions, 00:55:17.180 --> 00:55:20.990 align:middle line:84% it is a technique people try to use. 00:55:20.990 --> 00:55:24.110 align:middle line:84% OK, so let's look at slide 17 and talk a little bit 00:55:24.110 --> 00:55:24.770 align:middle line:90% about SIMS. 00:55:24.770 --> 00:55:26.180 align:middle line:84% I've already mentioned that in the past, 00:55:26.180 --> 00:55:28.222 align:middle line:84% but now we're going to talk about it specifically 00:55:28.222 --> 00:55:30.470 align:middle line:90% for depth profiling of dopants. 00:55:30.470 --> 00:55:31.880 align:middle line:90% There are two modes for SIMS. 00:55:31.880 --> 00:55:34.160 align:middle line:84% There's what's called dynamic or static. 00:55:34.160 --> 00:55:35.720 align:middle line:84% Dynamic is what you typically use. 00:55:35.720 --> 00:55:39.260 align:middle line:84% Dynamic means as the ion beam comes in and hits the surface, 00:55:39.260 --> 00:55:41.835 align:middle line:84% it's sputtering away a significant amount. 00:55:41.835 --> 00:55:44.210 align:middle line:84% And it continues to go deeper and deeper into the surface 00:55:44.210 --> 00:55:47.090 align:middle line:84% as a function of time, at some constant sputter rate, 00:55:47.090 --> 00:55:49.160 align:middle line:90% say 5 angstroms per second. 00:55:49.160 --> 00:55:50.570 align:middle line:90% It sputters away the surface. 00:55:50.570 --> 00:55:53.840 align:middle line:84% And it looks at the atoms that come off it. 00:55:53.840 --> 00:55:54.890 align:middle line:90% They get ionized. 00:55:54.890 --> 00:55:57.230 align:middle line:84% It puts them in a mass spec and it tells you 00:55:57.230 --> 00:55:59.300 align:middle line:84% at any given depth what's coming off. 00:55:59.300 --> 00:56:00.900 align:middle line:84% Static SIMS is a little different. 00:56:00.900 --> 00:56:04.490 align:middle line:84% The energy and the angle are adjusted of the primary ion beam 00:56:04.490 --> 00:56:07.760 align:middle line:84% such that it doesn't actually sputter very much. 00:56:07.760 --> 00:56:10.320 align:middle line:84% It's primarily just taking off what's at the surface. 00:56:10.320 --> 00:56:12.170 align:middle line:84% So it's very gentle and low energy. 00:56:12.170 --> 00:56:15.890 align:middle line:84% That's just for looking at just what atoms or molecules are 00:56:15.890 --> 00:56:17.670 align:middle line:90% at the surface. 00:56:17.670 --> 00:56:19.340 align:middle line:84% But for depth profiling of dopants, 00:56:19.340 --> 00:56:22.850 align:middle line:90% typically using dynamic SIMS. 00:56:22.850 --> 00:56:24.412 align:middle line:84% How does it work for depth profiling? 00:56:24.412 --> 00:56:26.870 align:middle line:84% Well, it's somewhat intuitive, and you should take yourself 00:56:26.870 --> 00:56:28.078 align:middle line:90% through these three cartoons. 00:56:28.078 --> 00:56:29.990 align:middle line:84% I think you'll have a better understanding. 00:56:29.990 --> 00:56:32.640 align:middle line:84% First case, I have a sample of silicon. 00:56:32.640 --> 00:56:35.240 align:middle line:84% It has some dopant A up at the top. 00:56:35.240 --> 00:56:37.400 align:middle line:84% In some depth, there's a layer of B. 00:56:37.400 --> 00:56:38.900 align:middle line:84% At this interface, let's say there's 00:56:38.900 --> 00:56:41.690 align:middle line:84% a spike of X. It's a different dopant 00:56:41.690 --> 00:56:44.840 align:middle line:84% or a different contaminant, maybe carbon or oxygen. 00:56:44.840 --> 00:56:47.180 align:middle line:84% And down here it's doped with C, whatever 00:56:47.180 --> 00:56:48.530 align:middle line:90% these three elements are. 00:56:48.530 --> 00:56:49.478 align:middle line:90% So what happens? 00:56:49.478 --> 00:56:51.770 align:middle line:84% As I'm sputtering, I'm bringing in my initial ion beam, 00:56:51.770 --> 00:56:53.390 align:middle line:90% it starts to create a crater. 00:56:53.390 --> 00:56:55.302 align:middle line:84% And it constantly is cratering the sample. 00:56:55.302 --> 00:56:57.260 align:middle line:84% And you're looking off-- as a function of time, 00:56:57.260 --> 00:56:59.720 align:middle line:84% you're looking at what atoms come off in a spectrometer. 00:56:59.720 --> 00:57:03.170 align:middle line:84% So if you look at the intensity as a function of time, 00:57:03.170 --> 00:57:06.050 align:middle line:84% the spectrometer can scan several different masses. 00:57:06.050 --> 00:57:08.930 align:middle line:84% Well, lo and behold, it finds for this time period, 00:57:08.930 --> 00:57:11.630 align:middle line:84% while it's sputtering through this cap region, 00:57:11.630 --> 00:57:15.540 align:middle line:84% it just detects dopant A. When it gets to this interface right 00:57:15.540 --> 00:57:17.820 align:middle line:84% here, it's starting to sputter off 00:57:17.820 --> 00:57:21.090 align:middle line:84% not only a little bit of dopant A, but a little bit of B, 00:57:21.090 --> 00:57:23.380 align:middle line:90% and also X pops in. 00:57:23.380 --> 00:57:25.890 align:middle line:84% And then as you continue to crater down 00:57:25.890 --> 00:57:29.670 align:middle line:84% and you get into this point, you're sputtering off B. 00:57:29.670 --> 00:57:32.670 align:middle line:84% So you're linearly in time sputtering through the sample. 00:57:32.670 --> 00:57:35.200 align:middle line:84% And you collect as a function of time the intensity. 00:57:35.200 --> 00:57:36.658 align:middle line:84% So that's what you get out of SIMS. 00:57:36.658 --> 00:57:39.190 align:middle line:84% You don't get doping concentration versus depth. 00:57:39.190 --> 00:57:40.200 align:middle line:90% You get the intensity. 00:57:40.200 --> 00:57:42.060 align:middle line:84% How many ions are coming off per second? 00:57:42.060 --> 00:57:43.770 align:middle line:84% It counts per second on a detector 00:57:43.770 --> 00:57:45.900 align:middle line:90% as a function of sputter time. 00:57:45.900 --> 00:57:49.230 align:middle line:84% So you have to somehow convert the x-axis of time into depth. 00:57:49.230 --> 00:57:51.300 align:middle line:84% Well, that seems obvious on this plot. 00:57:51.300 --> 00:57:55.205 align:middle line:84% If you know the sputter rate, you figure out-- 00:57:55.205 --> 00:57:56.580 align:middle line:84% let's say you measure at the end. 00:57:56.580 --> 00:57:58.920 align:middle line:84% You put it in a deck tack and you measure how deep 00:57:58.920 --> 00:58:00.300 align:middle line:90% the hole is, the crater is. 00:58:00.300 --> 00:58:02.010 align:middle line:84% And you assume it's linear in time. 00:58:02.010 --> 00:58:03.510 align:middle line:84% Well, then I can figure out how many 00:58:03.510 --> 00:58:05.010 align:middle line:90% angstroms came off per second. 00:58:05.010 --> 00:58:07.380 align:middle line:90% And I can convert time to depth. 00:58:07.380 --> 00:58:08.790 align:middle line:84% And that's a big assumption there 00:58:08.790 --> 00:58:10.950 align:middle line:84% because what you're assuming is that the sputtering rate is 00:58:10.950 --> 00:58:13.360 align:middle line:84% constant throughout the entire experiment and measurement. 00:58:13.360 --> 00:58:14.735 align:middle line:84% If you have different materials-- 00:58:14.735 --> 00:58:16.750 align:middle line:84% maybe you're going through oxides, silicon oxide 00:58:16.750 --> 00:58:19.180 align:middle line:84% and silicon, sputter rates differ in those materials. 00:58:19.180 --> 00:58:21.340 align:middle line:84% So you run into some distortion of profiles. 00:58:21.340 --> 00:58:22.810 align:middle line:90% So you have to be very careful. 00:58:22.810 --> 00:58:25.790 align:middle line:84% But it's an assumption pretty much that people need to make. 00:58:25.790 --> 00:58:28.270 align:middle line:84% So you convert the time axis to depth. 00:58:28.270 --> 00:58:33.730 align:middle line:84% Intensity, that's even trickier because it's just intensity. 00:58:33.730 --> 00:58:36.370 align:middle line:84% It has to be calibrated to convert that 00:58:36.370 --> 00:58:38.690 align:middle line:90% to atoms per cubic centimeter. 00:58:38.690 --> 00:58:42.080 align:middle line:84% So I'll say a few words about how that conversion is done. 00:58:42.080 --> 00:58:43.710 align:middle line:84% But let me first show you just a-- 00:58:43.710 --> 00:58:47.808 align:middle line:84% I took this off the Charles Evans website, www.cea.com. 00:58:47.808 --> 00:58:49.600 align:middle line:84% Again, they're a large commercial company-- 00:58:49.600 --> 00:58:51.590 align:middle line:84% they're probably the largest in the world-- 00:58:51.590 --> 00:58:53.920 align:middle line:84% international company that for a business 00:58:53.920 --> 00:58:56.540 align:middle line:90% does materials analysis. 00:58:56.540 --> 00:58:58.930 align:middle line:84% And one of their big thing that they focus on 00:58:58.930 --> 00:59:02.770 align:middle line:84% is dynamic SIMS, primarily-- well, for a lot of industries, 00:59:02.770 --> 00:59:06.730 align:middle line:84% primarily for semiconductor and magnetic industries. 00:59:06.730 --> 00:59:09.730 align:middle line:84% And this shows you just is a little thing that they 00:59:09.730 --> 00:59:13.480 align:middle line:84% like to advertise just to give you an idea of the detection 00:59:13.480 --> 00:59:16.720 align:middle line:84% limit, so the number of parts per billion 00:59:16.720 --> 00:59:19.840 align:middle line:84% or the percent of an impurity you can measure. 00:59:19.840 --> 00:59:21.790 align:middle line:84% It tends to be related, to a certain extent, 00:59:21.790 --> 00:59:23.330 align:middle line:90% to the analytical spot size. 00:59:23.330 --> 00:59:26.830 align:middle line:84% So how big is the little spot that you're looking at? 00:59:26.830 --> 00:59:29.440 align:middle line:84% And there are lots of different acronyms. 00:59:29.440 --> 00:59:30.790 align:middle line:90% And I apologize for all this. 00:59:30.790 --> 00:59:32.373 align:middle line:84% If you want to go on to their website, 00:59:32.373 --> 00:59:34.392 align:middle line:84% they have each one of these acronyms is defined. 00:59:34.392 --> 00:59:36.100 align:middle line:84% In fact, we've talked about some of them. 00:59:36.100 --> 00:59:37.820 align:middle line:84% We talked about earlier in the course, 00:59:37.820 --> 00:59:40.450 align:middle line:84% we talked about TXRF, total XY fluorescence. 00:59:40.450 --> 00:59:41.920 align:middle line:90% It measures about a centimeter. 00:59:41.920 --> 00:59:43.510 align:middle line:90% It only measures at the surface. 00:59:43.510 --> 00:59:47.830 align:middle line:84% And it's good for measuring in this range, 10 00:59:47.830 --> 00:59:50.110 align:middle line:90% to the 17th atoms per CC. 00:59:50.110 --> 00:59:53.530 align:middle line:84% The most sense-- as you go down to get to parts per trillion, 00:59:53.530 --> 00:59:55.923 align:middle line:84% the only technique that can get into that range, 00:59:55.923 --> 00:59:58.090 align:middle line:84% and it's only for certain elements, is dynamic SIMS. 00:59:58.090 --> 01:00:00.020 align:middle line:84% You see this little bubble is in this range. 01:00:00.020 --> 01:00:03.650 align:middle line:84% It has a spot size maybe 10 microns. 01:00:03.650 --> 01:00:06.760 align:middle line:84% Maybe closer to 100 microns is more typical these days. 01:00:06.760 --> 01:00:08.440 align:middle line:90% Maybe 100-micron spot size. 01:00:08.440 --> 01:00:11.560 align:middle line:84% But you can get elemental information 01:00:11.560 --> 01:00:14.590 align:middle line:84% down with dynamic SIMS down into the part per billion, 01:00:14.590 --> 01:00:18.760 align:middle line:84% and maybe even hundreds of parts per trillion kind of range. 01:00:18.760 --> 01:00:21.653 align:middle line:84% So it's what's used for profiling dopant atoms 01:00:21.653 --> 01:00:23.320 align:middle line:84% because remember, dopant atoms can exist 01:00:23.320 --> 01:00:25.390 align:middle line:90% at very low concentrations. 01:00:25.390 --> 01:00:26.620 align:middle line:90% 10 to the 14th. 01:00:26.620 --> 01:00:28.600 align:middle line:84% That could be a typical doping concentrations. 01:00:28.600 --> 01:00:31.017 align:middle line:84% And SIMS is the only thing that can measure that right now 01:00:31.017 --> 01:00:34.250 align:middle line:90% from a chemical point of view. 01:00:34.250 --> 01:00:39.880 align:middle line:84% So the primary ions that we typically use-- 01:00:39.880 --> 01:00:44.080 align:middle line:84% I'll just mention there are two primary ones or common ones. 01:00:44.080 --> 01:00:47.200 align:middle line:84% Oxygen is an ion coming in, has come in. 01:00:47.200 --> 01:00:51.580 align:middle line:84% People use oxygen because it enhances the secondary ions that 01:00:51.580 --> 01:00:52.180 align:middle line:90% come off. 01:00:52.180 --> 01:00:54.250 align:middle line:84% It enhances the production of positive. 01:00:54.250 --> 01:00:57.290 align:middle line:84% Oxygen tends to strip off electrons. 01:00:57.290 --> 01:00:59.170 align:middle line:90% So O2 plus. 01:00:59.170 --> 01:01:01.060 align:middle line:84% So it will enhance the ionization 01:01:01.060 --> 01:01:02.260 align:middle line:90% of the atoms coming off. 01:01:02.260 --> 01:01:04.750 align:middle line:84% Because remember, if the atoms come off as neutrals, 01:01:04.750 --> 01:01:06.913 align:middle line:84% you can't mass analyze them in a spectrometer. 01:01:06.913 --> 01:01:08.830 align:middle line:84% So you've got to get the atoms off the sample, 01:01:08.830 --> 01:01:11.110 align:middle line:84% and you have to hope that they come off ionized. 01:01:11.110 --> 01:01:14.930 align:middle line:84% And the way you increase the ionization yield, so to speak, 01:01:14.930 --> 01:01:18.700 align:middle line:84% is you use oxygen to increase the positive ion production. 01:01:18.700 --> 01:01:22.450 align:middle line:84% It's good for groups 1 through 3 if you're trying to measure-- 01:01:22.450 --> 01:01:26.260 align:middle line:84% and the transition metals in silicon. 01:01:26.260 --> 01:01:27.910 align:middle line:84% For instance, for boron, typically 01:01:27.910 --> 01:01:30.580 align:middle line:84% if you're profiling for boron, you use O2 plus beam. 01:01:30.580 --> 01:01:33.260 align:middle line:84% Cesium plus, on the other hand, is just the opposite. 01:01:33.260 --> 01:01:35.420 align:middle line:84% It enhances the negative ion production. 01:01:35.420 --> 01:01:40.750 align:middle line:84% So it's used for groups 4 through 7. 01:01:40.750 --> 01:01:43.810 align:middle line:84% And these are good electron acceptors, 01:01:43.810 --> 01:01:45.710 align:middle line:84% and they form negative secondary ions. 01:01:45.710 --> 01:01:48.458 align:middle line:84% So arsenic, you would typically use cesium primary beam. 01:01:48.458 --> 01:01:50.750 align:middle line:84% And they have machines set up for these two different-- 01:01:50.750 --> 01:01:52.417 align:middle line:84% so you use a different machine depending 01:01:52.417 --> 01:01:53.680 align:middle line:90% on what your profiling yield. 01:01:53.680 --> 01:01:56.210 align:middle line:84% Now, the ion yields, when I mean the ion yield-- 01:01:56.210 --> 01:01:59.530 align:middle line:84% so that's the number of ionized species 01:01:59.530 --> 01:02:02.450 align:middle line:84% that are coming off of some element, 01:02:02.450 --> 01:02:04.930 align:middle line:84% say arsenic, compared to the total amount of sputtering 01:02:04.930 --> 01:02:06.610 align:middle line:90% of the silicon, that yield. 01:02:06.610 --> 01:02:08.720 align:middle line:84% That depends on the matrix material. 01:02:08.720 --> 01:02:12.940 align:middle line:84% So if you have arsenic at the same concentration in oxide 01:02:12.940 --> 01:02:15.160 align:middle line:84% and in silicon at the identical concentration, 01:02:15.160 --> 01:02:17.540 align:middle line:84% the ionization yield will be different. 01:02:17.540 --> 01:02:19.572 align:middle line:84% So it will come off with different intensities. 01:02:19.572 --> 01:02:21.030 align:middle line:84% So that's called the matrix effect. 01:02:21.030 --> 01:02:22.238 align:middle line:90% So that's a bit of a problem. 01:02:22.238 --> 01:02:27.040 align:middle line:84% So the measured intensity has to be measured 01:02:27.040 --> 01:02:29.380 align:middle line:84% on a test sample that's calibrated where 01:02:29.380 --> 01:02:30.610 align:middle line:90% you know the concentration. 01:02:30.610 --> 01:02:32.950 align:middle line:84% And you compare that intensity on the same day 01:02:32.950 --> 01:02:35.990 align:middle line:84% to whatever's coming off of your unknown sample. 01:02:35.990 --> 01:02:38.260 align:middle line:84% And so it's always calibrated to a known sample. 01:02:38.260 --> 01:02:40.840 align:middle line:84% And that's one of the big drawbacks of SIMS. 01:02:40.840 --> 01:02:41.632 align:middle line:90% You need standards. 01:02:41.632 --> 01:02:43.423 align:middle line:84% It's not an absolute measurement technique. 01:02:43.423 --> 01:02:44.410 align:middle line:90% It's always relative. 01:02:44.410 --> 01:02:47.880 align:middle line:84% It's only as good as your standards. 01:02:47.880 --> 01:02:51.530 align:middle line:84% And in fact, on slide 21, I have an example of some actual SIMS 01:02:51.530 --> 01:02:54.740 align:middle line:90% data and how people quantify. 01:02:54.740 --> 01:02:57.170 align:middle line:84% The x-axis we talked about, quantifying is not too bad. 01:02:57.170 --> 01:02:58.310 align:middle line:90% You use a deck tack. 01:02:58.310 --> 01:02:59.800 align:middle line:84% You assume constant sputter rate. 01:02:59.800 --> 01:03:00.795 align:middle line:90% You cross your fingers. 01:03:00.795 --> 01:03:02.420 align:middle line:84% And that's how you get the depth scale. 01:03:02.420 --> 01:03:05.120 align:middle line:84% How do I get the y scale, which was originally intensity? 01:03:05.120 --> 01:03:07.370 align:middle line:84% I need to convert that to concentration. 01:03:07.370 --> 01:03:09.250 align:middle line:84% Well, typically what people do is 01:03:09.250 --> 01:03:11.000 align:middle line:84% they take a sample that was ion implanted. 01:03:11.000 --> 01:03:12.500 align:middle line:84% And again, we haven't talked about implantation. 01:03:12.500 --> 01:03:13.580 align:middle line:90% That's next lecture. 01:03:13.580 --> 01:03:17.420 align:middle line:84% Implantation is electrical means of very accurately controlling 01:03:17.420 --> 01:03:21.020 align:middle line:84% the integrated dose, the integral under the curve, 01:03:21.020 --> 01:03:25.100 align:middle line:84% of an element that you implant into a sample. 01:03:25.100 --> 01:03:27.230 align:middle line:84% And that accuracy of that control 01:03:27.230 --> 01:03:29.780 align:middle line:84% makes the implanter a very good way 01:03:29.780 --> 01:03:32.420 align:middle line:84% of generating SIM standards because the implanter can 01:03:32.420 --> 01:03:36.590 align:middle line:84% exactly control the total number of atoms per square centimeter 01:03:36.590 --> 01:03:37.850 align:middle line:90% that go into the sample. 01:03:37.850 --> 01:03:40.010 align:middle line:84% And in fact, this was a phosphorus implant 01:03:40.010 --> 01:03:44.000 align:middle line:84% at a total dose of 1 times 10 to the 14th phosphorus 01:03:44.000 --> 01:03:45.120 align:middle line:90% per square centimeter. 01:03:45.120 --> 01:03:46.760 align:middle line:90% So that's given as a known. 01:03:46.760 --> 01:03:51.430 align:middle line:84% So once we know that, since we know this area under the curve, 01:03:51.430 --> 01:03:54.280 align:middle line:84% we can then convert intensity coming off 01:03:54.280 --> 01:03:58.000 align:middle line:84% on that given day to a certain concentration of phosphorus. 01:03:58.000 --> 01:04:00.170 align:middle line:84% So every time we want to measure an unknown-- 01:04:00.170 --> 01:04:02.230 align:middle line:84% so the right-hand sample was unknown. 01:04:02.230 --> 01:04:04.385 align:middle line:84% The left-hand sample, the concentration 01:04:04.385 --> 01:04:06.010 align:middle line:84% was known because it was ion implanted. 01:04:06.010 --> 01:04:08.120 align:middle line:90% So you use a known dose. 01:04:08.120 --> 01:04:12.610 align:middle line:84% So from this integrated ion implant dose, 01:04:12.610 --> 01:04:14.590 align:middle line:84% I can generate a sensitivity factor 01:04:14.590 --> 01:04:17.770 align:middle line:84% that enables me to convert from intensity coming off 01:04:17.770 --> 01:04:21.140 align:middle line:84% to a phosphorus concentration on the unknown sample. 01:04:21.140 --> 01:04:24.820 align:middle line:84% And so this is what I get, for example, on an unknown sample. 01:04:24.820 --> 01:04:28.900 align:middle line:84% But you always need a standard which you trust in order 01:04:28.900 --> 01:04:29.790 align:middle line:90% to compare it to. 01:04:29.790 --> 01:04:31.540 align:middle line:84% And it has to be compared on that same day 01:04:31.540 --> 01:04:34.180 align:middle line:84% because the SIMS machines, their calibrations 01:04:34.180 --> 01:04:35.750 align:middle line:90% can be changing from day to day. 01:04:35.750 --> 01:04:38.110 align:middle line:84% And it has to be, in fact, a sample hopefully 01:04:38.110 --> 01:04:41.050 align:middle line:84% that has roughly the same total amount of peak phosphorus as 01:04:41.050 --> 01:04:41.770 align:middle line:90% in your unknown. 01:04:41.770 --> 01:04:44.020 align:middle line:84% If it was dramatically different, [? MIP ?] effects. 01:04:44.020 --> 01:04:45.603 align:middle line:84% And it should be in the same material. 01:04:45.603 --> 01:04:48.580 align:middle line:84% Notice this was phosphorus in silicon in a known sample. 01:04:48.580 --> 01:04:50.960 align:middle line:84% This is phosphorus in silicon in an unknown sample. 01:04:50.960 --> 01:04:52.918 align:middle line:84% You wouldn't want to use phosphorus and silicon 01:04:52.918 --> 01:04:56.240 align:middle line:84% dioxide to calibrate this because the matrix effect would 01:04:56.240 --> 01:04:58.980 align:middle line:90% kill you. 01:04:58.980 --> 01:05:00.870 align:middle line:84% OK, so that's an example of a practical idea 01:05:00.870 --> 01:05:03.750 align:middle line:90% of how the SIMS actually works. 01:05:03.750 --> 01:05:05.070 align:middle line:90% These are some considerations. 01:05:05.070 --> 01:05:07.278 align:middle line:84% People are very concerned about the depth resolution. 01:05:07.278 --> 01:05:07.950 align:middle line:90% What do I mean? 01:05:07.950 --> 01:05:10.075 align:middle line:84% Actually, let me go back for a minute for the depth 01:05:10.075 --> 01:05:14.490 align:middle line:84% resolution-- is let's say this actual sample is really a box. 01:05:14.490 --> 01:05:16.590 align:middle line:84% Let's say it's really a box-like profile. 01:05:16.590 --> 01:05:19.020 align:middle line:84% What SIMS does to it is it smears it out a little. 01:05:19.020 --> 01:05:21.360 align:middle line:84% The edges are not perfectly straight up and down. 01:05:21.360 --> 01:05:24.240 align:middle line:84% They have a little bit of exponential decay 01:05:24.240 --> 01:05:25.920 align:middle line:90% on the front and the back. 01:05:25.920 --> 01:05:27.060 align:middle line:90% How much of that is real? 01:05:27.060 --> 01:05:29.220 align:middle line:84% Is the phosphorus really decaying exponentially? 01:05:29.220 --> 01:05:32.340 align:middle line:84% Or is it really a box-like profile? 01:05:32.340 --> 01:05:34.980 align:middle line:84% What effects determine how well I can 01:05:34.980 --> 01:05:41.130 align:middle line:90% resolve the profile in depth? 01:05:41.130 --> 01:05:43.250 align:middle line:84% So these are some considerations. 01:05:43.250 --> 01:05:45.422 align:middle line:84% The depth resolution depends on the element 01:05:45.422 --> 01:05:47.630 align:middle line:84% you're profiling-- phosphorous or boron or whatever-- 01:05:47.630 --> 01:05:51.350 align:middle line:84% and the matrix that it's in, because after all, the impact 01:05:51.350 --> 01:05:53.690 align:middle line:84% conditions-- remember, these primary cesium ions 01:05:53.690 --> 01:05:54.530 align:middle line:90% are coming in. 01:05:54.530 --> 01:05:57.500 align:middle line:84% They're hitting the phosphorous or the arsenic, 01:05:57.500 --> 01:06:00.060 align:middle line:84% and they're imparting energy to it. 01:06:00.060 --> 01:06:02.450 align:middle line:84% So of course, they can knock that arsenic or phosphorus 01:06:02.450 --> 01:06:03.260 align:middle line:90% in a little deeper. 01:06:03.260 --> 01:06:05.720 align:middle line:84% And of course they could smear out a profile. 01:06:05.720 --> 01:06:08.780 align:middle line:84% So you try to change it so you can minimize the amount 01:06:08.780 --> 01:06:11.420 align:middle line:90% of ion damage or ion smearing. 01:06:11.420 --> 01:06:15.260 align:middle line:84% For sputter depth, the deeper you go into that and the deeper 01:06:15.260 --> 01:06:17.870 align:middle line:84% you make your crater, the more the bottom of the crater gets 01:06:17.870 --> 01:06:20.780 align:middle line:84% roughened just by the sputtering process as a random process. 01:06:20.780 --> 01:06:23.450 align:middle line:84% When you have a rough bottom to your crater, well, 01:06:23.450 --> 01:06:26.360 align:middle line:84% you're pulling atoms off from slightly different depths 01:06:26.360 --> 01:06:27.840 align:middle line:90% at that point in space. 01:06:27.840 --> 01:06:30.780 align:middle line:84% So the deeper you sputter, the worse 01:06:30.780 --> 01:06:32.030 align:middle line:90% the depth resolution for SIMS. 01:06:32.030 --> 01:06:34.000 align:middle line:84% So if you want to measure a sharp profile, 01:06:34.000 --> 01:06:35.750 align:middle line:84% try to put it near the surface, and you'll 01:06:35.750 --> 01:06:37.730 align:middle line:84% get much more box-like profile than putting 01:06:37.730 --> 01:06:41.130 align:middle line:84% it 1 or 2 microns in where the sputtering process has roughened 01:06:41.130 --> 01:06:43.620 align:middle line:90% the bottom of your crater. 01:06:43.620 --> 01:06:46.350 align:middle line:84% So what people have improved these days 01:06:46.350 --> 01:06:48.990 align:middle line:84% to try to get sputtering processes that 01:06:48.990 --> 01:06:52.080 align:middle line:84% are as smooth as possible by rotating the sample, 01:06:52.080 --> 01:06:55.230 align:middle line:84% and rastering the beam, and trying to make it really 01:06:55.230 --> 01:06:59.460 align:middle line:84% a nice, flat, perfectly shaped crater bottom. 01:06:59.460 --> 01:07:02.040 align:middle line:84% So they've done a lot of techniques. 01:07:02.040 --> 01:07:04.380 align:middle line:84% Also, these days they have ultra low-energy SIMS has 01:07:04.380 --> 01:07:06.270 align:middle line:84% been developed where the incoming beam has 01:07:06.270 --> 01:07:10.380 align:middle line:84% such a low energy, it doesn't perturb the profiles too much. 01:07:10.380 --> 01:07:12.750 align:middle line:84% And that's an important low-energy SIMS 01:07:12.750 --> 01:07:15.630 align:middle line:84% that's been developed in the last 10 years. 01:07:15.630 --> 01:07:17.130 align:middle line:84% OK, so that's chemical measurements. 01:07:17.130 --> 01:07:18.300 align:middle line:90% How about electrical? 01:07:18.300 --> 01:07:21.825 align:middle line:84% Well, remember I talked about beveling and staining? 01:07:21.825 --> 01:07:23.700 align:middle line:84% Well, you don't have to just bevel and stain. 01:07:23.700 --> 01:07:26.033 align:middle line:84% You can actually bevel, just like I talked about before. 01:07:26.033 --> 01:07:30.330 align:middle line:84% You create this surface that's beveled at a certain angle. 01:07:30.330 --> 01:07:33.130 align:middle line:84% And instead of staining, you take two little probes 01:07:33.130 --> 01:07:35.670 align:middle line:84% and you measure the resistance between those two probes. 01:07:35.670 --> 01:07:38.490 align:middle line:84% You flow a current and measure the voltage drop 01:07:38.490 --> 01:07:42.140 align:middle line:84% as a function of lateral distance along the bevel. 01:07:42.140 --> 01:07:44.730 align:middle line:84% As you move along the bevel laterally, of course 01:07:44.730 --> 01:07:45.980 align:middle line:90% you're also moving in depth. 01:07:45.980 --> 01:07:49.070 align:middle line:84% So you're essentially spreading out by the cosine theta. 01:07:49.070 --> 01:07:50.930 align:middle line:84% You're spreading out-- or the sine theta. 01:07:50.930 --> 01:07:52.430 align:middle line:84% You're spreading out that profile. 01:07:52.430 --> 01:07:53.870 align:middle line:90% So you can move laterally. 01:07:53.870 --> 01:07:56.300 align:middle line:84% And literally, it takes the probes on a machine, 01:07:56.300 --> 01:07:59.300 align:middle line:84% moves it laterally by certain steps. 01:07:59.300 --> 01:08:03.410 align:middle line:84% And you can convert this, then, to a resistivity, or resistance 01:08:03.410 --> 01:08:05.180 align:middle line:90% plot, as a function of depth. 01:08:05.180 --> 01:08:11.190 align:middle line:84% And you convert resistivity into carrier concentration. 01:08:11.190 --> 01:08:13.550 align:middle line:84% So this measures the doping concentration 01:08:13.550 --> 01:08:15.770 align:middle line:90% versus depth, not the dopant. 01:08:15.770 --> 01:08:19.069 align:middle line:84% Doping refers to the electrons or holes. 01:08:19.069 --> 01:08:21.770 align:middle line:84% So it's complementary to SIMS, which provides 01:08:21.770 --> 01:08:24.649 align:middle line:90% the chemical information. 01:08:24.649 --> 01:08:27.109 align:middle line:84% The depth resolution is not nearly as good. 01:08:27.109 --> 01:08:29.062 align:middle line:84% I mean, with spreading resistance, 01:08:29.062 --> 01:08:30.770 align:middle line:84% you're lucky to measure a junction that's 01:08:30.770 --> 01:08:32.180 align:middle line:90% 1,000 angstroms deep. 01:08:32.180 --> 01:08:34.140 align:middle line:84% Typically with SIMS, you can measure 01:08:34.140 --> 01:08:36.800 align:middle line:90% 100-angstrom deep junctions. 01:08:36.800 --> 01:08:39.140 align:middle line:84% And the big problem is, again, it needs some standards. 01:08:39.140 --> 01:08:42.500 align:middle line:84% You need to know how to convert how from resistivity to carrier 01:08:42.500 --> 01:08:43.290 align:middle line:90% concentration. 01:08:43.290 --> 01:08:44.720 align:middle line:84% So you need to know these curves. 01:08:44.720 --> 01:08:47.630 align:middle line:84% There's some famous curves on the Silicon website. 01:08:47.630 --> 01:08:49.939 align:middle line:84% This company Silicon does spreading resistance 01:08:49.939 --> 01:08:51.213 align:middle line:90% for commercial purposes. 01:08:51.213 --> 01:08:52.880 align:middle line:84% You can go onto there, and they show you 01:08:52.880 --> 01:08:53.922 align:middle line:90% their calibration curves. 01:08:53.922 --> 01:08:55.937 align:middle line:84% But if you have a material other than silicon, 01:08:55.937 --> 01:08:57.979 align:middle line:84% single crystal-- let's say you have polysilicon-- 01:08:57.979 --> 01:09:01.340 align:middle line:84% the relationship between carrier concentration N 01:09:01.340 --> 01:09:04.825 align:middle line:84% and the dopant concentration is not very well understood. 01:09:04.825 --> 01:09:06.200 align:middle line:84% Or if you have silicon germanium, 01:09:06.200 --> 01:09:07.399 align:middle line:90% there are no standards. 01:09:07.399 --> 01:09:10.250 align:middle line:84% So spreading resistance is OK, but it 01:09:10.250 --> 01:09:14.300 align:middle line:90% does have some limitations. 01:09:14.300 --> 01:09:16.180 align:middle line:84% I won't go through this in any great detail. 01:09:16.180 --> 01:09:17.816 align:middle line:90% This is shown on slide 25. 01:09:17.816 --> 01:09:18.899 align:middle line:90% I'm referring you to the-- 01:09:18.899 --> 01:09:20.950 align:middle line:84% I pulled this off the Silicon website. 01:09:20.950 --> 01:09:24.370 align:middle line:84% But in fact, even in the most perfect case, 01:09:24.370 --> 01:09:28.439 align:middle line:84% you can try to correct the data for artifacts 01:09:28.439 --> 01:09:31.890 align:middle line:84% by solving Poisson's equation to account for things like space 01:09:31.890 --> 01:09:34.380 align:middle line:84% charge layers where you have an N and a P region meeting 01:09:34.380 --> 01:09:35.430 align:middle line:90% and things like that. 01:09:35.430 --> 01:09:36.930 align:middle line:84% There's a lot of literature on this. 01:09:36.930 --> 01:09:40.080 align:middle line:84% But you can see it's measuring junctions 01:09:40.080 --> 01:09:43.920 align:middle line:84% that are pretty deep, microns deep, not hundreds of angstroms. 01:09:43.920 --> 01:09:46.380 align:middle line:84% But it can be used to measure the well profile 01:09:46.380 --> 01:09:48.330 align:middle line:90% and things like that. 01:09:48.330 --> 01:09:51.550 align:middle line:84% Slide 26 actually has kind of an interesting technique. 01:09:51.550 --> 01:09:55.110 align:middle line:84% It's not quantitative, but if you want to talk about 2D, 01:09:55.110 --> 01:09:56.260 align:middle line:90% it can work. 01:09:56.260 --> 01:09:57.900 align:middle line:90% This is a cross-section TEM. 01:09:57.900 --> 01:10:02.520 align:middle line:84% So you're taking a sample from a silicon MOSFET 01:10:02.520 --> 01:10:04.470 align:middle line:84% and you've cut it and cross-sectioned it. 01:10:04.470 --> 01:10:07.260 align:middle line:84% And you've made that thickness of that specimen only about 01:10:07.260 --> 01:10:09.363 align:middle line:90% 2,000 angstroms thick. 01:10:09.363 --> 01:10:12.030 align:middle line:84% There's special ways of cutting through and cross-sectioning it. 01:10:12.030 --> 01:10:13.410 align:middle line:84% And then you send electrons through 01:10:13.410 --> 01:10:15.202 align:middle line:84% and you look at their diffraction patterns. 01:10:15.202 --> 01:10:16.800 align:middle line:84% So you can actually image the gate, 01:10:16.800 --> 01:10:19.200 align:middle line:90% the gate oxide, the silicon. 01:10:19.200 --> 01:10:20.947 align:middle line:84% And interestingly, what people have done 01:10:20.947 --> 01:10:23.280 align:middle line:84% is you take the specimen after you've cross-sectioned it 01:10:23.280 --> 01:10:25.110 align:middle line:90% and you dump it in some acid. 01:10:25.110 --> 01:10:27.960 align:middle line:84% And it turns out the acid etches much more rapidly 01:10:27.960 --> 01:10:30.150 align:middle line:84% regions that are very heavily N-type. 01:10:30.150 --> 01:10:33.090 align:middle line:84% So when you etch that region, you change the thickness 01:10:33.090 --> 01:10:35.610 align:middle line:84% of the sample and you change the transparency of the sample 01:10:35.610 --> 01:10:37.030 align:middle line:90% to electron beams. 01:10:37.030 --> 01:10:40.080 align:middle line:84% So where it's very heavily doped, it appears very light. 01:10:40.080 --> 01:10:42.690 align:middle line:84% The electrons don't-- they go right through. 01:10:42.690 --> 01:10:46.980 align:middle line:84% So the contrast on this gives you 01:10:46.980 --> 01:10:48.360 align:middle line:90% good qualitative information. 01:10:48.360 --> 01:10:50.610 align:middle line:84% And people believe that it delineates 01:10:50.610 --> 01:10:53.760 align:middle line:84% this line, this dark line, corresponds to a concentration 01:10:53.760 --> 01:10:55.020 align:middle line:90% of about 10 to the 19th. 01:10:55.020 --> 01:10:58.140 align:middle line:84% So it gives you an idea of where the edge of the source and drain 01:10:58.140 --> 01:10:59.730 align:middle line:90% might be, but it's qualitative. 01:10:59.730 --> 01:11:03.290 align:middle line:90% And it's very time-consuming. 01:11:03.290 --> 01:11:06.490 align:middle line:84% There's another 2D technique, again, based on beveling. 01:11:06.490 --> 01:11:08.530 align:middle line:84% Again, we'll go back to the same old bevel idea. 01:11:08.530 --> 01:11:10.660 align:middle line:84% Here's a MOSFET with a source and drain. 01:11:10.660 --> 01:11:15.190 align:middle line:84% People actually take an atomic force microscope 01:11:15.190 --> 01:11:18.190 align:middle line:90% with AFM cantilever, little tip. 01:11:18.190 --> 01:11:21.730 align:middle line:84% And they measure where they are across the sample. 01:11:21.730 --> 01:11:25.250 align:middle line:84% And they measure at each point, a CV curve. 01:11:25.250 --> 01:11:28.360 align:middle line:84% So it's like very locally doing a capacitance voltage 01:11:28.360 --> 01:11:30.340 align:middle line:84% measurement where the tip corresponds 01:11:30.340 --> 01:11:34.120 align:middle line:90% to the metal point of the CV. 01:11:34.120 --> 01:11:37.390 align:middle line:84% And the backside contact corresponds to the back. 01:11:37.390 --> 01:11:40.360 align:middle line:84% And you're actually measuring-- you know from CV-- remember, 01:11:40.360 --> 01:11:42.100 align:middle line:90% we talked about CV on dots. 01:11:42.100 --> 01:11:44.530 align:middle line:84% If I put a dot over a uniformly doped sample, 01:11:44.530 --> 01:11:47.980 align:middle line:84% you can extract from the CV the local doping concentration. 01:11:47.980 --> 01:11:50.290 align:middle line:84% Well, they're doing it, but here on a very small scale 01:11:50.290 --> 01:11:52.220 align:middle line:90% with a very small AFM tip. 01:11:52.220 --> 01:11:55.300 align:middle line:84% So this is scanning capacitance microscopy. 01:11:55.300 --> 01:11:59.620 align:middle line:84% It's very tricky, though, the spatial resolution issues, 01:11:59.620 --> 01:12:01.060 align:middle line:90% limited by the probe size. 01:12:01.060 --> 01:12:02.600 align:middle line:90% The tip is only so small. 01:12:02.600 --> 01:12:04.830 align:middle line:84% And then it has fringing electric fields. 01:12:04.830 --> 01:12:06.620 align:middle line:84% So the actual area of the capacitor 01:12:06.620 --> 01:12:09.470 align:middle line:84% that you're creating with the tip is somewhat uncertain. 01:12:09.470 --> 01:12:14.000 align:middle line:84% It has to be modeled with sophisticated ENM modeling. 01:12:14.000 --> 01:12:15.860 align:middle line:84% But just to give you an idea, again, this 01:12:15.860 --> 01:12:18.830 align:middle line:84% is the website if you want to go there, if you're interested. 01:12:18.830 --> 01:12:22.880 align:middle line:84% Basically how it works on an N-type CV curve, 01:12:22.880 --> 01:12:27.320 align:middle line:84% basically it takes DC by DV, the derivative of the capacitor 01:12:27.320 --> 01:12:28.820 align:middle line:90% with respect to the voltage. 01:12:28.820 --> 01:12:32.090 align:middle line:84% And you can relate that locally to the carrier concentration. 01:12:32.090 --> 01:12:39.230 align:middle line:84% Very similar to what you do in 1D CV, but now over a surface. 01:12:39.230 --> 01:12:41.780 align:middle line:84% And in fact, here's a beveled junction 01:12:41.780 --> 01:12:45.000 align:middle line:84% where this region corresponds to phosphorus. 01:12:45.000 --> 01:12:47.370 align:middle line:84% This is the scanning capacitance microscopy image. 01:12:47.370 --> 01:12:48.590 align:middle line:90% So this is very high doped. 01:12:48.590 --> 01:12:51.920 align:middle line:84% This is the junction region in p-type silicon 01:12:51.920 --> 01:12:52.970 align:middle line:90% near the edge of a mask. 01:12:52.970 --> 01:12:53.750 align:middle line:90% So here's a mask. 01:12:53.750 --> 01:12:55.250 align:middle line:90% There's no phosphorus over here. 01:12:55.250 --> 01:12:56.690 align:middle line:90% It's lightly doped. 01:12:56.690 --> 01:12:58.100 align:middle line:90% So it's tricky. 01:12:58.100 --> 01:12:59.600 align:middle line:84% It's still under development, but it 01:12:59.600 --> 01:13:07.370 align:middle line:84% is kind of a popular topic for modern metrology. 01:13:07.370 --> 01:13:09.210 align:middle line:84% So let me just summarize about techniques 01:13:09.210 --> 01:13:10.210 align:middle line:90% for profile measurement. 01:13:10.210 --> 01:13:12.400 align:middle line:84% We talked about SIMS, the most popular. 01:13:12.400 --> 01:13:15.280 align:middle line:84% It does very good 1D profiles in depth, 01:13:15.280 --> 01:13:17.980 align:middle line:84% excellent as the best sensitivity of any technique 01:13:17.980 --> 01:13:20.110 align:middle line:90% to the dopant concentration. 01:13:20.110 --> 01:13:22.192 align:middle line:90% Excellent depth resolution. 01:13:22.192 --> 01:13:23.650 align:middle line:84% Methods are still under development 01:13:23.650 --> 01:13:24.700 align:middle line:90% trying to improve it. 01:13:24.700 --> 01:13:27.070 align:middle line:84% The very near surface region is troublesome, 01:13:27.070 --> 01:13:29.232 align:middle line:84% but there have been recent improvements. 01:13:29.232 --> 01:13:30.940 align:middle line:84% You have to watch out for matrix effects. 01:13:30.940 --> 01:13:34.120 align:middle line:84% If you're profiling a dopant in oxide or nitride or silicon, 01:13:34.120 --> 01:13:36.160 align:middle line:84% the ion yield varies dramatically, 01:13:36.160 --> 01:13:37.990 align:middle line:90% it has to be calibrated. 01:13:37.990 --> 01:13:40.728 align:middle line:84% Spreading resistance is only generally mostly 01:13:40.728 --> 01:13:42.520 align:middle line:84% one-dimensional, although people are trying 01:13:42.520 --> 01:13:45.970 align:middle line:90% to do it two-dimensional. 01:13:45.970 --> 01:13:49.690 align:middle line:84% But it measures carriers, so the active electrons and holes. 01:13:49.690 --> 01:13:51.190 align:middle line:90% Pretty good sensitivity. 01:13:51.190 --> 01:13:53.590 align:middle line:90% Depth resolution is not great. 01:13:53.590 --> 01:13:55.910 align:middle line:84% And it's hard to do shallow junctions. 01:13:55.910 --> 01:13:57.910 align:middle line:84% And you need to do some electromagnetic modeling 01:13:57.910 --> 01:13:59.320 align:middle line:90% to really understand it. 01:13:59.320 --> 01:14:01.810 align:middle line:84% These newer techniques are kind of exciting. 01:14:01.810 --> 01:14:03.610 align:middle line:84% These two-dimensional scanning capacitance 01:14:03.610 --> 01:14:05.620 align:middle line:84% and scanning resistance microscopy 01:14:05.620 --> 01:14:10.420 align:middle line:84% with using small probes are very interesting. 01:14:10.420 --> 01:14:13.220 align:middle line:84% They do rely on beveling, but there's 01:14:13.220 --> 01:14:15.470 align:middle line:84% a lot of advanced models for the process 01:14:15.470 --> 01:14:17.792 align:middle line:84% itself that are being developed in R&D today 01:14:17.792 --> 01:14:19.250 align:middle line:84% to try to come up with a better way 01:14:19.250 --> 01:14:23.000 align:middle line:84% to get quantitative two-dimensional dopant profile 01:14:23.000 --> 01:14:24.900 align:middle line:90% measurements. 01:14:24.900 --> 01:14:27.380 align:middle line:84% So summarizing on what we've talked about so 01:14:27.380 --> 01:14:30.470 align:middle line:84% far on dopant diffusion, we said that they 01:14:30.470 --> 01:14:32.720 align:middle line:84% diffuse by interacting with point defects, vacancies, 01:14:32.720 --> 01:14:34.850 align:middle line:90% and interstitials. 01:14:34.850 --> 01:14:37.100 align:middle line:84% The diffusivity is proportional to the concentration 01:14:37.100 --> 01:14:39.530 align:middle line:90% of those point defects. 01:14:39.530 --> 01:14:41.180 align:middle line:84% These point defect concentrations 01:14:41.180 --> 01:14:43.920 align:middle line:84% go up exponentially as I increase the temperature. 01:14:43.920 --> 01:14:47.480 align:middle line:84% And so the diffusivity goes up exponentially. 01:14:47.480 --> 01:14:50.600 align:middle line:84% They can also be changed by things other than temperature-- 01:14:50.600 --> 01:14:53.330 align:middle line:84% the local Fermi level-- the local doping concentration, that 01:14:53.330 --> 01:14:54.110 align:middle line:90% is. 01:14:54.110 --> 01:14:56.690 align:middle line:84% Ion implant damage, as we'll see in the next chapter, 01:14:56.690 --> 01:14:58.790 align:middle line:84% can change the point defect concentration. 01:14:58.790 --> 01:15:02.090 align:middle line:84% Surface processes like oxidation and nitrogen change it. 01:15:02.090 --> 01:15:05.370 align:middle line:84% All of these affect the effect of diffusivity. 01:15:05.370 --> 01:15:08.090 align:middle line:84% So the dopant diffusivity can vary in space. 01:15:08.090 --> 01:15:09.740 align:middle line:90% It can vary in time. 01:15:09.740 --> 01:15:13.040 align:middle line:84% All of that means that we cannot calculate accurate profiles 01:15:13.040 --> 01:15:14.840 align:middle line:90% in Silicon devices by hand. 01:15:14.840 --> 01:15:16.880 align:middle line:84% We're pretty much have to monitor all that 01:15:16.880 --> 01:15:19.310 align:middle line:90% by doing numerical solutions. 01:15:19.310 --> 01:15:22.100 align:middle line:84% There's been a lot of progress in the last 10 or 15 years 01:15:22.100 --> 01:15:26.450 align:middle line:84% on getting physically based models for dopant diffusion that 01:15:26.450 --> 01:15:29.720 align:middle line:84% will actually help you predict electrical behavior. 01:15:29.720 --> 01:15:31.580 align:middle line:84% These simulators-- and we'll talk about it 01:15:31.580 --> 01:15:34.217 align:middle line:84% more when we give a lecture on SUPREM IV. 01:15:34.217 --> 01:15:36.050 align:middle line:84% They allow you to fully couple the diffusion 01:15:36.050 --> 01:15:37.170 align:middle line:90% of the point defects. 01:15:37.170 --> 01:15:39.380 align:middle line:84% So you solve for the diffusion of the interstitials 01:15:39.380 --> 01:15:41.960 align:middle line:84% and vacancies, and you solve diffusion of the dopants 01:15:41.960 --> 01:15:43.075 align:middle line:90% at the same time. 01:15:43.075 --> 01:15:44.450 align:middle line:84% The problem with all these models 01:15:44.450 --> 01:15:46.100 align:middle line:90% is there's a lot of parameters. 01:15:46.100 --> 01:15:48.530 align:middle line:84% And so any parameters that you don't know, 01:15:48.530 --> 01:15:51.020 align:middle line:84% you can get beautiful profiles, but all the parameters 01:15:51.020 --> 01:15:52.640 align:middle line:90% need to be calibrated. 01:15:52.640 --> 01:15:55.380 align:middle line:84% So that's about all I have for today. 01:15:55.380 --> 01:15:57.290 align:middle line:84% And if you're handing in your homework 3, 01:15:57.290 --> 01:16:01.060 align:middle line:84% please bring it up front to this folder. 01:16:01.060 --> 01:16:02.000 align:middle line:90%