WEBVTT 00:00:00.000 --> 00:00:02.882 align:middle line:84% JUDY HOYT: Go ahead and get started with today's class. 00:00:02.882 --> 00:00:04.340 align:middle line:84% I've got a couple of announcements. 00:00:04.340 --> 00:00:07.070 align:middle line:84% There's one handout for today, which is in the back. 00:00:07.070 --> 00:00:09.110 align:middle line:84% Hopefully you all have a copy of that. 00:00:09.110 --> 00:00:13.580 align:middle line:84% And I've brought with me the clipboard 00:00:13.580 --> 00:00:15.590 align:middle line:90% with the project signup sheet. 00:00:15.590 --> 00:00:21.720 align:middle line:84% So I'd like you to put down your name on one of the lines here. 00:00:21.720 --> 00:00:23.840 align:middle line:84% And the most important thing today 00:00:23.840 --> 00:00:27.360 align:middle line:84% is whether you want to give a written or an oral. 00:00:27.360 --> 00:00:29.900 align:middle line:84% Written would be at 20-page written report. 00:00:29.900 --> 00:00:33.890 align:middle line:84% The presentation would be a 15 to 20 minute presentation 00:00:33.890 --> 00:00:34.730 align:middle line:90% to the class. 00:00:34.730 --> 00:00:36.525 align:middle line:84% And all of that is described in the handout 00:00:36.525 --> 00:00:38.900 align:middle line:84% I gave to you about a week ago, which hopefully you have. 00:00:38.900 --> 00:00:41.360 align:middle line:84% If you don't have a copy of it, it's on the web 00:00:41.360 --> 00:00:46.040 align:middle line:90% or it's here on this clipboard. 00:00:46.040 --> 00:00:49.790 align:middle line:84% So I'd like to know today or Thursday at the latest 00:00:49.790 --> 00:00:52.820 align:middle line:84% whether you want to do a written report or an oral report. 00:00:52.820 --> 00:00:54.570 align:middle line:84% Even if you don't know your topic. 00:00:54.570 --> 00:00:57.740 align:middle line:84% This will help me in scheduling your oral presentations. 00:00:57.740 --> 00:01:01.940 align:middle line:84% I have to figure out when at the end of the term, 00:01:01.940 --> 00:01:05.540 align:middle line:84% which class periods I'm going to dedicate to oral presentations. 00:01:05.540 --> 00:01:08.510 align:middle line:84% And then if you know your topic, that'd be great. 00:01:08.510 --> 00:01:10.010 align:middle line:90% Go ahead and write that in. 00:01:10.010 --> 00:01:14.090 align:middle line:84% The last column on this signup sheet says whether it's approved 00:01:14.090 --> 00:01:14.960 align:middle line:90% or not. 00:01:14.960 --> 00:01:17.600 align:middle line:84% And I'll look through this over the next few weeks. 00:01:17.600 --> 00:01:20.690 align:middle line:84% And as time goes on, I'll look at your topics. 00:01:20.690 --> 00:01:21.750 align:middle line:90% If I have a question. 00:01:21.750 --> 00:01:22.890 align:middle line:90% I'll talk to you about it. 00:01:22.890 --> 00:01:26.190 align:middle line:84% And if I don't, I'll just go ahead and approve it. 00:01:26.190 --> 00:01:29.310 align:middle line:84% So when it's checked off, then your topic is approved. 00:01:29.310 --> 00:01:31.580 align:middle line:84% So if you can fill that information out, 00:01:31.580 --> 00:01:34.340 align:middle line:84% the sooner the better, on the written versus 00:01:34.340 --> 00:01:36.660 align:middle line:84% oral, and as well as on your topic. 00:01:36.660 --> 00:01:40.530 align:middle line:84% If you have any questions about topics, feel free to ask me. 00:01:40.530 --> 00:01:42.350 align:middle line:84% So I'm going to start passing that around. 00:01:42.350 --> 00:01:46.120 align:middle line:90% 00:01:46.120 --> 00:01:47.380 align:middle line:90% One of the things, homework. 00:01:47.380 --> 00:01:48.980 align:middle line:84% Homework number 3 is being graded. 00:01:48.980 --> 00:01:52.300 align:middle line:84% Hopefully we'll have that back to you soon. 00:01:52.300 --> 00:01:53.895 align:middle line:84% Homework number 4 went out last time. 00:01:53.895 --> 00:01:55.270 align:middle line:84% Hopefully you got a copy of that. 00:01:55.270 --> 00:01:57.020 align:middle line:84% If you didn't, it's all posted on the web. 00:01:57.020 --> 00:01:59.330 align:middle line:84% Everything is posted on the website. 00:01:59.330 --> 00:02:01.150 align:middle line:84% This is where we are on the class schedule. 00:02:01.150 --> 00:02:03.200 align:middle line:84% What I'm looking at here is this Excel file, 00:02:03.200 --> 00:02:06.160 align:middle line:84% which just sort of shows that we're at lecture 14. 00:02:06.160 --> 00:02:08.860 align:middle line:84% We're going to talk today about transient enhanced diffusion 00:02:08.860 --> 00:02:11.470 align:middle line:90% from Chapter 8. 00:02:11.470 --> 00:02:14.470 align:middle line:84% And you've got a couple of more lectures. 00:02:14.470 --> 00:02:16.600 align:middle line:84% The next homework due date is homework 00:02:16.600 --> 00:02:21.420 align:middle line:84% number 4, which is due a week from today, election day, 00:02:21.420 --> 00:02:24.340 align:middle line:90% November 2. 00:02:24.340 --> 00:02:29.300 align:middle line:84% So let's go ahead and start with today's lecture. 00:02:29.300 --> 00:02:32.800 align:middle line:90% 00:02:32.800 --> 00:02:39.040 align:middle line:84% The notes are handout number 24, and this is the third lecture 00:02:39.040 --> 00:02:40.060 align:middle line:90% on chapter number eight. 00:02:40.060 --> 00:02:42.310 align:middle line:84% Chapter 8, hopefully you've been here reading through. 00:02:42.310 --> 00:02:47.070 align:middle line:84% Chapter 8 at this point, chapter 8 is all about ion implantation. 00:02:47.070 --> 00:02:49.040 align:middle line:84% But this lecture and the next lecture 00:02:49.040 --> 00:02:52.080 align:middle line:84% are about transit enhanced diffusion. 00:02:52.080 --> 00:02:54.620 align:middle line:84% So let me just remind you what we talked about last time. 00:02:54.620 --> 00:02:57.830 align:middle line:84% We talked about the physics of nuclear stopping 00:02:57.830 --> 00:03:00.290 align:middle line:84% and electronic stopping, or electronic energy loss 00:03:00.290 --> 00:03:01.220 align:middle line:90% processes. 00:03:01.220 --> 00:03:05.000 align:middle line:84% We said that if you have a heavy ion-- 00:03:05.000 --> 00:03:07.940 align:middle line:84% say if you're implanting antimony-- and heavy and lighter 00:03:07.940 --> 00:03:09.810 align:middle line:84% always relative to the substrate. 00:03:09.810 --> 00:03:11.580 align:middle line:84% So antimony and arsenic, for example, 00:03:11.580 --> 00:03:14.030 align:middle line:84% are very heavy compared to silicon, 00:03:14.030 --> 00:03:17.480 align:middle line:84% then nuclear stopping tends to dominate over their entire path 00:03:17.480 --> 00:03:20.030 align:middle line:84% as they go into the silicon substrate 00:03:20.030 --> 00:03:21.440 align:middle line:90% and as they come to rest. 00:03:21.440 --> 00:03:24.320 align:middle line:90% Nuclear stopping is dominant. 00:03:24.320 --> 00:03:28.160 align:middle line:84% If you have a heavy or a light ion, 00:03:28.160 --> 00:03:30.920 align:middle line:84% then nuclear stop stopping dominates towards the end 00:03:30.920 --> 00:03:32.570 align:middle line:90% of path, the end of range. 00:03:32.570 --> 00:03:34.100 align:middle line:84% So when the energy gets low enough. 00:03:34.100 --> 00:03:37.400 align:middle line:84% So as we saw last time, the nuclear stopping power 00:03:37.400 --> 00:03:41.810 align:middle line:84% goes down as energy increases, and the electronic stopping 00:03:41.810 --> 00:03:42.560 align:middle line:90% power goes up. 00:03:42.560 --> 00:03:44.900 align:middle line:84% So only at very low energies do you 00:03:44.900 --> 00:03:49.460 align:middle line:84% have a lot of nuclear scattering for a light ion. 00:03:49.460 --> 00:03:51.680 align:middle line:84% It's the nuclear stopping, not the electronic. 00:03:51.680 --> 00:03:53.510 align:middle line:84% It's the nuclear stopping, the collisions, 00:03:53.510 --> 00:03:55.790 align:middle line:84% that contribute to crystal damage clearly. 00:03:55.790 --> 00:03:58.412 align:middle line:84% So the ions are coming in, and in a nuclear event, 00:03:58.412 --> 00:03:59.870 align:middle line:84% you have a billiard ball collision, 00:03:59.870 --> 00:04:03.200 align:middle line:84% and you're knocking the silicon off its lattice site. 00:04:03.200 --> 00:04:06.170 align:middle line:84% And you're creating, in that process, silicon interstitials 00:04:06.170 --> 00:04:08.990 align:middle line:90% and vacancies. 00:04:08.990 --> 00:04:10.820 align:middle line:84% And these results in something which 00:04:10.820 --> 00:04:13.220 align:middle line:90% we call the collision cascade. 00:04:13.220 --> 00:04:14.960 align:middle line:84% We talked a little bit to how people have 00:04:14.960 --> 00:04:16.620 align:middle line:90% calculated damage profiles. 00:04:16.620 --> 00:04:18.470 align:middle line:84% So they calculate the amount of energy 00:04:18.470 --> 00:04:21.079 align:middle line:84% deposited into these nuclear stopping processes 00:04:21.079 --> 00:04:22.310 align:middle line:90% as a function of depth. 00:04:22.310 --> 00:04:24.180 align:middle line:90% And the peak damage-- 00:04:24.180 --> 00:04:26.240 align:middle line:84% so the most amount of damage you do-- 00:04:26.240 --> 00:04:28.370 align:middle line:84% the profile tends to peak near the projected 00:04:28.370 --> 00:04:29.870 align:middle line:90% range of the primary ion. 00:04:29.870 --> 00:04:34.430 align:middle line:84% Maybe just slightly shorter or shallower 00:04:34.430 --> 00:04:36.210 align:middle line:90% than the projected range RP. 00:04:36.210 --> 00:04:38.960 align:middle line:84% So let's say you're doing an ion implant of arsenic, 00:04:38.960 --> 00:04:41.330 align:middle line:84% and you can easily calculate, using 00:04:41.330 --> 00:04:45.880 align:middle line:84% one of the theories, the arsenic profile. 00:04:45.880 --> 00:04:48.943 align:middle line:84% You can use the rain statistics for the arsenic, whatever. 00:04:48.943 --> 00:04:50.610 align:middle line:84% You know where the RP of the arsenic is, 00:04:50.610 --> 00:04:52.735 align:middle line:84% and you can figure out where the most of the damage 00:04:52.735 --> 00:04:53.960 align:middle line:90% is going to be done. 00:04:53.960 --> 00:04:57.270 align:middle line:90% It'll be just about 90% or so. 00:04:57.270 --> 00:05:01.010 align:middle line:84% It will be the peak of that damage profile. 00:05:01.010 --> 00:05:04.610 align:middle line:84% For a heavy ion like arsenic or antimony and silicon, 00:05:04.610 --> 00:05:07.190 align:middle line:90% the damage is more stable. 00:05:07.190 --> 00:05:10.010 align:middle line:84% So it doesn't tend to anneal out at room temperature. 00:05:10.010 --> 00:05:13.880 align:middle line:84% It's relatively easy to form an amorphous layer with a heavy ion 00:05:13.880 --> 00:05:15.620 align:middle line:90% at room temperature. 00:05:15.620 --> 00:05:17.330 align:middle line:90% And this can then be regrown. 00:05:17.330 --> 00:05:19.970 align:middle line:84% We talked about a process called solid phase epitaxy 00:05:19.970 --> 00:05:21.990 align:middle line:90% to regrow that amorphous layer. 00:05:21.990 --> 00:05:25.310 align:middle line:84% And so this is a relatively efficient way 00:05:25.310 --> 00:05:28.027 align:middle line:90% to do dopant activation. 00:05:28.027 --> 00:05:30.110 align:middle line:84% I'll say a little bit more about dopant activation 00:05:30.110 --> 00:05:31.920 align:middle line:90% in this lecture. 00:05:31.920 --> 00:05:33.950 align:middle line:84% And finally, we mentioned last time, we just 00:05:33.950 --> 00:05:37.670 align:middle line:84% started this topic, we said that the excess interstitials that 00:05:37.670 --> 00:05:41.390 align:middle line:84% are created by this implant, all these nuclear collisions, 00:05:41.390 --> 00:05:44.030 align:middle line:84% they can cluster into a particular type of defect 00:05:44.030 --> 00:05:45.980 align:middle line:90% called a 311 defect. 00:05:45.980 --> 00:05:50.180 align:middle line:84% Later, the 311s dissolve and they give off interstitials. 00:05:50.180 --> 00:05:53.330 align:middle line:84% And these interstitials then are what 00:05:53.330 --> 00:05:55.970 align:middle line:84% determine the kinetics of transient enhanced diffusion 00:05:55.970 --> 00:05:58.670 align:middle line:90% of boron and other dopants. 00:05:58.670 --> 00:06:01.260 align:middle line:84% So that's just a review of what we talked about last time. 00:06:01.260 --> 00:06:03.530 align:middle line:84% What I want to cover this time, I 00:06:03.530 --> 00:06:06.480 align:middle line:84% have a few slides in this lecture on dopant activation 00:06:06.480 --> 00:06:09.760 align:middle line:84% just to go through that a little bit more carefully. 00:06:09.760 --> 00:06:11.310 align:middle line:84% And then most of the lecture is going 00:06:11.310 --> 00:06:14.400 align:middle line:84% to be talking about transient enhanced diffusion this, TED 00:06:14.400 --> 00:06:17.650 align:middle line:90% effect and how it's modeled. 00:06:17.650 --> 00:06:20.950 align:middle line:84% So let's go on to slide number 2. 00:06:20.950 --> 00:06:26.490 align:middle line:84% Well I think I showed this last time, this cross-section PEM. 00:06:26.490 --> 00:06:28.980 align:middle line:84% We're going to talk about this case on slide number two, 00:06:28.980 --> 00:06:31.320 align:middle line:84% when the dose and the mass are high enough 00:06:31.320 --> 00:06:33.840 align:middle line:90% to amortize the silicon. 00:06:33.840 --> 00:06:36.990 align:middle line:84% And these are cross-section transmission electron micrograph 00:06:36.990 --> 00:06:43.350 align:middle line:84% images of a sample that has been ion implanted and amorphized. 00:06:43.350 --> 00:06:46.740 align:middle line:84% And then it is being regrown by putting it 00:06:46.740 --> 00:06:50.970 align:middle line:84% in a furnace at 525 degrees C. The initial implant 00:06:50.970 --> 00:06:53.040 align:middle line:90% was 200 keV of antimony. 00:06:53.040 --> 00:06:54.390 align:middle line:90% And look at the antimony dose. 00:06:54.390 --> 00:06:57.240 align:middle line:84% Quite high, 610 to the 15th per square centimeter. 00:06:57.240 --> 00:06:58.420 align:middle line:90% That's a high dose. 00:06:58.420 --> 00:07:00.613 align:middle line:84% And so you can see-- this should say zero minutes, 00:07:00.613 --> 00:07:02.280 align:middle line:84% I'm not sure what happened to the zero-- 00:07:02.280 --> 00:07:05.550 align:middle line:84% but anyway, this means when you're 00:07:05.550 --> 00:07:07.860 align:middle line:84% close to starting up what you have 00:07:07.860 --> 00:07:11.070 align:middle line:84% is an amorphous layer from the surface down to some depth. 00:07:11.070 --> 00:07:13.210 align:middle line:84% And in fact here's the scale bar. 00:07:13.210 --> 00:07:15.400 align:middle line:84% This is 100 nanometers from here to here. 00:07:15.400 --> 00:07:18.660 align:middle line:84% So that's maybe 300 nanometers, 3,000 angstroms deep, 00:07:18.660 --> 00:07:19.530 align:middle line:90% something like that. 00:07:19.530 --> 00:07:21.130 align:middle line:90% It's all amorphized. 00:07:21.130 --> 00:07:23.770 align:middle line:84% The crystal structure is completely destroyed. 00:07:23.770 --> 00:07:26.050 align:middle line:90% You have an amorphous solid. 00:07:26.050 --> 00:07:27.940 align:middle line:84% Now after 10 minutes, what has happened? 00:07:27.940 --> 00:07:30.880 align:middle line:84% Well the amorphous crystal interface has moved up. 00:07:30.880 --> 00:07:32.920 align:middle line:90% So we have regrowth. 00:07:32.920 --> 00:07:36.190 align:middle line:84% We have solid phase epitaxy, the layer by layer process. 00:07:36.190 --> 00:07:40.300 align:middle line:84% This epitaxy process is not that different from growth 00:07:40.300 --> 00:07:42.040 align:middle line:84% from the melt. The only difference here 00:07:42.040 --> 00:07:44.620 align:middle line:84% is we're talking about, we're getting a phase transition, 00:07:44.620 --> 00:07:48.190 align:middle line:84% or we're getting a transition from in the solid phase 00:07:48.190 --> 00:07:51.550 align:middle line:84% from amorphous to solid phase single crystal. 00:07:51.550 --> 00:07:55.210 align:middle line:84% And that's happening in a layer by layer fashion here. 00:07:55.210 --> 00:07:57.940 align:middle line:84% After 10 minutes, I've grown up a little distance. 00:07:57.940 --> 00:08:01.060 align:middle line:84% 15 minutes, you can see the amorphous crystal 00:08:01.060 --> 00:08:02.530 align:middle line:90% interface has progressed. 00:08:02.530 --> 00:08:06.130 align:middle line:84% And in fact, this is a linear growth rate, you'll find. 00:08:06.130 --> 00:08:08.980 align:middle line:84% On the right hand side all the way on the right at 20 minutes, 00:08:08.980 --> 00:08:11.320 align:middle line:84% there's only a small amorphous layer remaining. 00:08:11.320 --> 00:08:14.530 align:middle line:84% And if we were to go longer, the amorphous layer would entirely 00:08:14.530 --> 00:08:19.500 align:middle line:84% regrow and you would have single crystal silicon completely 00:08:19.500 --> 00:08:21.970 align:middle line:84% in depth from the surface on down. 00:08:21.970 --> 00:08:23.765 align:middle line:84% Then the only thing you're left with, 00:08:23.765 --> 00:08:25.390 align:middle line:84% you still have single crystal material, 00:08:25.390 --> 00:08:29.910 align:middle line:84% is down just below the original amorphous crystal 00:08:29.910 --> 00:08:31.660 align:middle line:84% interface, you are left with what's called 00:08:31.660 --> 00:08:33.429 align:middle line:90% these end of rage damage. 00:08:33.429 --> 00:08:37.150 align:middle line:84% It's a series of these dislocation loops and other sort 00:08:37.150 --> 00:08:39.730 align:middle line:84% of extended defects that don't anneal out. 00:08:39.730 --> 00:08:42.400 align:middle line:84% End of range damage, in general, unless she 00:08:42.400 --> 00:08:44.950 align:middle line:84% were to melt the sample or do something, 00:08:44.950 --> 00:08:46.610 align:middle line:84% it's something we most of the time, 00:08:46.610 --> 00:08:49.412 align:middle line:84% we end up having to live with to a certain extent. 00:08:49.412 --> 00:08:50.620 align:middle line:90% It's very hard to get rid of. 00:08:50.620 --> 00:08:52.600 align:middle line:84% But the amorphous layer is gone, and we 00:08:52.600 --> 00:08:54.570 align:middle line:90% have single crystal silicon. 00:08:54.570 --> 00:08:56.320 align:middle line:84% So it's just a reminder when we're 00:08:56.320 --> 00:09:00.280 align:middle line:84% talking about amorphization and a process 00:09:00.280 --> 00:09:05.460 align:middle line:84% for restoring the crystal to its single crystal nature. 00:09:05.460 --> 00:09:07.310 align:middle line:90% So let's go on to slide 3. 00:09:07.310 --> 00:09:13.890 align:middle line:84% I wanted to just remind us about dopant activation. 00:09:13.890 --> 00:09:18.260 align:middle line:84% And this particularly applies to boron and silicon. 00:09:18.260 --> 00:09:22.160 align:middle line:84% It's much more difficult to anneal a silicon sample. 00:09:22.160 --> 00:09:24.770 align:middle line:84% That is, when I say difficult to anneal, 00:09:24.770 --> 00:09:27.080 align:middle line:84% really what we mean is it's difficult to activate, 00:09:27.080 --> 00:09:28.370 align:middle line:90% to electrically activate. 00:09:28.370 --> 00:09:31.340 align:middle line:84% So to get when-- what do we mean by electrically activate? 00:09:31.340 --> 00:09:33.650 align:middle line:84% Well, for every ion I implant, I like 00:09:33.650 --> 00:09:35.700 align:middle line:84% to have it go into a substitutional place. 00:09:35.700 --> 00:09:38.000 align:middle line:84% And if it's a donor, I like to donate an electron 00:09:38.000 --> 00:09:39.050 align:middle line:90% so I get a free electron. 00:09:39.050 --> 00:09:41.420 align:middle line:84% If it's an acceptor, I'd like to get a free hole. 00:09:41.420 --> 00:09:43.590 align:middle line:84% That's the whole purpose of doing the ion implant. 00:09:43.590 --> 00:09:47.510 align:middle line:84% So if I implant a dose of 10 to the 15th of arsenic or boron, 00:09:47.510 --> 00:09:50.150 align:middle line:84% I'd like to get 10 to the 15th per square centimeter free 00:09:50.150 --> 00:09:51.200 align:middle line:90% electrons or free holes. 00:09:51.200 --> 00:09:52.790 align:middle line:84% That's what I mean by activating. 00:09:52.790 --> 00:09:58.670 align:middle line:84% This activation is more difficult, ironically, 00:09:58.670 --> 00:10:01.910 align:middle line:84% when you've only partially damaged the silicon. 00:10:01.910 --> 00:10:05.460 align:middle line:84% Particularly intermediate doses are difficult. 00:10:05.460 --> 00:10:07.063 align:middle line:84% So let's just take the range of doses. 00:10:07.063 --> 00:10:09.230 align:middle line:84% I think we talked a little bit about this last time. 00:10:09.230 --> 00:10:12.320 align:middle line:84% If we have a very low dose, 10 to the 12th atoms 00:10:12.320 --> 00:10:16.460 align:middle line:84% per square centimeter, not much damage is done, 00:10:16.460 --> 00:10:19.830 align:middle line:84% and it's not too hard to anneal the sample, 00:10:19.830 --> 00:10:22.860 align:middle line:84% get the crystal structure restored 00:10:22.860 --> 00:10:27.000 align:middle line:84% to more of a perfect state and to activate all the dopants 00:10:27.000 --> 00:10:28.770 align:middle line:90% and substitutional sites. 00:10:28.770 --> 00:10:31.200 align:middle line:84% A very high dose, you create amorphous layer 00:10:31.200 --> 00:10:33.130 align:middle line:84% like we just saw on the previous slide. 00:10:33.130 --> 00:10:37.980 align:middle line:84% And it's relatively easy to anneal out the amorphous layer 00:10:37.980 --> 00:10:39.240 align:middle line:90% by solid-phase epi. 00:10:39.240 --> 00:10:42.670 align:middle line:84% Solid-phase epi can take place at 500 or 600 degrees. 00:10:42.670 --> 00:10:44.700 align:middle line:84% So you don't have to go very hot. 00:10:44.700 --> 00:10:47.640 align:middle line:84% Typically you would go a little higher than that, maybe 00:10:47.640 --> 00:10:51.810 align:middle line:84% after this SPE regrowth step you might go to 800 or 900 00:10:51.810 --> 00:10:54.330 align:middle line:84% to get a little better dopant activation. 00:10:54.330 --> 00:10:55.380 align:middle line:90% But that's not so hard. 00:10:55.380 --> 00:10:57.430 align:middle line:84% The hard one is the last one listed here. 00:10:57.430 --> 00:11:00.640 align:middle line:84% These are the intermediate doses. 00:11:00.640 --> 00:11:04.560 align:middle line:84% And this is a dose that is high enough to do some damage, 00:11:04.560 --> 00:11:07.560 align:middle line:84% but it's not high enough to create complete amorphous layer. 00:11:07.560 --> 00:11:11.290 align:middle line:84% So you cannot have solid phase layer by layer regrowth. 00:11:11.290 --> 00:11:14.850 align:middle line:84% So it's right in the middle that you have a problem. 00:11:14.850 --> 00:11:18.330 align:middle line:84% And this leads to a lot of complex behavior 00:11:18.330 --> 00:11:20.970 align:middle line:84% where secondary defects, other types 00:11:20.970 --> 00:11:24.420 align:middle line:84% of defects besides just interstitials and vacancies, 00:11:24.420 --> 00:11:26.430 align:middle line:90% can form. 00:11:26.430 --> 00:11:28.260 align:middle line:84% And particularly for boron, which 00:11:28.260 --> 00:11:30.870 align:middle line:84% is a light ion, because of the nature of the type of damage 00:11:30.870 --> 00:11:34.710 align:middle line:84% it does, this intermediate dose range is a real problem. 00:11:34.710 --> 00:11:38.280 align:middle line:84% And this complicated behavior can occur over 00:11:38.280 --> 00:11:41.820 align:middle line:84% a wide range of boron doses that are used in practice 00:11:41.820 --> 00:11:44.408 align:middle line:90% in CMOS fabrication. 00:11:44.408 --> 00:11:46.950 align:middle line:84% And it's because of the nature of the damage created by boron 00:11:46.950 --> 00:11:47.492 align:middle line:90% is different. 00:11:47.492 --> 00:11:48.300 align:middle line:90% It's a light ion. 00:11:48.300 --> 00:11:52.290 align:middle line:84% So it's not doing that much very effective nuclear damage, 00:11:52.290 --> 00:11:56.560 align:middle line:84% at least until you get towards its end of range. 00:11:56.560 --> 00:11:59.048 align:middle line:84% So you'll hear people say, oh, boron is a lot harder 00:11:59.048 --> 00:12:00.090 align:middle line:90% to activate than arsenic. 00:12:00.090 --> 00:12:00.720 align:middle line:90% Indeed it is. 00:12:00.720 --> 00:12:04.740 align:middle line:84% It's harder to repair the damage from a boron implant in silicon 00:12:04.740 --> 00:12:07.800 align:middle line:84% than from an arsenic implant in silicon. 00:12:07.800 --> 00:12:09.157 align:middle line:90% What do people do about this? 00:12:09.157 --> 00:12:10.740 align:middle line:84% Well, there are a couple of approaches 00:12:10.740 --> 00:12:12.330 align:middle line:90% I think we mentioned last time. 00:12:12.330 --> 00:12:13.980 align:middle line:90% Boron is light. 00:12:13.980 --> 00:12:15.660 align:middle line:90% OK, that's a problem. 00:12:15.660 --> 00:12:18.640 align:middle line:84% In some sense it's doing damage, but not enough damage. 00:12:18.640 --> 00:12:21.720 align:middle line:84% So within the dose range that you want to implant it. 00:12:21.720 --> 00:12:25.620 align:middle line:84% Sometimes what people do is they don't implant pure boron. 00:12:25.620 --> 00:12:28.830 align:middle line:90% They implant a molecule, BF2. 00:12:28.830 --> 00:12:32.730 align:middle line:84% So these two extra fluorines add quite a bit of extra mass 00:12:32.730 --> 00:12:35.500 align:middle line:84% to the species that your ion implanting. 00:12:35.500 --> 00:12:39.450 align:middle line:84% So it's not just boron 11, it's boron with two fluorine 00:12:39.450 --> 00:12:40.840 align:middle line:90% atoms attached. 00:12:40.840 --> 00:12:43.710 align:middle line:84% And this is the ion that you ionize and the ion implanter, 00:12:43.710 --> 00:12:47.340 align:middle line:84% and that you impart energy and you put into the silicon. 00:12:47.340 --> 00:12:52.163 align:middle line:84% So when the BF2 molecule hits the silicon, what happens? 00:12:52.163 --> 00:12:53.580 align:middle line:84% Well, it dissociates, most likely. 00:12:53.580 --> 00:12:56.280 align:middle line:84% It has so much energy, and the boron goes along 00:12:56.280 --> 00:12:57.510 align:middle line:90% and the fluorine goes in. 00:12:57.510 --> 00:12:59.790 align:middle line:84% And they both impart energy though, they both can 00:12:59.790 --> 00:13:01.780 align:middle line:90% do some kind of nuclear damage. 00:13:01.780 --> 00:13:05.940 align:middle line:84% So we can kind of treat this, we can 00:13:05.940 --> 00:13:08.310 align:middle line:84% say that the energy is apportioned, 00:13:08.310 --> 00:13:10.110 align:middle line:90% a certain amount to the boron-- 00:13:10.110 --> 00:13:14.370 align:middle line:84% in ratio to its z number-- and a certain fraction of the energy 00:13:14.370 --> 00:13:15.360 align:middle line:90% goes to the fluorine. 00:13:15.360 --> 00:13:17.130 align:middle line:84% And having the extra fluorine in there 00:13:17.130 --> 00:13:19.660 align:middle line:84% is a way to amorphize the sample. 00:13:19.660 --> 00:13:24.090 align:middle line:84% So BF2, sometimes people use to try to improve the activation. 00:13:24.090 --> 00:13:25.890 align:middle line:84% It's also a way of getting, effectively, 00:13:25.890 --> 00:13:27.420 align:middle line:90% a lower energy implant. 00:13:27.420 --> 00:13:32.730 align:middle line:84% Because if you have a certain energy imparted to BF2, 00:13:32.730 --> 00:13:35.250 align:middle line:84% the boron only shares a certain fraction 00:13:35.250 --> 00:13:38.130 align:middle line:84% of that when it actually hits the sample. 00:13:38.130 --> 00:13:39.990 align:middle line:84% The other thing people do is they do what's 00:13:39.990 --> 00:13:41.160 align:middle line:90% called pre-amorphization. 00:13:41.160 --> 00:13:41.790 align:middle line:90% Pre-what? 00:13:41.790 --> 00:13:44.340 align:middle line:84% That means prior to implanting the boron, 00:13:44.340 --> 00:13:47.220 align:middle line:84% they modify the sample with another species. 00:13:47.220 --> 00:13:49.620 align:middle line:84% Typically you would not want to use an anti-dopant, 00:13:49.620 --> 00:13:51.412 align:middle line:84% because then you're compensating the boron. 00:13:51.412 --> 00:13:55.140 align:middle line:84% So typically you use either silicon or germanium, 00:13:55.140 --> 00:13:56.890 align:middle line:84% which are not electrically active per se. 00:13:56.890 --> 00:13:57.390 align:middle line:90% Right? 00:13:57.390 --> 00:13:59.282 align:middle line:84% Silicon is the same as silicon, so it's not 00:13:59.282 --> 00:14:00.990 align:middle line:84% going to produce any anti-dopant effects. 00:14:00.990 --> 00:14:02.970 align:middle line:84% Germanium is also in column four, 00:14:02.970 --> 00:14:06.270 align:middle line:84% it turns out it does not produce a doping effect. 00:14:06.270 --> 00:14:10.290 align:middle line:84% That is, it does not add p or n type character to the substrate. 00:14:10.290 --> 00:14:13.100 align:middle line:84% And it's heavy, so it's easy to amorphize. 00:14:13.100 --> 00:14:17.210 align:middle line:84% So you'll see people doing prior to a shallow implant, 00:14:17.210 --> 00:14:21.440 align:middle line:84% they may implant silicon and liquid nitrogen or germanium 00:14:21.440 --> 00:14:25.150 align:middle line:84% at room temperature, create an amorphous layer. 00:14:25.150 --> 00:14:28.090 align:middle line:84% Into that amorphous layer, implant the boron, 00:14:28.090 --> 00:14:30.850 align:middle line:84% and then do a relatively low temperature activation 00:14:30.850 --> 00:14:37.360 align:middle line:84% to try to activate the boron and get a little bit 00:14:37.360 --> 00:14:41.110 align:middle line:90% of a better annealing behavior. 00:14:41.110 --> 00:14:43.480 align:middle line:84% Pre-amorphization also has another advantage 00:14:43.480 --> 00:14:45.063 align:middle line:90% if you want to think about it. 00:14:45.063 --> 00:14:47.230 align:middle line:84% Remember when we were talking about ion implantation 00:14:47.230 --> 00:14:48.140 align:middle line:90% a few lectures ago? 00:14:48.140 --> 00:14:50.980 align:middle line:84% We were talking about ion channeling, and the fact 00:14:50.980 --> 00:14:53.083 align:middle line:84% that ions can be knocked into these channels 00:14:53.083 --> 00:14:55.000 align:middle line:84% because you have a perfect crystal that can go 00:14:55.000 --> 00:14:56.830 align:middle line:90% a long ways before they stop. 00:14:56.830 --> 00:14:59.470 align:middle line:84% And this creates these long tails, 00:14:59.470 --> 00:15:02.410 align:middle line:84% it makes it very hard to get an abrupt, shallow junction. 00:15:02.410 --> 00:15:05.740 align:middle line:84% Well, if you amorphize the top 3,000 angstroms 00:15:05.740 --> 00:15:07.657 align:middle line:84% prior to putting the boron in, that 00:15:07.657 --> 00:15:09.490 align:middle line:84% eliminates the possibility of ion channeling 00:15:09.490 --> 00:15:10.698 align:middle line:90% in those top 3,000 angstroms. 00:15:10.698 --> 00:15:11.620 align:middle line:90% There is no crystal. 00:15:11.620 --> 00:15:14.000 align:middle line:84% It's not single crystal, it's completely random. 00:15:14.000 --> 00:15:17.230 align:middle line:84% So pre-amorphization has two benefits. 00:15:17.230 --> 00:15:19.515 align:middle line:84% You can get a little better activation of the boron, 00:15:19.515 --> 00:15:20.890 align:middle line:84% and it eliminates ion channeling, 00:15:20.890 --> 00:15:22.480 align:middle line:84% so you can do shallower junctions. 00:15:22.480 --> 00:15:25.430 align:middle line:84% It costs more money, it takes time, 00:15:25.430 --> 00:15:27.170 align:middle line:84% it does create end of range damage, 00:15:27.170 --> 00:15:31.240 align:middle line:84% so there are tradeoffs in using pre-amorphization 00:15:31.240 --> 00:15:35.780 align:middle line:90% as a way to do boron implants. 00:15:35.780 --> 00:15:41.110 align:middle line:84% So that's mainly comments I wanted to make 00:15:41.110 --> 00:15:42.550 align:middle line:90% about dopant activation. 00:15:42.550 --> 00:15:45.772 align:middle line:84% One more comment before I leave slide number 3, 00:15:45.772 --> 00:15:47.980 align:middle line:84% because we probably have a homework problem coming up 00:15:47.980 --> 00:15:50.950 align:middle line:90% in homework 5 about activation. 00:15:50.950 --> 00:15:52.990 align:middle line:84% When you're using Supreme, Supreme 00:15:52.990 --> 00:15:56.770 align:middle line:84% can model dopant activation in a very crude way. 00:15:56.770 --> 00:15:59.205 align:middle line:84% If you do an ion implant in Supreme-- 00:15:59.205 --> 00:16:00.580 align:middle line:84% you let's say you implant arsenic 00:16:00.580 --> 00:16:02.860 align:middle line:84% to a certain concentration or dose-- 00:16:02.860 --> 00:16:06.730 align:middle line:84% and then you anneal it at just about any temperature, 00:16:06.730 --> 00:16:10.210 align:middle line:84% the default assumption is that everything 00:16:10.210 --> 00:16:13.748 align:middle line:84% is activated almost immediately within a few microseconds 00:16:13.748 --> 00:16:14.290 align:middle line:90% or something. 00:16:14.290 --> 00:16:17.140 align:middle line:84% So Supreme doesn't really have any good kinetics, any time 00:16:17.140 --> 00:16:18.560 align:middle line:90% dependence of the activation. 00:16:18.560 --> 00:16:22.450 align:middle line:84% So you do a one minute anneal at 800, 00:16:22.450 --> 00:16:24.820 align:middle line:84% it assumes you're getting the same amount of activation 00:16:24.820 --> 00:16:27.100 align:middle line:90% as a 30-minute initial at 800. 00:16:27.100 --> 00:16:29.350 align:middle line:84% It doesn't have kinetics to activation built in. 00:16:29.350 --> 00:16:30.790 align:middle line:90% But it can plot for you. 00:16:30.790 --> 00:16:33.700 align:middle line:84% It will plot the active carrier concentration. 00:16:33.700 --> 00:16:36.810 align:middle line:84% And it will clip it off at the solubility limit. 00:16:36.810 --> 00:16:40.560 align:middle line:84% So if you implant arsenic to a peak of 10 to the 21, 00:16:40.560 --> 00:16:43.760 align:middle line:84% let's say, a huge peak per cubic centimeter, 00:16:43.760 --> 00:16:45.860 align:middle line:84% and then you tell it, I want to anneal it 00:16:45.860 --> 00:16:49.910 align:middle line:84% at 1,000 degrees for ten seconds, fine. 00:16:49.910 --> 00:16:52.010 align:middle line:84% It'll give you the active arsenic. 00:16:52.010 --> 00:16:53.760 align:middle line:84% It'll take it up to at 1,000 degrees, 00:16:53.760 --> 00:16:55.010 align:middle line:90% whatever the solubility limit. 00:16:55.010 --> 00:16:59.140 align:middle line:84% Is say it's 3e20, and just clip off the profile and go down from 00:16:59.140 --> 00:16:59.640 align:middle line:90% there. 00:16:59.640 --> 00:17:02.570 align:middle line:84% So it imposes a very kindergarten-like, sort 00:17:02.570 --> 00:17:04.910 align:middle line:90% of elementary activation model. 00:17:04.910 --> 00:17:06.963 align:middle line:84% But it can still be useful if you're 00:17:06.963 --> 00:17:09.380 align:middle line:84% trying to figure out what your sheet resistance should be. 00:17:09.380 --> 00:17:13.770 align:middle line:84% But it doesn't have a lot of these kinetics built in. 00:17:13.770 --> 00:17:16.400 align:middle line:84% People need to do that more empirically. 00:17:16.400 --> 00:17:20.210 align:middle line:84% Do an implant, do an anneal at various temperatures, 00:17:20.210 --> 00:17:25.609 align:middle line:84% and see what your activation ratio is. 00:17:25.609 --> 00:17:28.099 align:middle line:90% OK, so let's go on to slide 4. 00:17:28.099 --> 00:17:30.210 align:middle line:84% And this is, again, review from last time, 00:17:30.210 --> 00:17:31.918 align:middle line:84% but I think it's important to review this 00:17:31.918 --> 00:17:34.640 align:middle line:84% before we talk about transient enhanced diffusion. 00:17:34.640 --> 00:17:36.320 align:middle line:84% Last time we talked about this model 00:17:36.320 --> 00:17:41.900 align:middle line:84% with a funny name called the plus 1 model of implant damage, 00:17:41.900 --> 00:17:43.850 align:middle line:84% or plus-one model for residual damage. 00:17:43.850 --> 00:17:47.450 align:middle line:84% It was published by Giles back in 1991. 00:17:47.450 --> 00:17:50.230 align:middle line:90% And the idea was this. 00:17:50.230 --> 00:17:54.320 align:middle line:84% Or what the model says is most of the recoiled silicon 00:17:54.320 --> 00:17:57.350 align:middle line:84% interstitials and vacancies recombine 00:17:57.350 --> 00:18:00.980 align:middle line:84% very rapidly in the first few milliseconds, or hundredths 00:18:00.980 --> 00:18:04.760 align:middle line:84% of a second, during the implant, or else just when you just 00:18:04.760 --> 00:18:07.800 align:middle line:90% put it into the anneal. 00:18:07.800 --> 00:18:09.360 align:middle line:84% So you create a huge number of these. 00:18:09.360 --> 00:18:11.570 align:middle line:84% But most of the interstitials find a vacancy, 00:18:11.570 --> 00:18:14.660 align:middle line:84% and they find a place to go back to. 00:18:14.660 --> 00:18:15.950 align:middle line:90% How about the remaining? 00:18:15.950 --> 00:18:19.320 align:middle line:84% It's only the net remaining that we care about. 00:18:19.320 --> 00:18:23.120 align:middle line:84% So it's the distribution of the remaining interstitials, 00:18:23.120 --> 00:18:26.180 align:middle line:84% or the recoils, shows a net-- tends 00:18:26.180 --> 00:18:29.360 align:middle line:84% to have a net excess of vacancies near the surface 00:18:29.360 --> 00:18:32.330 align:middle line:84% and a net excess of interstitials towards the bulk. 00:18:32.330 --> 00:18:37.470 align:middle line:84% So in fact, if you plot on this plot-- 00:18:37.470 --> 00:18:38.690 align:middle line:90% this is a plot from Giles-- 00:18:38.690 --> 00:18:42.380 align:middle line:84% concentration versus step, this is the total number 00:18:42.380 --> 00:18:45.350 align:middle line:84% of interstitials up here, in the 10 to the 21 range, 00:18:45.350 --> 00:18:48.680 align:middle line:84% or high 10 to the 20s for this phosphorus implant. 00:18:48.680 --> 00:18:50.630 align:middle line:84% And the total vacancies, you can't even 00:18:50.630 --> 00:18:52.100 align:middle line:90% distinguish the two curves. 00:18:52.100 --> 00:18:53.600 align:middle line:84% They're practically-- they're really 00:18:53.600 --> 00:18:55.183 align:middle line:84% on top of each other on the log scale. 00:18:55.183 --> 00:18:58.400 align:middle line:84% When you subtract them from each other, what you find-- 00:18:58.400 --> 00:19:02.060 align:middle line:84% so you subtract interstitials from the vacancies-- 00:19:02.060 --> 00:19:03.767 align:middle line:84% that the net vacancy concentration 00:19:03.767 --> 00:19:04.850 align:middle line:90% looks something like this. 00:19:04.850 --> 00:19:07.770 align:middle line:84% That's what's shown by this little profile here. 00:19:07.770 --> 00:19:10.640 align:middle line:84% So near the surface, we have some extra vacancies 00:19:10.640 --> 00:19:12.920 align:middle line:84% of a concentration, in this example, of about 10 00:19:12.920 --> 00:19:13.820 align:middle line:90% to the 17th. 00:19:13.820 --> 00:19:15.800 align:middle line:84% In the bulk, a little bit deeper, 00:19:15.800 --> 00:19:17.630 align:middle line:90% we have net interstitials. 00:19:17.630 --> 00:19:20.120 align:middle line:84% But their total numbers is orders of magnitude 00:19:20.120 --> 00:19:23.540 align:middle line:84% lower, because a lot of them have recombined. 00:19:23.540 --> 00:19:25.910 align:middle line:84% And look at their order of magnitude. 00:19:25.910 --> 00:19:27.230 align:middle line:90% What is their height? 00:19:27.230 --> 00:19:29.930 align:middle line:84% Well, lo and behold, the height of these net 00:19:29.930 --> 00:19:32.300 align:middle line:84% interstitials, its concentration is 00:19:32.300 --> 00:19:36.740 align:middle line:84% very close to the concentration of the phosphorus implant-- 00:19:36.740 --> 00:19:39.450 align:middle line:84% very, very close-- so of order of magnitude. 00:19:39.450 --> 00:19:42.950 align:middle line:84% So to first order, what Giles said, 00:19:42.950 --> 00:19:45.650 align:middle line:84% is that all of the original implant damage 00:19:45.650 --> 00:19:49.100 align:middle line:84% recombines and leaves behind only one excess interstitial 00:19:49.100 --> 00:19:51.440 align:middle line:84% for every dopant atom you ion implanted. 00:19:51.440 --> 00:19:54.830 align:middle line:84% So if I ion implanted, in this case, 10 to the 13th phosphorus, 00:19:54.830 --> 00:19:58.490 align:middle line:84% then he would say that the number of interstitials 00:19:58.490 --> 00:20:01.070 align:middle line:84% left behind is 10 to the 13th per square centimeter-- 00:20:01.070 --> 00:20:03.800 align:middle line:84% because every phosphorus atom eventually finds 00:20:03.800 --> 00:20:05.750 align:middle line:90% a home on a silicon lattice. 00:20:05.750 --> 00:20:08.690 align:middle line:84% And those 10 to the 13th silicon atoms 00:20:08.690 --> 00:20:11.120 align:middle line:90% must then be interstitials. 00:20:11.120 --> 00:20:15.890 align:middle line:84% So that's the most elementary model, so to speak, 00:20:15.890 --> 00:20:17.960 align:middle line:84% for the amount of damage that's produced. 00:20:17.960 --> 00:20:18.900 align:middle line:90% And it's easy to do. 00:20:18.900 --> 00:20:22.718 align:middle line:84% You just take the dose, and that's the answer more or less. 00:20:22.718 --> 00:20:25.010 align:middle line:84% Actually, if we want to be a little more sophisticated, 00:20:25.010 --> 00:20:27.770 align:middle line:84% people since that time have come up 00:20:27.770 --> 00:20:31.790 align:middle line:84% with what they call a plus-n model, where n is of order 00:20:31.790 --> 00:20:34.010 align:middle line:90% 1 but not exactly equal to 1. 00:20:34.010 --> 00:20:40.270 align:middle line:84% And this is Pelaz et al. from the MRS meeting in 1997-- 00:20:40.270 --> 00:20:43.020 align:middle line:84% came up with this sort of plus-n model. 00:20:43.020 --> 00:20:47.740 align:middle line:84% What they were saying is that the multiplier 00:20:47.740 --> 00:20:52.030 align:middle line:84% on the dose for the original ion implant dose, the multiplier 00:20:52.030 --> 00:20:53.950 align:middle line:90% may not be exactly 1. 00:20:53.950 --> 00:20:54.900 align:middle line:90% It may be 2. 00:20:54.900 --> 00:20:57.040 align:middle line:84% It may be 3-- something of that order. 00:20:57.040 --> 00:20:59.470 align:middle line:84% So this plus 1 approximation, which 00:20:59.470 --> 00:21:02.620 align:middle line:84% says that the number of interstitials created exactly 00:21:02.620 --> 00:21:07.060 align:middle line:84% equals the dose, it's reasonably good, 00:21:07.060 --> 00:21:08.890 align:middle line:84% but it's not necessarily perfect. 00:21:08.890 --> 00:21:12.955 align:middle line:84% And it may be particularly not as good for a heavy ion-- 00:21:12.955 --> 00:21:16.990 align:middle line:84% a low energy, or a low dose, particularly for heavy ions. 00:21:16.990 --> 00:21:19.180 align:middle line:84% The reason we don't think it's so great-- 00:21:19.180 --> 00:21:22.510 align:middle line:84% it's not as perfect-- is because there's a lot of recoils. 00:21:22.510 --> 00:21:25.360 align:middle line:84% If I implant arsenic, it's a very heavy ion. 00:21:25.360 --> 00:21:28.960 align:middle line:84% It comes in, it can impart a fair amount of energy 00:21:28.960 --> 00:21:30.970 align:middle line:84% to a silicon that's originally at rest. 00:21:30.970 --> 00:21:33.550 align:middle line:84% And then that creates more recoils. 00:21:33.550 --> 00:21:35.920 align:middle line:84% So you can have a large population 00:21:35.920 --> 00:21:41.120 align:middle line:84% of recoils for each ion relative to the ion population. 00:21:41.120 --> 00:21:42.730 align:middle line:84% And so that means they can essentially 00:21:42.730 --> 00:21:43.910 align:middle line:90% do a little more damage. 00:21:43.910 --> 00:21:50.140 align:middle line:84% So a simple approximation using a plus-n factor, 00:21:50.140 --> 00:21:52.718 align:middle line:84% which is a function of the ion species, the energy, 00:21:52.718 --> 00:21:53.260 align:middle line:90% and the dose. 00:21:53.260 --> 00:21:56.770 align:middle line:84% And here's an example of a plot from that paper. 00:21:56.770 --> 00:21:58.912 align:middle line:90% This is a plot of the n factor. 00:21:58.912 --> 00:22:00.370 align:middle line:84% So what do we mean by the n factor? 00:22:00.370 --> 00:22:02.800 align:middle line:84% That's the multiplier that you need to multiply 00:22:02.800 --> 00:22:05.830 align:middle line:90% the dose of the primary ion. 00:22:05.830 --> 00:22:08.500 align:middle line:84% And that will tell you the number, then the dose 00:22:08.500 --> 00:22:10.060 align:middle line:90% of excess interstitials. 00:22:10.060 --> 00:22:13.490 align:middle line:84% And so let's say if you're a boron. 00:22:13.490 --> 00:22:15.310 align:middle line:84% So let's look at this solid line. 00:22:15.310 --> 00:22:19.090 align:middle line:84% And we're doing boron somewhere around 5 to 10 Kev. 00:22:19.090 --> 00:22:21.580 align:middle line:84% Well, the n factor is very close to 1. 00:22:21.580 --> 00:22:24.650 align:middle line:84% So if I implant 10 to the 13th per square centimeter, 00:22:24.650 --> 00:22:27.100 align:middle line:84% I get 10 to the 13th per square centimeter interstitials 00:22:27.100 --> 00:22:29.620 align:middle line:90% excess created. 00:22:29.620 --> 00:22:31.750 align:middle line:84% Look at BF2, is a little heavier. 00:22:31.750 --> 00:22:35.200 align:middle line:84% And in that same range, the n factor is 1.5. 00:22:35.200 --> 00:22:39.423 align:middle line:84% So if I implant 1 times 10 to the 13th BF2 per square, 00:22:39.423 --> 00:22:41.590 align:middle line:84% then I would assume that the number of interstitials 00:22:41.590 --> 00:22:44.080 align:middle line:84% is 1.5 times 10 to the 13th in this model. 00:22:44.080 --> 00:22:44.950 align:middle line:90% And look at arsenic. 00:22:44.950 --> 00:22:48.010 align:middle line:84% It's actually almost up to a factor of 3 to 3.5. 00:22:48.010 --> 00:22:52.570 align:middle line:84% So somewhere between 1 and 3, and particularly at low energies 00:22:52.570 --> 00:22:54.550 align:middle line:84% where there's a lot of nuclear stopping, 00:22:54.550 --> 00:22:57.070 align:middle line:90% the n factor tends to increase. 00:22:57.070 --> 00:23:00.010 align:middle line:84% At high energies, they all approach one. 00:23:00.010 --> 00:23:05.200 align:middle line:84% And particularly for heavy ions, the n factor can be greater. 00:23:05.200 --> 00:23:06.970 align:middle line:84% Now the reason we're emphasizing this, 00:23:06.970 --> 00:23:09.402 align:middle line:84% you need to know the dose of interstitials. 00:23:09.402 --> 00:23:11.110 align:middle line:84% You need to understand that, because it's 00:23:11.110 --> 00:23:13.340 align:middle line:84% those excess interstitials that are 00:23:13.340 --> 00:23:17.160 align:middle line:84% going to be responsible for transient-m enhanced diffusion. 00:23:17.160 --> 00:23:19.160 align:middle line:84% So that's why people pay a lot of attention 00:23:19.160 --> 00:23:23.210 align:middle line:90% to these damage models. 00:23:23.210 --> 00:23:24.500 align:middle line:90% OK, so that's the next topic. 00:23:24.500 --> 00:23:27.350 align:middle line:84% We go on to Slide Number 6 on TED. 00:23:27.350 --> 00:23:31.100 align:middle line:84% I think I showed this last time as a way of finishing up. 00:23:31.100 --> 00:23:33.000 align:middle line:84% This is kind of an anomalous plot. 00:23:33.000 --> 00:23:35.180 align:middle line:84% It's a concentration as a function of depth. 00:23:35.180 --> 00:23:36.680 align:middle line:90% These are boron profiles. 00:23:36.680 --> 00:23:40.880 align:middle line:84% And what's anomalous about it is if you look at the blue profile 00:23:40.880 --> 00:23:43.640 align:middle line:84% here, it's a 10 second at 1,000 degrees 00:23:43.640 --> 00:23:47.930 align:middle line:84% at a very high temperature, as opposed to two minutes at 800. 00:23:47.930 --> 00:23:51.140 align:middle line:84% The 1,000-degree profile-- this is after being ion implanted-- 00:23:51.140 --> 00:23:54.350 align:middle line:84% the 1,000-degree profile is actually shallower-- 00:23:54.350 --> 00:23:56.670 align:middle line:84% less motion at a higher temperature. 00:23:56.670 --> 00:23:58.880 align:middle line:84% So this is very much non Fickian. 00:23:58.880 --> 00:24:01.130 align:middle line:84% This is very difficult to explain 00:24:01.130 --> 00:24:05.570 align:middle line:84% from a simple single diffusivity, which 00:24:05.570 --> 00:24:07.760 align:middle line:90% is exponentially activated. 00:24:07.760 --> 00:24:09.800 align:middle line:84% Because we know, if you look in your text 00:24:09.800 --> 00:24:14.990 align:middle line:84% for the intrinsic diffusion of boron, that at 1,000 degrees 00:24:14.990 --> 00:24:18.150 align:middle line:84% it's like two or three orders of magnitude higher. 00:24:18.150 --> 00:24:21.680 align:middle line:84% And yet here this cannot be normal regular intrinsic 00:24:21.680 --> 00:24:24.470 align:middle line:84% diffusion, because you're getting a lot less diffusion 00:24:24.470 --> 00:24:26.780 align:middle line:90% at 1,000. 00:24:26.780 --> 00:24:30.800 align:middle line:90% And so this is because of TED. 00:24:30.800 --> 00:24:33.320 align:middle line:84% And it'll turn out that-- we'll talk about 00:24:33.320 --> 00:24:34.850 align:middle line:84% in the modeling in this lecture why 00:24:34.850 --> 00:24:36.830 align:middle line:84% it is that at low temperature, we actually 00:24:36.830 --> 00:24:40.070 align:middle line:84% can get higher amounts of transient-enhanced diffusion-- 00:24:40.070 --> 00:24:42.770 align:middle line:84% higher amounts of this damage-induced diffusion 00:24:42.770 --> 00:24:45.000 align:middle line:90% than at high temperatures. 00:24:45.000 --> 00:24:46.610 align:middle line:84% People didn't see this for many years. 00:24:46.610 --> 00:24:50.300 align:middle line:84% This TED was first started to be observed in the mid '80s, 00:24:50.300 --> 00:24:54.620 align:middle line:84% and then by the early '90s it became pretty prevalent. 00:24:54.620 --> 00:24:55.618 align:middle line:90% And why not? 00:24:55.618 --> 00:24:56.660 align:middle line:90% Why didn't people see it? 00:24:56.660 --> 00:25:01.070 align:middle line:84% Well, for years annealed devices were very large. 00:25:01.070 --> 00:25:02.690 align:middle line:84% They were large in lateral dimension. 00:25:02.690 --> 00:25:04.350 align:middle line:84% They were large in vertical dimension. 00:25:04.350 --> 00:25:07.850 align:middle line:84% So annyas took place at reasonably high temperature, 00:25:07.850 --> 00:25:08.990 align:middle line:90% and they're very long. 00:25:08.990 --> 00:25:10.670 align:middle line:90% And so the TED effect-- 00:25:10.670 --> 00:25:12.440 align:middle line:84% the damage effects were completely 00:25:12.440 --> 00:25:14.065 align:middle line:90% masked by normal diffusion. 00:25:14.065 --> 00:25:15.440 align:middle line:84% Because TED, what does that mean? 00:25:15.440 --> 00:25:16.130 align:middle line:90% Transient. 00:25:16.130 --> 00:25:18.560 align:middle line:84% It only lasts for a limited period of time-- 00:25:18.560 --> 00:25:19.650 align:middle line:90% a short period. 00:25:19.650 --> 00:25:24.980 align:middle line:84% So if you put a wafer in a furnace at 1,000 degrees, or 800 00:25:24.980 --> 00:25:26.930 align:middle line:84% for four or five hours-- a couple of hours-- 00:25:26.930 --> 00:25:28.080 align:middle line:90% you're not going to see it. 00:25:28.080 --> 00:25:31.040 align:middle line:84% It's only when people started trying to get very little amount 00:25:31.040 --> 00:25:34.100 align:middle line:84% of [INAUDIBLE],, and they cut back on the time-- 00:25:34.100 --> 00:25:36.740 align:middle line:84% 10 seconds at 1,000, or a few minutes-- so 00:25:36.740 --> 00:25:39.170 align:middle line:84% development of rapid thermal annealing techniques 00:25:39.170 --> 00:25:42.650 align:middle line:84% where the anomalous diffusion became obvious. 00:25:42.650 --> 00:25:44.120 align:middle line:84% Because the thermal budgets today 00:25:44.120 --> 00:25:47.240 align:middle line:84% are so small that, in fact, TEDs were actually 00:25:47.240 --> 00:25:49.970 align:middle line:84% the dominant effect that determines many junction 00:25:49.970 --> 00:25:54.320 align:middle line:84% depths, not ordinary diffusion that we taught you about 00:25:54.320 --> 00:25:57.320 align:middle line:90% earlier, a couple lectures ago. 00:25:57.320 --> 00:25:59.600 align:middle line:84% And even sometimes not even concentration-dependent 00:25:59.600 --> 00:26:01.850 align:middle line:84% diffusion-- doesn't really matter that much. 00:26:01.850 --> 00:26:05.180 align:middle line:84% A lot of it is dominated by the transient diffusion 00:26:05.180 --> 00:26:09.630 align:middle line:84% effect, at least for certain dopants-- particularly boron. 00:26:09.630 --> 00:26:12.380 align:middle line:84% So the type of enhancement we're talking about here, 00:26:12.380 --> 00:26:14.390 align:middle line:84% it may only last for a short period, 00:26:14.390 --> 00:26:17.900 align:middle line:84% but we're talking about maybe 20,000 times 00:26:17.900 --> 00:26:21.170 align:middle line:84% the diffusivity-- the ordinary diffusivity at 700, 00:26:21.170 --> 00:26:24.860 align:middle line:84% or maybe even 400 times the diffusivity at 1,000. 00:26:24.860 --> 00:26:26.450 align:middle line:90% So these are not negligible. 00:26:26.450 --> 00:26:28.910 align:middle line:90% These are huge enhancements. 00:26:28.910 --> 00:26:31.130 align:middle line:84% And there was a lot of work in the early days spent 00:26:31.130 --> 00:26:35.750 align:middle line:84% at trying to figure out what this could possibly be due to. 00:26:35.750 --> 00:26:39.590 align:middle line:90% So let's go on to Slide 7. 00:26:39.590 --> 00:26:42.200 align:middle line:84% The basic model for TED, what we assume 00:26:42.200 --> 00:26:44.600 align:middle line:84% is that all the implant damage recombines 00:26:44.600 --> 00:26:48.260 align:middle line:84% very quickly except for the one interstitial generated 00:26:48.260 --> 00:26:49.290 align:middle line:90% per dopant atom. 00:26:49.290 --> 00:26:51.530 align:middle line:84% So the easy way we think about it is just 00:26:51.530 --> 00:26:55.190 align:middle line:84% use the Giles plus 1 model, or plus n, 00:26:55.190 --> 00:26:56.790 align:middle line:84% if you want to be really accurate. 00:26:56.790 --> 00:26:59.150 align:middle line:84% But for now, we'll just do plus 1. 00:26:59.150 --> 00:27:04.700 align:middle line:84% And here's an example of how TED effects can be seen. 00:27:04.700 --> 00:27:07.575 align:middle line:84% And they're actually quite non-local. 00:27:07.575 --> 00:27:09.450 align:middle line:84% And that's what's interesting about them too. 00:27:09.450 --> 00:27:11.690 align:middle line:84% So here is an experiment that was done. 00:27:11.690 --> 00:27:14.460 align:middle line:84% This is a concentration as a function of depth-- 00:27:14.460 --> 00:27:16.070 align:middle line:90% so maybe a SIMS profile. 00:27:16.070 --> 00:27:20.460 align:middle line:84% And the initial profile before any annealing looked like this. 00:27:20.460 --> 00:27:23.760 align:middle line:84% So you have boron, which there's very low boron at the surface. 00:27:23.760 --> 00:27:25.790 align:middle line:84% And then you have a boron marker layer. 00:27:25.790 --> 00:27:27.920 align:middle line:90% So it has some depth. 00:27:27.920 --> 00:27:31.430 align:middle line:84% At some depth, there's a boron layer that's doped about 1 E18. 00:27:31.430 --> 00:27:34.580 align:middle line:84% This marker layer can be put in a variety of ways-- 00:27:34.580 --> 00:27:36.350 align:middle line:84% could be put in by epitaxial growth-- 00:27:36.350 --> 00:27:37.190 align:middle line:90% whatever. 00:27:37.190 --> 00:27:40.487 align:middle line:84% It's a region that's boron doped. 00:27:40.487 --> 00:27:41.570 align:middle line:90% We call it a marker layer. 00:27:41.570 --> 00:27:43.430 align:middle line:84% It could be the base of a bipolar transistor 00:27:43.430 --> 00:27:44.390 align:middle line:90% for all we know. 00:27:44.390 --> 00:27:47.090 align:middle line:84% And it looks like a box initially. 00:27:47.090 --> 00:27:51.350 align:middle line:84% And then you go and you ion implant arsenic above it. 00:27:51.350 --> 00:27:53.600 align:middle line:84% Now notice the arsenic never touches the boron. 00:27:53.600 --> 00:27:56.590 align:middle line:84% So I'm not ion implanting arsenic deep into the wafer, 00:27:56.590 --> 00:27:58.750 align:middle line:84% it's just in the near surface region. 00:27:58.750 --> 00:28:01.210 align:middle line:84% Now, this arsenic is a reasonably high dose. 00:28:01.210 --> 00:28:04.510 align:middle line:84% You can see the concentration is quite high. 00:28:04.510 --> 00:28:06.410 align:middle line:84% This arsenic does a lot of implant-- 00:28:06.410 --> 00:28:08.230 align:middle line:84% it creates a lot of implant damage. 00:28:08.230 --> 00:28:10.960 align:middle line:84% But the damage, of course, is confined to the near surface 00:28:10.960 --> 00:28:13.017 align:middle line:90% region. 00:28:13.017 --> 00:28:14.350 align:middle line:90% A lot of the damage will anneal. 00:28:14.350 --> 00:28:16.360 align:middle line:84% Because if it's amorphous, you get SPE, right? 00:28:16.360 --> 00:28:18.250 align:middle line:84% And the fact, this little dashed line 00:28:18.250 --> 00:28:21.340 align:middle line:84% was supposed to represent the amorphous crystal and interface. 00:28:21.340 --> 00:28:24.040 align:middle line:84% So everything to the left is amorphized. 00:28:24.040 --> 00:28:29.590 align:middle line:84% But we know that there is a certain amount 00:28:29.590 --> 00:28:31.700 align:middle line:90% of damage at the end of range. 00:28:31.700 --> 00:28:34.330 align:middle line:90% There are excess interstitials. 00:28:34.330 --> 00:28:36.400 align:middle line:84% And so these excess interstitials 00:28:36.400 --> 00:28:39.070 align:middle line:90% are then going to diffuse in. 00:28:39.070 --> 00:28:41.320 align:middle line:84% They're going to form these 311 defects. 00:28:41.320 --> 00:28:43.195 align:middle line:84% They're going to diffuse in, and then they're 00:28:43.195 --> 00:28:45.100 align:middle line:84% going to dramatically enhance the diffusion 00:28:45.100 --> 00:28:46.570 align:middle line:90% coefficient of the boron below. 00:28:46.570 --> 00:28:49.150 align:middle line:84% So don't think necessarily of the implant damage 00:28:49.150 --> 00:28:51.627 align:middle line:84% effect as being, oh, the implant damage 00:28:51.627 --> 00:28:53.210 align:middle line:84% and the enhanced diffusion occurs only 00:28:53.210 --> 00:28:54.560 align:middle line:90% where the implant is-- 00:28:54.560 --> 00:28:56.390 align:middle line:90% just like oxidation. 00:28:56.390 --> 00:28:59.270 align:middle line:84% Remember, in OED, you can have a process happening 00:28:59.270 --> 00:29:01.280 align:middle line:84% at the surface, and you can have interstitials 00:29:01.280 --> 00:29:05.030 align:middle line:84% injected and influencing diffusion going on much deeper. 00:29:05.030 --> 00:29:06.950 align:middle line:90% TED can be like that. 00:29:06.950 --> 00:29:10.262 align:middle line:84% The difference is that Ted is transient. 00:29:10.262 --> 00:29:11.720 align:middle line:84% It only lasts for a certain period, 00:29:11.720 --> 00:29:14.225 align:middle line:90% until the damage goes away. 00:29:14.225 --> 00:29:17.520 align:middle line:90% 00:29:17.520 --> 00:29:18.930 align:middle line:90% One question I just had. 00:29:18.930 --> 00:29:21.090 align:middle line:84% So in this schematic illustration, 00:29:21.090 --> 00:29:23.640 align:middle line:84% see the green profile after diffusion. 00:29:23.640 --> 00:29:25.080 align:middle line:90% Look at the amount of diffusion. 00:29:25.080 --> 00:29:28.050 align:middle line:84% There was a lot of TED of the boron and not 00:29:28.050 --> 00:29:30.270 align:middle line:90% much for the arsenic. 00:29:30.270 --> 00:29:32.340 align:middle line:84% Does anybody have any ideas, knowing 00:29:32.340 --> 00:29:35.970 align:middle line:84% what we know about the diffusion mechanisms of boron and arsenic 00:29:35.970 --> 00:29:39.450 align:middle line:84% and other things, why you would expect a lot more 00:29:39.450 --> 00:29:41.730 align:middle line:84% damage-enhanced diffusion for boron than you 00:29:41.730 --> 00:29:46.260 align:middle line:84% would for arsenic, as shown in this example? 00:29:46.260 --> 00:29:49.170 align:middle line:90% Anybody have any ideas? 00:29:49.170 --> 00:29:51.270 align:middle line:90% [AI Auditory hallucination] 00:29:51.270 --> 00:29:53.430 align:middle line:84% JUDY HOYT: What do we know about f sub i? 00:29:53.430 --> 00:29:56.730 align:middle line:84% What do we know about the diffusion mechanism of boron? 00:29:56.730 --> 00:30:01.140 align:middle line:84% Is it mostly interstitials, mostly vacancies, or both? 00:30:01.140 --> 00:30:03.000 align:middle line:84% Does anybody remember f sub i for boron? 00:30:03.000 --> 00:30:06.040 align:middle line:90% 00:30:06.040 --> 00:30:07.090 align:middle line:90% Well, let's take a vote. 00:30:07.090 --> 00:30:11.450 align:middle line:84% How many people think it's 1, f sub i? 00:30:11.450 --> 00:30:11.950 align:middle line:90% All right. 00:30:11.950 --> 00:30:12.970 align:middle line:90% Yeah, it's 1. 00:30:12.970 --> 00:30:14.530 align:middle line:84% So what that means is f sub i-- it 00:30:14.530 --> 00:30:17.440 align:middle line:84% means boron-diffusion mechanism is almost 00:30:17.440 --> 00:30:21.200 align:middle line:84% entirely by interstitials, as opposed to diffusing 00:30:21.200 --> 00:30:22.880 align:middle line:90% with vacancies, OK? 00:30:22.880 --> 00:30:25.100 align:middle line:84% So excess interstitials-- boron needs 00:30:25.100 --> 00:30:26.900 align:middle line:84% interstitials around in order to move. 00:30:26.900 --> 00:30:28.940 align:middle line:90% That's its mechanism of moving. 00:30:28.940 --> 00:30:29.880 align:middle line:90% How do we know that? 00:30:29.880 --> 00:30:33.680 align:middle line:84% We know that from a whole series of oxidation-enhanced diffusion 00:30:33.680 --> 00:30:35.990 align:middle line:84% experiments and nitrodation-retarded diffusion 00:30:35.990 --> 00:30:37.850 align:middle line:84% experiments that people have done-- 00:30:37.850 --> 00:30:40.400 align:middle line:84% injecting interstitials, injecting vacancies, 00:30:40.400 --> 00:30:42.540 align:middle line:84% and they see what happens to boron. 00:30:42.540 --> 00:30:45.020 align:middle line:84% So in TED modeling what we're going to say 00:30:45.020 --> 00:30:49.190 align:middle line:84% is that this implant damage is going to inject into the silicon 00:30:49.190 --> 00:30:51.050 align:middle line:90% a lot of excess interstitials. 00:30:51.050 --> 00:30:53.840 align:middle line:90% Boron diffuses by interstitials. 00:30:53.840 --> 00:30:56.270 align:middle line:84% And its diffusion coefficient is going to be enhanced, 00:30:56.270 --> 00:30:59.390 align:middle line:84% or pumped up by these excess interstitials. 00:30:59.390 --> 00:31:03.050 align:middle line:84% Arsenic-- what about the f sub i for arsenic, 00:31:03.050 --> 00:31:04.130 align:middle line:90% what do we think that is? 00:31:04.130 --> 00:31:06.100 align:middle line:90% Is it 1? 00:31:06.100 --> 00:31:08.320 align:middle line:90% .5? 00:31:08.320 --> 00:31:10.780 align:middle line:90% Anybody vote for a half? 00:31:10.780 --> 00:31:14.060 align:middle line:84% Yeah, it's on the order of half, roughly-- 00:31:14.060 --> 00:31:15.920 align:middle line:84% maybe 60%-- depends on who you talk to. 00:31:15.920 --> 00:31:19.520 align:middle line:84% People who do this for a living will argue their career on it. 00:31:19.520 --> 00:31:21.950 align:middle line:84% But you know, I think it's close to 60%. 00:31:21.950 --> 00:31:24.897 align:middle line:84% Anyway, it's partly enhanced by interstitials. 00:31:24.897 --> 00:31:27.230 align:middle line:84% Rather, it's partly diffusing with interstitials, partly 00:31:27.230 --> 00:31:28.170 align:middle line:90% with vacancies. 00:31:28.170 --> 00:31:29.600 align:middle line:90% So you don't expect-- 00:31:29.600 --> 00:31:32.150 align:middle line:84% it doesn't have quite as much dependence on interstitials 00:31:32.150 --> 00:31:34.310 align:middle line:90% as does boron. 00:31:34.310 --> 00:31:36.252 align:middle line:84% And also most of the arsenic profile here-- 00:31:36.252 --> 00:31:38.210 align:middle line:84% it's a little tricky question-- but most of it, 00:31:38.210 --> 00:31:40.650 align:middle line:84% remember, was to the left of the dashed line. 00:31:40.650 --> 00:31:44.450 align:middle line:84% So most of it occurred in the region where there was SPE. 00:31:44.450 --> 00:31:46.490 align:middle line:84% So that's going to regrow very quickly 00:31:46.490 --> 00:31:49.290 align:middle line:84% and not cause too much diffusion. 00:31:49.290 --> 00:31:53.450 align:middle line:84% So it'll turn out, as you'll see in most examples-- not all-- 00:31:53.450 --> 00:31:56.240 align:middle line:84% arsenic certainly has some TED, but it's 00:31:56.240 --> 00:31:59.288 align:middle line:90% much more prevalent for boron. 00:31:59.288 --> 00:32:01.330 align:middle line:84% In fact, I want to show you some actual examples. 00:32:01.330 --> 00:32:02.590 align:middle line:90% That was a cartoon picture. 00:32:02.590 --> 00:32:06.370 align:middle line:84% But it's based on things that people observed in real life. 00:32:06.370 --> 00:32:08.290 align:middle line:84% Here's an example I want to show you 00:32:08.290 --> 00:32:13.360 align:middle line:84% of some data in the literature on where TED can affect 00:32:13.360 --> 00:32:16.660 align:middle line:90% a bipolar-transistor structure. 00:32:16.660 --> 00:32:18.922 align:middle line:90% And these are epitaxially grown. 00:32:18.922 --> 00:32:20.380 align:middle line:84% I haven't talked about epitaxy yet, 00:32:20.380 --> 00:32:22.660 align:middle line:84% but it's a crystal growth technique 00:32:22.660 --> 00:32:26.530 align:middle line:84% by CVD, by which you can put in fairly arbitrary and quite 00:32:26.530 --> 00:32:28.970 align:middle line:90% abrupt doping profiles. 00:32:28.970 --> 00:32:31.000 align:middle line:84% So let's take a look at the inset up here. 00:32:31.000 --> 00:32:34.360 align:middle line:84% And in the inset shows schematically 00:32:34.360 --> 00:32:38.230 align:middle line:84% the initial epitaxial structure of this bipolar transistor. 00:32:38.230 --> 00:32:42.110 align:middle line:84% So there's a region on the bottom in depth, 00:32:42.110 --> 00:32:44.680 align:middle line:90% which is n minus silicon. 00:32:44.680 --> 00:32:47.950 align:middle line:84% And then there's a region that is p plus. 00:32:47.950 --> 00:32:50.690 align:middle line:84% So it's got a high amount of boron-- silicon germanium. 00:32:50.690 --> 00:32:54.040 align:middle line:84% And then there's some lightly doped region. 00:32:54.040 --> 00:32:56.860 align:middle line:84% And then there's an n minus silicon cap. 00:32:56.860 --> 00:33:00.320 align:middle line:84% So it looks like in effect, if you look at the SIMS data-- 00:33:00.320 --> 00:33:03.020 align:middle line:90% boron versus depth-- 00:33:03.020 --> 00:33:05.540 align:middle line:84% the region down here marked silicon, 00:33:05.540 --> 00:33:07.310 align:middle line:90% that's all epitaxial silicon. 00:33:07.310 --> 00:33:10.490 align:middle line:84% The region in the center is epitaxial silicon germanium. 00:33:10.490 --> 00:33:12.800 align:middle line:84% It's an alloy of silicon and germanium. 00:33:12.800 --> 00:33:16.610 align:middle line:84% It's used in a lot of high-speed bipolar transistors these days. 00:33:16.610 --> 00:33:20.480 align:middle line:84% And the cap on top is single-crystal silicon. 00:33:20.480 --> 00:33:21.890 align:middle line:90% And those are the dimensions. 00:33:21.890 --> 00:33:23.930 align:middle line:84% And the silicon germanium region, 00:33:23.930 --> 00:33:26.690 align:middle line:84% when it was epitaxially grown, was doped with boron. 00:33:26.690 --> 00:33:30.110 align:middle line:84% And in fact here, the as grown profile is the diamonds. 00:33:30.110 --> 00:33:32.810 align:middle line:84% It's a little hard to see, but see these diamonds. 00:33:32.810 --> 00:33:34.070 align:middle line:90% It's a box. 00:33:34.070 --> 00:33:36.470 align:middle line:84% As grown it looks like a box, pretty much. 00:33:36.470 --> 00:33:39.620 align:middle line:84% And it has a height, or a doping level of about 3 times 10 00:33:39.620 --> 00:33:40.400 align:middle line:90% to the 19th. 00:33:40.400 --> 00:33:44.870 align:middle line:84% So that's the as grown, very abrupt profile by EPI. 00:33:44.870 --> 00:33:47.400 align:middle line:84% This little tail that you see here, this is SIMS knock on. 00:33:47.400 --> 00:33:49.010 align:middle line:84% So again, this is a SIMS profile, 00:33:49.010 --> 00:33:52.500 align:middle line:84% so it has some broadening due to the measurement technique. 00:33:52.500 --> 00:33:55.370 align:middle line:84% So that's what it looked like in the as grown. 00:33:55.370 --> 00:34:00.710 align:middle line:84% And if you look at the crosses, if you do no ion implant-- 00:34:00.710 --> 00:34:02.780 align:middle line:84% so you do not implant the emitter-- 00:34:02.780 --> 00:34:04.730 align:middle line:84% after you anneal it, you get something that 00:34:04.730 --> 00:34:08.150 align:middle line:90% looks just like the as grown. 00:34:08.150 --> 00:34:10.909 align:middle line:84% So with the anneal-- and this particular anneal 00:34:10.909 --> 00:34:12.770 align:middle line:90% is 850 for 10 seconds. 00:34:12.770 --> 00:34:14.270 align:middle line:90% So it's an RTA. 00:34:14.270 --> 00:34:16.310 align:middle line:84% You don't expect much diffusion of the boron. 00:34:16.310 --> 00:34:19.550 align:middle line:84% And in fact, you don't get any measured by SIMS. 00:34:19.550 --> 00:34:21.290 align:middle line:90% It's still perfectly abrupt. 00:34:21.290 --> 00:34:24.830 align:middle line:84% Now the third wafer, which is shown by these triangles, 00:34:24.830 --> 00:34:28.100 align:middle line:84% had an arsenic implant shown in the upper surface region-- 00:34:28.100 --> 00:34:30.380 align:middle line:84% just like I showed you in that cartoon. 00:34:30.380 --> 00:34:31.429 align:middle line:90% And this is actual data. 00:34:31.429 --> 00:34:33.650 align:middle line:84% And now look at the boron profile. 00:34:33.650 --> 00:34:36.800 align:middle line:84% The open triangles for the exact same anneal, 00:34:36.800 --> 00:34:39.440 align:middle line:84% when you implanted the emitter, the open triangles 00:34:39.440 --> 00:34:40.280 align:middle line:90% have broadened. 00:34:40.280 --> 00:34:41.900 align:middle line:84% That profile is completely broadened. 00:34:41.900 --> 00:34:44.239 align:middle line:84% The P concentration is dropped, and now you 00:34:44.239 --> 00:34:46.600 align:middle line:90% have these large wings. 00:34:46.600 --> 00:34:50.840 align:middle line:84% Well, there's a lot of enhanced boron diffusion. 00:34:50.840 --> 00:34:51.620 align:middle line:90% This is TED. 00:34:51.620 --> 00:34:54.659 align:middle line:84% And this makes the device essentially inoperable. 00:34:54.659 --> 00:34:58.730 align:middle line:84% So you cannot-- the HBT doesn't work when it looks like this. 00:34:58.730 --> 00:34:59.970 align:middle line:90% The device is ruined. 00:34:59.970 --> 00:35:03.660 align:middle line:84% So a simple structure where you would calculate, oh, this anneal 00:35:03.660 --> 00:35:05.550 align:middle line:90% should be no problem. 00:35:05.550 --> 00:35:07.620 align:middle line:84% Here you do an arsenic implant on top. 00:35:07.620 --> 00:35:09.420 align:middle line:84% And all the interstitials injected 00:35:09.420 --> 00:35:13.000 align:middle line:84% cause this dramatic enhancement in the boron diffusion. 00:35:13.000 --> 00:35:19.280 align:middle line:84% So it happens in real-life structures, and it's an issue. 00:35:19.280 --> 00:35:20.920 align:middle line:84% Yeah, people have found ways around. 00:35:20.920 --> 00:35:25.400 align:middle line:84% In fact, from that same article on Slide 9, 00:35:25.400 --> 00:35:27.973 align:middle line:84% here's some example of some attempts that 00:35:27.973 --> 00:35:30.140 align:middle line:84% were made in that article-- some of them successful, 00:35:30.140 --> 00:35:33.410 align:middle line:90% some not-- to get rid of TED. 00:35:33.410 --> 00:35:37.490 align:middle line:84% Well, one attempt was people thought, OK, 00:35:37.490 --> 00:35:40.850 align:middle line:84% after you implant the arsenic, just do an anneal-- 00:35:40.850 --> 00:35:42.830 align:middle line:90% 600 degrees. 00:35:42.830 --> 00:35:45.800 align:middle line:84% Low enough temperature so the boron shouldn't diffuse, 00:35:45.800 --> 00:35:48.470 align:middle line:84% but maybe high enough to get rid of all the interstitials. 00:35:48.470 --> 00:35:51.350 align:middle line:84% OK, that seems maybe like a reasonable idea, 00:35:51.350 --> 00:35:54.030 align:middle line:90% but doesn't help at all. 00:35:54.030 --> 00:35:57.710 align:middle line:84% In fact, if you look at these diamonds-- again, 00:35:57.710 --> 00:35:59.810 align:middle line:84% these diamonds are for-- the anneal 00:35:59.810 --> 00:36:02.120 align:middle line:84% that took place at 600 degrees followed 00:36:02.120 --> 00:36:04.220 align:middle line:90% by the usual 850 10 seconds. 00:36:04.220 --> 00:36:06.650 align:middle line:84% And it's still just as broad as it was before-- 00:36:06.650 --> 00:36:07.400 align:middle line:90% plenty of TED. 00:36:07.400 --> 00:36:09.380 align:middle line:84% So 600 degree annealing doesn't seem 00:36:09.380 --> 00:36:13.010 align:middle line:84% to be a way to get rid of the damage very effectively. 00:36:13.010 --> 00:36:15.977 align:middle line:84% Well, the second panel down shows you another idea. 00:36:15.977 --> 00:36:17.060 align:middle line:90% How about melt the sample? 00:36:17.060 --> 00:36:18.590 align:middle line:90% That's pretty drastic. 00:36:18.590 --> 00:36:22.050 align:middle line:84% Hit it with a laser and melt it for a few nanoseconds-- 00:36:22.050 --> 00:36:25.370 align:middle line:84% so it completely melts, but it melts for so short a time 00:36:25.370 --> 00:36:27.050 align:middle line:90% that nothing moves. 00:36:27.050 --> 00:36:32.720 align:middle line:84% OK, that's melt induced-laser annealing and regrowth. 00:36:32.720 --> 00:36:34.430 align:middle line:90% And you can see there-- 00:36:34.430 --> 00:36:36.950 align:middle line:84% and then after you do that-- you've melted the sample, 00:36:36.950 --> 00:36:40.760 align:middle line:84% you get rid of everything, then you do the 850 10-second RTA. 00:36:40.760 --> 00:36:43.560 align:middle line:84% And lo and behold, all those wings are gone, 00:36:43.560 --> 00:36:46.920 align:middle line:90% so the boron stays put. 00:36:46.920 --> 00:36:49.590 align:middle line:84% So one way to get rid of that TED, of course, 00:36:49.590 --> 00:36:52.760 align:middle line:84% is to melt the sample, but that's kind of extreme. 00:36:52.760 --> 00:36:54.907 align:middle line:84% You need to use a laser, but it does 00:36:54.907 --> 00:36:56.990 align:middle line:84% prove that you can get rid of excess interstitials 00:36:56.990 --> 00:37:00.120 align:middle line:90% by melting, of course. 00:37:00.120 --> 00:37:02.990 align:middle line:84% And then when you do an 850 RTA, there's 00:37:02.990 --> 00:37:05.820 align:middle line:84% normal diffusion-- no more of the TED effect. 00:37:05.820 --> 00:37:08.750 align:middle line:84% So you can restore diffusion to normal. 00:37:08.750 --> 00:37:10.340 align:middle line:84% And this was another interesting-- 00:37:10.340 --> 00:37:16.400 align:middle line:84% on the bottom panel, this was a sample where it was just 00:37:16.400 --> 00:37:19.550 align:middle line:84% annealed at 850 for 10 seconds, but there was a very high 00:37:19.550 --> 00:37:21.230 align:middle line:90% concentration of oxygen-- 00:37:21.230 --> 00:37:23.280 align:middle line:90% backround oxygen in the sample. 00:37:23.280 --> 00:37:27.720 align:middle line:84% In fact, the oxygen in the sample was about 10 to the 20. 00:37:27.720 --> 00:37:31.970 align:middle line:84% So during the epitaxial growth, the silicon germanium layer 00:37:31.970 --> 00:37:33.875 align:middle line:84% was accidentally doped with oxygen. 00:37:33.875 --> 00:37:36.530 align:middle line:84% It was not really high purity material. 00:37:36.530 --> 00:37:39.560 align:middle line:84% And interestingly, TED is completely 00:37:39.560 --> 00:37:42.170 align:middle line:84% eliminated in the presence of a very high concentration 00:37:42.170 --> 00:37:46.200 align:middle line:84% of oxygen. In fact, you can see these plus signs are the boron 00:37:46.200 --> 00:37:49.320 align:middle line:84% profile on a sample anneal-- that, again, 850 00:37:49.320 --> 00:37:50.820 align:middle line:90% 10 seconds-- same RTA. 00:37:50.820 --> 00:37:54.180 align:middle line:84% The difference is-- and there was the same damage implant done 00:37:54.180 --> 00:37:55.140 align:middle line:90% on top-- 00:37:55.140 --> 00:37:58.530 align:middle line:84% in the presence of a high concentration of oxygen, 00:37:58.530 --> 00:38:00.990 align:middle line:90% there was no TED. 00:38:00.990 --> 00:38:02.880 align:middle line:90% So that's kind of strange. 00:38:02.880 --> 00:38:07.395 align:middle line:84% And in fact, similar results since that time 00:38:07.395 --> 00:38:08.520 align:middle line:90% have been found for carbon. 00:38:08.520 --> 00:38:10.020 align:middle line:84% You don't need quite so much carbon. 00:38:10.020 --> 00:38:11.310 align:middle line:90% You don't need 10 to the 20th. 00:38:11.310 --> 00:38:13.950 align:middle line:84% You can get away with about 10 of a 19th carbon. 00:38:13.950 --> 00:38:17.610 align:middle line:84% So people intentionally dope carbon now in silicon, 00:38:17.610 --> 00:38:20.460 align:middle line:84% in those regions where they want to get rid of TED. 00:38:20.460 --> 00:38:22.890 align:middle line:84% So this was kind of an accidental discovery 00:38:22.890 --> 00:38:25.170 align:middle line:84% initially, but pretty soon people 00:38:25.170 --> 00:38:28.030 align:middle line:84% started to realize this is a tremendous benefit. 00:38:28.030 --> 00:38:30.930 align:middle line:84% So towards the end of today, we'll 00:38:30.930 --> 00:38:33.540 align:middle line:84% understand a little better where these interstitials are 00:38:33.540 --> 00:38:34.950 align:middle line:90% coming from. 00:38:34.950 --> 00:38:37.440 align:middle line:84% But anything you can do to create a sink 00:38:37.440 --> 00:38:39.420 align:middle line:84% for interstitials-- be it a high oxygen-- 00:38:39.420 --> 00:38:41.430 align:middle line:84% oxygen is not the best element to use. 00:38:41.430 --> 00:38:43.027 align:middle line:90% It also kills the lifetime-- 00:38:43.027 --> 00:38:44.110 align:middle line:90% minority carrier lifetime. 00:38:44.110 --> 00:38:45.485 align:middle line:84% So your bipolar transistor is not 00:38:45.485 --> 00:38:46.770 align:middle line:90% the best bipolar in the world. 00:38:46.770 --> 00:38:50.190 align:middle line:84% But neither is this one, where the boron base is diffused out 00:38:50.190 --> 00:38:51.900 align:middle line:90% completely. 00:38:51.900 --> 00:38:53.830 align:middle line:84% Carbon turns out to be a little better to use. 00:38:53.830 --> 00:38:54.810 align:middle line:90% You don't need as much. 00:38:54.810 --> 00:38:57.370 align:middle line:84% You only need maybe a tenth the amount of carbon. 00:38:57.370 --> 00:39:00.330 align:middle line:84% And so because it's in the lower concentration, 00:39:00.330 --> 00:39:04.000 align:middle line:84% it doesn't disturb the lifetime quite as much as the oxygen. 00:39:04.000 --> 00:39:06.900 align:middle line:84% So people have found, they can dope with carbon 00:39:06.900 --> 00:39:10.740 align:middle line:84% without inducing a lot of bad electrical effects, 00:39:10.740 --> 00:39:12.278 align:middle line:90% and then completely kill TED. 00:39:12.278 --> 00:39:14.820 align:middle line:84% And in fact, this is a topic-- we're not going to get to talk 00:39:14.820 --> 00:39:16.560 align:middle line:84% about it too much in this course-- 00:39:16.560 --> 00:39:18.630 align:middle line:84% maybe a little-- but this is a good topic, 00:39:18.630 --> 00:39:22.410 align:middle line:84% if anyone's interested in researching for their final 00:39:22.410 --> 00:39:23.100 align:middle line:90% report-- 00:39:23.100 --> 00:39:24.683 align:middle line:84% because we won't get to talk about it. 00:39:24.683 --> 00:39:26.640 align:middle line:84% But it is being used in production today. 00:39:26.640 --> 00:39:28.680 align:middle line:84% Bipolar transistors, the highest speed, 00:39:28.680 --> 00:39:31.470 align:middle line:84% are doped with carbon to eliminate the boron TED. 00:39:31.470 --> 00:39:33.600 align:middle line:84% Otherwise, the base width would be really wide. 00:39:33.600 --> 00:39:37.090 align:middle line:84% The device would be really slow, and it would be a problem. 00:39:37.090 --> 00:39:41.260 align:middle line:84% So it's kind of an interesting story about how that developed. 00:39:41.260 --> 00:39:42.900 align:middle line:84% So if you're interested, please think 00:39:42.900 --> 00:39:44.275 align:middle line:84% about signing up for that topic-- 00:39:44.275 --> 00:39:46.330 align:middle line:84% although I only want one person to do one topic. 00:39:46.330 --> 00:39:48.330 align:middle line:84% So you might have to fight a fight a little bit. 00:39:48.330 --> 00:39:50.760 align:middle line:84% There's plenty of topics to go around. 00:39:50.760 --> 00:39:53.130 align:middle line:84% OK, given that a little bit experimental introduction, 00:39:53.130 --> 00:39:54.963 align:middle line:84% now we finally get to talk about, all right, 00:39:54.963 --> 00:39:56.550 align:middle line:90% how do people model TED? 00:39:56.550 --> 00:39:58.590 align:middle line:84% Well, I showed this slide last time. 00:39:58.590 --> 00:40:01.570 align:middle line:84% I just want to review what a 311 defect looks like. 00:40:01.570 --> 00:40:04.770 align:middle line:84% Here's a high-resolution electron micrograph. 00:40:04.770 --> 00:40:07.620 align:middle line:90% So this is electron microscopy. 00:40:07.620 --> 00:40:10.200 align:middle line:84% High resolution-- the electron microscope 00:40:10.200 --> 00:40:14.430 align:middle line:84% is looking at a very high magnification. 00:40:14.430 --> 00:40:17.790 align:middle line:84% In fact, you can see these little rows of dots, 00:40:17.790 --> 00:40:21.420 align:middle line:84% each dot corresponds to a dimer-- to two silicon atoms. 00:40:21.420 --> 00:40:23.820 align:middle line:84% And the reason they're in such nice, regular planes 00:40:23.820 --> 00:40:25.860 align:middle line:84% is because they are in nice, regular planes. 00:40:25.860 --> 00:40:28.420 align:middle line:90% It's a single-crystal material. 00:40:28.420 --> 00:40:31.050 align:middle line:84% But here you see this diffraction contrast-- 00:40:31.050 --> 00:40:33.690 align:middle line:84% this dark region, where the perfect rows are 00:40:33.690 --> 00:40:36.490 align:middle line:84% disturbed-- their symmetry, because there's a defect. 00:40:36.490 --> 00:40:39.900 align:middle line:84% And that's what we look at in cross-section TEM. 00:40:39.900 --> 00:40:44.160 align:middle line:84% We're looking for diffraction disturbances. 00:40:44.160 --> 00:40:46.050 align:middle line:84% And we see that by this dark region. 00:40:46.050 --> 00:40:48.600 align:middle line:84% And this dark region has been analyzed to death 00:40:48.600 --> 00:40:49.860 align:middle line:90% by microscopists. 00:40:49.860 --> 00:40:53.380 align:middle line:84% And it lies along a certain plane, which 00:40:53.380 --> 00:40:56.830 align:middle line:90% is typically 311 direction. 00:40:56.830 --> 00:40:58.420 align:middle line:90% That's where it gets its name. 00:40:58.420 --> 00:41:02.770 align:middle line:84% And what it's believed to be is a ribbon-like defect, 00:41:02.770 --> 00:41:06.040 align:middle line:84% where this direction, this arrow points along 311-- 00:41:06.040 --> 00:41:09.070 align:middle line:84% and this direction, where the length 00:41:09.070 --> 00:41:13.630 align:middle line:84% of the long section into the page is lying along 110. 00:41:13.630 --> 00:41:19.720 align:middle line:84% And it is a whole series of dimers of silicon, or imers-- 00:41:19.720 --> 00:41:22.840 align:middle line:84% little silicon clusters into this defect. 00:41:22.840 --> 00:41:26.860 align:middle line:84% And it may be 100 angstroms long-- let's say, 00:41:26.860 --> 00:41:29.860 align:middle line:84% 10 nanometers-- and maybe 30 or so 00:41:29.860 --> 00:41:33.580 align:middle line:84% in this direction-- something like that. 00:41:33.580 --> 00:41:37.060 align:middle line:84% So it's a little cluster of interstitials, 00:41:37.060 --> 00:41:39.880 align:middle line:84% that has a particular orientation to the cluster. 00:41:39.880 --> 00:41:45.340 align:middle line:84% And these 311 defects, they form during the first few fractions 00:41:45.340 --> 00:41:46.600 align:middle line:90% of a second of annealing. 00:41:46.600 --> 00:41:51.450 align:middle line:84% They can even be formed during the implant itself. 00:41:51.450 --> 00:41:52.950 align:middle line:90% So their formation is important. 00:41:52.950 --> 00:41:55.930 align:middle line:84% More important is, how do they dissolve? 00:41:55.930 --> 00:41:58.480 align:middle line:84% They anneal out in the time range 00:41:58.480 --> 00:42:00.400 align:middle line:84% that's on the order of seconds to minutes. 00:42:00.400 --> 00:42:04.550 align:middle line:84% It could even be longer times at moderate temperatures. 00:42:04.550 --> 00:42:06.732 align:middle line:84% So as they anneal out-- once they form, 00:42:06.732 --> 00:42:09.190 align:middle line:84% they form very quickly, and then they gradually anneal out. 00:42:09.190 --> 00:42:12.790 align:middle line:84% As they anneal out, they give off excess interstitials. 00:42:12.790 --> 00:42:15.430 align:middle line:84% And it's these excess interstitials given off 00:42:15.430 --> 00:42:20.702 align:middle line:84% by the evaporating 311s that cause the boron TED 00:42:20.702 --> 00:42:21.535 align:middle line:90% that people observe. 00:42:21.535 --> 00:42:24.410 align:middle line:90% 00:42:24.410 --> 00:42:27.170 align:middle line:84% So atomic-level understanding of TED. 00:42:27.170 --> 00:42:30.180 align:middle line:90% Let's go on to Slide Number 11. 00:42:30.180 --> 00:42:31.640 align:middle line:90% How did people discover this? 00:42:31.640 --> 00:42:34.670 align:middle line:84% This seems really weird, or it seems very subtle. 00:42:34.670 --> 00:42:36.440 align:middle line:84% And in some ways, you might think of it 00:42:36.440 --> 00:42:38.930 align:middle line:90% as maybe partly accidental. 00:42:38.930 --> 00:42:41.510 align:middle line:84% People were looking in the microscope 00:42:41.510 --> 00:42:45.290 align:middle line:84% for years at these kind of interesting defects 00:42:45.290 --> 00:42:47.570 align:middle line:90% that they saw. 00:42:47.570 --> 00:42:51.260 align:middle line:84% And in fact, they looked at the kinetics of the defects. 00:42:51.260 --> 00:42:54.620 align:middle line:84% They looked at how their concentration changed over time. 00:42:54.620 --> 00:42:58.880 align:middle line:84% And they noticed that the time it took to shrink all the 311s, 00:42:58.880 --> 00:43:01.850 align:middle line:84% or get rid of them, was about of the same order of magnitude 00:43:01.850 --> 00:43:04.160 align:middle line:90% as the time the TED lasted. 00:43:04.160 --> 00:43:06.290 align:middle line:84% So people were doing TED experiments. 00:43:06.290 --> 00:43:08.120 align:middle line:84% And they said, oh yeah, let's see, 00:43:08.120 --> 00:43:12.470 align:middle line:84% at 800 degrees TED lasts for a certain number of minutes. 00:43:12.470 --> 00:43:14.450 align:middle line:84% And other microscopists were looking at it 00:43:14.450 --> 00:43:17.180 align:middle line:84% and saying, gee, at 800 degrees these 311s hang 00:43:17.180 --> 00:43:19.100 align:middle line:84% around for about that same amount of time-- 00:43:19.100 --> 00:43:20.750 align:middle line:84% could the two phenomena be related? 00:43:20.750 --> 00:43:22.100 align:middle line:90% And in fact, they are. 00:43:22.100 --> 00:43:26.040 align:middle line:84% People found that the time scale of TED 00:43:26.040 --> 00:43:29.220 align:middle line:84% is the same as that of the time scale of the shrinkage 00:43:29.220 --> 00:43:30.420 align:middle line:90% of these defects. 00:43:30.420 --> 00:43:32.340 align:middle line:84% And when we're talking about shrinkage, 00:43:32.340 --> 00:43:34.840 align:middle line:84% people sometimes use the word evaporation. 00:43:34.840 --> 00:43:36.750 align:middle line:84% So the little 311 is sitting there 00:43:36.750 --> 00:43:41.920 align:middle line:84% evaporating off, or giving off interstitials from the clusters. 00:43:41.920 --> 00:43:43.410 align:middle line:90% This is some experimental data. 00:43:43.410 --> 00:43:44.933 align:middle line:90% I took this from your textbook. 00:43:44.933 --> 00:43:45.600 align:middle line:90% It's referenced. 00:43:45.600 --> 00:43:47.910 align:middle line:90% It comes out of Bell Labs. 00:43:47.910 --> 00:43:50.640 align:middle line:84% And it shows-- it's a plot of the silicon 00:43:50.640 --> 00:43:53.910 align:middle line:84% self-interstitial density, in number 00:43:53.910 --> 00:43:55.770 align:middle line:84% of interstitials per square centimeter, 00:43:55.770 --> 00:43:57.873 align:middle line:90% contained in 311 defects. 00:43:57.873 --> 00:43:59.790 align:middle line:84% So they're basically looking in the microscope 00:43:59.790 --> 00:44:01.680 align:middle line:84% and counting the density of 311 defects 00:44:01.680 --> 00:44:04.200 align:middle line:84% and then estimating from their size and density how 00:44:04.200 --> 00:44:07.770 align:middle line:84% Many interstitials are in them, as a function of time 00:44:07.770 --> 00:44:09.180 align:middle line:90% at different temperatures. 00:44:09.180 --> 00:44:11.910 align:middle line:90% Let's take the red boxes. 00:44:11.910 --> 00:44:16.290 align:middle line:84% Here at 815 degrees, initially at the very first beginning 00:44:16.290 --> 00:44:18.570 align:middle line:84% after the implant, there's a certain density-- 00:44:18.570 --> 00:44:21.840 align:middle line:84% maybe mid times 10 to the 13th interstitials 00:44:21.840 --> 00:44:24.300 align:middle line:84% per square centimeter-- contained in these defects. 00:44:24.300 --> 00:44:26.710 align:middle line:84% And then what you find is exponentially-- 00:44:26.710 --> 00:44:28.460 align:middle line:84% so the defect density is sort of constant, 00:44:28.460 --> 00:44:31.085 align:middle line:84% then it goes down exponentially after a certain amount of time. 00:44:31.085 --> 00:44:32.320 align:middle line:90% It just drops like a rocket. 00:44:32.320 --> 00:44:35.670 align:middle line:84% So after 200 seconds, it's gone down 00:44:35.670 --> 00:44:38.500 align:middle line:90% by several orders of magnitude. 00:44:38.500 --> 00:44:41.350 align:middle line:84% So these 311 defects, a lot of them have disappeared. 00:44:41.350 --> 00:44:45.510 align:middle line:84% And so they're dissolving, or evaporating 00:44:45.510 --> 00:44:48.030 align:middle line:90% at a certain rate-- at 800. 00:44:48.030 --> 00:44:50.670 align:middle line:84% So let's take a look at the red circles over here. 00:44:50.670 --> 00:44:51.840 align:middle line:90% Those are at 670-- 00:44:51.840 --> 00:44:53.370 align:middle line:90% so a much lower temperature. 00:44:53.370 --> 00:44:54.540 align:middle line:90% Look at this. 00:44:54.540 --> 00:44:58.470 align:middle line:84% You get a high concentration of them-- say, 10 to the 14th, 00:44:58.470 --> 00:45:00.090 align:middle line:90% or mid 10 to the 13th. 00:45:00.090 --> 00:45:02.640 align:middle line:90% And then they last a long time-- 00:45:02.640 --> 00:45:05.100 align:middle line:84% maybe 10 to the 4th, or 10 to the 5th seconds, 00:45:05.100 --> 00:45:07.450 align:middle line:84% and then it starts to drop dramatically. 00:45:07.450 --> 00:45:11.110 align:middle line:84% So we're talking at a very long time at low temperatures. 00:45:11.110 --> 00:45:14.160 align:middle line:84% So this is sort of the kinetics of the disappearance 00:45:14.160 --> 00:45:14.790 align:middle line:90% of these 311s. 00:45:14.790 --> 00:45:18.290 align:middle line:90% 00:45:18.290 --> 00:45:23.660 align:middle line:84% And in fact, these are some micrographs that people used, 00:45:23.660 --> 00:45:27.150 align:middle line:84% I'm just showing you on Slide 12, to obtain this data. 00:45:27.150 --> 00:45:29.360 align:middle line:84% This is from Dave Eaglesham at Bell Labs, 00:45:29.360 --> 00:45:32.690 align:middle line:84% published in 1994 in Applied Physics Letters. 00:45:32.690 --> 00:45:36.320 align:middle line:84% And what he's showing here in the upper diagram, 00:45:36.320 --> 00:45:39.000 align:middle line:84% these are both plan-view TEM images. 00:45:39.000 --> 00:45:40.820 align:middle line:84% This is a sample of silicon that's 00:45:40.820 --> 00:45:43.070 align:middle line:84% been implanted with an intermediate dose-- 00:45:43.070 --> 00:45:48.050 align:middle line:84% 5 times 10 to the 13th boron per square centimeter-- 00:45:48.050 --> 00:45:49.190 align:middle line:90% into the silicon substrate. 00:45:49.190 --> 00:45:51.110 align:middle line:90% And it's been annealed at 810. 00:45:51.110 --> 00:45:53.338 align:middle line:90% And this is after 5 seconds. 00:45:53.338 --> 00:45:55.130 align:middle line:84% And you see, you're looking at a plan view. 00:45:55.130 --> 00:45:59.210 align:middle line:84% And each one of these little sort of dot areas 00:45:59.210 --> 00:46:00.630 align:middle line:90% is a 311 defect. 00:46:00.630 --> 00:46:02.503 align:middle line:84% So there's a huge density of defects. 00:46:02.503 --> 00:46:03.920 align:middle line:84% And the scale bar is a little hard 00:46:03.920 --> 00:46:06.080 align:middle line:84% to see, in the upper left from here 00:46:06.080 --> 00:46:08.570 align:middle line:90% to here, that's 40 nanometers. 00:46:08.570 --> 00:46:09.900 align:middle line:90% That's 400 angstroms. 00:46:09.900 --> 00:46:12.510 align:middle line:84% So you have a huge number of these-- a lot of these defects. 00:46:12.510 --> 00:46:15.140 align:middle line:84% So again, if I go back one slide to Slide 11, 00:46:15.140 --> 00:46:18.780 align:middle line:84% he's starting out here after just a few seconds. 00:46:18.780 --> 00:46:20.700 align:middle line:90% That's the number of-- 00:46:20.700 --> 00:46:24.300 align:middle line:84% that's where he got this interstitial density, at 815. 00:46:24.300 --> 00:46:26.700 align:middle line:90% Now look at the bottom-- 00:46:26.700 --> 00:46:29.580 align:middle line:84% on Slide 12, look at the bottom TEM-- bottom 00:46:29.580 --> 00:46:32.220 align:middle line:84% left, in B. This is after 100 seconds. 00:46:32.220 --> 00:46:34.812 align:middle line:84% Again, the number of defects here is now 311. 00:46:34.812 --> 00:46:35.520 align:middle line:90% It's a lot lower. 00:46:35.520 --> 00:46:36.562 align:middle line:90% I can almost count them-- 00:46:36.562 --> 00:46:40.870 align:middle line:90% 1-2-3-4-5-6-7-8-- of some order. 00:46:40.870 --> 00:46:42.780 align:middle line:84% And based on their size and density, 00:46:42.780 --> 00:46:45.420 align:middle line:84% you can calculate after 100 seconds. 00:46:45.420 --> 00:46:47.320 align:middle line:84% Oops, sorry, let me go back one more. 00:46:47.320 --> 00:46:49.290 align:middle line:84% So here we are at 100 seconds, and it's down 00:46:49.290 --> 00:46:51.100 align:middle line:90% by several orders of magnitude. 00:46:51.100 --> 00:46:55.320 align:middle line:84% So people sat in this paper and counted all these defects-- 00:46:55.320 --> 00:46:58.440 align:middle line:84% figured out the silicon interstitial density 00:46:58.440 --> 00:47:01.710 align:middle line:84% and how it was changing with time at different temperatures. 00:47:01.710 --> 00:47:05.210 align:middle line:90% 00:47:05.210 --> 00:47:08.840 align:middle line:84% And so in fact, I'm showing here now, also from your textbook, 00:47:08.840 --> 00:47:12.410 align:middle line:84% on Slide 13, this is a diagram that's 00:47:12.410 --> 00:47:15.650 align:middle line:84% supposed to give you an idea of the kinetics of what's 00:47:15.650 --> 00:47:16.890 align:middle line:90% going on with these defects. 00:47:16.890 --> 00:47:20.300 align:middle line:90% So this is simulated, though. 00:47:20.300 --> 00:47:22.070 align:middle line:84% What I just showed you was actual data. 00:47:22.070 --> 00:47:23.910 align:middle line:90% This is more simulation. 00:47:23.910 --> 00:47:27.980 align:middle line:84% So this is on the left axis, or the vertical axis 00:47:27.980 --> 00:47:30.150 align:middle line:84% is silicone self-interstitial density. 00:47:30.150 --> 00:47:31.203 align:middle line:90% Now this is in terms of-- 00:47:31.203 --> 00:47:32.870 align:middle line:84% there's different ways of expressing it. 00:47:32.870 --> 00:47:34.650 align:middle line:90% This is per cubic centimeter. 00:47:34.650 --> 00:47:37.400 align:middle line:84% And this is as a function of depth. 00:47:37.400 --> 00:47:39.800 align:middle line:84% So there's a particular implant that's been done-- 00:47:39.800 --> 00:47:42.370 align:middle line:90% 40 Kev boron, 10 to the 14th. 00:47:42.370 --> 00:47:46.720 align:middle line:84% And initially this red line represents 00:47:46.720 --> 00:47:48.410 align:middle line:90% the initial plus-1 damage. 00:47:48.410 --> 00:47:52.180 align:middle line:84% So right after the implant is done, 00:47:52.180 --> 00:47:54.640 align:middle line:84% you would assume that you had this damage-- 00:47:54.640 --> 00:47:56.500 align:middle line:84% this amount-- number of interstitials. 00:47:56.500 --> 00:47:59.440 align:middle line:84% So the interstitial density peaks here very, very high. 00:47:59.440 --> 00:48:01.600 align:middle line:84% After a microsecond, it's about the same. 00:48:01.600 --> 00:48:05.200 align:middle line:84% But look at it after a tenth of a second, 00:48:05.200 --> 00:48:06.890 align:middle line:90% or a hundredth of a second. 00:48:06.890 --> 00:48:09.560 align:middle line:84% We're talking about this flat profile right here. 00:48:09.560 --> 00:48:13.270 align:middle line:84% So after a tenth of a second at 750, 00:48:13.270 --> 00:48:15.490 align:middle line:90% we formed all these 311 defects. 00:48:15.490 --> 00:48:17.050 align:middle line:84% And the interstitial concentration 00:48:17.050 --> 00:48:19.750 align:middle line:84% is now down to about mid 10 to the 12, 00:48:19.750 --> 00:48:22.240 align:middle line:84% or 10 to the 13th per cubic centimeter, 00:48:22.240 --> 00:48:23.230 align:middle line:90% according to Supreme. 00:48:23.230 --> 00:48:25.360 align:middle line:90% And it's fairly uniform. 00:48:25.360 --> 00:48:27.440 align:middle line:90% OK, let's think about that. 00:48:27.440 --> 00:48:29.470 align:middle line:90% What is CI star? 00:48:29.470 --> 00:48:32.740 align:middle line:84% We have equations in your textbook from a prior chapter. 00:48:32.740 --> 00:48:36.320 align:middle line:84% The equilibrium silicon interstitial density is about 10 00:48:36.320 --> 00:48:38.900 align:middle line:84% to the 8th per cubic centimeter at 750. 00:48:38.900 --> 00:48:40.910 align:middle line:84% So what is that enhancement ratio? 00:48:40.910 --> 00:48:42.770 align:middle line:90% CI over CI star. 00:48:42.770 --> 00:48:45.980 align:middle line:84% That's 10 to the 13th over 10 to the 8th, roughly. 00:48:45.980 --> 00:48:50.850 align:middle line:90% It's still greater than 10,000. 00:48:50.850 --> 00:48:53.570 align:middle line:84% So we've gotten rid of most of this initial damage, 00:48:53.570 --> 00:48:57.380 align:middle line:84% but now we have this sort of uniform concentration of-- 00:48:57.380 --> 00:48:58.970 align:middle line:84% we have this concentration of 311s. 00:48:58.970 --> 00:49:02.240 align:middle line:84% And the silicon self-interstitial density CI 00:49:02.240 --> 00:49:04.790 align:middle line:84% over CI star is still much larger 00:49:04.790 --> 00:49:09.740 align:middle line:84% than it would be in equilibrium, but maybe by a factor of 10,000, 00:49:09.740 --> 00:49:10.520 align:middle line:90% in this case. 00:49:10.520 --> 00:49:13.520 align:middle line:84% So the TED is going to occur between this period-- 00:49:13.520 --> 00:49:16.953 align:middle line:84% this period here of 0.1 seconds and 1,000 seconds, 00:49:16.953 --> 00:49:18.620 align:middle line:84% depending on the temperature that you're 00:49:18.620 --> 00:49:21.860 align:middle line:84% at-- how long it takes to evaporate the 311s. 00:49:21.860 --> 00:49:26.720 align:middle line:84% During that period when the supersaturation ratio is large, 00:49:26.720 --> 00:49:28.560 align:middle line:84% it's going to be some high number-- 00:49:28.560 --> 00:49:32.330 align:middle line:84% could be a factor of 10, 100, 100,000-- something like that-- 00:49:32.330 --> 00:49:34.790 align:middle line:90% and uniform in depth. 00:49:34.790 --> 00:49:37.550 align:middle line:84% So as the 311 defects, they've all been formed, 00:49:37.550 --> 00:49:40.580 align:middle line:84% now they start evaporating and emitting interstitials. 00:49:40.580 --> 00:49:42.290 align:middle line:84% Eventually, they're all evaporated away, 00:49:42.290 --> 00:49:44.030 align:middle line:90% and TED will be over. 00:49:44.030 --> 00:49:46.160 align:middle line:84% But for some period, they'll be evaporating, 00:49:46.160 --> 00:49:49.310 align:middle line:84% and they'll be holding CI over CI star very high, 00:49:49.310 --> 00:49:54.275 align:middle line:84% and therefore they'll be holding the boron diffusivity very high. 00:49:54.275 --> 00:49:56.780 align:middle line:90% 00:49:56.780 --> 00:50:00.610 align:middle line:90% So let's go on to Slide 14. 00:50:00.610 --> 00:50:03.970 align:middle line:84% And this is a model that was proposed in the mid '90s 00:50:03.970 --> 00:50:06.710 align:middle line:90% or so for 311 growth. 00:50:06.710 --> 00:50:09.730 align:middle line:84% So we have the growth of these clusters and their evaporation, 00:50:09.730 --> 00:50:10.600 align:middle line:90% or shrinkage. 00:50:10.600 --> 00:50:13.420 align:middle line:84% And this kinetic model, then, is going 00:50:13.420 --> 00:50:16.390 align:middle line:84% to determine the time dependence and the magnitude 00:50:16.390 --> 00:50:18.170 align:middle line:90% of transit-enhanced diffusion. 00:50:18.170 --> 00:50:23.140 align:middle line:84% So what people wrote down in this paper 00:50:23.140 --> 00:50:25.025 align:middle line:84% was-- and there's a reference in your text. 00:50:25.025 --> 00:50:26.650 align:middle line:84% If you want to read the original paper, 00:50:26.650 --> 00:50:29.020 align:middle line:90% I would invite you to read that. 00:50:29.020 --> 00:50:32.820 align:middle line:84% You can write down an equation that describes cluster growth. 00:50:32.820 --> 00:50:35.750 align:middle line:84% So CL sub n in this equation is just 00:50:35.750 --> 00:50:38.750 align:middle line:84% a 311 cluster that has n number of interstitials. 00:50:38.750 --> 00:50:39.425 align:middle line:90% n could be 100. 00:50:39.425 --> 00:50:41.240 align:middle line:90% It could be 1,000-- whatever. 00:50:41.240 --> 00:50:42.350 align:middle line:90% It's a cluster. 00:50:42.350 --> 00:50:47.180 align:middle line:84% And if I add to that n number one more interstitial, 00:50:47.180 --> 00:50:48.860 align:middle line:90% I get CL to the n plus 1. 00:50:48.860 --> 00:50:50.630 align:middle line:84% So this equation could go either way. 00:50:50.630 --> 00:50:53.210 align:middle line:84% I can either add an interstitial and grow the cluster. 00:50:53.210 --> 00:50:58.610 align:middle line:84% I can evaporate away, or take away the interstitial 00:50:58.610 --> 00:51:01.890 align:middle line:84% and shrink the cluster-- either way. 00:51:01.890 --> 00:51:04.170 align:middle line:84% So given a simple equation like this, 00:51:04.170 --> 00:51:08.510 align:middle line:84% then we can actually write down a time dependence. 00:51:08.510 --> 00:51:13.973 align:middle line:84% We can say that the time rate of change of the cluster-- 00:51:13.973 --> 00:51:16.140 align:middle line:84% number of interstitials in the cluster-- as a unit-- 00:51:16.140 --> 00:51:17.990 align:middle line:84% as a function of time-- the partial-- 00:51:17.990 --> 00:51:19.070 align:middle line:90% is equal to this. 00:51:19.070 --> 00:51:22.400 align:middle line:84% There's a growth term, on the left, minus the shrinkage term. 00:51:22.400 --> 00:51:26.960 align:middle line:84% So the growth term has some equilibrium constant, K sub f, 00:51:26.960 --> 00:51:28.700 align:middle line:84% for the forward reaction that says-- 00:51:28.700 --> 00:51:31.530 align:middle line:84% where I'm adding interstitials, and I'm growing this thing. 00:51:31.530 --> 00:51:35.130 align:middle line:84% So it was a constant case of f times the concentration 00:51:35.130 --> 00:51:37.680 align:middle line:84% of interstitials times the concentration of clusters. 00:51:37.680 --> 00:51:41.460 align:middle line:84% That is the forward term-- minus the reverse reaction. 00:51:41.460 --> 00:51:43.690 align:middle line:84% If I shrink it, I go the other way 00:51:43.690 --> 00:51:45.210 align:middle line:90% and I release an interstitial. 00:51:45.210 --> 00:51:51.090 align:middle line:84% So the reverse reaction has an equilibrium constant KR 00:51:51.090 --> 00:51:55.740 align:middle line:84% and some concentration of clusters CL. 00:51:55.740 --> 00:51:58.530 align:middle line:84% So we write a simple differential equation-- time 00:51:58.530 --> 00:52:03.480 align:middle line:84% dependence depends on a growth term minus a shrinkage term. 00:52:03.480 --> 00:52:06.030 align:middle line:84% And now this is a little hand-wavy. 00:52:06.030 --> 00:52:09.990 align:middle line:84% But in your text, we talk about how this forward reaction 00:52:09.990 --> 00:52:12.030 align:middle line:84% rate is believed to be diffusion limited. 00:52:12.030 --> 00:52:15.930 align:middle line:84% So the interstitials have to diffuse into this cluster. 00:52:15.930 --> 00:52:18.120 align:middle line:84% They're created throughout the crystal, 00:52:18.120 --> 00:52:20.800 align:middle line:84% but they have to diffuse into the 311 cluster. 00:52:20.800 --> 00:52:24.420 align:middle line:84% So we usually say that this forward reaction constant, 00:52:24.420 --> 00:52:28.110 align:middle line:84% K sub f, is somehow proportional to some nearest neighbor 00:52:28.110 --> 00:52:31.650 align:middle line:84% distance, A, and an interstitial diffusivity-- 00:52:31.650 --> 00:52:32.700 align:middle line:90% D sub i. 00:52:32.700 --> 00:52:36.430 align:middle line:84% So at least we know what kind of parameters go into that. 00:52:36.430 --> 00:52:40.120 align:middle line:84% So that's what we write for K sub f. 00:52:40.120 --> 00:52:43.310 align:middle line:84% And the exact form doesn't have to be perfect. 00:52:43.310 --> 00:52:45.400 align:middle line:84% We just want to get the temperature dependencies 00:52:45.400 --> 00:52:46.910 align:middle line:90% in most of these cases. 00:52:46.910 --> 00:52:49.240 align:middle line:84% The reverse reaction-- so going the other way-- 00:52:49.240 --> 00:52:51.100 align:middle line:84% for the evaporation of the shrinkage 00:52:51.100 --> 00:52:56.950 align:middle line:84% is actually dominated by a diffusion mechanism, as well. 00:52:56.950 --> 00:53:00.040 align:middle line:84% So there's this term that's related to the diffusivity 00:53:00.040 --> 00:53:02.200 align:middle line:90% of the interstitials, again-- 00:53:02.200 --> 00:53:05.920 align:middle line:84% it's actually like-- this looks like a hopping frequency-- 00:53:05.920 --> 00:53:08.680 align:middle line:84% times a Boltzmann factor, E to the minus EB 00:53:08.680 --> 00:53:10.983 align:middle line:84% over KT-- now, where EB is the binding energy. 00:53:10.983 --> 00:53:13.150 align:middle line:84% So again, if I'm going to get rid of an interstitial 00:53:13.150 --> 00:53:16.090 align:middle line:84% from the cluster, it's going to be bound by some energy. 00:53:16.090 --> 00:53:18.430 align:middle line:84% Somehow there's a lower energy to be in the cluster. 00:53:18.430 --> 00:53:20.570 align:middle line:84% I have to overcome that to get rid of it. 00:53:20.570 --> 00:53:23.320 align:middle line:84% And that's why you have this E to the minus EB over KT. 00:53:23.320 --> 00:53:27.460 align:middle line:84% So simple differential equation with 2K sub 00:53:27.460 --> 00:53:32.690 align:middle line:84% f and K sub r, that have certain temperature dependencies. 00:53:32.690 --> 00:53:34.330 align:middle line:90% Let's go to Slide 15. 00:53:34.330 --> 00:53:36.910 align:middle line:84% So the interesting part of this differential equation-- 00:53:36.910 --> 00:53:39.050 align:middle line:84% the interesting time is the period 00:53:39.050 --> 00:53:43.230 align:middle line:84% where steady state exists between cluster 00:53:43.230 --> 00:53:44.740 align:middle line:90% growth and cluster evaporation. 00:53:44.740 --> 00:53:46.330 align:middle line:84% So in fact, to make the equation easy, 00:53:46.330 --> 00:53:49.080 align:middle line:84% we're just going to solve for the case when it's equal to 0. 00:53:49.080 --> 00:53:51.685 align:middle line:90% 00:53:51.685 --> 00:53:53.060 align:middle line:84% We're going to solve for the case 00:53:53.060 --> 00:53:56.272 align:middle line:84% where the cluster concentration isn't really changing very much. 00:53:56.272 --> 00:53:57.980 align:middle line:84% And we're going to say that's equal to 0. 00:53:57.980 --> 00:54:00.248 align:middle line:90% So that's relatively easy. 00:54:00.248 --> 00:54:01.040 align:middle line:90% Let's just go back. 00:54:01.040 --> 00:54:04.160 align:middle line:84% I'm just setting this equation equal to 0. 00:54:04.160 --> 00:54:07.250 align:middle line:84% And now I'm going to solve now for the concentration 00:54:07.250 --> 00:54:11.580 align:middle line:84% of interstitials, because the cluster concentration drops out, 00:54:11.580 --> 00:54:12.080 align:middle line:90% right? 00:54:12.080 --> 00:54:14.030 align:middle line:84% So everything I can solve, then, for 00:54:14.030 --> 00:54:16.700 align:middle line:84% the maximum interstitial concentration just in terms 00:54:16.700 --> 00:54:19.160 align:middle line:90% of the ratio of KF and KR. 00:54:19.160 --> 00:54:22.640 align:middle line:84% So going back to your Slide 15, I 00:54:22.640 --> 00:54:27.260 align:middle line:84% can then figure out a maximum concentration of interstitials 00:54:27.260 --> 00:54:31.190 align:middle line:90% that are trapped in these 311s. 00:54:31.190 --> 00:54:33.930 align:middle line:84% It's just KR over KF, and it looks like this-- 00:54:33.930 --> 00:54:37.760 align:middle line:84% depends exponentially on the binding energy over KT. 00:54:37.760 --> 00:54:40.040 align:middle line:84% So that is an estimate of the maximum number 00:54:40.040 --> 00:54:41.960 align:middle line:90% of excess interstitials. 00:54:41.960 --> 00:54:45.050 align:middle line:84% If I divide that by CI star, that gives me 00:54:45.050 --> 00:54:47.030 align:middle line:90% the supersaturation ratio. 00:54:47.030 --> 00:54:48.380 align:middle line:90% Again, why do I want that? 00:54:48.380 --> 00:54:51.020 align:middle line:84% Remember in our discussion of diffusion, 00:54:51.020 --> 00:54:55.290 align:middle line:84% diffusion coefficient goes diffusivity times F sub i 00:54:55.290 --> 00:54:57.150 align:middle line:90% times CI over CS star. 00:54:57.150 --> 00:55:00.030 align:middle line:84% So whenever you enhance CI over CI star, 00:55:00.030 --> 00:55:02.070 align:middle line:90% you enhance the diffusivity-- 00:55:02.070 --> 00:55:04.180 align:middle line:90% say, of boron. 00:55:04.180 --> 00:55:06.120 align:middle line:90% So I write down this ratio. 00:55:06.120 --> 00:55:10.140 align:middle line:90% And we have to use the CI star. 00:55:10.140 --> 00:55:13.350 align:middle line:84% We use the formula for it coming from Chapter 3. 00:55:13.350 --> 00:55:17.850 align:middle line:84% And CI star brings in with it a formation energy 00:55:17.850 --> 00:55:20.670 align:middle line:84% of the silicon interstitial, that we're calling E sub f. 00:55:20.670 --> 00:55:24.220 align:middle line:84% That's not the Fermi energy, that's the formation energy. 00:55:24.220 --> 00:55:29.100 align:middle line:84% So this is the formula that was used for CI star. 00:55:29.100 --> 00:55:30.420 align:middle line:90% It's got a pre factor-- 00:55:30.420 --> 00:55:33.030 align:middle line:90% CI 0-- and an exponential-- 00:55:33.030 --> 00:55:35.130 align:middle line:90% E to the minus EF over KT. 00:55:35.130 --> 00:55:38.400 align:middle line:84% So the formation energy is about 3 electron volts, roughly, 00:55:38.400 --> 00:55:39.810 align:middle line:90% for silicon interstitial. 00:55:39.810 --> 00:55:42.900 align:middle line:84% The binding energy-- people have fit data 00:55:42.900 --> 00:55:46.530 align:middle line:84% to show that the binding energy of a silicon to this 311 cluster 00:55:46.530 --> 00:55:48.990 align:middle line:90% is about 1.8 electron volts. 00:55:48.990 --> 00:55:51.630 align:middle line:84% So people have estimates for this term here 00:55:51.630 --> 00:55:53.670 align:middle line:90% and this term here. 00:55:53.670 --> 00:55:55.545 align:middle line:84% You can put in estimates for, you know, 00:55:55.545 --> 00:55:58.570 align:middle line:84% the nearest neighbor distance, and CI 0 can be estimated. 00:55:58.570 --> 00:56:00.300 align:middle line:90% So you can plot this equation-- 00:56:00.300 --> 00:56:02.400 align:middle line:90% CI max over CI star-- 00:56:02.400 --> 00:56:04.560 align:middle line:90% as a function of temperature. 00:56:04.560 --> 00:56:08.190 align:middle line:84% And in fact, that's what Slide Number 16 shows. 00:56:08.190 --> 00:56:11.160 align:middle line:84% This is a plot of a simple equation 00:56:11.160 --> 00:56:14.160 align:middle line:84% as a function of temperature-- the interstitial supersaturation 00:56:14.160 --> 00:56:17.410 align:middle line:84% ratio as a function of temperature. 00:56:17.410 --> 00:56:20.410 align:middle line:90% So what does this tell you? 00:56:20.410 --> 00:56:23.190 align:middle line:84% Well, it gives you an idea of the maximum enhancement 00:56:23.190 --> 00:56:24.840 align:middle line:90% in the diffusivity, right? 00:56:24.840 --> 00:56:27.480 align:middle line:84% Because if I'm going to say that boron's diffusivity 00:56:27.480 --> 00:56:30.150 align:middle line:84% depends on F sub i times this ratio-- 00:56:30.150 --> 00:56:34.320 align:middle line:84% and let's say, I'm at 800, and I'm 00:56:34.320 --> 00:56:38.400 align:middle line:84% in a period where I have TED at 800, CI over CI star 00:56:38.400 --> 00:56:42.060 align:middle line:84% can be as large as almost 10 to the 4th-- 00:56:42.060 --> 00:56:43.500 align:middle line:90% maybe mid 10 to the 3rd. 00:56:43.500 --> 00:56:46.800 align:middle line:84% So it gives you an idea of the magnitude of the enhancement 00:56:46.800 --> 00:56:49.230 align:middle line:90% in the boron diffusivity. 00:56:49.230 --> 00:56:52.200 align:middle line:84% Relatively simple derivation-- you can get an idea right off 00:56:52.200 --> 00:56:54.690 align:middle line:84% the bat of how much CI over CI star 00:56:54.690 --> 00:56:58.542 align:middle line:84% can be enhanced during the steady state period. 00:56:58.542 --> 00:57:00.000 align:middle line:84% Now, eventually, it's going to end. 00:57:00.000 --> 00:57:02.880 align:middle line:84% Eventually, all the silicon will evaporate-- the 311s. 00:57:02.880 --> 00:57:06.780 align:middle line:84% There'll be no more excess interstitials, and TED is over. 00:57:06.780 --> 00:57:10.660 align:middle line:84% So the question on Slide 17 is, how long is that? 00:57:10.660 --> 00:57:13.590 align:middle line:84% So now I know how much CI over CI star 00:57:13.590 --> 00:57:16.230 align:middle line:84% is boosted up-- simply a function of temperature. 00:57:16.230 --> 00:57:18.990 align:middle line:84% You can pull it right off that plot. 00:57:18.990 --> 00:57:21.880 align:middle line:84% Now the question you ask me-- well, I know the temperature. 00:57:21.880 --> 00:57:23.350 align:middle line:90% How long does this event last? 00:57:23.350 --> 00:57:27.010 align:middle line:84% How long does it take to evaporate all these 311s? 00:57:27.010 --> 00:57:30.610 align:middle line:84% Well, eventually over time, the 311s all evaporate 00:57:30.610 --> 00:57:34.420 align:middle line:90% and CI over CI star goes back-- 00:57:34.420 --> 00:57:38.770 align:middle line:84% actually, it should go back to 1, basically. 00:57:38.770 --> 00:57:42.370 align:middle line:84% So here's an example, on Slide 17. 00:57:42.370 --> 00:57:44.440 align:middle line:84% This is from a Supreme simulation. 00:57:44.440 --> 00:57:48.160 align:middle line:90% This was for boron TED. 00:57:48.160 --> 00:57:50.752 align:middle line:84% And we're annealing at a certain temperature. 00:57:50.752 --> 00:57:52.210 align:middle line:84% This is the implant that was done-- 00:57:52.210 --> 00:57:57.370 align:middle line:84% 10 Kev boron, 10 to the 14th atoms per square centimeter. 00:57:57.370 --> 00:58:01.120 align:middle line:84% And here's the as-implanted concentration profile here, 00:58:01.120 --> 00:58:01.760 align:middle line:90% shown in blue. 00:58:01.760 --> 00:58:05.210 align:middle line:84% So that's the boron, just to give you an idea. 00:58:05.210 --> 00:58:07.420 align:middle line:84% And then after 1 minute at 750, this 00:58:07.420 --> 00:58:10.600 align:middle line:84% is how the boron has diffused-- the black line. 00:58:10.600 --> 00:58:14.650 align:middle line:84% And look, at 1 minute at 750, the dashed line 00:58:14.650 --> 00:58:16.090 align:middle line:90% refers to the right hand axis. 00:58:16.090 --> 00:58:17.423 align:middle line:90% Sorry, you should write that in. 00:58:17.423 --> 00:58:19.720 align:middle line:84% So this dashed line is to the right-hand axis. 00:58:19.720 --> 00:58:22.450 align:middle line:84% That's the interstitial supersaturation ratio. 00:58:22.450 --> 00:58:25.370 align:middle line:90% At 750 it's about 10 to the 4th. 00:58:25.370 --> 00:58:27.800 align:middle line:84% And it's pretty uniform throughout the sample. 00:58:27.800 --> 00:58:30.940 align:middle line:84% In fact, I could probably have put that off from the last plot. 00:58:30.940 --> 00:58:33.910 align:middle line:84% If you go back to your last slide-- 00:58:33.910 --> 00:58:36.310 align:middle line:90% 16-- 750, look it up-- 00:58:36.310 --> 00:58:38.750 align:middle line:84% CI over CI star is about 10 to the 4th. 00:58:38.750 --> 00:58:42.760 align:middle line:84% So you can use this as a simple back-of-the-envelope way 00:58:42.760 --> 00:58:44.980 align:middle line:84% of calculating the amount of enhancement-- 00:58:44.980 --> 00:58:46.090 align:middle line:90% CI over CI star. 00:58:46.090 --> 00:58:51.130 align:middle line:84% And then after 10 minutes, look how far the boron has gone. 00:58:51.130 --> 00:58:53.680 align:middle line:84% The boron profile has gone quite a ways. 00:58:53.680 --> 00:58:56.490 align:middle line:84% The junction depth now here is about 0.4 microns. 00:58:56.490 --> 00:58:58.960 align:middle line:90% So that's the red profile-- 00:58:58.960 --> 00:58:59.590 align:middle line:90% solid line. 00:58:59.590 --> 00:59:01.965 align:middle line:84% And the dashed line here, you should also reference that, 00:59:01.965 --> 00:59:03.010 align:middle line:90% to the right-hand axis. 00:59:03.010 --> 00:59:05.500 align:middle line:84% The interstitial supersaturation ratio is now down. 00:59:05.500 --> 00:59:07.930 align:middle line:84% Instead of 10 to the 4th, it's 10 to the 2. 00:59:07.930 --> 00:59:11.440 align:middle line:84% It's about 100 after 10 minutes, because we're 00:59:11.440 --> 00:59:12.820 align:middle line:90% getting rid of more 311s. 00:59:12.820 --> 00:59:15.290 align:middle line:84% And eventually the number of them is going down. 00:59:15.290 --> 00:59:18.310 align:middle line:84% So this thing only lasts so long. 00:59:18.310 --> 00:59:21.155 align:middle line:84% And so the question is, how do I figure out-- 00:59:21.155 --> 00:59:22.860 align:middle line:84% a back-of-the-envelope calculation-- 00:59:22.860 --> 00:59:25.740 align:middle line:84% how long I need to know that this enhancement is going 00:59:25.740 --> 00:59:30.100 align:middle line:84% to last as a function of temperature? 00:59:30.100 --> 00:59:33.000 align:middle line:90% So let's go to Slide Number 18. 00:59:33.000 --> 00:59:35.760 align:middle line:84% And here's a way-- a simple quick and dirty way 00:59:35.760 --> 00:59:37.260 align:middle line:90% of estimating it. 00:59:37.260 --> 00:59:39.900 align:middle line:84% What we say is that all these excess interstitials, 00:59:39.900 --> 00:59:41.670 align:middle line:90% how do we get rid of them? 00:59:41.670 --> 00:59:43.950 align:middle line:90% They are emitted by a 311. 00:59:43.950 --> 00:59:45.550 align:middle line:90% They don't just sit there. 00:59:45.550 --> 00:59:47.597 align:middle line:90% They're going to diffuse, OK? 00:59:47.597 --> 00:59:48.930 align:middle line:90% Where are they going to diffuse? 00:59:48.930 --> 00:59:51.750 align:middle line:84% Well, they're going to diffuse into the bulk 00:59:51.750 --> 00:59:53.157 align:middle line:90% and recombine in the bulk. 00:59:53.157 --> 00:59:54.990 align:middle line:84% And they're going to diffuse to the surface. 00:59:54.990 --> 00:59:57.330 align:middle line:84% And the surface, you know, is a perfect place 00:59:57.330 --> 00:59:59.233 align:middle line:84% to have recombination, because there's lots 00:59:59.233 --> 01:00:00.400 align:middle line:90% of vacancies at the surface. 01:00:00.400 --> 01:00:01.858 align:middle line:84% So an extra silicon atom can always 01:00:01.858 --> 01:00:03.670 align:middle line:90% be accommodated at the surface. 01:00:03.670 --> 01:00:07.300 align:middle line:84% So the diffusion, you have this-- 01:00:07.300 --> 01:00:10.770 align:middle line:84% let's say, this initial profile of excess interstitials. 01:00:10.770 --> 01:00:13.960 align:middle line:84% This is a very crude profile, as a function of depth. 01:00:13.960 --> 01:00:18.180 align:middle line:84% So this red line is meant to represent the surface. 01:00:18.180 --> 01:00:22.750 align:middle line:84% Moving from left to right, we're going in deeper in the sample. 01:00:22.750 --> 01:00:25.577 align:middle line:84% I have some dose Q of interstitials, 01:00:25.577 --> 01:00:26.410 align:middle line:90% that I've implanted. 01:00:26.410 --> 01:00:27.368 align:middle line:90% How did they get there? 01:00:27.368 --> 01:00:29.800 align:middle line:84% Well, they got there because they were recoiled. 01:00:29.800 --> 01:00:33.990 align:middle line:84% So here's my dose Q. And it peaks at some projected range 01:00:33.990 --> 01:00:34.690 align:middle line:90% RP. 01:00:34.690 --> 01:00:35.500 align:middle line:90% OK. 01:00:35.500 --> 01:00:38.933 align:middle line:84% And the surface being the dominant sink, 01:00:38.933 --> 01:00:40.600 align:middle line:84% especially if it's a low-energy implant, 01:00:40.600 --> 01:00:43.180 align:middle line:84% I'm going to have a certain flux of interstitials 01:00:43.180 --> 01:00:45.490 align:middle line:90% towards the surface. 01:00:45.490 --> 01:00:47.800 align:middle line:90% Well, how can I write that flux? 01:00:47.800 --> 01:00:51.940 align:middle line:84% Well, we can write it as the diffusivity, D sub i, times 01:00:51.940 --> 01:00:56.230 align:middle line:84% the peak concentration, CI max over RP, 01:00:56.230 --> 01:00:59.680 align:middle line:84% where RP is the distance-- where the peak is 01:00:59.680 --> 01:01:01.370 align:middle line:90% the range of the implant. 01:01:01.370 --> 01:01:02.330 align:middle line:90% How do we get that? 01:01:02.330 --> 01:01:04.480 align:middle line:90% Well, remember Fick's law. 01:01:04.480 --> 01:01:08.360 align:middle line:84% Flux is a diffusion coefficient times a concentration gradient. 01:01:08.360 --> 01:01:11.080 align:middle line:84% Well, here's a very crude way of estimating the concentration 01:01:11.080 --> 01:01:11.810 align:middle line:90% gradient. 01:01:11.810 --> 01:01:14.080 align:middle line:84% It's just the peak concentration divided 01:01:14.080 --> 01:01:16.740 align:middle line:84% by the distance over which it recombines, 01:01:16.740 --> 01:01:19.600 align:middle line:84% assuming they all recombine at the surface, 01:01:19.600 --> 01:01:20.680 align:middle line:90% or it recombines to 0. 01:01:20.680 --> 01:01:24.070 align:middle line:84% So here's a very quick estimate of the flux 01:01:24.070 --> 01:01:24.970 align:middle line:90% towards the surface-- 01:01:24.970 --> 01:01:28.150 align:middle line:90% DCI max over RP. 01:01:28.150 --> 01:01:29.950 align:middle line:84% Now, I need to know, how much time does it 01:01:29.950 --> 01:01:33.370 align:middle line:90% take to dissolve all those? 01:01:33.370 --> 01:01:39.820 align:middle line:84% It's going to be the dose Q, which is whatever I implanted, 01:01:39.820 --> 01:01:41.530 align:middle line:90% divided by that flux. 01:01:41.530 --> 01:01:43.790 align:middle line:90% Here's my flux. 01:01:43.790 --> 01:01:47.120 align:middle line:84% So at the bottom of Slide 18, I've just taken the dose, 01:01:47.120 --> 01:01:49.740 align:middle line:84% and I multiply it by 1 over the flux. 01:01:49.740 --> 01:01:53.680 align:middle line:84% So the time to dissolve these clusters 01:01:53.680 --> 01:01:56.800 align:middle line:84% is going to be Q times RP divided 01:01:56.800 --> 01:01:58.600 align:middle line:84% by the diffusivity of the interstitials 01:01:58.600 --> 01:02:00.250 align:middle line:84% times the maximum concentration-- 01:02:00.250 --> 01:02:02.260 align:middle line:84% CI max-- the maximum concentration. 01:02:02.260 --> 01:02:03.730 align:middle line:90% That gives me an idea. 01:02:03.730 --> 01:02:06.640 align:middle line:84% I have an idea-- how long will TED last? 01:02:06.640 --> 01:02:08.560 align:middle line:84% Well, it lasts until all the clusters have 01:02:08.560 --> 01:02:10.510 align:middle line:90% been dissolved, or evaporated. 01:02:10.510 --> 01:02:14.170 align:middle line:84% And you can see, if I implant a higher dose Q, 01:02:14.170 --> 01:02:16.345 align:middle line:90% I expect TED to last longer. 01:02:16.345 --> 01:02:19.310 align:middle line:90% 01:02:19.310 --> 01:02:24.170 align:middle line:84% If CI is larger than the concentration, 01:02:24.170 --> 01:02:27.180 align:middle line:84% then you expect the time to last a little shorter. 01:02:27.180 --> 01:02:29.510 align:middle line:90% So this gives us a rough idea. 01:02:29.510 --> 01:02:31.370 align:middle line:84% In fact, we can simplify this and put it 01:02:31.370 --> 01:02:33.020 align:middle line:84% in terms of a temperature dependence, 01:02:33.020 --> 01:02:35.250 align:middle line:90% if we go to Slide 19. 01:02:35.250 --> 01:02:40.060 align:middle line:84% So here is the time that TED lasts-- 01:02:40.060 --> 01:02:42.560 align:middle line:84% tau-- as I just showed it from the last slide. 01:02:42.560 --> 01:02:44.810 align:middle line:84% Now, I'm going to put in what CI max. 01:02:44.810 --> 01:02:47.810 align:middle line:84% We just calculated the maximum interstitial-- excess 01:02:47.810 --> 01:02:50.730 align:middle line:84% interstitial concentration induced by the implant. 01:02:50.730 --> 01:02:53.400 align:middle line:84% Remember, we said it was KR over KF. 01:02:53.400 --> 01:02:56.340 align:middle line:84% So we have that in terms of a Boltzmann factor 01:02:56.340 --> 01:02:58.660 align:middle line:90% on the binding energy. 01:02:58.660 --> 01:03:00.510 align:middle line:84% And so I can just substitute that in. 01:03:00.510 --> 01:03:02.230 align:middle line:84% And then in the middle of the slide, 01:03:02.230 --> 01:03:06.060 align:middle line:84% we can write down the time to resolve with the clusters, 01:03:06.060 --> 01:03:07.390 align:middle line:90% showing here. 01:03:07.390 --> 01:03:11.460 align:middle line:84% Well, it depends on Q, the dose implanted, RP, the diffusion 01:03:11.460 --> 01:03:14.880 align:middle line:84% rate, and an exponential of the binding energy of the silicon 01:03:14.880 --> 01:03:18.510 align:middle line:84% atom to the cluster of the silicon interstitials. 01:03:18.510 --> 01:03:20.940 align:middle line:84% We can put in what the diffusivity looks 01:03:20.940 --> 01:03:22.500 align:middle line:90% like for silicon interstitials. 01:03:22.500 --> 01:03:26.100 align:middle line:84% It's a cost prefactor times E to the minus E migration 01:03:26.100 --> 01:03:28.710 align:middle line:84% over KT, where people have estimated 01:03:28.710 --> 01:03:30.720 align:middle line:90% what that migration energy is. 01:03:30.720 --> 01:03:34.230 align:middle line:84% And here we have a relatively simple expression 01:03:34.230 --> 01:03:36.390 align:middle line:84% for the time constant-- the length of time 01:03:36.390 --> 01:03:38.740 align:middle line:84% that TED lasts as a function of temperature. 01:03:38.740 --> 01:03:40.950 align:middle line:84% It depends exponentially on the temperature. 01:03:40.950 --> 01:03:45.810 align:middle line:84% And inside the exponential over KT, 01:03:45.810 --> 01:03:50.410 align:middle line:84% I have the binding energy plus EM, the migration energy. 01:03:50.410 --> 01:03:55.450 align:middle line:84% So I have a nice little formula for how long TED lasts. 01:03:55.450 --> 01:03:57.760 align:middle line:84% It depends on the dose too, in RP. 01:03:57.760 --> 01:04:00.430 align:middle line:90% So let's go to Slide 20. 01:04:00.430 --> 01:04:03.980 align:middle line:84% Here's an actual example, using that simple formula. 01:04:03.980 --> 01:04:08.410 align:middle line:84% We're asked to calculate and plot how long TED lasts 01:04:08.410 --> 01:04:10.090 align:middle line:84% and how it depends on temperature 01:04:10.090 --> 01:04:15.370 align:middle line:84% for an implant of 40 Kev phosphorus at 10 to the 14th. 01:04:15.370 --> 01:04:18.050 align:middle line:90% Well, from the figure-- 01:04:18.050 --> 01:04:19.850 align:middle line:90% you can go back to Figure 8.3. 01:04:19.850 --> 01:04:22.120 align:middle line:84% It's just RP as a function of energy. 01:04:22.120 --> 01:04:24.190 align:middle line:84% You can figure out the projected range. 01:04:24.190 --> 01:04:26.470 align:middle line:90% It has an RP of 60 nanometers. 01:04:26.470 --> 01:04:28.810 align:middle line:84% And you have everything you need to in this formula. 01:04:28.810 --> 01:04:30.700 align:middle line:90% You have the dose. 01:04:30.700 --> 01:04:33.590 align:middle line:90% You have the RP estimate. 01:04:33.590 --> 01:04:36.520 align:middle line:84% We know EB-- binding energy is 1.7. 01:04:36.520 --> 01:04:37.840 align:middle line:90% The migration energy is 1.8. 01:04:37.840 --> 01:04:38.870 align:middle line:90% We add all that up. 01:04:38.870 --> 01:04:41.080 align:middle line:90% And here is the equation. 01:04:41.080 --> 01:04:42.580 align:middle line:84% So this gives us the time dependence 01:04:42.580 --> 01:04:45.040 align:middle line:84% for this particular energy and dose. 01:04:45.040 --> 01:04:48.950 align:middle line:84% And there it is on Slide Number 21. 01:04:48.950 --> 01:04:51.670 align:middle line:84% So this is the time-- the duration in seconds-- 01:04:51.670 --> 01:04:55.250 align:middle line:84% how long TED is going to last for this particular dose 01:04:55.250 --> 01:04:58.570 align:middle line:84% and energy of phosphorus as a function of temperature. 01:04:58.570 --> 01:05:01.000 align:middle line:84% And lo and behold, look what it shows. 01:05:01.000 --> 01:05:07.590 align:middle line:84% At 1,000 degrees, or maybe 950, TED only lasts about a second. 01:05:07.590 --> 01:05:09.600 align:middle line:90% OK, so it's very short. 01:05:09.600 --> 01:05:11.790 align:middle line:84% Because you form the 311s, and they have 01:05:11.790 --> 01:05:13.500 align:middle line:90% a pretty high evaporation rate. 01:05:13.500 --> 01:05:17.580 align:middle line:84% If you're down here at 800, TED lasts, maybe 01:05:17.580 --> 01:05:20.730 align:middle line:84% for this implant, about 100 seconds. 01:05:20.730 --> 01:05:24.480 align:middle line:84% OK, so it lasts a lot longer-- minutes. 01:05:24.480 --> 01:05:27.930 align:middle line:84% And the temperature dependence of this time 01:05:27.930 --> 01:05:29.250 align:middle line:90% is given by this equation. 01:05:29.250 --> 01:05:30.958 align:middle line:84% Now, if I have a higher dose-- let's say, 01:05:30.958 --> 01:05:32.070 align:middle line:90% I do 10 times the dose-- 01:05:32.070 --> 01:05:33.285 align:middle line:90% what happens to this line? 01:05:33.285 --> 01:05:36.950 align:middle line:90% 01:05:36.950 --> 01:05:39.200 align:middle line:84% The red line, does it stay the same? 01:05:39.200 --> 01:05:41.390 align:middle line:84% Does it move up by a factor of 10 times longer, 01:05:41.390 --> 01:05:43.970 align:middle line:90% or 10 times shorter? 01:05:43.970 --> 01:05:47.587 align:middle line:84% Based on-- let's just go back one slide. 01:05:47.587 --> 01:05:49.295 align:middle line:84% What is the dose dependence of that time? 01:05:49.295 --> 01:05:54.450 align:middle line:90% 01:05:54.450 --> 01:05:55.950 align:middle line:84% Depends directly on the dose, right? 01:05:55.950 --> 01:05:58.680 align:middle line:84% So if I implant 10 times the dose, 01:05:58.680 --> 01:06:01.260 align:middle line:84% TED is going to last 10 times as long. 01:06:01.260 --> 01:06:02.400 align:middle line:90% See, the Q dependence. 01:06:02.400 --> 01:06:06.120 align:middle line:84% So you can use this in a lot of your homework problems, 01:06:06.120 --> 01:06:07.860 align:middle line:90% or anytime you have a problem. 01:06:07.860 --> 01:06:09.970 align:middle line:84% Assuming the RP is about the same, 01:06:09.970 --> 01:06:12.090 align:middle line:84% you can use this nice curve, because it just 01:06:12.090 --> 01:06:13.840 align:middle line:90% scales linearly with the dose. 01:06:13.840 --> 01:06:16.980 align:middle line:84% So if I implant 10 to the 15th, then at 1,000 degrees, 01:06:16.980 --> 01:06:19.080 align:middle line:84% instead of lasting a fraction of a second, 01:06:19.080 --> 01:06:20.640 align:middle line:90% it could last a full second. 01:06:20.640 --> 01:06:22.860 align:middle line:84% At 800, instead of lasting 100 seconds, 01:06:22.860 --> 01:06:24.670 align:middle line:90% it could be 1,000 seconds. 01:06:24.670 --> 01:06:28.490 align:middle line:84% So that's the interesting thing about the dose of the implant, 01:06:28.490 --> 01:06:31.130 align:middle line:90% it tells you how long TED lasts. 01:06:31.130 --> 01:06:33.110 align:middle line:84% Because the dose injects a certain amount 01:06:33.110 --> 01:06:34.250 align:middle line:90% of these interstitials. 01:06:34.250 --> 01:06:36.440 align:middle line:90% They come together to form 311s. 01:06:36.440 --> 01:06:38.990 align:middle line:84% Depending on how many you originally form, 01:06:38.990 --> 01:06:41.930 align:middle line:84% it'll tell you how long it takes to get rid of them. 01:06:41.930 --> 01:06:44.230 align:middle line:84% And how long it takes to get rid of them 01:06:44.230 --> 01:06:46.105 align:middle line:84% is a strong function of temperature, as well. 01:06:46.105 --> 01:06:50.070 align:middle line:90% 01:06:50.070 --> 01:06:53.090 align:middle line:84% So Slide 22, I took this equation from your text. 01:06:53.090 --> 01:06:55.580 align:middle line:90% It looks a little mysterious. 01:06:55.580 --> 01:06:56.990 align:middle line:90% It shouldn't be. 01:06:56.990 --> 01:06:58.857 align:middle line:84% What this is saying is the overall amount 01:06:58.857 --> 01:07:00.440 align:middle line:84% of profile motion-- remember, we said, 01:07:00.440 --> 01:07:03.410 align:middle line:84% we could multiply-- we had something called the DT product. 01:07:03.410 --> 01:07:05.960 align:middle line:84% It gives you the idea of the thermal budget. 01:07:05.960 --> 01:07:10.640 align:middle line:84% The DT product effective of a dopant, 01:07:10.640 --> 01:07:13.880 align:middle line:84% remember, it depends on its equilibrium diffusivity, D, 01:07:13.880 --> 01:07:17.060 align:middle line:90% times CI over CI star. 01:07:17.060 --> 01:07:19.520 align:middle line:84% Now, instead of putting down time-- 01:07:19.520 --> 01:07:22.340 align:middle line:84% the total time of the implant of the anneal-- 01:07:22.340 --> 01:07:24.020 align:middle line:84% I'm going to put down tau enhance. 01:07:24.020 --> 01:07:28.320 align:middle line:84% Tau enhance is the time that TED lasts. 01:07:28.320 --> 01:07:31.560 align:middle line:84% So you can plug-in for those things-- 01:07:31.560 --> 01:07:33.068 align:middle line:84% CI over CI star and tau enhance-- 01:07:33.068 --> 01:07:34.860 align:middle line:84% and you get something that looks like this. 01:07:34.860 --> 01:07:37.590 align:middle line:90% 01:07:37.590 --> 01:07:41.400 align:middle line:84% OK, so it depends on the diffusivity of the dopant, 01:07:41.400 --> 01:07:45.960 align:middle line:84% the self-diffusion coefficient of silicon interstitials, 01:07:45.960 --> 01:07:50.370 align:middle line:84% the concentration of silicon in the dose, and RP. 01:07:50.370 --> 01:07:53.040 align:middle line:84% So the purpose of showing this is it 01:07:53.040 --> 01:07:56.295 align:middle line:84% explains the backwards, or anomalous temperature dependence 01:07:56.295 --> 01:07:58.800 align:middle line:90% of TED. 01:07:58.800 --> 01:08:00.600 align:middle line:84% Even though the dopant diffusivity 01:08:00.600 --> 01:08:03.570 align:middle line:84% has an activation energy of about 3.5-- 01:08:03.570 --> 01:08:05.910 align:middle line:84% so that's what you would expect for this thing-- 01:08:05.910 --> 01:08:08.490 align:middle line:84% this is being overwhelmed by the activation 01:08:08.490 --> 01:08:10.150 align:middle line:90% energy of the self-diffusion. 01:08:10.150 --> 01:08:12.330 align:middle line:84% So here we have DA-- the activation 01:08:12.330 --> 01:08:16.380 align:middle line:84% energy of the dopant diffusion-- might be E to the minus 3.5 01:08:16.380 --> 01:08:17.250 align:middle line:90% over KT. 01:08:17.250 --> 01:08:21.850 align:middle line:84% But in the denominator is the diffusion of silicon itself, 01:08:21.850 --> 01:08:23.729 align:middle line:84% which has a much higher activation energy-- 01:08:23.729 --> 01:08:27.149 align:middle line:90% E to the minus 4.8 over KT. 01:08:27.149 --> 01:08:30.569 align:middle line:84% So this is how we can-- when we ratio these two, we end up 01:08:30.569 --> 01:08:32.740 align:middle line:84% with a positive in the exponential. 01:08:32.740 --> 01:08:36.700 align:middle line:84% So this is how it's possible to get more broadening at a lower 01:08:36.700 --> 01:08:39.710 align:middle line:90% temperature. 01:08:39.710 --> 01:08:41.529 align:middle line:84% That's just from looking at the equation. 01:08:41.529 --> 01:08:44.260 align:middle line:84% The thinking behind this-- the rationale is you have a fixed 01:08:44.260 --> 01:08:48.069 align:middle line:84% amount of damage introduced by the implant, 01:08:48.069 --> 01:08:50.649 align:middle line:84% but the background point defect concentration-- 01:08:50.649 --> 01:08:54.640 align:middle line:84% CI star-- and the interstitial self-diffusion coefficient, 01:08:54.640 --> 01:08:56.950 align:middle line:84% they go down rapidly with temperature. 01:08:56.950 --> 01:08:57.520 align:middle line:90% OK. 01:08:57.520 --> 01:09:02.200 align:middle line:84% So again, the amount of profile motion depends on the ratio-- 01:09:02.200 --> 01:09:03.910 align:middle line:90% CI over CI star. 01:09:03.910 --> 01:09:08.300 align:middle line:84% So CI star is going down very rapidly with temperature. 01:09:08.300 --> 01:09:11.229 align:middle line:84% So the supersaturation is then going up 01:09:11.229 --> 01:09:13.870 align:middle line:90% as temperature is lowered. 01:09:13.870 --> 01:09:16.569 align:middle line:84% So it's partly because CI star goes down 01:09:16.569 --> 01:09:19.390 align:middle line:84% that this ratio is lowered, and so you get 01:09:19.390 --> 01:09:21.040 align:middle line:90% more TED at low temperatures. 01:09:21.040 --> 01:09:25.060 align:middle line:84% And also the duration of the excess interstitials 01:09:25.060 --> 01:09:28.510 align:middle line:84% is longer at low T, due to the lower diffusion coefficient. 01:09:28.510 --> 01:09:29.350 align:middle line:90% We just saw that. 01:09:29.350 --> 01:09:30.700 align:middle line:90% Look at this plot-- 01:09:30.700 --> 01:09:31.990 align:middle line:90% Slide 21. 01:09:31.990 --> 01:09:34.330 align:middle line:84% The lower I go in temperature, the longer 01:09:34.330 --> 01:09:36.729 align:middle line:84% it's going to take to evaporate all those interstitials 01:09:36.729 --> 01:09:37.609 align:middle line:90% and get rid of them. 01:09:37.609 --> 01:09:40.960 align:middle line:84% So TED lasts longer, and it can have a stronger 01:09:40.960 --> 01:09:44.990 align:middle line:90% effect at low temperatures. 01:09:44.990 --> 01:09:47.740 align:middle line:84% In fact, Slide 23 is just an example 01:09:47.740 --> 01:09:51.950 align:middle line:84% of that taken from Supreme simulation. 01:09:51.950 --> 01:09:56.030 align:middle line:84% This is a boron profile annealed at different temperatures. 01:09:56.030 --> 01:09:58.180 align:middle line:84% So its concentration versus depth. 01:09:58.180 --> 01:10:00.940 align:middle line:84% The solid lines here represent the boron, 01:10:00.940 --> 01:10:03.100 align:middle line:90% and they refer to the left axis. 01:10:03.100 --> 01:10:06.380 align:middle line:84% The dashed lines represent CI over CI star. 01:10:06.380 --> 01:10:09.030 align:middle line:90% They refer to the right axis. 01:10:09.030 --> 01:10:12.200 align:middle line:84% So let's see what happens to boron at different temperatures 01:10:12.200 --> 01:10:13.790 align:middle line:90% for the same amount of time-- 01:10:13.790 --> 01:10:19.800 align:middle line:84% 900 degrees, 800 degrees, 700 degrees. 01:10:19.800 --> 01:10:22.610 align:middle line:90% Look at CI over CI star at 700-- 01:10:22.610 --> 01:10:27.560 align:middle line:84% much higher than at 800 and also much higher than at 900. 01:10:27.560 --> 01:10:31.460 align:middle line:84% And it lasts a lot longer at 700. 01:10:31.460 --> 01:10:34.160 align:middle line:84% So we do a 30-minute anneal at 700, 01:10:34.160 --> 01:10:37.520 align:middle line:84% the entire period is transient-enhanced. 01:10:37.520 --> 01:10:42.320 align:middle line:84% Whereas if I do an anneal at 900, how long does it last? 01:10:42.320 --> 01:10:46.170 align:middle line:84% Well, of this order of magnitude of a second-- 01:10:46.170 --> 01:10:49.010 align:middle line:84% so only the first second is enhanced, 01:10:49.010 --> 01:10:51.120 align:middle line:90% and then TED goes away. 01:10:51.120 --> 01:10:55.310 align:middle line:84% So that's how you can explain a low temperature anneal ending up 01:10:55.310 --> 01:11:00.380 align:middle line:90% with so much more motion. 01:11:00.380 --> 01:11:03.050 align:middle line:84% It's got a higher CI over CI star, and it lasts longer. 01:11:03.050 --> 01:11:06.108 align:middle line:90% 01:11:06.108 --> 01:11:07.900 align:middle line:84% Slide 24-- just going through a little more 01:11:07.900 --> 01:11:09.370 align:middle line:90% of the subtle effects. 01:11:09.370 --> 01:11:12.520 align:middle line:84% And you can read through this in your text. 01:11:12.520 --> 01:11:16.600 align:middle line:84% We have this sort of equation that we just wrote down 01:11:16.600 --> 01:11:19.780 align:middle line:84% for the DT product, which is a measure 01:11:19.780 --> 01:11:26.470 align:middle line:84% of the amount of broadening for transient-enhanced diffusion. 01:11:26.470 --> 01:11:32.410 align:middle line:84% And the question is, how does it depend on energy and dose? 01:11:32.410 --> 01:11:37.510 align:middle line:84% Well, on the left-hand plot, this 01:11:37.510 --> 01:11:39.490 align:middle line:84% is some actual data that was taken. 01:11:39.490 --> 01:11:41.420 align:middle line:84% People measured the square root of DT-- 01:11:41.420 --> 01:11:46.900 align:middle line:84% how much does the does the dopant move 01:11:46.900 --> 01:11:49.750 align:middle line:84% as a function of the energy of the implant that 01:11:49.750 --> 01:11:51.620 align:middle line:90% was inducing the damage? 01:11:51.620 --> 01:11:55.570 align:middle line:84% And as you can see at high energies, 01:11:55.570 --> 01:11:57.510 align:middle line:84% you actually get a saturating effect. 01:11:57.510 --> 01:12:00.640 align:middle line:84% You see, this equation predicts that the amount of motion 01:12:00.640 --> 01:12:02.780 align:middle line:90% should depend on RP, linearly. 01:12:02.780 --> 01:12:07.790 align:middle line:84% So if you go to a higher energy, you expect a higher amount-- 01:12:07.790 --> 01:12:10.100 align:middle line:90% a larger amount of broadening. 01:12:10.100 --> 01:12:11.640 align:middle line:84% And that's true in the beginning. 01:12:11.640 --> 01:12:13.130 align:middle line:90% So here we go low energy here-- 01:12:13.130 --> 01:12:14.600 align:middle line:90% 10 Kev, 60. 01:12:14.600 --> 01:12:16.220 align:middle line:90% We do see this increase. 01:12:16.220 --> 01:12:17.720 align:middle line:90% And it starts to saturate out. 01:12:17.720 --> 01:12:20.430 align:middle line:84% And that's because high enough energy, 01:12:20.430 --> 01:12:24.530 align:middle line:84% the surface is no longer the dominant sink. 01:12:24.530 --> 01:12:26.450 align:middle line:84% In fact, you get bulk recombination 01:12:26.450 --> 01:12:28.490 align:middle line:90% as the profile gets really deep. 01:12:28.490 --> 01:12:31.070 align:middle line:84% And remember back here when we were doing this simple 01:12:31.070 --> 01:12:34.550 align:middle line:84% derivation-- back-of-the-envelope derivation 01:12:34.550 --> 01:12:36.140 align:middle line:90% on page 18-- 01:12:36.140 --> 01:12:37.970 align:middle line:84% remember, we were saying-- we ignored 01:12:37.970 --> 01:12:40.910 align:middle line:84% the diffusion flux that went into the bulk and recombined. 01:12:40.910 --> 01:12:42.680 align:middle line:84% For a simple back-of-the-envelope 01:12:42.680 --> 01:12:46.567 align:middle line:84% calculation, we said, all the interstitials diffuse towards 01:12:46.567 --> 01:12:47.900 align:middle line:90% the surface and recombine there. 01:12:47.900 --> 01:12:49.650 align:middle line:84% When you get them deep enough in the bulk, 01:12:49.650 --> 01:12:51.920 align:middle line:84% that's not necessarily the right model. 01:12:51.920 --> 01:12:54.770 align:middle line:84% Again, just to show, this is a little back of the envelope. 01:12:54.770 --> 01:12:59.330 align:middle line:84% So in real case, the motion-- the amount of TED 01:12:59.330 --> 01:13:02.360 align:middle line:84% will actually saturate at some energy. 01:13:02.360 --> 01:13:07.070 align:middle line:84% So take this RP dependence with a grain of salt. 01:13:07.070 --> 01:13:08.870 align:middle line:84% Same thing for the dose dependence. 01:13:08.870 --> 01:13:12.740 align:middle line:84% This is again the square root of DT-- the diffusion distance. 01:13:12.740 --> 01:13:17.360 align:middle line:84% Now this time versus anneal time, 01:13:17.360 --> 01:13:19.850 align:middle line:84% it turns out, if you look at different doses-- 01:13:19.850 --> 01:13:22.140 align:middle line:84% indeed, if you do a long enough time here, 01:13:22.140 --> 01:13:25.760 align:middle line:84% which I'm showing here-- say, close to 1,000 seconds, 01:13:25.760 --> 01:13:27.590 align:middle line:90% or close to 10,000 seconds-- 01:13:27.590 --> 01:13:30.440 align:middle line:90% you can see a dose dependence. 01:13:30.440 --> 01:13:33.440 align:middle line:84% And in fact, this open bullet is for 10 to the 13th. 01:13:33.440 --> 01:13:35.210 align:middle line:84% The closed bullet is 4 times that. 01:13:35.210 --> 01:13:38.130 align:middle line:84% And indeed, you do see about 4 times the dopant motion. 01:13:38.130 --> 01:13:41.510 align:middle line:84% So it does scale with the dose, but only at long enough times. 01:13:41.510 --> 01:13:45.200 align:middle line:84% At short times the dose dependent is not so evident. 01:13:45.200 --> 01:13:48.620 align:middle line:84% And that's because, again, we did a very simple calculation 01:13:48.620 --> 01:13:51.080 align:middle line:90% of that differential equation. 01:13:51.080 --> 01:13:52.610 align:middle line:84% We solved only for the steady state 01:13:52.610 --> 01:13:56.900 align:middle line:84% period, which takes a certain time to develop. 01:13:56.900 --> 01:13:59.593 align:middle line:84% So this is more of a second-order effect. 01:13:59.593 --> 01:14:02.010 align:middle line:84% So this equation, again, you take it with a grain of salt. 01:14:02.010 --> 01:14:06.770 align:middle line:84% It's meant to give you a back-of-the-envelope estimate. 01:14:06.770 --> 01:14:08.900 align:middle line:90% So on Slide 25-- 01:14:08.900 --> 01:14:12.560 align:middle line:84% when you walk away today, this is the general picture 01:14:12.560 --> 01:14:15.800 align:middle line:84% you should take in your head of TED. 01:14:15.800 --> 01:14:19.550 align:middle line:84% And what is, it's a plot of the enhancement in CI over CS star 01:14:19.550 --> 01:14:22.590 align:middle line:84% in a log scale as a function of time. 01:14:22.590 --> 01:14:26.000 align:middle line:84% And so what we say is we have some steady state period, 01:14:26.000 --> 01:14:28.730 align:middle line:84% and its length is called tau enhancement. 01:14:28.730 --> 01:14:32.870 align:middle line:84% It's the time during which the 311 clusters are decaying. 01:14:32.870 --> 01:14:34.580 align:middle line:90% It lasts a certain period-- 01:14:34.580 --> 01:14:36.020 align:middle line:90% tau. 01:14:36.020 --> 01:14:38.660 align:middle line:90% And that period depends on-- 01:14:38.660 --> 01:14:41.210 align:middle line:84% the duration depends on the dose, of how many 01:14:41.210 --> 01:14:42.230 align:middle line:90% interstitials I put in. 01:14:42.230 --> 01:14:43.730 align:middle line:84% And then after that period, it just 01:14:43.730 --> 01:14:47.690 align:middle line:84% rapidly exponentials-- exponentially decays. 01:14:47.690 --> 01:14:50.000 align:middle line:84% So the critical parameters are, what 01:14:50.000 --> 01:14:52.590 align:middle line:84% is the supersaturation height, or the level, 01:14:52.590 --> 01:14:54.890 align:middle line:84% which depends on the temperature-- as we know, 01:14:54.890 --> 01:14:57.680 align:middle line:84% it goes up as temperature goes down. 01:14:57.680 --> 01:15:00.620 align:middle line:84% And what is the duration of that steady state 01:15:00.620 --> 01:15:02.480 align:middle line:90% condition, tau enhanced? 01:15:02.480 --> 01:15:04.400 align:middle line:84% So with those two pieces of information, 01:15:04.400 --> 01:15:07.260 align:middle line:84% how high is it enhanced, and how long does it last, 01:15:07.260 --> 01:15:09.390 align:middle line:84% you can do a lot of predicting, roughly, 01:15:09.390 --> 01:15:11.520 align:middle line:84% of the amount of profile motion you're going 01:15:11.520 --> 01:15:15.360 align:middle line:90% to get due to the TED effect. 01:15:15.360 --> 01:15:19.260 align:middle line:84% OK, so let me just summarize what we've 01:15:19.260 --> 01:15:21.210 align:middle line:90% said about ion-implanted TED. 01:15:21.210 --> 01:15:24.360 align:middle line:84% Ion implanted is the dominant method for putting dopants in. 01:15:24.360 --> 01:15:25.850 align:middle line:84% We talked about Range statistics, 01:15:25.850 --> 01:15:28.890 align:middle line:84% that we can calculate using simple distributions. 01:15:28.890 --> 01:15:31.920 align:middle line:84% We talked about Pearson IV in amorphous targets-- 01:15:31.920 --> 01:15:33.780 align:middle line:90% how it works very well. 01:15:33.780 --> 01:15:36.060 align:middle line:84% Ion channeling has to be modeled by something 01:15:36.060 --> 01:15:39.510 align:middle line:84% more complex and complete, like Monte Carlo. 01:15:39.510 --> 01:15:42.480 align:middle line:84% Next time, I'll show you some ion channeling profiles 01:15:42.480 --> 01:15:45.600 align:middle line:84% and how they're fit by dual Pearson. 01:15:45.600 --> 01:15:48.570 align:middle line:84% We spent some time today talking about the plus-n model 01:15:48.570 --> 01:15:51.960 align:middle line:84% from for residual implant damage. 01:15:51.960 --> 01:15:54.870 align:middle line:84% It tells you that you get roughly n excess interstitials 01:15:54.870 --> 01:15:56.610 align:middle line:90% per primary ion. 01:15:56.610 --> 01:15:58.680 align:middle line:84% These excess interstitials all get together. 01:15:58.680 --> 01:16:02.680 align:middle line:84% They cluster into these 311s very quickly-- 01:16:02.680 --> 01:16:05.190 align:middle line:84% in less than a tenth of a second. 01:16:05.190 --> 01:16:06.870 align:middle line:90% And they dissolve very slowly. 01:16:06.870 --> 01:16:11.550 align:middle line:84% And their dissolving process, that gives rise to TED. 01:16:11.550 --> 01:16:14.052 align:middle line:84% And we have a simple model for TED. 01:16:14.052 --> 01:16:16.260 align:middle line:84% They can explain the time, the temperature, the dose, 01:16:16.260 --> 01:16:19.170 align:middle line:84% and, roughly, the energy dependence of TED. 01:16:19.170 --> 01:16:23.100 align:middle line:84% And so next time in class, we'll do a few calculation examples. 01:16:23.100 --> 01:16:24.900 align:middle line:84% If you can bring a calculator, we'll 01:16:24.900 --> 01:16:26.210 align:middle line:90% do some calculations together. 01:16:26.210 --> 01:16:28.050 align:middle line:84% If you have a calculator, it'll be easier. 01:16:28.050 --> 01:16:30.060 align:middle line:84% We'll actually do some calculations-- back 01:16:30.060 --> 01:16:33.600 align:middle line:84% of the envelope calculations on TED kinetics. 01:16:33.600 --> 01:16:35.580 align:middle line:84% And that clipboard is going around. 01:16:35.580 --> 01:16:36.900 align:middle line:90% Does everybody have that? 01:16:36.900 --> 01:16:39.480 align:middle line:84% Please sign up for your project, and at least sign up 01:16:39.480 --> 01:16:42.930 align:middle line:84% for whether you want to do written report or oral report. 01:16:42.930 --> 01:16:45.320 align:middle line:90% OK, thanks. 01:16:45.320 --> 01:16:51.000 align:middle line:90%