WEBVTT 00:00:00.000 --> 00:00:00.800 align:middle line:90% 00:00:00.800 --> 00:00:03.580 align:middle line:84% JUDY HOYT: So before we start with today's formal lecture, 00:00:03.580 --> 00:00:05.580 align:middle line:84% there's a couple of things I want to talk about. 00:00:05.580 --> 00:00:08.010 align:middle line:84% One is the schedule, which I have shown up here. 00:00:08.010 --> 00:00:10.460 align:middle line:84% And you'll notice, or if you remember, 00:00:10.460 --> 00:00:14.060 align:middle line:84% I've actually shifted around one of the lectures. 00:00:14.060 --> 00:00:17.120 align:middle line:84% Here we are today, I think October 19. 00:00:17.120 --> 00:00:19.910 align:middle line:84% And we're supposed to have this lecture on the SUPREM-IV process 00:00:19.910 --> 00:00:20.600 align:middle line:90% simulator. 00:00:20.600 --> 00:00:24.110 align:middle line:84% I decided I wanted to do that lecture later, 00:00:24.110 --> 00:00:26.060 align:middle line:84% primarily because I want to have talked 00:00:26.060 --> 00:00:29.120 align:middle line:84% about transient enhanced diffusion and those effects. 00:00:29.120 --> 00:00:32.150 align:middle line:84% A lot of the examples I show and how to use 00:00:32.150 --> 00:00:34.430 align:middle line:84% SUPREM relate to transient enhanced diffusion. 00:00:34.430 --> 00:00:36.080 align:middle line:90% And I realized I hadn't really-- 00:00:36.080 --> 00:00:38.580 align:middle line:90% I wouldn't have introduced it. 00:00:38.580 --> 00:00:41.330 align:middle line:84% So we're going to have instead the ion implantation lectures. 00:00:41.330 --> 00:00:44.270 align:middle line:84% There's four on ion implantation, two of those 00:00:44.270 --> 00:00:46.890 align:middle line:84% are on TED, and then we'll do that lecture. 00:00:46.890 --> 00:00:50.870 align:middle line:84% And as I mentioned also because of the Red Sox game last night, 00:00:50.870 --> 00:00:53.850 align:middle line:84% I don't have homework number 4 ready to go out to you yet. 00:00:53.850 --> 00:00:58.460 align:middle line:84% And so we can blame the Yankees for that. 00:00:58.460 --> 00:00:59.980 align:middle line:90% But I'll have it next time. 00:00:59.980 --> 00:01:03.236 align:middle line:84% There is another handout as well before we 00:01:03.236 --> 00:01:05.069 align:middle line:84% go to the formal lecture, handout number 20. 00:01:05.069 --> 00:01:06.480 align:middle line:90% It's a one-page document. 00:01:06.480 --> 00:01:08.760 align:middle line:90% Hopefully, you picked that up. 00:01:08.760 --> 00:01:11.415 align:middle line:84% I want you to start thinking about your term projects. 00:01:11.415 --> 00:01:13.540 align:middle line:84% And so it's a good time to start thinking about it. 00:01:13.540 --> 00:01:17.760 align:middle line:84% What I've listed here is maybe 15 or so potential topics 00:01:17.760 --> 00:01:20.760 align:middle line:84% that you might want to use for your term project. 00:01:20.760 --> 00:01:22.450 align:middle line:90% This is not an exhaustive list. 00:01:22.450 --> 00:01:23.920 align:middle line:90% These are just examples. 00:01:23.920 --> 00:01:27.510 align:middle line:84% So for example, you could study dopant diffusion 00:01:27.510 --> 00:01:28.440 align:middle line:90% in silicon germanium. 00:01:28.440 --> 00:01:29.523 align:middle line:90% You could read up on that. 00:01:29.523 --> 00:01:31.775 align:middle line:84% You could study laser annealing of ion implants 00:01:31.775 --> 00:01:32.650 align:middle line:90% for shallow junction. 00:01:32.650 --> 00:01:34.770 align:middle line:84% These are all things that we don't get a chance 00:01:34.770 --> 00:01:37.260 align:middle line:84% to cover any great detail-- selective epitaxial 00:01:37.260 --> 00:01:40.430 align:middle line:84% growth of silicon or silicon germanium. 00:01:40.430 --> 00:01:44.310 align:middle line:84% But they are related to front end processing 00:01:44.310 --> 00:01:46.800 align:middle line:84% I'd like you to learn more about in depth. 00:01:46.800 --> 00:01:49.290 align:middle line:84% So you pick a topic or you make up a topic. 00:01:49.290 --> 00:01:51.930 align:middle line:84% Any topic you pick or make up, it needs to be approved by me. 00:01:51.930 --> 00:01:54.023 align:middle line:84% And next time over the next couple of weeks, 00:01:54.023 --> 00:01:55.440 align:middle line:84% I'm going to bring in a clipboard. 00:01:55.440 --> 00:01:58.260 align:middle line:84% And you'll have a chance to sign up for a topic. 00:01:58.260 --> 00:01:59.850 align:middle line:84% And I also want to know whether you 00:01:59.850 --> 00:02:02.480 align:middle line:84% want to give an oral presentation or a written 00:02:02.480 --> 00:02:04.020 align:middle line:90% report. 00:02:04.020 --> 00:02:06.500 align:middle line:84% The written report is going to be-- it 00:02:06.500 --> 00:02:09.169 align:middle line:90% needs to be 20 pages or less. 00:02:09.169 --> 00:02:11.630 align:middle line:84% And an oral presentation in class 00:02:11.630 --> 00:02:15.080 align:middle line:84% is probably going to be about something like 15 to 17 minutes 00:02:15.080 --> 00:02:16.710 align:middle line:90% plus questions. 00:02:16.710 --> 00:02:18.440 align:middle line:84% And I need to start scheduling that so I 00:02:18.440 --> 00:02:21.020 align:middle line:84% need to know whether you would prefer to do your final term 00:02:21.020 --> 00:02:22.730 align:middle line:90% project as a written or oral. 00:02:22.730 --> 00:02:25.490 align:middle line:84% And the term project is not meant for you 00:02:25.490 --> 00:02:29.840 align:middle line:84% to go read one textbook or one paper and then regurgitate it. 00:02:29.840 --> 00:02:33.230 align:middle line:84% The whole idea is you go to a library, you go online, 00:02:33.230 --> 00:02:36.940 align:middle line:84% and you read a series of research papers, 00:02:36.940 --> 00:02:39.200 align:middle line:84% so maybe some texts, but most of these topics 00:02:39.200 --> 00:02:41.840 align:middle line:84% are new enough that you'll have to read research papers, 00:02:41.840 --> 00:02:45.410 align:middle line:84% and then write up a report or give an oral presentation 00:02:45.410 --> 00:02:47.340 align:middle line:90% about the topic. 00:02:47.340 --> 00:02:50.540 align:middle line:84% So I don't want you just to regurgitate one paper. 00:02:50.540 --> 00:02:53.817 align:middle line:84% And then the other thing is if you 00:02:53.817 --> 00:02:55.400 align:middle line:84% do decide to do a presentation, you'll 00:02:55.400 --> 00:02:58.940 align:middle line:84% need to have handouts for the class, just like the handouts 00:02:58.940 --> 00:03:01.040 align:middle line:90% that I give you, not as long. 00:03:01.040 --> 00:03:04.170 align:middle line:84% And if you need help making the handouts in terms 00:03:04.170 --> 00:03:06.300 align:middle line:84% of getting them xeroxed, my assistant 00:03:06.300 --> 00:03:07.800 align:middle line:90% will help you with that. 00:03:07.800 --> 00:03:10.540 align:middle line:84% So even if you do the presentation, 00:03:10.540 --> 00:03:15.090 align:middle line:84% there'll be some preparation of graphical information. 00:03:15.090 --> 00:03:17.077 align:middle line:84% So that's to get you started thinking. 00:03:17.077 --> 00:03:19.410 align:middle line:84% And as I say, next time I'm going to bring the clipboard 00:03:19.410 --> 00:03:22.780 align:middle line:84% and you can start signing up for topics. 00:03:22.780 --> 00:03:23.280 align:middle line:90% OK. 00:03:23.280 --> 00:03:27.210 align:middle line:84% So let's go to the formal lecture for today, 00:03:27.210 --> 00:03:31.502 align:middle line:90% which is handout number 19. 00:03:31.502 --> 00:03:33.460 align:middle line:84% And we're going to talk-- as I mentioned today, 00:03:33.460 --> 00:03:34.930 align:middle line:84% we're not doing the SUPREM-IV lecture. 00:03:34.930 --> 00:03:35.888 align:middle line:90% I shifted the schedule. 00:03:35.888 --> 00:03:38.290 align:middle line:84% And we're going to talk about chapter 8. 00:03:38.290 --> 00:03:41.710 align:middle line:84% The next four lectures are going to cover chapter 8 so I 00:03:41.710 --> 00:03:43.210 align:middle line:90% hope you will read it. 00:03:43.210 --> 00:03:48.330 align:middle line:84% Chapter 8 is about ion implantation and annealing. 00:03:48.330 --> 00:03:50.080 align:middle line:84% So we've already talked about introduction 00:03:50.080 --> 00:03:53.020 align:middle line:84% to the basic process flow in CMOS. 00:03:53.020 --> 00:03:55.520 align:middle line:84% We know how to fabricate wafers and clean them. 00:03:55.520 --> 00:03:58.480 align:middle line:84% We discussed in detail thermal oxidation 00:03:58.480 --> 00:03:59.650 align:middle line:90% and two-dimensional effects. 00:03:59.650 --> 00:04:02.770 align:middle line:84% And we spent the last four lectures talking about diffusion 00:04:02.770 --> 00:04:03.998 align:middle line:90% and how we model it. 00:04:03.998 --> 00:04:06.040 align:middle line:84% We're going to come back to diffusion after we've 00:04:06.040 --> 00:04:07.610 align:middle line:90% talked about ion implantation. 00:04:07.610 --> 00:04:10.120 align:middle line:84% But first, I'm going to spend the next couple of lectures 00:04:10.120 --> 00:04:12.400 align:middle line:84% talking about the basic concept of ion implant 00:04:12.400 --> 00:04:16.420 align:middle line:84% and how it's used, the impact of the crystal structure, 00:04:16.420 --> 00:04:19.120 align:middle line:84% there's a phenomenon that's called channeling, how 00:04:19.120 --> 00:04:23.110 align:middle line:84% ion implantation is modeled, and damage annealing, 00:04:23.110 --> 00:04:24.670 align:middle line:84% and transient enhanced diffusion. 00:04:24.670 --> 00:04:26.920 align:middle line:84% Ion implantation is somewhat unique in this course 00:04:26.920 --> 00:04:28.510 align:middle line:90% or in any course on processing. 00:04:28.510 --> 00:04:33.040 align:middle line:84% It is probably the only process that we can actually 00:04:33.040 --> 00:04:35.410 align:middle line:84% model from more or less first principles. 00:04:35.410 --> 00:04:37.720 align:middle line:84% That is, if you look at our models 00:04:37.720 --> 00:04:40.450 align:middle line:84% for [INAUDIBLE] models for oxidation, 00:04:40.450 --> 00:04:42.550 align:middle line:84% there are a lot of chemical processes involved, 00:04:42.550 --> 00:04:44.980 align:middle line:84% and there's a lot of unknown constants here and there. 00:04:44.980 --> 00:04:46.700 align:middle line:84% And the models tend to be very empirical. 00:04:46.700 --> 00:04:48.200 align:middle line:84% Ion implantation, on the other hand, 00:04:48.200 --> 00:04:50.660 align:middle line:84% is based on fundamental physics, a lot of it. 00:04:50.660 --> 00:04:52.270 align:middle line:84% And so it's one of the few processes 00:04:52.270 --> 00:04:55.660 align:middle line:84% you can actually model without too many free parameters. 00:04:55.660 --> 00:04:58.090 align:middle line:84% You'll see there are some parameters but not as much as 00:04:58.090 --> 00:04:59.180 align:middle line:90% other. 00:04:59.180 --> 00:05:01.450 align:middle line:84% So for people who like first principles modeling, 00:05:01.450 --> 00:05:03.890 align:middle line:90% it's somewhat satisfying. 00:05:03.890 --> 00:05:04.390 align:middle line:90% OK. 00:05:04.390 --> 00:05:07.810 align:middle line:84% So let's go on to slide number 2, 00:05:07.810 --> 00:05:11.050 align:middle line:84% showing you what I call the old fashioned or traditional 00:05:11.050 --> 00:05:14.290 align:middle line:84% approach to getting dopants into a wafer. 00:05:14.290 --> 00:05:15.640 align:middle line:90% You would coat it with oxide. 00:05:15.640 --> 00:05:16.870 align:middle line:90% You would open up a hole. 00:05:16.870 --> 00:05:19.960 align:middle line:84% And we talked about last time, last few times, 00:05:19.960 --> 00:05:22.090 align:middle line:84% doing what's called a predeposition. 00:05:22.090 --> 00:05:24.220 align:middle line:84% So that used to be, in predeposition, 00:05:24.220 --> 00:05:27.220 align:middle line:84% it was a high temperature in diffusion from the gas phase. 00:05:27.220 --> 00:05:32.270 align:middle line:84% Typically, in a pre-dep, you would have in the gas phase 00:05:32.270 --> 00:05:34.957 align:middle line:84% some kind of dopant gas like phosphine or whatever. 00:05:34.957 --> 00:05:37.040 align:middle line:84% And you would keep the concentration of the dopant 00:05:37.040 --> 00:05:38.660 align:middle line:84% at the surface at the solid solubility 00:05:38.660 --> 00:05:40.410 align:middle line:84% at that temperature at a very high value. 00:05:40.410 --> 00:05:42.500 align:middle line:84% And you would do it for a certain amount of time 00:05:42.500 --> 00:05:45.630 align:middle line:84% to put in a certain control dose. 00:05:45.630 --> 00:05:50.010 align:middle line:84% And then you would turn off the gas that had the dopant in it. 00:05:50.010 --> 00:05:54.500 align:middle line:84% And you would do a drive in, a deep diffusion drive in. 00:05:54.500 --> 00:05:56.297 align:middle line:84% A big problem with this method though, 00:05:56.297 --> 00:05:58.630 align:middle line:84% although it was the original method, it was very limited 00:05:58.630 --> 00:06:02.430 align:middle line:84% and it's very hard to control the actual dose, the integrated 00:06:02.430 --> 00:06:05.340 align:middle line:84% dose of the dopants that were put into the wafer. 00:06:05.340 --> 00:06:07.712 align:middle line:84% If you had an extra few minutes in the furnace 00:06:07.712 --> 00:06:09.795 align:middle line:84% or the furnace temperature was slightly different, 00:06:09.795 --> 00:06:12.280 align:middle line:84% you would get a completely different dose. 00:06:12.280 --> 00:06:14.160 align:middle line:84% So this method was good in the old days 00:06:14.160 --> 00:06:18.690 align:middle line:84% but it really gave way some time ago to ion implantation 00:06:18.690 --> 00:06:21.210 align:middle line:90% as the method. 00:06:21.210 --> 00:06:24.630 align:middle line:84% And the only problem with ion implantation, the good part 00:06:24.630 --> 00:06:27.360 align:middle line:84% is it has tremendous control of the dose. 00:06:27.360 --> 00:06:29.730 align:middle line:84% The bad part or the issues we have 00:06:29.730 --> 00:06:31.660 align:middle line:84% is that it does introduce damage. 00:06:31.660 --> 00:06:33.090 align:middle line:84% And we have to anneal that damage 00:06:33.090 --> 00:06:37.750 align:middle line:84% and repair the crystal in order to make a good device. 00:06:37.750 --> 00:06:39.570 align:middle line:90% So let's look on slide 3. 00:06:39.570 --> 00:06:42.510 align:middle line:84% And from this slide, we can understand 00:06:42.510 --> 00:06:45.990 align:middle line:84% why ion implantation was introduced into manufacturing 00:06:45.990 --> 00:06:47.970 align:middle line:90% in the late 1970s. 00:06:47.970 --> 00:06:50.500 align:middle line:84% And this is an interesting history. 00:06:50.500 --> 00:06:52.170 align:middle line:84% And it's also an interesting example 00:06:52.170 --> 00:06:53.880 align:middle line:84% because it gives you an idea of if you 00:06:53.880 --> 00:06:58.020 align:middle line:84% have a new idea-- let's say you're working here on your PhD 00:06:58.020 --> 00:07:01.810 align:middle line:84% and you have a new idea for some great new process. 00:07:01.810 --> 00:07:03.645 align:middle line:84% The new process, whatever it might be, 00:07:03.645 --> 00:07:05.760 align:middle line:84% has to really be an enabling technology. 00:07:05.760 --> 00:07:10.230 align:middle line:84% It has to do something that you cannot do by any other method 00:07:10.230 --> 00:07:13.110 align:middle line:84% because all new processes have some bad aspects to them. 00:07:13.110 --> 00:07:14.100 align:middle line:90% They cost money. 00:07:14.100 --> 00:07:15.710 align:middle line:90% There's development time. 00:07:15.710 --> 00:07:17.520 align:middle line:90% Ion implantation adds damage. 00:07:17.520 --> 00:07:18.930 align:middle line:90% Why would anybody want to do it? 00:07:18.930 --> 00:07:20.790 align:middle line:84% Well, this is why because it did something 00:07:20.790 --> 00:07:23.200 align:middle line:84% that they couldn't do in the past. 00:07:23.200 --> 00:07:25.530 align:middle line:84% And basically, in the late 1970s, 00:07:25.530 --> 00:07:29.700 align:middle line:84% ion implantation was introduced as the only means 00:07:29.700 --> 00:07:33.270 align:middle line:84% to accurately control the threshold voltage of a MOSFET. 00:07:33.270 --> 00:07:37.330 align:middle line:84% Without ion implantation, people couldn't make circuits 00:07:37.330 --> 00:07:40.330 align:middle line:84% because they could not control the VT at the level 00:07:40.330 --> 00:07:42.590 align:middle line:84% that they needed to be able to control it. 00:07:42.590 --> 00:07:45.820 align:middle line:84% So if you go back and look at this 00:07:45.820 --> 00:07:49.220 align:middle line:84% as an equation we introduced a number of lectures ago-- 00:07:49.220 --> 00:07:50.740 align:middle line:90% we didn't derive it. 00:07:50.740 --> 00:07:55.190 align:middle line:84% I just wrote it up there and you'll have to take it as truth. 00:07:55.190 --> 00:07:58.660 align:middle line:84% But what it says is that the threshold voltage of the MOSFET 00:07:58.660 --> 00:08:01.660 align:middle line:90% depends on a number of terms-- 00:08:01.660 --> 00:08:04.060 align:middle line:90% the flat band voltage. 00:08:04.060 --> 00:08:08.080 align:middle line:84% It depends on the doping in the substrate, 00:08:08.080 --> 00:08:10.810 align:middle line:84% the oxide thickness through SiOx and things like that. 00:08:10.810 --> 00:08:13.030 align:middle line:84% There's one last term here, which 00:08:13.030 --> 00:08:17.320 align:middle line:84% I circled, which is the electronic charge q times phi 00:08:17.320 --> 00:08:21.250 align:middle line:84% where phi is the dose of a dopant that's 00:08:21.250 --> 00:08:25.060 align:middle line:84% ion implanted into the surface of the wafer divided by SiOx. 00:08:25.060 --> 00:08:27.820 align:middle line:84% So this extra term, this isn't here 00:08:27.820 --> 00:08:30.490 align:middle line:84% unless you're doing an implant but that extra term 00:08:30.490 --> 00:08:32.470 align:middle line:90% can be added in. 00:08:32.470 --> 00:08:35.200 align:middle line:84% And if you can very precisely control phi, 00:08:35.200 --> 00:08:37.570 align:middle line:84% the dose, then you can very precisely 00:08:37.570 --> 00:08:40.530 align:middle line:84% control the threshold voltage and set it to a level 00:08:40.530 --> 00:08:42.412 align:middle line:90% that you need. 00:08:42.412 --> 00:08:45.690 align:middle line:84% So on the left-hand side, I'm just showing a schematic, 00:08:45.690 --> 00:08:48.630 align:middle line:84% just reminding you from the first lecture, what people do 00:08:48.630 --> 00:08:50.760 align:middle line:90% for a VT adjust implant. 00:08:50.760 --> 00:08:54.880 align:middle line:84% For example, if you're making an N-MOSFET on the right-hand side, 00:08:54.880 --> 00:08:57.930 align:middle line:84% you would ion implant with boron, a very, very thin surface 00:08:57.930 --> 00:08:58.470 align:middle line:90% region. 00:08:58.470 --> 00:09:03.420 align:middle line:84% You block off with photoresist, the PMOS area. 00:09:03.420 --> 00:09:06.900 align:middle line:84% And you would implant boron to adjust the threshold voltage. 00:09:06.900 --> 00:09:10.710 align:middle line:84% Typically, doses are pretty low, 10 to the 12, 10 to the 13, 00:09:10.710 --> 00:09:11.610 align:middle line:90% something like that. 00:09:11.610 --> 00:09:15.810 align:middle line:84% And energies in this range, we'll talk about dose and energy 00:09:15.810 --> 00:09:19.530 align:middle line:84% in more detail in the next couple of lectures. 00:09:19.530 --> 00:09:22.530 align:middle line:84% The nice thing is that this dose fee can be accurately 00:09:22.530 --> 00:09:24.270 align:middle line:84% controlled, and that's because it's 00:09:24.270 --> 00:09:28.130 align:middle line:84% based upon integrating a current, electronic charge that 00:09:28.130 --> 00:09:29.030 align:middle line:90% goes into the wafer. 00:09:29.030 --> 00:09:31.680 align:middle line:84% That's because of the way we do ion implantation. 00:09:31.680 --> 00:09:34.610 align:middle line:84% So it turns out the dose fee is just 1 00:09:34.610 --> 00:09:37.580 align:middle line:84% over the area, where the area is the implanted area, 00:09:37.580 --> 00:09:42.180 align:middle line:84% times the integral over time of i. 00:09:42.180 --> 00:09:44.790 align:middle line:84% That's supposed to be an i, i standing for the beam 00:09:44.790 --> 00:09:48.390 align:middle line:84% current that's collected into the wafer, divided 00:09:48.390 --> 00:09:52.000 align:middle line:84% by the electronic charge, q, integrated over time. 00:09:52.000 --> 00:09:54.630 align:middle line:84% So because the ions coming in are charged, 00:09:54.630 --> 00:09:57.180 align:middle line:84% they represent a current flow into the wafer. 00:09:57.180 --> 00:10:00.330 align:middle line:84% So they're charged, and as the current flows into the wafer, 00:10:00.330 --> 00:10:02.970 align:middle line:84% you can measure the current with an ammeter very accurately. 00:10:02.970 --> 00:10:04.720 align:middle line:84% And then you can integrate it over time. 00:10:04.720 --> 00:10:07.770 align:middle line:84% So you start the implant opening up a shutter, 00:10:07.770 --> 00:10:10.590 align:middle line:90% and then you iterate over time. 00:10:10.590 --> 00:10:13.470 align:middle line:84% Each charge that comes in gets counted, and then you stop. 00:10:13.470 --> 00:10:15.690 align:middle line:84% So you can very, very precisely because it's 00:10:15.690 --> 00:10:17.340 align:middle line:84% based on charge counting techniques, 00:10:17.340 --> 00:10:20.520 align:middle line:84% not on some chemistry pushing away from into a hot furnace, 00:10:20.520 --> 00:10:22.028 align:middle line:90% hope the temperature is right. 00:10:22.028 --> 00:10:23.820 align:middle line:84% Oh, you pushed it for ten seconds too long. 00:10:23.820 --> 00:10:24.320 align:middle line:90% What? 00:10:24.320 --> 00:10:25.590 align:middle line:90% Pull it out. 00:10:25.590 --> 00:10:27.935 align:middle line:84% It's more of a physics-based approach. 00:10:27.935 --> 00:10:30.372 align:middle line:90% 00:10:30.372 --> 00:10:31.830 align:middle line:84% From a manufacturing point of view, 00:10:31.830 --> 00:10:34.470 align:middle line:84% that was an important breakthrough 00:10:34.470 --> 00:10:39.120 align:middle line:90% in the fabrication of MOSFETs. 00:10:39.120 --> 00:10:42.580 align:middle line:84% Let's just do an example on slide 4 00:10:42.580 --> 00:10:45.850 align:middle line:84% that illustrates the controls that you can 00:10:45.850 --> 00:10:47.180 align:middle line:90% get during ion implantation. 00:10:47.180 --> 00:10:52.990 align:middle line:84% So let's say that we need to calculate the dose rate. 00:10:52.990 --> 00:10:54.730 align:middle line:84% OK, so that'll be the number of atoms 00:10:54.730 --> 00:10:57.370 align:middle line:84% per square centimeter going into the wafer per second 00:10:57.370 --> 00:11:00.010 align:middle line:90% or per unit time. 00:11:00.010 --> 00:11:02.920 align:middle line:84% I'm going to assume that we have an ion beam current, 00:11:02.920 --> 00:11:04.690 align:middle line:84% so that's the beam coming into the wafer. 00:11:04.690 --> 00:11:07.133 align:middle line:84% The beam current is 0.1 microamp. 00:11:07.133 --> 00:11:08.800 align:middle line:84% OK, and we measure that very accurately. 00:11:08.800 --> 00:11:11.020 align:middle line:90% It's a tenth of a microamp. 00:11:11.020 --> 00:11:13.360 align:middle line:84% And we assume we're implanting an area that's 00:11:13.360 --> 00:11:17.080 align:middle line:84% 20 by 20 square centimeters, just for the sake of-- 00:11:17.080 --> 00:11:19.130 align:middle line:90% we just know that's our area. 00:11:19.130 --> 00:11:22.690 align:middle line:84% So basically, I can calculate the dose. 00:11:22.690 --> 00:11:24.550 align:middle line:84% And just like that formula we just said, 00:11:24.550 --> 00:11:26.740 align:middle line:84% it's 1 over the area times the integral of the beam 00:11:26.740 --> 00:11:31.450 align:middle line:84% current, which is 0.1, over the electronic charge, dt. 00:11:31.450 --> 00:11:33.610 align:middle line:84% Now if the beam current doesn't vary with time-- 00:11:33.610 --> 00:11:35.440 align:middle line:90% say, it's a constant 0.1-- 00:11:35.440 --> 00:11:36.850 align:middle line:90% then the integral is easy. 00:11:36.850 --> 00:11:39.520 align:middle line:84% It's just the current times the total time 00:11:39.520 --> 00:11:43.990 align:middle line:84% of the implant divided by the electronic charge times the area 00:11:43.990 --> 00:11:46.710 align:middle line:90% for a constant current. 00:11:46.710 --> 00:11:50.580 align:middle line:84% OK, so the dose rate will then be, just take the dose 00:11:50.580 --> 00:11:52.230 align:middle line:90% and divide it by the total time. 00:11:52.230 --> 00:11:54.360 align:middle line:84% Average dose rate, dose divided by t, 00:11:54.360 --> 00:11:55.980 align:middle line:84% it's just the beam current divided 00:11:55.980 --> 00:11:58.970 align:middle line:84% by q, the electronic charge, times the area. 00:11:58.970 --> 00:12:01.750 align:middle line:90% So you end up with a dose rate. 00:12:01.750 --> 00:12:06.430 align:middle line:84% For that beam current, you're putting in about 1.6 times 10 00:12:06.430 --> 00:12:10.300 align:middle line:84% to the 9th atoms per square centimeter per second. 00:12:10.300 --> 00:12:12.010 align:middle line:90% So that's pretty good control. 00:12:12.010 --> 00:12:16.450 align:middle line:84% Let's say, I want to implant 10 to the 12th atoms 00:12:16.450 --> 00:12:18.430 align:middle line:90% per square centimeter. 00:12:18.430 --> 00:12:21.070 align:middle line:84% Well, you can just divide that into 10 of the 12th, 00:12:21.070 --> 00:12:23.370 align:middle line:84% and you figure out how many seconds it would take. 00:12:23.370 --> 00:12:24.920 align:middle line:84% It's a reasonable amount of time. 00:12:24.920 --> 00:12:28.330 align:middle line:84% And then you can adjust your beam current and the time 00:12:28.330 --> 00:12:31.750 align:middle line:84% to make it something that's physically realizable. 00:12:31.750 --> 00:12:34.720 align:middle line:84% So this has tremendous control, very good accuracy, 00:12:34.720 --> 00:12:36.910 align:middle line:90% and it's very reproducible. 00:12:36.910 --> 00:12:41.800 align:middle line:84% It has good dynamic range because you can adjust your beam 00:12:41.800 --> 00:12:45.290 align:middle line:84% current down from something like 0.01 microamps 00:12:45.290 --> 00:12:47.560 align:middle line:84% if you want to do a very, very low dose. 00:12:47.560 --> 00:12:50.380 align:middle line:84% You're putting at a very slow rate. 00:12:50.380 --> 00:12:53.263 align:middle line:84% You put the ions in, and you integrate them up. 00:12:53.263 --> 00:12:55.180 align:middle line:84% Or you can do it if you have a very high dose. 00:12:55.180 --> 00:12:57.820 align:middle line:84% You might have to have a milliamp of beam current going 00:12:57.820 --> 00:13:00.550 align:middle line:90% into the wafer. 00:13:00.550 --> 00:13:04.010 align:middle line:84% Either way, you get very, very good control. 00:13:04.010 --> 00:13:08.500 align:middle line:84% So let's compare this ion implant case 00:13:08.500 --> 00:13:11.630 align:middle line:84% to the case of where I want to use the old-fashioned method. 00:13:11.630 --> 00:13:13.810 align:middle line:84% So instead of implanting boron, I'm 00:13:13.810 --> 00:13:17.370 align:middle line:84% going to do a boron pre-dip at 1,000. 00:13:17.370 --> 00:13:19.360 align:middle line:84% And again, in order to control this, 00:13:19.360 --> 00:13:21.940 align:middle line:84% we don't want it to depend on the flow rate of the gas, 00:13:21.940 --> 00:13:25.680 align:middle line:84% so we typically do make it so that the surface concentration 00:13:25.680 --> 00:13:28.650 align:middle line:84% is at the solid solubility for boron, which is about 10 00:13:28.650 --> 00:13:31.510 align:middle line:84% to the 20th per cubic centimeter. 00:13:31.510 --> 00:13:33.990 align:middle line:84% So remember, when you're doing a pre-dip, 00:13:33.990 --> 00:13:36.480 align:middle line:84% you get a complementary error function profile 00:13:36.480 --> 00:13:38.670 align:middle line:84% and that the dose of the integral of that 00:13:38.670 --> 00:13:40.840 align:middle line:90% can be given by this equation. 00:13:40.840 --> 00:13:43.890 align:middle line:84% So the dose is 2 times the surface concentration 00:13:43.890 --> 00:13:48.060 align:middle line:84% divided by the square root of pi times the square root of dt, 00:13:48.060 --> 00:13:51.420 align:middle line:84% so where d is the diffusion rate, the diffusivity of boron 00:13:51.420 --> 00:13:52.990 align:middle line:90% in silicon at that temperature. 00:13:52.990 --> 00:13:55.930 align:middle line:84% And so we can look that up in the chart, so it's about 10 00:13:55.930 --> 00:13:58.540 align:middle line:84% to the minus 12 centimeters squared 00:13:58.540 --> 00:14:02.510 align:middle line:84% per second at that concentration and temperature. 00:14:02.510 --> 00:14:06.220 align:middle line:84% So in one second, you've already put into the wafer 10 00:14:06.220 --> 00:14:09.470 align:middle line:84% to the 14th atoms per square centimeter, a very high dose. 00:14:09.470 --> 00:14:12.100 align:middle line:84% So there's no way you could really do-- 00:14:12.100 --> 00:14:14.540 align:middle line:84% if I want an implant of 10 to the 12th, 00:14:14.540 --> 00:14:16.670 align:middle line:84% there's just no way you can get that low of a dose 00:14:16.670 --> 00:14:19.570 align:middle line:84% and with any kind of control by using 00:14:19.570 --> 00:14:21.500 align:middle line:90% a chemical pre-dip technique. 00:14:21.500 --> 00:14:25.420 align:middle line:84% So again, this was the big breakthrough 00:14:25.420 --> 00:14:26.830 align:middle line:90% in ion implantation. 00:14:26.830 --> 00:14:29.950 align:middle line:84% People found they needed to control threshold voltage, 00:14:29.950 --> 00:14:32.530 align:middle line:84% and they needed to implant relatively low doses 00:14:32.530 --> 00:14:35.320 align:middle line:84% very accurately so they get a very good number for VT. 00:14:35.320 --> 00:14:37.910 align:middle line:84% And pre-dip was not going to be a way to do it, 00:14:37.910 --> 00:14:40.825 align:middle line:90% so ion implant filled that need. 00:14:40.825 --> 00:14:43.920 align:middle line:90% 00:14:43.920 --> 00:14:47.280 align:middle line:84% OK, so let's go on to slide number 5. 00:14:47.280 --> 00:14:49.380 align:middle line:84% Before we get into the details of the physics, 00:14:49.380 --> 00:14:52.445 align:middle line:84% we'll just talk about some basic concepts. 00:14:52.445 --> 00:14:54.570 align:middle line:84% As I mentioned, it's the dominant method used today 00:14:54.570 --> 00:14:58.020 align:middle line:84% to introduce dopants, in spite of the fact that it 00:14:58.020 --> 00:15:00.900 align:middle line:84% has a huge amount of damage it does to the lattice. 00:15:00.900 --> 00:15:02.700 align:middle line:84% And these are all the good things about it. 00:15:02.700 --> 00:15:07.350 align:middle line:84% I've already mentioned control, but dynamic range, 00:15:07.350 --> 00:15:09.570 align:middle line:90% a large range of doses. 00:15:09.570 --> 00:15:13.680 align:middle line:84% It's essential to maintain or control the VT. 00:15:13.680 --> 00:15:16.630 align:middle line:84% You can make a buried or retrograde profile. 00:15:16.630 --> 00:15:19.230 align:middle line:84% Remember, with a complementary error function, 00:15:19.230 --> 00:15:24.580 align:middle line:84% if you plot the shape of the profile as a function of depth-- 00:15:24.580 --> 00:15:29.552 align:middle line:84% so this is depth, and this is the concentration-- 00:15:29.552 --> 00:15:31.260 align:middle line:84% in diffusion from the surface, you always 00:15:31.260 --> 00:15:34.345 align:middle line:84% get a higher concentration at the surface than you do here. 00:15:34.345 --> 00:15:35.970 align:middle line:84% But with an implant, you can actually-- 00:15:35.970 --> 00:15:38.040 align:middle line:84% if you want, you can make it look like that. 00:15:38.040 --> 00:15:40.830 align:middle line:84% You can bury the peak and make it look retrograde. 00:15:40.830 --> 00:15:42.540 align:middle line:84% So you have the ability to do that. 00:15:42.540 --> 00:15:45.238 align:middle line:84% You have the ability to control that. 00:15:45.238 --> 00:15:46.530 align:middle line:90% It's a low-temperature process. 00:15:46.530 --> 00:15:49.710 align:middle line:84% It happens at room temperature, which is an advantage. 00:15:49.710 --> 00:15:52.080 align:middle line:84% And there's a wide choice of masking materials. 00:15:52.080 --> 00:15:55.090 align:middle line:84% If you're trying to mask a diffusion, 00:15:55.090 --> 00:15:57.300 align:middle line:84% well, there's only a few materials you can put down, 00:15:57.300 --> 00:16:00.030 align:middle line:84% either oxide or nitride, that might keep the dopants 00:16:00.030 --> 00:16:01.243 align:middle line:90% from diffusing through there. 00:16:01.243 --> 00:16:02.910 align:middle line:84% If you're trying to mask an ion implant, 00:16:02.910 --> 00:16:05.490 align:middle line:84% you can use photoresist, a very simple, 00:16:05.490 --> 00:16:08.238 align:middle line:90% low-temperature material. 00:16:08.238 --> 00:16:09.780 align:middle line:84% There are some disadvantages, though. 00:16:09.780 --> 00:16:12.482 align:middle line:84% Of course, we mentioned that you are bashing up the crystal, 00:16:12.482 --> 00:16:13.440 align:middle line:90% and you're damaging it. 00:16:13.440 --> 00:16:16.200 align:middle line:84% And you have to remove that damage by heating it, 00:16:16.200 --> 00:16:20.310 align:middle line:84% and the heating causes some problems with diffusion. 00:16:20.310 --> 00:16:21.870 align:middle line:84% In fact, there's an anomalous type 00:16:21.870 --> 00:16:24.360 align:middle line:84% of diffusion due to ion implant damage that we're 00:16:24.360 --> 00:16:27.690 align:middle line:84% going to study called Transient Enhanced Diffusion, or TED, 00:16:27.690 --> 00:16:32.940 align:middle line:84% that happens due to the injected defects from the implant. 00:16:32.940 --> 00:16:35.550 align:middle line:84% Nevertheless, people have found out how to model TED, 00:16:35.550 --> 00:16:39.540 align:middle line:84% and they found, in some cases, ways around it. 00:16:39.540 --> 00:16:41.580 align:middle line:84% And the other disadvantage is you can insulate, 00:16:41.580 --> 00:16:43.860 align:middle line:84% and you can have oxide on the wafer. 00:16:43.860 --> 00:16:45.770 align:middle line:84% You can tend to charge it up, so you have 00:16:45.770 --> 00:16:46.990 align:middle line:90% to be a little bit careful. 00:16:46.990 --> 00:16:50.020 align:middle line:84% But there's ways to flood the wafer with an electron gun 00:16:50.020 --> 00:16:53.050 align:middle line:84% and all kinds of things to keep your wafer from charging up. 00:16:53.050 --> 00:16:55.930 align:middle line:90% 00:16:55.930 --> 00:17:00.130 align:middle line:84% If we go to slide 6, this is a schematic diagram 00:17:00.130 --> 00:17:02.320 align:middle line:84% of what an ion implanter looks like, 00:17:02.320 --> 00:17:05.650 align:middle line:84% at least a sort of a traditional diagram of how 00:17:05.650 --> 00:17:07.250 align:middle line:90% an implanter is designed. 00:17:07.250 --> 00:17:13.040 align:middle line:84% What you have here in this big box are two key things. 00:17:13.040 --> 00:17:14.810 align:middle line:84% And all of this is in a vacuum system, 00:17:14.810 --> 00:17:17.800 align:middle line:84% so this entire thing is being pumped down by a pump. 00:17:17.800 --> 00:17:19.930 align:middle line:90% You have an ion source. 00:17:19.930 --> 00:17:23.589 align:middle line:84% So that has a gas in it or something that ionizes 00:17:23.589 --> 00:17:25.839 align:middle line:90% the species of interest. 00:17:25.839 --> 00:17:27.520 align:middle line:90% Maybe you have a gas in there. 00:17:27.520 --> 00:17:29.710 align:middle line:90% You put BF2. 00:17:29.710 --> 00:17:32.590 align:middle line:90% OK, so BF2 gas or whatever. 00:17:32.590 --> 00:17:36.160 align:middle line:84% And then you're going to ionize, so you 00:17:36.160 --> 00:17:38.710 align:middle line:84% have a way with a hot filament of creating ions, 00:17:38.710 --> 00:17:42.700 align:middle line:84% and you create B double plus, B plus, fluorine, BF 2-plus. 00:17:42.700 --> 00:17:44.590 align:middle line:84% You create all these different ions, 00:17:44.590 --> 00:17:46.443 align:middle line:84% of which there are some that contain 00:17:46.443 --> 00:17:48.610 align:middle line:84% boron, which is what you want to implant, let's say, 00:17:48.610 --> 00:17:49.277 align:middle line:90% in this example. 00:17:49.277 --> 00:17:51.740 align:middle line:90% 00:17:51.740 --> 00:17:57.400 align:middle line:84% The ion source extracts the ions at a given energy, 00:17:57.400 --> 00:17:59.560 align:middle line:90% say, from 0 to 30 keV. 00:17:59.560 --> 00:18:03.130 align:middle line:84% So we can set the energy of the ions coming out just 00:18:03.130 --> 00:18:07.060 align:middle line:84% by knowing this extraction voltage, the extraction that we 00:18:07.060 --> 00:18:09.050 align:middle line:90% apply to this grid. 00:18:09.050 --> 00:18:11.380 align:middle line:84% So we know the energy of the ions coming out, 00:18:11.380 --> 00:18:13.030 align:middle line:84% and then we do a standard-- what's 00:18:13.030 --> 00:18:14.470 align:middle line:90% called an E cross B filter. 00:18:14.470 --> 00:18:16.767 align:middle line:84% This happens in any kind of mass analyzer. 00:18:16.767 --> 00:18:18.850 align:middle line:84% This is what's happening when you do secondary ion 00:18:18.850 --> 00:18:20.270 align:middle line:90% mass spectrometry or whatever. 00:18:20.270 --> 00:18:23.920 align:middle line:84% But if you know the energy of the particles coming out, 00:18:23.920 --> 00:18:25.750 align:middle line:84% and you bend them in a magnet, you 00:18:25.750 --> 00:18:28.660 align:middle line:84% can mass analyze them and only pick 00:18:28.660 --> 00:18:30.970 align:middle line:84% those ions that have the right mass. 00:18:30.970 --> 00:18:33.370 align:middle line:84% So I can be sure that I just implant boron. 00:18:33.370 --> 00:18:35.170 align:middle line:84% I don't want to implant fluorine. 00:18:35.170 --> 00:18:37.480 align:middle line:84% I don't want to plant nitrogen or oxygen or carbon 00:18:37.480 --> 00:18:39.563 align:middle line:84% or anything else that happens to be in the source. 00:18:39.563 --> 00:18:41.140 align:middle line:90% I only want to pick one species. 00:18:41.140 --> 00:18:43.380 align:middle line:90% In this case, let's say boron. 00:18:43.380 --> 00:18:45.410 align:middle line:84% So basically, how this works, if you go back 00:18:45.410 --> 00:18:47.690 align:middle line:84% to any of your elementary physics class, 00:18:47.690 --> 00:18:52.640 align:middle line:84% you know that what's happening here in the ions 00:18:52.640 --> 00:18:55.070 align:middle line:84% as they traverse this arc in the magnet, 00:18:55.070 --> 00:18:59.030 align:middle line:84% the centrifugal force is balanced by the magnetic force, 00:18:59.030 --> 00:19:00.590 align:middle line:90% the V cross B force. 00:19:00.590 --> 00:19:04.760 align:middle line:84% So that has to be the case for ions going through this arc. 00:19:04.760 --> 00:19:08.750 align:middle line:84% And you also know the velocity of the ions coming into the arc 00:19:08.750 --> 00:19:10.280 align:middle line:90% because you know their energy. 00:19:10.280 --> 00:19:12.210 align:middle line:84% And that is set by this extraction 00:19:12.210 --> 00:19:14.290 align:middle line:90% of voltage, the extraction. 00:19:14.290 --> 00:19:17.160 align:middle line:84% So I have a velocity that I can plug into this upper equation, 00:19:17.160 --> 00:19:19.140 align:middle line:84% and that is going to relate, then-- end up 00:19:19.140 --> 00:19:21.540 align:middle line:84% relating the mass of the ion that makes it 00:19:21.540 --> 00:19:23.670 align:middle line:90% through this resolving slit. 00:19:23.670 --> 00:19:26.130 align:middle line:84% That mass can then be related to the energy, which 00:19:26.130 --> 00:19:30.070 align:middle line:84% is related to the extraction voltage and the magnet current. 00:19:30.070 --> 00:19:32.640 align:middle line:84% So this is usually an electromagnet, 00:19:32.640 --> 00:19:34.110 align:middle line:90% which I can adjust the current. 00:19:34.110 --> 00:19:37.530 align:middle line:84% So all you need to do to be sure that you're implanting 00:19:37.530 --> 00:19:40.920 align:middle line:84% one particular species is, you adjust the extraction voltage, 00:19:40.920 --> 00:19:43.410 align:middle line:84% and you adjust the current going through the magnet. 00:19:43.410 --> 00:19:46.560 align:middle line:84% And then the only ions that make it are those that you want 00:19:46.560 --> 00:19:48.720 align:middle line:90% to implant with the right mass. 00:19:48.720 --> 00:19:49.980 align:middle line:90% So this is a way. 00:19:49.980 --> 00:19:52.170 align:middle line:84% And then once you have the ions that you need-- 00:19:52.170 --> 00:19:54.060 align:middle line:84% you've extracted out all the others, 00:19:54.060 --> 00:19:56.518 align:middle line:84% and you just have the ones you need-- then you can put them 00:19:56.518 --> 00:19:59.340 align:middle line:84% through a high-voltage accelerator to get them up to, 00:19:59.340 --> 00:20:03.380 align:middle line:84% if you want to implant very high voltages, say, 50 00:20:03.380 --> 00:20:06.120 align:middle line:90% to 100 or 200 kilovolts. 00:20:06.120 --> 00:20:07.710 align:middle line:84% You focus the beam, and then there 00:20:07.710 --> 00:20:14.910 align:middle line:84% are a series of XMY scan plates where you have an E field that's 00:20:14.910 --> 00:20:16.410 align:middle line:84% taking the beam and moving it around 00:20:16.410 --> 00:20:18.990 align:middle line:84% like I'm moving this laser pointer right now, scanning it 00:20:18.990 --> 00:20:20.407 align:middle line:90% randomly across the wafer. 00:20:20.407 --> 00:20:21.990 align:middle line:84% And that's how you do the ion implant. 00:20:21.990 --> 00:20:26.790 align:middle line:84% And then the important thing is that the wafer is attached here 00:20:26.790 --> 00:20:29.580 align:middle line:84% to this device, which has a current integrator, which 00:20:29.580 --> 00:20:31.230 align:middle line:84% integrates the dose going into it. 00:20:31.230 --> 00:20:34.670 align:middle line:84% So it knows when to start and stop the implant. 00:20:34.670 --> 00:20:36.710 align:middle line:84% So a very basic sort of physics-type 00:20:36.710 --> 00:20:38.750 align:middle line:90% of accelerator setup. 00:20:38.750 --> 00:20:41.380 align:middle line:90% 00:20:41.380 --> 00:20:43.960 align:middle line:90% We go on to slide 7. 00:20:43.960 --> 00:20:46.330 align:middle line:84% What I just showed was the practical aspects. 00:20:46.330 --> 00:20:47.870 align:middle line:90% Let's talk a little bit-- 00:20:47.870 --> 00:20:49.870 align:middle line:84% we won't talk about the physics of stopping yet, 00:20:49.870 --> 00:20:52.780 align:middle line:84% but let's just talk about what profiles look like. 00:20:52.780 --> 00:20:56.830 align:middle line:84% I drew a profile up here that I said is somewhat what 00:20:56.830 --> 00:20:58.130 align:middle line:90% an ion implant might look like. 00:20:58.130 --> 00:21:01.330 align:middle line:84% Let's think about what that might be. 00:21:01.330 --> 00:21:03.418 align:middle line:84% Imagine we have a surface of a silicon wafer. 00:21:03.418 --> 00:21:04.960 align:middle line:84% So the silicon is on the right here-- 00:21:04.960 --> 00:21:07.120 align:middle line:84% this is the interface with the vacuum-- 00:21:07.120 --> 00:21:08.500 align:middle line:90% and on the left is a vacuum. 00:21:08.500 --> 00:21:11.470 align:middle line:84% And you have a beam of ions coming, in this case, 00:21:11.470 --> 00:21:14.320 align:middle line:90% right in this red spot. 00:21:14.320 --> 00:21:16.810 align:middle line:84% Any given ion that comes in is going 00:21:16.810 --> 00:21:20.050 align:middle line:84% to come in and experience a series of collisions. 00:21:20.050 --> 00:21:23.082 align:middle line:84% And in fact, many of them are billiard ball-like. 00:21:23.082 --> 00:21:24.790 align:middle line:84% It's going to have a series of collisions 00:21:24.790 --> 00:21:26.735 align:middle line:90% with atoms in the substrate. 00:21:26.735 --> 00:21:29.110 align:middle line:84% You can see it's having little collisions here and there. 00:21:29.110 --> 00:21:32.350 align:middle line:84% And it loses energy as it goes in via these processes 00:21:32.350 --> 00:21:34.840 align:middle line:84% and eventually comes to rest at some point here, 00:21:34.840 --> 00:21:38.550 align:middle line:90% shown by this little blue dot. 00:21:38.550 --> 00:21:40.830 align:middle line:84% So there's a couple of pieces of terminology. 00:21:40.830 --> 00:21:44.430 align:middle line:84% We call the total range of this ion as the total path length. 00:21:44.430 --> 00:21:46.680 align:middle line:84% It's the sum of all these little lengths. 00:21:46.680 --> 00:21:49.080 align:middle line:84% That's the total length it traversed. 00:21:49.080 --> 00:21:51.060 align:middle line:84% The total length is not as interesting. 00:21:51.060 --> 00:21:54.280 align:middle line:84% What we usually care about is the depth. 00:21:54.280 --> 00:21:57.270 align:middle line:84% So the projected range, that's the projection 00:21:57.270 --> 00:22:01.600 align:middle line:84% of its total length along the normal to the surface. 00:22:01.600 --> 00:22:03.975 align:middle line:84% That's what we care about, how deep did it go. 00:22:03.975 --> 00:22:07.530 align:middle line:90% 00:22:07.530 --> 00:22:10.140 align:middle line:84% Usually, projected range is very near the peak 00:22:10.140 --> 00:22:11.980 align:middle line:90% of the distribution. 00:22:11.980 --> 00:22:13.620 align:middle line:84% So the things you need to remember 00:22:13.620 --> 00:22:15.660 align:middle line:84% are, ion implantation is a random process. 00:22:15.660 --> 00:22:16.680 align:middle line:90% Ions come in. 00:22:16.680 --> 00:22:18.840 align:middle line:84% A whole bunch of them come in, and they randomly 00:22:18.840 --> 00:22:21.870 align:middle line:84% hit various things and lose energy and end up 00:22:21.870 --> 00:22:24.190 align:middle line:90% in some distribution. 00:22:24.190 --> 00:22:28.450 align:middle line:84% So it's a statistical type of process. 00:22:28.450 --> 00:22:30.190 align:middle line:84% The ions are pretty high in energy. 00:22:30.190 --> 00:22:32.530 align:middle line:84% We're talking about 1 kilovolt at the lowest 00:22:32.530 --> 00:22:36.430 align:middle line:84% probably up to maybe a megavolt. That's the range of energies, 00:22:36.430 --> 00:22:39.790 align:middle line:84% believe it or not, that people use in making modern devices. 00:22:39.790 --> 00:22:42.460 align:middle line:84% They can even get as high as a megavolt. 00:22:42.460 --> 00:22:46.000 align:middle line:84% These hit the silicon substrate, and they lose energy. 00:22:46.000 --> 00:22:49.240 align:middle line:84% I already mentioned about these nuclear billiard ball-like 00:22:49.240 --> 00:22:51.790 align:middle line:84% collisions, just like on a pool table. 00:22:51.790 --> 00:22:53.510 align:middle line:84% There's also electronic drag forces. 00:22:53.510 --> 00:22:55.730 align:middle line:84% So there's two mechanisms, and in the next lecture, 00:22:55.730 --> 00:22:57.670 align:middle line:84% we'll talk in great detail about the physics 00:22:57.670 --> 00:23:01.300 align:middle line:84% of nuclear collisions and the physics of this electronic drag. 00:23:01.300 --> 00:23:03.610 align:middle line:84% Just for now, take it as a given that there 00:23:03.610 --> 00:23:06.370 align:middle line:84% are these forces, these things that slow the ion down 00:23:06.370 --> 00:23:09.940 align:middle line:84% so they eventually end up coming to rest in the crystal. 00:23:09.940 --> 00:23:13.210 align:middle line:90% 00:23:13.210 --> 00:23:18.300 align:middle line:84% So if we go on to slide 8, let's take a look 00:23:18.300 --> 00:23:21.780 align:middle line:84% at a plot of the distribution of ions implanted into silicon. 00:23:21.780 --> 00:23:25.900 align:middle line:84% Here's an example where the beam energy is 200 kilovolts. 00:23:25.900 --> 00:23:28.440 align:middle line:84% So you adjust the beam energy so that you 00:23:28.440 --> 00:23:30.720 align:middle line:90% have 200 keV ions coming in. 00:23:30.720 --> 00:23:33.360 align:middle line:84% And this is a plot of the concentration 00:23:33.360 --> 00:23:37.050 align:middle line:84% of the dopant in atoms per cubic centimeter 00:23:37.050 --> 00:23:39.870 align:middle line:84% as a function of depth into the crystal, into silicon. 00:23:39.870 --> 00:23:43.570 align:middle line:84% And we're showing several different types of ions. 00:23:43.570 --> 00:23:46.680 align:middle line:84% So if you look at this blue curve here, this is antimony. 00:23:46.680 --> 00:23:48.970 align:middle line:84% Notice the antimony didn't go very far. 00:23:48.970 --> 00:23:50.850 align:middle line:84% It ended up piling up, looks like 00:23:50.850 --> 00:23:53.640 align:middle line:84% a Gaussian-like distribution, pretty close to the surface. 00:23:53.640 --> 00:23:55.020 align:middle line:90% The black is phosphorus. 00:23:55.020 --> 00:23:57.990 align:middle line:90% It went a little further. 00:23:57.990 --> 00:23:58.890 align:middle line:90% Arsenic, I'm sorry. 00:23:58.890 --> 00:23:59.940 align:middle line:90% The black is arsenic. 00:23:59.940 --> 00:24:03.240 align:middle line:90% Phosphorus here is the red. 00:24:03.240 --> 00:24:03.990 align:middle line:90% It goes further. 00:24:03.990 --> 00:24:06.210 align:middle line:84% And the one that goes the furthest here is boron. 00:24:06.210 --> 00:24:08.580 align:middle line:90% That's shown in green. 00:24:08.580 --> 00:24:11.170 align:middle line:84% Boron is the lightest of all those elements, 00:24:11.170 --> 00:24:12.810 align:middle line:90% so it kind of makes sense. 00:24:12.810 --> 00:24:14.220 align:middle line:90% Boron is lighter. 00:24:14.220 --> 00:24:18.040 align:middle line:84% It's going to lose less energy in its collisions, 00:24:18.040 --> 00:24:19.860 align:middle line:84% so it's going to travel further overall. 00:24:19.860 --> 00:24:22.740 align:middle line:84% And not only does it travel further into the crystal, 00:24:22.740 --> 00:24:25.950 align:middle line:84% its projected range here is about 0.5 or 0.55. 00:24:25.950 --> 00:24:27.150 align:middle line:90% It's also broader. 00:24:27.150 --> 00:24:28.620 align:middle line:90% Its distribution is very broad. 00:24:28.620 --> 00:24:30.870 align:middle line:84% Look how broad this is compared to the antimony, which 00:24:30.870 --> 00:24:34.060 align:middle line:84% has a very, very tight distribution. 00:24:34.060 --> 00:24:39.520 align:middle line:84% So as a physical process, it depends very much on the mass. 00:24:39.520 --> 00:24:42.610 align:middle line:84% We often describe profiles very roughly 00:24:42.610 --> 00:24:44.860 align:middle line:90% by a Gaussian distribution. 00:24:44.860 --> 00:24:47.950 align:middle line:84% It's not really Gaussian, but for a heavy ion like antimony, 00:24:47.950 --> 00:24:50.240 align:middle line:84% it turns out to be reasonably accurate. 00:24:50.240 --> 00:24:53.230 align:middle line:84% So the first-order description is a Gaussian, 00:24:53.230 --> 00:24:56.840 align:middle line:84% and a Gaussian has two variables. 00:24:56.840 --> 00:25:00.760 align:middle line:84% One is the projected range, Rp, which gives the peak point 00:25:00.760 --> 00:25:04.480 align:middle line:84% in depth of the Gaussian, and the standard deviation, 00:25:04.480 --> 00:25:11.590 align:middle line:84% delta Rp, which for a Gaussian, is a measure of the half-width 00:25:11.590 --> 00:25:13.840 align:middle line:90% basically. 00:25:13.840 --> 00:25:17.940 align:middle line:84% So for a simple Gaussian, we only need two parameters. 00:25:17.940 --> 00:25:20.380 align:middle line:84% And in fact, you can write-- on slide 9, 00:25:20.380 --> 00:25:26.430 align:middle line:84% I've written down the equation for a simple Gaussian profile 00:25:26.430 --> 00:25:28.330 align:middle line:84% with a certain peak concentration. 00:25:28.330 --> 00:25:30.960 align:middle line:84% And this Gaussian is centered at Rp. 00:25:30.960 --> 00:25:34.140 align:middle line:84% You can see that just by plugging in x equals Rp, 00:25:34.140 --> 00:25:36.060 align:middle line:84% this whole thing goes e to the 0. 00:25:36.060 --> 00:25:38.970 align:middle line:84% So you get the peak concentration at x equals Rp, 00:25:38.970 --> 00:25:42.840 align:middle line:84% and it has a standard deviation, delta Rp. 00:25:42.840 --> 00:25:44.790 align:middle line:84% The integral of this, if you integrate 00:25:44.790 --> 00:25:48.600 align:middle line:84% the Gaussian, that Gaussian's is integral is known analytically. 00:25:48.600 --> 00:25:50.850 align:middle line:84% So the integrated dose is just square root 00:25:50.850 --> 00:25:55.090 align:middle line:84% of 2 pi times delta Rp times the p concentration. 00:25:55.090 --> 00:25:58.980 align:middle line:84% So this tells you, if I told you I implant antimony 00:25:58.980 --> 00:26:03.870 align:middle line:84% at a particular dose and energy, you can look up-- 00:26:03.870 --> 00:26:07.200 align:middle line:84% there are tables which you can look up the delta Rp, 00:26:07.200 --> 00:26:09.060 align:middle line:84% and then you can calculate, knowing 00:26:09.060 --> 00:26:11.730 align:middle line:84% that if I give you the dose, and you know delta Rp, 00:26:11.730 --> 00:26:14.220 align:middle line:84% you can calculate the peak concentration right away if you 00:26:14.220 --> 00:26:15.348 align:middle line:90% assumed it was a Gaussian. 00:26:15.348 --> 00:26:16.890 align:middle line:84% So you can do some very simple things 00:26:16.890 --> 00:26:19.360 align:middle line:90% with simple hand calculation. 00:26:19.360 --> 00:26:20.440 align:middle line:90% Again, what is q? 00:26:20.440 --> 00:26:21.220 align:middle line:90% It's the dose. 00:26:21.220 --> 00:26:23.840 align:middle line:84% It's the integrated number of ions per square centimeter. 00:26:23.840 --> 00:26:27.910 align:middle line:84% So literally, in this profile, if I took the area 00:26:27.910 --> 00:26:34.120 align:middle line:84% under this curve, under the concentration versus depth, 00:26:34.120 --> 00:26:37.320 align:middle line:84% that's the dose the number of ions per square centimeter. 00:26:37.320 --> 00:26:40.870 align:middle line:84% And again, we control that by measuring the integrated beam 00:26:40.870 --> 00:26:41.370 align:middle line:90% current. 00:26:41.370 --> 00:26:43.995 align:middle line:90% 00:26:43.995 --> 00:26:45.620 align:middle line:84% We'll say a little bit more about this. 00:26:45.620 --> 00:26:48.280 align:middle line:84% But if I go back briefly to slide 8, 00:26:48.280 --> 00:26:50.270 align:middle line:84% you notice some of these-- the antimony 00:26:50.270 --> 00:26:52.270 align:middle line:84% is quite symmetrical and quite Gaussian-looking. 00:26:52.270 --> 00:26:54.880 align:middle line:84% The boron profile is not so symmetrical. 00:26:54.880 --> 00:26:55.630 align:middle line:90% It's skewed. 00:26:55.630 --> 00:26:59.680 align:middle line:84% It has a larger sort of tail region or region 00:26:59.680 --> 00:27:00.950 align:middle line:90% towards the surface. 00:27:00.950 --> 00:27:03.520 align:middle line:84% It's got the skewness to it, and we'll talk a little bit more 00:27:03.520 --> 00:27:06.860 align:middle line:84% about why that is and how to model that. 00:27:06.860 --> 00:27:09.940 align:middle line:84% So it turns out the projected range, Rp, 00:27:09.940 --> 00:27:11.980 align:middle line:84% and delta Rp, the standard deviation, 00:27:11.980 --> 00:27:15.760 align:middle line:84% of all the common dopants in randomly oriented silicon, 00:27:15.760 --> 00:27:17.890 align:middle line:84% so assuming the silicon is amorphous, 00:27:17.890 --> 00:27:19.587 align:middle line:84% and there's no channeling going on-- 00:27:19.587 --> 00:27:21.670 align:middle line:84% we'll talk about channeling later-- these have all 00:27:21.670 --> 00:27:23.050 align:middle line:90% been measured experimentally. 00:27:23.050 --> 00:27:25.120 align:middle line:84% They've also been calculated very accurately 00:27:25.120 --> 00:27:27.890 align:middle line:90% from first principles. 00:27:27.890 --> 00:27:29.540 align:middle line:84% And these theoretical calculations 00:27:29.540 --> 00:27:31.700 align:middle line:84% can be done for almost any combination 00:27:31.700 --> 00:27:32.750 align:middle line:90% of ion and substrate. 00:27:32.750 --> 00:27:38.040 align:middle line:84% So you could be ion implanting cesium into carbon. 00:27:38.040 --> 00:27:42.410 align:middle line:84% And if you know the basic mass and the number of atoms 00:27:42.410 --> 00:27:47.510 align:middle line:84% per square or cubic centimeter in the substrate and the energy, 00:27:47.510 --> 00:27:49.220 align:middle line:84% you can calculate what the distribution 00:27:49.220 --> 00:27:52.095 align:middle line:84% looks like in an approximate sort of-- 00:27:52.095 --> 00:27:53.720 align:middle line:84% if you're assuming you have a Gaussian. 00:27:53.720 --> 00:27:56.000 align:middle line:84% So all of this has been calculated and measured. 00:27:56.000 --> 00:28:00.020 align:middle line:84% In fact, it's tabulated in a number of books. 00:28:00.020 --> 00:28:02.440 align:middle line:90% And it's in your textbook. 00:28:02.440 --> 00:28:05.410 align:middle line:84% Rather than tables, what your textbook does-- 00:28:05.410 --> 00:28:08.500 align:middle line:84% I took this directly from the text-- it gives you plots. 00:28:08.500 --> 00:28:12.760 align:middle line:84% So on the upper left here, this is a plot of Rp. 00:28:12.760 --> 00:28:16.660 align:middle line:84% So this is the depth in microns that the ion travels. 00:28:16.660 --> 00:28:21.550 align:middle line:84% It's the peak, Rp, as a function of the energy of the implant 00:28:21.550 --> 00:28:22.940 align:middle line:90% for the common dopants. 00:28:22.940 --> 00:28:23.860 align:middle line:90% So here's boron. 00:28:23.860 --> 00:28:25.790 align:middle line:84% Again, you can see boron goes very far. 00:28:25.790 --> 00:28:30.340 align:middle line:84% So if I'm at an energy, say, of 80 kilovolts, and I have boron, 00:28:30.340 --> 00:28:32.320 align:middle line:84% the projected range is a quarter micron. 00:28:32.320 --> 00:28:33.970 align:middle line:90% That's 0.25. 00:28:33.970 --> 00:28:36.850 align:middle line:84% For arsenic, at that same voltage or that same energy, 00:28:36.850 --> 00:28:42.700 align:middle line:84% rather, it's about 0.05 microns or about 500 angstroms. 00:28:42.700 --> 00:28:45.670 align:middle line:90% So it's much, much shallower. 00:28:45.670 --> 00:28:47.320 align:middle line:84% And so you can see Rp has been tabbed, 00:28:47.320 --> 00:28:50.710 align:middle line:84% has been is given by these straight lines here. 00:28:50.710 --> 00:28:53.140 align:middle line:84% And the standard deviation, delta Rp, 00:28:53.140 --> 00:28:54.920 align:middle line:84% as a function of energy is also given. 00:28:54.920 --> 00:28:58.750 align:middle line:84% So again, boron at 80 kilovolts in the lower right, 00:28:58.750 --> 00:29:01.700 align:middle line:84% it has a standard deviation of 0.08 microns. 00:29:01.700 --> 00:29:03.680 align:middle line:84% So it's going to be much broader than arsenic, 00:29:03.680 --> 00:29:06.850 align:middle line:84% which has a standard deviation of only 0.02 roughly. 00:29:06.850 --> 00:29:10.210 align:middle line:84% So you can read these right off the plot. 00:29:10.210 --> 00:29:12.010 align:middle line:84% And if you make the Gaussian assumption, 00:29:12.010 --> 00:29:14.980 align:middle line:84% all you need are these plots and a simple hand calculator, 00:29:14.980 --> 00:29:19.480 align:middle line:84% and you could draw the implant profile roughly 00:29:19.480 --> 00:29:25.650 align:middle line:84% for any of these species at a given energy. 00:29:25.650 --> 00:29:30.390 align:middle line:84% Now, these also assume that the substrate has been tilted 00:29:30.390 --> 00:29:31.050 align:middle line:90% and rotated-- 00:29:31.050 --> 00:29:32.250 align:middle line:84% and we'll talk a little bit about this-- 00:29:32.250 --> 00:29:33.360 align:middle line:90% to avoid channeling. 00:29:33.360 --> 00:29:36.390 align:middle line:84% So this is assuming the substrate is amorphous. 00:29:36.390 --> 00:29:39.770 align:middle line:90% 00:29:39.770 --> 00:29:42.300 align:middle line:84% So let's go on to slide 11 for a minute, 00:29:42.300 --> 00:29:44.465 align:middle line:84% and let's just think about what happens. 00:29:44.465 --> 00:29:45.590 align:middle line:90% So that's the distribution. 00:29:45.590 --> 00:29:47.007 align:middle line:84% Now, we want to think a little bit 00:29:47.007 --> 00:29:50.000 align:middle line:84% about what happens if I don't scan the beam across the wafer. 00:29:50.000 --> 00:29:53.090 align:middle line:84% I was saying, we take this laser beam in a real implanter, 00:29:53.090 --> 00:29:55.700 align:middle line:84% we're continuously scanning it to randomize 00:29:55.700 --> 00:29:59.880 align:middle line:84% and to implant the same dose everywhere on the surface. 00:29:59.880 --> 00:30:05.220 align:middle line:84% But if we just hold the ion beam at one point, and just look-- 00:30:05.220 --> 00:30:07.320 align:middle line:84% let's look at the case where the implant beam 00:30:07.320 --> 00:30:13.200 align:middle line:84% is centered on a point in space, x, y, and z, at the 0, 0, 0 00:30:13.200 --> 00:30:13.720 align:middle line:90% position. 00:30:13.720 --> 00:30:16.140 align:middle line:84% So if I draw axis x going this way, 00:30:16.140 --> 00:30:19.200 align:middle line:84% y going vertically, and z going out of the board 00:30:19.200 --> 00:30:22.050 align:middle line:84% or out of the page, at the 0, 0, 0 position, 00:30:22.050 --> 00:30:25.020 align:middle line:84% I imagine bringing in ion beam and just holding it 00:30:25.020 --> 00:30:29.360 align:middle line:84% there and then looking at this cloud of ions 00:30:29.360 --> 00:30:34.075 align:middle line:84% and where they end up, where they stop. 00:30:34.075 --> 00:30:36.200 align:middle line:84% And in fact, people have done this on the computer. 00:30:36.200 --> 00:30:39.110 align:middle line:84% It's not that hard to do a simulation called a Monte Carlo. 00:30:39.110 --> 00:30:44.300 align:middle line:84% Monte Carlo is just like gambling, just like in-- 00:30:44.300 --> 00:30:49.490 align:middle line:84% you send in a certain random distribution of ions. 00:30:49.490 --> 00:30:52.280 align:middle line:84% They have known energy but different impact angles, 00:30:52.280 --> 00:30:54.530 align:middle line:84% and you simulate these random trajectories 00:30:54.530 --> 00:30:55.550 align:middle line:90% for a group of ions. 00:30:55.550 --> 00:30:58.550 align:middle line:84% Maybe you could ion implant 10,000 ions 00:30:58.550 --> 00:30:59.702 align:middle line:90% at some spot in the wafer. 00:30:59.702 --> 00:31:01.160 align:middle line:84% And you see where they end up, what 00:31:01.160 --> 00:31:03.510 align:middle line:84% their three-dimensional distribution looks like. 00:31:03.510 --> 00:31:06.020 align:middle line:84% So this particular simulation is what 00:31:06.020 --> 00:31:09.800 align:middle line:84% 1,000 atoms of phosphorus that were shot into a silicon wafer 00:31:09.800 --> 00:31:11.670 align:middle line:90% at 35 kiloelectron volts. 00:31:11.670 --> 00:31:14.480 align:middle line:84% And that's what the cloud looks like. 00:31:14.480 --> 00:31:15.540 align:middle line:90% That's where they end up. 00:31:15.540 --> 00:31:17.600 align:middle line:84% And in fact, it's kind of an elongated 00:31:17.600 --> 00:31:23.070 align:middle line:84% ellipse in the x direction. x is the implant direction, 00:31:23.070 --> 00:31:26.120 align:middle line:84% and because a lot of the high energy ions 00:31:26.120 --> 00:31:28.200 align:middle line:84% undergo very small angle collisions. 00:31:28.200 --> 00:31:30.470 align:middle line:84% So they don't end up going sideways very much. 00:31:30.470 --> 00:31:32.420 align:middle line:84% They end up scattering forward and then 00:31:32.420 --> 00:31:38.290 align:middle line:84% eventually stopping when they lose all their energy. 00:31:38.290 --> 00:31:41.427 align:middle line:90% Let's go on to page 12. 00:31:41.427 --> 00:31:43.510 align:middle line:84% Now, I'm showing some two-dimensional projections. 00:31:43.510 --> 00:31:46.150 align:middle line:84% What I showed before was a three-dimensional picture 00:31:46.150 --> 00:31:48.850 align:middle line:84% of this elongated ellipse, this cloud 00:31:48.850 --> 00:31:50.590 align:middle line:90% of where all the ions ended up. 00:31:50.590 --> 00:31:56.540 align:middle line:84% Now, I'm projecting that cloud onto the yz plane here. 00:31:56.540 --> 00:31:59.305 align:middle line:84% So this is along the beam direction 00:31:59.305 --> 00:32:00.430 align:middle line:90% if you're looking straight. 00:32:00.430 --> 00:32:02.680 align:middle line:84% The beam is coming straight in here like this, 00:32:02.680 --> 00:32:04.150 align:middle line:90% right in the center. 00:32:04.150 --> 00:32:06.370 align:middle line:84% Along the beam direction, it has sort 00:32:06.370 --> 00:32:08.950 align:middle line:84% of a lateral distribution that's kind of symmetric, 00:32:08.950 --> 00:32:09.805 align:middle line:90% which makes sense. 00:32:09.805 --> 00:32:12.670 align:middle line:90% 00:32:12.670 --> 00:32:14.980 align:middle line:84% If we look at the top view, so looking top-down, 00:32:14.980 --> 00:32:18.470 align:middle line:84% and the beam is coming in here right at this point, y, in fact, 00:32:18.470 --> 00:32:19.270 align:middle line:90% it looks-- 00:32:19.270 --> 00:32:20.800 align:middle line:84% you can see the depth distribution. 00:32:20.800 --> 00:32:23.320 align:middle line:84% It's kind of peaking right around here at this point, 00:32:23.320 --> 00:32:27.140 align:middle line:84% and then it's kind of tailing off as you go in deeper. 00:32:27.140 --> 00:32:30.130 align:middle line:84% So you can approximate it by a Gaussian. 00:32:30.130 --> 00:32:33.430 align:middle line:84% If we guessed, the center is somewhere around here, 00:32:33.430 --> 00:32:34.570 align:middle line:90% around 50 nanometers. 00:32:34.570 --> 00:32:35.560 align:middle line:90% That's Rp. 00:32:35.560 --> 00:32:38.900 align:middle line:84% And delta Rp is about 20 nanometers. 00:32:38.900 --> 00:32:41.560 align:middle line:84% So that's the depth distribution. 00:32:41.560 --> 00:32:44.260 align:middle line:84% The lateral distribution is pretty Gaussian, 00:32:44.260 --> 00:32:46.330 align:middle line:84% and it has a certain straggle, what 00:32:46.330 --> 00:32:48.460 align:middle line:90% we call delta Rp perpendicular. 00:32:48.460 --> 00:32:51.020 align:middle line:84% That is in perpendicular to the beam direction. 00:32:51.020 --> 00:32:52.870 align:middle line:84% So we have two straddles to really think 00:32:52.870 --> 00:32:56.500 align:middle line:84% about or two standard deviations. 00:32:56.500 --> 00:32:59.147 align:middle line:84% There's the one in the beam direction, so in depth, 00:32:59.147 --> 00:33:00.730 align:middle line:84% and then there's the one perpendicular 00:33:00.730 --> 00:33:03.928 align:middle line:90% to that sort of in width. 00:33:03.928 --> 00:33:05.095 align:middle line:90% That's the lateral straggle. 00:33:05.095 --> 00:33:09.110 align:middle line:90% 00:33:09.110 --> 00:33:11.450 align:middle line:84% Now, I just showed that to give you an example, 00:33:11.450 --> 00:33:14.720 align:middle line:84% physically get a handle on what's going on at a given spot. 00:33:14.720 --> 00:33:16.850 align:middle line:84% But we don't usually just hold the beam 00:33:16.850 --> 00:33:18.050 align:middle line:90% on one spot of the wafer. 00:33:18.050 --> 00:33:19.760 align:middle line:90% As I said, we usually-- 00:33:19.760 --> 00:33:23.420 align:middle line:84% what you do is you randomly scan the beam 00:33:23.420 --> 00:33:26.090 align:middle line:90% across the entire wafer. 00:33:26.090 --> 00:33:29.060 align:middle line:84% If you want to mask at given region, 00:33:29.060 --> 00:33:32.790 align:middle line:84% you implant through a mask into a window. 00:33:32.790 --> 00:33:35.310 align:middle line:84% And the surrounding areas on either side of the window 00:33:35.310 --> 00:33:37.590 align:middle line:90% will be masked from the implant. 00:33:37.590 --> 00:33:39.870 align:middle line:84% For example, just showing here on the lower right, 00:33:39.870 --> 00:33:41.640 align:middle line:90% I've imagined I put down a mask. 00:33:41.640 --> 00:33:43.800 align:middle line:90% It could be photoresist. 00:33:43.800 --> 00:33:44.640 align:middle line:90% It could be oxide. 00:33:44.640 --> 00:33:46.260 align:middle line:84% Somehow, I've patterned the mask, 00:33:46.260 --> 00:33:48.000 align:middle line:90% and I've opened up a window. 00:33:48.000 --> 00:33:50.375 align:middle line:84% Now, when I do the ion implant, of course 00:33:50.375 --> 00:33:51.750 align:middle line:84% I implant across the whole wafer, 00:33:51.750 --> 00:33:55.200 align:middle line:84% so I'm implanting across everything here coming in. 00:33:55.200 --> 00:33:57.930 align:middle line:90% But the ions stop in the mask. 00:33:57.930 --> 00:34:00.270 align:middle line:84% The only ones that make it into the substrate 00:34:00.270 --> 00:34:04.050 align:middle line:84% in this particular example are the ones that come through. 00:34:04.050 --> 00:34:10.290 align:middle line:84% Only in this window area does the substrate get implanted. 00:34:10.290 --> 00:34:11.772 align:middle line:84% So in this course, we're interested 00:34:11.772 --> 00:34:13.230 align:middle line:84% not just in the depth distribution, 00:34:13.230 --> 00:34:15.639 align:middle line:84% but in the lateral distribution of the profile. 00:34:15.639 --> 00:34:17.790 align:middle line:90% So I care about this window. 00:34:17.790 --> 00:34:20.969 align:middle line:84% I'm interested to know not only how deep do the ions go, 00:34:20.969 --> 00:34:23.352 align:middle line:84% but how do they spread laterally. 00:34:23.352 --> 00:34:24.810 align:middle line:84% If I'm making the source and drain, 00:34:24.810 --> 00:34:27.630 align:middle line:84% I care about how they spread laterally into the channel. 00:34:27.630 --> 00:34:29.409 align:middle line:84% That's an important thing to note. 00:34:29.409 --> 00:34:33.850 align:middle line:84% So in the lateral direction, of course, measuring the profile 00:34:33.850 --> 00:34:34.400 align:middle line:90% is hard. 00:34:34.400 --> 00:34:38.000 align:middle line:84% We saw last time two-dimensional profiles 00:34:38.000 --> 00:34:39.250 align:middle line:90% are very difficult to measure. 00:34:39.250 --> 00:34:43.239 align:middle line:84% But we actually mathematically model them 00:34:43.239 --> 00:34:46.600 align:middle line:84% by assuming that the profile is composed 00:34:46.600 --> 00:34:50.730 align:middle line:84% of a product of a vertical and a lateral distribution. 00:34:50.730 --> 00:34:54.139 align:middle line:84% So in terms of the x and y, let's say 00:34:54.139 --> 00:34:57.890 align:middle line:84% in this particular example that the x is depth. 00:34:57.890 --> 00:35:00.110 align:middle line:84% OK, going deep into the wafer, into the crystal. 00:35:00.110 --> 00:35:02.690 align:middle line:84% And the y is the lateral dimension. 00:35:02.690 --> 00:35:08.120 align:middle line:84% Then we can approximate the concentration of xy distribution 00:35:08.120 --> 00:35:10.290 align:middle line:84% as being some vertical distribution, 00:35:10.290 --> 00:35:12.590 align:middle line:84% be it Gaussian or whatever we'll talk about, 00:35:12.590 --> 00:35:16.190 align:middle line:90% times a lateral Gaussian. 00:35:16.190 --> 00:35:18.740 align:middle line:84% You recognize this as a Gaussian function, 00:35:18.740 --> 00:35:25.080 align:middle line:84% e to the minus y squared over 2 delta r perpendicular squared. 00:35:25.080 --> 00:35:28.890 align:middle line:84% OK, so it's a Gaussian with a standard deviation, delta r 00:35:28.890 --> 00:35:33.520 align:middle line:84% perpendicular, in the y or the lateral direction. 00:35:33.520 --> 00:35:35.730 align:middle line:84% So I've written over here on the left what we 00:35:35.730 --> 00:35:37.080 align:middle line:90% call a point response function. 00:35:37.080 --> 00:35:39.870 align:middle line:84% If I just shoot the beam in at one point, 00:35:39.870 --> 00:35:43.500 align:middle line:84% you can see what that looks like. 00:35:43.500 --> 00:35:47.450 align:middle line:84% And when you go to do this simulation that's 00:35:47.450 --> 00:35:49.970 align:middle line:84% being done at SUPREM-IV, what it's doing 00:35:49.970 --> 00:35:52.040 align:middle line:84% is it's taking this point response function 00:35:52.040 --> 00:35:55.160 align:middle line:84% and then superimposing that response function 00:35:55.160 --> 00:35:57.650 align:middle line:90% across the whole window. 00:35:57.650 --> 00:36:00.365 align:middle line:84% And then it can give you, then, laterally what 00:36:00.365 --> 00:36:02.990 align:middle line:84% the distribution looks like, not only in the lateral direction, 00:36:02.990 --> 00:36:07.220 align:middle line:90% but in the depth direction. 00:36:07.220 --> 00:36:08.940 align:middle line:84% In fact, if you do this properly, 00:36:08.940 --> 00:36:10.850 align:middle line:84% and SUPREM-IV does it for you, it 00:36:10.850 --> 00:36:13.490 align:middle line:84% leads to some kind of lateral distribution 00:36:13.490 --> 00:36:16.130 align:middle line:90% under the mask edge. 00:36:16.130 --> 00:36:17.540 align:middle line:90% So that's just to remind you-- 00:36:17.540 --> 00:36:18.830 align:middle line:84% I haven't told you anything about the physics 00:36:18.830 --> 00:36:20.480 align:middle line:84% of stopping-- just to remind you how 00:36:20.480 --> 00:36:22.670 align:middle line:90% these profiles vary in x and y. 00:36:22.670 --> 00:36:25.630 align:middle line:90% 00:36:25.630 --> 00:36:31.220 align:middle line:84% So let's go on to slide 14 and think about what 00:36:31.220 --> 00:36:32.343 align:middle line:90% happens at a mask edge. 00:36:32.343 --> 00:36:34.760 align:middle line:84% And this is very important because you're making a MOSFET, 00:36:34.760 --> 00:36:37.850 align:middle line:84% because you're defining the source and drain extensions 00:36:37.850 --> 00:36:40.040 align:middle line:90% with some kind of mask. 00:36:40.040 --> 00:36:43.140 align:middle line:84% Let's assume the mask is thick enough to block the implant, 00:36:43.140 --> 00:36:45.080 align:middle line:90% so the mask might be the gate. 00:36:45.080 --> 00:36:47.113 align:middle line:84% You have the polysilicon gate of the MOSFET, 00:36:47.113 --> 00:36:48.530 align:middle line:84% and you want to implant everywhere 00:36:48.530 --> 00:36:52.980 align:middle line:84% around it so it blocks the implant from hitting 00:36:52.980 --> 00:36:53.910 align:middle line:90% the substrate. 00:36:53.910 --> 00:36:56.250 align:middle line:84% So the lateral profile under the mask 00:36:56.250 --> 00:36:57.840 align:middle line:84% is going to be determined by what 00:36:57.840 --> 00:37:00.060 align:middle line:84% we call this delta Rp perpendicular, 00:37:00.060 --> 00:37:02.610 align:middle line:90% this lateral straggle. 00:37:02.610 --> 00:37:04.410 align:middle line:84% And this is an example of looking 00:37:04.410 --> 00:37:05.820 align:middle line:90% at two different implants. 00:37:05.820 --> 00:37:11.490 align:middle line:84% Here on the left, this is a 35 keV implant of arsenic 00:37:11.490 --> 00:37:16.830 align:middle line:84% and a 120 keV implant at the edge of a poly gate. 00:37:16.830 --> 00:37:19.020 align:middle line:84% So basically, over here on the right, 00:37:19.020 --> 00:37:21.270 align:middle line:84% see this, all these different grains? 00:37:21.270 --> 00:37:22.740 align:middle line:84% That's the polycrystalline silicon. 00:37:22.740 --> 00:37:23.550 align:middle line:90% That's the gate. 00:37:23.550 --> 00:37:26.397 align:middle line:84% This is the gate oxide underneath the gate. 00:37:26.397 --> 00:37:28.980 align:middle line:84% And this is the region to the left of the gate, which we often 00:37:28.980 --> 00:37:29.938 align:middle line:90% think of as the source. 00:37:29.938 --> 00:37:33.300 align:middle line:84% And you can see this contour defines 00:37:33.300 --> 00:37:36.340 align:middle line:84% sort of where the-- the edge of where the arsenic ended up. 00:37:36.340 --> 00:37:38.220 align:middle line:84% In fact, this is a cross-section TEM, 00:37:38.220 --> 00:37:40.380 align:middle line:84% and we showed something like this last time. 00:37:40.380 --> 00:37:43.260 align:middle line:84% This was done by Transmission Electron Microscopy 00:37:43.260 --> 00:37:45.450 align:middle line:84% with staining of the junction area. 00:37:45.450 --> 00:37:49.230 align:middle line:84% So they actually take the thin TEM sample, they dip it in acid, 00:37:49.230 --> 00:37:51.880 align:middle line:84% and the acid preferentially etches 00:37:51.880 --> 00:37:54.910 align:middle line:84% and makes very thin the regions that are very heavily doped 00:37:54.910 --> 00:37:55.570 align:middle line:90% with arsenic. 00:37:55.570 --> 00:37:59.410 align:middle line:84% So this is how you can see, with your eyes or with a microscope, 00:37:59.410 --> 00:38:02.540 align:middle line:84% how you can see where the junction ends up. 00:38:02.540 --> 00:38:04.850 align:middle line:84% And you can see this profile right here 00:38:04.850 --> 00:38:08.480 align:middle line:84% underneath the mask edge or under the gate, 00:38:08.480 --> 00:38:10.340 align:middle line:84% this distance from here to here is 00:38:10.340 --> 00:38:13.310 align:middle line:84% dominated by this lateral straggle of the implant, 00:38:13.310 --> 00:38:16.890 align:middle line:84% depending on how much annealing you do afterwards. 00:38:16.890 --> 00:38:19.220 align:middle line:84% So as we decrease the device geometry, 00:38:19.220 --> 00:38:22.370 align:middle line:84% as we make this gate length shorter and shorter, 00:38:22.370 --> 00:38:24.230 align:middle line:84% the implant straggle under the mask 00:38:24.230 --> 00:38:28.730 align:middle line:84% becomes a more dominant effect on determining 00:38:28.730 --> 00:38:30.620 align:middle line:90% the actual channel length. 00:38:30.620 --> 00:38:33.345 align:middle line:84% Knowing the lateral straggle is an important feature of MOSFETs. 00:38:33.345 --> 00:38:35.720 align:middle line:84% They not only determine the channel length, but remember, 00:38:35.720 --> 00:38:39.367 align:middle line:84% we gave examples that the shape of that lateral profile 00:38:39.367 --> 00:38:41.450 align:middle line:84% also determines some of the short channel effects, 00:38:41.450 --> 00:38:43.280 align:middle line:84% like VT roll-off and things like that. 00:38:43.280 --> 00:38:46.650 align:middle line:90% 00:38:46.650 --> 00:38:47.820 align:middle line:90% OK. 00:38:47.820 --> 00:38:52.200 align:middle line:84% Again, covering some of the more practical issues 00:38:52.200 --> 00:38:54.870 align:middle line:84% before we talk about the fundamental physics, 00:38:54.870 --> 00:38:58.080 align:middle line:84% on slide 15, I've mentioned a couple times this idea 00:38:58.080 --> 00:39:00.820 align:middle line:90% of masking and implant. 00:39:00.820 --> 00:39:01.420 align:middle line:90% OK? 00:39:01.420 --> 00:39:03.250 align:middle line:90% So what do I mean about that? 00:39:03.250 --> 00:39:07.970 align:middle line:84% And how would you calculate how thick a mask you might need? 00:39:07.970 --> 00:39:10.780 align:middle line:84% So this is an example of masking an implant. 00:39:10.780 --> 00:39:13.270 align:middle line:84% I'm doing an implant, and again, the beam 00:39:13.270 --> 00:39:15.610 align:middle line:84% is rastered over the entire wafer, 00:39:15.610 --> 00:39:18.400 align:middle line:84% but I only want to implant certain regions, maybe only 00:39:18.400 --> 00:39:21.560 align:middle line:84% the P-MOS regions or N-MOS regions. 00:39:21.560 --> 00:39:24.760 align:middle line:84% So I have to put some photoresist 00:39:24.760 --> 00:39:25.780 align:middle line:90% over a certain region. 00:39:25.780 --> 00:39:29.170 align:middle line:84% And the question is, how thick does that material have to be? 00:39:29.170 --> 00:39:32.980 align:middle line:84% If it's for resist or if it's nitride or silicon dioxide, 00:39:32.980 --> 00:39:35.330 align:middle line:90% how thick does it have to be? 00:39:35.330 --> 00:39:39.010 align:middle line:84% Well, it turns out that a dense material, has a high density, 00:39:39.010 --> 00:39:41.080 align:middle line:84% can be a lot thinner than a light material, 00:39:41.080 --> 00:39:44.940 align:middle line:84% because a light material allows the beam to go in deeper. 00:39:44.940 --> 00:39:46.040 align:middle line:90% So here's an example. 00:39:46.040 --> 00:39:48.260 align:middle line:84% I'm showing you a plot here, concentration 00:39:48.260 --> 00:39:51.110 align:middle line:84% on the vertical axis as a function of depth. 00:39:51.110 --> 00:39:53.910 align:middle line:84% And let's say, this is what it looks like. 00:39:53.910 --> 00:39:58.020 align:middle line:84% This profile right here is what the ion distribution looks like. 00:39:58.020 --> 00:40:01.220 align:middle line:84% And this depth right here marked x 00:40:01.220 --> 00:40:05.370 align:middle line:84% sub m, that's the thickness of the mask. 00:40:05.370 --> 00:40:07.070 align:middle line:84% And you can see what I've done here. 00:40:07.070 --> 00:40:08.750 align:middle line:84% Actually, I've chosen a mask that was 00:40:08.750 --> 00:40:10.760 align:middle line:90% too thin sort of intentionally. 00:40:10.760 --> 00:40:12.530 align:middle line:84% What happens is all this distribution 00:40:12.530 --> 00:40:15.440 align:middle line:84% got implanted into the mask, and a little bit of its tail 00:40:15.440 --> 00:40:18.320 align:middle line:84% right here, which is hatched by this red hatch 00:40:18.320 --> 00:40:22.020 align:middle line:84% region, a little bit this tail actually got into the silicon. 00:40:22.020 --> 00:40:25.870 align:middle line:84% Generally not desired, but just to show you as an example. 00:40:25.870 --> 00:40:30.990 align:middle line:84% So the concentration, c star, at xm 00:40:30.990 --> 00:40:33.600 align:middle line:84% gives you an idea of the concentration that will now be 00:40:33.600 --> 00:40:35.490 align:middle line:90% at the surface of the silicon. 00:40:35.490 --> 00:40:39.660 align:middle line:84% And this whole dose is what got into the silicon. 00:40:39.660 --> 00:40:43.530 align:middle line:84% So for masking, what we do is we calculate the concentration 00:40:43.530 --> 00:40:45.060 align:middle line:90% profile in the mask material. 00:40:45.060 --> 00:40:47.180 align:middle line:84% And the reason we have the star here, 00:40:47.180 --> 00:40:48.930 align:middle line:84% and I know that we use star in this course 00:40:48.930 --> 00:40:50.347 align:middle line:84% to mean a lot of different things, 00:40:50.347 --> 00:40:52.530 align:middle line:84% but this star means you're in the mask material. 00:40:52.530 --> 00:40:54.420 align:middle line:84% So whatever that material is, you 00:40:54.420 --> 00:40:59.520 align:middle line:84% have to use the projected range, Rp star, of boron 00:40:59.520 --> 00:41:03.000 align:middle line:84% in that material or the standard deviation, delta Rp star, 00:41:03.000 --> 00:41:06.430 align:middle line:84% of boron in that material in this equation. 00:41:06.430 --> 00:41:08.550 align:middle line:84% So this is just like a regular Gaussian. 00:41:08.550 --> 00:41:12.180 align:middle line:84% The only difference I've done is I've 00:41:12.180 --> 00:41:17.260 align:middle line:84% got this represented as Rp star and delta Rp star. 00:41:17.260 --> 00:41:21.870 align:middle line:84% So what I want is this concentration, c star, 00:41:21.870 --> 00:41:26.140 align:middle line:84% at this point to be less than some background concentration, 00:41:26.140 --> 00:41:27.390 align:middle line:90% whatever it might be. 00:41:27.390 --> 00:41:28.770 align:middle line:84% Let's say, your wafer is doped 10 00:41:28.770 --> 00:41:31.870 align:middle line:84% to the 14th per cubic centimeter. 00:41:31.870 --> 00:41:34.570 align:middle line:84% You want to make sure that the concentration 00:41:34.570 --> 00:41:38.500 align:middle line:84% profile in the mask is such that by the time that the profile 00:41:38.500 --> 00:41:41.440 align:middle line:84% gets to the edge of the mask, it's down below 10 of the 14 00:41:41.440 --> 00:41:42.860 align:middle line:90% so you really can't see it. 00:41:42.860 --> 00:41:44.260 align:middle line:90% That means you have a good mask. 00:41:44.260 --> 00:41:46.060 align:middle line:84% You've designed it to be thick enough. 00:41:46.060 --> 00:41:47.860 align:middle line:84% If it's thinner, then you get too much 00:41:47.860 --> 00:41:52.520 align:middle line:84% of the material, of the species is implanted into the wafer 00:41:52.520 --> 00:41:53.020 align:middle line:90% itself. 00:41:53.020 --> 00:41:53.895 align:middle line:90% It's not a good mask. 00:41:53.895 --> 00:41:57.260 align:middle line:90% 00:41:57.260 --> 00:41:59.710 align:middle line:90% So let's look at slide 16. 00:41:59.710 --> 00:42:03.160 align:middle line:84% And in fact, here what we want to calculate is-- 00:42:03.160 --> 00:42:05.230 align:middle line:84% we'll calculate the area of this red region. 00:42:05.230 --> 00:42:07.270 align:middle line:84% That's the dose that penetrated the mask 00:42:07.270 --> 00:42:11.900 align:middle line:84% and made it into the silicon or into the material below. 00:42:11.900 --> 00:42:16.720 align:middle line:84% So we can actually calculate the required mask thickness 00:42:16.720 --> 00:42:20.650 align:middle line:84% from this equation that I just showed back on slide 15. 00:42:20.650 --> 00:42:22.352 align:middle line:84% I'm going to set this concentration 00:42:22.352 --> 00:42:24.310 align:middle line:84% equal to the background concentration, whatever 00:42:24.310 --> 00:42:28.160 align:middle line:84% it is in the wafer, solve for that, 00:42:28.160 --> 00:42:30.430 align:middle line:84% and that gives me the mask thickness, xm, 00:42:30.430 --> 00:42:34.690 align:middle line:84% in terms of Rp star in the material 00:42:34.690 --> 00:42:38.350 align:middle line:84% and the standard deviation, delta Rp. 00:42:38.350 --> 00:42:41.110 align:middle line:84% So basically, it says the mask should be as thick 00:42:41.110 --> 00:42:45.700 align:middle line:84% as Rp, obviously, plus some multiple m 00:42:45.700 --> 00:42:48.580 align:middle line:90% of the standard deviation. 00:42:48.580 --> 00:42:52.390 align:middle line:84% Typically, m might be five standard deviations of thickness 00:42:52.390 --> 00:42:55.560 align:middle line:90% or something like that. 00:42:55.560 --> 00:42:58.340 align:middle line:84% And so the dose that penetrates the mask, 00:42:58.340 --> 00:42:59.990 align:middle line:84% then, I can just substitute that in. 00:42:59.990 --> 00:43:02.840 align:middle line:84% All you need to do is integrate this little red region. 00:43:02.840 --> 00:43:03.800 align:middle line:90% It's given by this. 00:43:03.800 --> 00:43:06.075 align:middle line:84% It turns out to be a complementary error function. 00:43:06.075 --> 00:43:07.700 align:middle line:84% So you can actually figure out how much 00:43:07.700 --> 00:43:08.780 align:middle line:90% you made in into silicon. 00:43:08.780 --> 00:43:12.180 align:middle line:84% Generally, design the mask so that it doesn't make it in. 00:43:12.180 --> 00:43:15.390 align:middle line:84% And there's a calculation on page 457 of your text, the hand 00:43:15.390 --> 00:43:18.645 align:middle line:84% calculation of this type of thing to give you an idea. 00:43:18.645 --> 00:43:20.910 align:middle line:84% A lot of times, people use hand calculations 00:43:20.910 --> 00:43:23.950 align:middle line:84% or they use SUPREM-IV to figure out, OK, 00:43:23.950 --> 00:43:27.150 align:middle line:84% if I have a certain thickness, I have a half micron of oxide, 00:43:27.150 --> 00:43:29.338 align:middle line:84% how far is boron going to go into that? 00:43:29.338 --> 00:43:31.380 align:middle line:84% And is it thick enough for me to mask my implant? 00:43:31.380 --> 00:43:35.210 align:middle line:90% 00:43:35.210 --> 00:43:37.922 align:middle line:84% So that's masking in terms of the vertical direction. 00:43:37.922 --> 00:43:39.380 align:middle line:84% How about in the lateral direction? 00:43:39.380 --> 00:43:41.390 align:middle line:84% This is a little bit more tricky, 00:43:41.390 --> 00:43:43.700 align:middle line:84% and you just have to think here intuitively. 00:43:43.700 --> 00:43:46.850 align:middle line:90% This is on slide 17. 00:43:46.850 --> 00:43:50.420 align:middle line:84% Implants are, by the way, rarely done perfectly vertically. 00:43:50.420 --> 00:43:52.190 align:middle line:84% If this is the wafer, it's very rare 00:43:52.190 --> 00:43:53.930 align:middle line:84% that the incoming beam is at 90 degrees. 00:43:53.930 --> 00:43:56.840 align:middle line:84% And we'll talk in a little bit about why that is. 00:43:56.840 --> 00:43:59.300 align:middle line:84% But it turns out a lot of implants, 00:43:59.300 --> 00:44:01.820 align:middle line:84% either for device design reasons or whatever, 00:44:01.820 --> 00:44:05.013 align:middle line:90% are done at some tilt angle. 00:44:05.013 --> 00:44:05.930 align:middle line:90% The beam is like this. 00:44:05.930 --> 00:44:09.180 align:middle line:90% You actually tilt the wafer. 00:44:09.180 --> 00:44:11.630 align:middle line:84% And in fact, halo implants are almost always done 00:44:11.630 --> 00:44:14.990 align:middle line:84% at some kind of tilt. And the reason you tilt it in 00:44:14.990 --> 00:44:18.063 align:middle line:84% is because you want to, in this case-- this is the gate, 00:44:18.063 --> 00:44:19.730 align:middle line:84% and I'm trying to do an implant, and I'm 00:44:19.730 --> 00:44:22.880 align:middle line:84% trying to get the ions to sneak a little bit underneath the gate 00:44:22.880 --> 00:44:24.890 align:middle line:84% a certain distance, and use the implant 00:44:24.890 --> 00:44:26.400 align:middle line:84% to get the ions underneath there. 00:44:26.400 --> 00:44:30.290 align:middle line:84% So in that case, I'll have to take this tilt into account 00:44:30.290 --> 00:44:31.850 align:middle line:84% when I'm calculating the profile. 00:44:31.850 --> 00:44:34.800 align:middle line:84% And in fact, you can get shadowing effects. 00:44:34.800 --> 00:44:38.960 align:middle line:84% This is an example of a 50 KB phosphorus implant, 00:44:38.960 --> 00:44:42.450 align:middle line:84% and this was tilted at a very high angle, say, 30 degrees. 00:44:42.450 --> 00:44:45.080 align:middle line:84% And this red region, which represents 00:44:45.080 --> 00:44:48.420 align:middle line:84% the gate, the polysilicon gate, it ends up shadowing the beam. 00:44:48.420 --> 00:44:52.220 align:middle line:84% So you end up with a little space here where the shadow was, 00:44:52.220 --> 00:44:54.080 align:middle line:84% so that did not get ion implanted. 00:44:54.080 --> 00:44:57.710 align:middle line:84% So if I want to reproduce a symmetric profile on the source 00:44:57.710 --> 00:44:59.480 align:middle line:84% side and the drain side, I then need 00:44:59.480 --> 00:45:01.430 align:middle line:84% to tilt the wafer the other way and come in 00:45:01.430 --> 00:45:06.232 align:middle line:84% at 30 degrees to the normal in this direction for symmetry. 00:45:06.232 --> 00:45:07.690 align:middle line:84% So if you're doing tilted implants, 00:45:07.690 --> 00:45:10.420 align:middle line:84% you have to think about how your device is oriented with respect 00:45:10.420 --> 00:45:12.190 align:middle line:90% to the tilt direction. 00:45:12.190 --> 00:45:17.915 align:middle line:84% And maybe do some other implants to symmetrize what's going on. 00:45:17.915 --> 00:45:19.540 align:middle line:84% And again, that's a geometrical effect. 00:45:19.540 --> 00:45:20.915 align:middle line:84% It's relatively easy to simulate. 00:45:20.915 --> 00:45:23.170 align:middle line:90% This is a SUPREM-IV simulation. 00:45:23.170 --> 00:45:24.970 align:middle line:84% You just have to keep track of that. 00:45:24.970 --> 00:45:28.240 align:middle line:90% 00:45:28.240 --> 00:45:30.880 align:middle line:84% OK, the next concept I want to introduce 00:45:30.880 --> 00:45:33.700 align:middle line:84% is thinking a little bit about, how 00:45:33.700 --> 00:45:36.370 align:middle line:84% does this Gaussian-- let's say, you implant a Gaussian profile. 00:45:36.370 --> 00:45:38.590 align:middle line:90% OK, here on slide 18. 00:45:38.590 --> 00:45:40.078 align:middle line:84% How does that profile evolve when 00:45:40.078 --> 00:45:42.620 align:middle line:84% I'm going to have to heat the wafer to get rid of the damage? 00:45:42.620 --> 00:45:43.703 align:middle line:90% How is it going to evolve? 00:45:43.703 --> 00:45:46.780 align:middle line:84% Well, we first do a very, very simple back of the envelope 00:45:46.780 --> 00:45:50.560 align:middle line:90% type of calculation. 00:45:50.560 --> 00:45:53.620 align:middle line:84% And let's look at a Gaussian implant distribution. 00:45:53.620 --> 00:45:54.580 align:middle line:90% This is what I just-- 00:45:54.580 --> 00:45:57.520 align:middle line:84% the equation 1 in what we just put down for a Gaussian implant. 00:45:57.520 --> 00:46:00.070 align:middle line:84% It's characterized by this Rp, projected range, 00:46:00.070 --> 00:46:02.620 align:middle line:84% and a standard deviation, delta Rp. 00:46:02.620 --> 00:46:06.190 align:middle line:84% Now, if we go back to a prior handout, 14, 00:46:06.190 --> 00:46:08.770 align:middle line:84% when we were talking about diffusion of Gaussians, 00:46:08.770 --> 00:46:11.170 align:middle line:84% we actually wrote it like this, the concentration 00:46:11.170 --> 00:46:12.880 align:middle line:90% can be written in terms of. 00:46:12.880 --> 00:46:14.770 align:middle line:84% And look at the denominator here. 00:46:14.770 --> 00:46:19.460 align:middle line:84% You got 4 dt in it as opposed to 2 delta Rp squared. 00:46:19.460 --> 00:46:21.940 align:middle line:84% So in fact, these are both Gaussian functions. 00:46:21.940 --> 00:46:23.500 align:middle line:84% They are mathematically equivalent, 00:46:23.500 --> 00:46:25.930 align:middle line:84% and I can make them equal if I just 00:46:25.930 --> 00:46:28.250 align:middle line:84% set delta Rp equal to the square root of dt. 00:46:28.250 --> 00:46:31.320 align:middle line:90% 00:46:31.320 --> 00:46:35.150 align:middle line:84% I can equalize these two arguments. 00:46:35.150 --> 00:46:40.720 align:middle line:84% So we can then write down an equation, a very simple equation 00:46:40.720 --> 00:46:41.530 align:middle line:90% for the impacts. 00:46:41.530 --> 00:46:43.900 align:middle line:84% If I do an implant, and you assume it's Gaussian, 00:46:43.900 --> 00:46:46.120 align:middle line:84% and then I anneal it in a case where 00:46:46.120 --> 00:46:47.710 align:middle line:84% it's non-concentration-dependent, 00:46:47.710 --> 00:46:50.290 align:middle line:84% I expect the final profile to remain Gaussian. 00:46:50.290 --> 00:46:53.592 align:middle line:84% So a Gaussian remains a Gaussian, preserves its shape 00:46:53.592 --> 00:46:54.550 align:middle line:90% upon further annealing. 00:46:54.550 --> 00:46:55.967 align:middle line:84% And in fact, I can just write down 00:46:55.967 --> 00:46:59.380 align:middle line:84% by inspection what should happen to that. 00:46:59.380 --> 00:47:01.600 align:middle line:84% If you start out with this distribution here-- 00:47:01.600 --> 00:47:04.390 align:middle line:84% this is the ion implant distribution-- 00:47:04.390 --> 00:47:08.560 align:middle line:84% what I replaced for the argument in the denominator 00:47:08.560 --> 00:47:13.330 align:middle line:84% of the exponential, instead of having just this for 4 dt, 00:47:13.330 --> 00:47:15.620 align:middle line:84% I've got a new standard deviation, 00:47:15.620 --> 00:47:21.390 align:middle line:84% which is delta Rp squared, plus that essentially. 00:47:21.390 --> 00:47:24.270 align:middle line:84% And again, where we see the square root of dt, 00:47:24.270 --> 00:47:27.360 align:middle line:84% you can also write that out here in the pre-exponential 00:47:27.360 --> 00:47:32.740 align:middle line:90% in terms of delta Rp and dt. 00:47:32.740 --> 00:47:35.530 align:middle line:84% For the very simplest case, you have to do a hand calculation. 00:47:35.530 --> 00:47:38.412 align:middle line:84% We know how a Gaussian implant profile will evolve. 00:47:38.412 --> 00:47:40.120 align:middle line:84% We're going to go, of course, beyond that 00:47:40.120 --> 00:47:42.830 align:middle line:84% in the next few lectures, talk in more detail. 00:47:42.830 --> 00:47:46.910 align:middle line:84% Here's an example on slide 19 of just those equations. 00:47:46.910 --> 00:47:51.720 align:middle line:84% So this is assumed to be as implanted, the red, 00:47:51.720 --> 00:47:54.870 align:middle line:84% assuming a very simple Gaussian distribution 00:47:54.870 --> 00:47:57.300 align:middle line:84% with a certain standard deviation, delta Rp. 00:47:57.300 --> 00:47:59.310 align:middle line:84% And after it's gone through diffusion, 00:47:59.310 --> 00:48:03.030 align:middle line:90% it's shown here in the blue. 00:48:03.030 --> 00:48:07.030 align:middle line:84% The peak has dropped, and now it has a new standard deviation, 00:48:07.030 --> 00:48:08.940 align:middle line:84% which is delta Rp plus the square root of dt. 00:48:08.940 --> 00:48:14.883 align:middle line:90% 00:48:14.883 --> 00:48:16.300 align:middle line:84% So this gives us an idea of how we 00:48:16.300 --> 00:48:19.660 align:middle line:84% can evolve an implanted Gaussian during a diffusion step. 00:48:19.660 --> 00:48:23.030 align:middle line:90% 00:48:23.030 --> 00:48:27.940 align:middle line:84% So let's go on to slide 20 and talk about a real profile. 00:48:27.940 --> 00:48:31.390 align:middle line:84% Real profiles are not perfectly Gaussian. 00:48:31.390 --> 00:48:33.830 align:middle line:84% In some cases, they're more Gaussian than others, 00:48:33.830 --> 00:48:36.700 align:middle line:84% but they're generally more complex. 00:48:36.700 --> 00:48:40.510 align:middle line:84% If we look at the profile for a light ion, 00:48:40.510 --> 00:48:44.980 align:middle line:84% and light means very light compared to silicon, 00:48:44.980 --> 00:48:50.200 align:middle line:84% say, boron, these light ions tend to backscatter. 00:48:50.200 --> 00:48:53.230 align:middle line:84% Imagine you have a big, heavy bowling ball, 00:48:53.230 --> 00:48:55.432 align:middle line:84% and you're throwing a ping pong ball at it. 00:48:55.432 --> 00:48:56.140 align:middle line:90% That's the boron. 00:48:56.140 --> 00:48:57.190 align:middle line:90% It's a ping pong ball. 00:48:57.190 --> 00:48:59.732 align:middle line:84% Well, a lot of those boron atoms will ping right back, right? 00:48:59.732 --> 00:49:02.065 align:middle line:84% A few of them will scatter in forward, but a lot of them 00:49:02.065 --> 00:49:03.080 align:middle line:90% can come right back. 00:49:03.080 --> 00:49:07.300 align:middle line:84% And so you can see that if you look at a boron distribution, 00:49:07.300 --> 00:49:10.747 align:middle line:84% towards the surface, it's actually skewed. 00:49:10.747 --> 00:49:12.580 align:middle line:84% The concentration profile is a little higher 00:49:12.580 --> 00:49:14.663 align:middle line:84% towards the surface, as if a lot of the boron ions 00:49:14.663 --> 00:49:17.050 align:middle line:84% came in and just got pinged right back. 00:49:17.050 --> 00:49:20.530 align:middle line:84% So this blue distribution that represents boron at 38 keV, 00:49:20.530 --> 00:49:23.160 align:middle line:90% it's skewed towards the surface. 00:49:23.160 --> 00:49:24.870 align:middle line:84% And it relates to the fundamental physics 00:49:24.870 --> 00:49:25.680 align:middle line:90% of the scattering. 00:49:25.680 --> 00:49:30.630 align:middle line:84% Heavy ions like antimony, they actually tend to scatter deeper. 00:49:30.630 --> 00:49:31.962 align:middle line:90% They're heavier than silicon. 00:49:31.962 --> 00:49:33.420 align:middle line:84% They can knock the silicon forward, 00:49:33.420 --> 00:49:35.902 align:middle line:84% and they themselves retain a lot of forward momentum 00:49:35.902 --> 00:49:37.110 align:middle line:90% because they're like a truck. 00:49:37.110 --> 00:49:39.555 align:middle line:84% If the truck hits a little Subaru, 00:49:39.555 --> 00:49:41.430 align:middle line:84% kind of tends to go right through the Subaru. 00:49:41.430 --> 00:49:45.870 align:middle line:84% So the heavy ions like antimony have this skewed-- or skew 00:49:45.870 --> 00:49:48.923 align:middle line:90% deeper into the substrate. 00:49:48.923 --> 00:49:50.840 align:middle line:84% The interesting thing about these two protons, 00:49:50.840 --> 00:49:53.610 align:middle line:90% so this is antimony at 360 keV. 00:49:53.610 --> 00:49:56.825 align:middle line:84% So we adjusted the energy to give them the same projected 00:49:56.825 --> 00:49:58.950 align:middle line:84% range, so you notice they peaked at the same point. 00:49:58.950 --> 00:50:03.690 align:middle line:84% 38 keV peaks at the same point as 360 keV antimony, 00:50:03.690 --> 00:50:07.550 align:middle line:84% but they have very different skewness. 00:50:07.550 --> 00:50:10.387 align:middle line:84% A Gaussian distribution by definition is not skewed, right? 00:50:10.387 --> 00:50:12.470 align:middle line:84% A Gaussian, by definition, is perfectly symmetric. 00:50:12.470 --> 00:50:14.060 align:middle line:90% That's what the equation says. 00:50:14.060 --> 00:50:15.980 align:middle line:84% So if we're going to represent this, 00:50:15.980 --> 00:50:17.780 align:middle line:84% we need a little more complicated 00:50:17.780 --> 00:50:19.970 align:middle line:84% mathematical function than a Gaussian. 00:50:19.970 --> 00:50:25.230 align:middle line:84% And we'll talk a little bit about that type of function. 00:50:25.230 --> 00:50:28.760 align:middle line:84% So here's an example just on slide 21 00:50:28.760 --> 00:50:32.670 align:middle line:84% of some different energy boron implants. 00:50:32.670 --> 00:50:36.680 align:middle line:84% So I have concentration of boron versus depth. 00:50:36.680 --> 00:50:38.600 align:middle line:90% And here's a 50 keV implant. 00:50:38.600 --> 00:50:40.700 align:middle line:84% Interestingly, it looks pretty symmetrical. 00:50:40.700 --> 00:50:41.900 align:middle line:90% It's fairly Gaussian. 00:50:41.900 --> 00:50:43.010 align:middle line:90% 100 keV. 00:50:43.010 --> 00:50:45.650 align:middle line:84% But as I'm going to higher and higher energies, 00:50:45.650 --> 00:50:48.320 align:middle line:84% it's becoming less and less symmetrical. 00:50:48.320 --> 00:50:52.730 align:middle line:84% So just looking at this black curve right here at 500 keV, 00:50:52.730 --> 00:50:54.980 align:middle line:84% look how skewed that is towards the surface. 00:50:54.980 --> 00:50:57.563 align:middle line:84% Whereas, if I had used the Gaussian approximation 00:50:57.563 --> 00:50:59.480 align:middle line:84% that you can do with a simple hand calculator, 00:50:59.480 --> 00:51:00.897 align:middle line:84% this dashed line is what you would 00:51:00.897 --> 00:51:02.580 align:middle line:90% have gotten for the profile. 00:51:02.580 --> 00:51:04.542 align:middle line:84% So the Gaussian is somewhat accurate. 00:51:04.542 --> 00:51:06.500 align:middle line:84% It gives you a rough idea of where the peak is, 00:51:06.500 --> 00:51:09.680 align:middle line:84% but it doesn't represent this forward scattering 00:51:09.680 --> 00:51:11.180 align:middle line:90% of the skewness. 00:51:11.180 --> 00:51:14.090 align:middle line:84% In fact, these black profiles are 00:51:14.090 --> 00:51:17.750 align:middle line:84% called something called Pearson IV distributions. 00:51:17.750 --> 00:51:19.760 align:middle line:84% Those are the solid lines in that plot. 00:51:19.760 --> 00:51:21.590 align:middle line:84% And Pearson IV is one of the most popular. 00:51:21.590 --> 00:51:23.060 align:middle line:90% It's a statistical function. 00:51:23.060 --> 00:51:25.920 align:middle line:84% It's one of the most popular types of profiles 00:51:25.920 --> 00:51:29.880 align:middle line:84% to use to accurately represent distributions, 00:51:29.880 --> 00:51:33.390 align:middle line:84% range distributions for ion-implanted atoms in silicon. 00:51:33.390 --> 00:51:34.890 align:middle line:90% They work really well. 00:51:34.890 --> 00:51:36.900 align:middle line:84% Pearson IV works really well as long, 00:51:36.900 --> 00:51:39.390 align:middle line:84% as you don't have ion channeling. 00:51:39.390 --> 00:51:42.210 align:middle line:84% It does an excellent job of describing the ion implant 00:51:42.210 --> 00:51:42.990 align:middle line:90% profiles. 00:51:42.990 --> 00:51:46.350 align:middle line:84% As the name suggests, Pearson IV needs four variables. 00:51:46.350 --> 00:51:49.710 align:middle line:84% It has four moments, so to speak. 00:51:49.710 --> 00:51:52.025 align:middle line:84% Gaussian only has two, so naturally the Gaussian 00:51:52.025 --> 00:51:52.650 align:middle line:90% is more simple. 00:51:52.650 --> 00:51:55.760 align:middle line:90% 00:51:55.760 --> 00:52:00.910 align:middle line:84% In fact, on slide 22, just reminding you or introducing you 00:52:00.910 --> 00:52:05.530 align:middle line:84% to the idea that an arbitrary statistical distribution 00:52:05.530 --> 00:52:08.590 align:middle line:84% can be described by a series of moments. 00:52:08.590 --> 00:52:10.660 align:middle line:84% And here are the first four moments 00:52:10.660 --> 00:52:12.840 align:middle line:90% of an arbitrary distribution. 00:52:12.840 --> 00:52:14.590 align:middle line:84% The first two, we've already talked about. 00:52:14.590 --> 00:52:17.920 align:middle line:84% The first moment is called the projected range, Rp. 00:52:17.920 --> 00:52:22.510 align:middle line:84% And mathematically, you can derive it or calculate it by-- 00:52:22.510 --> 00:52:24.490 align:middle line:84% it's the first moment, so it's the integral 00:52:24.490 --> 00:52:29.470 align:middle line:84% over all space of x of x times the concentration, c, of x. 00:52:29.470 --> 00:52:31.240 align:middle line:84% So you take the weighted integral, 00:52:31.240 --> 00:52:34.508 align:middle line:84% and that is the definition of Rp. 00:52:34.508 --> 00:52:36.550 align:middle line:84% You may have seen some of these types of concepts 00:52:36.550 --> 00:52:38.710 align:middle line:84% in statistical or statistics classes. 00:52:38.710 --> 00:52:41.260 align:middle line:84% The standard deviation is the second moment. 00:52:41.260 --> 00:52:45.160 align:middle line:84% It's actually the integral of x minus Rp quantity 00:52:45.160 --> 00:52:50.440 align:middle line:84% squared times the constant concentration, that whole thing 00:52:50.440 --> 00:52:52.420 align:middle line:90% divided by the integrated dose. 00:52:52.420 --> 00:52:54.400 align:middle line:84% Remember, the integrated dose, q. 00:52:54.400 --> 00:52:58.520 align:middle line:84% Just remember that q here is equal to the integral 00:52:58.520 --> 00:53:00.230 align:middle line:90% of the concentration-- 00:53:00.230 --> 00:53:02.300 align:middle line:90% overall space, dx. 00:53:02.300 --> 00:53:03.770 align:middle line:84% So you're always normalizing this. 00:53:03.770 --> 00:53:06.470 align:middle line:90% 00:53:06.470 --> 00:53:08.220 align:middle line:84% So the first moment and the second moment, 00:53:08.220 --> 00:53:11.380 align:middle line:84% they're used, of course, in the Gaussian distribution. 00:53:11.380 --> 00:53:15.060 align:middle line:84% The third and fourth moments are used in the Pearson IV. 00:53:15.060 --> 00:53:16.350 align:middle line:90% One is called the skewness. 00:53:16.350 --> 00:53:19.800 align:middle line:84% Again, that's x minus Rp cubed, the weighted integral 00:53:19.800 --> 00:53:23.910 align:middle line:84% of that, divided by q times delta Rp cubed. 00:53:23.910 --> 00:53:27.210 align:middle line:84% And the kurtosis is defined in terms of the fourth-- 00:53:27.210 --> 00:53:30.330 align:middle line:84% the x minus Rp to the fourth power. 00:53:30.330 --> 00:53:33.930 align:middle line:84% And this skewness and kurtosis, as they've been defined here, 00:53:33.930 --> 00:53:36.900 align:middle line:84% they're actually gamma and beta are dimensionless, 00:53:36.900 --> 00:53:40.650 align:middle line:84% because you notice we're dividing by delta Rp cubed here 00:53:40.650 --> 00:53:42.150 align:middle line:90% and delta Rp to the fourth. 00:53:42.150 --> 00:53:46.140 align:middle line:90% 00:53:46.140 --> 00:53:47.850 align:middle line:84% Just so you know, if you run SUPREM-IV, 00:53:47.850 --> 00:53:49.180 align:middle line:90% you won't have to do it. 00:53:49.180 --> 00:53:50.910 align:middle line:84% But if you were stuck on a desert island, 00:53:50.910 --> 00:53:54.180 align:middle line:84% and all you had was an HP calculator, you could actually-- 00:53:54.180 --> 00:53:55.650 align:middle line:84% and your life depended on it-- you 00:53:55.650 --> 00:53:58.920 align:middle line:84% could actually calculate the Pearson IV distribution 00:53:58.920 --> 00:54:03.000 align:middle line:84% from the simple differential equation. 00:54:03.000 --> 00:54:04.680 align:middle line:90% It's the solution f. 00:54:04.680 --> 00:54:07.960 align:middle line:84% The Pearson IV is a solution f to this differential equation. 00:54:07.960 --> 00:54:09.660 align:middle line:84% So the differential equation says 00:54:09.660 --> 00:54:16.890 align:middle line:84% df by dxn, where xn is this variable here, x minus Rp, 00:54:16.890 --> 00:54:19.020 align:middle line:84% is equal to this function over here, 00:54:19.020 --> 00:54:22.080 align:middle line:84% is equal to xn minus a quantity times f divided 00:54:22.080 --> 00:54:25.770 align:middle line:90% by this polynomial. 00:54:25.770 --> 00:54:28.490 align:middle line:84% So it turns out this differential equation 00:54:28.490 --> 00:54:33.770 align:middle line:84% can be resolved relatively simply using a numerical method 00:54:33.770 --> 00:54:37.430 align:middle line:84% if you know these moments, so if these numbers, a, 00:54:37.430 --> 00:54:39.530 align:middle line:90% b0, b1, and b2. 00:54:39.530 --> 00:54:42.980 align:middle line:84% And each one of these variables, like a, a 00:54:42.980 --> 00:54:47.780 align:middle line:84% is defined in terms of the skewness, the kurtosis, 00:54:47.780 --> 00:54:51.650 align:middle line:84% and of course, delta Rp, the standard deviation. 00:54:51.650 --> 00:54:54.030 align:middle line:90% b is related, as shown here. 00:54:54.030 --> 00:54:56.180 align:middle line:84% So all these constants are defined 00:54:56.180 --> 00:55:00.100 align:middle line:84% in terms of the moments of the Pearson IV. 00:55:00.100 --> 00:55:03.970 align:middle line:84% It turns out that if the skewness, gamma, 00:55:03.970 --> 00:55:06.730 align:middle line:84% for most dopants in silicon, you can actually 00:55:06.730 --> 00:55:09.400 align:middle line:84% estimate the kurtosis, beta, from the simple little 00:55:09.400 --> 00:55:10.490 align:middle line:90% analytical formula. 00:55:10.490 --> 00:55:12.650 align:middle line:84% So in fact, they're related this way. 00:55:12.650 --> 00:55:14.440 align:middle line:84% So really, for most dopants, there's 00:55:14.440 --> 00:55:19.690 align:middle line:84% only three independent moments, Rp, delta Rp, and beta-- 00:55:19.690 --> 00:55:24.780 align:middle line:84% and gamma, because you can calculate beta from gamma. 00:55:24.780 --> 00:55:26.310 align:middle line:84% If you just look at this equation 00:55:26.310 --> 00:55:28.810 align:middle line:84% just for a moment-- you don't to solve it-- but just looking 00:55:28.810 --> 00:55:31.620 align:middle line:84% at it, what are some properties of this function? 00:55:31.620 --> 00:55:34.030 align:middle line:84% Well, the peak, where does the peak occur? 00:55:34.030 --> 00:55:36.810 align:middle line:84% Well, the peak occurs wherever a function is set equal to 0. 00:55:36.810 --> 00:55:40.410 align:middle line:84% So the peak occurs where this-- or the derivative 00:55:40.410 --> 00:55:43.200 align:middle line:90% of the function is 0. 00:55:43.200 --> 00:55:49.860 align:middle line:84% So it actually occurs at xn minus a, which is Rp plus a. 00:55:49.860 --> 00:55:52.260 align:middle line:84% So it doesn't occur directly at Rp. 00:55:52.260 --> 00:55:54.660 align:middle line:84% Unlike the Gaussian, the peak of this 00:55:54.660 --> 00:55:58.500 align:middle line:84% occurs just slightly to the left or the right of Rp. 00:55:58.500 --> 00:56:04.680 align:middle line:84% So when the skewness, gamma, is 0-- 00:56:04.680 --> 00:56:08.670 align:middle line:84% so when gamma is 0, f simplifies to a Gaussian. 00:56:08.670 --> 00:56:11.533 align:middle line:84% So if I just take this and a goes to 0, 00:56:11.533 --> 00:56:13.200 align:middle line:84% then I'm going to get a simple Gaussian. 00:56:13.200 --> 00:56:14.250 align:middle line:90% There's no skewness. 00:56:14.250 --> 00:56:17.190 align:middle line:84% If the skewness is negative, so gamma is negative, 00:56:17.190 --> 00:56:21.520 align:middle line:84% like in the case of boron, a is going to be positive. 00:56:21.520 --> 00:56:24.900 align:middle line:84% So if gamma is negative, a positive quantity, 00:56:24.900 --> 00:56:28.050 align:middle line:84% and the peak of the distribution occurs deeper than Rp. 00:56:28.050 --> 00:56:30.750 align:middle line:84% So for boron, if you're careful about calculating it 00:56:30.750 --> 00:56:34.110 align:middle line:84% in Pearson IV, the peak will just be slightly deeper than Rp. 00:56:34.110 --> 00:56:35.640 align:middle line:90% It'll be Rp plus a. 00:56:35.640 --> 00:56:37.980 align:middle line:84% When the skewness is positive, like for arsenic, 00:56:37.980 --> 00:56:39.780 align:middle line:84% a heavy atom like arsenic or antimony, 00:56:39.780 --> 00:56:43.800 align:middle line:84% the peak is going to be slightly shallower than Rp. 00:56:43.800 --> 00:56:47.790 align:middle line:84% So again, slightly more sophisticated than a Gaussian 00:56:47.790 --> 00:56:49.830 align:middle line:90% is the Pearson IV. 00:56:49.830 --> 00:56:53.980 align:middle line:84% And that's how it's actually calculated by the computer. 00:56:53.980 --> 00:56:56.160 align:middle line:84% So these four moments that we've been talking about, 00:56:56.160 --> 00:56:58.050 align:middle line:90% they've actually been tabulated. 00:56:58.050 --> 00:57:00.900 align:middle line:84% I took this particular table I copied out 00:57:00.900 --> 00:57:06.000 align:middle line:84% of a 1980 book edited by Gibbons on ion implantation. 00:57:06.000 --> 00:57:09.480 align:middle line:84% And it's just showing as a function of energy 00:57:09.480 --> 00:57:13.620 align:middle line:84% and a couple different energies, 20 50, 100, and 200 keV. 00:57:13.620 --> 00:57:17.670 align:middle line:84% For three common dopants, it's showing Rp, sigma p-- now, 00:57:17.670 --> 00:57:19.200 align:middle line:90% sigma p is the same as delta Rp. 00:57:19.200 --> 00:57:21.240 align:middle line:90% It's just a different notation-- 00:57:21.240 --> 00:57:26.460 align:middle line:84% the skewness, gamma, and sigma p perpendicular, 00:57:26.460 --> 00:57:29.160 align:middle line:90% or delta Rp perpendicular. 00:57:29.160 --> 00:57:32.430 align:middle line:84% So just looking at boron, again, its skewness is negative, right? 00:57:32.430 --> 00:57:34.750 align:middle line:84% All of these gamma numbers are negative. 00:57:34.750 --> 00:57:37.630 align:middle line:84% That's why it's skewed towards the surface. 00:57:37.630 --> 00:57:40.200 align:middle line:84% And so you can look up in tables like this, 00:57:40.200 --> 00:57:41.700 align:middle line:84% and if you have your calculator, you 00:57:41.700 --> 00:57:44.190 align:middle line:84% can do the Pearson IV equation, and you 00:57:44.190 --> 00:57:48.345 align:middle line:84% can calculate what the profile should look like. 00:57:48.345 --> 00:57:51.560 align:middle line:90% 00:57:51.560 --> 00:57:53.660 align:middle line:84% OK, so that gives you some idea of how 00:57:53.660 --> 00:57:56.180 align:middle line:90% engineers use these numbers. 00:57:56.180 --> 00:57:59.810 align:middle line:84% Now, let's go on to slide 25, and let's talk 00:57:59.810 --> 00:58:02.283 align:middle line:90% about implants in real silicon. 00:58:02.283 --> 00:58:03.700 align:middle line:84% Well, to be a little more careful, 00:58:03.700 --> 00:58:05.410 align:middle line:84% real silicon is single crystal, right? 00:58:05.410 --> 00:58:08.050 align:middle line:84% We know it has the diamond cubic structure, 00:58:08.050 --> 00:58:11.410 align:middle line:84% and it has a regularity to its structure. 00:58:11.410 --> 00:58:14.672 align:middle line:84% And in fact, I'm hoping not to make anybody car sick here. 00:58:14.672 --> 00:58:16.630 align:middle line:84% But be careful, don't shake your head too fast. 00:58:16.630 --> 00:58:21.220 align:middle line:84% But this is a picture of looking down 00:58:21.220 --> 00:58:24.940 align:middle line:84% the 1,1,0 direction, the axial channels in crystalline silicon. 00:58:24.940 --> 00:58:26.600 align:middle line:90% What do you see in this picture? 00:58:26.600 --> 00:58:31.090 align:middle line:84% What you see, well, you see a very regular pattern of atoms, 00:58:31.090 --> 00:58:35.410 align:middle line:84% and you see big openings, wide open spaces where there 00:58:35.410 --> 00:58:39.010 align:middle line:84% aren't-- where the atoms at the surface block the atoms below. 00:58:39.010 --> 00:58:42.740 align:middle line:84% So you can imagine being an ion going down this crystal. 00:58:42.740 --> 00:58:46.270 align:middle line:84% And if you're aligned, if your energy or your momentum 00:58:46.270 --> 00:58:48.730 align:middle line:84% is aligned just in the right direction, 00:58:48.730 --> 00:58:52.390 align:middle line:84% you can channel right down some of those channels. 00:58:52.390 --> 00:58:54.220 align:middle line:84% And you can imagine going down there 00:58:54.220 --> 00:58:57.160 align:middle line:84% without losing much energy, without banging 00:58:57.160 --> 00:59:01.100 align:middle line:84% into a lot of the silicon atoms because of this regular crystal 00:59:01.100 --> 00:59:01.600 align:middle line:90% structure. 00:59:01.600 --> 00:59:04.190 align:middle line:84% And in fact, this is a two-dimensional representation, 00:59:04.190 --> 00:59:06.470 align:middle line:84% a cartoon up here of what I'm talking about. 00:59:06.470 --> 00:59:08.700 align:middle line:84% Imagine these red atoms are silicon. 00:59:08.700 --> 00:59:11.810 align:middle line:84% They're all lined up in a row, and my incoming ion 00:59:11.810 --> 00:59:14.150 align:middle line:84% comes in just pointing down that channel. 00:59:14.150 --> 00:59:16.940 align:middle line:84% It can just barely skim the edges of the channel, 00:59:16.940 --> 00:59:19.730 align:middle line:84% have very few small angle collisions, 00:59:19.730 --> 00:59:23.640 align:middle line:84% and be steered a long way before it stops. 00:59:23.640 --> 00:59:26.250 align:middle line:84% That's very, very different than going into a random material 00:59:26.250 --> 00:59:29.400 align:middle line:84% where there are silicon atoms all over this page. 00:59:29.400 --> 00:59:32.220 align:middle line:84% So ion channeling, because the material is single crystal, 00:59:32.220 --> 00:59:34.890 align:middle line:84% is really going to complicate all those equations 00:59:34.890 --> 00:59:37.727 align:middle line:84% I just talked about, the Gaussian, Pearson IV. 00:59:37.727 --> 00:59:39.810 align:middle line:84% They're all assuming that the atoms of the crystal 00:59:39.810 --> 00:59:41.460 align:middle line:90% were randomly oriented. 00:59:41.460 --> 00:59:44.040 align:middle line:84% They didn't say anything about going down a channel. 00:59:44.040 --> 00:59:46.560 align:middle line:84% The physics of channeling is quite a bit 00:59:46.560 --> 00:59:50.500 align:middle line:84% different from what we've just been talking about. 00:59:50.500 --> 00:59:52.980 align:middle line:90% So channeling is good and bad. 00:59:52.980 --> 00:59:56.190 align:middle line:84% Mostly, it's bad because it can produce 00:59:56.190 --> 00:59:58.360 align:middle line:90% some really unexpected results. 00:59:58.360 --> 01:00:02.250 align:middle line:84% As you can imagine, if this is your crystal, 01:00:02.250 --> 01:00:04.780 align:middle line:84% and you're looking down the 1,0,0 channel axis-- 01:00:04.780 --> 01:00:06.750 align:middle line:84% so these are all the open spaces. 01:00:06.750 --> 01:00:09.810 align:middle line:84% If you happen to be aligned, the beam, right to that axis, 01:00:09.810 --> 01:00:12.270 align:middle line:84% you can get profiles that go a lot deeper than you 01:00:12.270 --> 01:00:14.230 align:middle line:90% would have expected. 01:00:14.230 --> 01:00:17.490 align:middle line:84% So this is an example of implanting phosphorus at 40 keV 01:00:17.490 --> 01:00:19.060 align:middle line:90% into silicon. 01:00:19.060 --> 01:00:22.210 align:middle line:84% And here's the concentration of phosphorus 01:00:22.210 --> 01:00:24.160 align:middle line:90% as a function of depth. 01:00:24.160 --> 01:00:25.840 align:middle line:84% And in fact, looking at different doses, 01:00:25.840 --> 01:00:28.930 align:middle line:84% the very low dose here is about 1 times 10 to the 13th. 01:00:28.930 --> 01:00:32.678 align:middle line:84% Look how deep the phosphorus went, all the way down to-- 01:00:32.678 --> 01:00:33.220 align:middle line:90% I don't know. 01:00:33.220 --> 01:00:34.460 align:middle line:90% It's got the shoulder here. 01:00:34.460 --> 01:00:37.810 align:middle line:84% Goes down to about 0.6 or 0.8 microns. 01:00:37.810 --> 01:00:40.120 align:middle line:84% As we go higher in dose, notice this. 01:00:40.120 --> 01:00:42.730 align:middle line:84% The very highest dose 7 times 10 to the 14th, 01:00:42.730 --> 01:00:46.130 align:middle line:84% you don't see that channeling tail. 01:00:46.130 --> 01:00:47.150 align:middle line:90% Why would that be? 01:00:47.150 --> 01:00:50.150 align:middle line:84% Does anybody have any idea why this very high dose 01:00:50.150 --> 01:00:53.930 align:middle line:84% implant didn't go in real deeply, whereas the low dose 01:00:53.930 --> 01:00:54.470 align:middle line:90% one did? 01:00:54.470 --> 01:01:02.820 align:middle line:90% 01:01:02.820 --> 01:01:03.960 align:middle line:90% [INAUDIBLE] 01:01:03.960 --> 01:01:10.890 align:middle line:90% 01:01:10.890 --> 01:01:11.400 align:middle line:90% OK. 01:01:11.400 --> 01:01:13.240 align:middle line:84% So you have a high dose is coming in. 01:01:13.240 --> 01:01:15.930 align:middle line:84% So what is that dose going to do to that beautiful crystal, all 01:01:15.930 --> 01:01:17.130 align:middle line:90% those beautiful channels? 01:01:17.130 --> 01:01:18.760 align:middle line:90% Smash them up. 01:01:18.760 --> 01:01:20.370 align:middle line:84% Basically, just imagine taking that, 01:01:20.370 --> 01:01:22.620 align:middle line:84% just throwing a bunch of baseballs at that thing. 01:01:22.620 --> 01:01:25.080 align:middle line:84% And pretty soon after you've thrown enough baseballs, 01:01:25.080 --> 01:01:26.700 align:middle line:84% that perfectly nice-looking channel, 01:01:26.700 --> 01:01:28.200 align:middle line:84% there's a whole bunch of atoms in it 01:01:28.200 --> 01:01:30.450 align:middle line:84% because you completely randomized the crystal. 01:01:30.450 --> 01:01:32.940 align:middle line:90% And that's called amorphization. 01:01:32.940 --> 01:01:36.150 align:middle line:84% So when you put in enough dose, you throw enough baseballs 01:01:36.150 --> 01:01:37.990 align:middle line:84% at this thing that you randomly-- now, 01:01:37.990 --> 01:01:39.990 align:middle line:84% instead of having a beautiful crystal structure, 01:01:39.990 --> 01:01:41.730 align:middle line:84% the silicon is completely amorphous. 01:01:41.730 --> 01:01:43.860 align:middle line:90% There is no structure left. 01:01:43.860 --> 01:01:46.950 align:middle line:84% Then you are going in, and now this implant 01:01:46.950 --> 01:01:48.540 align:middle line:84% was essentially done, most of it, 01:01:48.540 --> 01:01:50.332 align:middle line:84% into a material that didn't look like this. 01:01:50.332 --> 01:01:52.080 align:middle line:84% It just looks like an amorphous mess. 01:01:52.080 --> 01:01:54.540 align:middle line:84% And that's why you don't get this channeling tail. 01:01:54.540 --> 01:01:56.610 align:middle line:84% This implant was such a low dose, 01:01:56.610 --> 01:01:59.040 align:middle line:84% it barely did damage the crystal at all. 01:01:59.040 --> 01:02:01.600 align:middle line:84% The crystal maintained its nice structure, 01:02:01.600 --> 01:02:07.870 align:middle line:84% and so the ions were able to channel in and go very deeply. 01:02:07.870 --> 01:02:10.020 align:middle line:84% So this is bad because it turns out 01:02:10.020 --> 01:02:12.240 align:middle line:84% it's very hard to control what this tail looks like. 01:02:12.240 --> 01:02:15.010 align:middle line:84% And a lot of times, you don't want such a deep profile. 01:02:15.010 --> 01:02:16.950 align:middle line:84% So in fact, in this case, channeling 01:02:16.950 --> 01:02:18.705 align:middle line:84% is viewed as something one wants to avoid. 01:02:18.705 --> 01:02:21.570 align:middle line:90% 01:02:21.570 --> 01:02:24.780 align:middle line:84% Actually on page 28, here's another example, 01:02:24.780 --> 01:02:27.390 align:middle line:90% just as we just saw, of boron. 01:02:27.390 --> 01:02:30.150 align:middle line:84% Boron is a famous ion for doing a lot of channeling. 01:02:30.150 --> 01:02:32.760 align:middle line:84% It tends to be steered very easily. 01:02:32.760 --> 01:02:38.130 align:middle line:84% One problem with ion channeling is that the profile shapes 01:02:38.130 --> 01:02:41.190 align:middle line:84% don't scale with those because, again, a low dose doesn't 01:02:41.190 --> 01:02:42.750 align:middle line:90% damage the profile much. 01:02:42.750 --> 01:02:47.710 align:middle line:84% A high dose here, like 2E15, does a lot of damage. 01:02:47.710 --> 01:02:51.270 align:middle line:84% And so this green profile is not simply 01:02:51.270 --> 01:02:54.900 align:middle line:84% equal to the 2E13 profile, bumped up 01:02:54.900 --> 01:02:56.763 align:middle line:90% by 2 orders of magnitude. 01:02:56.763 --> 01:02:58.180 align:middle line:84% That's what you think it would be. 01:02:58.180 --> 01:03:00.240 align:middle line:84% But in fact, it's got a different shape 01:03:00.240 --> 01:03:01.843 align:middle line:84% because as you were doing the implant, 01:03:01.843 --> 01:03:03.510 align:middle line:84% you're doing a certain amount of damage, 01:03:03.510 --> 01:03:05.820 align:middle line:84% and you're changing the appearance 01:03:05.820 --> 01:03:07.920 align:middle line:90% of the crystal and channels. 01:03:07.920 --> 01:03:10.130 align:middle line:84% So there's all kinds of issues when you're 01:03:10.130 --> 01:03:14.230 align:middle line:90% trying to model ion channeling. 01:03:14.230 --> 01:03:16.535 align:middle line:84% Page 28 actually has a little bit more information 01:03:16.535 --> 01:03:17.410 align:middle line:90% about ion channeling. 01:03:17.410 --> 01:03:19.120 align:middle line:84% There is something in ion channeling 01:03:19.120 --> 01:03:20.770 align:middle line:90% called the critical angle. 01:03:20.770 --> 01:03:22.670 align:middle line:90% What is the critical angle, psi? 01:03:22.670 --> 01:03:24.730 align:middle line:90% Well, it's the maximum angle. 01:03:24.730 --> 01:03:28.330 align:middle line:84% It's the largest angle of the incoming beam with respect 01:03:28.330 --> 01:03:32.050 align:middle line:84% to the axis of the channel before the steering 01:03:32.050 --> 01:03:34.220 align:middle line:90% action of the row is lost. 01:03:34.220 --> 01:03:37.060 align:middle line:84% So at this angle, you can just barely come in 01:03:37.060 --> 01:03:40.130 align:middle line:84% and be steered and go in and out and in and out. 01:03:40.130 --> 01:03:42.130 align:middle line:84% And if you have a slightly higher angle, what's 01:03:42.130 --> 01:03:44.213 align:middle line:84% going to happen is you're going to get knocked out 01:03:44.213 --> 01:03:45.127 align:middle line:90% of the channel. 01:03:45.127 --> 01:03:46.960 align:middle line:84% So that critical angle is important to know. 01:03:46.960 --> 01:03:49.750 align:middle line:84% It tells you how well does the beam have to be aligned 01:03:49.750 --> 01:03:54.570 align:middle line:84% to the channel to be sure that you get this channeling effect. 01:03:54.570 --> 01:03:57.240 align:middle line:84% And psi, see here what's called the critical angle, 01:03:57.240 --> 01:04:00.620 align:middle line:84% in fact the reference above has a little bit of information 01:04:00.620 --> 01:04:01.860 align:middle line:90% on how to calculate it. 01:04:01.860 --> 01:04:05.270 align:middle line:84% And these are some examples of critical angles. 01:04:05.270 --> 01:04:09.350 align:middle line:84% Say, along the 1,1,0 direction for boron is 3 degrees. 01:04:09.350 --> 01:04:11.840 align:middle line:90% Arsenic is about 4.4. 01:04:11.840 --> 01:04:14.840 align:middle line:84% So it gives you an idea, if this is my crystal 01:04:14.840 --> 01:04:17.170 align:middle line:84% and I'm coming in, well, if I'm within 3 01:04:17.170 --> 01:04:19.520 align:middle line:84% or 4 degrees of that axis, I'm going 01:04:19.520 --> 01:04:21.890 align:middle line:90% to get a lot of channeling. 01:04:21.890 --> 01:04:25.190 align:middle line:84% If I tilt the crystal, so I'm outside 3 or 4 degrees-- say, 01:04:25.190 --> 01:04:27.290 align:middle line:90% I'm at 7 degree tilt-- 01:04:27.290 --> 01:04:29.810 align:middle line:84% most of the ions will come in, and they won't actually 01:04:29.810 --> 01:04:31.130 align:middle line:90% be aligned with the channel. 01:04:31.130 --> 01:04:33.420 align:middle line:84% So you won't get much channeling. 01:04:33.420 --> 01:04:35.457 align:middle line:84% So it kind of gives you an idea of how much 01:04:35.457 --> 01:04:37.290 align:middle line:84% accuracy, when you're shooting your ions in, 01:04:37.290 --> 01:04:41.138 align:middle line:84% do you have to have to enable channeling. 01:04:41.138 --> 01:04:45.570 align:middle line:90% 01:04:45.570 --> 01:04:47.250 align:middle line:84% As we see here on slide 20, people 01:04:47.250 --> 01:04:50.400 align:middle line:84% do something called controlled misalignment of the crystal 01:04:50.400 --> 01:04:53.730 align:middle line:84% when they put the wafers in the ion implanter. 01:04:53.730 --> 01:04:56.160 align:middle line:84% And they don't put them in like this. 01:04:56.160 --> 01:04:58.410 align:middle line:84% They try not to put them in so you're looking straight 01:04:58.410 --> 01:04:59.730 align:middle line:90% down the 1,0,0 axis. 01:04:59.730 --> 01:05:01.507 align:middle line:84% What they do is, they take the wafer 01:05:01.507 --> 01:05:03.090 align:middle line:84% and they put it on the plate, and they 01:05:03.090 --> 01:05:05.298 align:middle line:84% tilt the plate a little bit with respect to the beam. 01:05:05.298 --> 01:05:08.130 align:middle line:84% In fact, typical tilts are about 7 degrees. 01:05:08.130 --> 01:05:10.150 align:middle line:84% And they actually also rotate it. 01:05:10.150 --> 01:05:12.500 align:middle line:84% So if I've just taken this crystal here, 01:05:12.500 --> 01:05:15.630 align:middle line:84% and in the computer, they tilted the crystal and rotate it. 01:05:15.630 --> 01:05:18.690 align:middle line:84% And look, lo and behold, a perfectly crystalline material 01:05:18.690 --> 01:05:22.190 align:middle line:84% all of a sudden looks somewhat random to the eye. 01:05:22.190 --> 01:05:25.395 align:middle line:84% And so it looks somewhat random to the incoming beam. 01:05:25.395 --> 01:05:26.270 align:middle line:90% You see the channels. 01:05:26.270 --> 01:05:27.728 align:middle line:84% A lot of them have now been blocked 01:05:27.728 --> 01:05:29.180 align:middle line:90% by the tilting and rotation. 01:05:29.180 --> 01:05:30.830 align:middle line:84% And when it looks random, that's good. 01:05:30.830 --> 01:05:34.432 align:middle line:84% That means you're not going to have a lot of channeling. 01:05:34.432 --> 01:05:36.140 align:middle line:84% You can never get rid of it all together. 01:05:36.140 --> 01:05:37.820 align:middle line:90% You can minimize it. 01:05:37.820 --> 01:05:39.780 align:middle line:84% Because the problem is, as I come in here, 01:05:39.780 --> 01:05:42.050 align:middle line:84% it looks pretty random, but then I might get knocked. 01:05:42.050 --> 01:05:45.890 align:middle line:84% Maybe I get knocked by 7 degrees and rotated some of the ions, 01:05:45.890 --> 01:05:49.940 align:middle line:84% and they get knocked back into a channel. 01:05:49.940 --> 01:05:52.700 align:middle line:84% So you can scatter incident ions back 01:05:52.700 --> 01:05:55.290 align:middle line:84% into channeling directions in their first few collisions. 01:05:55.290 --> 01:05:58.250 align:middle line:84% So you can't get rid of it, but you can minimize it. 01:05:58.250 --> 01:06:01.280 align:middle line:84% And ions that are not channeled early in the process, 01:06:01.280 --> 01:06:04.250 align:middle line:84% as they get closer to their end of range, as they lose energy, 01:06:04.250 --> 01:06:05.540 align:middle line:90% the critical angle increases. 01:06:05.540 --> 01:06:06.832 align:middle line:90% In fact, I didn't mention that. 01:06:06.832 --> 01:06:09.920 align:middle line:84% If I go back one page to slide 28, 01:06:09.920 --> 01:06:11.720 align:middle line:84% this was [? Linhart's ?] expression 01:06:11.720 --> 01:06:13.130 align:middle line:90% for the critical angle. 01:06:13.130 --> 01:06:16.940 align:middle line:84% It depends on some constant, e1, divided by e. 01:06:16.940 --> 01:06:19.490 align:middle line:90% So this psi goes up. 01:06:19.490 --> 01:06:23.040 align:middle line:84% As I get slower and slower, then the critical angle goes up, 01:06:23.040 --> 01:06:24.830 align:middle line:84% so the probability of channeling is 01:06:24.830 --> 01:06:29.570 align:middle line:84% going to be bigger at the tail of a profile. 01:06:29.570 --> 01:06:32.840 align:middle line:84% In fact, you see that on slide 30. 01:06:32.840 --> 01:06:34.520 align:middle line:84% That's very evident when we actually 01:06:34.520 --> 01:06:38.060 align:middle line:84% look at a profile that was ion implanted, 01:06:38.060 --> 01:06:43.340 align:middle line:84% where we tried to eliminate channeling by tilting 01:06:43.340 --> 01:06:48.810 align:middle line:84% the profile, tilting the wafer by 7 degrees off the 1,1,1 axis. 01:06:48.810 --> 01:06:51.110 align:middle line:84% So this is concentration versus depth, 01:06:51.110 --> 01:06:55.618 align:middle line:84% and there's a couple of different profiles here. 01:06:55.618 --> 01:06:57.410 align:middle line:84% In fact, what people were trying to do was, 01:06:57.410 --> 01:06:59.600 align:middle line:84% they were also trying to cover the wafer 01:06:59.600 --> 01:07:01.130 align:middle line:90% with an amorphous material. 01:07:01.130 --> 01:07:03.980 align:middle line:84% People thought, oh, well, if I-- why don't I 01:07:03.980 --> 01:07:05.810 align:middle line:84% put a layer of something amorphous? 01:07:05.810 --> 01:07:07.310 align:middle line:84% That will prevent channeling, right? 01:07:07.310 --> 01:07:09.920 align:middle line:84% Because I'm covering up the crystal with these 01:07:09.920 --> 01:07:11.600 align:middle line:90% amorphous material. 01:07:11.600 --> 01:07:14.060 align:middle line:84% But in fact, it doesn't really avoid channeling. 01:07:14.060 --> 01:07:17.000 align:middle line:84% Putting on a little bit of nitride doesn't really help. 01:07:17.000 --> 01:07:20.480 align:middle line:84% You still get this so-called exponential channeling tail. 01:07:20.480 --> 01:07:24.530 align:middle line:84% You see, all four profiles have this exponential tail. 01:07:24.530 --> 01:07:25.610 align:middle line:90% That's due to channeling. 01:07:25.610 --> 01:07:28.010 align:middle line:84% As the ions get to their end of range, 01:07:28.010 --> 01:07:30.897 align:middle line:84% these ions down here have lost a lot of their energy. 01:07:30.897 --> 01:07:33.480 align:middle line:84% When they get to this point, the critical angle for channeling 01:07:33.480 --> 01:07:35.355 align:middle line:84% goes up because it's much more likely they 01:07:35.355 --> 01:07:36.480 align:middle line:90% get steered into a channel. 01:07:36.480 --> 01:07:38.170 align:middle line:84% And oops, they go a little further. 01:07:38.170 --> 01:07:43.230 align:middle line:84% So this tail is called residual channeling. 01:07:43.230 --> 01:07:47.400 align:middle line:84% Even an amorphous overlayer will not eliminate it, 01:07:47.400 --> 01:07:49.470 align:middle line:84% and tilting the sample will not eliminate. 01:07:49.470 --> 01:07:52.050 align:middle line:84% So this tail does need to be modeled 01:07:52.050 --> 01:07:55.110 align:middle line:84% if you want to get a very accurate simulation of what 01:07:55.110 --> 01:07:56.610 align:middle line:90% your profile really looks like. 01:07:56.610 --> 01:08:01.480 align:middle line:90% 01:08:01.480 --> 01:08:04.260 align:middle line:84% So let me just summarize a little bit about-- 01:08:04.260 --> 01:08:06.660 align:middle line:84% so far, I haven't talked about the physics of scattering 01:08:06.660 --> 01:08:08.160 align:middle line:90% or of stopping or whatever. 01:08:08.160 --> 01:08:11.700 align:middle line:84% But we've just talked about how one analytically might 01:08:11.700 --> 01:08:15.100 align:middle line:90% treat ion implant profiles. 01:08:15.100 --> 01:08:18.240 align:middle line:84% We have a Gaussian distribution, which has two coefficients. 01:08:18.240 --> 01:08:19.290 align:middle line:90% It does an OK job. 01:08:19.290 --> 01:08:20.850 align:middle line:84% It's not very good, but it's good. 01:08:20.850 --> 01:08:21.600 align:middle line:90% It's OK. 01:08:21.600 --> 01:08:23.819 align:middle line:84% Pearson IV has four coefficients. 01:08:23.819 --> 01:08:25.859 align:middle line:84% It's very good for amorphous, but it 01:08:25.859 --> 01:08:27.990 align:middle line:90% doesn't include channeling. 01:08:27.990 --> 01:08:30.939 align:middle line:84% If I take Pearson IV, and I add an exponential tail, 01:08:30.939 --> 01:08:34.590 align:middle line:84% so now I need six coefficients, I can include channeling. 01:08:34.590 --> 01:08:37.660 align:middle line:90% And it works in some cases. 01:08:37.660 --> 01:08:40.410 align:middle line:84% There's something called a dual Pearson, which we'll talk about. 01:08:40.410 --> 01:08:43.109 align:middle line:84% That's two Pearson profiles superimposed, 01:08:43.109 --> 01:08:44.859 align:middle line:90% has nine coefficients. 01:08:44.859 --> 01:08:46.810 align:middle line:84% So look, as I'm going from top to bottom, 01:08:46.810 --> 01:08:49.170 align:middle line:84% I'm adding more and more free parameters. 01:08:49.170 --> 01:08:50.939 align:middle line:84% Of course, you can model anything. 01:08:50.939 --> 01:08:53.550 align:middle line:84% You can model an elephant with enough free parameters. 01:08:53.550 --> 01:08:55.830 align:middle line:84% Legendre polynomials have 19 coefficients. 01:08:55.830 --> 01:08:57.840 align:middle line:84% That's getting kind of ridiculous. 01:08:57.840 --> 01:09:00.930 align:middle line:84% But there are tables of a lot of these coefficients 01:09:00.930 --> 01:09:04.710 align:middle line:84% that are built into textbooks or into SUPREM-IV. 01:09:04.710 --> 01:09:07.319 align:middle line:84% And they have a lot of these coefficients 01:09:07.319 --> 01:09:11.920 align:middle line:84% as a function of mass, energy, dose, tilt angle, all that. 01:09:11.920 --> 01:09:14.180 align:middle line:84% These analytic calculations are very fast. 01:09:14.180 --> 01:09:15.319 align:middle line:90% They're very efficient. 01:09:15.319 --> 01:09:17.109 align:middle line:84% But you have to be very careful when 01:09:17.109 --> 01:09:20.620 align:middle line:84% you're using them because the coefficients for dual Pearson 01:09:20.620 --> 01:09:24.189 align:middle line:84% or coefficients for this Legendre polynomials, 01:09:24.189 --> 01:09:26.590 align:middle line:84% whatever it is, a lot of times people 01:09:26.590 --> 01:09:28.510 align:middle line:84% are just fitting experimental data, which 01:09:28.510 --> 01:09:30.050 align:middle line:90% may have artifacts of its own. 01:09:30.050 --> 01:09:32.920 align:middle line:84% Remember, when we talked about SIMS, 01:09:32.920 --> 01:09:34.850 align:middle line:84% we talked about a knock-on process. 01:09:34.850 --> 01:09:38.439 align:middle line:84% So SIMS itself will tend to produce tails, 01:09:38.439 --> 01:09:42.399 align:middle line:84% just from the secondary ion mass spectrometers, 01:09:42.399 --> 01:09:44.359 align:middle line:84% from the analytical technique I used. 01:09:44.359 --> 01:09:45.880 align:middle line:84% So you have to be sure that somebody 01:09:45.880 --> 01:09:51.700 align:middle line:84% wasn't actually modeling an experimental artifact. 01:09:51.700 --> 01:09:53.439 align:middle line:84% Anything based on tables, you have 01:09:53.439 --> 01:09:57.130 align:middle line:84% to take with a grain of salt and just be a little careful. 01:09:57.130 --> 01:09:58.780 align:middle line:90% Check it out. 01:09:58.780 --> 01:10:03.520 align:middle line:84% Slide 32 actually just shows you some SUPREM-IV, 01:10:03.520 --> 01:10:08.020 align:middle line:84% four different models of varying complexity for modeling 01:10:08.020 --> 01:10:10.000 align:middle line:90% a particular implant. 01:10:10.000 --> 01:10:11.960 align:middle line:84% These are concentration contours. 01:10:11.960 --> 01:10:14.540 align:middle line:84% Each color or each grayscale represents 01:10:14.540 --> 01:10:18.560 align:middle line:84% a different concentration of the dopant. 01:10:18.560 --> 01:10:21.980 align:middle line:84% This is a polysilicon mask edge, so none of the dopant 01:10:21.980 --> 01:10:25.520 align:middle line:84% can make it into the mask over here. 01:10:25.520 --> 01:10:27.950 align:middle line:84% And it only is implanted on the right-hand side. 01:10:27.950 --> 01:10:31.400 align:middle line:90% 01:10:31.400 --> 01:10:34.040 align:middle line:84% So it's particularly tricky to get the right profile. 01:10:34.040 --> 01:10:35.840 align:middle line:84% So this particular model, upper left, 01:10:35.840 --> 01:10:38.490 align:middle line:84% is assuming you're going into amorphous silicon, 01:10:38.490 --> 01:10:41.340 align:middle line:90% so it has a very simple shape. 01:10:41.340 --> 01:10:44.010 align:middle line:84% This is assuming the dual Pearson type of model, 01:10:44.010 --> 01:10:46.250 align:middle line:84% so it's going to have some skewness. 01:10:46.250 --> 01:10:48.770 align:middle line:84% This particular profile is dual Pearson, 01:10:48.770 --> 01:10:50.840 align:middle line:84% where there are extra coefficients that 01:10:50.840 --> 01:10:53.550 align:middle line:84% take into account tilt of the wafer and rotation. 01:10:53.550 --> 01:10:56.450 align:middle line:84% You can see it looks quite different from that. 01:10:56.450 --> 01:10:58.850 align:middle line:84% All three of these here in the upper left corner, 01:10:58.850 --> 01:11:00.530 align:middle line:84% these three are what we call analytic. 01:11:00.530 --> 01:11:04.370 align:middle line:84% They're based on these equations that we've been talking about. 01:11:04.370 --> 01:11:06.260 align:middle line:84% Monte Carlo model is quite different, 01:11:06.260 --> 01:11:07.760 align:middle line:84% and we'll talk about that next time. 01:11:07.760 --> 01:11:09.830 align:middle line:84% Monte Carlo, literally in the computer, 01:11:09.830 --> 01:11:12.238 align:middle line:84% you shoot ions into the crystal, and you follow 01:11:12.238 --> 01:11:13.280 align:middle line:90% the scattering processes. 01:11:13.280 --> 01:11:15.470 align:middle line:84% And you will see where all those ions end up. 01:11:15.470 --> 01:11:16.430 align:middle line:90% A computer can do that. 01:11:16.430 --> 01:11:20.180 align:middle line:84% It can sit there all day, and it can calculate the trajectories 01:11:20.180 --> 01:11:23.820 align:middle line:84% for 10,000 ions and then plot their statistical distribution. 01:11:23.820 --> 01:11:25.920 align:middle line:84% So Monte Carlo tends to be quite accurate 01:11:25.920 --> 01:11:27.170 align:middle line:90% if you have enough physics in. 01:11:27.170 --> 01:11:28.628 align:middle line:84% Unfortunately, it takes a long time 01:11:28.628 --> 01:11:31.170 align:middle line:84% because the computer has to go in there and follow every ion, 01:11:31.170 --> 01:11:34.470 align:middle line:90% see where it ended up. 01:11:34.470 --> 01:11:38.970 align:middle line:84% Here's an example, actually, a few words about Monte Carlo. 01:11:38.970 --> 01:11:41.310 align:middle line:84% What you do is, you integrate the equation 01:11:41.310 --> 01:11:45.900 align:middle line:84% of motion for a representative ion from the point 01:11:45.900 --> 01:11:47.940 align:middle line:84% when it hits the surface of the silicon 01:11:47.940 --> 01:11:51.990 align:middle line:84% until the point where it comes to a rest, where it stops. 01:11:51.990 --> 01:11:53.640 align:middle line:90% And you repeat this process. 01:11:53.640 --> 01:11:56.820 align:middle line:84% You follow the ions for as many times as you can, 01:11:56.820 --> 01:12:01.810 align:middle line:84% using random starting impact parameters. 01:12:01.810 --> 01:12:04.990 align:middle line:84% And there is this so-called law of large numbers 01:12:04.990 --> 01:12:09.670 align:middle line:84% that says, the error, the scatter in what you're 01:12:09.670 --> 01:12:13.630 align:middle line:84% going to see, goes like 1 over the square root of n. 01:12:13.630 --> 01:12:17.860 align:middle line:84% So if you want three decades of a profile to be accurate, 01:12:17.860 --> 01:12:19.510 align:middle line:90% then you need-- 01:12:19.510 --> 01:12:23.080 align:middle line:84% with less than 10% error-- you need 10 to the 5th ions. 01:12:23.080 --> 01:12:27.400 align:middle line:84% So 10,000 ions, or 100,000 ions, rather, is about the minimum 01:12:27.400 --> 01:12:29.607 align:middle line:84% that you need to get a nice smooth profile. 01:12:29.607 --> 01:12:30.940 align:middle line:90% So that's going to take a while. 01:12:30.940 --> 01:12:32.967 align:middle line:84% You can try on some of your homework, 01:12:32.967 --> 01:12:35.050 align:middle line:84% so you may end up trying a Monte Carlo simulation. 01:12:35.050 --> 01:12:35.440 align:middle line:90% You could see. 01:12:35.440 --> 01:12:36.940 align:middle line:84% It could take half an hour, it could 01:12:36.940 --> 01:12:38.650 align:middle line:84% take overnight simulating one implant, 01:12:38.650 --> 01:12:41.830 align:middle line:84% depending on how many ions you need to follow. 01:12:41.830 --> 01:12:44.650 align:middle line:84% This is an example of some Monte Carlo simulations 01:12:44.650 --> 01:12:48.100 align:middle line:84% that were published back in 1997 for-- 01:12:48.100 --> 01:12:51.670 align:middle line:84% here, they're doing relatively low-energy boron. 01:12:51.670 --> 01:12:54.310 align:middle line:84% And get that here, 0.5 keV, 1 keV. 01:12:54.310 --> 01:12:57.700 align:middle line:84% And you can see the statistical nature of these profiles. 01:12:57.700 --> 01:13:01.540 align:middle line:84% The simulations are these little boxed sort 01:13:01.540 --> 01:13:03.910 align:middle line:84% of digitized looking things because they're actually 01:13:03.910 --> 01:13:06.910 align:middle line:84% following individual ions and trying to build up 01:13:06.910 --> 01:13:08.720 align:middle line:90% a distribution based on that. 01:13:08.720 --> 01:13:11.823 align:middle line:84% So the nice thing is you can get reasonable accuracy. 01:13:11.823 --> 01:13:13.240 align:middle line:84% The bad thing is it could take you 01:13:13.240 --> 01:13:15.850 align:middle line:84% days if you're trying to fit a profile, literally 01:13:15.850 --> 01:13:19.300 align:middle line:90% days to do that. 01:13:19.300 --> 01:13:20.820 align:middle line:84% And before we finish up, I wanted 01:13:20.820 --> 01:13:23.280 align:middle line:84% to mention there's one other type of calculation that's 01:13:23.280 --> 01:13:28.710 align:middle line:84% not very popular but was developed a while back 01:13:28.710 --> 01:13:31.680 align:middle line:84% and actually is kind of a compromise between Monte Carlo 01:13:31.680 --> 01:13:32.550 align:middle line:90% and analytic. 01:13:32.550 --> 01:13:35.100 align:middle line:84% It's something called the Boltzmann Transport Equation, 01:13:35.100 --> 01:13:38.070 align:middle line:90% or the BTE, developed by Giles. 01:13:38.070 --> 01:13:41.730 align:middle line:84% And he was able to write down a Boltzmann transport equation 01:13:41.730 --> 01:13:45.990 align:middle line:84% and then model an ion distribution. 01:13:45.990 --> 01:13:47.880 align:middle line:84% Instead of following individual ions, 01:13:47.880 --> 01:13:50.220 align:middle line:84% he was following the distribution, the momentum 01:13:50.220 --> 01:13:53.170 align:middle line:84% and the energy distribution of these ions. 01:13:53.170 --> 01:13:55.980 align:middle line:84% So there's economy of scale in doing that. 01:13:55.980 --> 01:13:58.890 align:middle line:84% And he actually followed the distribution as it changed 01:13:58.890 --> 01:14:01.650 align:middle line:84% and as it evolves in the computer. 01:14:01.650 --> 01:14:03.660 align:middle line:84% I won't go into the detail, but basically 01:14:03.660 --> 01:14:07.380 align:middle line:84% by following distributions instead of following ions, 01:14:07.380 --> 01:14:09.480 align:middle line:84% it's much faster than Monte Carlo. 01:14:09.480 --> 01:14:11.250 align:middle line:84% But it can have as good accuracy. 01:14:11.250 --> 01:14:13.510 align:middle line:84% Unfortunately, it never became very popular, 01:14:13.510 --> 01:14:15.630 align:middle line:84% so I don't think it's in SUPREM-IV. 01:14:15.630 --> 01:14:17.880 align:middle line:84% There may be some versions of simulators out there out 01:14:17.880 --> 01:14:20.250 align:middle line:84% in the world, though, you may come upon that have 01:14:20.250 --> 01:14:22.040 align:middle line:90% BTE method for ion implant. 01:14:22.040 --> 01:14:23.800 align:middle line:84% I think it's actually a very good method. 01:14:23.800 --> 01:14:25.990 align:middle line:84% It's just too bad it didn't catch on in a big way. 01:14:25.990 --> 01:14:29.450 align:middle line:90% 01:14:29.450 --> 01:14:32.920 align:middle line:84% So on slide 35, let me summarize. 01:14:32.920 --> 01:14:35.230 align:middle line:84% We saw the ion implant is the preferred process 01:14:35.230 --> 01:14:36.290 align:middle line:90% for introducing dopants. 01:14:36.290 --> 01:14:37.360 align:middle line:90% It has excellent control. 01:14:37.360 --> 01:14:40.750 align:middle line:84% It's very reproducible and uniform. 01:14:40.750 --> 01:14:44.560 align:middle line:84% The key parameters, energy of the incoming beam, the dose, 01:14:44.560 --> 01:14:46.990 align:middle line:84% the tilt of the wafer with respect to the beam, 01:14:46.990 --> 01:14:49.750 align:middle line:84% the rotation of the axis of the wafer, 01:14:49.750 --> 01:14:52.842 align:middle line:84% whether there are any masking materials on the wafer. 01:14:52.842 --> 01:14:55.300 align:middle line:84% Controlling the temperature of the wafer during the implant 01:14:55.300 --> 01:14:58.608 align:middle line:84% is actually somewhat important because it'll 01:14:58.608 --> 01:15:00.400 align:middle line:84% control the damage to a certain extent that 01:15:00.400 --> 01:15:01.780 align:middle line:90% gets done to the crystal. 01:15:01.780 --> 01:15:04.133 align:middle line:84% The dose rate, the beam current, how quickly 01:15:04.133 --> 01:15:05.050 align:middle line:90% are you putting it in. 01:15:05.050 --> 01:15:06.730 align:middle line:84% Actually, the dose rate determines 01:15:06.730 --> 01:15:09.860 align:middle line:84% how much you heat the wafer up, and that's important. 01:15:09.860 --> 01:15:13.000 align:middle line:84% So in practice, there are a number of key parameters. 01:15:13.000 --> 01:15:16.300 align:middle line:84% There are tables for the first three moments, Rp, delta Rp, 01:15:16.300 --> 01:15:22.080 align:middle line:84% and skewness, that you can get out of the literature. 01:15:22.080 --> 01:15:25.640 align:middle line:84% The most popular analytic equation to use or formulation 01:15:25.640 --> 01:15:28.250 align:middle line:84% is the Pearson IV for nonchanneling. 01:15:28.250 --> 01:15:31.340 align:middle line:84% If you want to model channeling, you need more parameters 01:15:31.340 --> 01:15:32.750 align:middle line:90% than four. 01:15:32.750 --> 01:15:37.580 align:middle line:84% Usually, people use dual Pearson and lookup tables. 01:15:37.580 --> 01:15:41.453 align:middle line:84% Monte Carlo is slow, but it's probably the most accurate 01:15:41.453 --> 01:15:42.620 align:middle line:90% or one of the most accurate. 01:15:42.620 --> 01:15:46.430 align:middle line:84% The BTE is another approach you may find in the literature. 01:15:46.430 --> 01:15:48.800 align:middle line:84% It's an alternative to Monte Carlo, 01:15:48.800 --> 01:15:53.150 align:middle line:84% but it's faster, but not that widely used. 01:15:53.150 --> 01:15:54.685 align:middle line:84% What I didn't get to cover today, 01:15:54.685 --> 01:15:56.060 align:middle line:84% we'll spend the lecture next time 01:15:56.060 --> 01:15:58.340 align:middle line:84% on the detailed physics of these billiard ball 01:15:58.340 --> 01:16:00.530 align:middle line:84% collisions, the physics and modeling 01:16:00.530 --> 01:16:03.350 align:middle line:84% of this nuclear stopping, these collisions 01:16:03.350 --> 01:16:04.910 align:middle line:90% and this electronic drag force. 01:16:04.910 --> 01:16:07.370 align:middle line:84% So we can actually see in more detail 01:16:07.370 --> 01:16:09.110 align:middle line:90% how the physics of the implant. 01:16:09.110 --> 01:16:12.170 align:middle line:84% Today, I just mostly talked about practical aspects. 01:16:12.170 --> 01:16:14.870 align:middle line:84% OK, if you came in late, a couple reminders. 01:16:14.870 --> 01:16:17.090 align:middle line:90% Pick up this handout number 20. 01:16:17.090 --> 01:16:19.100 align:middle line:84% This describes your final term projects. 01:16:19.100 --> 01:16:22.040 align:middle line:84% And next time, I'm going to bring a sign-up sheet. 01:16:22.040 --> 01:16:25.610 align:middle line:84% You can sign up for the topic you want to use or study, 01:16:25.610 --> 01:16:27.080 align:middle line:84% and most importantly, whether you 01:16:27.080 --> 01:16:32.000 align:middle line:84% want to do an oral report or a written report. 01:16:32.000 --> 01:16:34.660 align:middle line:84% And next time, I'll have the homework. 01:16:34.660 --> 01:16:37.000 align:middle line:90%