WEBVTT 00:00:00.000 --> 00:00:01.510 align:middle line:90% 00:00:01.510 --> 00:00:03.850 align:middle line:84% JUDY HOYT: So we're moving along pretty quickly 00:00:03.850 --> 00:00:05.860 align:middle line:84% with the first part of the course here. 00:00:05.860 --> 00:00:10.060 align:middle line:84% I'm hoping you'll be reading Chapter 3 of the textbook 00:00:10.060 --> 00:00:13.450 align:middle line:84% at this point, which is on-- covers crystal growth, wafer 00:00:13.450 --> 00:00:16.000 align:middle line:84% fabrication, and some of the basic properties of silicon. 00:00:16.000 --> 00:00:18.640 align:middle line:84% I'm going to finish up Chapter 3-- 00:00:18.640 --> 00:00:20.590 align:middle line:90% the lectures on Chapter 3 today. 00:00:20.590 --> 00:00:22.720 align:middle line:84% And then I'm going to start Chapter 4, 00:00:22.720 --> 00:00:24.910 align:middle line:90% so you can start that as well. 00:00:24.910 --> 00:00:27.670 align:middle line:84% Chapter 4 is relatively easy reading, 00:00:27.670 --> 00:00:30.370 align:middle line:90% not tremendously mathematical. 00:00:30.370 --> 00:00:32.018 align:middle line:90% It's about how we-- 00:00:32.018 --> 00:00:33.560 align:middle line:84% although it's a very important topic. 00:00:33.560 --> 00:00:36.280 align:middle line:84% It's about how we clean wafers and how we 00:00:36.280 --> 00:00:39.352 align:middle line:90% get our impurities in wafers. 00:00:39.352 --> 00:00:42.060 align:middle line:84% So the last lecture, let me just remind you what we talked about. 00:00:42.060 --> 00:00:45.210 align:middle line:84% We talked about cubic crystal structures. 00:00:45.210 --> 00:00:47.160 align:middle line:84% We discussed wafer manufacturing, 00:00:47.160 --> 00:00:51.240 align:middle line:84% basic characteristics of Czochralski wafers. 00:00:51.240 --> 00:00:53.580 align:middle line:84% And we'll continue on with that a little bit today. 00:00:53.580 --> 00:00:57.240 align:middle line:84% We presented a very simple mathematical model differential 00:00:57.240 --> 00:00:58.440 align:middle line:90% equation for-- 00:00:58.440 --> 00:01:02.700 align:middle line:84% based on heat flux for modeling the Czochralski growth process. 00:01:02.700 --> 00:01:05.040 align:middle line:84% And, at the very end, I had three slides 00:01:05.040 --> 00:01:08.430 align:middle line:84% on the different methods of fabricating SOI, silicon 00:01:08.430 --> 00:01:09.090 align:middle line:90% insulator. 00:01:09.090 --> 00:01:12.720 align:middle line:84% And, in fact, if you're interested in SOI 00:01:12.720 --> 00:01:14.820 align:middle line:84% and getting into it more detail, that's a topic 00:01:14.820 --> 00:01:17.010 align:middle line:84% you might consider for one of you-- 00:01:17.010 --> 00:01:18.693 align:middle line:84% someone to do for your final project. 00:01:18.693 --> 00:01:21.360 align:middle line:84% There's a lot of literature out there on how SOI is really made. 00:01:21.360 --> 00:01:22.650 align:middle line:90% I only gave you three slides. 00:01:22.650 --> 00:01:24.400 align:middle line:84% I'm sure the class would like to hear more 00:01:24.400 --> 00:01:26.880 align:middle line:84% about it if you want to do that as your research topic. 00:01:26.880 --> 00:01:29.250 align:middle line:84% Today I want to talk about more specifically 00:01:29.250 --> 00:01:31.770 align:middle line:84% the mathematics and the statistics of point defects 00:01:31.770 --> 00:01:35.410 align:middle line:84% in silicon, a little bit more detail about carbon and oxygen. 00:01:35.410 --> 00:01:37.110 align:middle line:84% They are so critical to Czochralski 00:01:37.110 --> 00:01:41.870 align:middle line:84% silicon and its properties, and then introduce Chapter 4. 00:01:41.870 --> 00:01:47.130 align:middle line:84% So let's go on to the second slide, page slide two. 00:01:47.130 --> 00:01:48.200 align:middle line:90% We're going to just-- 00:01:48.200 --> 00:01:50.492 align:middle line:84% since we're going to talk about modeling point defects, 00:01:50.492 --> 00:01:52.070 align:middle line:84% let's just define them once again. 00:01:52.070 --> 00:01:56.570 align:middle line:84% We did this last time, but this is a very schematic ball 00:01:56.570 --> 00:01:59.540 align:middle line:84% and stick two-dimensional diagram 00:01:59.540 --> 00:02:02.450 align:middle line:84% of what a lattice might look like, let's say, 00:02:02.450 --> 00:02:03.980 align:middle line:90% highly, highly simplified. 00:02:03.980 --> 00:02:06.890 align:middle line:84% And the vacancy is shown here in this region 00:02:06.890 --> 00:02:08.905 align:middle line:84% where a silicon atom is completely missing 00:02:08.905 --> 00:02:09.530 align:middle line:90% from a lattice. 00:02:09.530 --> 00:02:10.639 align:middle line:90% You just pulled it out. 00:02:10.639 --> 00:02:14.430 align:middle line:84% And there are broken bonds associated with that. 00:02:14.430 --> 00:02:16.810 align:middle line:84% An interstitial is a little bit more complicated. 00:02:16.810 --> 00:02:19.600 align:middle line:84% There's actually-- there's two different types of interstitials 00:02:19.600 --> 00:02:20.100 align:middle line:90% here. 00:02:20.100 --> 00:02:22.420 align:middle line:84% There's one which is shown right here. 00:02:22.420 --> 00:02:24.150 align:middle line:90% And this is a pure interstitial. 00:02:24.150 --> 00:02:26.580 align:middle line:84% It's actually an unbonded extra silicon atom, 00:02:26.580 --> 00:02:30.060 align:middle line:84% like you just stuffed an atom in there in an interstitial space. 00:02:30.060 --> 00:02:32.700 align:middle line:90% It's not bonded to anything. 00:02:32.700 --> 00:02:34.530 align:middle line:90% That's the pure interstitial. 00:02:34.530 --> 00:02:36.900 align:middle line:84% Some people, the defect experts, also 00:02:36.900 --> 00:02:38.970 align:middle line:84% refer to a type of defect which is 00:02:38.970 --> 00:02:43.170 align:middle line:84% an interstitial type called an interstitial sea, by analogy 00:02:43.170 --> 00:02:44.100 align:middle line:90% to a vacancy. 00:02:44.100 --> 00:02:45.880 align:middle line:84% And what it is, it is an extra atom, 00:02:45.880 --> 00:02:49.060 align:middle line:84% but it's actually two atoms that are sharing a lattice site. 00:02:49.060 --> 00:02:50.520 align:middle line:90% So these two are together. 00:02:50.520 --> 00:02:52.920 align:middle line:84% And there is some bonding to neighbors as opposed 00:02:52.920 --> 00:02:55.440 align:middle line:90% to a pure interstitial. 00:02:55.440 --> 00:02:58.500 align:middle line:84% A lot of people believe that the interstitial sea is actually 00:02:58.500 --> 00:03:01.650 align:middle line:84% the most likely configuration of the interstitial defect 00:03:01.650 --> 00:03:05.850 align:middle line:84% in silicon because it takes a lower energy to create it. 00:03:05.850 --> 00:03:07.800 align:middle line:84% Just to share a lattice site isn't that hard 00:03:07.800 --> 00:03:12.340 align:middle line:84% compared to stuffing an unbonded atom in there. 00:03:12.340 --> 00:03:15.540 align:middle line:84% But the truth is, the distinction is really not 00:03:15.540 --> 00:03:16.860 align:middle line:90% important in process modeling. 00:03:16.860 --> 00:03:19.282 align:middle line:84% For the purpose of this class, for modeling processes, 00:03:19.282 --> 00:03:20.490 align:middle line:90% there's two types of defects. 00:03:20.490 --> 00:03:22.590 align:middle line:84% We think of the i-type, the interstitial type. 00:03:22.590 --> 00:03:24.690 align:middle line:84% Exactly how it's configured, we're not sure. 00:03:24.690 --> 00:03:26.760 align:middle line:84% We'll just use the symbol I, capital I, 00:03:26.760 --> 00:03:30.150 align:middle line:84% to refer to an excess silicon atom. 00:03:30.150 --> 00:03:32.610 align:middle line:84% And these point defects, these V and I, 00:03:32.610 --> 00:03:34.680 align:middle line:84% they turn out to pay really fundamental role 00:03:34.680 --> 00:03:35.820 align:middle line:90% in a lot of processes. 00:03:35.820 --> 00:03:37.170 align:middle line:90% They control diffusion. 00:03:37.170 --> 00:03:40.530 align:middle line:84% When we get to Chapter 7 and 8, we're 00:03:40.530 --> 00:03:42.910 align:middle line:84% talking about diffusion, extremely important. 00:03:42.910 --> 00:03:46.770 align:middle line:84% The oxidation, the point defects play a very important role 00:03:46.770 --> 00:03:48.570 align:middle line:90% activating dopants. 00:03:48.570 --> 00:03:50.640 align:middle line:90% So there's a lot of importance. 00:03:50.640 --> 00:03:52.682 align:middle line:84% And that's why we're going to spend a little time 00:03:52.682 --> 00:03:54.870 align:middle line:84% today on understanding the statistics of vacancies 00:03:54.870 --> 00:03:55.980 align:middle line:90% and interstitials. 00:03:55.980 --> 00:03:57.570 align:middle line:90% So let's go on to slide 3. 00:03:57.570 --> 00:04:00.930 align:middle line:84% If you're interested, I've listed here five papers, 00:04:00.930 --> 00:04:04.320 align:middle line:84% all of them fairly old but classic. 00:04:04.320 --> 00:04:07.830 align:middle line:84% Shockley, the Shockley, who also did the transistor studies, 00:04:07.830 --> 00:04:11.610 align:middle line:84% had a paper in the late '50s on the first understanding 00:04:11.610 --> 00:04:16.120 align:middle line:84% of statistics for vacancies and their charge distribution. 00:04:16.120 --> 00:04:20.529 align:middle line:84% Shockley and Moll, also famous names, Watkins, 00:04:20.529 --> 00:04:22.089 align:middle line:84% did some of the very first studies 00:04:22.089 --> 00:04:25.480 align:middle line:84% where people actually detected vacancies 00:04:25.480 --> 00:04:28.360 align:middle line:84% in the lattice using a type of technique 00:04:28.360 --> 00:04:32.515 align:middle line:84% called EPR, electron paramagnetic resonance. 00:04:32.515 --> 00:04:33.890 align:middle line:84% So, if you're interested in that, 00:04:33.890 --> 00:04:36.040 align:middle line:84% you can go back to some of the original papers. 00:04:36.040 --> 00:04:38.500 align:middle line:84% People actually have some evidence 00:04:38.500 --> 00:04:41.800 align:middle line:90% that these things do exist. 00:04:41.800 --> 00:04:44.020 align:middle line:90% Let's go on to slide 4. 00:04:44.020 --> 00:04:47.020 align:middle line:84% And we're going to talk about modeling these native point 00:04:47.020 --> 00:04:48.760 align:middle line:90% defects. 00:04:48.760 --> 00:04:51.058 align:middle line:84% Basically, the presence of native point defects, 00:04:51.058 --> 00:04:52.600 align:middle line:84% that is, vacancies and interstitials, 00:04:52.600 --> 00:04:54.433 align:middle line:84% it minimizes the free energy of the crystal. 00:04:54.433 --> 00:04:58.090 align:middle line:84% It increases the configurational entropy. 00:04:58.090 --> 00:05:00.767 align:middle line:84% If you want a derivation of that, 00:05:00.767 --> 00:05:02.350 align:middle line:84% you can look at Mayer and Laus, that's 00:05:02.350 --> 00:05:05.620 align:middle line:84% one of the textbooks I referred to earlier in the class. 00:05:05.620 --> 00:05:10.250 align:middle line:84% Their 1988 text has a little derivation on that. 00:05:10.250 --> 00:05:13.210 align:middle line:84% But, basically, it seems physically intuitive 00:05:13.210 --> 00:05:15.370 align:middle line:84% that we can write the following expression 00:05:15.370 --> 00:05:17.980 align:middle line:84% for the concentration of neutral vacancies 00:05:17.980 --> 00:05:19.150 align:middle line:90% and neutral interstitials. 00:05:19.150 --> 00:05:21.880 align:middle line:84% And the notation here is a little bit cumbersome, 00:05:21.880 --> 00:05:23.650 align:middle line:90% c meaning the concentration. 00:05:23.650 --> 00:05:27.430 align:middle line:84% The star here, the superscript star means-- the asterisk-- 00:05:27.430 --> 00:05:28.600 align:middle line:90% that we're in equilibrium. 00:05:28.600 --> 00:05:31.100 align:middle line:84% We're going to talk a lot about in this class when we're not 00:05:31.100 --> 00:05:34.750 align:middle line:84% in equilibrium, when we have injected 00:05:34.750 --> 00:05:37.720 align:middle line:84% excess vacancies by various processes, ion implantation, 00:05:37.720 --> 00:05:38.290 align:middle line:90% or whatever. 00:05:38.290 --> 00:05:40.880 align:middle line:84% But, for now, we're going to stick to equilibrium. 00:05:40.880 --> 00:05:43.510 align:middle line:84% This subscript tells you the type of defect, vacancy 00:05:43.510 --> 00:05:44.200 align:middle line:90% or interstitium. 00:05:44.200 --> 00:05:46.840 align:middle line:84% And then, this little zero means neutral-- 00:05:46.840 --> 00:05:48.070 align:middle line:90% uncharged. 00:05:48.070 --> 00:05:50.290 align:middle line:84% Well, as we'll see today, vacancies and interstitials 00:05:50.290 --> 00:05:52.012 align:middle line:90% can exist in charged states. 00:05:52.012 --> 00:05:53.470 align:middle line:84% But, for now, if we're just talking 00:05:53.470 --> 00:05:56.170 align:middle line:84% about the neutral and the uncharged vacancies 00:05:56.170 --> 00:06:00.070 align:middle line:84% or interstitials, we can write them in this type of expression. 00:06:00.070 --> 00:06:02.740 align:middle line:84% They have a temperature dependence. 00:06:02.740 --> 00:06:04.838 align:middle line:84% They depend on a constant, ns, which 00:06:04.838 --> 00:06:06.130 align:middle line:90% is the number of lattice sites. 00:06:06.130 --> 00:06:06.730 align:middle line:90% We know that. 00:06:06.730 --> 00:06:08.560 align:middle line:90% That's 5, 10 of a 22nd. 00:06:08.560 --> 00:06:12.190 align:middle line:84% And they depend exponentially on the formation entropy 00:06:12.190 --> 00:06:17.380 align:middle line:84% of the defect, which is this s sub f and on the formation 00:06:17.380 --> 00:06:19.450 align:middle line:90% enthalpy of the defect over kt. 00:06:19.450 --> 00:06:23.870 align:middle line:84% So we expect to see this thermally activated behavior. 00:06:23.870 --> 00:06:25.390 align:middle line:84% So the concentration of these things 00:06:25.390 --> 00:06:31.060 align:middle line:84% is going to go up exponentially as I increase the temperature. 00:06:31.060 --> 00:06:34.840 align:middle line:84% In general, down here, the equation at the bottom is true. 00:06:34.840 --> 00:06:36.940 align:middle line:84% The concentration of neutral interstitials 00:06:36.940 --> 00:06:37.900 align:middle line:90% is not in equilibrium. 00:06:37.900 --> 00:06:40.250 align:middle line:84% It's not necessarily equal to that of vacancies. 00:06:40.250 --> 00:06:42.407 align:middle line:84% It may be easier or harder to form. 00:06:42.407 --> 00:06:44.740 align:middle line:84% So don't think that they have to be equal to each other, 00:06:44.740 --> 00:06:46.365 align:middle line:84% because there's a lot of different ways 00:06:46.365 --> 00:06:50.130 align:middle line:84% to form these two different types of defects. 00:06:50.130 --> 00:06:51.570 align:middle line:90% Let's go on to slide 5. 00:06:51.570 --> 00:06:54.030 align:middle line:84% In fact, let's talk about a couple of different ways 00:06:54.030 --> 00:06:57.720 align:middle line:84% we can take a perfect crystal and form these defects. 00:06:57.720 --> 00:07:00.180 align:middle line:84% The simplest way-- and if the way 00:07:00.180 --> 00:07:03.010 align:middle line:84% you would probably imagine, if I asked you is, well, 00:07:03.010 --> 00:07:05.040 align:middle line:84% how do we create an interstitium and a vacancy? 00:07:05.040 --> 00:07:07.080 align:middle line:90% Well, it just pull a silicon-- 00:07:07.080 --> 00:07:09.120 align:middle line:84% rip it out of its lattice site and stick it 00:07:09.120 --> 00:07:10.830 align:middle line:84% somewhere, an extra atom, then have 00:07:10.830 --> 00:07:13.350 align:middle line:84% a vacancy where the atom was left 00:07:13.350 --> 00:07:15.240 align:middle line:84% behind-- where the space was left behind, 00:07:15.240 --> 00:07:16.560 align:middle line:90% and I have an interstitial. 00:07:16.560 --> 00:07:19.860 align:middle line:84% In fact, this pair right here, this vacancy interstitial pair, 00:07:19.860 --> 00:07:23.120 align:middle line:90% is called a Frenkel pair. 00:07:23.120 --> 00:07:24.930 align:middle line:90% Incidentally, this can happen. 00:07:24.930 --> 00:07:26.930 align:middle line:84% People believe it costs a fair amount of energy. 00:07:26.930 --> 00:07:28.305 align:middle line:84% That is, it's somewhat hard to do 00:07:28.305 --> 00:07:30.640 align:middle line:84% because you have to break all four bonds 00:07:30.640 --> 00:07:32.390 align:middle line:84% because you're in the bulk of the crystal. 00:07:32.390 --> 00:07:34.640 align:middle line:84% Remember, in silicon, every silicon atom 00:07:34.640 --> 00:07:35.720 align:middle line:90% is four-fold coordinated. 00:07:35.720 --> 00:07:40.640 align:middle line:84% It has four nearest neighbors that are with covalent bonding. 00:07:40.640 --> 00:07:42.050 align:middle line:84% Obviously, the Frankel process is 00:07:42.050 --> 00:07:44.340 align:middle line:84% going to create one interstitial for every vacancy. 00:07:44.340 --> 00:07:46.670 align:middle line:84% So if Frenkel were the only mechanism by which we could 00:07:46.670 --> 00:07:48.890 align:middle line:84% create point defects, then c sub i 00:07:48.890 --> 00:07:51.440 align:middle line:84% would be equal to c sub v in equilibrium. 00:07:51.440 --> 00:07:53.940 align:middle line:84% But it turns out that's not the case. 00:07:53.940 --> 00:08:00.470 align:middle line:84% It turns out surface processes are a dominant way of creating 00:08:00.470 --> 00:08:01.730 align:middle line:90% these point defects. 00:08:01.730 --> 00:08:04.340 align:middle line:84% For example, we can have generation and recombination 00:08:04.340 --> 00:08:06.690 align:middle line:84% of vacancies or interstitials at the surface. 00:08:06.690 --> 00:08:09.440 align:middle line:84% And they may create only one type. 00:08:09.440 --> 00:08:12.630 align:middle line:84% For example-- and this is, again, a schematic. 00:08:12.630 --> 00:08:14.850 align:middle line:84% This is meant to be now a cross-section of a lattice. 00:08:14.850 --> 00:08:17.300 align:middle line:84% So imagine up here, this is the top of my lattice. 00:08:17.300 --> 00:08:20.100 align:middle line:84% Above it is free space below it is the wafer. 00:08:20.100 --> 00:08:23.340 align:middle line:84% And so, this is the top row of surface atoms. 00:08:23.340 --> 00:08:26.300 align:middle line:84% So I can take an atom off the surface. 00:08:26.300 --> 00:08:29.210 align:middle line:84% And it's not for a full bonded because, by nature, the surface 00:08:29.210 --> 00:08:31.323 align:middle line:90% is a point of discontinuity. 00:08:31.323 --> 00:08:33.740 align:middle line:84% There's only a couple of bonds for an atom at the surface. 00:08:33.740 --> 00:08:37.130 align:middle line:84% I can-- doesn't take much energy to pull that out and stuff it-- 00:08:37.130 --> 00:08:41.970 align:middle line:84% and put it in the bulk and create a silicon interstitial. 00:08:41.970 --> 00:08:43.590 align:middle line:84% So there's a lot of different ways. 00:08:43.590 --> 00:08:46.040 align:middle line:84% The surface generation and recombination is very common. 00:08:46.040 --> 00:08:47.790 align:middle line:84% The crystal has a number of different ways 00:08:47.790 --> 00:08:53.070 align:middle line:84% to achieve different concentrations of vacancies 00:08:53.070 --> 00:08:57.030 align:middle line:84% and interstitials, even in equilibrium. 00:08:57.030 --> 00:08:58.620 align:middle line:84% And when we change the temperature 00:08:58.620 --> 00:09:00.983 align:middle line:84% of the crystal, the concentration of the vacancies, 00:09:00.983 --> 00:09:02.400 align:middle line:84% the concentration of interstitials 00:09:02.400 --> 00:09:06.390 align:middle line:84% will change by the creation of either Frenkel pairs or atoms 00:09:06.390 --> 00:09:10.275 align:middle line:84% moving in and out of the surface and interstitials diffusing in. 00:09:10.275 --> 00:09:13.730 align:middle line:90% 00:09:13.730 --> 00:09:18.750 align:middle line:84% So we'll go on to page 6, or slide 6. 00:09:18.750 --> 00:09:21.000 align:middle line:84% It turns out that the equilibrium, no one's 00:09:21.000 --> 00:09:25.230 align:middle line:84% ever really measured exactly the equilibrium concentration of v 00:09:25.230 --> 00:09:29.665 align:middle line:84% and i by any direct process, particularly at the silicon 00:09:29.665 --> 00:09:30.540 align:middle line:90% process temperatures. 00:09:30.540 --> 00:09:33.180 align:middle line:84% The truth is, the concentration is so small 00:09:33.180 --> 00:09:34.630 align:middle line:90% compared to numbers-- 00:09:34.630 --> 00:09:37.300 align:middle line:84% physically reasonable macroscopic numbers, 00:09:37.300 --> 00:09:39.970 align:middle line:84% like the number of silicon atoms. 00:09:39.970 --> 00:09:42.180 align:middle line:84% The number of silicon atoms 5, 10 to the 22. 00:09:42.180 --> 00:09:45.990 align:middle line:84% We're going to see that vacancy concentrations are in the 10 00:09:45.990 --> 00:09:49.990 align:middle line:84% to the 12 range, one part in 10 to the 10, much, much lower. 00:09:49.990 --> 00:09:52.590 align:middle line:84% And so, it's just very hard to measure them directly. 00:09:52.590 --> 00:09:54.660 align:middle line:90% But people have estimated them. 00:09:54.660 --> 00:09:57.600 align:middle line:84% And the way they've estimated them is going to-- a little bit 00:09:57.600 --> 00:09:58.350 align:middle line:90% circular argument. 00:09:58.350 --> 00:10:00.225 align:middle line:84% But it's going to be come out in this course, 00:10:00.225 --> 00:10:02.440 align:middle line:84% by fitting impurity diffusion data. 00:10:02.440 --> 00:10:04.290 align:middle line:84% In other words, people hypothesize 00:10:04.290 --> 00:10:07.830 align:middle line:84% that the diffusivity of a dopant requires 00:10:07.830 --> 00:10:10.830 align:middle line:84% the formation-- the existence of certain vacancies. 00:10:10.830 --> 00:10:14.310 align:middle line:84% And then, they see diffusivities increasing and decreasing 00:10:14.310 --> 00:10:17.040 align:middle line:84% according to temperature or charge states they say, 00:10:17.040 --> 00:10:18.670 align:middle line:84% oh, the concentration of vacancies 00:10:18.670 --> 00:10:20.050 align:middle line:90% must be going up by this much. 00:10:20.050 --> 00:10:22.900 align:middle line:84% So people measure diffusivities and infer concentration 00:10:22.900 --> 00:10:24.070 align:middle line:90% of point defects. 00:10:24.070 --> 00:10:26.740 align:middle line:84% It's a little bit circular but, in any case, that's 00:10:26.740 --> 00:10:29.440 align:middle line:84% how a lot of people have estimated these things. 00:10:29.440 --> 00:10:31.750 align:middle line:84% So don't expect to find anywhere in the literature 00:10:31.750 --> 00:10:32.830 align:middle line:90% some perfect equation. 00:10:32.830 --> 00:10:34.280 align:middle line:90% There's a lot of controversy. 00:10:34.280 --> 00:10:37.570 align:middle line:84% But there's some agreement these days 00:10:37.570 --> 00:10:39.200 align:middle line:90% that these are rough numbers. 00:10:39.200 --> 00:10:41.770 align:middle line:84% So here's a rough equation for the concentration 00:10:41.770 --> 00:10:44.113 align:middle line:84% of neutral interstitials in equilibrium. 00:10:44.113 --> 00:10:45.280 align:middle line:90% It goes something like this. 00:10:45.280 --> 00:10:46.780 align:middle line:84% Again, it's exponentially activated. 00:10:46.780 --> 00:10:49.270 align:middle line:84% As I increase the temperature, I get a lot more-- 00:10:49.270 --> 00:10:51.310 align:middle line:84% I get more interstitials exponentially. 00:10:51.310 --> 00:10:53.620 align:middle line:84% But if you calculate it, put in room temperature 00:10:53.620 --> 00:10:57.055 align:middle line:84% here, you calculate it out, it's close to zero. 00:10:57.055 --> 00:10:58.930 align:middle line:84% I mean, there's just-- there aren't very many 00:10:58.930 --> 00:11:02.020 align:middle line:84% at room temperature of these things. 00:11:02.020 --> 00:11:03.580 align:middle line:84% The concentration is quite small. 00:11:03.580 --> 00:11:06.520 align:middle line:84% At 1,000 degrees, that's where we might be doing an oxidation. 00:11:06.520 --> 00:11:08.290 align:middle line:84% We put a wafer in a furnace and oxidize it 00:11:08.290 --> 00:11:11.170 align:middle line:84% at 1,000 degrees or something, or just anneal it. 00:11:11.170 --> 00:11:13.510 align:middle line:84% At 1,000 degrees, it's something like in the range of 10 00:11:13.510 --> 00:11:16.420 align:middle line:84% to the 12 to 10 to the 14, still very small 00:11:16.420 --> 00:11:18.370 align:middle line:90% compared to 5, 10 to the 22. 00:11:18.370 --> 00:11:24.550 align:middle line:84% Nevertheless, it can have a huge impact on the dopant diffusion. 00:11:24.550 --> 00:11:27.640 align:middle line:84% Typical doping levels are in this 10 to the 14 to 10 00:11:27.640 --> 00:11:30.290 align:middle line:90% to the 15 to 10 to the 20 range. 00:11:30.290 --> 00:11:32.120 align:middle line:84% And, again, the point defect concentrations 00:11:32.120 --> 00:11:33.078 align:middle line:90% are smaller than these. 00:11:33.078 --> 00:11:35.460 align:middle line:84% This will have some important implications. 00:11:35.460 --> 00:11:37.700 align:middle line:84% What it means is that the doping, 00:11:37.700 --> 00:11:39.950 align:middle line:84% the dopant concentration, the concentration of arsenic 00:11:39.950 --> 00:11:43.700 align:middle line:84% or boron, is what sets the electron concentration 00:11:43.700 --> 00:11:46.670 align:middle line:84% and the hole concentration in the crystal, not the vacancies 00:11:46.670 --> 00:11:47.780 align:middle line:90% or the interstitials. 00:11:47.780 --> 00:11:51.250 align:middle line:90% 00:11:51.250 --> 00:11:54.430 align:middle line:84% Let's go on to slide number 7 and a little bit 00:11:54.430 --> 00:11:56.890 align:middle line:84% now about-- so that all was about neutral. 00:11:56.890 --> 00:11:59.540 align:middle line:84% So, as we were saying, as we increase the temperature, 00:11:59.540 --> 00:12:02.350 align:middle line:84% the concentration of neutral vacancies and interstitials 00:12:02.350 --> 00:12:04.660 align:middle line:90% goes up exponentially. 00:12:04.660 --> 00:12:08.780 align:middle line:84% But it turns out, these defects can have charge states as well. 00:12:08.780 --> 00:12:10.780 align:middle line:84% In fact, they can be singly charged, 00:12:10.780 --> 00:12:13.330 align:middle line:84% positive or negative, or doubly charged, 00:12:13.330 --> 00:12:17.380 align:middle line:84% double plus or double negative vacancies. 00:12:17.380 --> 00:12:19.150 align:middle line:84% They've been identified experimentally 00:12:19.150 --> 00:12:24.490 align:middle line:84% using things like this electron paramagnetic resonance. 00:12:24.490 --> 00:12:27.520 align:middle line:84% And particularly when people bombard the lattice 00:12:27.520 --> 00:12:29.410 align:middle line:84% with high-energy electrons and then 00:12:29.410 --> 00:12:31.688 align:middle line:84% they see what kind of vacancies they 00:12:31.688 --> 00:12:33.730 align:middle line:84% can see by these techniques, and they do see them 00:12:33.730 --> 00:12:36.310 align:middle line:90% in various charge states. 00:12:36.310 --> 00:12:40.210 align:middle line:84% Interstitials are believed to have similar charge states, 00:12:40.210 --> 00:12:41.890 align:middle line:84% but they really haven't been measured-- 00:12:41.890 --> 00:12:43.473 align:middle line:84% the charge states of the interstitials 00:12:43.473 --> 00:12:45.497 align:middle line:84% are more difficult to measure, probably 00:12:45.497 --> 00:12:47.830 align:middle line:84% because the interstitials diffuse throughout the lattice 00:12:47.830 --> 00:12:49.490 align:middle line:90% much faster than the vacancies. 00:12:49.490 --> 00:12:51.365 align:middle line:84% We're going to see the interstitial diffusion 00:12:51.365 --> 00:12:53.440 align:middle line:84% coefficients themselves for excess silicon atoms. 00:12:53.440 --> 00:12:56.500 align:middle line:84% They can go whizzing through the lattice. 00:12:56.500 --> 00:13:00.068 align:middle line:90% So they're even harder to see. 00:13:00.068 --> 00:13:02.360 align:middle line:84% So let's look at another, again, a very two-dimensional 00:13:02.360 --> 00:13:04.730 align:middle line:84% schematic way of looking at a vacancy. 00:13:04.730 --> 00:13:07.250 align:middle line:84% That was what I'm showing here at the bottom of this page. 00:13:07.250 --> 00:13:10.340 align:middle line:84% The silicon atoms are these round dots in black. 00:13:10.340 --> 00:13:12.170 align:middle line:84% And these are supposed to represent 00:13:12.170 --> 00:13:14.360 align:middle line:84% bonds, these ellipsoidal things, it's 00:13:14.360 --> 00:13:15.770 align:middle line:90% supposed to be a covalent bond. 00:13:15.770 --> 00:13:18.960 align:middle line:84% Each bond should have two electrons associated with it. 00:13:18.960 --> 00:13:20.870 align:middle line:84% Remember, silicon is in the fourth column 00:13:20.870 --> 00:13:24.330 align:middle line:84% of the periodic chart, so it has four valence electrons. 00:13:24.330 --> 00:13:27.680 align:middle line:84% So this atom here can be completely satisfied 00:13:27.680 --> 00:13:28.940 align:middle line:90% with four covalent bonds. 00:13:28.940 --> 00:13:32.000 align:middle line:84% All of its electrons valence electrons can be bonded. 00:13:32.000 --> 00:13:36.140 align:middle line:84% If I rip out a silicon atom here, the vacant site, 00:13:36.140 --> 00:13:38.120 align:middle line:84% it's going to distort the nearby lattice. 00:13:38.120 --> 00:13:41.480 align:middle line:84% It's going to have some change in the bonding configuration. 00:13:41.480 --> 00:13:45.810 align:middle line:84% And this causes a local change in the energy band structure. 00:13:45.810 --> 00:13:47.810 align:middle line:84% For those of you who've had solid state physics, 00:13:47.810 --> 00:13:50.150 align:middle line:90% you know about energy bands. 00:13:50.150 --> 00:13:54.560 align:middle line:84% It's going to cause extra states, actually, 00:13:54.560 --> 00:13:56.330 align:middle line:90% in the energy gap. 00:13:56.330 --> 00:13:58.460 align:middle line:84% And we're going to call these deep levels. 00:13:58.460 --> 00:14:01.110 align:middle line:84% And we'll show you how we represent them-- 00:14:01.110 --> 00:14:04.140 align:middle line:84% are going to be introduced by the presence of these defects. 00:14:04.140 --> 00:14:07.020 align:middle line:84% These deep levels exist in the bandgap, and they're split off. 00:14:07.020 --> 00:14:09.970 align:middle line:84% They're not in the conduction band or in the valence band. 00:14:09.970 --> 00:14:14.070 align:middle line:84% So having a vacancy or an interstitial 00:14:14.070 --> 00:14:16.890 align:middle line:84% creates a localized deep level in the bandgap. 00:14:16.890 --> 00:14:20.260 align:middle line:90% 00:14:20.260 --> 00:14:24.370 align:middle line:84% So let's take a look at page 8 from your handouts, or slide 8. 00:14:24.370 --> 00:14:29.260 align:middle line:84% And this slide shows very schematically or approximately 00:14:29.260 --> 00:14:31.600 align:middle line:84% the location of where people believe 00:14:31.600 --> 00:14:35.563 align:middle line:84% they can see energy levels exist in the silicone bandgap. 00:14:35.563 --> 00:14:37.480 align:middle line:84% Now, hopefully, you've read through Chapter 1. 00:14:37.480 --> 00:14:39.290 align:middle line:84% If you haven't, you can, right after this lecture, 00:14:39.290 --> 00:14:40.840 align:middle line:84% you can run out and read Chapter 1. 00:14:40.840 --> 00:14:43.390 align:middle line:84% And so, in that chapter, it talks a little bit 00:14:43.390 --> 00:14:45.010 align:middle line:90% about the silicon bandgap. 00:14:45.010 --> 00:14:48.490 align:middle line:84% This line up here is meant to represent the conduction band 00:14:48.490 --> 00:14:50.260 align:middle line:90% energy. 00:14:50.260 --> 00:14:53.380 align:middle line:84% Above this there are lots of free electrons. 00:14:53.380 --> 00:14:54.940 align:middle line:84% This line down here at the bottom 00:14:54.940 --> 00:14:56.650 align:middle line:84% represents the valence band energy, 00:14:56.650 --> 00:14:58.150 align:middle line:90% the top of the valence band. 00:14:58.150 --> 00:15:00.340 align:middle line:84% In between there's a forbidden gap. 00:15:00.340 --> 00:15:03.100 align:middle line:84% So the carriers cannot have energy-- 00:15:03.100 --> 00:15:07.460 align:middle line:84% free carriers don't exist with energies in that energy range. 00:15:07.460 --> 00:15:09.130 align:middle line:84% And we know this bandgap is something 00:15:09.130 --> 00:15:12.190 align:middle line:84% on the order of 1 electron volt, 1.1 for silicon. 00:15:12.190 --> 00:15:16.330 align:middle line:84% These lines here, the line marked v-double-minus, the line 00:15:16.330 --> 00:15:18.790 align:middle line:84% marked v-minus, v-double-plus, and v-plus, 00:15:18.790 --> 00:15:21.100 align:middle line:84% they represent the positions in the energy band-- 00:15:21.100 --> 00:15:23.590 align:middle line:84% in the forbidden gap of these defects. 00:15:23.590 --> 00:15:28.930 align:middle line:84% These are localized states that are formed by the fact 00:15:28.930 --> 00:15:31.810 align:middle line:84% that we're ripping electrons-- we're taking silicon atoms out 00:15:31.810 --> 00:15:32.440 align:middle line:90% of the lattice. 00:15:32.440 --> 00:15:33.940 align:middle line:84% We no longer have a perfect lattice. 00:15:33.940 --> 00:15:36.370 align:middle line:84% But we're putting an extra interstitial silicon 00:15:36.370 --> 00:15:38.090 align:middle line:90% atom in the lattice. 00:15:38.090 --> 00:15:42.580 align:middle line:84% So and these are in various charge states. 00:15:42.580 --> 00:15:45.220 align:middle line:84% This level here, in the mid-gap, it's 00:15:45.220 --> 00:15:47.470 align:middle line:84% right in the middle of the bandgap is marked ei. 00:15:47.470 --> 00:15:49.160 align:middle line:84% That's the intrinsic energy level. 00:15:49.160 --> 00:15:52.960 align:middle line:84% So that's, by definition, that's pretty much close to halfway, 00:15:52.960 --> 00:15:56.710 align:middle line:84% right at the mid-gap point between ec and ev. 00:15:56.710 --> 00:16:00.790 align:middle line:84% And this line right here, marked e sub f, is the Fermi level-- 00:16:00.790 --> 00:16:01.880 align:middle line:90% the Fermi energy. 00:16:01.880 --> 00:16:04.840 align:middle line:84% And, again, hopefully you've read Chapter 1. 00:16:04.840 --> 00:16:06.970 align:middle line:84% Fermi energy is a concept that comes in. 00:16:06.970 --> 00:16:10.840 align:middle line:84% It basically is the energy level at which the probability 00:16:10.840 --> 00:16:12.850 align:middle line:90% of finding an electron is 1/2. 00:16:12.850 --> 00:16:14.380 align:middle line:90% That's the exact definition. 00:16:14.380 --> 00:16:16.588 align:middle line:84% The main thing you need to know about the Fermi level 00:16:16.588 --> 00:16:18.970 align:middle line:84% is, if the Fermi level is at mid-gap, 00:16:18.970 --> 00:16:21.250 align:middle line:90% the semiconductor is intrinsic. 00:16:21.250 --> 00:16:23.500 align:middle line:84% There are very few electrons and holes. 00:16:23.500 --> 00:16:25.000 align:middle line:84% The only electrons and holes we have 00:16:25.000 --> 00:16:28.270 align:middle line:84% are those created by thermally breaking a bond 00:16:28.270 --> 00:16:31.390 align:middle line:84% and ionizing an electron from the valence band 00:16:31.390 --> 00:16:33.290 align:middle line:84% and bringing it up to the conduction band. 00:16:33.290 --> 00:16:37.600 align:middle line:84% So the intrinsic concentration is going to be relatively low. 00:16:37.600 --> 00:16:41.270 align:middle line:84% As I add n-type dopants, the Fermi level moves up. 00:16:41.270 --> 00:16:42.920 align:middle line:84% In fact, this picture is for where 00:16:42.920 --> 00:16:44.670 align:middle line:84% I've added a certain type of n-type dopant 00:16:44.670 --> 00:16:46.503 align:middle line:84% and it moves up towards the conduction band. 00:16:46.503 --> 00:16:49.190 align:middle line:84% The higher it goes towards ec, the more free 00:16:49.190 --> 00:16:51.620 align:middle line:84% electrons we get in the crystal, the more free electrons 00:16:51.620 --> 00:16:52.910 align:middle line:90% I have in the conduction band. 00:16:52.910 --> 00:16:56.727 align:middle line:84% If the Fermi level moves down towards ev, I have more holes. 00:16:56.727 --> 00:16:58.310 align:middle line:84% So you can think of it as the position 00:16:58.310 --> 00:17:02.390 align:middle line:84% of this level in the band gap going up creates more electrons. 00:17:02.390 --> 00:17:04.880 align:middle line:84% As more holes are created, it goes down. 00:17:04.880 --> 00:17:07.910 align:middle line:84% It's just a way in energy space of keeping 00:17:07.910 --> 00:17:09.530 align:middle line:90% track of those densities. 00:17:09.530 --> 00:17:12.079 align:middle line:84% So let's take-- let's just convince ourselves 00:17:12.079 --> 00:17:14.750 align:middle line:84% that it's possible for these vacancies 00:17:14.750 --> 00:17:16.310 align:middle line:90% to exist in charge states. 00:17:16.310 --> 00:17:21.589 align:middle line:84% And so, here's a very crude picture of a vacancy-- 00:17:21.589 --> 00:17:23.339 align:middle line:90% of a neutral vacancy. 00:17:23.339 --> 00:17:26.630 align:middle line:84% So what's happened here is we've taken the silicon black atom out 00:17:26.630 --> 00:17:28.040 align:middle line:90% in the center. 00:17:28.040 --> 00:17:31.100 align:middle line:84% And we've taken out all four of its valence electrons. 00:17:31.100 --> 00:17:32.930 align:middle line:90% They've been pulled out. 00:17:32.930 --> 00:17:35.480 align:middle line:84% So what happens is, well, again, each one 00:17:35.480 --> 00:17:37.130 align:middle line:84% of these little ellipsoids is supposed 00:17:37.130 --> 00:17:38.640 align:middle line:90% to have two electrons in it. 00:17:38.640 --> 00:17:40.390 align:middle line:84% And this is supposed to represent one dot, 00:17:40.390 --> 00:17:42.050 align:middle line:90% one electron from this atom. 00:17:42.050 --> 00:17:45.000 align:middle line:84% And this represents one electron from the atom down here. 00:17:45.000 --> 00:17:46.583 align:middle line:90% So there's a covalent bond here. 00:17:46.583 --> 00:17:47.750 align:middle line:90% There's some kind of a bond. 00:17:47.750 --> 00:17:48.810 align:middle line:90% There's a bond here. 00:17:48.810 --> 00:17:50.020 align:middle line:90% So this is all satisfied. 00:17:50.020 --> 00:17:53.960 align:middle line:84% So there are-- this area of the crystal is net neutral. 00:17:53.960 --> 00:17:57.650 align:middle line:84% There's a vacancy there, but there's no extra electron 00:17:57.650 --> 00:17:59.190 align:middle line:90% or absence of an electron. 00:17:59.190 --> 00:18:01.370 align:middle line:84% So we call-- we can imagine this in your mind 00:18:01.370 --> 00:18:03.080 align:middle line:84% as a neutral vacancy configuration. 00:18:03.080 --> 00:18:08.070 align:middle line:84% Again, it's very crude but it gives you some pictorial idea. 00:18:08.070 --> 00:18:11.280 align:middle line:84% In the center, at the bottom, this picture 00:18:11.280 --> 00:18:14.230 align:middle line:84% represents a single negatively charged vacancy. 00:18:14.230 --> 00:18:18.120 align:middle line:84% So what we do is we have a silicon vacancy. 00:18:18.120 --> 00:18:19.470 align:middle line:90% We ripped out a silicon atom. 00:18:19.470 --> 00:18:23.940 align:middle line:84% But we left behind an extra electron or an extra electron 00:18:23.940 --> 00:18:26.220 align:middle line:84% found its way there, however you want to say it. 00:18:26.220 --> 00:18:27.030 align:middle line:90% And here it is. 00:18:27.030 --> 00:18:29.890 align:middle line:84% Here's an extra electron sitting here. 00:18:29.890 --> 00:18:34.050 align:middle line:84% And so, then if you count up the electrons here associated 00:18:34.050 --> 00:18:35.770 align:middle line:84% with this region, we have one extra. 00:18:35.770 --> 00:18:40.570 align:middle line:84% So this has a single negatively charged net in our charge state. 00:18:40.570 --> 00:18:45.500 align:middle line:84% So this can represent a v-minus pictorially. 00:18:45.500 --> 00:18:49.160 align:middle line:84% And, similarly, we can take out a silicon atom 00:18:49.160 --> 00:18:51.680 align:middle line:84% and we can pull an extra electron out. 00:18:51.680 --> 00:18:53.840 align:middle line:84% So not only the four valence electrons, 00:18:53.840 --> 00:18:56.630 align:middle line:84% but let's take even a fifth one out and remove it. 00:18:56.630 --> 00:19:00.843 align:middle line:84% And now, this region has a net positive charge associated 00:19:00.843 --> 00:19:02.510 align:middle line:84% with it because we have the nuclear-- we 00:19:02.510 --> 00:19:04.370 align:middle line:84% have the charge of these silicon atoms, 00:19:04.370 --> 00:19:06.660 align:middle line:90% and we've unbalanced them. 00:19:06.660 --> 00:19:08.900 align:middle line:90% So now we have a v-plus. 00:19:08.900 --> 00:19:10.740 align:middle line:84% So it's certainly possible, you can imagine, 00:19:10.740 --> 00:19:12.410 align:middle line:84% depending on this vacancy region, 00:19:12.410 --> 00:19:15.230 align:middle line:84% how many electrons are sitting around it 00:19:15.230 --> 00:19:17.780 align:middle line:84% to have these different charge states. 00:19:17.780 --> 00:19:20.662 align:middle line:84% And people have detected these unpaired spins 00:19:20.662 --> 00:19:22.370 align:middle line:84% of these electrons, the fact that there's 00:19:22.370 --> 00:19:25.010 align:middle line:84% an extra unpaired spin here and there's lacking unpaired spin 00:19:25.010 --> 00:19:27.980 align:middle line:84% here, they've been detected by this technique called EPR. 00:19:27.980 --> 00:19:30.612 align:middle line:90% 00:19:30.612 --> 00:19:32.320 align:middle line:84% So we believe that these different charge 00:19:32.320 --> 00:19:33.700 align:middle line:90% states can exist. 00:19:33.700 --> 00:19:37.880 align:middle line:84% Let's go on to page 9 now and talk a little bit more. 00:19:37.880 --> 00:19:40.390 align:middle line:84% We want to talk a little bit more about the statistics. 00:19:40.390 --> 00:19:44.620 align:middle line:84% And, again, I'm showing the energy band diagram. 00:19:44.620 --> 00:19:48.310 align:middle line:84% This time, on page 9, we're showing the energy band diagram 00:19:48.310 --> 00:19:51.080 align:middle line:84% where the Fermi level is right at mid-gap. 00:19:51.080 --> 00:19:55.340 align:middle line:84% So the material is said to be intrinsic. 00:19:55.340 --> 00:19:58.970 align:middle line:84% And so, the only electron and hole pairs that are created 00:19:58.970 --> 00:20:02.240 align:middle line:84% are those created equally when we break bonds 00:20:02.240 --> 00:20:05.420 align:middle line:84% and the Fermi level is at mid-gap. 00:20:05.420 --> 00:20:09.590 align:middle line:84% Let's say we're at 1,000 degrees Centigrade with a semiconductor. 00:20:09.590 --> 00:20:11.420 align:middle line:84% You look up in Chapter 1, there's 00:20:11.420 --> 00:20:14.330 align:middle line:84% a simple expression for the dependence of ni, 00:20:14.330 --> 00:20:19.280 align:middle line:84% the intrinsic carrier concentration on temperature, 00:20:19.280 --> 00:20:20.930 align:middle line:84% and it's about 7 times 10 to the 18. 00:20:20.930 --> 00:20:24.890 align:middle line:84% So there's that many intrinsic free electrons and that many 00:20:24.890 --> 00:20:26.540 align:middle line:84% intrinsic free holes in the material 00:20:26.540 --> 00:20:28.913 align:middle line:84% just by virtue of the temperature. 00:20:28.913 --> 00:20:30.830 align:middle line:84% The temperature allows a lot of bond-breaking, 00:20:30.830 --> 00:20:34.490 align:middle line:84% a lot of electrons to be released from the valence band 00:20:34.490 --> 00:20:38.280 align:middle line:84% up and energized into the conduction band. 00:20:38.280 --> 00:20:41.000 align:middle line:84% So the Fermi at this temperature, 00:20:41.000 --> 00:20:42.440 align:middle line:90% the Fermi level is-- 00:20:42.440 --> 00:20:45.320 align:middle line:84% for any doping level less than 7, 10 to the 18, 00:20:45.320 --> 00:20:48.040 align:middle line:90% the Fermi level is at mid-gap. 00:20:48.040 --> 00:20:53.110 align:middle line:84% Now, we have to recall something about how donors and acceptors 00:20:53.110 --> 00:20:57.350 align:middle line:84% levels are ionized and whether they're occupied by electrons 00:20:57.350 --> 00:20:57.850 align:middle line:90% or not. 00:20:57.850 --> 00:20:59.767 align:middle line:84% And, again, if you've had solid state physics, 00:20:59.767 --> 00:21:00.610 align:middle line:90% you'll recall this. 00:21:00.610 --> 00:21:03.130 align:middle line:84% Otherwise, it's discussed in Chapter 1. 00:21:03.130 --> 00:21:07.570 align:middle line:84% But a shallow donor or acceptor is usually ionized. 00:21:07.570 --> 00:21:09.182 align:middle line:84% And what do I mean by a shallow donor? 00:21:09.182 --> 00:21:10.640 align:middle line:84% I didn't include a picture of that. 00:21:10.640 --> 00:21:12.781 align:middle line:90% I should have. 00:21:12.781 --> 00:21:19.600 align:middle line:84% Let me just check out here if this chalk box will 00:21:19.600 --> 00:21:22.480 align:middle line:90% open which, of course, is-- 00:21:22.480 --> 00:21:25.870 align:middle line:84% let's just-- what do I mean by a shallow donor? 00:21:25.870 --> 00:21:28.850 align:middle line:84% If this is the energy bandgap and the forbidden gap, 00:21:28.850 --> 00:21:32.815 align:middle line:84% so to speak, and those are the valence and conduction bands, 00:21:32.815 --> 00:21:34.540 align:middle line:90% a shallow donor is like arsenic. 00:21:34.540 --> 00:21:36.530 align:middle line:84% Remember, we had arsenic or phosphorus. 00:21:36.530 --> 00:21:38.350 align:middle line:84% And it's shallow because it's energy 00:21:38.350 --> 00:21:42.040 align:middle line:84% level-- it's a deep level, or it's a localized state also. 00:21:42.040 --> 00:21:45.490 align:middle line:84% But it's very close to the conduction band, 00:21:45.490 --> 00:21:53.000 align:middle line:84% say within a few tens of millivolts, 0.03 electron volts. 00:21:53.000 --> 00:21:56.830 align:middle line:84% And so, what happens is that those donors can 00:21:56.830 --> 00:21:58.750 align:middle line:90% very easily donate electrons. 00:21:58.750 --> 00:22:00.370 align:middle line:90% They're easily ionized. 00:22:00.370 --> 00:22:03.100 align:middle line:84% And they donate a free electron to the conduction band. 00:22:03.100 --> 00:22:04.990 align:middle line:84% That's how they dope the semiconductor. 00:22:04.990 --> 00:22:07.360 align:middle line:84% Each one, each donor, by putting 10 to the 18, 00:22:07.360 --> 00:22:09.850 align:middle line:84% each one donates its electron to make a free electron, 00:22:09.850 --> 00:22:14.020 align:middle line:84% and it's very easy for that process to happen. 00:22:14.020 --> 00:22:17.230 align:middle line:84% So they're usually what we call ionized. 00:22:17.230 --> 00:22:19.450 align:middle line:84% That is, the electrons have been donated 00:22:19.450 --> 00:22:22.980 align:middle line:84% and they leave behind a net charge. 00:22:22.980 --> 00:22:25.980 align:middle line:84% If the level is deeper, that is deeper in the bandgap, 00:22:25.980 --> 00:22:30.420 align:middle line:84% say, like v-double-minus, or v-minus, let's say, down here, 00:22:30.420 --> 00:22:33.510 align:middle line:84% this is where my v-minus level is, its energy. 00:22:33.510 --> 00:22:37.230 align:middle line:84% So it's much further away from the conduction band. 00:22:37.230 --> 00:22:40.810 align:middle line:84% Deep donors are only ionized when f is below them. 00:22:40.810 --> 00:22:44.910 align:middle line:84% So the Fermi level would have to be below here. 00:22:44.910 --> 00:22:48.420 align:middle line:84% The Fermi level is below here, as I'm showing here. 00:22:48.420 --> 00:22:54.375 align:middle line:84% Then this is ionized and it's put an electron up here. 00:22:54.375 --> 00:22:56.500 align:middle line:84% So we have to remember these rules for deep donors. 00:22:56.500 --> 00:22:58.720 align:middle line:84% We don't usually think about them for shallow donors 00:22:58.720 --> 00:23:00.637 align:middle line:84% because they're all ionized because they're so 00:23:00.637 --> 00:23:03.710 align:middle line:90% close to the conduction band. 00:23:03.710 --> 00:23:06.150 align:middle line:84% A deep accepter, on the other hand, 00:23:06.150 --> 00:23:08.760 align:middle line:84% is ionized only when the Fermi level is above it. 00:23:08.760 --> 00:23:14.208 align:middle line:84% So these are rules from solid state physics and statistics. 00:23:14.208 --> 00:23:15.500 align:middle line:90% And if you know them, it helps. 00:23:15.500 --> 00:23:18.620 align:middle line:84% Otherwise, you have to take them as rules 00:23:18.620 --> 00:23:20.010 align:middle line:90% for the purpose of this course. 00:23:20.010 --> 00:23:22.220 align:middle line:84% But if we look at-- if we're in intrinsic material 00:23:22.220 --> 00:23:24.140 align:middle line:84% and we look at all these levels, these 00:23:24.140 --> 00:23:29.080 align:middle line:84% are deep acceptors and deep donors. 00:23:29.080 --> 00:23:31.010 align:middle line:84% In this particular case, the Fermi level, 00:23:31.010 --> 00:23:34.580 align:middle line:84% which is right here, ei, is above the vacancy donor level. 00:23:34.580 --> 00:23:36.630 align:middle line:90% So it's above these guys. 00:23:36.630 --> 00:23:39.140 align:middle line:90% So these will not be ionized. 00:23:39.140 --> 00:23:40.550 align:middle line:90% And same thing here. 00:23:40.550 --> 00:23:43.880 align:middle line:84% The Fermi level is below these vacancy acceptor levels. 00:23:43.880 --> 00:23:45.240 align:middle line:90% It's down here. 00:23:45.240 --> 00:23:46.980 align:middle line:84% So these levels won't be ionized. 00:23:46.980 --> 00:23:51.660 align:middle line:84% So what this means is that, in intrinsic material, so it's 00:23:51.660 --> 00:23:55.767 align:middle line:84% intrinsic at that temperature, the neutral vacancy, which 00:23:55.767 --> 00:23:57.600 align:middle line:84% does not depend on the Fermi level position, 00:23:57.600 --> 00:24:00.110 align:middle line:84% that's going to be the dominant vacancy charge state. 00:24:00.110 --> 00:24:04.650 align:middle line:84% Its v0 is what dominates when you're in intrinsic material. 00:24:04.650 --> 00:24:07.320 align:middle line:84% As I now take this Fermi level and move it up, 00:24:07.320 --> 00:24:10.025 align:middle line:84% we'll see that these guys will dominate. 00:24:10.025 --> 00:24:12.150 align:middle line:84% You'll get more and more of these charge vacancies. 00:24:12.150 --> 00:24:14.483 align:middle line:84% And if I move it down, we'll get more and more of these. 00:24:14.483 --> 00:24:17.550 align:middle line:84% But, if we're neutral, if we're intrinsic, 00:24:17.550 --> 00:24:22.080 align:middle line:84% then it's the neutral vacancy concentration that dominates. 00:24:22.080 --> 00:24:26.500 align:middle line:84% And we'll show some equations to actually how to calculate that. 00:24:26.500 --> 00:24:28.530 align:middle line:90% So let's move on to slide 10. 00:24:28.530 --> 00:24:31.890 align:middle line:84% And now I'm doing a different case. 00:24:31.890 --> 00:24:34.440 align:middle line:84% Notice, I've moved the Fermi level away from the mid-gap. 00:24:34.440 --> 00:24:37.100 align:middle line:84% It's no longer in ei, it's up here. 00:24:37.100 --> 00:24:39.710 align:middle line:84% So I have doped this with arsenic or something. 00:24:39.710 --> 00:24:40.920 align:middle line:90% I've made it n-type. 00:24:40.920 --> 00:24:43.370 align:middle line:84% So I've moved the Fermi level closer to ec. 00:24:43.370 --> 00:24:45.620 align:middle line:84% The closer I move it to ec, the more n-type 00:24:45.620 --> 00:24:49.430 align:middle line:84% I make it, the more electrons we have. 00:24:49.430 --> 00:24:52.220 align:middle line:84% So I'm going to assume the material is extrinsic. 00:24:52.220 --> 00:24:53.220 align:middle line:90% What does that mean? 00:24:53.220 --> 00:24:55.940 align:middle line:84% That means the n-type doping concentration 00:24:55.940 --> 00:24:57.620 align:middle line:90% is greater than ni. 00:24:57.620 --> 00:24:59.610 align:middle line:90% That's the definition. 00:24:59.610 --> 00:25:01.880 align:middle line:84% So if I were to dope this with arsenic 00:25:01.880 --> 00:25:06.650 align:middle line:84% to, say, mid 10 to the 19, or 10 to the 20, 00:25:06.650 --> 00:25:09.410 align:middle line:84% I would be well above-- orders of magnitude above ni. 00:25:09.410 --> 00:25:11.090 align:middle line:90% And so, it's extrinsic. 00:25:11.090 --> 00:25:13.820 align:middle line:84% The electron concentration is controlled 00:25:13.820 --> 00:25:18.120 align:middle line:84% by the donor concentration, not by the temperature. 00:25:18.120 --> 00:25:19.730 align:middle line:90% So, in this case, I've doped it. 00:25:19.730 --> 00:25:21.020 align:middle line:90% The Fermi level is here. 00:25:21.020 --> 00:25:24.660 align:middle line:84% It's now-- the ef is now above the v-minus level. 00:25:24.660 --> 00:25:27.420 align:middle line:84% So ef is up here above the v-minus level. 00:25:27.420 --> 00:25:30.230 align:middle line:84% So it means this level is occupied with an electron. 00:25:30.230 --> 00:25:31.850 align:middle line:90% So it's acting like an acceptor. 00:25:31.850 --> 00:25:33.770 align:middle line:84% And, in fact, v-minus is going to be, 00:25:33.770 --> 00:25:36.500 align:middle line:84% in this particular case for this position of the Fermi level, 00:25:36.500 --> 00:25:39.010 align:middle line:84% it will be the dominant vacancy charge state. 00:25:39.010 --> 00:25:41.677 align:middle line:84% So as before, when I had it mid-gap, 00:25:41.677 --> 00:25:43.260 align:middle line:84% the dominant charge state was neutral. 00:25:43.260 --> 00:25:45.180 align:middle line:84% As I move it up, all of a sudden, 00:25:45.180 --> 00:25:47.130 align:middle line:90% now I've got lots of v-minus. 00:25:47.130 --> 00:25:49.680 align:middle line:84% If I move it up even further, above this v-minus, 00:25:49.680 --> 00:25:52.710 align:middle line:84% v-double-minus, I'll have lots of those. 00:25:52.710 --> 00:25:55.700 align:middle line:84% So as I move the Fermi level up and down, just imagine, 00:25:55.700 --> 00:25:58.400 align:middle line:84% with doping, I can control the concentrations 00:25:58.400 --> 00:26:01.400 align:middle line:84% of these types of vacancies, these charge vacancies, 00:26:01.400 --> 00:26:06.240 align:middle line:90% either v-minus or v-plus. 00:26:06.240 --> 00:26:09.180 align:middle line:84% If I move it down in p-type material, all of a sudden, 00:26:09.180 --> 00:26:14.800 align:middle line:84% I get lots of these, v-plus and v-double-plus. 00:26:14.800 --> 00:26:17.380 align:middle line:84% So just by changing the doping, I 00:26:17.380 --> 00:26:21.170 align:middle line:84% can create more vacancies and more interstitials. 00:26:21.170 --> 00:26:23.170 align:middle line:84% So it's not just temperature, because I'm 00:26:23.170 --> 00:26:28.050 align:middle line:84% changing their charge-- the charge populations. 00:26:28.050 --> 00:26:31.110 align:middle line:84% So let's take a look at page 11, or slide 11, where we actually 00:26:31.110 --> 00:26:32.160 align:middle line:90% do this quantitatively. 00:26:32.160 --> 00:26:33.420 align:middle line:84% Now, I've been talking very qualitatively. 00:26:33.420 --> 00:26:34.890 align:middle line:84% I say, we move the Fermi level up, 00:26:34.890 --> 00:26:38.940 align:middle line:84% we get more of cv-minus and cv-double-minus. 00:26:38.940 --> 00:26:42.450 align:middle line:84% Well, there's actual simple mathematical equations 00:26:42.450 --> 00:26:46.230 align:middle line:84% that Shockley's paper first wrote down 00:26:46.230 --> 00:26:48.850 align:middle line:90% on these charge point defects. 00:26:48.850 --> 00:26:53.640 align:middle line:84% And, in fact, they obey exactly the same statistics as 00:26:53.640 --> 00:26:55.800 align:middle line:84% are described in Chapter 1 of your textbook 00:26:55.800 --> 00:26:59.860 align:middle line:84% for shallow donors and shallow acceptors. 00:26:59.860 --> 00:27:01.930 align:middle line:84% In your textbook, in Chapter 1, I 00:27:01.930 --> 00:27:05.020 align:middle line:84% think there's a simple equation that was written down, 00:27:05.020 --> 00:27:08.050 align:middle line:84% just gives the electron concentration 00:27:08.050 --> 00:27:12.700 align:middle line:84% n is equal to some constant, which we happen to call n sub c. 00:27:12.700 --> 00:27:15.880 align:middle line:84% And we said, it depends exponentially in Chapter 1, 00:27:15.880 --> 00:27:19.810 align:middle line:84% if you go back and read that, on the distance 00:27:19.810 --> 00:27:24.110 align:middle line:84% between the conduction band energy level and the Fermi 00:27:24.110 --> 00:27:24.610 align:middle line:90% level. 00:27:24.610 --> 00:27:27.570 align:middle line:90% 00:27:27.570 --> 00:27:28.890 align:middle line:90% That's how we-- 00:27:28.890 --> 00:27:33.880 align:middle line:84% Chapter 1, there's a simple derivation of this relationship. 00:27:33.880 --> 00:27:38.482 align:middle line:84% So the electron concentration, as you take this shallow donor 00:27:38.482 --> 00:27:40.440 align:middle line:84% and move it around a little bit in the bandgap, 00:27:40.440 --> 00:27:43.530 align:middle line:84% you'll change the electron concentration exponentially 00:27:43.530 --> 00:27:46.260 align:middle line:84% according to the distance between ec and e Fermi. 00:27:46.260 --> 00:27:48.770 align:middle line:90% 00:27:48.770 --> 00:27:51.260 align:middle line:84% You may see this-- if you take solid state physics-- 00:27:51.260 --> 00:27:54.680 align:middle line:84% people rewrite it sometimes to say that n-- 00:27:54.680 --> 00:27:57.300 align:middle line:84% there's another way to rewrite this. 00:27:57.300 --> 00:28:00.500 align:middle line:84% And instead of referencing it to the conduction band energy, 00:28:00.500 --> 00:28:05.870 align:middle line:84% sometimes people reference it to mid-gap, e Fermi minus ei. 00:28:05.870 --> 00:28:09.110 align:middle line:84% Either way, it's essentially the same relationship. 00:28:09.110 --> 00:28:10.730 align:middle line:84% Just says, the electron concentration 00:28:10.730 --> 00:28:14.600 align:middle line:84% goes up exponentially depending on the distance 00:28:14.600 --> 00:28:17.720 align:middle line:84% between the Fermi level and either the conduction 00:28:17.720 --> 00:28:19.340 align:middle line:90% band or the mid-gap point. 00:28:19.340 --> 00:28:21.720 align:middle line:90% The exact same thing-- 00:28:21.720 --> 00:28:23.700 align:middle line:84% so this is the concentration of electrons. 00:28:23.700 --> 00:28:26.060 align:middle line:84% This is, instead, the concentration of these 00:28:26.060 --> 00:28:30.690 align:middle line:84% charged vacancies obeys a very, very similar relationship. 00:28:30.690 --> 00:28:35.360 align:middle line:84% So, in equilibrium, the concentration of the cv-plus, 00:28:35.360 --> 00:28:37.730 align:middle line:84% these are single positively charged vacancies, 00:28:37.730 --> 00:28:40.190 align:middle line:84% depends on the concentration of neutrals. 00:28:40.190 --> 00:28:41.390 align:middle line:90% All of these depend-- 00:28:41.390 --> 00:28:44.300 align:middle line:84% the pre-exponential is the neutral concentration-- 00:28:44.300 --> 00:28:46.760 align:middle line:84% concentration of neutral vacancies-- times 00:28:46.760 --> 00:28:50.640 align:middle line:84% exponential, in this case, of the distance between ev-plus 00:28:50.640 --> 00:28:53.540 align:middle line:90% and the Fermi level over kt. 00:28:53.540 --> 00:28:56.500 align:middle line:90% 00:28:56.500 --> 00:29:00.700 align:middle line:84% Similarly, cv star-- cv-minus-- -single-minus, 00:29:00.700 --> 00:29:03.220 align:middle line:84% depends on the neutral concentration 00:29:03.220 --> 00:29:08.270 align:middle line:84% times the exponential of e Fermi minus ev-minus, just going back. 00:29:08.270 --> 00:29:11.860 align:middle line:84% So we're just looking at-- it's just depending on e Fermi 00:29:11.860 --> 00:29:12.370 align:middle line:90% minus-- 00:29:12.370 --> 00:29:14.770 align:middle line:84% so it's this distance right here that 00:29:14.770 --> 00:29:19.700 align:middle line:84% tells you what the concentration is going to be. 00:29:19.700 --> 00:29:22.780 align:middle line:84% So it's just a simple exponential type equations. 00:29:22.780 --> 00:29:25.630 align:middle line:84% You can write down very similar and analogous equations 00:29:25.630 --> 00:29:29.830 align:middle line:84% by replacing all the v's by i's for interstitial point defects, 00:29:29.830 --> 00:29:33.430 align:middle line:84% assuming that they have energy levels in the mid-gap 00:29:33.430 --> 00:29:34.180 align:middle line:90% or in the bandgap. 00:29:34.180 --> 00:29:37.160 align:middle line:90% 00:29:37.160 --> 00:29:40.126 align:middle line:90% So let's just go on to Chapter-- 00:29:40.126 --> 00:29:42.340 align:middle line:90% to page-- slide 12. 00:29:42.340 --> 00:29:44.840 align:middle line:84% Here's a picture where I've actually filled in some numbers. 00:29:44.840 --> 00:29:46.467 align:middle line:84% People think they know these numbers. 00:29:46.467 --> 00:29:48.050 align:middle line:84% They're not known all that accurately. 00:29:48.050 --> 00:29:51.905 align:middle line:84% But it's believed that the double negatively charged 00:29:51.905 --> 00:29:53.930 align:middle line:84% v-double-minus level, deep level, 00:29:53.930 --> 00:29:58.160 align:middle line:84% is about 100 millivolts, so 110 millivolts, 0.1 00:29:58.160 --> 00:30:00.740 align:middle line:90% eV, below the conduction band. 00:30:00.740 --> 00:30:04.160 align:middle line:84% And, similarly, it's believed that this v-minus level 00:30:04.160 --> 00:30:05.930 align:middle line:90% is close to mid-gap. 00:30:05.930 --> 00:30:09.530 align:middle line:84% It's about 0.57 electron volts or so below the conduction band. 00:30:09.530 --> 00:30:11.780 align:middle line:84% People have done studies where they feel that they 00:30:11.780 --> 00:30:14.730 align:middle line:90% can measure these numbers. 00:30:14.730 --> 00:30:17.300 align:middle line:84% And so, as I move the Fermi level around, again, 00:30:17.300 --> 00:30:19.862 align:middle line:84% as I move this up, I'm going to change 00:30:19.862 --> 00:30:22.070 align:middle line:84% the distance between the Fermi level and these deep-- 00:30:22.070 --> 00:30:24.112 align:middle line:84% these energy level positions and therefore change 00:30:24.112 --> 00:30:28.050 align:middle line:84% the concentrations of these charge defects. 00:30:28.050 --> 00:30:30.870 align:middle line:84% Yeah, for people who've had solid state physics here 00:30:30.870 --> 00:30:32.010 align:middle line:90% will be saying, oh, dear. 00:30:32.010 --> 00:30:32.760 align:middle line:90% Oh, wait a minute. 00:30:32.760 --> 00:30:34.440 align:middle line:90% We have a circular problem here. 00:30:34.440 --> 00:30:36.570 align:middle line:84% If the vacancies are charged, then how 00:30:36.570 --> 00:30:38.760 align:middle line:84% do we calculate the Fermi level position? 00:30:38.760 --> 00:30:41.370 align:middle line:84% So it can become a very complicated problem. 00:30:41.370 --> 00:30:43.360 align:middle line:90% It turns out, it's very simple. 00:30:43.360 --> 00:30:45.503 align:middle line:84% In fact, the concentration-- remember, 00:30:45.503 --> 00:30:46.920 align:middle line:84% we said the concentration of these 00:30:46.920 --> 00:30:50.010 align:middle line:84% charged vacancies is always in the 10 of the 12, 10 to the 14 00:30:50.010 --> 00:30:53.490 align:middle line:84% range, much smaller than the concentration 00:30:53.490 --> 00:30:55.920 align:middle line:84% of electrons due to the dopant atoms. 00:30:55.920 --> 00:30:58.290 align:middle line:84% Our doping is usually always over 10 to the 14. 00:30:58.290 --> 00:31:00.060 align:middle line:84% We typically dope 10 to the 15, 10 00:31:00.060 --> 00:31:01.930 align:middle line:84% to the 16 orders of magnitude above that. 00:31:01.930 --> 00:31:04.740 align:middle line:84% So, in fact, the Fermi level position, what we do 00:31:04.740 --> 00:31:08.550 align:middle line:84% is we set the Fermi level just by the dopant concentration, 00:31:08.550 --> 00:31:11.190 align:middle line:84% just by the amount of arsenic or the amount of boron. 00:31:11.190 --> 00:31:12.760 align:middle line:90% That fixes Fermi level. 00:31:12.760 --> 00:31:15.300 align:middle line:84% And then we calculate where the vacancies are just 00:31:15.300 --> 00:31:18.830 align:middle line:84% based on those equations on the previous page. 00:31:18.830 --> 00:31:21.627 align:middle line:90% So there's a lot of simplifying. 00:31:21.627 --> 00:31:22.960 align:middle line:90% And, in fact, if we go to page-- 00:31:22.960 --> 00:31:24.170 align:middle line:90% I just gave away the answer. 00:31:24.170 --> 00:31:27.910 align:middle line:84% But, on slide 13, that's exactly what we're saying. 00:31:27.910 --> 00:31:30.160 align:middle line:84% The concentration of these neutral vacancies 00:31:30.160 --> 00:31:31.750 align:middle line:84% and interstitials is so much smaller 00:31:31.750 --> 00:31:34.540 align:middle line:84% than either ni at typical processing 00:31:34.540 --> 00:31:36.550 align:middle line:84% temperatures or doping concentrations, 00:31:36.550 --> 00:31:38.950 align:middle line:90% that we can do a very-- 00:31:38.950 --> 00:31:41.110 align:middle line:84% the amount of electrons and holes 00:31:41.110 --> 00:31:43.060 align:middle line:84% that are actually bound to these guys 00:31:43.060 --> 00:31:46.030 align:middle line:84% is always negligible compared to the total number 00:31:46.030 --> 00:31:49.090 align:middle line:84% of electrons or holes present in the silicon that are there 00:31:49.090 --> 00:31:52.690 align:middle line:84% either due to thermal activation just due to ni 00:31:52.690 --> 00:31:56.860 align:middle line:90% or due to the extrinsic doping. 00:31:56.860 --> 00:32:00.550 align:middle line:84% So here's how we simplify the charge defect calculations. 00:32:00.550 --> 00:32:05.000 align:middle line:84% First, you're given the donor or the acceptor 00:32:05.000 --> 00:32:06.250 align:middle line:90% concentrations in the crystal. 00:32:06.250 --> 00:32:08.950 align:middle line:90% That is a given, typically. 00:32:08.950 --> 00:32:11.238 align:middle line:84% And we calculate the Fermi level in the usual way 00:32:11.238 --> 00:32:12.280 align:middle line:90% from solid state physics. 00:32:12.280 --> 00:32:14.470 align:middle line:84% We just ignore the fact that the vacancies and interstitials 00:32:14.470 --> 00:32:15.200 align:middle line:90% exist. 00:32:15.200 --> 00:32:16.330 align:middle line:90% So we use these simple-- 00:32:16.330 --> 00:32:17.328 align:middle line:90% we use these equations. 00:32:17.328 --> 00:32:19.870 align:middle line:84% In fact, here's the equation I wrote up on the board earlier. 00:32:19.870 --> 00:32:23.890 align:middle line:84% n equals ni e to the exponential of the distance 00:32:23.890 --> 00:32:26.725 align:middle line:84% between the Fermi level ef minus ei 00:32:26.725 --> 00:32:30.460 align:middle line:84% of the intrinsic level over kt, and a similar expression 00:32:30.460 --> 00:32:33.080 align:middle line:90% for hole density. 00:32:33.080 --> 00:32:37.150 align:middle line:84% So we use these to figure out-- and charge neutrality-- 00:32:37.150 --> 00:32:39.403 align:middle line:84% to figure out the position of the Fermi level 00:32:39.403 --> 00:32:40.195 align:middle line:90% knowing the doping. 00:32:40.195 --> 00:32:44.000 align:middle line:90% 00:32:44.000 --> 00:32:46.000 align:middle line:84% And then, once we have the Fermi level position, 00:32:46.000 --> 00:32:48.970 align:middle line:84% we can just calculate the concentrations of charge defects 00:32:48.970 --> 00:32:53.230 align:middle line:84% using that value of ef and the equations from Shockley 00:32:53.230 --> 00:32:56.200 align:middle line:84% on the different-- on the exponential dependence 00:32:56.200 --> 00:32:58.250 align:middle line:90% of the vacancy concentrations. 00:32:58.250 --> 00:33:01.350 align:middle line:90% So it's actually not that hard. 00:33:01.350 --> 00:33:05.490 align:middle line:90% So let's go on to slide 14. 00:33:05.490 --> 00:33:07.550 align:middle line:84% So another thing to realize-- this 00:33:07.550 --> 00:33:08.970 align:middle line:84% is kind of obvious, but sometimes 00:33:08.970 --> 00:33:12.660 align:middle line:84% we forget it-- is that as the doping changes, 00:33:12.660 --> 00:33:14.970 align:middle line:84% as dope the crystal more heavily, let's say, 00:33:14.970 --> 00:33:18.360 align:middle line:84% and, therefore, the Fermi level changes, 00:33:18.360 --> 00:33:20.640 align:middle line:84% not only do I change the charge states, 00:33:20.640 --> 00:33:25.073 align:middle line:84% but I, actually, the total number of vacancies changes. 00:33:25.073 --> 00:33:27.240 align:middle line:84% It's not just that I'm taking a certain fixed number 00:33:27.240 --> 00:33:29.310 align:middle line:84% and changing their charge distributions, 00:33:29.310 --> 00:33:30.270 align:middle line:90% how they're charged. 00:33:30.270 --> 00:33:32.880 align:middle line:84% So thinking about it this way, this 00:33:32.880 --> 00:33:36.300 align:middle line:84% is the expression we wrote here, this equation, 00:33:36.300 --> 00:33:38.460 align:middle line:84% for the neutral vacancy population. 00:33:38.460 --> 00:33:41.040 align:middle line:84% It's only a function of temperature, not doping, 00:33:41.040 --> 00:33:42.950 align:middle line:90% or not the Fermi level. 00:33:42.950 --> 00:33:44.420 align:middle line:90% So that's very simple. 00:33:44.420 --> 00:33:48.360 align:middle line:84% It's just an exponential dependence on temperature. 00:33:48.360 --> 00:33:50.490 align:middle line:84% But the total vacancy population is 00:33:50.490 --> 00:33:53.940 align:middle line:84% the sum of the neutral vacancies plus the sum 00:33:53.940 --> 00:33:58.200 align:middle line:84% of adding in all the charged defects, cv-minus, 00:33:58.200 --> 00:34:00.970 align:middle line:90% cv-double-minus, cv-plus. 00:34:00.970 --> 00:34:04.910 align:middle line:84% If I increase all these charge defects in their concentration, 00:34:04.910 --> 00:34:09.284 align:middle line:84% then the total concentration has to go up, basically, just 00:34:09.284 --> 00:34:10.409 align:middle line:90% thinking about it that way. 00:34:10.409 --> 00:34:12.710 align:middle line:84% So, in fact, as I thinking about it-- 00:34:12.710 --> 00:34:15.230 align:middle line:84% you never thought about this-- when I'm-- as I add arsenic 00:34:15.230 --> 00:34:19.040 align:middle line:84% to a crystal, as to silicon, I make it more n-type, 00:34:19.040 --> 00:34:21.790 align:middle line:84% I'm increasing the amount of electrons, free electrons, 00:34:21.790 --> 00:34:22.790 align:middle line:90% that are in the crystal. 00:34:22.790 --> 00:34:23.870 align:middle line:90% That's why we add dopants. 00:34:23.870 --> 00:34:25.370 align:middle line:84% I'm also increasing the total number 00:34:25.370 --> 00:34:27.980 align:middle line:84% of vacancies, their concentration, in the crystal, 00:34:27.980 --> 00:34:30.920 align:middle line:84% because I'm making it a lot easier-- it's much more 00:34:30.920 --> 00:34:33.170 align:middle line:84% favorable to form vacancies because all 00:34:33.170 --> 00:34:35.880 align:middle line:84% those extra electrons are available. 00:34:35.880 --> 00:34:39.560 align:middle line:84% So I can form extra cv-minus and cv-double-minus. 00:34:39.560 --> 00:34:41.989 align:middle line:84% So as I move the Fermi level up and down, 00:34:41.989 --> 00:34:44.179 align:middle line:84% I'm actually creating extra point defects. 00:34:44.179 --> 00:34:47.719 align:middle line:84% That's important, because, if I move the Fermi level up, 00:34:47.719 --> 00:34:50.000 align:middle line:84% I create all these extra vacancies, all of a sudden, 00:34:50.000 --> 00:34:54.080 align:middle line:84% dopants that rely on those vacancies to diffuse, 00:34:54.080 --> 00:34:56.005 align:middle line:90% they can diffuse a lot faster. 00:34:56.005 --> 00:34:58.380 align:middle line:84% And, in fact, we'll see that in the chapter on diffusion. 00:34:58.380 --> 00:35:01.250 align:middle line:84% We'll see what so-called Fermi level affects. 00:35:01.250 --> 00:35:03.560 align:middle line:84% People move the Fermi level up and down. 00:35:03.560 --> 00:35:06.560 align:middle line:84% When it's up really high, all of a sudden, the [INAUDIBLE] 00:35:06.560 --> 00:35:08.000 align:middle line:90% of arsenic goes way up. 00:35:08.000 --> 00:35:10.670 align:middle line:84% And the explanation is related to the fact 00:35:10.670 --> 00:35:12.530 align:middle line:84% that you've just stuffed the crystal 00:35:12.530 --> 00:35:15.370 align:middle line:90% with a lot more vacancies. 00:35:15.370 --> 00:35:16.150 align:middle line:90% Yeah. 00:35:16.150 --> 00:35:21.016 align:middle line:84% STUDENT: We've lost the original [INAUDIBLE].. 00:35:21.016 --> 00:35:22.510 align:middle line:90% JUDY HOYT: Mm-hmm. 00:35:22.510 --> 00:35:25.630 align:middle line:84% STUDENT: And the on surface [INAUDIBLE] about. 00:35:25.630 --> 00:35:27.423 align:middle line:84% Is this those dependencies still? 00:35:27.423 --> 00:35:28.090 align:middle line:90% JUDY HOYT: Yeah. 00:35:28.090 --> 00:35:29.596 align:middle line:90% STUDENT: [INAUDIBLE] 00:35:29.596 --> 00:35:33.080 align:middle line:90% 00:35:33.080 --> 00:35:35.750 align:middle line:84% JUDY HOYT: We are talking about going back to this concentration 00:35:35.750 --> 00:35:36.410 align:middle line:90% right here? 00:35:36.410 --> 00:35:39.810 align:middle line:84% STUDENT: Or just in, I guess, the original slide-- 00:35:39.810 --> 00:35:41.103 align:middle line:90% page 4. 00:35:41.103 --> 00:35:43.270 align:middle line:84% JUDY HOYT: OK, let's go back all the way to slide 4. 00:35:43.270 --> 00:35:45.960 align:middle line:90% 00:35:45.960 --> 00:35:50.340 align:middle line:84% This concentration here, ah, how it depends-- this refers to-- 00:35:50.340 --> 00:35:52.320 align:middle line:84% yeah, you would have to change the formation 00:35:52.320 --> 00:35:54.905 align:middle line:90% enthalpy and entropy. 00:35:54.905 --> 00:35:56.280 align:middle line:84% But what we're talking about here 00:35:56.280 --> 00:36:00.450 align:middle line:84% is the total concentration of vacancies 00:36:00.450 --> 00:36:02.850 align:middle line:90% created by whatever processes. 00:36:02.850 --> 00:36:06.268 align:middle line:84% We're not exactly saying, in this explanation, 00:36:06.268 --> 00:36:07.560 align:middle line:90% how they were actually created. 00:36:07.560 --> 00:36:10.710 align:middle line:84% We're just going to assume that these relationships exist. 00:36:10.710 --> 00:36:14.340 align:middle line:84% If you wanted to know it in detail, 00:36:14.340 --> 00:36:16.507 align:middle line:84% you can probably break it out into different origins 00:36:16.507 --> 00:36:18.715 align:middle line:84% of vacancies and interstitial, but we don't take that 00:36:18.715 --> 00:36:21.570 align:middle line:84% into account in any of these equations, the actual mechanism 00:36:21.570 --> 00:36:23.600 align:middle line:90% by which they're formed. 00:36:23.600 --> 00:36:26.350 align:middle line:84% So we lump all of this into a single-- 00:36:26.350 --> 00:36:29.980 align:middle line:84% when we wrote down this equation right here, 00:36:29.980 --> 00:36:32.620 align:middle line:84% we lumped it into a single activation energy, 00:36:32.620 --> 00:36:36.430 align:middle line:84% all the different processes, basically, 00:36:36.430 --> 00:36:38.150 align:middle line:90% whether it's a surface process-- 00:36:38.150 --> 00:36:39.400 align:middle line:90% again, this is an equilibrium. 00:36:39.400 --> 00:36:41.200 align:middle line:84% Whether it's a surface process, or a bulk process, 00:36:41.200 --> 00:36:42.820 align:middle line:84% by Frenkel pair which it was created, 00:36:42.820 --> 00:36:46.000 align:middle line:90% this equation doesn't tell you. 00:36:46.000 --> 00:36:48.290 align:middle line:84% It's probably the sum of a lot of different processes. 00:36:48.290 --> 00:36:51.700 align:middle line:90% So it's an approximation. 00:36:51.700 --> 00:36:53.710 align:middle line:84% Any other questions about vacancy interstitial 00:36:53.710 --> 00:36:54.340 align:middle line:90% populations? 00:36:54.340 --> 00:36:56.170 align:middle line:90% It's kind of weird. 00:36:56.170 --> 00:36:58.180 align:middle line:84% And if you've had solid state physics, 00:36:58.180 --> 00:37:00.208 align:middle line:90% it doesn't seem that strange. 00:37:00.208 --> 00:37:01.750 align:middle line:84% If not, you should definitely go back 00:37:01.750 --> 00:37:08.260 align:middle line:84% and read Chapter 1 to remind yourself of these statistics. 00:37:08.260 --> 00:37:12.560 align:middle line:84% Let's go back-- jump back to slide 15. 00:37:12.560 --> 00:37:16.940 align:middle line:84% And I pulled this-- this slide 15 shows a table from Chapter 3. 00:37:16.940 --> 00:37:20.040 align:middle line:84% I pulled this right out of your textbook. 00:37:20.040 --> 00:37:23.070 align:middle line:84% And what it is, is a table of these energy level 00:37:23.070 --> 00:37:27.430 align:middle line:84% positions as best as they're known today. 00:37:27.430 --> 00:37:30.790 align:middle line:84% And first thing you'll notice is, in the vacancy levels, 00:37:30.790 --> 00:37:32.730 align:middle line:84% there's the numbers are all printed down. 00:37:32.730 --> 00:37:35.100 align:middle line:84% The interstitial levels, there's a bunch of double question marks 00:37:35.100 --> 00:37:36.250 align:middle line:90% and single question marks. 00:37:36.250 --> 00:37:39.030 align:middle line:84% So the truth is, we really don't in the case of interstitials 00:37:39.030 --> 00:37:40.798 align:middle line:84% very well exactly where these are. 00:37:40.798 --> 00:37:42.840 align:middle line:84% The interstitials, no one's ever pinned them down 00:37:42.840 --> 00:37:45.330 align:middle line:84% to be able to do electron paramagnetic resonance. 00:37:45.330 --> 00:37:46.690 align:middle line:90% They move around too much. 00:37:46.690 --> 00:37:48.810 align:middle line:84% So the vacancy levels, we have some ideas. 00:37:48.810 --> 00:37:50.910 align:middle line:84% Even these, I would take to a certain extent 00:37:50.910 --> 00:37:54.120 align:middle line:84% with a grain of salt. But they give me rough ideas. 00:37:54.120 --> 00:37:57.705 align:middle line:84% And the other thing you need to know-- so you 00:37:57.705 --> 00:37:58.890 align:middle line:90% know these distances now. 00:37:58.890 --> 00:38:02.220 align:middle line:84% So you can plug all those into the equations. 00:38:02.220 --> 00:38:06.870 align:middle line:84% The question is, where are these energy levels referenced to? 00:38:06.870 --> 00:38:09.720 align:middle line:84% In fact, we're going to reference them to the band edge. 00:38:09.720 --> 00:38:12.270 align:middle line:84% So as I increase the temperature, remember, 00:38:12.270 --> 00:38:14.520 align:middle line:84% the bandgap shrinks, I'm going to say 00:38:14.520 --> 00:38:18.510 align:middle line:84% that this distance between the band edge and the vacancy level 00:38:18.510 --> 00:38:21.400 align:middle line:84% maintains a constant, even though the bandgap is shrinking. 00:38:21.400 --> 00:38:23.470 align:middle line:90% Again, and that's an assumption. 00:38:23.470 --> 00:38:26.050 align:middle line:84% But that's-- we're going to assume the defect levels track 00:38:26.050 --> 00:38:27.220 align:middle line:90% their respective band edges. 00:38:27.220 --> 00:38:30.760 align:middle line:84% So these v-minus levels track the conduction band, 00:38:30.760 --> 00:38:32.110 align:middle line:90% and the v-pluses-- 00:38:32.110 --> 00:38:35.320 align:middle line:84% if I go back to another slide where I have a picture-- 00:38:35.320 --> 00:38:38.560 align:middle line:84% jumping back for a moment to slide 12. 00:38:38.560 --> 00:38:40.240 align:middle line:84% These guys here, the v-minus, are going 00:38:40.240 --> 00:38:41.448 align:middle line:90% to track the conduction band. 00:38:41.448 --> 00:38:45.160 align:middle line:84% So this distance, 0.11 electron volts and 0.57, 00:38:45.160 --> 00:38:47.860 align:middle line:84% is going to stay fixed even as I squeeze 00:38:47.860 --> 00:38:49.582 align:middle line:84% the whole bandgap due to-- remember, 00:38:49.582 --> 00:38:51.790 align:middle line:84% when you increase temperature, the bandgap goes down, 00:38:51.790 --> 00:38:53.690 align:middle line:84% but these distances are going to stay constant. 00:38:53.690 --> 00:38:56.232 align:middle line:84% And, similarly, these are going to stay constant with respect 00:38:56.232 --> 00:38:57.680 align:middle line:90% to the valence band edge. 00:38:57.680 --> 00:39:00.490 align:middle line:90% It's an assumption. 00:39:00.490 --> 00:39:02.380 align:middle line:84% How justified it is, it's not really clear. 00:39:02.380 --> 00:39:03.880 align:middle line:84% But that's an assumption that people 00:39:03.880 --> 00:39:10.050 align:middle line:84% make when they actually plug in into the Shockley equations. 00:39:10.050 --> 00:39:11.990 align:middle line:84% So let's just do an example since we've 00:39:11.990 --> 00:39:14.300 align:middle line:84% thrown a bunch of the Shockley equations out there. 00:39:14.300 --> 00:39:15.710 align:middle line:90% And that's shown on page-- 00:39:15.710 --> 00:39:17.747 align:middle line:90% slide 16 of the handouts. 00:39:17.747 --> 00:39:19.580 align:middle line:84% And I pulled this right out of the textbook. 00:39:19.580 --> 00:39:21.470 align:middle line:84% So you can go back and reread from the text 00:39:21.470 --> 00:39:23.840 align:middle line:90% if you'd like to do that. 00:39:23.840 --> 00:39:26.570 align:middle line:84% Here's a picture of a slide-- a piece of silicon. 00:39:26.570 --> 00:39:28.700 align:middle line:84% And this region up here in the upper right 00:39:28.700 --> 00:39:31.040 align:middle line:84% is been doped very heavily with arsenic. 00:39:31.040 --> 00:39:34.190 align:middle line:84% So it has a donor concentration of 5 times 10 00:39:34.190 --> 00:39:36.170 align:middle line:90% to the 19 per cubic centimeter. 00:39:36.170 --> 00:39:39.770 align:middle line:84% And the rest of the crystal is boron or p-type-doped 00:39:39.770 --> 00:39:42.660 align:middle line:84% at very lightly, at 10 to the 15. 00:39:42.660 --> 00:39:44.880 align:middle line:84% And we take this pn junction, and we heat it up 00:39:44.880 --> 00:39:47.430 align:middle line:90% to 1,000 degrees in a furnace. 00:39:47.430 --> 00:39:51.030 align:middle line:84% And the question is, let's sit down and calculate, 00:39:51.030 --> 00:39:54.600 align:middle line:84% using the Shockley equations, the concentration of all 00:39:54.600 --> 00:39:56.340 align:middle line:84% the different charged states of vacancies 00:39:56.340 --> 00:39:57.880 align:middle line:84% and all the different charged states of interstitials. 00:39:57.880 --> 00:40:00.600 align:middle line:84% And let's just see, in those two different regions, 00:40:00.600 --> 00:40:05.350 align:middle line:84% what the concentration of these point defects is, here and here. 00:40:05.350 --> 00:40:08.280 align:middle line:84% Well, first of all, we go to 1,000 degrees, and you look up, 00:40:08.280 --> 00:40:11.190 align:middle line:84% in Chapter 1, you notice, the bandgap has shrunk. 00:40:11.190 --> 00:40:13.170 align:middle line:84% At room temperature, the energy bandgap 00:40:13.170 --> 00:40:18.175 align:middle line:84% is distance from ec to ev, that's 1.1 electron volts. 00:40:18.175 --> 00:40:20.550 align:middle line:84% As we go up in temperature, the bandgap actually shrinks. 00:40:20.550 --> 00:40:22.960 align:middle line:84% And there's an expression for that in Chapter 1. 00:40:22.960 --> 00:40:27.900 align:middle line:84% In fact, it's shrunk down to 0.78 or so electron volts. 00:40:27.900 --> 00:40:33.090 align:middle line:84% As a result, of course, it's easier to ionize an electron, 00:40:33.090 --> 00:40:34.020 align:middle line:90% or to bring-- 00:40:34.020 --> 00:40:35.500 align:middle line:90% create electron hole pairs. 00:40:35.500 --> 00:40:37.710 align:middle line:84% So the intrinsic carrier concentration 00:40:37.710 --> 00:40:38.640 align:middle line:90% is now pretty high. 00:40:38.640 --> 00:40:41.370 align:middle line:84% It's 7 times 10 to the 18 at this temperature. 00:40:41.370 --> 00:40:43.680 align:middle line:84% Does anyone remember, if you've taken 6012, 00:40:43.680 --> 00:40:47.110 align:middle line:84% at room temperature, what is ni roughly? 00:40:47.110 --> 00:40:48.340 align:middle line:90% 10 to the 10, right. 00:40:48.340 --> 00:40:50.192 align:middle line:84% So it's gone up by 8 orders of magnitude, 00:40:50.192 --> 00:40:52.150 align:middle line:84% almost 9 orders of magnitude, just because I've 00:40:52.150 --> 00:40:53.360 align:middle line:90% increased temperature. 00:40:53.360 --> 00:40:54.670 align:middle line:84% So those of you who work in electronics, 00:40:54.670 --> 00:40:56.337 align:middle line:84% at room temperature, ni is 10 to the 10, 00:40:56.337 --> 00:40:58.970 align:middle line:84% get that out of your head. ni is a function of temperature. 00:40:58.970 --> 00:41:03.790 align:middle line:84% And it's a pretty big number at these processing temperatures. 00:41:03.790 --> 00:41:08.300 align:middle line:84% So, in fact, in the p-type region, 00:41:08.300 --> 00:41:10.130 align:middle line:84% the semiconductor at this temperature 00:41:10.130 --> 00:41:12.920 align:middle line:84% is intrinsic because ni is many orders of magnitude 00:41:12.920 --> 00:41:15.570 align:middle line:84% larger than the boron doping concentration. 00:41:15.570 --> 00:41:18.995 align:middle line:84% So in the p-type region, the Fermi level is at mid-gap. 00:41:18.995 --> 00:41:21.290 align:middle line:84% I swore I put it here, ef equals ei. 00:41:21.290 --> 00:41:23.720 align:middle line:84% It's at this mid-gap position because the material 00:41:23.720 --> 00:41:26.980 align:middle line:90% is intrinsic. 00:41:26.980 --> 00:41:29.740 align:middle line:84% In the n region, actually, the donor concentration 00:41:29.740 --> 00:41:31.540 align:middle line:84% is still pretty high, 5 10 to the 19 00:41:31.540 --> 00:41:33.310 align:middle line:90% is still much greater than ni. 00:41:33.310 --> 00:41:35.980 align:middle line:90% So its extrinsic. 00:41:35.980 --> 00:41:38.650 align:middle line:84% And we use the usual equation, which we just 00:41:38.650 --> 00:41:41.690 align:middle line:84% showed on the prior pages, to get the Fermi level position. 00:41:41.690 --> 00:41:45.280 align:middle line:84% In fact, this is the equation, n equals ni, e to the e Fermi, 00:41:45.280 --> 00:41:46.930 align:middle line:90% minus ei over kt. 00:41:46.930 --> 00:41:48.550 align:middle line:90% I know the temperature. 00:41:48.550 --> 00:41:50.800 align:middle line:90% And I know n sub i. 00:41:50.800 --> 00:41:54.950 align:middle line:84% So and I know n is just going to be the donor concentration, 5 10 00:41:54.950 --> 00:41:55.450 align:middle line:90% to the 19. 00:41:55.450 --> 00:41:57.670 align:middle line:84% So I have everything I need to find ef minus ei. 00:41:57.670 --> 00:42:01.330 align:middle line:84% And, in fact, if you plug in a calculator, this ef minus ei 00:42:01.330 --> 00:42:04.090 align:middle line:84% distance here, from here to here, 00:42:04.090 --> 00:42:08.150 align:middle line:84% that's 0.2 electron volts or 0.21 roughly. 00:42:08.150 --> 00:42:10.640 align:middle line:84% So I can place the Fermi level on the p-type region 00:42:10.640 --> 00:42:11.600 align:middle line:90% as a mid-gap. 00:42:11.600 --> 00:42:14.690 align:middle line:84% And, here, on this diagram, this position right here, 00:42:14.690 --> 00:42:16.610 align:middle line:84% this dashed line, shows the Fermi level 00:42:16.610 --> 00:42:18.560 align:middle line:90% in the n-type region. 00:42:18.560 --> 00:42:21.380 align:middle line:84% And then, we've just drawn in the bandgap, the band 00:42:21.380 --> 00:42:23.780 align:middle line:84% edges here, here, and here, ec and ev. 00:42:23.780 --> 00:42:26.240 align:middle line:90% And each line here represents-- 00:42:26.240 --> 00:42:28.400 align:middle line:90% we know these energy levels. 00:42:28.400 --> 00:42:30.530 align:middle line:90% They're positioned numerically. 00:42:30.530 --> 00:42:35.180 align:middle line:84% This is 0.11 electron volts for the v-double-minus. 00:42:35.180 --> 00:42:36.140 align:middle line:90% This is 0.57. 00:42:36.140 --> 00:42:39.650 align:middle line:84% So we can draw this quantitatively, this diagram, 00:42:39.650 --> 00:42:42.650 align:middle line:84% in the p-type region as well as in the n-type region. 00:42:42.650 --> 00:42:45.380 align:middle line:84% And, here, we're showing mostly the vacancies just 00:42:45.380 --> 00:42:48.830 align:middle line:84% for illustration purposes and, here, mostly the interstitials. 00:42:48.830 --> 00:42:51.830 align:middle line:84% But you could write down the interstitial's levels 00:42:51.830 --> 00:42:54.780 align:middle line:84% in the p-type region as well just to show the picture. 00:42:54.780 --> 00:42:57.350 align:middle line:84% So if you sit down and then you plug all these numbers 00:42:57.350 --> 00:43:00.460 align:middle line:84% into the Shockley equation, this is what you come up 00:43:00.460 --> 00:43:03.190 align:middle line:90% with and on slide 17. 00:43:03.190 --> 00:43:06.160 align:middle line:84% And, again, this table is taken directly from your textbook. 00:43:06.160 --> 00:43:09.610 align:middle line:84% And all it is, is tabulating, in the p-type and the n-type 00:43:09.610 --> 00:43:13.550 align:middle line:84% region, the concentration of all these interesting quantities. 00:43:13.550 --> 00:43:15.760 align:middle line:84% For example, let's just take the p-type region. 00:43:15.760 --> 00:43:19.090 align:middle line:84% The doping, we were told, is 1 times 10 to the 15. 00:43:19.090 --> 00:43:20.260 align:middle line:90% That was a given. 00:43:20.260 --> 00:43:22.870 align:middle line:90% ni is 7 times 10 to the 18. 00:43:22.870 --> 00:43:25.030 align:middle line:84% That's the same in both sides because that's 00:43:25.030 --> 00:43:26.710 align:middle line:90% just due to the temperature. 00:43:26.710 --> 00:43:29.090 align:middle line:84% The neutral vacancy concentration, 00:43:29.090 --> 00:43:32.500 align:middle line:84% which is calculated from that simple exponential we gave 00:43:32.500 --> 00:43:34.630 align:middle line:84% earlier, depends only on temperature, 00:43:34.630 --> 00:43:36.910 align:middle line:84% and it's about 5 times 10 to the 13. 00:43:36.910 --> 00:43:39.430 align:middle line:84% And it's the same in the p and the e region. 00:43:39.430 --> 00:43:40.930 align:middle line:84% Again, the neutral vacancies doesn't 00:43:40.930 --> 00:43:42.310 align:middle line:90% depend on the Fermi level. 00:43:42.310 --> 00:43:45.490 align:middle line:84% Here's where the differences start coming up. 00:43:45.490 --> 00:43:50.050 align:middle line:84% In the p-type region, look at the concentration of v-minus. 00:43:50.050 --> 00:43:55.510 align:middle line:84% It's about 2 times 10 to the 14, almost an order of magnitude 00:43:55.510 --> 00:43:56.750 align:middle line:90% larger than the neutral. 00:43:56.750 --> 00:43:58.690 align:middle line:84% So here the neutral and the v-minus 00:43:58.690 --> 00:44:00.550 align:middle line:90% are dominating here in red. 00:44:00.550 --> 00:44:04.060 align:middle line:84% Everything below on the chart, v-double-minus, 00:44:04.060 --> 00:44:06.860 align:middle line:84% v-plus, these are all very small, small numbers. 00:44:06.860 --> 00:44:10.420 align:middle line:84% And that's because of the Fermi level position basically. 00:44:10.420 --> 00:44:12.790 align:middle line:84% And, again, the concentration goes-- 00:44:12.790 --> 00:44:15.220 align:middle line:84% depends on the position of the Fermi level respect 00:44:15.220 --> 00:44:17.030 align:middle line:90% to these vacancy levels. 00:44:17.030 --> 00:44:20.740 align:middle line:84% So here these guys dominate, the v-minus. 00:44:20.740 --> 00:44:22.960 align:middle line:84% In the n-type region, what's in red, 00:44:22.960 --> 00:44:25.060 align:middle line:90% I've highlighted what dominates. 00:44:25.060 --> 00:44:29.080 align:middle line:84% Actually, now, both v-minus and v-double-minus 00:44:29.080 --> 00:44:30.930 align:middle line:84% in the heavily doped n-type region dominate. 00:44:30.930 --> 00:44:33.430 align:middle line:84% And not only do they dominate, look, they're so much bigger. 00:44:33.430 --> 00:44:35.080 align:middle line:84% If you were to add up all these numbers, 00:44:35.080 --> 00:44:36.580 align:middle line:84% look at the total vacancy population 00:44:36.580 --> 00:44:40.750 align:middle line:84% now is well above 1 times 10 to the 15, 00:44:40.750 --> 00:44:44.110 align:middle line:84% much larger than it is in intrinsic material 00:44:44.110 --> 00:44:48.070 align:middle line:84% where it was here in the 10 to the 14 range. 00:44:48.070 --> 00:44:50.350 align:middle line:84% So, again, that just shows, in the n-type region 00:44:50.350 --> 00:44:53.620 align:middle line:84% of the crystal, there's a lot more vacancies total. 00:44:53.620 --> 00:44:56.680 align:middle line:84% So, in that region, if you have a dopant that's 00:44:56.680 --> 00:44:58.630 align:middle line:84% diffusivity depends on the vacancy population, 00:44:58.630 --> 00:45:02.620 align:middle line:84% it's going to go up its diffusivity. 00:45:02.620 --> 00:45:04.150 align:middle line:84% Clearly, the different charge states 00:45:04.150 --> 00:45:07.070 align:middle line:84% dominate in the different regions. 00:45:07.070 --> 00:45:10.910 align:middle line:84% And I'm not going to go-- we won't introduce right yet, 00:45:10.910 --> 00:45:13.630 align:middle line:84% but when we get to the Chapter 7 on diffusion 00:45:13.630 --> 00:45:15.070 align:middle line:84% and Chapter 8 on ion implantation 00:45:15.070 --> 00:45:17.710 align:middle line:84% and even in the oxidation models, these numbers, 00:45:17.710 --> 00:45:20.680 align:middle line:84% these concentrations of point defects will be very important. 00:45:20.680 --> 00:45:22.570 align:middle line:84% For now, you just get an intuitive feel. 00:45:22.570 --> 00:45:26.170 align:middle line:84% As I go n-type, oh, OK, the v-minus and the v-double-minus 00:45:26.170 --> 00:45:27.040 align:middle line:90% go way up. 00:45:27.040 --> 00:45:30.450 align:middle line:90% As I go p-type, these-- 00:45:30.450 --> 00:45:31.450 align:middle line:90% well, this is intrinsic. 00:45:31.450 --> 00:45:32.200 align:middle line:90% It's not actually p-type. 00:45:32.200 --> 00:45:33.880 align:middle line:84% In p-type, if I made it heavily p-type, 00:45:33.880 --> 00:45:36.460 align:middle line:84% these numbers would go up, the v-plus 00:45:36.460 --> 00:45:38.590 align:middle line:84% and the v-double-plus concentrations. 00:45:38.590 --> 00:45:42.060 align:middle line:90% 00:45:42.060 --> 00:45:43.710 align:middle line:84% So I'm going to leave the vacancy. 00:45:43.710 --> 00:45:45.900 align:middle line:84% When we switch to slide 18, I'm going 00:45:45.900 --> 00:45:47.607 align:middle line:84% to leave the vacancy and interstitial. 00:45:47.607 --> 00:45:50.190 align:middle line:84% You'll get a chance to look at some of those in your homework. 00:45:50.190 --> 00:45:51.790 align:middle line:84% But that's an example from the text. 00:45:51.790 --> 00:45:53.123 align:middle line:90% I'm going to leave that for now. 00:45:53.123 --> 00:45:54.985 align:middle line:84% And we'll, as we go along each process 00:45:54.985 --> 00:45:56.610 align:middle line:84% we talk about, we're going to come back 00:45:56.610 --> 00:46:00.490 align:middle line:84% to the importance of vacancies and interstitials. 00:46:00.490 --> 00:46:03.490 align:middle line:84% There are two other things about the crystal that 00:46:03.490 --> 00:46:06.580 align:middle line:84% are very important that I wanted to talk about and discuss 00:46:06.580 --> 00:46:10.960 align:middle line:84% that's discussed in Chapter 3, and that is oxygen and carbon. 00:46:10.960 --> 00:46:13.420 align:middle line:84% We said yesterday, or on Tuesday, 00:46:13.420 --> 00:46:15.910 align:middle line:84% that the Czochralski growth process inherently 00:46:15.910 --> 00:46:18.310 align:middle line:84% introduces oxygen from the quartz crucible 00:46:18.310 --> 00:46:19.630 align:middle line:90% and a certain amount of carbon. 00:46:19.630 --> 00:46:20.860 align:middle line:90% And we can't get around that. 00:46:20.860 --> 00:46:23.770 align:middle line:84% And these are typical numbers, oxygen about 10 to the 18, 00:46:23.770 --> 00:46:26.830 align:middle line:84% carbon concentration about 10 to the 16. 00:46:26.830 --> 00:46:29.050 align:middle line:84% And they both have some important effects. 00:46:29.050 --> 00:46:30.970 align:middle line:84% For example, for oxygen, these are 00:46:30.970 --> 00:46:35.580 align:middle line:90% three effects that are listed. 00:46:35.580 --> 00:46:39.425 align:middle line:84% This is a simple-- or it's an equation you learn from 6012, 00:46:39.425 --> 00:46:42.260 align:middle line:84% or if you've taken an electrical engineering class. 00:46:42.260 --> 00:46:45.060 align:middle line:84% If you haven't, just take the equation as given. 00:46:45.060 --> 00:46:49.520 align:middle line:84% It's equation for vth, the threshold voltage, 00:46:49.520 --> 00:46:52.250 align:middle line:84% as a function of various physical parameters. 00:46:52.250 --> 00:46:55.130 align:middle line:84% The vth, that is very important to the circuit designer. 00:46:55.130 --> 00:46:57.440 align:middle line:84% It tells you, and to the device person as well, 00:46:57.440 --> 00:47:01.460 align:middle line:84% it tells when you apply that gate voltage, 00:47:01.460 --> 00:47:04.380 align:middle line:84% the inversion layer forms and you start getting conduction. 00:47:04.380 --> 00:47:08.630 align:middle line:84% So circuits behave very badly if your threshold voltage varies 00:47:08.630 --> 00:47:11.310 align:middle line:84% from device to device all over the place. 00:47:11.310 --> 00:47:13.670 align:middle line:84% There are-- all these depend on things you can control, 00:47:13.670 --> 00:47:15.878 align:middle line:84% like the doping, and the wafer, and things like that. 00:47:15.878 --> 00:47:20.910 align:middle line:84% But this one term, this last term, qqm over cx, 00:47:20.910 --> 00:47:23.790 align:middle line:84% where q sub m is the concentration of mobile ions, 00:47:23.790 --> 00:47:27.030 align:middle line:84% be it, say, sodium, potassium, calcium, 00:47:27.030 --> 00:47:28.860 align:middle line:84% whatever, that exists in the oxide are 00:47:28.860 --> 00:47:31.260 align:middle line:84% right at the interface between the oxide and the silicon. 00:47:31.260 --> 00:47:33.390 align:middle line:84% And this, we write as the number of charges 00:47:33.390 --> 00:47:35.760 align:middle line:90% per square centimeter. 00:47:35.760 --> 00:47:39.170 align:middle line:84% So it could be the sodium concentration in sodium atoms 00:47:39.170 --> 00:47:40.162 align:middle line:90% per square centimeter. 00:47:40.162 --> 00:47:41.870 align:middle line:84% Well, you just plug some numbers in here, 00:47:41.870 --> 00:47:45.390 align:middle line:84% put in an oxide thickness of 10 nanometers, 00:47:45.390 --> 00:47:47.450 align:middle line:84% which is reasonable for these days. 00:47:47.450 --> 00:47:52.100 align:middle line:84% Then I calculate a vth change or a shift of 0.1 volts 00:47:52.100 --> 00:47:56.210 align:middle line:84% by having qm be just about 6 times 10 to the 11, 00:47:56.210 --> 00:47:57.110 align:middle line:90% not very much. 00:47:57.110 --> 00:47:59.850 align:middle line:84% That's only 10 ppm, 10 parts per million. 00:47:59.850 --> 00:48:05.270 align:middle line:84% But, already, that amount, 6 times 10 to the 11 sodium atoms, 00:48:05.270 --> 00:48:08.060 align:middle line:84% can shift the threshold voltage in one device 00:48:08.060 --> 00:48:11.600 align:middle line:84% to the next if it varies by that much, by a tenth of a volt. 00:48:11.600 --> 00:48:15.000 align:middle line:84% And that's a big deal to either a device person or a circuit 00:48:15.000 --> 00:48:15.500 align:middle line:90% person. 00:48:15.500 --> 00:48:17.240 align:middle line:84% So you really need to-- that's why you'll 00:48:17.240 --> 00:48:20.060 align:middle line:84% see the concentrations of these things in the ITRS 00:48:20.060 --> 00:48:21.980 align:middle line:84% have to be 10 to the 10 or below because they 00:48:21.980 --> 00:48:23.120 align:middle line:90% want it to be a small. 00:48:23.120 --> 00:48:26.190 align:middle line:84% They don't want any chance of a 100-millivolt threshold voltage 00:48:26.190 --> 00:48:26.690 align:middle line:90% shift. 00:48:26.690 --> 00:48:28.740 align:middle line:90% That's just way too much. 00:48:28.740 --> 00:48:31.460 align:middle line:84% So that's one reason for people making logic devices. 00:48:31.460 --> 00:48:35.160 align:middle line:84% People in memory devices are even more paranoid, even 00:48:35.160 --> 00:48:38.340 align:middle line:90% more scared of contamination. 00:48:38.340 --> 00:48:43.020 align:middle line:84% And here's an example, number two on slide 25. 00:48:43.020 --> 00:48:46.570 align:middle line:84% This is schematically a dynamic random access memory. 00:48:46.570 --> 00:48:50.730 align:middle line:84% So this is a DRAM that all of us have in all of our computers. 00:48:50.730 --> 00:48:53.400 align:middle line:84% And what it consists of is a transistor 00:48:53.400 --> 00:48:55.740 align:middle line:90% and that access this-- 00:48:55.740 --> 00:48:58.500 align:middle line:84% basically this charge stored on the analyst capacitor. 00:48:58.500 --> 00:49:02.010 align:middle line:84% If charge is stored on there, then it's a certain logic state, 00:49:02.010 --> 00:49:04.940 align:middle line:84% a one, if there's no charge, it's a zero. 00:49:04.940 --> 00:49:08.090 align:middle line:84% Well, it turns out we have to refresh this periodically. 00:49:08.090 --> 00:49:10.670 align:middle line:84% We have a certain amount of charge stored in that node, 00:49:10.670 --> 00:49:12.500 align:middle line:90% but it leaks out over time. 00:49:12.500 --> 00:49:19.580 align:middle line:84% And, typically, the DRAM has to refresh that bit of information 00:49:19.580 --> 00:49:21.630 align:middle line:90% every few milliseconds. 00:49:21.630 --> 00:49:23.550 align:middle line:84% But if it's leaking out really fast, 00:49:23.550 --> 00:49:25.040 align:middle line:90% it has to refresh it more often. 00:49:25.040 --> 00:49:27.830 align:middle line:84% And you suck down your battery power 00:49:27.830 --> 00:49:29.700 align:middle line:84% and then the chip doesn't work very well. 00:49:29.700 --> 00:49:33.170 align:middle line:84% So, it turns out, a refresh time of several milliseconds 00:49:33.170 --> 00:49:34.920 align:middle line:90% requires a lifetime. 00:49:34.920 --> 00:49:38.480 align:middle line:84% This is a measure of the purity of the silicon, a generation 00:49:38.480 --> 00:49:42.140 align:middle line:84% lifetime, that goes to tg that goes 1 over a number 00:49:42.140 --> 00:49:45.170 align:middle line:84% sigma, which is given by this number, 00:49:45.170 --> 00:49:48.740 align:middle line:84% times the thermal velocity, which is also a constant, times 00:49:48.740 --> 00:49:50.540 align:middle line:90% nt. 00:49:50.540 --> 00:49:53.540 align:middle line:84% n sub t here is the concentration in per 00:49:53.540 --> 00:49:55.340 align:middle line:90% cubic centimeter of traps. 00:49:55.340 --> 00:49:58.910 align:middle line:84% So if I know sigma, typically the cross-section 00:49:58.910 --> 00:50:02.000 align:middle line:84% for a typical deep level is this number, 10 to the minus 15, 00:50:02.000 --> 00:50:05.120 align:middle line:84% I know the thermal velocity, I can solve for nt. 00:50:05.120 --> 00:50:06.770 align:middle line:84% This requires that I have less than 10 00:50:06.770 --> 00:50:11.510 align:middle line:84% to the 12 per cubic centimeter or 0.02 part per billion 00:50:11.510 --> 00:50:13.830 align:middle line:84% of these traps in the semiconductor. 00:50:13.830 --> 00:50:15.110 align:middle line:90% So it's extremely important. 00:50:15.110 --> 00:50:17.540 align:middle line:84% If you have more than that, your charge 00:50:17.540 --> 00:50:21.050 align:middle line:84% is going to leak out faster and your DRAM is not going to work. 00:50:21.050 --> 00:50:23.830 align:middle line:84% So it's very important to keep these impurity concentrations 00:50:23.830 --> 00:50:24.760 align:middle line:90% low for that reason. 00:50:24.760 --> 00:50:28.970 align:middle line:90% 00:50:28.970 --> 00:50:31.220 align:middle line:84% So what are these traps associated with? 00:50:31.220 --> 00:50:34.940 align:middle line:84% Well, it turns out that trap density scales 00:50:34.940 --> 00:50:36.758 align:middle line:84% with the density of certain bad actors. 00:50:36.758 --> 00:50:39.050 align:middle line:84% And we'll talk next time about who these bad actors are 00:50:39.050 --> 00:50:43.670 align:middle line:84% in silicon impurities, such as heavy metals, gold, 00:50:43.670 --> 00:50:46.640 align:middle line:84% transition metals like copper, iron, nickel. 00:50:46.640 --> 00:50:50.780 align:middle line:84% A lot of these turn out to be traps, deep levels, 00:50:50.780 --> 00:50:53.553 align:middle line:90% that destroy the lifetime. 00:50:53.553 --> 00:50:55.470 align:middle line:84% But, anyway, just to give you a rule of thumb, 00:50:55.470 --> 00:50:58.117 align:middle line:84% you need to be in the ppb range or lower. 00:50:58.117 --> 00:51:00.450 align:middle line:84% In fact, it turns out the requirements are a little more 00:51:00.450 --> 00:51:02.075 align:middle line:84% severe than that simple equation I just 00:51:02.075 --> 00:51:07.020 align:middle line:84% did because these elements also have a very bad tendency 00:51:07.020 --> 00:51:09.510 align:middle line:84% to accumulate in heavily doped regions, 00:51:09.510 --> 00:51:11.610 align:middle line:84% like in the pn junction or source drain, 00:51:11.610 --> 00:51:14.490 align:middle line:84% they tend to be-- we'll talk about why they have-- they 00:51:14.490 --> 00:51:16.360 align:middle line:90% like to be in those regions. 00:51:16.360 --> 00:51:18.790 align:middle line:84% So that's the worst place for them. 00:51:18.790 --> 00:51:21.750 align:middle line:84% So that's why we even require lower carbon concentrations-- 00:51:21.750 --> 00:51:23.130 align:middle line:90% or iron. 00:51:23.130 --> 00:51:27.570 align:middle line:84% Back here on page 25, I said 10 to the 12 per cubic centimeter. 00:51:27.570 --> 00:51:30.690 align:middle line:84% In fact, people, if you look at the NTRS or ITRS, 00:51:30.690 --> 00:51:33.520 align:middle line:84% it'll ask for much less than that. 00:51:33.520 --> 00:51:36.840 align:middle line:84% So the truth is, it's impossible to keep our wafers that clean. 00:51:36.840 --> 00:51:43.180 align:middle line:84% No matter how careful we are in the lab or in the process fab. 00:51:43.180 --> 00:51:46.500 align:middle line:84% So what we do, what people do in manufacturing anyway, 00:51:46.500 --> 00:51:48.420 align:middle line:84% is to use a process like gettering, 00:51:48.420 --> 00:51:52.110 align:middle line:84% so that it will try to remove these unwanted iron, gold, 00:51:52.110 --> 00:51:54.358 align:middle line:84% and copper from the regions of the wafers 00:51:54.358 --> 00:51:55.900 align:middle line:84% where the actual devices are located. 00:51:55.900 --> 00:51:59.100 align:middle line:84% So this is a special type of process we do, 00:51:59.100 --> 00:52:01.020 align:middle line:84% usually done at the beginning of the process. 00:52:01.020 --> 00:52:02.335 align:middle line:90% We do something to the wafer-- 00:52:02.335 --> 00:52:03.960 align:middle line:84% or maybe in the middle of the process-- 00:52:03.960 --> 00:52:06.870 align:middle line:84% to try to attract these to another location. 00:52:06.870 --> 00:52:10.410 align:middle line:90% 00:52:10.410 --> 00:52:13.290 align:middle line:84% So we'll talk about those three types, three levels. 00:52:13.290 --> 00:52:14.850 align:middle line:84% First is just the clean room, how do 00:52:14.850 --> 00:52:16.080 align:middle line:90% we keep the clean room clean? 00:52:16.080 --> 00:52:17.430 align:middle line:84% Second is how we clean the wafers? 00:52:17.430 --> 00:52:18.810 align:middle line:84% And third is how we do gettering? 00:52:18.810 --> 00:52:23.340 align:middle line:84% So, for today, I'm just going to do this level one control. 00:52:23.340 --> 00:52:26.490 align:middle line:84% And hopefully some of you have seen clean rooms. 00:52:26.490 --> 00:52:28.860 align:middle line:84% But, basically, what we do in a clean room is 00:52:28.860 --> 00:52:31.830 align:middle line:84% we try to keep the air free of particles. 00:52:31.830 --> 00:52:36.630 align:middle line:84% And we do this in practice by these tremendous filters, 00:52:36.630 --> 00:52:39.130 align:middle line:84% high efficiency filters, that really trap all particles. 00:52:39.130 --> 00:52:41.670 align:middle line:84% So the air coming into the clean room comes from the top. 00:52:41.670 --> 00:52:44.087 align:middle line:84% These high-efficiency filters remove all of the particles, 00:52:44.087 --> 00:52:45.600 align:middle line:90% and the air goes out the sides. 00:52:45.600 --> 00:52:47.580 align:middle line:84% And it keeps washing the air continuously. 00:52:47.580 --> 00:52:51.630 align:middle line:84% We have this constant flow of air taking particles 00:52:51.630 --> 00:52:54.300 align:middle line:84% and removing them down to the floor 00:52:54.300 --> 00:52:55.950 align:middle line:84% so that they don't get on your wafers. 00:52:55.950 --> 00:52:59.730 align:middle line:84% And, in fact, we actually quote the class 00:52:59.730 --> 00:53:02.400 align:middle line:84% of a clean room, where the room gets 00:53:02.400 --> 00:53:04.120 align:middle line:90% cleaner as the class goes down. 00:53:04.120 --> 00:53:06.240 align:middle line:84% So this is a plot of the total particles 00:53:06.240 --> 00:53:11.730 align:middle line:84% per cubic foot in the air of a clean room as a function 00:53:11.730 --> 00:53:12.930 align:middle line:90% of the size of the particle. 00:53:12.930 --> 00:53:15.673 align:middle line:84% And the line, each line is parametrized 00:53:15.673 --> 00:53:16.590 align:middle line:90% according to a number. 00:53:16.590 --> 00:53:17.770 align:middle line:90% That's the class clean room. 00:53:17.770 --> 00:53:21.240 align:middle line:84% So, for example, here in MTL, the clean room 00:53:21.240 --> 00:53:24.450 align:middle line:84% is nominally rated, at least the integrated circuits 00:53:24.450 --> 00:53:26.190 align:middle line:90% lab, at about class 100. 00:53:26.190 --> 00:53:28.160 align:middle line:90% So that's this line right here. 00:53:28.160 --> 00:53:32.860 align:middle line:84% So a class 100 says, here we are at a micron-sized particle, 00:53:32.860 --> 00:53:35.440 align:middle line:84% you can read off roughly the number of particles 00:53:35.440 --> 00:53:37.840 align:middle line:84% per cubic foot in the range of 50 or something like that. 00:53:37.840 --> 00:53:40.340 align:middle line:84% Gives you an idea of the number of particles per cubic foot. 00:53:40.340 --> 00:53:41.840 align:middle line:84% If you have more than that, then you 00:53:41.840 --> 00:53:43.788 align:middle line:84% move to a class of 1,000 or 10,000. 00:53:43.788 --> 00:53:44.830 align:middle line:90% So that's a dirtier room. 00:53:44.830 --> 00:53:46.990 align:middle line:84% The higher the class, the lower the number, 00:53:46.990 --> 00:53:49.180 align:middle line:84% like a class one, that's the best-- that's 00:53:49.180 --> 00:53:50.710 align:middle line:90% the cleanest type of clean room. 00:53:50.710 --> 00:53:54.500 align:middle line:90% 00:53:54.500 --> 00:53:56.210 align:middle line:90% Here's an example I just-- 00:53:56.210 --> 00:54:00.042 align:middle line:90% here on slide 28-- 00:54:00.042 --> 00:54:02.000 align:middle line:84% of just some pictures of different clean rooms. 00:54:02.000 --> 00:54:04.820 align:middle line:84% And, basically, we clean the factory environment-- 00:54:04.820 --> 00:54:07.790 align:middle line:84% I mentioned these HEPA filters, these high-efficiency particle 00:54:07.790 --> 00:54:10.890 align:middle line:84% filters, that recirculate the air constantly. 00:54:10.890 --> 00:54:13.490 align:middle line:84% So it's being filtered all the time. 00:54:13.490 --> 00:54:16.190 align:middle line:84% We put people in little suits called bunny suits. 00:54:16.190 --> 00:54:20.360 align:middle line:84% Here's an example of a student in a university R&D 00:54:20.360 --> 00:54:21.440 align:middle line:90% lab wearing a bunny suit. 00:54:21.440 --> 00:54:23.210 align:middle line:90% So you try to cover yourself. 00:54:23.210 --> 00:54:26.180 align:middle line:84% People are the worst source-- the biggest source of particles. 00:54:26.180 --> 00:54:27.380 align:middle line:90% We shed skin constantly. 00:54:27.380 --> 00:54:28.260 align:middle line:90% We can't help it. 00:54:28.260 --> 00:54:29.360 align:middle line:90% It's part of our natural thing. 00:54:29.360 --> 00:54:31.485 align:middle line:84% Even if you don't have dandruff, it doesn't matter. 00:54:31.485 --> 00:54:33.870 align:middle line:84% You're shedding constantly small particles. 00:54:33.870 --> 00:54:37.400 align:middle line:84% So we try to keep as much as possible our clothes contained 00:54:37.400 --> 00:54:39.590 align:middle line:90% in these clean suits. 00:54:39.590 --> 00:54:41.990 align:middle line:84% This is in a university-style R&D lab. 00:54:41.990 --> 00:54:44.240 align:middle line:84% In a manufacturing, here's an industrial fab. 00:54:44.240 --> 00:54:47.390 align:middle line:84% This is a picture I pulled off the Intel website a while ago. 00:54:47.390 --> 00:54:49.580 align:middle line:84% Actually, we sometimes put the workers in spacesuits 00:54:49.580 --> 00:54:51.240 align:middle line:84% so that not even their face is exposed 00:54:51.240 --> 00:54:53.940 align:middle line:84% so they can't spit particles, so they can't breathe particles 00:54:53.940 --> 00:54:54.850 align:middle line:90% onto the wafers. 00:54:54.850 --> 00:54:56.530 align:middle line:84% So here's a worker in a spacesuit. 00:54:56.530 --> 00:54:59.050 align:middle line:84% And he's breathing through a tube. 00:54:59.050 --> 00:55:00.808 align:middle line:84% We, also, besides the air, we have 00:55:00.808 --> 00:55:02.100 align:middle line:90% to use ultra-high purity water. 00:55:02.100 --> 00:55:03.683 align:middle line:84% We have to filter the water so there's 00:55:03.683 --> 00:55:06.210 align:middle line:84% no impurities in the water, no ionized, no sodium, 00:55:06.210 --> 00:55:08.910 align:middle line:90% no potassium, no particles. 00:55:08.910 --> 00:55:12.720 align:middle line:84% And all the chemicals we use are produced in special chemical 00:55:12.720 --> 00:55:16.315 align:middle line:84% factories where they reduce the amount of sodium, potassium, 00:55:16.315 --> 00:55:18.190 align:middle line:84% iron, and copper, all that from the chemical. 00:55:18.190 --> 00:55:19.648 align:middle line:84% So everything is ultra-high purity, 00:55:19.648 --> 00:55:21.180 align:middle line:90% all the gases are purified. 00:55:21.180 --> 00:55:24.120 align:middle line:84% So everything that goes onto that wafer surface is purified. 00:55:24.120 --> 00:55:26.340 align:middle line:84% And we use a lot of protocols in manufacturing. 00:55:26.340 --> 00:55:28.980 align:middle line:84% Oh, by the way, these days, in 300-millimeter fabs-- 00:55:28.980 --> 00:55:31.290 align:middle line:90% so this is a 200-millimeter-- 00:55:31.290 --> 00:55:33.270 align:middle line:84% 300-millimeter, which is the next generation, 00:55:33.270 --> 00:55:35.850 align:middle line:84% fab they're going to actually even reduce 00:55:35.850 --> 00:55:39.480 align:middle line:84% the number of people walking around, even in spacesuits. 00:55:39.480 --> 00:55:41.040 align:middle line:84% And what they do is they use robots. 00:55:41.040 --> 00:55:42.150 align:middle line:90% Here's a robotic. 00:55:42.150 --> 00:55:44.800 align:middle line:84% I took this off of a commercial website. 00:55:44.800 --> 00:55:48.930 align:middle line:84% This is a track near the ceiling of a 300-millimeter fab. 00:55:48.930 --> 00:55:54.210 align:middle line:84% And these little pods, these little square or cubic pods, 00:55:54.210 --> 00:55:55.470 align:middle line:90% hold wafers in them. 00:55:55.470 --> 00:55:57.240 align:middle line:90% And these travel. 00:55:57.240 --> 00:55:59.380 align:middle line:90% These pods travel on the track. 00:55:59.380 --> 00:56:01.890 align:middle line:84% They automatically go down to a piece of equipment, open up, 00:56:01.890 --> 00:56:02.790 align:middle line:90% and the wafers get loaded. 00:56:02.790 --> 00:56:04.920 align:middle line:84% So the wafers actually never get exposed to the clean room 00:56:04.920 --> 00:56:05.420 align:middle line:90% environment. 00:56:05.420 --> 00:56:07.140 align:middle line:84% They're kept in pods the entire time. 00:56:07.140 --> 00:56:11.607 align:middle line:84% They go from a pod into a vacuum system or pod into another tool. 00:56:11.607 --> 00:56:13.440 align:middle line:84% And so, they minimize the exposure this way. 00:56:13.440 --> 00:56:16.800 align:middle line:84% So we even have now a lot of robotics just 00:56:16.800 --> 00:56:19.560 align:middle line:84% to clean up the process even more. 00:56:19.560 --> 00:56:22.170 align:middle line:90% 00:56:22.170 --> 00:56:24.550 align:middle line:90% Slide 29 I talk about-- 00:56:24.550 --> 00:56:26.550 align:middle line:84% we'll continue this in more detail next time. 00:56:26.550 --> 00:56:30.300 align:middle line:90% But I talk about wafer cleaning. 00:56:30.300 --> 00:56:33.330 align:middle line:84% We do introduce onto the wafer a certain amount 00:56:33.330 --> 00:56:34.415 align:middle line:90% of impurities ourselves. 00:56:34.415 --> 00:56:36.165 align:middle line:84% In the photolithography process, remember, 00:56:36.165 --> 00:56:40.260 align:middle line:84% is that organic material, photoresist, it turns out, 00:56:40.260 --> 00:56:41.440 align:middle line:90% is a contaminant. 00:56:41.440 --> 00:56:43.440 align:middle line:84% But we have to use it because it happens to do-- 00:56:43.440 --> 00:56:44.460 align:middle line:90% it does photolithography. 00:56:44.460 --> 00:56:46.793 align:middle line:84% But we have to remove it every step because we certainly 00:56:46.793 --> 00:56:48.600 align:middle line:84% don't want it on the wafer when we're 00:56:48.600 --> 00:56:51.100 align:middle line:84% doing any high-temperature processing. 00:56:51.100 --> 00:56:53.880 align:middle line:84% So after we do resist strip, we typically then 00:56:53.880 --> 00:56:56.760 align:middle line:84% have to clean the wafer using a special clean that we'll talk 00:56:56.760 --> 00:56:58.620 align:middle line:90% about next time in RCA clean. 00:56:58.620 --> 00:57:00.520 align:middle line:90% And then we do the process step. 00:57:00.520 --> 00:57:02.670 align:middle line:84% So the process of semiconductor fabrication 00:57:02.670 --> 00:57:06.240 align:middle line:84% consists of pattern something, transfer the pattern, 00:57:06.240 --> 00:57:08.490 align:middle line:84% get all the resist off, do a clean, 00:57:08.490 --> 00:57:10.470 align:middle line:84% and then maybe go into a high-temperature step, 00:57:10.470 --> 00:57:11.845 align:middle line:84% and repeat the whole thing again. 00:57:11.845 --> 00:57:13.740 align:middle line:84% So you can have tens, five, 10, who 00:57:13.740 --> 00:57:15.698 align:middle line:84% knows how many cleans that go on depending 00:57:15.698 --> 00:57:17.490 align:middle line:84% on the number of mask levels and the number 00:57:17.490 --> 00:57:18.573 align:middle line:90% of high-temperature steps. 00:57:18.573 --> 00:57:22.640 align:middle line:90% 00:57:22.640 --> 00:57:24.790 align:middle line:84% So why are we trying to remove these things? 00:57:24.790 --> 00:57:27.190 align:middle line:84% And, I already indicated, and what we're 00:57:27.190 --> 00:57:31.360 align:middle line:84% trying to remove these organic films or trace organics? 00:57:31.360 --> 00:57:33.850 align:middle line:84% All of the organics are bad because they can cause leakage 00:57:33.850 --> 00:57:35.140 align:middle line:90% in the gate. 00:57:35.140 --> 00:57:37.480 align:middle line:90% And they can act like a mask. 00:57:37.480 --> 00:57:40.257 align:middle line:84% They prevent you from cleaning the underlying surface. 00:57:40.257 --> 00:57:41.590 align:middle line:90% So you need to get organics off. 00:57:41.590 --> 00:57:43.870 align:middle line:84% Typically, a first step of any cleaning 00:57:43.870 --> 00:57:45.700 align:middle line:90% is try to remove organics. 00:57:45.700 --> 00:57:48.280 align:middle line:84% Particles, well we already-- that's fairly obvious. 00:57:48.280 --> 00:57:51.010 align:middle line:90% They can cause defects. 00:57:51.010 --> 00:57:54.930 align:middle line:84% Particles very often carry metals in them 00:57:54.930 --> 00:57:57.430 align:middle line:84% because you get particles from the wafer handling equipment. 00:57:57.430 --> 00:58:00.070 align:middle line:84% Most equipment's made of stainless steel, which is what? 00:58:00.070 --> 00:58:01.550 align:middle line:90% It's iron and nickel. 00:58:01.550 --> 00:58:02.632 align:middle line:90% So it's a very-- 00:58:02.632 --> 00:58:04.090 align:middle line:84% particles are bad because they tend 00:58:04.090 --> 00:58:07.480 align:middle line:90% to carry metals into the wafer. 00:58:07.480 --> 00:58:12.640 align:middle line:84% Alkali metals, I've mentioned, sodium, potassium, calcium, 00:58:12.640 --> 00:58:15.220 align:middle line:90% these move easily in oxides. 00:58:15.220 --> 00:58:16.793 align:middle line:84% They can shift the threshold voltage, 00:58:16.793 --> 00:58:18.460 align:middle line:84% like we saw in our calculation, and they 00:58:18.460 --> 00:58:20.380 align:middle line:90% can cause reliability problems. 00:58:20.380 --> 00:58:23.510 align:middle line:84% And we already mentioned the transition metals 00:58:23.510 --> 00:58:24.650 align:middle line:90% having bad properties. 00:58:24.650 --> 00:58:27.020 align:middle line:84% They reduce the carrier lifetime. 00:58:27.020 --> 00:58:30.080 align:middle line:84% They reduce the mobility, which is an important property. 00:58:30.080 --> 00:58:32.210 align:middle line:84% They're also bad because they can diffuse 00:58:32.210 --> 00:58:33.860 align:middle line:90% very easily into the wafer. 00:58:33.860 --> 00:58:36.800 align:middle line:84% And they can roughen the surface. 00:58:36.800 --> 00:58:40.100 align:middle line:84% So these have a very, very bad-- among CMOS people 00:58:40.100 --> 00:58:43.760 align:middle line:84% gold, copper, and nickel, iron, very bad reputation. 00:58:43.760 --> 00:58:47.240 align:middle line:90% 00:58:47.240 --> 00:58:52.030 align:middle line:84% So, these, we take major organic contaminants, like photoresist, 00:58:52.030 --> 00:58:55.180 align:middle line:84% and we typically remove them in a solution of sulfuric acid 00:58:55.180 --> 00:58:58.360 align:middle line:84% or oxygen plasma prior to do any real refined cleaning, 00:58:58.360 --> 00:59:00.010 align:middle line:90% like RCA clean. 00:59:00.010 --> 00:59:03.090 align:middle line:84% And then we remove trace organics for the RCA 00:59:03.090 --> 00:59:04.090 align:middle line:90% clean along with metals. 00:59:04.090 --> 00:59:06.280 align:middle line:90% So that's the philosophy. 00:59:06.280 --> 00:59:10.910 align:middle line:84% And we'll talk about that next time. 00:59:10.910 --> 00:59:13.090 align:middle line:84% This is just a picture of an RCA cleaning bench. 00:59:13.090 --> 00:59:15.820 align:middle line:84% And the next time we'll go through how it works. 00:59:15.820 --> 00:59:17.050 align:middle line:90% It's a standard process. 00:59:17.050 --> 00:59:20.050 align:middle line:84% And, again, it removes trace organics, not heavy organics, 00:59:20.050 --> 00:59:22.780 align:middle line:84% trace heavy metals, and alkali ions. 00:59:22.780 --> 00:59:25.010 align:middle line:84% And there's very specific chemicals that are used, 00:59:25.010 --> 00:59:27.310 align:middle line:84% which we'll discuss next time too-- 00:59:27.310 --> 00:59:30.130 align:middle line:90% on how that's done. 00:59:30.130 --> 00:59:33.810 align:middle line:84% So let me just summarize what we talked about-- 00:59:33.810 --> 00:59:34.860 align:middle line:90% a wide range of things. 00:59:34.860 --> 00:59:37.140 align:middle line:84% We talked about native point defects, these vacancies 00:59:37.140 --> 00:59:37.890 align:middle line:90% and interstitials. 00:59:37.890 --> 00:59:40.380 align:middle line:84% They can be either neutral or charged. 00:59:40.380 --> 00:59:44.460 align:middle line:84% The charge defects obey the same statistics as shallow donors 00:59:44.460 --> 00:59:45.160 align:middle line:90% and acceptors. 00:59:45.160 --> 00:59:46.660 align:middle line:84% So as we move the Fermi level and we 00:59:46.660 --> 00:59:48.780 align:middle line:84% dope the crystal n-type or p-type, 00:59:48.780 --> 00:59:51.973 align:middle line:84% I can change the number of the concentration of these defects. 00:59:51.973 --> 00:59:53.640 align:middle line:84% The good thing, though, is they're still 00:59:53.640 --> 00:59:55.890 align:middle line:84% low enough in number that I don't need to use them 00:59:55.890 --> 00:59:57.807 align:middle line:84% when I'm calculating the Fermi level position. 00:59:57.807 --> 01:00:00.430 align:middle line:90% So that makes it easier. 01:00:00.430 --> 01:00:03.400 align:middle line:84% There are both v-type vacancy type and i-type defects. 01:00:03.400 --> 01:00:06.270 align:middle line:84% And we'll talk about how they play a very important role 01:00:06.270 --> 01:00:07.830 align:middle line:90% in understanding the processes. 01:00:07.830 --> 01:00:10.920 align:middle line:84% And I introduced the idea of contamination control. 01:00:10.920 --> 01:00:12.030 align:middle line:90% That's in Chapter 4. 01:00:12.030 --> 01:00:16.500 align:middle line:84% And we'll discuss that in greater depth next time. 01:00:16.500 --> 01:00:18.810 align:middle line:84% OK, so that's all I have for today. 01:00:18.810 --> 01:00:21.510 align:middle line:84% And, on Tuesday, remember that your first problem set, 01:00:21.510 --> 01:00:23.480 align:middle line:90% your first homework set is due. 01:00:23.480 --> 01:00:25.340 align:middle line:90% Thank you. 01:00:25.340 --> 01:00:36.000 align:middle line:90%