WEBVTT 00:00:00.000 --> 00:00:01.917 align:middle line:84% JUDY HOYT: It's very simple, but doesn't fully 00:00:01.917 --> 00:00:03.980 align:middle line:90% capture all of the reality. 00:00:03.980 --> 00:00:08.240 align:middle line:84% The simplest analytic expression that captures profiles 00:00:08.240 --> 00:00:12.380 align:middle line:84% reasonably well is the Pearson four, which has four moments, 00:00:12.380 --> 00:00:16.070 align:middle line:84% and those moments are generally tabulated in tables. 00:00:16.070 --> 00:00:19.610 align:middle line:84% We also presented the idea of Monte Carlo 00:00:19.610 --> 00:00:22.250 align:middle line:84% or numerical solutions, for example, Monte Carlo 00:00:22.250 --> 00:00:27.270 align:middle line:84% simulation, which is quite accurate. 00:00:27.270 --> 00:00:29.965 align:middle line:84% And another thing called the Boltzmann transport equation 00:00:29.965 --> 00:00:30.465 align:middle line:90% solution. 00:00:30.465 --> 00:00:32.740 align:middle line:90% 00:00:32.740 --> 00:00:35.610 align:middle line:84% The other thing we mentioned is that there's this process 00:00:35.610 --> 00:00:36.990 align:middle line:90% called ion channeling. 00:00:36.990 --> 00:00:39.840 align:middle line:84% Ion channeling itself is quite a challenge 00:00:39.840 --> 00:00:41.490 align:middle line:90% in calculating profiles. 00:00:41.490 --> 00:00:44.010 align:middle line:84% Calculating the profiles pretty accurately 00:00:44.010 --> 00:00:47.400 align:middle line:84% into amorphous solids, or amorphous materials, 00:00:47.400 --> 00:00:49.520 align:middle line:90% is reasonably routine. 00:00:49.520 --> 00:00:51.270 align:middle line:84% But once you have to model ion channeling, 00:00:51.270 --> 00:00:53.620 align:middle line:90% it gets a little tricky. 00:00:53.620 --> 00:00:55.620 align:middle line:84% Today I want to cover some things that we didn't 00:00:55.620 --> 00:00:56.745 align:middle line:90% get a chance to talk about. 00:00:56.745 --> 00:00:58.380 align:middle line:84% We never even talked about, last time, 00:00:58.380 --> 00:01:02.700 align:middle line:84% the physics of the modeling of the ion implantation process, 00:01:02.700 --> 00:01:05.982 align:middle line:84% that is the physical energy loss mechanisms of the ions 00:01:05.982 --> 00:01:06.690 align:middle line:90% as they traverse. 00:01:06.690 --> 00:01:07.890 align:middle line:90% We want to talk about that. 00:01:07.890 --> 00:01:11.520 align:middle line:84% Once we've covered that, we want to talk about damage. 00:01:11.520 --> 00:01:13.290 align:middle line:84% How do we model the damage that takes 00:01:13.290 --> 00:01:16.950 align:middle line:84% place in the silicon substrate, and how do we anneal it? 00:01:16.950 --> 00:01:19.397 align:middle line:84% And then I'll give a very brief introduction 00:01:19.397 --> 00:01:20.730 align:middle line:90% to transient enhanced diffusion. 00:01:20.730 --> 00:01:22.500 align:middle line:84% The next lecture, next Tuesday, is 00:01:22.500 --> 00:01:24.750 align:middle line:84% going to be dedicated to talking about TED, 00:01:24.750 --> 00:01:29.400 align:middle line:84% but I'll at least briefly introduce the topic. 00:01:29.400 --> 00:01:29.900 align:middle line:90% OK. 00:01:29.900 --> 00:01:31.265 align:middle line:90% Let's go on to slide number 2. 00:01:31.265 --> 00:01:35.110 align:middle line:90% 00:01:35.110 --> 00:01:37.570 align:middle line:84% The right hand side of this slide 00:01:37.570 --> 00:01:41.140 align:middle line:84% is just a schematic picture of a cartoon 00:01:41.140 --> 00:01:45.520 align:middle line:84% where you're shooting an ion into a silicon surface. 00:01:45.520 --> 00:01:48.670 align:middle line:84% And all these little open symbols 00:01:48.670 --> 00:01:51.790 align:middle line:84% here represent silicon atoms on some kind of a lattice. 00:01:51.790 --> 00:01:55.450 align:middle line:84% You see an ion, which is this dark bullet here. 00:01:55.450 --> 00:01:57.760 align:middle line:84% It comes in and it hits the target. 00:01:57.760 --> 00:02:00.430 align:middle line:84% And when it does, it may have some kind 00:02:00.430 --> 00:02:01.690 align:middle line:90% of a nuclear collision here. 00:02:01.690 --> 00:02:05.632 align:middle line:84% It may collide with the target atom and be deflected. 00:02:05.632 --> 00:02:07.090 align:middle line:84% There'll be some energy loss there. 00:02:07.090 --> 00:02:12.300 align:middle line:84% Then the target atom itself is going to be recoiled 00:02:12.300 --> 00:02:14.830 align:middle line:84% and will have some energy imparted to it. 00:02:14.830 --> 00:02:18.970 align:middle line:84% But that deflection is going to then knock the ion a little bit 00:02:18.970 --> 00:02:21.220 align:middle line:84% into a different direction, change its direction. 00:02:21.220 --> 00:02:23.440 align:middle line:84% And interestingly, you see it going down a path. 00:02:23.440 --> 00:02:26.140 align:middle line:84% And right here, after this collision right here, 00:02:26.140 --> 00:02:28.900 align:middle line:84% interestingly, the ion got knocked into a channel, 00:02:28.900 --> 00:02:30.400 align:middle line:84% is what we're supposed to represent. 00:02:30.400 --> 00:02:32.810 align:middle line:84% You see, its direction got changed 00:02:32.810 --> 00:02:35.570 align:middle line:84% by this nuclear collision and now it's 00:02:35.570 --> 00:02:37.610 align:middle line:84% working its way down a little bit of a channel. 00:02:37.610 --> 00:02:41.120 align:middle line:84% Still losing energy, perhaps at a slightly different rate. 00:02:41.120 --> 00:02:45.770 align:middle line:84% And still with each collision creating a silicon recoil 00:02:45.770 --> 00:02:48.690 align:middle line:84% that's been knocked off its lattice. 00:02:48.690 --> 00:02:50.470 align:middle line:84% So just a very schematic picture. 00:02:50.470 --> 00:02:52.890 align:middle line:84% So again, we're bombarding the wafer. 00:02:52.890 --> 00:02:56.340 align:middle line:84% The energy of this incoming dark-colored ion 00:02:56.340 --> 00:02:59.160 align:middle line:84% is typically anywhere, well, some of the lowest energy 00:02:59.160 --> 00:03:01.413 align:middle line:84% implants being done today are one kilovolt, 00:03:01.413 --> 00:03:02.580 align:middle line:90% or maybe even slightly less. 00:03:02.580 --> 00:03:05.190 align:middle line:84% That's very low, but that is being done. 00:03:05.190 --> 00:03:08.250 align:middle line:84% And some of the highest energy implants for making, 00:03:08.250 --> 00:03:12.060 align:middle line:84% in bipolar they make selectively implanted collector regions 00:03:12.060 --> 00:03:13.710 align:middle line:90% that are quite deep. 00:03:13.710 --> 00:03:16.570 align:middle line:84% They can work in the 1 MeV range. 00:03:16.570 --> 00:03:18.733 align:middle line:84% So there's a very wide range that people 00:03:18.733 --> 00:03:19.650 align:middle line:90% are eyeing at playing. 00:03:19.650 --> 00:03:22.980 align:middle line:84% Typically, implants are between something like 10 to 100 keV, 00:03:22.980 --> 00:03:25.020 align:middle line:84% but people do use the full range. 00:03:25.020 --> 00:03:28.020 align:middle line:84% Now look at the binding energy of a silicon atom 00:03:28.020 --> 00:03:29.010 align:middle line:90% on the lattice. 00:03:29.010 --> 00:03:31.410 align:middle line:90% That's only 15 electron volts. 00:03:31.410 --> 00:03:35.490 align:middle line:84% So you can imagine that we're coming in with a species that 00:03:35.490 --> 00:03:38.800 align:middle line:84% has thousands of times more energy than the binding energy. 00:03:38.800 --> 00:03:41.640 align:middle line:84% So obviously, it's quite possible 00:03:41.640 --> 00:03:43.410 align:middle line:84% to have billiard ball-like collisions, 00:03:43.410 --> 00:03:45.900 align:middle line:84% where you knock these silicon atoms off of their lattice 00:03:45.900 --> 00:03:46.950 align:middle line:90% sites. 00:03:46.950 --> 00:03:51.270 align:middle line:84% So the ions collide, and they collide elastically. 00:03:51.270 --> 00:03:56.070 align:middle line:84% And they have, as a result, we have ion deflections, which 00:03:56.070 --> 00:03:58.050 align:middle line:84% I just showed you here, where the ions change 00:03:58.050 --> 00:03:58.960 align:middle line:90% their direction. 00:03:58.960 --> 00:04:00.480 align:middle line:84% And when you collide, of course, you 00:04:00.480 --> 00:04:02.670 align:middle line:90% lose a certain amount of energy. 00:04:02.670 --> 00:04:04.620 align:middle line:84% The ion loses some energy, and it 00:04:04.620 --> 00:04:08.720 align:middle line:84% displaces silicon atoms, which we end up calling recoils. 00:04:08.720 --> 00:04:12.080 align:middle line:84% In addition to this collision, this sort of pool table 00:04:12.080 --> 00:04:14.930 align:middle line:84% type of collision of billiard balls, 00:04:14.930 --> 00:04:19.790 align:middle line:84% the ions can also suffer sort of an inelastic drag force 00:04:19.790 --> 00:04:21.480 align:middle line:90% from the target electrons. 00:04:21.480 --> 00:04:24.620 align:middle line:84% And so this leads to electronic stopping, where 00:04:24.620 --> 00:04:27.290 align:middle line:84% you lose ion energy and it actually heats the lattice, 00:04:27.290 --> 00:04:29.000 align:middle line:90% to a certain extent. 00:04:29.000 --> 00:04:33.710 align:middle line:84% Because they're in this median that has electrons in it. 00:04:33.710 --> 00:04:35.600 align:middle line:84% Eventually, this ion and all the ions 00:04:35.600 --> 00:04:38.090 align:middle line:84% come to rest after they've lost all of their energy 00:04:38.090 --> 00:04:42.230 align:middle line:84% in both collisional processes and in this drag force. 00:04:42.230 --> 00:04:45.560 align:middle line:84% And channeling, as I mentioned, we talked about last time. 00:04:45.560 --> 00:04:47.660 align:middle line:84% Along certain directions, ions can 00:04:47.660 --> 00:04:50.990 align:middle line:84% travel in the crystal with very few collisions and little drag. 00:04:50.990 --> 00:04:54.230 align:middle line:84% So they can go deeper than they would otherwise, 00:04:54.230 --> 00:04:56.930 align:middle line:90% and that's tough to model. 00:04:56.930 --> 00:05:01.810 align:middle line:84% So if we go to page 3, or slide 3, 00:05:01.810 --> 00:05:03.700 align:middle line:84% how do we model these range statistics? 00:05:03.700 --> 00:05:07.660 align:middle line:84% Well, what we do is we write down the total energy 00:05:07.660 --> 00:05:11.530 align:middle line:84% loss during an ion trajectory, and we write it 00:05:11.530 --> 00:05:13.220 align:middle line:90% as a linear sum. 00:05:13.220 --> 00:05:17.710 align:middle line:84% So we treat these two processes independently, nuclear losses 00:05:17.710 --> 00:05:19.340 align:middle line:90% and electronic losses. 00:05:19.340 --> 00:05:24.250 align:middle line:84% So we write the rate of energy loss as a function of distance, 00:05:24.250 --> 00:05:26.320 align:middle line:90% as this equation, de by dx. 00:05:26.320 --> 00:05:30.790 align:middle line:90% 00:05:30.790 --> 00:05:33.430 align:middle line:84% It's a negative number, because you're losing energy. 00:05:33.430 --> 00:05:36.370 align:middle line:84% N, where n is the target atom density, atoms 00:05:36.370 --> 00:05:40.540 align:middle line:84% per cubic centimeter, times the sum of these two quantities 00:05:40.540 --> 00:05:44.030 align:middle line:90% s sub n plus s sub e. 00:05:44.030 --> 00:05:45.680 align:middle line:84% Again, n is the target atom density. 00:05:45.680 --> 00:05:47.960 align:middle line:90% S sub n is a function of energy. 00:05:47.960 --> 00:05:50.630 align:middle line:90% It's the nuclear stopping power. 00:05:50.630 --> 00:05:54.930 align:middle line:84% And it has units of energy times area. 00:05:54.930 --> 00:06:00.380 align:middle line:84% So it's eV dash centimeter squared is a typical unit. 00:06:00.380 --> 00:06:02.870 align:middle line:84% And s sub e is the electronic stopping power, 00:06:02.870 --> 00:06:04.250 align:middle line:90% again eV centimeter squared. 00:06:04.250 --> 00:06:06.650 align:middle line:90% you can see the units work out. 00:06:06.650 --> 00:06:09.560 align:middle line:84% If s has units of eV centimeter squared, 00:06:09.560 --> 00:06:11.870 align:middle line:84% you multiply it by atoms per cubic centimeter, 00:06:11.870 --> 00:06:14.750 align:middle line:84% you get a certain amount of eV per centimeter, 00:06:14.750 --> 00:06:20.903 align:middle line:84% or energy loss per unit length in going into the crystal. 00:06:20.903 --> 00:06:22.820 align:middle line:84% The thing to remember is that these functions, 00:06:22.820 --> 00:06:25.190 align:middle line:84% these are in general these stopping powers are going 00:06:25.190 --> 00:06:27.260 align:middle line:90% to be a function of the energy. 00:06:27.260 --> 00:06:29.595 align:middle line:84% That is, the rate at which you lose energy 00:06:29.595 --> 00:06:31.220 align:middle line:84% is a function of how fast you're going, 00:06:31.220 --> 00:06:32.762 align:middle line:84% of how much energy you actually have. 00:06:32.762 --> 00:06:34.700 align:middle line:90% 00:06:34.700 --> 00:06:38.180 align:middle line:84% If we know s sub n of e as a function, and we know s sub e, 00:06:38.180 --> 00:06:40.590 align:middle line:84% the electronic stopping as a function of energy, 00:06:40.590 --> 00:06:44.420 align:middle line:84% then you can simply compute the range by doing this integral. 00:06:44.420 --> 00:06:45.710 align:middle line:90% So you integrate. 00:06:45.710 --> 00:06:50.150 align:middle line:84% The range would just be the integral from 0 to e, e naught. 00:06:50.150 --> 00:06:53.540 align:middle line:84% Whatever your incoming energy is, your ion-implanted energy, 00:06:53.540 --> 00:07:00.500 align:middle line:84% say 100 kilovolts of d e divided by the sum of the two stopping 00:07:00.500 --> 00:07:01.010 align:middle line:90% powers. 00:07:01.010 --> 00:07:03.680 align:middle line:84% And here again, the density is a constant number. 00:07:03.680 --> 00:07:05.390 align:middle line:90% It's just been pulled out. 00:07:05.390 --> 00:07:08.150 align:middle line:84% So you can find the range mathematically 00:07:08.150 --> 00:07:10.955 align:middle line:84% if you know the physics of these two stopping powers. 00:07:10.955 --> 00:07:12.930 align:middle line:90% 00:07:12.930 --> 00:07:15.590 align:middle line:84% So that's where a lot of the modeling 00:07:15.590 --> 00:07:18.980 align:middle line:84% has been done in understanding the physics of s sub n s sub e. 00:07:18.980 --> 00:07:21.650 align:middle line:84% And we'll first talk about, on slide 4, 00:07:21.650 --> 00:07:24.380 align:middle line:84% we'll talk about nuclear stopping. 00:07:24.380 --> 00:07:28.640 align:middle line:84% Above a certain energy, so it's about half a kilovolt, 00:07:28.640 --> 00:07:29.870 align:middle line:90% or 500 eV. 00:07:29.870 --> 00:07:32.780 align:middle line:84% Now be careful, because we're approaching this range for some 00:07:32.780 --> 00:07:34.790 align:middle line:84% of our very lowest energy implants, 00:07:34.790 --> 00:07:37.190 align:middle line:84% making very shallow source drain extensions. 00:07:37.190 --> 00:07:38.720 align:middle line:84% People are using quite low energies. 00:07:38.720 --> 00:07:42.260 align:middle line:84% But if you're above this, it's reasonably valid 00:07:42.260 --> 00:07:46.310 align:middle line:84% to model nuclear stopping as a classical two-body collision 00:07:46.310 --> 00:07:50.510 align:middle line:84% between a silicon atom that's sitting still 00:07:50.510 --> 00:07:53.760 align:middle line:84% and an incident ion that's coming in with some velocity. 00:07:53.760 --> 00:07:57.500 align:middle line:84% So it can be modeled as, just like on a pool table, two balls 00:07:57.500 --> 00:08:00.448 align:middle line:84% colliding, using the conservation of energy 00:08:00.448 --> 00:08:02.240 align:middle line:84% and the conservation of momentum principles 00:08:02.240 --> 00:08:06.230 align:middle line:84% that you learned in your basic physics class. 00:08:06.230 --> 00:08:09.020 align:middle line:84% Now, why does this have to be above a certain energy? 00:08:09.020 --> 00:08:10.500 align:middle line:90% Why is that the case? 00:08:10.500 --> 00:08:13.590 align:middle line:84% Well, it turns out, if the energy is lower than this, 00:08:13.590 --> 00:08:15.690 align:middle line:84% or significantly lower, then what happens 00:08:15.690 --> 00:08:17.790 align:middle line:84% is, as this incident ion comes in, 00:08:17.790 --> 00:08:21.540 align:middle line:84% instead of looking like a billiard ball, a hard sphere 00:08:21.540 --> 00:08:25.950 align:middle line:84% model, this ion has time to sort of hang around the target atom, 00:08:25.950 --> 00:08:29.490 align:middle line:84% and the interaction is not just like a Hartsfeld collision. 00:08:29.490 --> 00:08:31.620 align:middle line:84% You have other types of interactions. 00:08:31.620 --> 00:08:35.280 align:middle line:84% You can have multiple interacts with a lattice, maybe, 00:08:35.280 --> 00:08:37.530 align:middle line:84% in the sense of it's going slow enough 00:08:37.530 --> 00:08:39.330 align:middle line:84% that as it passes by the nucleus, 00:08:39.330 --> 00:08:41.169 align:middle line:84% it has different types of interaction. 00:08:41.169 --> 00:08:44.882 align:middle line:84% So if your energy is low enough, these models break down. 00:08:44.882 --> 00:08:47.340 align:middle line:84% But the good thing about ion implantation, most of the time 00:08:47.340 --> 00:08:50.700 align:middle line:84% you're well above that threshold. 00:08:50.700 --> 00:08:54.060 align:middle line:84% So, as you remember from your basic physics class, 00:08:54.060 --> 00:08:55.640 align:middle line:84% we have an incident ball coming in, 00:08:55.640 --> 00:08:57.950 align:middle line:84% hitting another ball that was originally at rest. 00:08:57.950 --> 00:09:01.790 align:middle line:84% This incident ion is going to be scattered at some angle. 00:09:01.790 --> 00:09:05.330 align:middle line:84% And you can figure that out once the interaction potential, v 00:09:05.330 --> 00:09:08.180 align:middle line:84% as a function of r, r being the distance between the two 00:09:08.180 --> 00:09:09.660 align:middle line:90% bodies. 00:09:09.660 --> 00:09:12.470 align:middle line:84% Once that's known, then you integrate 00:09:12.470 --> 00:09:14.775 align:middle line:90% that along the path of the ion. 00:09:14.775 --> 00:09:17.150 align:middle line:84% You can calculate the scattering angle for the collision, 00:09:17.150 --> 00:09:21.725 align:middle line:84% and you can do it once and then look in a lookup table. 00:09:21.725 --> 00:09:23.580 align:middle line:90% 00:09:23.580 --> 00:09:26.237 align:middle line:84% So you apply basic physics of conservation 00:09:26.237 --> 00:09:28.320 align:middle line:84% of energy and momentum, you can get these numbers. 00:09:28.320 --> 00:09:30.487 align:middle line:84% Again, the interesting thing about ion implantation, 00:09:30.487 --> 00:09:32.910 align:middle line:84% of all the processes we talk about in this class or anyone 00:09:32.910 --> 00:09:35.550 align:middle line:84% does, in IC Fab, it's the only one where, 00:09:35.550 --> 00:09:37.050 align:middle line:84% from first principles physics, you 00:09:37.050 --> 00:09:38.342 align:middle line:90% can actually predict something. 00:09:38.342 --> 00:09:41.190 align:middle line:84% You don't have too many free variables the way 00:09:41.190 --> 00:09:43.350 align:middle line:84% you do in some of these chemical processes. 00:09:43.350 --> 00:09:46.240 align:middle line:90% 00:09:46.240 --> 00:09:49.840 align:middle line:84% So what it boils down to as far as nuclear scattering goes, 00:09:49.840 --> 00:09:53.530 align:middle line:84% is figuring out what is the appropriate interaction 00:09:53.530 --> 00:09:56.380 align:middle line:84% potential, the nuclear scattering potential? 00:09:56.380 --> 00:10:02.080 align:middle line:84% Well, if you think about these two bodies, an ion 00:10:02.080 --> 00:10:04.660 align:middle line:84% and a silicon atom with the iron approaching it, 00:10:04.660 --> 00:10:07.330 align:middle line:84% the first thing you might think about 00:10:07.330 --> 00:10:09.520 align:middle line:84% is, because you know the nucleus is charged, 00:10:09.520 --> 00:10:11.800 align:middle line:84% and it has a certain charge, which 00:10:11.800 --> 00:10:16.105 align:middle line:84% is the charge on the electron q times it's z number. 00:10:16.105 --> 00:10:17.810 align:middle line:90% 00:10:17.810 --> 00:10:18.310 align:middle line:90% OK. 00:10:18.310 --> 00:10:21.010 align:middle line:84% So you might imagine that the simplest 00:10:21.010 --> 00:10:23.170 align:middle line:84% type of potential interaction between these two 00:10:23.170 --> 00:10:27.370 align:middle line:84% charged nuclei is just the coulombic potential, which 00:10:27.370 --> 00:10:31.390 align:middle line:84% is just given by the z numbers multiplied together 00:10:31.390 --> 00:10:32.140 align:middle line:90% divided by r. 00:10:32.140 --> 00:10:35.200 align:middle line:84% So it's a 1 over r type of good, old-fashioned Coulomb 00:10:35.200 --> 00:10:36.867 align:middle line:90% potential. 00:10:36.867 --> 00:10:39.200 align:middle line:84% That's a little bit too simple, though, because the atom 00:10:39.200 --> 00:10:40.100 align:middle line:90% is just not a nucleus. 00:10:40.100 --> 00:10:41.767 align:middle line:84% An atom has an electron cloud around it. 00:10:41.767 --> 00:10:45.320 align:middle line:84% So the electrons around the target atom nucleus 00:10:45.320 --> 00:10:47.720 align:middle line:84% actually ends up screening the core potential 00:10:47.720 --> 00:10:51.830 align:middle line:84% of the nucleus, to a certain extent, from the incoming ion. 00:10:51.830 --> 00:10:54.320 align:middle line:84% So it's not, this is a little bit oversimplified. 00:10:54.320 --> 00:10:57.500 align:middle line:84% So what people do is they put in a generalized function, 00:10:57.500 --> 00:11:01.790 align:middle line:84% f, which they multiply by the classical Coulomb 00:11:01.790 --> 00:11:03.350 align:middle line:84% unscreened potential, and then this 00:11:03.350 --> 00:11:06.650 align:middle line:84% becomes the screened potential, v as a function of r. 00:11:06.650 --> 00:11:10.940 align:middle line:84% F is some generalized function of r over a. 00:11:10.940 --> 00:11:15.640 align:middle line:84% Again, r is the distance between the two nuclei, 00:11:15.640 --> 00:11:19.540 align:middle line:84% and a is a thomas-fermi parameter, which 00:11:19.540 --> 00:11:21.310 align:middle line:90% is related to the Bohr radius. 00:11:21.310 --> 00:11:24.190 align:middle line:84% It's some function of the Bohr radius 00:11:24.190 --> 00:11:26.650 align:middle line:84% times a function of the z numbers. 00:11:26.650 --> 00:11:28.570 align:middle line:84% So it gives you, a is some measure 00:11:28.570 --> 00:11:32.410 align:middle line:84% of the, if you want to call it the size of the atom, 00:11:32.410 --> 00:11:33.820 align:middle line:90% in some way. 00:11:33.820 --> 00:11:35.440 align:middle line:84% And r is, of course, the distance 00:11:35.440 --> 00:11:40.100 align:middle line:84% between the two, the colliding ion and the silicon atom. 00:11:40.100 --> 00:11:42.745 align:middle line:84% So a very common potential that's often used 00:11:42.745 --> 00:11:43.870 align:middle line:90% is an exponential function. 00:11:43.870 --> 00:11:49.060 align:middle line:84% You assume that the electrons exponentially dampen out 00:11:49.060 --> 00:11:52.180 align:middle line:84% the Coulomb potential, and the people 00:11:52.180 --> 00:11:54.700 align:middle line:84% use what's called a thomas-fermi potential. 00:11:54.700 --> 00:11:58.300 align:middle line:84% So this function here, shown on the third equation on slide 5 00:11:58.300 --> 00:12:01.730 align:middle line:84% is the thomas-fermi potential for ion implantation. 00:12:01.730 --> 00:12:05.980 align:middle line:84% So it's got a 1 over r dependence times an exponential 00:12:05.980 --> 00:12:08.980 align:middle line:84% e to the minus r over a, where again, a 00:12:08.980 --> 00:12:12.137 align:middle line:84% is this thomas-fermi screening parameter. 00:12:12.137 --> 00:12:12.970 align:middle line:90% So that's potential. 00:12:12.970 --> 00:12:14.890 align:middle line:84% That's one that was often used in modeling 00:12:14.890 --> 00:12:16.130 align:middle line:90% of ion implantation. 00:12:16.130 --> 00:12:20.550 align:middle line:90% 00:12:20.550 --> 00:12:26.950 align:middle line:84% So it turns out that when the screening function is, instead 00:12:26.950 --> 00:12:29.590 align:middle line:84% of using exponential, if you use a screening function f just 00:12:29.590 --> 00:12:36.670 align:middle line:84% to be a over r, then it turns out that if f is just a over r, 00:12:36.670 --> 00:12:39.230 align:middle line:84% and this just the potential just goes like 1 over r squared. 00:12:39.230 --> 00:12:42.380 align:middle line:84% That's another way of doing the screening function. 00:12:42.380 --> 00:12:44.830 align:middle line:84% In that case, the nuclear stopping power 00:12:44.830 --> 00:12:46.495 align:middle line:84% can be approximated by a constant. 00:12:46.495 --> 00:12:49.030 align:middle line:90% 00:12:49.030 --> 00:12:52.378 align:middle line:84% So it turns out that this number, and if you 00:12:52.378 --> 00:12:54.670 align:middle line:84% want to see that derivation, you can go to this article 00:12:54.670 --> 00:12:58.180 align:middle line:84% by Gibbons back from the proceedings of the IEEE, 00:12:58.180 --> 00:13:00.490 align:middle line:90% oh, back in 1968. 00:13:00.490 --> 00:13:04.600 align:middle line:84% And in fact, they derive that it can be a constant number. 00:13:04.600 --> 00:13:08.800 align:middle line:84% That depends just on the z number of the ion, 00:13:08.800 --> 00:13:11.320 align:middle line:84% and the mass of the ion, and the z number 00:13:11.320 --> 00:13:13.460 align:middle line:90% and the mass of the substrate. 00:13:13.460 --> 00:13:15.670 align:middle line:84% So this is a simple equation you can use if you're 00:13:15.670 --> 00:13:16.960 align:middle line:90% stuck on a desert island. 00:13:16.960 --> 00:13:19.270 align:middle line:84% You need to know nuclear stopping power, 00:13:19.270 --> 00:13:21.430 align:middle line:84% you can just program this into your calculator. 00:13:21.430 --> 00:13:23.260 align:middle line:84% And I just did a simple calculation 00:13:23.260 --> 00:13:26.260 align:middle line:84% for phosphorus, which has a z number of 15 00:13:26.260 --> 00:13:29.560 align:middle line:84% and an atomic mass of twice that, or roughly a 31. 00:13:29.560 --> 00:13:33.640 align:middle line:84% Silicon has a z number of 14, a mass of 28 amu. 00:13:33.640 --> 00:13:36.680 align:middle line:84% You plug these numbers in and you do the calculation, 00:13:36.680 --> 00:13:40.750 align:middle line:84% I get an s sub n number of about 550 kiloelectron volts 00:13:40.750 --> 00:13:42.380 align:middle line:90% per micron. 00:13:42.380 --> 00:13:44.270 align:middle line:84% So that's how much energy I lose, 00:13:44.270 --> 00:13:47.210 align:middle line:84% if phosphorus going in, assuming it's 00:13:47.210 --> 00:13:50.930 align:middle line:84% a constant linear number, 550 keV per micron, just 00:13:50.930 --> 00:13:53.030 align:middle line:90% gives you a rough idea. 00:13:53.030 --> 00:13:55.790 align:middle line:84% And that's again, assuming a screening function is just a 1 00:13:55.790 --> 00:13:58.490 align:middle line:84% over r type of screening, due to the electrons 00:13:58.490 --> 00:14:01.020 align:middle line:90% around the nucleus. 00:14:01.020 --> 00:14:04.760 align:middle line:84% And in fact, if you go on to slide 7 of your handout, 00:14:04.760 --> 00:14:06.950 align:middle line:84% I took this plot from Mayer and Lao's book. 00:14:06.950 --> 00:14:10.530 align:middle line:84% I referred to Mayer and Lao earlier in the course. 00:14:10.530 --> 00:14:13.310 align:middle line:84% In fact, handout one has the full reference 00:14:13.310 --> 00:14:14.600 align:middle line:90% for his textbook. 00:14:14.600 --> 00:14:18.140 align:middle line:84% And what he's plotting here is de by dx. 00:14:18.140 --> 00:14:20.750 align:middle line:84% So again, that's a keV per micron. 00:14:20.750 --> 00:14:23.360 align:middle line:90% So it's a stopping power. 00:14:23.360 --> 00:14:26.810 align:middle line:84% Or, if you want, you can change both the energy unit 00:14:26.810 --> 00:14:27.860 align:middle line:90% and the length unit. 00:14:27.860 --> 00:14:29.940 align:middle line:84% It's equivalent to eV per nanometer. 00:14:29.940 --> 00:14:32.150 align:middle line:84% I prefer to think of keV per micron, 00:14:32.150 --> 00:14:34.460 align:middle line:90% but it's just either way. 00:14:34.460 --> 00:14:37.430 align:middle line:84% And it's on a log log plot, and the x-axis 00:14:37.430 --> 00:14:40.330 align:middle line:90% is the energy of the ion. 00:14:40.330 --> 00:14:42.580 align:middle line:84% And there are two different types 00:14:42.580 --> 00:14:44.050 align:middle line:90% of stopping powers shown here. 00:14:44.050 --> 00:14:45.425 align:middle line:84% Right now, all we've talked about 00:14:45.425 --> 00:14:47.410 align:middle line:84% is nuclear, but let's focus on this dashed line 00:14:47.410 --> 00:14:48.700 align:middle line:90% here for phosphorus. 00:14:48.700 --> 00:14:53.530 align:middle line:84% That starts up at 10 keV and it's about 500 or so, 00:14:53.530 --> 00:14:56.230 align:middle line:84% a little over 500 keV per micron. 00:14:56.230 --> 00:14:58.180 align:middle line:84% And then, as you can see, in reality, 00:14:58.180 --> 00:15:00.640 align:middle line:84% the nuclear stopping power given by this dashed line 00:15:00.640 --> 00:15:03.160 align:middle line:84% is actually going down as you go to higher energies. 00:15:03.160 --> 00:15:05.170 align:middle line:84% But lo and behold, the number we just 00:15:05.170 --> 00:15:07.270 align:middle line:84% calculated in our simple calculator, 00:15:07.270 --> 00:15:11.350 align:middle line:84% again, assuming a thomas-fermi screening function of 1 over r, 00:15:11.350 --> 00:15:14.260 align:middle line:84% comes out at low energies to give you pretty close, 00:15:14.260 --> 00:15:16.540 align:middle line:84% asymptotically, to what people calculate 00:15:16.540 --> 00:15:20.500 align:middle line:84% with more sophisticated screening functions. 00:15:20.500 --> 00:15:23.170 align:middle line:84% Indeed, my calculation here of 550 keV 00:15:23.170 --> 00:15:25.780 align:middle line:84% per micron at 10 kilovolts is pretty darn close 00:15:25.780 --> 00:15:27.797 align:middle line:84% to that dashed line for phosphorus. 00:15:27.797 --> 00:15:28.630 align:middle line:90% So it's interesting. 00:15:28.630 --> 00:15:30.550 align:middle line:84% And you can check it out yourself for arsenic. 00:15:30.550 --> 00:15:31.960 align:middle line:84% Again, you know the z number and the mass, 00:15:31.960 --> 00:15:34.690 align:middle line:84% you can check it out to see how accurate, at low energies, 00:15:34.690 --> 00:15:37.190 align:middle line:90% it asymptotically approaches. 00:15:37.190 --> 00:15:38.720 align:middle line:90% So what do we notice? 00:15:38.720 --> 00:15:43.430 align:middle line:84% Well, obvious, arsenic is a very high z number, a high mass 00:15:43.430 --> 00:15:46.980 align:middle line:84% element, and it's nuclear stopping power is quite large. 00:15:46.980 --> 00:15:50.630 align:middle line:84% It's on the order of 1,000 keV per micron, 00:15:50.630 --> 00:15:51.830 align:middle line:90% something like that. 00:15:51.830 --> 00:15:55.250 align:middle line:84% Phosphorus is being less, and boron nuclear stopping 00:15:55.250 --> 00:15:56.840 align:middle line:84% even lower, an order of magnitude 00:15:56.840 --> 00:16:00.760 align:middle line:90% lower than for arsenic. 00:16:00.760 --> 00:16:04.270 align:middle line:84% The other thing on this plot, besides these nuclear stopping 00:16:04.270 --> 00:16:07.900 align:middle line:84% powers, the ones sub n are nuclear, these straight lines 00:16:07.900 --> 00:16:11.020 align:middle line:84% that increase with energy, these are the electronic stopping 00:16:11.020 --> 00:16:12.730 align:middle line:84% powers, and we'll talk about that next. 00:16:12.730 --> 00:16:15.940 align:middle line:84% This is the type of stopping that's due to the drag 00:16:15.940 --> 00:16:19.290 align:middle line:84% force of the electrons in the substrate. 00:16:19.290 --> 00:16:25.360 align:middle line:84% So let's go on to slide 8 and talk exactly about that, 00:16:25.360 --> 00:16:27.670 align:middle line:90% this sort of non-local. 00:16:27.670 --> 00:16:28.600 align:middle line:90% Why is it non-local? 00:16:28.600 --> 00:16:31.330 align:middle line:84% Well, the nuclear stopping power is local in the sense of, 00:16:31.330 --> 00:16:32.560 align:middle line:90% you're having a collision. 00:16:32.560 --> 00:16:36.340 align:middle line:84% The ion is coming very close to the atom and the substrate. 00:16:36.340 --> 00:16:37.490 align:middle line:90% You're having a deflection. 00:16:37.490 --> 00:16:41.530 align:middle line:84% So it's an actual physical collision, 00:16:41.530 --> 00:16:44.880 align:middle line:84% and they interact by this coulombic force. 00:16:44.880 --> 00:16:49.710 align:middle line:84% This is a non-local phenomenon called non-local 00:16:49.710 --> 00:16:51.600 align:middle line:84% or local electronic stopping, and there 00:16:51.600 --> 00:16:53.820 align:middle line:90% are two ways of viewing it. 00:16:53.820 --> 00:16:57.960 align:middle line:84% You can imagine some kind of drag force caused by the fact 00:16:57.960 --> 00:17:00.670 align:middle line:84% that I have a charged ion coming in, going at some velocity. 00:17:00.670 --> 00:17:03.420 align:middle line:84% So it's as plus, arsenic plus, or boron plus. 00:17:03.420 --> 00:17:09.300 align:middle line:84% Boron minus is in this sea of electrons, the sea of electrons 00:17:09.300 --> 00:17:10.270 align:middle line:90% where they come from. 00:17:10.270 --> 00:17:15.448 align:middle line:84% Well, every atom in the crystal has electrons 00:17:15.448 --> 00:17:16.240 align:middle line:90% associated with it. 00:17:16.240 --> 00:17:18.960 align:middle line:84% And in fact, there are covalent bonds. 00:17:18.960 --> 00:17:22.890 align:middle line:84% There are four covalent bonds for every silicon atom, 00:17:22.890 --> 00:17:28.710 align:middle line:84% with eight electrons participating per atom. 00:17:28.710 --> 00:17:31.980 align:middle line:84% And these covalent electrons, essentially, 00:17:31.980 --> 00:17:37.520 align:middle line:84% can produce a retarding effect on the ion going through it. 00:17:37.520 --> 00:17:40.920 align:middle line:84% So you can think of it as sort of a retarding field. 00:17:40.920 --> 00:17:42.860 align:middle line:84% Imagine the silicon or the substrate that's 00:17:42.860 --> 00:17:44.930 align:middle line:90% some kind of dielectric medium. 00:17:44.930 --> 00:17:47.420 align:middle line:84% You have an ion coming through it at some velocity. 00:17:47.420 --> 00:17:50.570 align:middle line:84% This blue circle was meant to represent, say, 00:17:50.570 --> 00:17:52.670 align:middle line:90% the boron or the arsenic ion. 00:17:52.670 --> 00:17:56.352 align:middle line:84% And there's this retarding electric field. 00:17:56.352 --> 00:17:58.560 align:middle line:84% So the interesting thing, the thing you need to note, 00:17:58.560 --> 00:18:01.190 align:middle line:84% the main point is, this is a dissipative loss mechanism, 00:18:01.190 --> 00:18:03.110 align:middle line:84% but it doesn't change the direction. 00:18:03.110 --> 00:18:05.840 align:middle line:90% The electrons are way too light. 00:18:05.840 --> 00:18:06.900 align:middle line:90% They're very, very light. 00:18:06.900 --> 00:18:08.480 align:middle line:84% They can retard or slow down the ion, 00:18:08.480 --> 00:18:10.397 align:middle line:84% but they're not going to change its direction. 00:18:10.397 --> 00:18:12.660 align:middle line:84% There's no deflection as a result of this. 00:18:12.660 --> 00:18:15.180 align:middle line:90% So, unlike nuclear scattering. 00:18:15.180 --> 00:18:17.250 align:middle line:84% So that's one way of thinking of it as a drag 00:18:17.250 --> 00:18:18.940 align:middle line:90% force in a dielectric medium. 00:18:18.940 --> 00:18:23.040 align:middle line:84% The other way is you can imagine a quote unquote collision. 00:18:23.040 --> 00:18:25.820 align:middle line:84% Now, just be careful in the word collision, the use of it, 00:18:25.820 --> 00:18:30.320 align:middle line:84% with electrons around the atoms transferring some momentum 00:18:30.320 --> 00:18:38.610 align:middle line:84% to those electrons from the electrons from the ion itself. 00:18:38.610 --> 00:18:40.910 align:middle line:84% So you can imagine, here's this target atom. 00:18:40.910 --> 00:18:43.640 align:middle line:84% It's got this electron cloud around it. 00:18:43.640 --> 00:18:48.650 align:middle line:84% And it transfers momentum and actually results 00:18:48.650 --> 00:18:54.440 align:middle line:84% in locally slowing down this ion, basically, 00:18:54.440 --> 00:18:56.578 align:middle line:90% reducing its velocity. 00:18:56.578 --> 00:18:58.370 align:middle line:84% Again, there's no change in this mechanism, 00:18:58.370 --> 00:19:02.030 align:middle line:84% no change in the direction of the incoming ion 00:19:02.030 --> 00:19:04.100 align:middle line:90% when this process happens. 00:19:04.100 --> 00:19:07.010 align:middle line:84% So both of these don't change direction, 00:19:07.010 --> 00:19:10.640 align:middle line:84% and both mechanisms are related to, or involve, 00:19:10.640 --> 00:19:12.740 align:middle line:84% the speed or the velocity of the ion. 00:19:12.740 --> 00:19:15.910 align:middle line:90% 00:19:15.910 --> 00:19:16.420 align:middle line:90% OK. 00:19:16.420 --> 00:19:21.640 align:middle line:84% So if we go to the next slide on slide 9, to first order, 00:19:21.640 --> 00:19:24.250 align:middle line:84% people have found they can write the electronic stopping 00:19:24.250 --> 00:19:27.230 align:middle line:84% power as some constant times the velocity. 00:19:27.230 --> 00:19:32.350 align:middle line:84% So this drag mechanism, the keV loss per micron, 00:19:32.350 --> 00:19:34.840 align:middle line:84% due to electronic stopping, increases 00:19:34.840 --> 00:19:40.220 align:middle line:84% directly proportionally to the velocity of the electron. 00:19:40.220 --> 00:19:41.345 align:middle line:90% And what is the velocity? 00:19:41.345 --> 00:19:43.845 align:middle line:84% Well, the velocity just goes like the square root of energy, 00:19:43.845 --> 00:19:44.780 align:middle line:90% right? 00:19:44.780 --> 00:19:47.000 align:middle line:84% So you can write electronic stopping 00:19:47.000 --> 00:19:49.430 align:middle line:84% as some constant, k times the square root of e. 00:19:49.430 --> 00:19:51.500 align:middle line:84% And in fact, k has this, very roughly, 00:19:51.500 --> 00:19:54.920 align:middle line:84% you can approximate k by about 2 times 10 00:19:54.920 --> 00:19:59.330 align:middle line:84% to the minus 14th square root eV centimeter squared, as shown up 00:19:59.330 --> 00:20:00.630 align:middle line:90% on the top of that slide. 00:20:00.630 --> 00:20:03.650 align:middle line:84% So this is an approximation, but to first order, 00:20:03.650 --> 00:20:06.195 align:middle line:90% it seems to work. 00:20:06.195 --> 00:20:08.570 align:middle line:84% I should note here, I'm noting in the upper right corner, 00:20:08.570 --> 00:20:10.490 align:middle line:84% that a lot of the improvements in ion implant 00:20:10.490 --> 00:20:13.820 align:middle line:84% modeling over the last 5, 10 years, or however long, 00:20:13.820 --> 00:20:16.852 align:middle line:84% have actually come from a better, more accurate treatment 00:20:16.852 --> 00:20:17.810 align:middle line:90% of electronic stopping. 00:20:17.810 --> 00:20:19.820 align:middle line:84% Nuclear stopping is very much nuclear physics, 00:20:19.820 --> 00:20:22.580 align:middle line:84% and that's been known for a long time now. 00:20:22.580 --> 00:20:25.280 align:middle line:84% But this electronic drag force is a little bit more 00:20:25.280 --> 00:20:27.508 align:middle line:84% mysterious, a little bit more difficult to model. 00:20:27.508 --> 00:20:29.300 align:middle line:84% And this is where a lot of the improvements 00:20:29.300 --> 00:20:32.390 align:middle line:90% have come in the literature. 00:20:32.390 --> 00:20:35.360 align:middle line:84% And particularly, this affects light ions 00:20:35.360 --> 00:20:38.270 align:middle line:84% like boron, for which most of this stopping 00:20:38.270 --> 00:20:39.500 align:middle line:90% is actually electronic. 00:20:39.500 --> 00:20:40.930 align:middle line:90% Boron isn't very heavy. 00:20:40.930 --> 00:20:43.170 align:middle line:84% It doesn't experience that much nuclear stopping. 00:20:43.170 --> 00:20:46.650 align:middle line:84% Most of what slows down a boron ion implanted into silicon 00:20:46.650 --> 00:20:47.610 align:middle line:90% is electronic stopping. 00:20:47.610 --> 00:20:50.760 align:middle line:84% So boron profiles have become more accurate, 00:20:50.760 --> 00:20:53.330 align:middle line:84% more accurately modeled over the last x number of years, 00:20:53.330 --> 00:20:55.080 align:middle line:84% because people have a little better models 00:20:55.080 --> 00:20:56.680 align:middle line:90% for electronic stopping. 00:20:56.680 --> 00:20:59.920 align:middle line:84% So if we look at this plot on slide 9, 00:20:59.920 --> 00:21:02.020 align:middle line:84% this is the total stopping power. 00:21:02.020 --> 00:21:04.300 align:middle line:84% It plots both the nuclear and electronic. 00:21:04.300 --> 00:21:07.930 align:middle line:84% So again, the units are keV per micron in the vertical axis, 00:21:07.930 --> 00:21:09.842 align:middle line:90% and keV on the y-axis. 00:21:09.842 --> 00:21:11.800 align:middle line:84% And these are the same plots I just showed you, 00:21:11.800 --> 00:21:13.008 align:middle line:90% they're just different color. 00:21:13.008 --> 00:21:16.600 align:middle line:84% Here's arsenic nuclear stopping, phosphorus nuclear, boron 00:21:16.600 --> 00:21:20.520 align:middle line:84% nuclear stopping, and here is the electronic stopping. 00:21:20.520 --> 00:21:25.083 align:middle line:84% And again, it's just basically proportional to the velocity. 00:21:25.083 --> 00:21:27.750 align:middle line:84% There's only a small dependence, and we don't even show it here, 00:21:27.750 --> 00:21:29.110 align:middle line:90% on the type of ion. 00:21:29.110 --> 00:21:32.850 align:middle line:84% So we're just writing this as this black line. 00:21:32.850 --> 00:21:36.620 align:middle line:84% So interestingly, what you see, an interesting energy 00:21:36.620 --> 00:21:39.770 align:middle line:84% to point out is the energy at which these lines cross. 00:21:39.770 --> 00:21:42.560 align:middle line:84% And that's called the critical energy, e sub c. 00:21:42.560 --> 00:21:46.820 align:middle line:84% And at that point, the nuclear electronic stopping are equal. 00:21:46.820 --> 00:21:48.610 align:middle line:84% Beyond that, the electronic stopping 00:21:48.610 --> 00:21:49.610 align:middle line:90% has actually taken over. 00:21:49.610 --> 00:21:50.600 align:middle line:90% It's much larger. 00:21:50.600 --> 00:21:52.640 align:middle line:84% Because again, the nuclear stopping power 00:21:52.640 --> 00:21:58.550 align:middle line:84% is going down as you go faster, or increases as you go slower. 00:21:58.550 --> 00:22:00.690 align:middle line:84% But the electronic is going the opposite direction. 00:22:00.690 --> 00:22:06.340 align:middle line:84% So boron at 17 keV, above that or below that energy, 00:22:06.340 --> 00:22:08.560 align:middle line:84% basically, nuclear stopping will be important. 00:22:08.560 --> 00:22:11.620 align:middle line:84% Above that energy, which is a lot of our implants, 00:22:11.620 --> 00:22:15.760 align:middle line:84% boron is pretty much being stopped by electronic stopping. 00:22:15.760 --> 00:22:18.040 align:middle line:90% Phosphorus is about 150. 00:22:18.040 --> 00:22:20.860 align:middle line:84% So any energy less than 150, you're 00:22:20.860 --> 00:22:23.320 align:middle line:84% going to be dominated by nuclear stopping. 00:22:23.320 --> 00:22:26.050 align:middle line:90% Above that will be electronic. 00:22:26.050 --> 00:22:29.860 align:middle line:84% And arsenic is almost always dominated, 00:22:29.860 --> 00:22:32.785 align:middle line:84% at least in the beginning of its path, by nuclear stopping. 00:22:32.785 --> 00:22:34.160 align:middle line:84% The interesting thing about this, 00:22:34.160 --> 00:22:36.220 align:middle line:84% though, think about an individual ion. 00:22:36.220 --> 00:22:37.680 align:middle line:84% As an ion comes in, of course, it 00:22:37.680 --> 00:22:40.630 align:middle line:84% comes in with a lot of energy, 10 keV, 100. 00:22:40.630 --> 00:22:42.640 align:middle line:84% But by the time it stops, it's got 0. 00:22:42.640 --> 00:22:44.530 align:middle line:90% So every ion has to traverse. 00:22:44.530 --> 00:22:49.890 align:middle line:84% As I first come in, let's say I started coming in at 10 keV, 00:22:49.890 --> 00:22:53.330 align:middle line:84% or rather, 100 keV, and I'm right here. 00:22:53.330 --> 00:22:58.780 align:middle line:84% So as I'm coming in here for boron, you'd say at 100 keV, 00:22:58.780 --> 00:23:01.000 align:middle line:84% well, electronic stopping is dominant. 00:23:01.000 --> 00:23:01.720 align:middle line:90% That's true. 00:23:01.720 --> 00:23:04.880 align:middle line:84% But as the boron ion slows down, it walks down this curve 00:23:04.880 --> 00:23:06.360 align:middle line:90% and walks up this point. 00:23:06.360 --> 00:23:08.780 align:middle line:84% And when it gets to very low energy just before it stops, 00:23:08.780 --> 00:23:12.110 align:middle line:84% in fact, nuclear stopping always takes over. 00:23:12.110 --> 00:23:13.880 align:middle line:84% Because at low energies, you really 00:23:13.880 --> 00:23:16.800 align:middle line:84% can have a lot of billiard-ball-like collisions. 00:23:16.800 --> 00:23:19.910 align:middle line:84% So that's why at the end of the range, 00:23:19.910 --> 00:23:22.340 align:middle line:84% back at the depths of the implant that's 00:23:22.340 --> 00:23:24.830 align:middle line:84% near the end of range, there's a lot of nuclear stopping 00:23:24.830 --> 00:23:25.400 align:middle line:90% that goes on. 00:23:25.400 --> 00:23:28.940 align:middle line:84% And we'll talk about what impact that has for damage profiles. 00:23:28.940 --> 00:23:31.720 align:middle line:90% 00:23:31.720 --> 00:23:34.057 align:middle line:84% And here's just an example on page 10 00:23:34.057 --> 00:23:35.140 align:middle line:90% on different type of plot. 00:23:35.140 --> 00:23:37.090 align:middle line:90% That was a log log plot. 00:23:37.090 --> 00:23:41.225 align:middle line:84% I've plotted these nuclear and electronic now on linear axes, 00:23:41.225 --> 00:23:43.600 align:middle line:84% just so you get a feel for what they look like on linear. 00:23:43.600 --> 00:23:45.640 align:middle line:90% So this is de by dx. 00:23:45.640 --> 00:23:49.400 align:middle line:84% And this is, well, it's actually a square root of energy. 00:23:49.400 --> 00:23:52.570 align:middle line:84% That helps linearize the, this straight line, of course, 00:23:52.570 --> 00:23:55.360 align:middle line:84% then, is the electronic stopping. 00:23:55.360 --> 00:24:00.165 align:middle line:84% And this other line here, that it peaks at some energy, E1, 00:24:00.165 --> 00:24:01.540 align:middle line:84% and then starts to decrease down, 00:24:01.540 --> 00:24:02.620 align:middle line:90% that's the nuclear stopping. 00:24:02.620 --> 00:24:04.203 align:middle line:84% So on a linear scale, you can actually 00:24:04.203 --> 00:24:05.840 align:middle line:90% see what it looks like. 00:24:05.840 --> 00:24:08.260 align:middle line:84% And again, I took this from Mayer and Lao's textbook. 00:24:08.260 --> 00:24:10.720 align:middle line:84% In general, the nuclear stopping dominates, 00:24:10.720 --> 00:24:14.350 align:middle line:84% as we said, at low energy towards the end of the range. 00:24:14.350 --> 00:24:18.785 align:middle line:84% And that's the location in the substrate where 00:24:18.785 --> 00:24:21.410 align:middle line:84% the nuclear collisions are going to produce most of the damage. 00:24:21.410 --> 00:24:24.300 align:middle line:84% So we call that end of range damage. 00:24:24.300 --> 00:24:27.210 align:middle line:84% At very high energies up here, where I'm up here, 00:24:27.210 --> 00:24:29.020 align:middle line:90% particles travel very quickly. 00:24:29.020 --> 00:24:31.150 align:middle line:84% They have less time to interact with the nucleus. 00:24:31.150 --> 00:24:34.710 align:middle line:84% So nuclear stopping is not as important. 00:24:34.710 --> 00:24:37.650 align:middle line:84% They have less interaction time, and so they 00:24:37.650 --> 00:24:38.880 align:middle line:90% tend to be dragged down. 00:24:38.880 --> 00:24:41.010 align:middle line:84% Nuclear stopping is going down with energy, 00:24:41.010 --> 00:24:44.150 align:middle line:90% where electronic is increasing. 00:24:44.150 --> 00:24:47.460 align:middle line:84% OK, so that gives you an idea of some of the physics of the loss 00:24:47.460 --> 00:24:49.780 align:middle line:90% mechanisms. 00:24:49.780 --> 00:24:51.180 align:middle line:90% So let's go on to slide 11. 00:24:51.180 --> 00:24:54.103 align:middle line:84% So let's say I have these nuclear stopping 00:24:54.103 --> 00:24:56.520 align:middle line:84% powers as a function of energy, and I have the electronic. 00:24:56.520 --> 00:24:59.370 align:middle line:84% How do I get from that to a calculated profile? 00:24:59.370 --> 00:25:01.050 align:middle line:84% Well, we know we just simply need 00:25:01.050 --> 00:25:05.700 align:middle line:84% to do this integral if you want to compute the range. 00:25:05.700 --> 00:25:09.660 align:middle line:84% Or you can, directly from Monte Carlo simulations, 00:25:09.660 --> 00:25:11.820 align:middle line:84% you can actually simulate that billiard ball 00:25:11.820 --> 00:25:14.850 align:middle line:84% and those electronic stopping processes. 00:25:14.850 --> 00:25:18.540 align:middle line:84% Many years ago, three folks, Lindhard, Scharff, and Schiott, 00:25:18.540 --> 00:25:20.910 align:middle line:84% actually took these equations, put 00:25:20.910 --> 00:25:23.610 align:middle line:84% in nuclear and electronic stopping powers, 00:25:23.610 --> 00:25:29.520 align:middle line:84% and computed the moments of distributions, given s sub n 00:25:29.520 --> 00:25:30.900 align:middle line:90% and s sub b. 00:25:30.900 --> 00:25:35.080 align:middle line:84% And in fact, that so-called LSS Theory generated these tables, 00:25:35.080 --> 00:25:38.640 align:middle line:84% I think we showed these tables last time for common dopants 00:25:38.640 --> 00:25:42.240 align:middle line:84% in silicon, generated tables of the first few moments. 00:25:42.240 --> 00:25:43.770 align:middle line:84% Maybe the first three moments, that 00:25:43.770 --> 00:25:47.160 align:middle line:84% generated rp, this delta rp, or the standard deviation 00:25:47.160 --> 00:25:49.450 align:middle line:90% sigma, and the skewness gamma. 00:25:49.450 --> 00:25:54.460 align:middle line:84% They are tabulated and they were calculated originally by LSS, 00:25:54.460 --> 00:25:56.410 align:middle line:84% or they've been fit to experimental data. 00:25:56.410 --> 00:25:58.390 align:middle line:84% But you can calculate these moments 00:25:58.390 --> 00:26:01.540 align:middle line:84% from first principles physics estimates of s 00:26:01.540 --> 00:26:03.640 align:middle line:84% sub n as a function of energy and s 00:26:03.640 --> 00:26:05.230 align:middle line:90% sub e as a function of energy. 00:26:05.230 --> 00:26:08.430 align:middle line:90% 00:26:08.430 --> 00:26:08.930 align:middle line:90% OK. 00:26:08.930 --> 00:26:12.620 align:middle line:84% So that's basically how people do the calculations. 00:26:12.620 --> 00:26:15.860 align:middle line:84% What it boils down to, the calculations 00:26:15.860 --> 00:26:18.512 align:middle line:84% boil down to how accurately do I know the nuclear stopping 00:26:18.512 --> 00:26:20.720 align:middle line:84% power as a function of energy in electronic stopping? 00:26:20.720 --> 00:26:23.030 align:middle line:84% If I know that, I can use a computer, 00:26:23.030 --> 00:26:25.543 align:middle line:84% you can regenerate the old LSS statistics, 00:26:25.543 --> 00:26:26.960 align:middle line:84% or you can actually use a computer 00:26:26.960 --> 00:26:29.660 align:middle line:90% to do Monte Carlo simulation. 00:26:29.660 --> 00:26:32.870 align:middle line:84% Because once you know those stopping powers. 00:26:32.870 --> 00:26:35.378 align:middle line:84% Given that, OK, so we can figure out 00:26:35.378 --> 00:26:36.920 align:middle line:84% where the ions end up in the lattice. 00:26:36.920 --> 00:26:39.500 align:middle line:84% Now we want to know about, what kind of damage 00:26:39.500 --> 00:26:43.130 align:middle line:84% does this incoming ion coming in at a certain energy 00:26:43.130 --> 00:26:43.880 align:middle line:90% do to the lattice? 00:26:43.880 --> 00:26:48.860 align:middle line:84% So imagine I have 30 kiloelectronvolts arsenic which 00:26:48.860 --> 00:26:50.610 align:middle line:84% is coming into the silicon lattice. 00:26:50.610 --> 00:26:55.010 align:middle line:84% And if you look that up in your table in your textbook, 00:26:55.010 --> 00:26:59.200 align:middle line:84% you'll find it has a range of 25 nanometers, 00:26:59.200 --> 00:27:02.830 align:middle line:90% or about 250 angstroms. 00:27:02.830 --> 00:27:05.950 align:middle line:84% So in 250 angstroms, actually, you 00:27:05.950 --> 00:27:08.770 align:middle line:84% can figure that out, that is equivalent to roughly 00:27:08.770 --> 00:27:10.753 align:middle line:90% 100 atomic planes. 00:27:10.753 --> 00:27:14.320 align:middle line:84% It is about 0.25 or 2 and 1/2 angstroms 00:27:14.320 --> 00:27:18.100 align:middle line:90% per plane, interplanar spacing. 00:27:18.100 --> 00:27:20.620 align:middle line:84% So you can imagine this arsenic ion is coming in. 00:27:20.620 --> 00:27:23.500 align:middle line:84% It goes through about 100 atomic planes. 00:27:23.500 --> 00:27:25.750 align:middle line:84% And how many, so in fact, you can 00:27:25.750 --> 00:27:28.630 align:middle line:84% think of this 30 keV arsenic ion is coming in like this. 00:27:28.630 --> 00:27:30.970 align:middle line:84% This squiggly line is meant to represent its path. 00:27:30.970 --> 00:27:32.420 align:middle line:90% Here's where it ends up. 00:27:32.420 --> 00:27:37.420 align:middle line:84% And you can think of a cylinder around that, sort of a cylinder 00:27:37.420 --> 00:27:40.600 align:middle line:84% that represents the region, which is damaged, 00:27:40.600 --> 00:27:42.490 align:middle line:84% because it does a lot of nuclear stopping 00:27:42.490 --> 00:27:44.950 align:middle line:84% and you have a lot of recoils generated 00:27:44.950 --> 00:27:47.230 align:middle line:90% until it comes to stop. 00:27:47.230 --> 00:27:50.590 align:middle line:84% And in fact, there's a simplified formula, the kp 00:27:50.590 --> 00:27:53.500 align:middle line:84% formula, that people use to figure out, 00:27:53.500 --> 00:27:56.360 align:middle line:84% roughly, the number of displaced particles. 00:27:56.360 --> 00:27:59.200 align:middle line:84% So that'd be the number of displaced silicon atoms created 00:27:59.200 --> 00:28:00.730 align:middle line:90% by an incoming ion. 00:28:00.730 --> 00:28:03.430 align:middle line:84% And basically, in simple, you can 00:28:03.430 --> 00:28:07.360 align:middle line:84% imagine it might be related to the energy of that ion, which 00:28:07.360 --> 00:28:13.190 align:middle line:84% is 300 kiloelectron volts, so that's 30,000 electron volts, 00:28:13.190 --> 00:28:15.635 align:middle line:84% and divided by the displacement energy. 00:28:15.635 --> 00:28:17.760 align:middle line:84% Well, we use a factor of one half in front of that. 00:28:17.760 --> 00:28:20.990 align:middle line:84% But the displacement energy, we said, was 15 electron volts. 00:28:20.990 --> 00:28:24.380 align:middle line:84% So, just order of magnitude estimate, 00:28:24.380 --> 00:28:26.420 align:middle line:84% by comparing the incoming energy to the energy 00:28:26.420 --> 00:28:29.420 align:middle line:84% it takes to displace an atom from the lattice, 00:28:29.420 --> 00:28:33.380 align:middle line:84% we're talking about maybe 1,000 recoils of silicon 00:28:33.380 --> 00:28:35.980 align:middle line:84% are created by this one arsenic atom. 00:28:35.980 --> 00:28:37.320 align:middle line:90% That's quite a bit. 00:28:37.320 --> 00:28:39.640 align:middle line:84% So you're essentially doing little ion implants 00:28:39.640 --> 00:28:44.290 align:middle line:84% inside the substrate every time an arsenic 00:28:44.290 --> 00:28:46.020 align:middle line:90% atom deflects silicon. 00:28:46.020 --> 00:28:48.670 align:middle line:84% It creates what they call silicon knock-ons. 00:28:48.670 --> 00:28:50.710 align:middle line:84% The silicons are knocked on, and they themselves 00:28:50.710 --> 00:28:52.835 align:middle line:84% have a certain energy, and they can do more damage. 00:28:52.835 --> 00:28:56.770 align:middle line:84% So it creates this sort of cylinder-like region of damage, 00:28:56.770 --> 00:29:00.070 align:middle line:90% just due to one ion. 00:29:00.070 --> 00:29:04.900 align:middle line:84% And in fact, that was a very schematic cartoon that we just 00:29:04.900 --> 00:29:06.200 align:middle line:90% drew with the computer. 00:29:06.200 --> 00:29:09.190 align:middle line:84% This is a little more sophisticated on slide 13. 00:29:09.190 --> 00:29:13.120 align:middle line:84% These are actually what's called molecular dynamics simulations, 00:29:13.120 --> 00:29:14.578 align:middle line:84% where people build in the computer. 00:29:14.578 --> 00:29:16.995 align:middle line:84% And of course, this is done at Lawrence Livermore National 00:29:16.995 --> 00:29:19.240 align:middle line:84% Lab, would have huge supercomputing capability. 00:29:19.240 --> 00:29:23.560 align:middle line:84% They build up a model of the silicon lattice, 00:29:23.560 --> 00:29:26.750 align:middle line:84% and they actually model the physics of an incoming atom 00:29:26.750 --> 00:29:27.250 align:middle line:90% or ion. 00:29:27.250 --> 00:29:29.590 align:middle line:84% Here's a 5 keV boron ion coming in. 00:29:29.590 --> 00:29:31.240 align:middle line:84% This ion implanted into the substrate. 00:29:31.240 --> 00:29:34.060 align:middle line:84% And they actually follow a whole bunch of ions 00:29:34.060 --> 00:29:36.130 align:middle line:84% and actually look at what happens 00:29:36.130 --> 00:29:38.110 align:middle line:90% to these displaced recoils. 00:29:38.110 --> 00:29:41.170 align:middle line:84% And each little snapshot picture here, I apologize, 00:29:41.170 --> 00:29:43.600 align:middle line:84% it didn't come out very well when we copied it, 00:29:43.600 --> 00:29:44.960 align:middle line:90% is a snapshot in time. 00:29:44.960 --> 00:29:47.800 align:middle line:84% So the first little cube is supposed 00:29:47.800 --> 00:29:50.320 align:middle line:84% to represent a region of the silicon where, 00:29:50.320 --> 00:29:52.340 align:middle line:90% after 0.1 picoseconds. 00:29:52.340 --> 00:29:54.130 align:middle line:84% So this ion has come in, and just 00:29:54.130 --> 00:29:56.770 align:middle line:84% at the time of 0.1 picoseconds, there's this little cloud here. 00:29:56.770 --> 00:29:58.020 align:middle line:90% You can see this little cloud. 00:29:58.020 --> 00:30:00.960 align:middle line:84% That cloud represents all the displaced silicon atoms. 00:30:00.960 --> 00:30:03.500 align:middle line:84% So they're actually following all these atoms displaced 00:30:03.500 --> 00:30:05.960 align:middle line:90% from their lattice sites. 00:30:05.960 --> 00:30:09.320 align:middle line:84% And then at five times that time, so at half a picosecond, 00:30:09.320 --> 00:30:11.000 align:middle line:84% look at how that cloud has grown. 00:30:11.000 --> 00:30:15.850 align:middle line:84% It's gone in deeper, and it's expanded sort of laterally. 00:30:15.850 --> 00:30:18.550 align:middle line:84% And then, interestingly, at 10 times that again, 00:30:18.550 --> 00:30:20.860 align:middle line:84% roughly, at 6 picoseconds, the cloud 00:30:20.860 --> 00:30:22.090 align:middle line:90% looks a little bit smaller. 00:30:22.090 --> 00:30:24.580 align:middle line:84% It's reached some size, not that much different 00:30:24.580 --> 00:30:26.470 align:middle line:90% from its first size, but why? 00:30:26.470 --> 00:30:29.200 align:middle line:84% Well, what's happened is that some of these silicon 00:30:29.200 --> 00:30:33.370 align:middle line:84% atoms that were knocked off have found that vacant lattice 00:30:33.370 --> 00:30:33.940 align:middle line:90% sites. 00:30:33.940 --> 00:30:36.280 align:middle line:84% So you're creating ions of silicon atoms 00:30:36.280 --> 00:30:39.430 align:middle line:84% that are displaced, but they find holes in the lattice 00:30:39.430 --> 00:30:40.630 align:middle line:90% where they can sit. 00:30:40.630 --> 00:30:44.710 align:middle line:84% And so this becomes sort of what the off-site silicon atoms look 00:30:44.710 --> 00:30:46.790 align:middle line:90% like after about 6 picoseconds. 00:30:46.790 --> 00:30:48.400 align:middle line:84% So people actually do try to simulate 00:30:48.400 --> 00:30:50.530 align:middle line:84% this from first principles physics as well. 00:30:50.530 --> 00:30:52.850 align:middle line:90% 00:30:52.850 --> 00:30:56.680 align:middle line:84% So that's a more modern kind of calculation. 00:30:56.680 --> 00:30:59.230 align:middle line:84% On slide 14, I'm showing you, maybe, 00:30:59.230 --> 00:31:00.730 align:middle line:84% a little bit more traditional or old 00:31:00.730 --> 00:31:04.190 align:middle line:84% fashioned calculation, what people used to do in the 1980s. 00:31:04.190 --> 00:31:06.880 align:middle line:84% In fact, this was taken from a book called 00:31:06.880 --> 00:31:09.610 align:middle line:84% The Handbook on Semiconductors on Ion Implantation, published 00:31:09.610 --> 00:31:10.780 align:middle line:90% back in 1980. 00:31:10.780 --> 00:31:15.880 align:middle line:84% But what it is, rather than that following every atom 00:31:15.880 --> 00:31:18.100 align:middle line:84% and figuring out what people do, is 00:31:18.100 --> 00:31:20.470 align:middle line:84% they found a way to calculate the energy 00:31:20.470 --> 00:31:22.630 align:middle line:84% deposited into nuclear processes. 00:31:22.630 --> 00:31:26.950 align:middle line:84% Again, know the nuclear stopping power as a function of energy. 00:31:26.950 --> 00:31:29.310 align:middle line:84% So as we integrate those equations in depth, 00:31:29.310 --> 00:31:31.335 align:middle line:84% we can figure out, at any given depth, 00:31:31.335 --> 00:31:35.910 align:middle line:84% we know the energy of the ion, we can integrate that up 00:31:35.910 --> 00:31:39.210 align:middle line:84% and figure out how much nuclear stopping is taking place 00:31:39.210 --> 00:31:40.110 align:middle line:90% at that depth. 00:31:40.110 --> 00:31:42.990 align:middle line:84% And therefore, you can think of how much of the energy 00:31:42.990 --> 00:31:48.870 align:middle line:84% loss in keV per micron or eV per angstrom 00:31:48.870 --> 00:31:51.090 align:middle line:90% is there at a given depth. 00:31:51.090 --> 00:31:52.950 align:middle line:84% And here's a picture of that calculation 00:31:52.950 --> 00:31:55.960 align:middle line:84% or a plot, its so-called damage density. 00:31:55.960 --> 00:31:58.860 align:middle line:84% So it's the amount of energy that 00:31:58.860 --> 00:32:02.370 align:middle line:84% is lost at a given depth due to nuclear processes, 00:32:02.370 --> 00:32:05.700 align:middle line:84% and it has the units of eV per angstrom 00:32:05.700 --> 00:32:08.010 align:middle line:90% as a function of depth. 00:32:08.010 --> 00:32:10.650 align:middle line:84% And this is for a particular ion implant. 00:32:10.650 --> 00:32:13.140 align:middle line:84% This is boron 11 being implanted into silicon 00:32:13.140 --> 00:32:14.910 align:middle line:90% at 100 kiloelectron volts. 00:32:14.910 --> 00:32:17.010 align:middle line:84% And you can see the damage energy. 00:32:17.010 --> 00:32:20.190 align:middle line:84% The damage energy density has a certain profile. 00:32:20.190 --> 00:32:23.130 align:middle line:84% And this solid line represents a calculation 00:32:23.130 --> 00:32:26.430 align:middle line:84% where it includes the silicon recoils, that is the silicon 00:32:26.430 --> 00:32:27.690 align:middle line:90% ions that are generated. 00:32:27.690 --> 00:32:30.630 align:middle line:84% And the dashed line is when we have only the primary ion. 00:32:30.630 --> 00:32:33.730 align:middle line:84% So there's not much difference in this case. 00:32:33.730 --> 00:32:35.640 align:middle line:84% But here's an example of boron silicon. 00:32:35.640 --> 00:32:38.428 align:middle line:90% It's a relatively light ion. 00:32:38.428 --> 00:32:40.470 align:middle line:84% And the interesting thing that it's plotted here, 00:32:40.470 --> 00:32:42.690 align:middle line:90% is as a function of x over rp. 00:32:42.690 --> 00:32:45.780 align:middle line:84% So remember, rp is going to be roughly close to 00:32:45.780 --> 00:32:47.050 align:middle line:90% where the peak of the boron. 00:32:47.050 --> 00:32:48.900 align:middle line:84% So the boron would peak here at 1. 00:32:48.900 --> 00:32:50.960 align:middle line:90% 00:32:50.960 --> 00:32:52.710 align:middle line:84% So the range of the boron atom is actually 00:32:52.710 --> 00:32:55.763 align:middle line:84% much greater than the range of the average silicon recoil. 00:32:55.763 --> 00:32:57.180 align:middle line:84% That's because the boron is light, 00:32:57.180 --> 00:33:00.610 align:middle line:84% so it can't push the silicon that much deeper in. 00:33:00.610 --> 00:33:02.842 align:middle line:84% So actually the damage density for silicon recoils 00:33:02.842 --> 00:33:04.050 align:middle line:90% doesn't contribute that much. 00:33:04.050 --> 00:33:06.217 align:middle line:84% So you can see that these two, dashed and the solid, 00:33:06.217 --> 00:33:07.530 align:middle line:90% look pretty much the same. 00:33:07.530 --> 00:33:10.530 align:middle line:84% But interestingly, where does the damage peak? 00:33:10.530 --> 00:33:11.760 align:middle line:90% Pretty close to rp. 00:33:11.760 --> 00:33:15.090 align:middle line:84% In fact, it's just at maybe 80% of rp. 00:33:15.090 --> 00:33:16.710 align:middle line:84% And that's a good rule of thumb you 00:33:16.710 --> 00:33:18.660 align:middle line:84% can use if you want to know, all right, 00:33:18.660 --> 00:33:21.090 align:middle line:84% I'm going to ion implant something into a silicon 00:33:21.090 --> 00:33:22.272 align:middle line:90% substrate. 00:33:22.272 --> 00:33:24.480 align:middle line:84% Maybe I don't know how to calculate the damage energy 00:33:24.480 --> 00:33:26.105 align:middle line:84% density but I can know how to calculate 00:33:26.105 --> 00:33:27.420 align:middle line:90% the profile of that ion. 00:33:27.420 --> 00:33:28.920 align:middle line:90% Where is the maximum damage? 00:33:28.920 --> 00:33:32.610 align:middle line:84% Well, it's close to rp, but in fact, it's just shy of rp. 00:33:32.610 --> 00:33:34.410 align:middle line:84% So if you want to do a lot of damage, 00:33:34.410 --> 00:33:36.930 align:middle line:84% or usually you don't, or you want to minimize, 00:33:36.930 --> 00:33:39.490 align:middle line:84% you can figure out, just below rp 00:33:39.490 --> 00:33:41.830 align:middle line:84% is where you're going to peak in terms of doing the most 00:33:41.830 --> 00:33:43.000 align:middle line:90% damage to the substrate. 00:33:43.000 --> 00:33:45.460 align:middle line:90% 00:33:45.460 --> 00:33:49.810 align:middle line:84% Here's an example on slide 15, a different situation. 00:33:49.810 --> 00:33:51.540 align:middle line:90% Now this is the heavy ion. 00:33:51.540 --> 00:33:53.260 align:middle line:84% The same kind of calculations published 00:33:53.260 --> 00:33:57.070 align:middle line:84% in Gibson's book, Handbook on Semiconductors Ion Implantation 00:33:57.070 --> 00:33:58.860 align:middle line:90% Volume. 00:33:58.860 --> 00:34:01.680 align:middle line:84% Again, damage energy density in eV per angstrom, 00:34:01.680 --> 00:34:03.250 align:middle line:90% again, versus x over rp. 00:34:03.250 --> 00:34:03.990 align:middle line:90% But look at this. 00:34:03.990 --> 00:34:08.159 align:middle line:84% This time, the solid line, now again, includes recoils 00:34:08.159 --> 00:34:11.100 align:middle line:84% and you get this sort of distribution. 00:34:11.100 --> 00:34:14.370 align:middle line:84% The dashed line is for the damage done just 00:34:14.370 --> 00:34:16.739 align:middle line:90% by the antimony itself. 00:34:16.739 --> 00:34:19.600 align:middle line:84% And you get a very different damage distribution. 00:34:19.600 --> 00:34:22.920 align:middle line:84% So what this says is for a heavy ion like antimony, 00:34:22.920 --> 00:34:25.949 align:middle line:84% antimony is big enough that it can impart a lot of energy 00:34:25.949 --> 00:34:28.830 align:middle line:84% to silicon ions, or the silicon recoils. 00:34:28.830 --> 00:34:32.100 align:middle line:84% And the silicon recoils transport 00:34:32.100 --> 00:34:34.900 align:middle line:84% a lot of that damage energy deeper into the substrate. 00:34:34.900 --> 00:34:37.590 align:middle line:84% So if you don't take it when you calculate damage, 00:34:37.590 --> 00:34:39.155 align:middle line:84% and you have a heavy ion coming in, 00:34:39.155 --> 00:34:41.280 align:middle line:84% if you don't take into account the silicon recoils, 00:34:41.280 --> 00:34:42.900 align:middle line:84% you're going to get pretty somewhat 00:34:42.900 --> 00:34:46.360 align:middle line:84% inaccurate distribution of where most of the damage is done. 00:34:46.360 --> 00:34:48.360 align:middle line:84% So you really need to use the solid line 00:34:48.360 --> 00:34:50.580 align:middle line:84% and include the silicon recoils in your damage, 00:34:50.580 --> 00:34:52.199 align:middle line:84% because the silicon atoms then go on 00:34:52.199 --> 00:34:55.239 align:middle line:90% and damage further the lattice. 00:34:55.239 --> 00:34:58.900 align:middle line:84% They impart energy to other silicon atoms. 00:34:58.900 --> 00:35:01.053 align:middle line:84% This is for 100 kilovolt antimony. 00:35:01.053 --> 00:35:02.470 align:middle line:84% But again, look where the peak is. 00:35:02.470 --> 00:35:05.620 align:middle line:84% The peak and the damage still occurs at about close 00:35:05.620 --> 00:35:10.730 align:middle line:84% to 80% or so of the projected range of the antimony ion. 00:35:10.730 --> 00:35:12.370 align:middle line:90% So that's a handy rule of thumb. 00:35:12.370 --> 00:35:15.110 align:middle line:90% 00:35:15.110 --> 00:35:17.830 align:middle line:84% Now, what can we do with a damage energy 00:35:17.830 --> 00:35:23.320 align:middle line:84% profile like this, or damage density versus x, or x over rp? 00:35:23.320 --> 00:35:27.910 align:middle line:84% Well, if you know how much damage in a given angstrom, how 00:35:27.910 --> 00:35:30.550 align:middle line:84% much energy in a given angstrom will 00:35:30.550 --> 00:35:32.530 align:middle line:84% tend to produce amorphization, you 00:35:32.530 --> 00:35:35.320 align:middle line:84% could actually use this plot to figure out 00:35:35.320 --> 00:35:39.730 align:middle line:84% which part of the lattice is which depth, or amorphized. 00:35:39.730 --> 00:35:41.440 align:middle line:90% And so here's an example. 00:35:41.440 --> 00:35:43.840 align:middle line:84% What I'm doing here, I'm taking this calculation, which 00:35:43.840 --> 00:35:46.060 align:middle line:84% we showed for boron a couple of slides ago, 00:35:46.060 --> 00:35:49.660 align:middle line:84% and I'm assuming that there's a threshold for amorphization. 00:35:49.660 --> 00:35:51.280 align:middle line:84% Now this has been both calculated 00:35:51.280 --> 00:35:53.407 align:middle line:84% and people have tried to measure it. 00:35:53.407 --> 00:35:55.240 align:middle line:84% I'm assuming the threshold for amorphization 00:35:55.240 --> 00:35:58.330 align:middle line:84% at room temperature is 6 electron volts per angstrom. 00:35:58.330 --> 00:36:02.200 align:middle line:84% So people have kind of looked at this either theoretically 00:36:02.200 --> 00:36:06.370 align:middle line:84% or by looking at actual amorphization 00:36:06.370 --> 00:36:08.860 align:middle line:84% zones, amorphous zones, and said that when 00:36:08.860 --> 00:36:11.140 align:middle line:84% you get above about 6 electron volts deposited 00:36:11.140 --> 00:36:14.260 align:middle line:84% into nuclear processes per angstrom of depth, 00:36:14.260 --> 00:36:16.750 align:middle line:84% the silicon has so much damage that it goes amorphous. 00:36:16.750 --> 00:36:18.300 align:middle line:84% So it's lost its crystal structure. 00:36:18.300 --> 00:36:20.410 align:middle line:84% In fact, if I draw a line here at 6 00:36:20.410 --> 00:36:23.260 align:middle line:84% and I see where it cuts this profile, that 00:36:23.260 --> 00:36:27.370 align:middle line:84% would say that this substrate, if you're implanting boron 00:36:27.370 --> 00:36:32.320 align:middle line:84% at 100 kilovolts, I don't know what the dose 00:36:32.320 --> 00:36:33.550 align:middle line:90% was in this particular case. 00:36:33.550 --> 00:36:37.480 align:middle line:84% But it would be amorphized between about half of rp 00:36:37.480 --> 00:36:39.700 align:middle line:90% and up to about rp. 00:36:39.700 --> 00:36:43.540 align:middle line:84% So in that region between half rp and rp, 00:36:43.540 --> 00:36:46.420 align:middle line:84% between these two lines, it's predicted according 00:36:46.420 --> 00:36:47.950 align:middle line:84% to this model, and again, it's going 00:36:47.950 --> 00:36:50.380 align:middle line:84% to be very sensitive to your amorphization threshold, 00:36:50.380 --> 00:36:52.420 align:middle line:84% this region in here will be amorphized. 00:36:52.420 --> 00:36:54.960 align:middle line:84% Everything else will be heavily damaged. 00:36:54.960 --> 00:36:57.560 align:middle line:84% So you can see what boron tends to do. 00:36:57.560 --> 00:36:59.570 align:middle line:84% Because of its distribution, it tends 00:36:59.570 --> 00:37:01.670 align:middle line:84% to create a buried amorphous layer 00:37:01.670 --> 00:37:05.015 align:middle line:84% with heavily damaged single crystal silicon on either side. 00:37:05.015 --> 00:37:08.180 align:middle line:90% 00:37:08.180 --> 00:37:12.650 align:middle line:84% And I just want to say a little more about amorphization, 00:37:12.650 --> 00:37:16.540 align:middle line:90% shown here on slide 17. 00:37:16.540 --> 00:37:19.450 align:middle line:84% As we've talked about before, if you give it a high enough dose, 00:37:19.450 --> 00:37:21.627 align:middle line:84% you have enough of the crystal is displaced, 00:37:21.627 --> 00:37:22.960 align:middle line:90% it becomes completely amorphous. 00:37:22.960 --> 00:37:25.480 align:middle line:84% It loses all of its crystal structure. 00:37:25.480 --> 00:37:27.460 align:middle line:84% There's no more long-range order. 00:37:27.460 --> 00:37:30.220 align:middle line:84% At this point, we have a random arrangement. 00:37:30.220 --> 00:37:32.947 align:middle line:84% And the damage accumulation is saturated and really can't 00:37:32.947 --> 00:37:34.030 align:middle line:90% talk about damage anymore. 00:37:34.030 --> 00:37:36.490 align:middle line:84% Once you've amorphized, there are no lattice sites, 00:37:36.490 --> 00:37:38.980 align:middle line:84% so you can't really knock somebody off a lattice site 00:37:38.980 --> 00:37:40.660 align:middle line:84% because there is no lattice site. 00:37:40.660 --> 00:37:42.730 align:middle line:90% It's no longer a lattice. 00:37:42.730 --> 00:37:44.080 align:middle line:90% But it just gives you an idea. 00:37:44.080 --> 00:37:47.240 align:middle line:84% This is taken from your textbook. 00:37:47.240 --> 00:37:49.120 align:middle line:84% This is a cross sectional TEM, so this 00:37:49.120 --> 00:37:52.810 align:middle line:84% is transmission electron micrograph pictures 00:37:52.810 --> 00:37:56.410 align:middle line:84% of an amorphous layer formation with increasing implant dose 00:37:56.410 --> 00:37:57.740 align:middle line:90% from left to right. 00:37:57.740 --> 00:37:59.390 align:middle line:90% So this is at very high energy. 00:37:59.390 --> 00:38:02.830 align:middle line:84% It's 300 kilovolts silicon being implanted 00:38:02.830 --> 00:38:04.910 align:middle line:90% into a silicon substrate. 00:38:04.910 --> 00:38:07.270 align:middle line:84% So the interesting thing is, the ion now is silicon. 00:38:07.270 --> 00:38:10.370 align:middle line:84% It has the same mass as the substrate. 00:38:10.370 --> 00:38:11.660 align:middle line:90% It's relatively light, though. 00:38:11.660 --> 00:38:14.190 align:middle line:84% So here at 1 e 15, what do I see? 00:38:14.190 --> 00:38:16.580 align:middle line:84% Well, here's the surface of the silicon substrate. 00:38:16.580 --> 00:38:18.732 align:middle line:84% And you see there's this band, this region, where 00:38:18.732 --> 00:38:19.940 align:middle line:90% there appears to be darkness. 00:38:19.940 --> 00:38:21.950 align:middle line:84% There seems to be a lot of damage, 00:38:21.950 --> 00:38:23.660 align:middle line:90% a lot of stuff going on here. 00:38:23.660 --> 00:38:26.720 align:middle line:84% Dark contrast, you can imagine, might 00:38:26.720 --> 00:38:29.480 align:middle line:84% be associated with some kind of dislocation loops 00:38:29.480 --> 00:38:31.520 align:middle line:84% or some kind of damage in the substrate. 00:38:31.520 --> 00:38:33.150 align:middle line:90% Here's a band here. 00:38:33.150 --> 00:38:35.060 align:middle line:84% Now at 1 and 1/2 times 10 to the 15th, 00:38:35.060 --> 00:38:38.120 align:middle line:84% there's a band, which really has, it's buried 00:38:38.120 --> 00:38:40.460 align:middle line:84% and it's lost its crystalline structure. 00:38:40.460 --> 00:38:43.460 align:middle line:84% If we were to Zoom in here and do a selected area diffraction 00:38:43.460 --> 00:38:45.770 align:middle line:84% on this region, we'd find it's not a crystal. 00:38:45.770 --> 00:38:48.350 align:middle line:84% There will be no diffraction Laue spots. 00:38:48.350 --> 00:38:51.560 align:middle line:84% Whereas if you go down here, you would see crystalline. 00:38:51.560 --> 00:38:54.410 align:middle line:84% Here's that amorphous layer at 2 times 10 to the 15th. 00:38:54.410 --> 00:38:56.420 align:middle line:90% It's increased in its width. 00:38:56.420 --> 00:38:59.100 align:middle line:84% It still hasn't reached the surface, though. 00:38:59.100 --> 00:39:02.422 align:middle line:84% And at 4 10 to the 15th, it's increased in depth, 00:39:02.422 --> 00:39:04.380 align:middle line:84% but again, it hasn't quite reached the surface. 00:39:04.380 --> 00:39:06.780 align:middle line:90% 5 10 to the 15th, almost. 00:39:06.780 --> 00:39:11.375 align:middle line:84% And finally, at 10 to the 16th, that's a very large dose, 00:39:11.375 --> 00:39:12.750 align:middle line:84% you've created an amorphous layer 00:39:12.750 --> 00:39:15.420 align:middle line:84% all the way from the surface down to some depth. 00:39:15.420 --> 00:39:18.660 align:middle line:84% I don't know what this is, half micron or whatever, 00:39:18.660 --> 00:39:24.300 align:middle line:84% and completely amorphized from the surface down. 00:39:24.300 --> 00:39:27.260 align:middle line:84% And this is all at room temperature. 00:39:27.260 --> 00:39:29.960 align:middle line:84% It turns out, it's much easier to form an amorphous layer 00:39:29.960 --> 00:39:32.300 align:middle line:90% at low temperatures, 77 Kelvin. 00:39:32.300 --> 00:39:35.570 align:middle line:84% So you will sometimes see people specifying their implant 00:39:35.570 --> 00:39:36.300 align:middle line:90% energy. 00:39:36.300 --> 00:39:38.120 align:middle line:84% They want to use a special ion planter that 00:39:38.120 --> 00:39:40.580 align:middle line:84% does, if you're doing some of these materials 00:39:40.580 --> 00:39:43.310 align:middle line:84% experiments, that can hold the wafer at 77 Kelvin. 00:39:43.310 --> 00:39:46.050 align:middle line:84% That means the damage is much more stable. 00:39:46.050 --> 00:39:48.590 align:middle line:84% Remember, we were talking about that simulation 00:39:48.590 --> 00:39:50.600 align:middle line:90% from Lawrence Livermore Labs. 00:39:50.600 --> 00:39:53.570 align:middle line:84% You saw that damage cloud and then a lot of recombination 00:39:53.570 --> 00:39:54.920 align:middle line:90% by diffusion and things. 00:39:54.920 --> 00:39:56.480 align:middle line:84% Well, if you're at low temperatures, 00:39:56.480 --> 00:39:58.260 align:middle line:84% you have a lot less recombination, 00:39:58.260 --> 00:40:01.268 align:middle line:84% so the damage tend to be more stable, especially 00:40:01.268 --> 00:40:02.060 align:middle line:90% with the light ion. 00:40:02.060 --> 00:40:04.160 align:middle line:84% So if you want to amorphize silicon 00:40:04.160 --> 00:40:07.543 align:middle line:84% with a light ion like boron or silicon, you pretty much, 00:40:07.543 --> 00:40:08.960 align:middle line:84% to do it reliably, you pretty much 00:40:08.960 --> 00:40:11.840 align:middle line:84% have to hold the wafer at low temperatures like 77 Kelvin. 00:40:11.840 --> 00:40:15.080 align:middle line:84% If you have a heavy ion that does a lot of damage, 00:40:15.080 --> 00:40:16.850 align:middle line:84% like arsenic or antimony, you can easily 00:40:16.850 --> 00:40:18.980 align:middle line:84% amorphize a layer from the surface 00:40:18.980 --> 00:40:21.300 align:middle line:90% down at room temperature. 00:40:21.300 --> 00:40:24.410 align:middle line:90% 00:40:24.410 --> 00:40:24.910 align:middle line:90% OK. 00:40:24.910 --> 00:40:27.220 align:middle line:84% So let's go on to slide, that's a picture of damage. 00:40:27.220 --> 00:40:30.530 align:middle line:84% Let's go on to slide 18 and talk about damage annealing. 00:40:30.530 --> 00:40:34.210 align:middle line:84% So we have to do annealing after we do an ion implant, 00:40:34.210 --> 00:40:35.870 align:middle line:84% because we've bashed up the crystal. 00:40:35.870 --> 00:40:37.537 align:middle line:84% So what do we want to do when we anneal? 00:40:37.537 --> 00:40:40.390 align:middle line:84% We want to remove the primary damage caused by the implant. 00:40:40.390 --> 00:40:44.590 align:middle line:84% You want to put all the dopants onto substitutional sites, that 00:40:44.590 --> 00:40:47.710 align:middle line:84% way they can be donors or acceptors. 00:40:47.710 --> 00:40:51.340 align:middle line:84% We try to make the crystal as perfect as it 00:40:51.340 --> 00:40:52.630 align:middle line:90% was when you first started. 00:40:52.630 --> 00:40:54.338 align:middle line:84% You never really get it quite as perfect. 00:40:54.338 --> 00:40:55.950 align:middle line:90% 00:40:55.950 --> 00:40:58.860 align:middle line:84% We'd also, in doing that, we want to restore the electron 00:40:58.860 --> 00:41:01.560 align:middle line:84% and hole mobilities, and the carrier lifetime, hopefully, 00:41:01.560 --> 00:41:02.550 align:middle line:90% to what it was. 00:41:02.550 --> 00:41:05.160 align:middle line:84% And you want to do all these things without really 00:41:05.160 --> 00:41:07.750 align:middle line:90% having much dopant diffusion. 00:41:07.750 --> 00:41:09.400 align:middle line:90% So it's a tough job. 00:41:09.400 --> 00:41:11.050 align:middle line:90% It's a tough job. 00:41:11.050 --> 00:41:15.330 align:middle line:84% And this is a model for damage annealing, relatively simple, 00:41:15.330 --> 00:41:19.500 align:middle line:84% but that was published back in 1991, that is very famous now, 00:41:19.500 --> 00:41:23.460 align:middle line:84% by Martin Giles, which is called the plus-one model 00:41:23.460 --> 00:41:25.860 align:middle line:90% for residual damage. 00:41:25.860 --> 00:41:27.090 align:middle line:90% Kind of a funny name. 00:41:27.090 --> 00:41:30.930 align:middle line:84% But what Martin did was he said the following things. 00:41:30.930 --> 00:41:34.380 align:middle line:84% He said that most recoiled silicon interstitials-- 00:41:34.380 --> 00:41:36.630 align:middle line:84% so again, we're going to call this guy who's recoiled, 00:41:36.630 --> 00:41:39.750 align:middle line:84% who ends up in an interstitial space, an i, or a silicon 00:41:39.750 --> 00:41:42.270 align:middle line:84% interstitial-- most of them will find a vacancy. 00:41:42.270 --> 00:41:45.610 align:middle line:84% And they'll recombine very, very rapidly, 00:41:45.610 --> 00:41:47.650 align:middle line:84% either during the implantation process 00:41:47.650 --> 00:41:49.570 align:middle line:84% or in the first few seconds of annealing, 00:41:49.570 --> 00:41:52.960 align:middle line:84% a lot of recombination takes place. 00:41:52.960 --> 00:41:55.050 align:middle line:84% In fact, he calculated the distribution 00:41:55.050 --> 00:41:58.320 align:middle line:84% of remaining recoils after ion implantation, 00:41:58.320 --> 00:41:59.730 align:middle line:90% without even any annealing. 00:41:59.730 --> 00:42:01.770 align:middle line:84% And what he found, there's a net excess 00:42:01.770 --> 00:42:04.103 align:middle line:84% of vacancies near the surface and a net excess 00:42:04.103 --> 00:42:05.520 align:middle line:84% of interstitials towards the bulk. 00:42:05.520 --> 00:42:07.270 align:middle line:84% But there's still a lot of them recombine. 00:42:07.270 --> 00:42:09.330 align:middle line:84% So this is a calculation from Giles, 00:42:09.330 --> 00:42:13.230 align:middle line:84% and he's got concentration of interstitials and vacancies 00:42:13.230 --> 00:42:14.850 align:middle line:90% as a function of depth. 00:42:14.850 --> 00:42:17.910 align:middle line:84% This solid line, or this line on top 00:42:17.910 --> 00:42:20.970 align:middle line:84% here, that starts at around 10 to the 20 or mid 10 of the 20 00:42:20.970 --> 00:42:25.560 align:middle line:84% and then goes down, these are the total interstitials 00:42:25.560 --> 00:42:27.270 align:middle line:84% and vacancy concentrations he calculated. 00:42:27.270 --> 00:42:28.890 align:middle line:84% They're almost on top of each other. 00:42:28.890 --> 00:42:31.660 align:middle line:84% On this log scale, you can't tell the difference. 00:42:31.660 --> 00:42:33.930 align:middle line:84% So you create a tremendous number of interstitials, 00:42:33.930 --> 00:42:36.570 align:middle line:84% tremendous number of vacancies, but most of them 00:42:36.570 --> 00:42:38.420 align:middle line:90% all recombined. 00:42:38.420 --> 00:42:41.270 align:middle line:84% And in fact, what he's plotted here is the net interstitials. 00:42:41.270 --> 00:42:44.120 align:middle line:84% So that's the number of interstitials minus the number 00:42:44.120 --> 00:42:45.930 align:middle line:90% of vacancies at a given point. 00:42:45.930 --> 00:42:47.520 align:middle line:84% So that's how many are left over. 00:42:47.520 --> 00:42:50.310 align:middle line:84% So the net interstitials look like this. 00:42:50.310 --> 00:42:53.480 align:middle line:84% In fact, if you plot the net profiles here 00:42:53.480 --> 00:42:56.510 align:middle line:84% in the near surface region, you have net vacancies. 00:42:56.510 --> 00:42:58.070 align:middle line:90% So there's extra vacancies. 00:42:58.070 --> 00:43:01.100 align:middle line:84% Down in deep, you have net interstitials. 00:43:01.100 --> 00:43:03.200 align:middle line:84% But the total numbers of these net 00:43:03.200 --> 00:43:05.115 align:middle line:84% are much, much less than when you 00:43:05.115 --> 00:43:06.740 align:middle line:84% do the subtraction of the interstitials 00:43:06.740 --> 00:43:09.645 align:middle line:84% from the vacancies, than the total interstitial or vacancies 00:43:09.645 --> 00:43:10.770 align:middle line:90% that were actually created. 00:43:10.770 --> 00:43:12.611 align:middle line:90% So that's this point. 00:43:12.611 --> 00:43:14.330 align:middle line:84% To within three orders of magnitude, 00:43:14.330 --> 00:43:17.560 align:middle line:84% a lot, most of these guys recombine. 00:43:17.560 --> 00:43:19.440 align:middle line:84% So to first order, what he said is 00:43:19.440 --> 00:43:22.170 align:middle line:84% that you can imagine that all of the original damage 00:43:22.170 --> 00:43:27.240 align:middle line:84% recombines, and leaves behind only one interstitial created 00:43:27.240 --> 00:43:32.820 align:middle line:84% for every phosphorus atom, or every ion-implanted ion that 00:43:32.820 --> 00:43:33.640 align:middle line:90% is ion implanted. 00:43:33.640 --> 00:43:34.500 align:middle line:90% So you can imagine. 00:43:34.500 --> 00:43:37.500 align:middle line:84% Let's say you are implanting a dose of phosphorus. 00:43:37.500 --> 00:43:41.490 align:middle line:84% In this particular example, my guess is 80 keV, 10 to 13th. 00:43:41.490 --> 00:43:44.340 align:middle line:84% He was saying that there's one interstitial created 00:43:44.340 --> 00:43:46.410 align:middle line:90% for every phosphorus incoming. 00:43:46.410 --> 00:43:49.410 align:middle line:84% So he would say there's 10 to the 13th per square centimeter 00:43:49.410 --> 00:43:51.610 align:middle line:90% silicon interstitials created. 00:43:51.610 --> 00:43:53.560 align:middle line:90% So it's incredibly simple. 00:43:53.560 --> 00:43:57.003 align:middle line:84% You just take the dose of the atoms that are implanted, 00:43:57.003 --> 00:43:58.920 align:middle line:84% of the ions that are implanted, and say that's 00:43:58.920 --> 00:44:00.962 align:middle line:84% the number of interstitials per square centimeter 00:44:00.962 --> 00:44:01.590 align:middle line:90% that I create. 00:44:01.590 --> 00:44:03.390 align:middle line:90% 10 to the 13th. 00:44:03.390 --> 00:44:06.570 align:middle line:84% It's called plus-one because, and intuitively 00:44:06.570 --> 00:44:09.420 align:middle line:84% what he's saying is, if your implant is totally activated, 00:44:09.420 --> 00:44:12.810 align:middle line:84% so every implanted phosphorus ion finds 00:44:12.810 --> 00:44:16.290 align:middle line:84% a substitutional site, well, where did that silicon go? 00:44:16.290 --> 00:44:17.410 align:middle line:90% It had to knock. 00:44:17.410 --> 00:44:19.760 align:middle line:84% That silicon is somewhere as an interstitial. 00:44:19.760 --> 00:44:20.260 align:middle line:90% OK? 00:44:20.260 --> 00:44:21.340 align:middle line:90% And that's all he said. 00:44:21.340 --> 00:44:23.350 align:middle line:84% He said, assuming your annealing is good, 00:44:23.350 --> 00:44:25.670 align:middle line:84% you know what you're doing, to first order, 00:44:25.670 --> 00:44:28.080 align:middle line:84% so this is to get an order of magnitude estimate, 00:44:28.080 --> 00:44:29.580 align:middle line:84% the number of interstitials I create 00:44:29.580 --> 00:44:31.400 align:middle line:84% is equal to the dose of what I implanted. 00:44:31.400 --> 00:44:32.400 align:middle line:90% So that's pretty simple. 00:44:32.400 --> 00:44:34.110 align:middle line:84% I implant 10 to the 15th, I have 10 00:44:34.110 --> 00:44:36.780 align:middle line:84% to the 15th excess interstitials now in my crystal. 00:44:36.780 --> 00:44:38.640 align:middle line:84% And that's the so-called plus-one model. 00:44:38.640 --> 00:44:41.508 align:middle line:90% 00:44:41.508 --> 00:44:43.050 align:middle line:84% This just tells you a little bit more 00:44:43.050 --> 00:44:45.780 align:middle line:84% about how accurate that assumption might be. 00:44:45.780 --> 00:44:48.420 align:middle line:90% This is on slide number 19. 00:44:48.420 --> 00:44:50.960 align:middle line:90% I took this from your textbook. 00:44:50.960 --> 00:44:54.260 align:middle line:84% It's a little bit about damage evolution in time. 00:44:54.260 --> 00:45:00.520 align:middle line:84% So what it's a plot of is the annihilated interstitials, 00:45:00.520 --> 00:45:06.170 align:middle line:84% so the recombined ones, and vacancies per implanted ion. 00:45:06.170 --> 00:45:08.150 align:middle line:90% OK. 00:45:08.150 --> 00:45:12.330 align:middle line:84% And it's kind of here as a function of time. 00:45:12.330 --> 00:45:16.130 align:middle line:84% So if you look at, these are Monte Carlo simulations 00:45:16.130 --> 00:45:20.690 align:middle line:84% basically of interstitial and vacancy recombination. 00:45:20.690 --> 00:45:23.240 align:middle line:84% And if you go after a short time, 00:45:23.240 --> 00:45:27.640 align:middle line:84% really, only excess interstitials remain. 00:45:27.640 --> 00:45:30.280 align:middle line:84% And these can end up forming clusters. 00:45:30.280 --> 00:45:33.280 align:middle line:84% But basically, this bulk and surface recombination 00:45:33.280 --> 00:45:35.060 align:middle line:84% take place on a very short time scale. 00:45:35.060 --> 00:45:37.060 align:middle line:84% So look at the bulk recombination. 00:45:37.060 --> 00:45:41.020 align:middle line:84% Very quickly after here, after only, I don't know, 00:45:41.020 --> 00:45:44.110 align:middle line:84% 10 to the minus 6 seconds was at a microsecond. 00:45:44.110 --> 00:45:45.670 align:middle line:84% There's a lot of bulk recombination 00:45:45.670 --> 00:45:47.140 align:middle line:90% that's taken place. 00:45:47.140 --> 00:45:49.750 align:middle line:84% Surface recombination, for vacancies, 00:45:49.750 --> 00:45:51.010 align:middle line:90% takes a shorter time. 00:45:51.010 --> 00:45:54.760 align:middle line:84% And then finally surface interstitial recombination 00:45:54.760 --> 00:45:58.900 align:middle line:84% can take place within 100 to 1 second. 00:45:58.900 --> 00:46:02.710 align:middle line:84% So you have a lot of interstitial and vacancy 00:46:02.710 --> 00:46:06.280 align:middle line:84% recombination, that was the point of what Giles was saying, 00:46:06.280 --> 00:46:10.950 align:middle line:84% so that only plus 1 interstitial excess interstitial remains. 00:46:10.950 --> 00:46:13.110 align:middle line:84% Now, what happens to those 10 to the 15th? 00:46:13.110 --> 00:46:16.350 align:middle line:84% If I ion implant 10 to the 15th phosphorus atoms, 00:46:16.350 --> 00:46:19.050 align:middle line:84% I have 10 to the 15th excess interstitials. 00:46:19.050 --> 00:46:20.700 align:middle line:84% The name of the game is, what happens 00:46:20.700 --> 00:46:21.825 align:middle line:90% to all these interstitials? 00:46:21.825 --> 00:46:23.400 align:middle line:84% Well, it turns out they coalesce. 00:46:23.400 --> 00:46:26.080 align:middle line:84% They get together into little defects. 00:46:26.080 --> 00:46:28.620 align:middle line:84% And these little defects are called, in curly brackets, 00:46:28.620 --> 00:46:30.160 align:middle line:90% called 311 defects. 00:46:30.160 --> 00:46:33.270 align:middle line:84% And we'll talk in detail next time about 311s. 00:46:33.270 --> 00:46:35.790 align:middle line:84% But the interesting thing about these little clusters, 00:46:35.790 --> 00:46:38.610 align:middle line:84% these 311s, they are defects end up 00:46:38.610 --> 00:46:41.080 align:middle line:84% being stable for very long periods. 00:46:41.080 --> 00:46:42.600 align:middle line:84% So the interstitials come, we have 00:46:42.600 --> 00:46:44.730 align:middle line:84% all these excess interstitials, they end up 00:46:44.730 --> 00:46:47.160 align:middle line:84% getting together and forming little defects, which 00:46:47.160 --> 00:46:50.520 align:middle line:84% then can stay around for 10 seconds, 100 seconds, maybe 00:46:50.520 --> 00:46:53.160 align:middle line:84% even minutes and hours, depending on the temperature. 00:46:53.160 --> 00:46:56.130 align:middle line:84% And it's these little defects these 311s, that end up 00:46:56.130 --> 00:46:58.770 align:middle line:84% being responsible for the process of transenhanced fusion 00:46:58.770 --> 00:47:01.125 align:middle line:84% that we're going to model in the next lecture. 00:47:01.125 --> 00:47:03.820 align:middle line:90% 00:47:03.820 --> 00:47:08.500 align:middle line:84% In fact, on slide 20, just by way of introduction. 00:47:08.500 --> 00:47:12.910 align:middle line:84% These are pictures of [? 311 ?] defects. 00:47:12.910 --> 00:47:16.210 align:middle line:84% The right hand side is an actual high resolution 00:47:16.210 --> 00:47:18.550 align:middle line:84% cross-section transmission electron micrograph. 00:47:18.550 --> 00:47:20.050 align:middle line:84% And I can tell it's high resolution, 00:47:20.050 --> 00:47:24.315 align:middle line:84% because you can see these little dots, and they form in planes. 00:47:24.315 --> 00:47:25.690 align:middle line:84% Well, these little dots, each dot 00:47:25.690 --> 00:47:28.060 align:middle line:90% represents two silicon atoms. 00:47:28.060 --> 00:47:30.310 align:middle line:84% And they're all lined up in planes, 00:47:30.310 --> 00:47:35.330 align:middle line:84% because you're looking at the crystal planes in the silicon 00:47:35.330 --> 00:47:35.830 align:middle line:90% lattice. 00:47:35.830 --> 00:47:38.372 align:middle line:84% And you see this little funny looking thing right here that's 00:47:38.372 --> 00:47:39.400 align:middle line:90% tilted at an angle. 00:47:39.400 --> 00:47:42.490 align:middle line:84% It goes from this point here, this dark band of contrast, 00:47:42.490 --> 00:47:43.570 align:middle line:90% to this point here. 00:47:43.570 --> 00:47:47.050 align:middle line:84% That is a ribbon-like region that is identified. 00:47:47.050 --> 00:47:49.560 align:middle line:90% That is the [? 311 ?] defect. 00:47:49.560 --> 00:47:51.770 align:middle line:84% And that's an actual cross section TEM 00:47:51.770 --> 00:47:52.835 align:middle line:90% micrograph on the left. 00:47:52.835 --> 00:47:56.870 align:middle line:84% It is meant to represent a color cartoon of what 00:47:56.870 --> 00:47:58.400 align:middle line:90% this thing actually looks like. 00:47:58.400 --> 00:48:03.450 align:middle line:84% The axis here, along the defect, is represented by this vector 00:48:03.450 --> 00:48:06.878 align:middle line:84% here, that turns out to be, this vector 00:48:06.878 --> 00:48:08.670 align:middle line:84% turns out to be in the [? 311 ?] direction. 00:48:08.670 --> 00:48:10.295 align:middle line:84% That's how these things got their name. 00:48:10.295 --> 00:48:13.050 align:middle line:84% They were tilted in the [? 311 ?] direction. 00:48:13.050 --> 00:48:16.290 align:middle line:84% The long axis of the ribbon, this is a ribbon-like defect, 00:48:16.290 --> 00:48:19.920 align:middle line:84% the long axis points along 1 0 direction in the crystal. 00:48:19.920 --> 00:48:22.470 align:middle line:84% So the long axis here, you can't really see. 00:48:22.470 --> 00:48:27.450 align:middle line:84% It'll be into the board or into the slide. 00:48:27.450 --> 00:48:31.080 align:middle line:84% These little round things here, these circles, 00:48:31.080 --> 00:48:33.660 align:middle line:84% represent interstitials, and they're little dimers. 00:48:33.660 --> 00:48:36.810 align:middle line:84% They come in pairs, and they line up along this direction. 00:48:36.810 --> 00:48:39.840 align:middle line:90% Could be 100 angstroms long. 00:48:39.840 --> 00:48:44.090 align:middle line:84% And it's got some sort of width to it, which you can see here. 00:48:44.090 --> 00:48:45.840 align:middle line:84% And it has a certain capture radius. 00:48:45.840 --> 00:48:48.697 align:middle line:84% Within a certain region, it will capture these interstitials 00:48:48.697 --> 00:48:49.905 align:middle line:90% and form this little cluster. 00:48:49.905 --> 00:48:52.380 align:middle line:90% 00:48:52.380 --> 00:48:55.860 align:middle line:84% These [? 311 ?] defects, they flow in pretty quickly, 00:48:55.860 --> 00:48:58.950 align:middle line:90% in a matter of a second or less. 00:48:58.950 --> 00:49:02.190 align:middle line:84% But they anneal out in timescale of minutes, 00:49:02.190 --> 00:49:03.910 align:middle line:90% at moderate temperatures. 00:49:03.910 --> 00:49:06.690 align:middle line:84% And as they anneal out, as this ribbon heals, 00:49:06.690 --> 00:49:08.940 align:middle line:84% it spits out silicon interstitials. 00:49:08.940 --> 00:49:11.070 align:middle line:84% And it's these silicon interstitials 00:49:11.070 --> 00:49:13.995 align:middle line:84% that are coming out of this [? 311 ?] ribbon 00:49:13.995 --> 00:49:15.870 align:middle line:84% that lead to the transient enhanced diffusion 00:49:15.870 --> 00:49:19.640 align:middle line:84% effect, these excess silicon interstitials. 00:49:19.640 --> 00:49:22.040 align:middle line:84% It turns out that below a certain dose, 00:49:22.040 --> 00:49:25.490 align:middle line:84% or below a certain damage value, these [? 311 ?] defects 00:49:25.490 --> 00:49:27.468 align:middle line:90% can dissolve completely. 00:49:27.468 --> 00:49:28.510 align:middle line:90% So you can dissolve them. 00:49:28.510 --> 00:49:29.968 align:middle line:84% You can completely get rid of them. 00:49:29.968 --> 00:49:32.200 align:middle line:84% And at that point, when they're completely gone, 00:49:32.200 --> 00:49:34.420 align:middle line:84% you have no more TED after that amount of time. 00:49:34.420 --> 00:49:36.850 align:middle line:90% You go back to normal diffusion. 00:49:36.850 --> 00:49:39.460 align:middle line:84% Above a certain damage level, actually, it's 00:49:39.460 --> 00:49:41.500 align:middle line:90% a little more complicated. 00:49:41.500 --> 00:49:45.160 align:middle line:84% They actually get together, they turn into stable dislocation 00:49:45.160 --> 00:49:47.230 align:middle line:84% loops, which are more difficult or sometimes 00:49:47.230 --> 00:49:48.250 align:middle line:90% impossible to remove. 00:49:48.250 --> 00:49:50.237 align:middle line:90% That's like end of range damage. 00:49:50.237 --> 00:49:52.570 align:middle line:84% But there's a certain region in which you can remove all 00:49:52.570 --> 00:49:54.880 align:middle line:84% the [? 311 ?]s,s, certain amount of damage. 00:49:54.880 --> 00:49:57.750 align:middle line:90% 00:49:57.750 --> 00:49:58.250 align:middle line:90% OK. 00:49:58.250 --> 00:50:00.290 align:middle line:84% So when we're going to talk about [? 311 ?]ss 00:50:00.290 --> 00:50:03.450 align:middle line:84% and their annealing kinetics in great detail next lecture, 00:50:03.450 --> 00:50:07.160 align:middle line:84% when we go through the whole kinetics of transient enhanced 00:50:07.160 --> 00:50:08.145 align:middle line:90% diffusion. 00:50:08.145 --> 00:50:10.020 align:middle line:84% In the meantime, I want to go on and continue 00:50:10.020 --> 00:50:11.790 align:middle line:84% to talk about other aspects of annealing. 00:50:11.790 --> 00:50:13.680 align:middle line:84% So we know we create all these interstitials. 00:50:13.680 --> 00:50:16.260 align:middle line:90% They get together in [? 311 ?]s. 00:50:16.260 --> 00:50:18.432 align:middle line:84% We know if we go to high enough dose, 00:50:18.432 --> 00:50:20.640 align:middle line:84% remember I showed you a picture that we can amorphize 00:50:20.640 --> 00:50:23.880 align:middle line:84% the crystal, well, let's say I do create an amorphous layer 00:50:23.880 --> 00:50:24.870 align:middle line:90% at the surface. 00:50:24.870 --> 00:50:26.940 align:middle line:84% How can I get rid of that amorphous layer 00:50:26.940 --> 00:50:29.400 align:middle line:84% and restore the crystal to perfect, or to some kind 00:50:29.400 --> 00:50:30.270 align:middle line:90% of crystallinity? 00:50:30.270 --> 00:50:31.830 align:middle line:84% Well, this is exactly what happens. 00:50:31.830 --> 00:50:35.100 align:middle line:84% I'm showing here cross-section TEM images. 00:50:35.100 --> 00:50:37.920 align:middle line:84% This layer is originally amorphous from the surface 00:50:37.920 --> 00:50:41.900 align:middle line:84% of the wafer down to some depth, and we're regrowing it. 00:50:41.900 --> 00:50:45.200 align:middle line:84% So we're annealing the wafer at 525. 00:50:45.200 --> 00:50:47.100 align:middle line:84% The initial implant was quite high. 00:50:47.100 --> 00:50:50.360 align:middle line:84% It's 200 kilovolts, 6 times 10 to the 15th of antimony. 00:50:50.360 --> 00:50:52.620 align:middle line:84% Again, antimony is a very heavy atom, 00:50:52.620 --> 00:50:56.060 align:middle line:84% so it amorphized from the surface down. 00:50:56.060 --> 00:50:58.550 align:middle line:84% And we're looking here, initially, at 0 minutes. 00:50:58.550 --> 00:51:01.250 align:middle line:84% So guess that kind of got cut off of the slide, 00:51:01.250 --> 00:51:03.830 align:middle line:84% but this should be here at 0 minutes, 00:51:03.830 --> 00:51:05.450 align:middle line:90% so just when you first start. 00:51:05.450 --> 00:51:07.820 align:middle line:84% After 10 minutes of annealing at 525, 00:51:07.820 --> 00:51:11.210 align:middle line:84% look at the interface between the amorphous and the crystal 00:51:11.210 --> 00:51:13.600 align:middle line:90% substrate has moved up. 00:51:13.600 --> 00:51:17.620 align:middle line:84% So the amorphous layer is actually grown, or regrown, 00:51:17.620 --> 00:51:19.700 align:middle line:84% by a process called solid phase epitaxy. 00:51:19.700 --> 00:51:23.740 align:middle line:84% So there's no melting going on, but in a layer-by-layer method, 00:51:23.740 --> 00:51:27.070 align:middle line:84% the atoms in each layer are taking the template 00:51:27.070 --> 00:51:29.530 align:middle line:84% from the substrate and rearranging themselves back 00:51:29.530 --> 00:51:30.940 align:middle line:90% into a single crystal form. 00:51:30.940 --> 00:51:34.510 align:middle line:84% And this amorphous layer is progressing up 00:51:34.510 --> 00:51:36.310 align:middle line:84% from the depths towards the surface, 00:51:36.310 --> 00:51:40.180 align:middle line:84% you can see it as time goes on, in kind of a linear fashion 00:51:40.180 --> 00:51:42.600 align:middle line:90% in an epitaxial growth. 00:51:42.600 --> 00:51:45.140 align:middle line:84% So we call it solid phase EPI as opposed to vapor phase. 00:51:45.140 --> 00:51:48.350 align:middle line:84% Vapor phase would be if I were injecting xylene or something 00:51:48.350 --> 00:51:51.930 align:middle line:84% and growing EPI Here I just have a solid solution that's 00:51:51.930 --> 00:51:54.200 align:middle line:90% regrowing at 525. 00:51:54.200 --> 00:51:56.568 align:middle line:84% When you're done-- or, well, this isn't quite done. 00:51:56.568 --> 00:51:57.860 align:middle line:90% At 20 minutes it's almost done. 00:51:57.860 --> 00:52:02.030 align:middle line:84% Maybe half an hour-- you would see the entire amorphous region 00:52:02.030 --> 00:52:03.140 align:middle line:90% will have been regrown. 00:52:03.140 --> 00:52:04.520 align:middle line:90% It'll all be single crystal. 00:52:04.520 --> 00:52:06.350 align:middle line:84% And you'll be left with something though. 00:52:06.350 --> 00:52:09.630 align:middle line:84% There's a band of residual damage 00:52:09.630 --> 00:52:13.650 align:middle line:84% that occurs called end of range damage, or EOR. 00:52:13.650 --> 00:52:15.420 align:middle line:84% And these are defects that are just 00:52:15.420 --> 00:52:17.520 align:middle line:84% below the amorphous crystalline interface. 00:52:17.520 --> 00:52:19.080 align:middle line:84% So you get an idea of where they are. 00:52:19.080 --> 00:52:20.850 align:middle line:90% They're always just below that. 00:52:20.850 --> 00:52:22.740 align:middle line:84% And those are pretty hard to get out. 00:52:22.740 --> 00:52:24.683 align:middle line:84% Those generally don't ever go away. 00:52:24.683 --> 00:52:26.100 align:middle line:84% You have a certain amount of that, 00:52:26.100 --> 00:52:29.690 align:middle line:84% for such a high dose, that you have to live with. 00:52:29.690 --> 00:52:31.490 align:middle line:84% You have to find a way to deal with it. 00:52:31.490 --> 00:52:33.830 align:middle line:90% 00:52:33.830 --> 00:52:36.290 align:middle line:84% This slide on page 22 actually shows 00:52:36.290 --> 00:52:40.430 align:middle line:84% you some data from a book by Gibbons and Sigman, 00:52:40.430 --> 00:52:42.810 align:middle line:84% called Laser Annealing of Semiconductors. 00:52:42.810 --> 00:52:44.900 align:middle line:90% So it's about laser annealing. 00:52:44.900 --> 00:52:45.590 align:middle line:90% The book is. 00:52:45.590 --> 00:52:48.650 align:middle line:84% But this particular chapter is about solid-phase EPI 00:52:48.650 --> 00:52:52.130 align:middle line:84% or solid-phase regrowth, just in a furnace. 00:52:52.130 --> 00:52:55.050 align:middle line:84% And what they're plotting here is the regrowth rate. 00:52:55.050 --> 00:52:57.590 align:middle line:84% So this gives you the number of angstroms per minute 00:52:57.590 --> 00:53:00.733 align:middle line:84% as that amorphous layer traverses from down below up. 00:53:00.733 --> 00:53:02.150 align:middle line:84% The number of angstroms per minute 00:53:02.150 --> 00:53:05.330 align:middle line:84% that it goes, as a function of inverse temperature 00:53:05.330 --> 00:53:08.190 align:middle line:84% for silicon and under different conditions. 00:53:08.190 --> 00:53:09.830 align:middle line:90% So let's take a curve here. 00:53:09.830 --> 00:53:11.960 align:middle line:84% Let's take this one curve right here 00:53:11.960 --> 00:53:15.810 align:middle line:84% that is called 100 silicon undoped 00:53:15.810 --> 00:53:17.340 align:middle line:90% as a function of temperature. 00:53:17.340 --> 00:53:21.390 align:middle line:84% And you can see, for undoped silicon, say at 525, 00:53:21.390 --> 00:53:25.630 align:middle line:84% the regrowth rate is about 20 or 30 angstroms per minute. 00:53:25.630 --> 00:53:27.990 align:middle line:84% So as a constant rate, these people have measured this, 00:53:27.990 --> 00:53:30.600 align:middle line:84% there's a technique called Rutherford backscattering, ion 00:53:30.600 --> 00:53:33.720 align:middle line:84% channeling, you can actually measure this rate going up. 00:53:33.720 --> 00:53:37.110 align:middle line:84% And you can see how fast it goes. 00:53:37.110 --> 00:53:39.360 align:middle line:84% Gives you an idea of how that amorphous layer regrows. 00:53:39.360 --> 00:53:41.280 align:middle line:90% And that's at 525. 00:53:41.280 --> 00:53:43.080 align:middle line:84% So you can see, amorphous layer regrowth 00:53:43.080 --> 00:53:44.940 align:middle line:84% can happen at reasonably low temperatures. 00:53:44.940 --> 00:53:46.425 align:middle line:90% You don't have to go too hot. 00:53:46.425 --> 00:53:49.050 align:middle line:84% Interestingly, though, there are lots of different curves here. 00:53:49.050 --> 00:53:51.300 align:middle line:84% If you go to the 110 silicon, so if you 00:53:51.300 --> 00:53:55.320 align:middle line:84% buy a wafer that is 110 surface instead, 00:53:55.320 --> 00:53:58.380 align:middle line:84% you've got a different atomic density on that 110 plane, 00:53:58.380 --> 00:53:59.760 align:middle line:90% and in fact, it regrows slower. 00:53:59.760 --> 00:54:05.540 align:middle line:84% The same activation energy, ea of 2.3 electron volts. 00:54:05.540 --> 00:54:08.370 align:middle line:84% Interestingly, that number is kind of intriguing. 00:54:08.370 --> 00:54:10.970 align:middle line:84% That's also what people believe 2.2 is roughly 00:54:10.970 --> 00:54:13.100 align:middle line:90% the bond breaking energy. 00:54:13.100 --> 00:54:16.280 align:middle line:84% And so imagine that interface between the amorphous 00:54:16.280 --> 00:54:17.780 align:middle line:84% and the single crystal, you probably 00:54:17.780 --> 00:54:20.330 align:middle line:84% have to break some bonds there, initially 00:54:20.330 --> 00:54:23.280 align:middle line:90% in order to realign the atoms. 00:54:23.280 --> 00:54:25.010 align:middle line:90% So SPE is pretty fast. 00:54:25.010 --> 00:54:26.960 align:middle line:84% It depends on orientation, and it 00:54:26.960 --> 00:54:28.590 align:middle line:84% depends, what's really interesting, 00:54:28.590 --> 00:54:32.030 align:middle line:84% it depends very much so on doping. 00:54:32.030 --> 00:54:35.690 align:middle line:84% So for example, here's silicon that's doped with arsenic. 00:54:35.690 --> 00:54:40.100 align:middle line:84% You can be quite a bit faster, 3 to 5 times faster, 00:54:40.100 --> 00:54:42.320 align:middle line:90% or phosphorous, or boron. 00:54:42.320 --> 00:54:44.870 align:middle line:84% Boron is the fastest, it looks like. 00:54:44.870 --> 00:54:48.500 align:middle line:84% If you accidentally put oxygen or nitrogen into your sample, 00:54:48.500 --> 00:54:50.310 align:middle line:84% look what happens to the regrowth rate. 00:54:50.310 --> 00:54:52.410 align:middle line:84% You can go down by almost an order of magnitude. 00:54:52.410 --> 00:54:55.590 align:middle line:90% So impurities have a big effect. 00:54:55.590 --> 00:54:59.700 align:middle line:84% And argon would even really do it, 00:54:59.700 --> 00:55:01.500 align:middle line:90% really frustrates the regrowth. 00:55:01.500 --> 00:55:03.150 align:middle line:84% And so it's important to know what's 00:55:03.150 --> 00:55:05.670 align:middle line:84% in your crystal, what your ion implanting will 00:55:05.670 --> 00:55:07.620 align:middle line:84% have a big effect on the regrowth rate. 00:55:07.620 --> 00:55:10.920 align:middle line:84% Interestingly, when you do this, most of the dopant atoms, 00:55:10.920 --> 00:55:13.110 align:middle line:84% like arsenic, phosphorus, boron, are 00:55:13.110 --> 00:55:15.210 align:middle line:84% incorporated as that amorphous layer moves up. 00:55:15.210 --> 00:55:16.710 align:middle line:84% They're actually mostly incorporated 00:55:16.710 --> 00:55:19.120 align:middle line:84% on substitutional sites, even at low temperatures. 00:55:19.120 --> 00:55:23.520 align:middle line:84% So it turns out, if you can create an amorphous layer, 00:55:23.520 --> 00:55:28.560 align:middle line:84% this is one of the best ways of activating a dopant, 00:55:28.560 --> 00:55:30.540 align:middle line:84% is to create an amorphous layer in silicon. 00:55:30.540 --> 00:55:32.040 align:middle line:84% Now this is the way silicon anneals. 00:55:32.040 --> 00:55:34.270 align:middle line:84% Other semiconductors, gallium arsenide for example, 00:55:34.270 --> 00:55:35.160 align:middle line:90% is just the opposite. 00:55:35.160 --> 00:55:37.620 align:middle line:84% If you amorphize it, God help you 00:55:37.620 --> 00:55:41.652 align:middle line:84% trying to get the dopants to get activated. 00:55:41.652 --> 00:55:42.360 align:middle line:90% It's not so easy. 00:55:42.360 --> 00:55:44.130 align:middle line:84% But silicon has this beautiful property 00:55:44.130 --> 00:55:46.980 align:middle line:84% that as that layer moves up, a lot of the dopant atoms 00:55:46.980 --> 00:55:48.690 align:middle line:84% get forced onto substitutional sites. 00:55:48.690 --> 00:55:50.160 align:middle line:84% And then the donors and acceptors 00:55:50.160 --> 00:55:53.460 align:middle line:84% are already activated at low temperature, to a great degree. 00:55:53.460 --> 00:55:55.870 align:middle line:90% So that's a nice property. 00:55:55.870 --> 00:55:57.625 align:middle line:84% Assuming you fully amorphize the crystal. 00:55:57.625 --> 00:56:00.100 align:middle line:90% 00:56:00.100 --> 00:56:01.660 align:middle line:90% OK, let's go on to slide 23. 00:56:01.660 --> 00:56:04.870 align:middle line:84% I mentioned that life is not perfect. 00:56:04.870 --> 00:56:07.920 align:middle line:84% Even if you amorphize, you always 00:56:07.920 --> 00:56:10.380 align:middle line:84% end up with this end of range damage. 00:56:10.380 --> 00:56:14.230 align:middle line:84% And here's a plot on the left of, 00:56:14.230 --> 00:56:16.230 align:middle line:84% let's say this is the surface of a silicon wafer 00:56:16.230 --> 00:56:17.850 align:middle line:90% here, going down in depth. 00:56:17.850 --> 00:56:19.560 align:middle line:90% And here's my concentration. 00:56:19.560 --> 00:56:22.140 align:middle line:84% And let's say I have implanted something, maybe it's arsenic, 00:56:22.140 --> 00:56:22.890 align:middle line:90% I don't know what. 00:56:22.890 --> 00:56:24.450 align:middle line:84% And it has this ion implanted profile. 00:56:24.450 --> 00:56:25.242 align:middle line:90% It looks like this. 00:56:25.242 --> 00:56:27.720 align:middle line:90% 00:56:27.720 --> 00:56:34.290 align:middle line:84% And there is, the maximum damage for this particular profile 00:56:34.290 --> 00:56:37.420 align:middle line:84% is just below the amorphization threshold. 00:56:37.420 --> 00:56:42.062 align:middle line:84% So this region from here to here, from the surface down to, 00:56:42.062 --> 00:56:44.520 align:middle line:84% this dashed line is called the amorphous crystal interface, 00:56:44.520 --> 00:56:45.690 align:middle line:90% that's all amorphized. 00:56:45.690 --> 00:56:48.235 align:middle line:84% So that's going to regrow layer by layer 00:56:48.235 --> 00:56:50.610 align:middle line:84% and give you very good crystal quality, if I just go back 00:56:50.610 --> 00:56:51.870 align:middle line:90% a couple of slides here. 00:56:51.870 --> 00:56:56.340 align:middle line:84% Again, it was amorphized to this depth. 00:56:56.340 --> 00:56:59.040 align:middle line:84% If you look at this depth when you're done, 00:56:59.040 --> 00:57:00.780 align:middle line:90% there is no residual damage. 00:57:00.780 --> 00:57:02.850 align:middle line:84% It's below the initial amorphous crystal 00:57:02.850 --> 00:57:04.920 align:middle line:84% interface by some distance, that you end up 00:57:04.920 --> 00:57:07.050 align:middle line:90% with it's end of range. 00:57:07.050 --> 00:57:09.900 align:middle line:84% And it kind of makes sense, because at this point, 00:57:09.900 --> 00:57:12.630 align:middle line:84% you have deposited-- averted this depth enough energy 00:57:12.630 --> 00:57:14.070 align:middle line:90% to amorphize the crystal. 00:57:14.070 --> 00:57:16.680 align:middle line:84% Below that, you've deposited a huge amount of energy, 00:57:16.680 --> 00:57:17.940 align:middle line:90% but not enough to amorphize. 00:57:17.940 --> 00:57:20.190 align:middle line:84% So you've really bashed it up, but it's not amorphous, 00:57:20.190 --> 00:57:22.830 align:middle line:84% so it can't regrow by solid phase EPI Instead, 00:57:22.830 --> 00:57:24.900 align:middle line:84% it creates dislocation loops, and that's 00:57:24.900 --> 00:57:26.330 align:middle line:90% what we call the end of range. 00:57:26.330 --> 00:57:30.350 align:middle line:84% So if I go back to the slide number 23, 00:57:30.350 --> 00:57:33.690 align:middle line:84% just below the amorphous region of this end of range damage. 00:57:33.690 --> 00:57:36.050 align:middle line:84% And here is my ion implanted arsenic. 00:57:36.050 --> 00:57:36.560 align:middle line:90% OK. 00:57:36.560 --> 00:57:37.060 align:middle line:90% So. 00:57:37.060 --> 00:57:37.940 align:middle line:90% Now, let's see. 00:57:37.940 --> 00:57:41.420 align:middle line:84% I'm using this to make an np junction. 00:57:41.420 --> 00:57:45.220 align:middle line:84% So what I need to do, if I'm going to make an np junction, 00:57:45.220 --> 00:57:46.690 align:middle line:84% what I typically want to do is just 00:57:46.690 --> 00:57:49.420 align:middle line:84% to diffuse the n type dopant a little bit deeper 00:57:49.420 --> 00:57:51.890 align:middle line:90% than the end of range damage. 00:57:51.890 --> 00:57:55.660 align:middle line:84% So we tend to try to get a little bit of diffusion 00:57:55.660 --> 00:57:57.010 align:middle line:90% after we've done an ion implant. 00:57:57.010 --> 00:58:00.020 align:middle line:84% Sometimes, that can be helpful, because why would that matter? 00:58:00.020 --> 00:58:03.160 align:middle line:84% Well, here's my end of, I've done an overlay. 00:58:03.160 --> 00:58:05.560 align:middle line:84% This is a cross-section TEM micrograph. 00:58:05.560 --> 00:58:07.360 align:middle line:84% And here's my end of range damage, 00:58:07.360 --> 00:58:09.370 align:middle line:84% this little black dislocation bar. 00:58:09.370 --> 00:58:13.280 align:middle line:84% And imagine I diffuse this arsenic just a little deeper. 00:58:13.280 --> 00:58:15.640 align:middle line:84% So now I have an n plus region that goes just 00:58:15.640 --> 00:58:19.720 align:middle line:84% below the end of range damage, and then below that I have p. 00:58:19.720 --> 00:58:22.860 align:middle line:90% Well, this is n plus, this is p. 00:58:22.860 --> 00:58:25.980 align:middle line:84% The depletion region, again, always tends to extend, 00:58:25.980 --> 00:58:28.770 align:middle line:84% if you remember your np or pn junction physics, 00:58:28.770 --> 00:58:31.800 align:middle line:84% the depleted region is going to be in the lightly doped side, 00:58:31.800 --> 00:58:33.330 align:middle line:90% where the yellow is. 00:58:33.330 --> 00:58:35.460 align:middle line:84% So the yellow is depleted of free carriers. 00:58:35.460 --> 00:58:37.590 align:middle line:84% And you know, in the depletion region, 00:58:37.590 --> 00:58:40.530 align:middle line:84% that's where you get the most amount of recombination 00:58:40.530 --> 00:58:44.500 align:middle line:84% of electrons and holes to create leakage in a pn junction. 00:58:44.500 --> 00:58:46.950 align:middle line:84% So the depletion region is the last place 00:58:46.950 --> 00:58:50.010 align:middle line:84% you want damage or defects, because in the depletion 00:58:50.010 --> 00:58:51.630 align:middle line:84% region, electron hole recombination 00:58:51.630 --> 00:58:53.200 align:middle line:90% is very efficient. 00:58:53.200 --> 00:58:56.260 align:middle line:84% So what we do, what people do, this is kind of cheating, 00:58:56.260 --> 00:58:59.520 align:middle line:84% but they cover up the end of range damage 00:58:59.520 --> 00:59:01.870 align:middle line:90% with a heavily doped region. 00:59:01.870 --> 00:59:04.590 align:middle line:84% So if you see people making source drain junctions, 00:59:04.590 --> 00:59:08.310 align:middle line:84% they often diffuse it just a little ways beyond the EOR, 00:59:08.310 --> 00:59:10.800 align:middle line:84% and then they get diodes that are pretty good. 00:59:10.800 --> 00:59:11.730 align:middle line:90% Reasonably good. 00:59:11.730 --> 00:59:13.400 align:middle line:84% If they don't diffuse it at all, they 00:59:13.400 --> 00:59:16.890 align:middle line:84% say I'm going to have a perfect anneal, no diffusion, in fact, 00:59:16.890 --> 00:59:19.830 align:middle line:84% then the n plus junction might have been back here, 00:59:19.830 --> 00:59:22.090 align:middle line:84% and then the EOR might have been in the yellow region, 00:59:22.090 --> 00:59:24.257 align:middle line:84% in the depletion region, at the end of range damage, 00:59:24.257 --> 00:59:26.800 align:middle line:84% and you could get a lot leakier diode. 00:59:26.800 --> 00:59:29.520 align:middle line:84% So there's a lot of optimization when 00:59:29.520 --> 00:59:32.070 align:middle line:84% people activate source drains, or something 00:59:32.070 --> 00:59:33.690 align:middle line:90% where they care about leakage. 00:59:33.690 --> 00:59:36.720 align:middle line:84% There's a lot of optimization in just exactly how much 00:59:36.720 --> 00:59:39.360 align:middle line:84% damage dopant diffusion do I allow, 00:59:39.360 --> 00:59:46.210 align:middle line:84% and how much time do I allow to try to get rid of these loops? 00:59:46.210 --> 00:59:48.210 align:middle line:84% So it's kind of an interesting, damage annealing 00:59:48.210 --> 00:59:52.230 align:middle line:84% is an interesting combination between knowledge of p n 00:59:52.230 --> 00:59:55.860 align:middle line:84% junction physics, and electronic recombination mechanisms, 00:59:55.860 --> 00:59:57.570 align:middle line:84% and knowledge of the crystal structure 00:59:57.570 --> 00:59:58.920 align:middle line:84% and what kind of damage you've created. 00:59:58.920 --> 01:00:01.045 align:middle line:84% And you need to optimize that, because you'll never 01:00:01.045 --> 01:00:03.090 align:middle line:84% get rid of all damage, to a certain extent, 01:00:03.090 --> 01:00:04.252 align:middle line:90% for every single implant. 01:00:04.252 --> 01:00:06.210 align:middle line:84% Some implants are easier to anneal than others. 01:00:06.210 --> 01:00:08.900 align:middle line:90% 01:00:08.900 --> 01:00:09.400 align:middle line:90% OK. 01:00:09.400 --> 01:00:12.075 align:middle line:84% So that was in terms of, I spoke there quite a while 01:00:12.075 --> 01:00:14.200 align:middle line:84% about trying to get rid of damage, because I wanted 01:00:14.200 --> 01:00:15.560 align:middle line:90% to get good pn junctions. 01:00:15.560 --> 01:00:16.690 align:middle line:90% I want to get low leakage. 01:00:16.690 --> 01:00:17.190 align:middle line:90% OK. 01:00:17.190 --> 01:00:21.250 align:middle line:84% That's only one requirement, is low leakage in the crystal. 01:00:21.250 --> 01:00:23.110 align:middle line:84% I also want to activate the dopant. 01:00:23.110 --> 01:00:25.870 align:middle line:84% You want to ion implant 10 to the 15th arsenic 01:00:25.870 --> 01:00:27.460 align:middle line:84% atoms per square centimeter, you'd 01:00:27.460 --> 01:00:29.260 align:middle line:84% like to get 10 to the 15th electrons 01:00:29.260 --> 01:00:30.310 align:middle line:90% per square centimeter. 01:00:30.310 --> 01:00:32.018 align:middle line:84% You'd like to have all of that activated. 01:00:32.018 --> 01:00:32.650 align:middle line:90% Or boron. 01:00:32.650 --> 01:00:34.060 align:middle line:84% That's the whole reason you're putting it in. 01:00:34.060 --> 01:00:35.860 align:middle line:84% You don't care about boron in the lattice. 01:00:35.860 --> 01:00:38.830 align:middle line:84% It's the holes that it produces, or the electrons 01:00:38.830 --> 01:00:40.780 align:middle line:90% that arsenic produces. 01:00:40.780 --> 01:00:44.690 align:middle line:84% Well, it turns out, if you amorphize the substrate, 01:00:44.690 --> 01:00:46.240 align:middle line:84% again this only applies to silicon, 01:00:46.240 --> 01:00:47.823 align:middle line:84% gallium arsenide is just the opposite. 01:00:47.823 --> 01:00:51.070 align:middle line:84% But if you amorphize the silicon that we mentioned, 01:00:51.070 --> 01:00:53.645 align:middle line:84% that a solid phase epi is an ideal way of repairing 01:00:53.645 --> 01:00:55.270 align:middle line:84% the damage and also getting the dopants 01:00:55.270 --> 01:00:57.930 align:middle line:90% onto substitutional sites. 01:00:57.930 --> 01:01:01.410 align:middle line:84% If you don't amorphize, so you do a lower dose that 01:01:01.410 --> 01:01:04.350 align:middle line:84% does a lot of damage but doesn't create an amorphous layer, 01:01:04.350 --> 01:01:06.780 align:middle line:84% so you can't have SPE, it turns out 01:01:06.780 --> 01:01:08.790 align:middle line:84% that activation is a lot more complex, 01:01:08.790 --> 01:01:12.180 align:middle line:84% because you create defects that are somewhat stable over time 01:01:12.180 --> 01:01:13.300 align:middle line:90% and temperature. 01:01:13.300 --> 01:01:16.290 align:middle line:84% So here's just an example, of a plot of the annealing 01:01:16.290 --> 01:01:17.940 align:middle line:84% characteristics of arsenic and silicon 01:01:17.940 --> 01:01:20.380 align:middle line:90% I took out of your textbook. 01:01:20.380 --> 01:01:23.350 align:middle line:84% And the y-axis here is the fraction active. 01:01:23.350 --> 01:01:24.820 align:middle line:90% So I want to be up to one. 01:01:24.820 --> 01:01:27.520 align:middle line:84% If I'm at one, that means every single arsenic atom 01:01:27.520 --> 01:01:29.740 align:middle line:84% that I implanted contributes electron 01:01:29.740 --> 01:01:31.240 align:middle line:84% and they're all electrically active. 01:01:31.240 --> 01:01:35.240 align:middle line:84% And this is as a function of annealing temperature. 01:01:35.240 --> 01:01:37.070 align:middle line:84% And there are different doses shown here. 01:01:37.070 --> 01:01:40.102 align:middle line:84% So the red curve assumes I've amorphized the silicon. 01:01:40.102 --> 01:01:40.810 align:middle line:90% And look at this. 01:01:40.810 --> 01:01:41.518 align:middle line:90% Very interesting. 01:01:41.518 --> 01:01:45.640 align:middle line:84% At 550, 525, I can activate for 1e-15 implant, 01:01:45.640 --> 01:01:47.950 align:middle line:90% I can activate almost 80%. 01:01:47.950 --> 01:01:49.130 align:middle line:90% That's pretty good. 01:01:49.130 --> 01:01:51.065 align:middle line:84% And if I increase the temperature up to 800, 01:01:51.065 --> 01:01:52.690 align:middle line:84% it doesn't actually activate much more. 01:01:52.690 --> 01:01:55.540 align:middle line:84% So if I want to do a really low temperature anneal in silicon, 01:01:55.540 --> 01:01:58.060 align:middle line:84% I can do that with a 1e-15 implant. 01:01:58.060 --> 01:02:01.000 align:middle line:84% Except for 20% of my atoms, I get them active. 01:02:01.000 --> 01:02:05.140 align:middle line:84% But let's say I only implanted 1e-14 instead. 01:02:05.140 --> 01:02:08.080 align:middle line:84% At that same temperature, only 10% are active. 01:02:08.080 --> 01:02:09.190 align:middle line:90% Very few. 01:02:09.190 --> 01:02:12.160 align:middle line:84% So if I have an intermediate dose 01:02:12.160 --> 01:02:14.410 align:middle line:84% 1e-14 might be more typical dose, 01:02:14.410 --> 01:02:16.390 align:middle line:84% say, for the source strain extensions, 01:02:16.390 --> 01:02:21.320 align:middle line:84% might be 1e-14 That's a miserable dose, because it's 01:02:21.320 --> 01:02:23.447 align:middle line:84% pretty high to do some damage, but it's low enough 01:02:23.447 --> 01:02:24.530 align:middle line:90% that it doesn't amorphize. 01:02:24.530 --> 01:02:26.900 align:middle line:84% And so to activate the extensions here, 01:02:26.900 --> 01:02:29.000 align:middle line:84% this 1e-14 dose, you really need to get up 01:02:29.000 --> 01:02:33.650 align:middle line:84% to 750, 800 or whatever to get 80% activation. 01:02:33.650 --> 01:02:35.860 align:middle line:90% 01:02:35.860 --> 01:02:38.200 align:middle line:84% So we don't just think, oh for any implant 01:02:38.200 --> 01:02:40.310 align:middle line:84% I want I just do a certain anneal 01:02:40.310 --> 01:02:41.560 align:middle line:90% and I'll get the same results. 01:02:41.560 --> 01:02:44.890 align:middle line:84% It really depends on the amount of damage I did, 01:02:44.890 --> 01:02:47.980 align:middle line:84% and whether I was below or above the amorphization threshold. 01:02:47.980 --> 01:02:51.280 align:middle line:84% Here, if you go to really low doses, it's a piece of cake. 01:02:51.280 --> 01:02:54.070 align:middle line:84% Again, here at 10 to the 12th it's not bad. 01:02:54.070 --> 01:02:57.460 align:middle line:84% Because you did so little damage even at 600, 700, 01:02:57.460 --> 01:03:00.380 align:middle line:84% you can get pretty close to 80% to 100% activation. 01:03:00.380 --> 01:03:03.130 align:middle line:84% So the tough spot is this intermediate dose regime 01:03:03.130 --> 01:03:05.170 align:middle line:84% which is exactly the dose regime where 01:03:05.170 --> 01:03:07.550 align:middle line:84% we're ion implanting source drain tips or source drain 01:03:07.550 --> 01:03:08.050 align:middle line:90% extensions. 01:03:08.050 --> 01:03:10.240 align:middle line:84% And those need to be active as full as possible. 01:03:10.240 --> 01:03:13.660 align:middle line:84% So unfortunately, it does make our life 01:03:13.660 --> 01:03:16.980 align:middle line:90% a little more challenging. 01:03:16.980 --> 01:03:18.660 align:middle line:90% That was arsenic. 01:03:18.660 --> 01:03:20.100 align:middle line:90% That actually isn't that bad. 01:03:20.100 --> 01:03:23.040 align:middle line:90% Even more complicated is boron. 01:03:23.040 --> 01:03:27.210 align:middle line:84% And again, I took this plot from your textbook. 01:03:27.210 --> 01:03:29.880 align:middle line:84% It's the same kind of plot, now I'm on a semi-log plot, 01:03:29.880 --> 01:03:33.720 align:middle line:84% so I've got a log scale on the y-axis and temperature 01:03:33.720 --> 01:03:35.700 align:middle line:90% of annealing on the x-axis. 01:03:35.700 --> 01:03:38.040 align:middle line:90% And different doses again. 01:03:38.040 --> 01:03:40.950 align:middle line:84% So for boron, if you have a low dose up here, 01:03:40.950 --> 01:03:44.280 align:middle line:84% 8 times 10 to the 12th, again at 550, 600, 01:03:44.280 --> 01:03:48.870 align:middle line:84% I can get, oh, maybe 70, or 50% to 60% active. 01:03:48.870 --> 01:03:52.500 align:middle line:84% Not that great, but not terrible. 01:03:52.500 --> 01:03:54.780 align:middle line:84% Interestingly, at the very high dose regime, 01:03:54.780 --> 01:03:58.080 align:middle line:84% 2 times 10 to the 15th, if I kneel at very low temperatures, 01:03:58.080 --> 01:04:00.900 align:middle line:84% say 500, I get a reasonable active, 01:04:00.900 --> 01:04:01.900 align:middle line:90% well it's not very good. 01:04:01.900 --> 01:04:03.210 align:middle line:90% It's only 1 in 10. 01:04:03.210 --> 01:04:05.433 align:middle line:90% But it actually goes down. 01:04:05.433 --> 01:04:07.350 align:middle line:84% It actually goes down in a certain temperature 01:04:07.350 --> 01:04:09.318 align:middle line:90% range between 550 and 700. 01:04:09.318 --> 01:04:10.860 align:middle line:84% So you're actually reverse annealing. 01:04:10.860 --> 01:04:12.660 align:middle line:84% You're taking the dopant atoms off site. 01:04:12.660 --> 01:04:14.160 align:middle line:84% And then finally, it takes up again. 01:04:14.160 --> 01:04:16.660 align:middle line:84% When it takes off again, when you get up 01:04:16.660 --> 01:04:19.150 align:middle line:90% above about 750 or 800. 01:04:19.150 --> 01:04:21.490 align:middle line:84% So to get full activation of boron, 01:04:21.490 --> 01:04:23.633 align:middle line:84% you really need to be in silicon. 01:04:23.633 --> 01:04:26.050 align:middle line:84% At almost any dose, you need to be in the high temperature 01:04:26.050 --> 01:04:28.030 align:middle line:90% regime, 900 or above. 01:04:28.030 --> 01:04:29.510 align:middle line:90% And that's a real problem. 01:04:29.510 --> 01:04:31.930 align:middle line:84% That's why you will hear people say, oh boron 01:04:31.930 --> 01:04:33.370 align:middle line:90% is hard to activate. 01:04:33.370 --> 01:04:35.560 align:middle line:84% In general, it requires higher temperatures 01:04:35.560 --> 01:04:37.180 align:middle line:84% or some kind of more sophisticated 01:04:37.180 --> 01:04:38.650 align:middle line:84% annealing technique than arsenic. 01:04:38.650 --> 01:04:40.810 align:middle line:84% And that's because of the type of damage it does. 01:04:40.810 --> 01:04:43.870 align:middle line:84% It does not tend to amorphize, unless you 01:04:43.870 --> 01:04:44.902 align:middle line:90% go to really high doses. 01:04:44.902 --> 01:04:46.360 align:middle line:84% It's very hard to get an amorphous. 01:04:46.360 --> 01:04:49.780 align:middle line:84% And so you cannot take advantage as easily of the solid phase 01:04:49.780 --> 01:04:50.425 align:middle line:90% epi regrowth. 01:04:50.425 --> 01:04:52.760 align:middle line:90% 01:04:52.760 --> 01:04:54.290 align:middle line:90% Now, one thing you can do. 01:04:54.290 --> 01:04:55.970 align:middle line:84% You say, OK, boron doesn't amorphize. 01:04:55.970 --> 01:04:56.690 align:middle line:90% What could I do? 01:04:56.690 --> 01:04:58.970 align:middle line:84% People do something called pre-amorphization. 01:04:58.970 --> 01:05:01.700 align:middle line:84% So before they implant a boron profile, 01:05:01.700 --> 01:05:03.980 align:middle line:84% they might implant a high dose of silicon, 01:05:03.980 --> 01:05:06.140 align:middle line:84% amorphize the crystal to a certain depth, 01:05:06.140 --> 01:05:08.480 align:middle line:84% then put the boron in by implant, 01:05:08.480 --> 01:05:10.520 align:middle line:84% and then regrow the whole thing by SPE. 01:05:10.520 --> 01:05:12.890 align:middle line:84% And you can cheat that way, in some sense, 01:05:12.890 --> 01:05:14.827 align:middle line:84% or it's an extra step, but then you 01:05:14.827 --> 01:05:16.910 align:middle line:84% can get a little better annealing characteristics. 01:05:16.910 --> 01:05:19.310 align:middle line:84% But this is assuming you didn't do any pre-amorphization. 01:05:19.310 --> 01:05:21.470 align:middle line:84% This is just, implant the boron at this dose, 01:05:21.470 --> 01:05:23.900 align:middle line:90% and try to anneal it. 01:05:23.900 --> 01:05:29.600 align:middle line:84% So what is this reverse annealing behavior? 01:05:29.600 --> 01:05:32.720 align:middle line:84% Well, it's probably, oh, there's a typo here. 01:05:32.720 --> 01:05:33.620 align:middle line:90% It's thought. 01:05:33.620 --> 01:05:34.580 align:middle line:90% There's a T missing. 01:05:34.580 --> 01:05:35.600 align:middle line:90% It's thought to occur. 01:05:35.600 --> 01:05:37.340 align:middle line:84% Because there's some kind of competition 01:05:37.340 --> 01:05:39.680 align:middle line:84% here between the native interstitial point 01:05:39.680 --> 01:05:44.210 align:middle line:84% defects, the things that you're creating-- remember, 01:05:44.210 --> 01:05:45.710 align:middle line:84% you create more point defects as you 01:05:45.710 --> 01:05:48.453 align:middle line:84% raise the temperature-- and the boron atoms themselves 01:05:48.453 --> 01:05:49.370 align:middle line:90% for the lattice sites. 01:05:49.370 --> 01:05:51.770 align:middle line:84% Because again, we did not amorphize the crystal. 01:05:51.770 --> 01:05:54.180 align:middle line:90% We just created a lot of damage. 01:05:54.180 --> 01:05:55.940 align:middle line:84% So there's a sort of range where you just 01:05:55.940 --> 01:05:57.350 align:middle line:90% don't want to be annealing. 01:05:57.350 --> 01:06:00.620 align:middle line:84% Here at this dose of 2 times 10 to the 14th, 01:06:00.620 --> 01:06:02.995 align:middle line:84% you want to take the boron up higher. 01:06:02.995 --> 01:06:05.370 align:middle line:84% The problem with going to higher temperatures, of course, 01:06:05.370 --> 01:06:06.453 align:middle line:90% is you get more diffusion. 01:06:06.453 --> 01:06:10.540 align:middle line:90% 01:06:10.540 --> 01:06:13.320 align:middle line:84% So let me go on to slide 26 and just say a few words. 01:06:13.320 --> 01:06:16.072 align:middle line:84% We're going to spend the entire next lecture on this, 01:06:16.072 --> 01:06:18.030 align:middle line:84% on something called transit enhanced diffusion, 01:06:18.030 --> 01:06:20.860 align:middle line:84% and this is sort of exemplified here. 01:06:20.860 --> 01:06:26.067 align:middle line:84% Here is an implant that was done, say, of it 01:06:26.067 --> 01:06:27.150 align:middle line:90% could be boron or arsenic. 01:06:27.150 --> 01:06:28.775 align:middle line:84% It doesn't really matter at this point. 01:06:28.775 --> 01:06:29.850 align:middle line:90% But let's say it's boron. 01:06:29.850 --> 01:06:31.680 align:middle line:84% And we see two different anneals. 01:06:31.680 --> 01:06:37.080 align:middle line:84% The blue curve I did 1,000 degrees C for 10 seconds, 01:06:37.080 --> 01:06:42.930 align:middle line:84% and I got that diffusion profile after I implanted the boron. 01:06:42.930 --> 01:06:48.120 align:middle line:84% And now the red curve is 2 minutes at 800. 01:06:48.120 --> 01:06:51.000 align:middle line:84% And so, interestingly, you would think, well, 01:06:51.000 --> 01:06:52.680 align:middle line:90% I'm annealing it at 800. 01:06:52.680 --> 01:06:54.270 align:middle line:90% That's a much lower temperature. 01:06:54.270 --> 01:06:56.010 align:middle line:84% The boron diffusion coefficient is 01:06:56.010 --> 01:06:57.990 align:middle line:84% down by two orders of magnitude at 800. 01:06:57.990 --> 01:07:01.770 align:middle line:84% So even though I'm annealing it for a slightly longer time, 01:07:01.770 --> 01:07:05.520 align:middle line:84% it's certainly not 100 times longer or 200 times longer. 01:07:05.520 --> 01:07:08.310 align:middle line:84% So you would think that the 800 degrees C profile should 01:07:08.310 --> 01:07:09.840 align:middle line:90% be shallower than the 1,000. 01:07:09.840 --> 01:07:13.170 align:middle line:84% So TED, unfortunately, is this strange effect, 01:07:13.170 --> 01:07:15.120 align:middle line:84% and we'll talk about how this can happen, 01:07:15.120 --> 01:07:16.860 align:middle line:84% is that even at lower temperatures 01:07:16.860 --> 01:07:18.630 align:middle line:84% you can even get deeper junctions than you 01:07:18.630 --> 01:07:19.922 align:middle line:90% can get at higher temperatures. 01:07:19.922 --> 01:07:22.710 align:middle line:84% So this really annoyed people and was quite confusing 01:07:22.710 --> 01:07:26.410 align:middle line:84% and it needs to be explained by the implant damage 01:07:26.410 --> 01:07:28.770 align:middle line:84% and its effect on how the boron diffuses. 01:07:28.770 --> 01:07:31.110 align:middle line:84% And in fact, TED today is pretty much 01:07:31.110 --> 01:07:33.565 align:middle line:84% the dominant effect that determines junction depths 01:07:33.565 --> 01:07:34.440 align:middle line:90% and shallow profiles. 01:07:34.440 --> 01:07:37.727 align:middle line:84% It's not so much ordinary diffusion or concentration 01:07:37.727 --> 01:07:38.560 align:middle line:90% dependent diffusion. 01:07:38.560 --> 01:07:41.070 align:middle line:84% Well, for arsenic, maybe, but for boron, everything is. 01:07:41.070 --> 01:07:44.580 align:middle line:84% You cannot possibly model a shallow junction unless you 01:07:44.580 --> 01:07:47.130 align:middle line:90% know how to model TED. 01:07:47.130 --> 01:07:50.000 align:middle line:84% And if I just go on to the next slide, just to show you, 01:07:50.000 --> 01:07:53.580 align:middle line:84% if I had given you that problem and told you nothing about TED, 01:07:53.580 --> 01:07:55.980 align:middle line:84% and you would have looked up in your book, 01:07:55.980 --> 01:07:59.020 align:middle line:90% say, at 800 degrees-- 01:07:59.020 --> 01:08:00.580 align:middle line:84% which is somewhere right around here, 01:08:00.580 --> 01:08:02.430 align:middle line:84% here's the boron diffusion coefficient, 01:08:02.430 --> 01:08:03.420 align:middle line:90% right at this point-- 01:08:03.420 --> 01:08:05.760 align:middle line:84% and that at 1,000 degrees it's up here 01:08:05.760 --> 01:08:07.230 align:middle line:84% and the difference between the two 01:08:07.230 --> 01:08:09.840 align:middle line:84% is more than two orders of magnitude. 01:08:09.840 --> 01:08:12.820 align:middle line:84% So it's almost a factor of 1,000. 01:08:12.820 --> 01:08:15.820 align:middle line:84% So clearly, if you're diffusing at 800, 01:08:15.820 --> 01:08:18.939 align:middle line:84% it should be a lot less, a lot shallower 01:08:18.939 --> 01:08:23.335 align:middle line:84% junction, even if you're doing it for two minutes versus ten 01:08:23.335 --> 01:08:24.010 align:middle line:90% seconds. 01:08:24.010 --> 01:08:26.870 align:middle line:84% Two minutes is 120 seconds, so 10 into that. 01:08:26.870 --> 01:08:28.250 align:middle line:90% So I'm doing it 12 times longer. 01:08:28.250 --> 01:08:28.750 align:middle line:90% Fine. 01:08:28.750 --> 01:08:31.830 align:middle line:84% But the diffusion coefficient is 1,000 times, 01:08:31.830 --> 01:08:34.995 align:middle line:84% should be 1,000 times slower at 800, but it's not. 01:08:34.995 --> 01:08:36.370 align:middle line:84% In fact, it's 1,000 times faster. 01:08:36.370 --> 01:08:37.460 align:middle line:90% It's a lot faster. 01:08:37.460 --> 01:08:40.450 align:middle line:84% And that whole effect is called trans enhanced diffusion. 01:08:40.450 --> 01:08:43.420 align:middle line:84% It results from all the interstitials that were 01:08:43.420 --> 01:08:46.569 align:middle line:84% implanted, that plus-one interstitials giving rise 01:08:46.569 --> 01:08:48.220 align:middle line:90% to [? 311 ?]s and all that. 01:08:48.220 --> 01:08:49.720 align:middle line:84% And so the next lecture, we're going 01:08:49.720 --> 01:08:53.770 align:middle line:84% to spend trying to understand these profiles and their time 01:08:53.770 --> 01:08:54.490 align:middle line:90% dependence. 01:08:54.490 --> 01:08:56.899 align:middle line:90% 01:08:56.899 --> 01:08:59.270 align:middle line:90% So let me summarize on slide 28. 01:08:59.270 --> 01:09:01.800 align:middle line:84% Basically, so far, in this lecture, 01:09:01.800 --> 01:09:06.020 align:middle line:84% we said that we can separate the energy loss processes 01:09:06.020 --> 01:09:08.090 align:middle line:84% completely independent of each other. 01:09:08.090 --> 01:09:10.189 align:middle line:84% To first order, we have nuclear processes, 01:09:10.189 --> 01:09:12.319 align:middle line:84% which are these billiard ball collisions, 01:09:12.319 --> 01:09:14.840 align:middle line:84% and we have electronic drag force. 01:09:14.840 --> 01:09:16.620 align:middle line:84% The nuclear stopping dominates when 01:09:16.620 --> 01:09:20.300 align:middle line:84% you have a heavy ion over most of its path. 01:09:20.300 --> 01:09:22.130 align:middle line:84% For a light ion, nuclear stopping 01:09:22.130 --> 01:09:27.680 align:middle line:84% dominates only at the end of range, at very low energies. 01:09:27.680 --> 01:09:31.010 align:middle line:84% It's the nuclear stopping that damages the crystal 01:09:31.010 --> 01:09:33.149 align:middle line:84% by the creation of silicon recoil. 01:09:33.149 --> 01:09:35.930 align:middle line:84% So it knocks silicons off of their lattice sites and they 01:09:35.930 --> 01:09:38.450 align:middle line:90% knock other atoms off. 01:09:38.450 --> 01:09:40.939 align:middle line:84% And that creates what's called a collision cascade. 01:09:40.939 --> 01:09:45.170 align:middle line:84% The damage profile peaks right near rp. 01:09:45.170 --> 01:09:48.470 align:middle line:84% If you want to calculate that, you can just, maybe 80% of rp 01:09:48.470 --> 01:09:51.350 align:middle line:84% gives you a rough idea of the depth of damage. 01:09:51.350 --> 01:09:53.840 align:middle line:84% For heavy ions, the damage is more stable. 01:09:53.840 --> 01:09:56.030 align:middle line:84% That is, it doesn't tend to anneal out in the ion 01:09:56.030 --> 01:09:58.560 align:middle line:90% implanter at room temperature. 01:09:58.560 --> 01:10:00.810 align:middle line:84% And there's a tendency for a heavy ion 01:10:00.810 --> 01:10:03.240 align:middle line:84% to form an amorphous layer from the surface 01:10:03.240 --> 01:10:04.680 align:middle line:90% all the way down to some depth. 01:10:04.680 --> 01:10:07.470 align:middle line:84% That amorphous layer can be regrown relatively easily 01:10:07.470 --> 01:10:08.310 align:middle line:90% in silicon. 01:10:08.310 --> 01:10:10.920 align:middle line:84% Not true in other semiconductors, however. 01:10:10.920 --> 01:10:15.460 align:middle line:84% It results in relatively efficient dopant activation. 01:10:15.460 --> 01:10:17.680 align:middle line:84% For light ions like boron and phosphorus, 01:10:17.680 --> 01:10:19.930 align:middle line:84% below a certain dose, it is difficult to produce 01:10:19.930 --> 01:10:21.970 align:middle line:84% an amorphous layer at room temperature. 01:10:21.970 --> 01:10:24.070 align:middle line:84% And as a result, the activation of the dopants 01:10:24.070 --> 01:10:25.000 align:middle line:90% is a lot more complex. 01:10:25.000 --> 01:10:27.760 align:middle line:84% It's very dose dependent, and it can be temperature 01:10:27.760 --> 01:10:30.710 align:middle line:90% dependent in an odd fashion. 01:10:30.710 --> 01:10:33.770 align:middle line:84% There is this plus-one model for residual damage 01:10:33.770 --> 01:10:35.300 align:middle line:84% that says that there's roughly one 01:10:35.300 --> 01:10:37.790 align:middle line:84% excess interstitial for every primary ion 01:10:37.790 --> 01:10:38.960 align:middle line:90% that I ion implanted. 01:10:38.960 --> 01:10:42.860 align:middle line:84% So it's relatively easy order of magnitude estimate. 01:10:42.860 --> 01:10:44.635 align:middle line:84% And this is after the initial vacancy 01:10:44.635 --> 01:10:46.010 align:middle line:84% and interstitial recombination is 01:10:46.010 --> 01:10:49.670 align:middle line:84% taking place, which only takes a few fractions of a second. 01:10:49.670 --> 01:10:51.770 align:middle line:84% These excess interstitials, however, they 01:10:51.770 --> 01:10:54.020 align:middle line:84% cluster into little [? 311 ?] defects. 01:10:54.020 --> 01:10:57.170 align:middle line:84% Those defects dissolve at a relatively slow rate 01:10:57.170 --> 01:10:59.360 align:middle line:84% on the order of ten seconds to minutes, 01:10:59.360 --> 01:11:01.850 align:middle line:84% and it's those little, that [? 311 ?] 01:11:01.850 --> 01:11:05.300 align:middle line:84% evaporation or dissolution, that gives rise 01:11:05.300 --> 01:11:07.370 align:middle line:90% to the time dependence of TED. 01:11:07.370 --> 01:11:11.100 align:middle line:84% So by understanding [? 311 ?] defects to a certain extent, 01:11:11.100 --> 01:11:14.120 align:middle line:84% we can understand the time dependence of TED and, in fact, 01:11:14.120 --> 01:11:15.660 align:middle line:84% by understanding [? 311 ?] defects, 01:11:15.660 --> 01:11:17.410 align:middle line:84% we'll be able to come up with a model that 01:11:17.410 --> 01:11:22.080 align:middle line:84% could predict this kind of strange looking behavior. 01:11:22.080 --> 01:11:22.580 align:middle line:90% OK. 01:11:22.580 --> 01:11:26.120 align:middle line:84% So that's what I wanted to go through today. 01:11:26.120 --> 01:11:27.230 align:middle line:90% There were three handouts. 01:11:27.230 --> 01:11:28.313 align:middle line:90% Make sure you've got them. 01:11:28.313 --> 01:11:30.480 align:middle line:84% Today's lecture notes, homework number four 01:11:30.480 --> 01:11:32.552 align:middle line:84% which is due on November 2, and the solutions 01:11:32.552 --> 01:11:33.510 align:middle line:90% to homework number two. 01:11:33.510 --> 01:11:35.468 align:middle line:84% The solutions have been on the web for a while. 01:11:35.468 --> 01:11:38.370 align:middle line:84% I just forgot to hand out the paper copy. 01:11:38.370 --> 01:11:39.060 align:middle line:90% OK. 01:11:39.060 --> 01:11:41.610 align:middle line:90% So we'll see you next Tuesday. 01:11:41.610 --> 01:11:44.630 align:middle line:84% Hopefully we get to watch the World Series. 01:11:44.630 --> 01:11:49.000 align:middle line:90%