1 00:00:17,684 --> 00:00:21,654 We are talking about semiconductors today. 2 00:00:21,654 --> 00:00:22,155 Yeah. 3 00:00:25,759 --> 00:00:28,294 I finished our exam 2 concept 4 00:00:28,294 --> 00:00:30,864 math that I thought maybe you guys would find useful. 5 00:00:31,164 --> 00:00:34,634 This is much like the last time, when I gave you 6 00:00:34,634 --> 00:00:35,602 guys the concept map. 7 00:00:35,602 --> 00:00:37,971 I'm just giving it a little earlier this time. 8 00:00:37,971 --> 00:00:41,307 And here, you can see all the connections 9 00:00:41,307 --> 00:00:46,913 between the lectures, the recitations, the problem 10 00:00:46,913 --> 00:00:53,153 sets, the quizzes over here, the goody bags, and the exam 11 00:00:53,153 --> 00:00:55,455 topics. 12 00:00:55,455 --> 00:00:58,892 Speaking of the quizzes, tomorrow, there's a quiz. 13 00:00:58,892 --> 00:01:01,094 And so you can look up here and say, OK, well, what's 14 00:01:01,094 --> 00:01:03,430 going to be on that quiz? 15 00:01:03,430 --> 00:01:05,465 Might cover some molecular orbital theory. 16 00:01:05,465 --> 00:01:09,569 Might cover the band gap stuff that we did on Monday 17 00:01:09,569 --> 00:01:12,405 and that you covered in recitation yesterday. 18 00:01:12,405 --> 00:01:15,942 Oh, and intermolecular forces we also did. 19 00:01:15,942 --> 00:01:19,079 And you're asked to bring to the quiz 20 00:01:19,079 --> 00:01:24,417 the voltmeter and these large LEDs. 21 00:01:24,417 --> 00:01:27,353 Now, I'll talk about that, a little bit more about this, 22 00:01:27,353 --> 00:01:29,622 in a few minutes. 23 00:01:29,622 --> 00:01:30,890 So remember to bring that. 24 00:01:30,890 --> 00:01:34,761 Laura will also send a reminder email about that. 25 00:01:34,761 --> 00:01:37,263 OK, you have voltmeters. 26 00:01:37,263 --> 00:01:40,533 You and voltmeters. 27 00:01:40,533 --> 00:01:42,168 How many of you, this is the first time 28 00:01:42,168 --> 00:01:44,604 you're using a voltmeter? 29 00:01:44,604 --> 00:01:47,440 How many of you haven't used one but you've never seen one-- 30 00:01:47,440 --> 00:01:49,075 you've used it before, but you've never 31 00:01:49,075 --> 00:01:53,079 had one this accurate as the 3091, right? 32 00:01:53,079 --> 00:01:55,081 Yeah. 33 00:01:55,081 --> 00:01:57,015 You never know when you need a voltmeter. 34 00:01:57,015 --> 00:02:01,788 You should always carry it with you with the periodic table. 35 00:02:01,788 --> 00:02:06,759 Now, on Monday, this is what we had. 36 00:02:06,759 --> 00:02:08,862 This was a conduction band. 37 00:02:08,862 --> 00:02:10,663 This was a valance band. 38 00:02:10,663 --> 00:02:16,236 And then we had a conduction band and valence 39 00:02:16,236 --> 00:02:20,640 band that were a little bit closer together. 40 00:02:20,640 --> 00:02:26,412 And then, we had this case, where maybe it's 41 00:02:26,412 --> 00:02:29,349 filled up somewhere in the middle of the band. 42 00:02:29,349 --> 00:02:32,918 And remember, the valance band is filled with electrons, 43 00:02:32,918 --> 00:02:40,560 and the conduction band is not, right, in the simplest picture. 44 00:02:40,560 --> 00:02:45,965 And this difference in energy between this VBN-- 45 00:02:45,965 --> 00:02:49,602 that's the VBN, the maximum level of the valence band-- 46 00:02:49,602 --> 00:02:51,304 and the CBN-- 47 00:02:51,304 --> 00:02:53,273 the minimum level of the conduction band-- 48 00:02:53,273 --> 00:02:59,245 that energy difference is the gap of the material. 49 00:02:59,245 --> 00:03:04,117 Here, you can see energy gap equals zero. 50 00:03:04,117 --> 00:03:06,286 Well, in this case, it's a metal. 51 00:03:06,286 --> 00:03:08,353 Or if you want, it's a conductor. 52 00:03:08,353 --> 00:03:12,759 And we'll talk about why it's a conductor more on Friday, 53 00:03:12,759 --> 00:03:14,827 but a little bit today, why metals are conductors. 54 00:03:14,827 --> 00:03:17,797 Today, I really want to focus on this case. 55 00:03:17,797 --> 00:03:20,533 All right, so that's a metal when there 56 00:03:20,533 --> 00:03:24,270 is no gap in the material. 57 00:03:24,270 --> 00:03:28,007 If the gap is large, then that is an insulator. 58 00:03:32,445 --> 00:03:33,579 What do I mean by large? 59 00:03:33,579 --> 00:03:39,085 Well, what I mean is it's not in the range of this special case, 60 00:03:39,085 --> 00:03:42,956 which would be, say, zero less than the gap 61 00:03:42,956 --> 00:03:47,360 less than around 3.5 electron volts. 62 00:03:47,360 --> 00:03:51,064 This is the case that I want to talk about today. 63 00:03:51,064 --> 00:03:53,900 I want to spend today talking about semiconductors. 64 00:03:53,900 --> 00:03:57,070 Those are called semiconductors. 65 00:03:57,070 --> 00:03:59,038 Let's write that here. 66 00:03:59,038 --> 00:04:00,106 Semiconductors. 67 00:04:07,280 --> 00:04:11,050 Sometimes you'll see them called metaloids. 68 00:04:11,050 --> 00:04:15,521 Sometimes you'll see them called insulators with small gaps. 69 00:04:15,521 --> 00:04:16,589 They're all kind of right. 70 00:04:19,926 --> 00:04:22,996 Metaloid, thank you. 71 00:04:22,996 --> 00:04:28,067 Now, the reason why we classify these and why this range of gap 72 00:04:28,067 --> 00:04:31,638 is so important is what I want to convey to you today. 73 00:04:31,638 --> 00:04:33,573 These are really special materials, 74 00:04:33,573 --> 00:04:36,175 these semiconductors. 75 00:04:36,175 --> 00:04:42,382 Now, before I do that, I want to just clarify one thing. 76 00:04:42,382 --> 00:04:47,453 And I'm going to use diamond and graphite as an example. 77 00:04:47,453 --> 00:04:51,324 On Monday, what we did is we talked 78 00:04:51,324 --> 00:04:57,163 about the concept of bands with a very simple 1D model, right? 79 00:04:57,163 --> 00:05:04,570 This was a 1D model of s orbitals, 1s orbitals. 80 00:05:04,570 --> 00:05:09,175 I said, well, if I have a mole of 1s orbitals, 81 00:05:09,175 --> 00:05:13,780 then that goes into a band. 82 00:05:13,780 --> 00:05:17,317 And I called it a 1s band. 83 00:05:17,317 --> 00:05:18,918 I always say, well, if you fill it 84 00:05:18,918 --> 00:05:21,888 in different ways, that is what determines the properties. 85 00:05:21,888 --> 00:05:24,190 But I want to be clear-- and I stressed this on Monday, 86 00:05:24,190 --> 00:05:27,694 and I want to stress it again. 87 00:05:27,694 --> 00:05:31,230 Whether this forms this and then the next set-- 88 00:05:31,230 --> 00:05:33,232 you know, whether you get a 1s that 89 00:05:33,232 --> 00:05:35,335 forms a band like this and then a 2s 90 00:05:35,335 --> 00:05:38,438 that forms a band like this and then another one, 91 00:05:38,438 --> 00:05:40,707 maybe 2p, like this. 92 00:05:40,707 --> 00:05:43,609 Or whether there's breaks in them, 93 00:05:43,609 --> 00:05:45,778 or maybe these kind of overlap-- 94 00:05:45,778 --> 00:05:50,316 so you get overlap, and you get sort of something like that. 95 00:05:50,316 --> 00:05:57,223 All that depends on more than just those atomic orbitals. 96 00:05:57,223 --> 00:05:58,191 It depends on more. 97 00:05:58,191 --> 00:06:00,259 It depends on how these things are bonded. 98 00:06:00,259 --> 00:06:02,628 This is such a great example. 99 00:06:02,628 --> 00:06:04,664 I've got the same element here. 100 00:06:04,664 --> 00:06:07,133 Its carbon. 101 00:06:07,133 --> 00:06:08,935 There's nothing else in this system. 102 00:06:08,935 --> 00:06:10,036 Carbon, pure carbon. 103 00:06:10,036 --> 00:06:11,437 Everywhere is carbon. 104 00:06:11,437 --> 00:06:14,674 But on the one hand, I've arranged it in a certain way. 105 00:06:14,674 --> 00:06:17,343 And on the other hand, I've arranged it in another way, 106 00:06:17,343 --> 00:06:21,814 and their properties couldn't be more different. 107 00:06:21,814 --> 00:06:28,154 So just to take this a little further, 108 00:06:28,154 --> 00:06:33,893 if I think about diamond on the left, diamond is an insulator. 109 00:06:33,893 --> 00:06:37,463 Diamond has a gap of 5 and 1/2 electronvolts. 110 00:06:37,463 --> 00:06:38,931 5 and 1/2 electronvolts. 111 00:06:38,931 --> 00:06:41,300 It's an insulator. 112 00:06:41,300 --> 00:06:43,569 But OK, that makes me think of methane. 113 00:06:43,569 --> 00:06:46,139 Remember, methane, you had these SP3 states-- 114 00:06:46,139 --> 00:06:51,944 SP3, SP3, SP3. 115 00:06:51,944 --> 00:06:58,151 And the reason it formed SP3 is because all these H1s states 116 00:06:58,151 --> 00:06:59,652 came along-- 117 00:06:59,652 --> 00:07:07,293 H, H, H, H. These are 1s's, 1s. 118 00:07:07,293 --> 00:07:10,897 And so carbon came along, and it said, well, if I arrange-- 119 00:07:10,897 --> 00:07:17,336 if I got four of you here like this and I arrange myself-- 120 00:07:17,336 --> 00:07:19,539 if I arrange my orbitals in such a way 121 00:07:19,539 --> 00:07:23,576 that then I can arrange so that they're minimizing repulsions, 122 00:07:23,576 --> 00:07:24,710 that gives me methane. 123 00:07:24,710 --> 00:07:26,446 That gives me the ground state of methane. 124 00:07:26,446 --> 00:07:28,981 But the only way to do that is to have four equivalent 125 00:07:28,981 --> 00:07:29,682 orbitals. 126 00:07:29,682 --> 00:07:31,951 Those are hybrid orbitals. 127 00:07:31,951 --> 00:07:34,887 We talked about this when we talked about hybridization. 128 00:07:34,887 --> 00:07:39,058 The idea being that if I took one of these and one of those-- 129 00:07:39,058 --> 00:07:41,360 so now you can imagine how it's going to look. 130 00:07:41,360 --> 00:07:43,296 You know all this now, right? 131 00:07:43,296 --> 00:07:46,566 There's a 1s orbital of hydrogen. 132 00:07:46,566 --> 00:07:52,071 You know that those will form a sigma and a sigma star 133 00:07:52,071 --> 00:07:54,407 and occupy that bonding orbital. 134 00:07:54,407 --> 00:07:56,509 That's the idea of methane. 135 00:07:56,509 --> 00:07:58,945 That's the idea of molecular orbital theory 136 00:07:58,945 --> 00:08:01,747 with some hybridization. 137 00:08:01,747 --> 00:08:04,817 And it's going to form those bonds along each direction. 138 00:08:04,817 --> 00:08:07,386 But now I'm talking about something different. 139 00:08:07,386 --> 00:08:10,389 I'm not talking about such a simple case. 140 00:08:10,389 --> 00:08:16,762 I'm talking about one mole of SP3. 141 00:08:16,762 --> 00:08:18,498 That's what diamond is. 142 00:08:18,498 --> 00:08:21,601 Look, the carbon atoms have done the same thing. 143 00:08:21,601 --> 00:08:24,103 They said, hey, wait a second, OK, it's not four hydrogens. 144 00:08:24,103 --> 00:08:29,075 It's like 10 to the 23 carbons all in one small space. 145 00:08:29,075 --> 00:08:33,712 How can we organize to lower our energy? 146 00:08:33,712 --> 00:08:34,780 And so they form-- 147 00:08:34,780 --> 00:08:38,317 well, we know this, that it's going to form a band. 148 00:08:38,317 --> 00:08:43,389 But it doesn't just form a band and then half fill it. 149 00:08:43,389 --> 00:08:45,758 That's not what diamond does. 150 00:08:45,758 --> 00:08:50,296 No, actually, diamond breaks this apart so 151 00:08:50,296 --> 00:08:54,500 that you have a huge gap. 152 00:08:54,500 --> 00:08:59,338 And those are filled, and then those are not. 153 00:08:59,338 --> 00:09:05,478 The SP3 band in diamond breaks apart 154 00:09:05,478 --> 00:09:08,981 into a valence and a conduction band. 155 00:09:08,981 --> 00:09:10,416 The valance band is full. 156 00:09:10,416 --> 00:09:12,418 The conduction band is empty. 157 00:09:12,418 --> 00:09:12,919 Why? 158 00:09:12,919 --> 00:09:15,888 Well, you don't need to learn the specifics of how 159 00:09:15,888 --> 00:09:17,023 to get from there to there. 160 00:09:17,023 --> 00:09:19,992 But I wanted to show you how complicated this is. 161 00:09:19,992 --> 00:09:24,964 I will ask you whether the SP3 band splits or not. 162 00:09:24,964 --> 00:09:27,133 I just wanted to show you how dependent this is. 163 00:09:27,133 --> 00:09:30,703 Because now, look, you can understand this now, right? 164 00:09:30,703 --> 00:09:32,672 So I've got four electrons per atom going here. 165 00:09:32,672 --> 00:09:35,474 There's a huge gap, and then nothing in there. 166 00:09:35,474 --> 00:09:36,576 That's diamond. 167 00:09:36,576 --> 00:09:40,680 5.5 eV gap. 168 00:09:40,680 --> 00:09:44,116 One mole of SP3 in diamond. 169 00:09:44,116 --> 00:09:46,218 Now, it depends on the structure. 170 00:09:46,218 --> 00:09:49,188 If I had just put them together in some amorphous soup 171 00:09:49,188 --> 00:09:50,289 with no-- 172 00:09:50,289 --> 00:09:51,524 oh, amorphous. 173 00:09:51,524 --> 00:09:53,793 That's a word that's coming later. 174 00:09:53,793 --> 00:09:56,562 But if I just put them together with no order, 175 00:09:56,562 --> 00:09:59,865 I wouldn't get this, this splitting. 176 00:09:59,865 --> 00:10:03,102 You take graphene, which is one of those sheets, 177 00:10:03,102 --> 00:10:05,271 and make stacks and you've got graphite. 178 00:10:05,271 --> 00:10:07,840 It's another form of pure carbon. 179 00:10:07,840 --> 00:10:12,278 In that case, you've got your SP2 bonds to form in the plane, 180 00:10:12,278 --> 00:10:14,780 and those also split and they fill. 181 00:10:14,780 --> 00:10:21,287 But now you've got your pi bonds, and those don't split. 182 00:10:21,287 --> 00:10:28,694 So in graphite, what you get is you've got your SP2's. 183 00:10:28,694 --> 00:10:33,032 You've got a mole of those, and you've got your P electron. 184 00:10:33,032 --> 00:10:34,533 Remember those? 185 00:10:34,533 --> 00:10:38,571 Now you do a mole of that, and you've got the same thing. 186 00:10:38,571 --> 00:10:40,873 But see now, you've got-- 187 00:10:40,873 --> 00:10:42,274 these are the SP2 bands. 188 00:10:44,944 --> 00:10:47,179 It also split. 189 00:10:47,179 --> 00:10:49,348 Remember, I've got my electrons here, 190 00:10:49,348 --> 00:10:51,450 my SP2 electrons and those there. 191 00:10:51,450 --> 00:10:57,023 But now, I've got the pi bands that didn't split. 192 00:10:57,023 --> 00:10:59,859 Graphite is a metal. 193 00:10:59,859 --> 00:11:03,462 You can understand it by looking at the bands 194 00:11:03,462 --> 00:11:05,364 of these materials. 195 00:11:05,364 --> 00:11:07,299 Now, again, let me emphasize, I am not 196 00:11:07,299 --> 00:11:09,835 going to ask you to know when something 197 00:11:09,835 --> 00:11:13,205 splits like this or not. 198 00:11:13,205 --> 00:11:17,543 Why didn't the pi band split into two like these did? 199 00:11:17,543 --> 00:11:21,213 When does an S and a P become a single band versus an S 200 00:11:21,213 --> 00:11:22,715 band separated by a P band? 201 00:11:22,715 --> 00:11:24,283 I'm not going to ask you to know that, 202 00:11:24,283 --> 00:11:25,951 but I wanted you to see it. 203 00:11:25,951 --> 00:11:27,953 It doesn't just depend on the initial states. 204 00:11:27,953 --> 00:11:31,557 It depends on the structure of those atoms. 205 00:11:31,557 --> 00:11:35,728 It depends on how those atoms are bonded together. 206 00:11:35,728 --> 00:11:42,134 Now, what about this semi-conductor? 207 00:11:42,134 --> 00:11:44,003 What about this semiconductor? 208 00:11:44,003 --> 00:11:48,641 Well, if we take a semiconductor and we look at it-- 209 00:11:48,641 --> 00:11:49,775 I told you this on Monday. 210 00:11:49,775 --> 00:11:54,714 There are two things that you can do in your goody bag, 211 00:11:54,714 --> 00:11:55,614 especially. 212 00:11:55,614 --> 00:12:01,754 One is you can take an electron, and you can shine a light 213 00:12:01,754 --> 00:12:06,759 on it, and it's going to excite this electron up, just 214 00:12:06,759 --> 00:12:08,561 like in the Bohr atom, right? 215 00:12:08,561 --> 00:12:12,732 You can absorb photons if the photon energy is the energy 216 00:12:12,732 --> 00:12:14,800 between one state and another. 217 00:12:14,800 --> 00:12:16,335 We did a lot of this earlier. 218 00:12:16,335 --> 00:12:20,740 But see, in a semiconductor, remember, 219 00:12:20,740 --> 00:12:23,075 I've got an almost infinite number of states here. 220 00:12:25,711 --> 00:12:28,013 And so what I need is for that photon-- 221 00:12:28,013 --> 00:12:29,849 there's not an exact value here. 222 00:12:29,849 --> 00:12:31,550 There's a continuum. 223 00:12:31,550 --> 00:12:34,153 But here, it's forbidden, just like in the Bohr atom. 224 00:12:34,153 --> 00:12:35,187 There's no states. 225 00:12:35,187 --> 00:12:37,022 There's no electron. 226 00:12:37,022 --> 00:12:45,264 So here, the energy of the photon absorbed-- 227 00:12:45,264 --> 00:12:48,100 let's write this out-- 228 00:12:48,100 --> 00:12:52,171 has to be greater than the energy of the gap. 229 00:12:52,171 --> 00:12:56,108 This is the energy of the gap. 230 00:12:56,108 --> 00:12:58,410 This is the energy of the gap. 231 00:12:58,410 --> 00:13:02,214 Now, by the same token, I can take the same semiconductor 232 00:13:02,214 --> 00:13:04,383 and run it the other way. 233 00:13:04,383 --> 00:13:08,988 I can put a current on it and feed electrons, 234 00:13:08,988 --> 00:13:12,057 electrons from current. 235 00:13:14,794 --> 00:13:20,599 So I can attach it to a battery, and there you go. 236 00:13:20,599 --> 00:13:23,869 This is a semiconductor where I'm literally-- 237 00:13:23,869 --> 00:13:27,840 all I'm doing is I'm feeding electrons into its conduction 238 00:13:27,840 --> 00:13:29,275 band. 239 00:13:29,275 --> 00:13:32,645 But now, when those electrons fall down 240 00:13:32,645 --> 00:13:38,184 into the valence band, they emit a photon. 241 00:13:38,184 --> 00:13:39,885 Photon emitted. 242 00:13:42,755 --> 00:13:49,929 And just so I have room, with energy of the photon emitted 243 00:13:49,929 --> 00:13:53,465 is going to be exactly equal to the energy of the gap. 244 00:13:53,465 --> 00:13:56,101 You can see that because these electrons, 245 00:13:56,101 --> 00:13:58,370 I might inject them into the conduction band anywhere, 246 00:13:58,370 --> 00:14:01,040 but they're going to wind up very, very, 247 00:14:01,040 --> 00:14:06,278 very quickly going to this minimum conduction band state. 248 00:14:06,278 --> 00:14:08,380 And that gets me to another important point, which 249 00:14:08,380 --> 00:14:12,251 is on the absorption side, I can overshoot this. 250 00:14:12,251 --> 00:14:14,887 Like I said, I can absorb higher than the gap. 251 00:14:14,887 --> 00:14:19,225 I can't absorb lower, but I can absorb higher. 252 00:14:19,225 --> 00:14:24,196 And if I do, if I absorb higher than the gap-- 253 00:14:24,196 --> 00:14:28,000 so let's say this is my state. 254 00:14:28,000 --> 00:14:31,904 So if my photon comes in and it kicks in electron up really 255 00:14:31,904 --> 00:14:36,508 high, it's a high-energy photon, then that electron very quickly 256 00:14:36,508 --> 00:14:38,277 will go back down. 257 00:14:38,277 --> 00:14:42,114 And that's called thermalization. 258 00:14:42,114 --> 00:14:49,688 So what happens is that electron loses energy 259 00:14:49,688 --> 00:14:55,561 to heat to get to the CBM. 260 00:14:58,864 --> 00:15:01,133 We'll come back to this later. 261 00:15:01,133 --> 00:15:02,101 That's thermalization. 262 00:15:02,101 --> 00:15:06,472 So the electron can be kicked up by light to any level, 263 00:15:06,472 --> 00:15:08,807 but it's going to very, very quickly go to the CBM. 264 00:15:08,807 --> 00:15:10,409 That's why when I inject it-- that's 265 00:15:10,409 --> 00:15:12,444 why these are the same color. 266 00:15:12,444 --> 00:15:17,082 These are high-quality LEDs, clearly. 267 00:15:17,082 --> 00:15:17,983 Well, they work. 268 00:15:17,983 --> 00:15:20,052 That's a good thing. 269 00:15:20,052 --> 00:15:22,121 So the batteries might be slightly different, 270 00:15:22,121 --> 00:15:24,223 and the currents might be different, a little bit. 271 00:15:24,223 --> 00:15:26,458 I might be injecting electrons at different parts 272 00:15:26,458 --> 00:15:28,694 of these conduction bands, but this is always green, 273 00:15:28,694 --> 00:15:29,795 and this is always red. 274 00:15:29,795 --> 00:15:33,565 And that's because those electrons very quickly get down 275 00:15:33,565 --> 00:15:34,767 to the CBM and the VBM. 276 00:15:34,767 --> 00:15:37,870 And the CBM and the VBM are determined by the semiconductor 277 00:15:37,870 --> 00:15:38,370 inside. 278 00:15:43,575 --> 00:15:45,477 Well, you've also got-- 279 00:15:45,477 --> 00:15:49,081 so this is a photon emitter right here. 280 00:15:49,081 --> 00:15:52,985 I've made a light emitter, right? 281 00:15:52,985 --> 00:15:54,653 But I've also got a detector, which 282 00:15:54,653 --> 00:15:56,121 here's what I said on Monday. 283 00:15:56,121 --> 00:16:01,694 So now, I take an LED, and I hold it-- 284 00:16:01,694 --> 00:16:02,728 gesundheit. 285 00:16:02,728 --> 00:16:04,463 And this is what's inside of the emitter. 286 00:16:04,463 --> 00:16:05,397 It's the same thing. 287 00:16:05,397 --> 00:16:06,398 It's a semiconductor. 288 00:16:06,398 --> 00:16:09,969 But these two semiconductors have different band gaps. 289 00:16:09,969 --> 00:16:12,004 That's why the light is different. 290 00:16:12,004 --> 00:16:13,973 They have different band gaps. 291 00:16:13,973 --> 00:16:16,241 Now I've got one with some band gap, 292 00:16:16,241 --> 00:16:21,347 and I hook it up to my voltmeter, and I just look. 293 00:16:21,347 --> 00:16:24,350 Is there a current or not? 294 00:16:24,350 --> 00:16:27,453 If this thing conducts through it, 295 00:16:27,453 --> 00:16:29,888 it means that electrons have been 296 00:16:29,888 --> 00:16:32,091 promoted from here to here. 297 00:16:32,091 --> 00:16:35,227 And that's something we're going to talk about today. 298 00:16:35,227 --> 00:16:37,796 Electrons cannot move around easily 299 00:16:37,796 --> 00:16:39,131 if they're in the valence band. 300 00:16:39,131 --> 00:16:42,368 But once they're in that conduction band, they're free. 301 00:16:42,368 --> 00:16:43,702 How do I get them there? 302 00:16:43,702 --> 00:16:45,437 Well, you've got power. 303 00:16:45,437 --> 00:16:46,905 Shine red light on it. 304 00:16:46,905 --> 00:16:47,773 Does it conduct? 305 00:16:47,773 --> 00:16:49,975 Check the voltmeter. 306 00:16:49,975 --> 00:16:52,111 I'm literally holding two semiconductors 307 00:16:52,111 --> 00:16:56,615 and doing these two processes right here in each hand. 308 00:16:56,615 --> 00:16:58,717 It's a power that I have. 309 00:16:58,717 --> 00:17:01,587 I have semiconductor making light, semiconductor 310 00:17:01,587 --> 00:17:04,156 absorbing light, or maybe not. 311 00:17:04,156 --> 00:17:06,692 If I shine right on this and I get no current, 312 00:17:06,692 --> 00:17:11,563 well, it means that the energy of the photon from a red light 313 00:17:11,563 --> 00:17:12,998 source is too low. 314 00:17:12,998 --> 00:17:16,868 Maybe it's able to excite it up to here but not up to here, 315 00:17:16,868 --> 00:17:19,371 given whatever the gap in here is. 316 00:17:19,371 --> 00:17:20,339 You see that? 317 00:17:20,339 --> 00:17:23,308 So the semiconductor has this powerful-- maybe 318 00:17:23,308 --> 00:17:26,712 I take a different semiconductor and red excites it. 319 00:17:26,712 --> 00:17:30,783 Or maybe it doesn't, so I go to a higher energy photon. 320 00:17:30,783 --> 00:17:33,085 With this goody bag, you're touching and feeling 321 00:17:33,085 --> 00:17:37,289 semiconductor physics and chemistry. 322 00:17:37,289 --> 00:17:42,694 Because band gaps in materials are rare. 323 00:17:42,694 --> 00:17:45,964 You see, if you look at the periodic table 324 00:17:45,964 --> 00:17:52,137 and you classify it by metals, metals and nonmetals-- 325 00:17:52,137 --> 00:17:54,940 so insulators, conductors, and then 326 00:17:54,940 --> 00:17:58,310 these weird things in between-- 327 00:17:58,310 --> 00:18:01,213 there aren't that many of them. 328 00:18:01,213 --> 00:18:03,048 There aren't that many of them. 329 00:18:03,048 --> 00:18:07,252 But as you can see, these are really, really important 330 00:18:07,252 --> 00:18:09,688 technological materials. 331 00:18:09,688 --> 00:18:10,355 Why? 332 00:18:10,355 --> 00:18:13,225 Because this is visible light. 333 00:18:13,225 --> 00:18:16,929 This semiconductor range here is in the range of light 334 00:18:16,929 --> 00:18:18,697 we care about-- 335 00:18:18,697 --> 00:18:20,265 visible, UV. 336 00:18:20,265 --> 00:18:22,534 So I've got an electronic material where 337 00:18:22,534 --> 00:18:28,974 the electrons in it can interact with currents, small currents 338 00:18:28,974 --> 00:18:32,778 even, and wavelengths of light that are things we can see. 339 00:18:32,778 --> 00:18:35,681 You can imagine how important this could be, for example, 340 00:18:35,681 --> 00:18:37,382 for making LEDs. 341 00:18:37,382 --> 00:18:42,154 But I need a lot more flexibility in my material set, 342 00:18:42,154 --> 00:18:43,655 and that's where chemistry comes in. 343 00:18:43,655 --> 00:18:46,325 So this is, one, why this matters for today. 344 00:18:46,325 --> 00:18:48,927 So, look, I mentioned that getting red 345 00:18:48,927 --> 00:18:51,864 was hard back in the day for color TV, 346 00:18:51,864 --> 00:18:54,533 because the red phosphorus were difficult to make. 347 00:18:54,533 --> 00:18:56,969 For LEDs, it was blue. 348 00:18:56,969 --> 00:18:59,304 In fact, there was a lot of work around gallium nitride. 349 00:18:59,304 --> 00:19:01,373 Here's gallium nitride in one structure. 350 00:19:01,373 --> 00:19:02,608 Notice this. 351 00:19:02,608 --> 00:19:03,876 There's gallium nitride. 352 00:19:03,876 --> 00:19:05,177 It's not on here. 353 00:19:05,177 --> 00:19:05,844 Darn it. 354 00:19:05,844 --> 00:19:09,081 Gallium nitride in other structures have different gaps. 355 00:19:09,081 --> 00:19:09,748 Oh, there it is. 356 00:19:09,748 --> 00:19:11,250 There's one. 357 00:19:11,250 --> 00:19:13,452 But the point was they wanted blue. 358 00:19:13,452 --> 00:19:14,853 They wanted blue, and they needed 359 00:19:14,853 --> 00:19:18,624 to make a material that was both cheap to make and lasted, 360 00:19:18,624 --> 00:19:21,793 so it didn't degrade, and gave you a blue light. 361 00:19:21,793 --> 00:19:22,861 And that was really hard. 362 00:19:22,861 --> 00:19:26,498 And that's what the Nobel Prize was given for in 2014. 363 00:19:26,498 --> 00:19:29,668 Because without blue, you can't make white light. 364 00:19:29,668 --> 00:19:31,570 So there's all sorts of technologies 365 00:19:31,570 --> 00:19:34,940 you simply can't go into with LEDs until you get blue. 366 00:19:34,940 --> 00:19:35,741 How did it happen? 367 00:19:35,741 --> 00:19:38,810 It happened because of chemistry because people figured out 368 00:19:38,810 --> 00:19:41,947 how to change the how to take one element another element 369 00:19:41,947 --> 00:19:43,916 and then maybe alloy them together. 370 00:19:43,916 --> 00:19:46,318 Maybe you take gallium nitride and you alloy a little bit 371 00:19:46,318 --> 00:19:49,054 of aluminum in here. 372 00:19:49,054 --> 00:19:50,756 That means mixing it in. 373 00:19:50,756 --> 00:19:54,660 Now, all of a sudden, you've got a different band gap. 374 00:19:54,660 --> 00:19:58,630 Band gap engineering is really the centerpiece 375 00:19:58,630 --> 00:20:01,800 of the semiconductor revolution. 376 00:20:01,800 --> 00:20:04,937 Now, the connectivity. 377 00:20:04,937 --> 00:20:06,838 We've been talking about connectivity. 378 00:20:06,838 --> 00:20:09,474 And we'll talk about metals on Friday. 379 00:20:09,474 --> 00:20:10,108 Here we are. 380 00:20:10,108 --> 00:20:12,211 Insulator's really low. 381 00:20:12,211 --> 00:20:15,447 Least conducting, 10 to the minus 25. 382 00:20:15,447 --> 00:20:18,016 Hook your voltmeter up to Teflon. 383 00:20:18,016 --> 00:20:19,017 10 to the minus-- 384 00:20:19,017 --> 00:20:21,019 wood. 385 00:20:21,019 --> 00:20:22,788 Low-conducting materials. 386 00:20:22,788 --> 00:20:24,790 But we're interested in these, and these 387 00:20:24,790 --> 00:20:25,757 are kind of in-between. 388 00:20:25,757 --> 00:20:27,759 They're not very good conductors. 389 00:20:27,759 --> 00:20:31,263 That's why they're called semiconductors. 390 00:20:31,263 --> 00:20:34,933 But the fact of the matter goes back to what I've been saying. 391 00:20:34,933 --> 00:20:37,436 And this is the next point I want to talk about, 392 00:20:37,436 --> 00:20:43,976 which is I cannot have-- 393 00:20:43,976 --> 00:20:49,748 so in a semiconductor, there's no electrons. 394 00:20:49,748 --> 00:20:53,952 If there's no electrons in the conduction band, 395 00:20:53,952 --> 00:21:00,525 then there's no electron conduction. 396 00:21:00,525 --> 00:21:02,561 Now, I've said this before. 397 00:21:02,561 --> 00:21:03,462 I said this on Monday. 398 00:21:03,462 --> 00:21:04,263 I said it already. 399 00:21:04,263 --> 00:21:05,430 Why not? 400 00:21:05,430 --> 00:21:08,567 On Monday, I said, well, these electrons are stuck. 401 00:21:08,567 --> 00:21:10,068 What does that mean, they're stuck? 402 00:21:10,068 --> 00:21:12,571 Stuck in the bonds, stuck in the anti-bonds. 403 00:21:12,571 --> 00:21:15,207 They're stuck in states. 404 00:21:15,207 --> 00:21:20,912 The point is, here, that this valance band is filled. 405 00:21:20,912 --> 00:21:25,050 Now, if I want an electron to move through a material, 406 00:21:25,050 --> 00:21:27,986 which is what conductivity is, after all-- 407 00:21:27,986 --> 00:21:32,824 by the way, siemens, conductance, one over ohms. 408 00:21:32,824 --> 00:21:38,563 If I want electrons to move in a material, they need freedom. 409 00:21:38,563 --> 00:21:40,932 They need freedom. 410 00:21:40,932 --> 00:21:42,134 What does that mean? 411 00:21:42,134 --> 00:21:45,904 Well, it means that I'm trying to move through this wire. 412 00:21:45,904 --> 00:21:47,906 And for an electron, freedom means 413 00:21:47,906 --> 00:21:50,175 I can go to any state that's nearby. 414 00:21:50,175 --> 00:21:54,379 State, a wave function, a state of probability 415 00:21:54,379 --> 00:21:56,648 that I can move to. 416 00:21:56,648 --> 00:21:58,483 And then to that one. 417 00:21:58,483 --> 00:21:59,484 And then over here. 418 00:21:59,484 --> 00:22:00,986 And then there's is something there. 419 00:22:00,986 --> 00:22:01,787 I don't want to be. 420 00:22:01,787 --> 00:22:03,055 I've got to go this way. 421 00:22:03,055 --> 00:22:04,856 There's a bad thing over there. 422 00:22:04,856 --> 00:22:06,124 It's scattering me. 423 00:22:06,124 --> 00:22:07,259 I'll go this way. 424 00:22:07,259 --> 00:22:09,528 But if electrons don't have the ability 425 00:22:09,528 --> 00:22:13,732 to move into a free state, they're not going to conduct. 426 00:22:13,732 --> 00:22:17,369 That's why you've got to get the electron up here. 427 00:22:17,369 --> 00:22:17,869 Why? 428 00:22:17,869 --> 00:22:20,138 Because the conduction band-- 429 00:22:20,138 --> 00:22:21,840 I shouldn't really fill this in. 430 00:22:21,840 --> 00:22:24,643 I'm just showing you empty states there. 431 00:22:24,643 --> 00:22:28,013 The conduction band has 10 to the 24 states. 432 00:22:28,013 --> 00:22:29,715 Freedom. 433 00:22:29,715 --> 00:22:31,450 Freedom. 434 00:22:31,450 --> 00:22:33,952 So as soon as an electron gets up there, it's like, oh, 435 00:22:33,952 --> 00:22:35,120 I can go anywhere I want. 436 00:22:35,120 --> 00:22:36,054 I can be there. 437 00:22:36,054 --> 00:22:36,922 I can be there. 438 00:22:36,922 --> 00:22:40,425 I can move in response to this field that's pushing at me. 439 00:22:43,195 --> 00:22:44,763 I can conduct. 440 00:22:44,763 --> 00:22:47,132 I can't do that unless I have conduction, 441 00:22:47,132 --> 00:22:49,134 unless I get electrons into the conduction band. 442 00:22:49,134 --> 00:22:50,469 This is OK. 443 00:22:50,469 --> 00:22:54,272 Now, this is why, you can see right there, metals are clearly 444 00:22:54,272 --> 00:22:56,808 good conductors, based on our band picture. 445 00:22:56,808 --> 00:23:00,379 Because those electrons near that line there, 446 00:23:00,379 --> 00:23:02,481 you fill them up, and they're halfway in a band. 447 00:23:02,481 --> 00:23:06,418 But right up above there, an almost infinitesimally small 448 00:23:06,418 --> 00:23:11,656 energy away, is an empty state and another empty state. 449 00:23:11,656 --> 00:23:15,260 These ones you can see, it's going to be hard. 450 00:23:15,260 --> 00:23:17,462 I'm going to have to shine really high energy light 451 00:23:17,462 --> 00:23:21,133 to even get-- or really high temperatures. 452 00:23:21,133 --> 00:23:24,336 Again, semiconductors are special, 453 00:23:24,336 --> 00:23:27,472 because their gaps are right in that range where 454 00:23:27,472 --> 00:23:30,842 I can get electrons to go from the valence band 455 00:23:30,842 --> 00:23:33,612 to the conduction band in different ways. 456 00:23:33,612 --> 00:23:37,716 And there's two different ways that I want to talk about. 457 00:23:37,716 --> 00:23:40,352 The first way is simply with heat, 458 00:23:40,352 --> 00:23:43,121 and this is why I mentioned this on Monday. 459 00:23:43,121 --> 00:23:45,056 Actually, no matter what, there's 460 00:23:45,056 --> 00:23:47,359 some probability for an electron to have 461 00:23:47,359 --> 00:23:49,227 a high enough thermal energy. 462 00:23:49,227 --> 00:23:52,130 Yeah, electrons get hot, too, right? 463 00:23:52,130 --> 00:23:55,133 Everybody feels the heat. 464 00:23:55,133 --> 00:23:59,571 So that the thermal energy can be enough to get the electron 465 00:23:59,571 --> 00:24:01,273 to knock it up above. 466 00:24:03,975 --> 00:24:09,014 So with thermal energy, you can get-- 467 00:24:09,014 --> 00:24:10,315 let's see. 468 00:24:10,315 --> 00:24:14,986 At room temperature for silicon. 469 00:24:14,986 --> 00:24:18,824 So this is the case of silicon, which has a 1.1 electronvolt 470 00:24:18,824 --> 00:24:20,125 gap. 471 00:24:20,125 --> 00:24:24,463 Silicon, 1.1 electronvolt band gap. 472 00:24:24,463 --> 00:24:26,598 It's a really important semiconductor. 473 00:24:26,598 --> 00:24:30,936 And for silicon, at room temperature, I got about 10 474 00:24:30,936 --> 00:24:40,979 to the 10 electrons in the conduction band per centimeter 475 00:24:40,979 --> 00:24:42,347 cubed of material. 476 00:24:42,347 --> 00:24:43,949 This is how we think about it. 477 00:24:43,949 --> 00:24:48,553 We think about how many of these do I have per volume. 478 00:24:48,553 --> 00:24:49,855 It's a good way to measure it. 479 00:24:49,855 --> 00:24:55,794 These are also an electron in a conduction band 480 00:24:55,794 --> 00:24:57,028 also is called a carrier. 481 00:24:59,865 --> 00:25:04,402 So for silicon at room temperature, I will have-- 482 00:25:04,402 --> 00:25:08,440 just because I can't help it, because there's that many-- 483 00:25:08,440 --> 00:25:13,512 about 10 to the 10 carriers in the conduction band. 484 00:25:13,512 --> 00:25:17,516 Now, carrier is a carrier of electricity. 485 00:25:17,516 --> 00:25:19,451 That's why it's called a carrier, right? 486 00:25:19,451 --> 00:25:21,486 It carries electricity. 487 00:25:21,486 --> 00:25:23,154 So those are the ones that are carriers, 488 00:25:23,154 --> 00:25:24,890 the ones that made it up. 489 00:25:24,890 --> 00:25:26,625 But if I go to 600-- 490 00:25:26,625 --> 00:25:30,328 so now I'm going to go to 600 kelvin. 491 00:25:30,328 --> 00:25:32,330 Oh, we only use kelvin. 492 00:25:32,330 --> 00:25:35,200 Kelvin is the thermodynamic energy scale, 493 00:25:35,200 --> 00:25:37,302 temperature scale. 494 00:25:37,302 --> 00:25:46,411 10 to the 15 carriers per centimeter cubed. 495 00:25:46,411 --> 00:25:51,416 This seems like a big number, but is it a big number? 496 00:25:51,416 --> 00:25:54,553 What's a big number we know and like in this class? 497 00:25:54,553 --> 00:25:55,520 The mole. 498 00:25:55,520 --> 00:25:59,658 So like roughly-ish, is this all a big number 499 00:25:59,658 --> 00:26:02,227 per centimeter cubed or not? 500 00:26:02,227 --> 00:26:04,763 It's actually very small. 501 00:26:04,763 --> 00:26:10,535 But I need them to be there if I want better connectivity. 502 00:26:10,535 --> 00:26:13,271 If I want conduction in these semiconductors, 503 00:26:13,271 --> 00:26:19,044 I've got to put electrons up in the conduction band. 504 00:26:19,044 --> 00:26:22,881 Do you remember, just as an important point, 505 00:26:22,881 --> 00:26:26,351 I mentioned the energy of room temperature, the thermal energy 506 00:26:26,351 --> 00:26:30,589 of room temperature kBT is about 0.025 electronvolts. 507 00:26:30,589 --> 00:26:33,658 That seems way smaller than 1.1 eV. 508 00:26:33,658 --> 00:26:34,859 It is. 509 00:26:34,859 --> 00:26:37,529 But that's because that's not what temperature really 510 00:26:37,529 --> 00:26:38,229 looks like. 511 00:26:38,229 --> 00:26:41,299 Temperature is a distribution. 512 00:26:41,299 --> 00:26:42,267 There's a distribution. 513 00:26:42,267 --> 00:26:44,402 Now, you don't need to know that for the band gaps. 514 00:26:44,402 --> 00:26:46,338 We're going to come back to distributions, 515 00:26:46,338 --> 00:26:48,974 Boltzmann distributions, when we talk about reactions, reaction 516 00:26:48,974 --> 00:26:51,509 kinetics, later. 517 00:26:51,509 --> 00:26:55,680 But that's why, at room temperature, the tails-- 518 00:26:55,680 --> 00:26:58,516 hot means a range of energies. 519 00:26:58,516 --> 00:27:01,753 Hotter means a wider range of energies. 520 00:27:01,753 --> 00:27:05,090 And it's those tails that have enough energy 521 00:27:05,090 --> 00:27:09,194 to get over the gap and into the conduction band. 522 00:27:09,194 --> 00:27:09,928 It's those tails. 523 00:27:09,928 --> 00:27:12,797 That's why I've got a little bit of electrons that get 524 00:27:12,797 --> 00:27:15,166 up there at room temperature. 525 00:27:15,166 --> 00:27:18,536 Now, if you look at a plot-- 526 00:27:18,536 --> 00:27:20,071 here's a great way. 527 00:27:20,071 --> 00:27:22,207 There's the log connectivity of silicon. 528 00:27:22,207 --> 00:27:23,475 It's from [INAUDIBLE]. 529 00:27:23,475 --> 00:27:26,645 And there's the log connectivity on this side of tungsten. 530 00:27:26,645 --> 00:27:28,380 That's a metal. 531 00:27:28,380 --> 00:27:31,583 Totally different behavior. 532 00:27:31,583 --> 00:27:32,450 How is that possible? 533 00:27:32,450 --> 00:27:35,720 Well, we're going to explain the metal on Friday. 534 00:27:35,720 --> 00:27:39,024 Today, we're interested in this. 535 00:27:39,024 --> 00:27:41,159 This one, now we understand. 536 00:27:41,159 --> 00:27:44,329 Thermal energy excites carriers into the place where 537 00:27:44,329 --> 00:27:47,098 they can be free and conduct. 538 00:27:47,098 --> 00:27:50,335 So as I increase the temperature hotter and hotter-- 539 00:27:50,335 --> 00:27:52,237 there's the temperature in kelvin. 540 00:27:52,237 --> 00:27:54,472 I just gave you examples from down here, 541 00:27:54,472 --> 00:27:56,041 and now we're going higher and higher. 542 00:27:56,041 --> 00:27:58,510 I can get the connectivity up orders of magnitude 543 00:27:58,510 --> 00:28:00,011 higher for silicon. 544 00:28:00,011 --> 00:28:01,179 You know why now. 545 00:28:01,179 --> 00:28:02,514 I'm populating. 546 00:28:02,514 --> 00:28:04,749 I'm getting over this gap, and I'm 547 00:28:04,749 --> 00:28:06,718 populating the conduction band. 548 00:28:06,718 --> 00:28:10,355 So the answer is we just need to run our semiconductor 549 00:28:10,355 --> 00:28:15,160 industry and our phones and our lights at around 1,000 kelvin, 550 00:28:15,160 --> 00:28:15,760 right? 551 00:28:15,760 --> 00:28:17,295 No problem. 552 00:28:17,295 --> 00:28:18,263 All our devices. 553 00:28:18,263 --> 00:28:22,600 No, that's obviously not a good idea. 554 00:28:22,600 --> 00:28:23,702 How do we get around this? 555 00:28:23,702 --> 00:28:29,541 The answer, such a good word, it's chemistry. 556 00:28:29,541 --> 00:28:30,842 Chemistry gets us. 557 00:28:30,842 --> 00:28:35,013 Chemistry saves us, as always. 558 00:28:35,013 --> 00:28:40,885 You've got to know your chemistry. 559 00:28:40,885 --> 00:28:43,121 And in particular, this is not the doping 560 00:28:43,121 --> 00:28:45,356 that you may read about in the news related 561 00:28:45,356 --> 00:28:46,257 to Olympic athletes. 562 00:28:52,197 --> 00:29:02,207 This is the introduction of some small amount of an impurity. 563 00:29:02,207 --> 00:29:05,810 An impurity is something that wasn't there normally. 564 00:29:05,810 --> 00:29:09,981 It's like something I mixed in that's not normally there. 565 00:29:09,981 --> 00:29:12,851 If I put a small amount of something in it, 566 00:29:12,851 --> 00:29:16,521 then I can tune the properties. 567 00:29:16,521 --> 00:29:26,131 And in this case, I'm talking about the connectivity. 568 00:29:26,131 --> 00:29:29,334 So how does this work? 569 00:29:29,334 --> 00:29:30,935 If I look at this case-- 570 00:29:30,935 --> 00:29:33,138 I'll do one case here. 571 00:29:33,138 --> 00:29:37,308 I've got my silicon atoms arranged in the solid that 572 00:29:37,308 --> 00:29:38,843 gave me a band gap. 573 00:29:38,843 --> 00:29:43,081 And again, that is due to the arrangement of them. 574 00:29:43,081 --> 00:29:45,049 If I didn't arrange them in this particular way, 575 00:29:45,049 --> 00:29:47,085 I might not have that band gap. 576 00:29:47,085 --> 00:29:50,622 I might not have the same band structures. 577 00:29:50,622 --> 00:29:51,856 It depends. 578 00:29:51,856 --> 00:29:54,993 But this is what I get for the silicon arrangement 579 00:29:54,993 --> 00:29:57,929 when the band gap is 1.1 eV, which is the one we 580 00:29:57,929 --> 00:30:01,966 use in most of our electronics. 581 00:30:01,966 --> 00:30:04,235 But the thing is, I want-- 582 00:30:04,235 --> 00:30:07,272 so this would be silicon. 583 00:30:07,272 --> 00:30:11,576 This is just silicon by itself, valance band, 584 00:30:11,576 --> 00:30:16,848 and here's the conduction band, CB, VB. 585 00:30:16,848 --> 00:30:21,619 Now, I want to add electrons into this material. 586 00:30:21,619 --> 00:30:23,655 And so you can just kind of imagine 587 00:30:23,655 --> 00:30:25,056 how this would work, right? 588 00:30:25,056 --> 00:30:29,227 If I just look at a Lewis dot diagram for silicon-- let's 589 00:30:29,227 --> 00:30:33,097 just forget about this structure for a second. 590 00:30:33,097 --> 00:30:35,433 Silicon has these four valence electrons. 591 00:30:35,433 --> 00:30:41,606 So you can imagine silicon might look something like this. 592 00:30:41,606 --> 00:30:44,609 And OK, I'm going along, and I'm going along. 593 00:30:44,609 --> 00:30:46,411 It's tetrahedral and stuff. 594 00:30:46,411 --> 00:30:49,914 But now, I'm going to take one out. 595 00:30:49,914 --> 00:30:51,382 I'm going to take this out, and I'm 596 00:30:51,382 --> 00:30:54,519 going to make it phosphorus. 597 00:30:54,519 --> 00:30:56,120 What is phosphorus? 598 00:30:56,120 --> 00:30:59,824 It's, wait, where did it go? 599 00:30:59,824 --> 00:31:01,359 Panic, and then-- 600 00:31:01,359 --> 00:31:03,761 I'm recreating what happens for you guys-- 601 00:31:03,761 --> 00:31:04,362 I found it. 602 00:31:07,832 --> 00:31:08,900 That was close. 603 00:31:08,900 --> 00:31:11,002 But phosphorus is right there. 604 00:31:11,002 --> 00:31:12,804 It's right next to silicon. 605 00:31:12,804 --> 00:31:15,373 It's group 15 instead of 14. 606 00:31:15,373 --> 00:31:17,508 But it just has one extra electron, right? 607 00:31:17,508 --> 00:31:19,844 So maybe it could do the same thing, 608 00:31:19,844 --> 00:31:24,782 but then have this one extra electron. 609 00:31:24,782 --> 00:31:27,652 That's doping. 610 00:31:27,652 --> 00:31:29,420 Where does it go? 611 00:31:29,420 --> 00:31:30,455 It's all about freedom. 612 00:31:30,455 --> 00:31:32,190 It looks down and says, wait a second. 613 00:31:32,190 --> 00:31:35,226 There's no states here I can go to. 614 00:31:35,226 --> 00:31:36,628 No states. 615 00:31:36,628 --> 00:31:37,962 I can't go anywhere here. 616 00:31:37,962 --> 00:31:41,065 So I will have a state, because I have picked phosphorus 617 00:31:41,065 --> 00:31:42,200 carefully. 618 00:31:42,200 --> 00:31:44,469 And because of the way the chemistry and the bonding 619 00:31:44,469 --> 00:31:46,838 worked with phosphorus in silicon, 620 00:31:46,838 --> 00:31:52,277 this will introduce a state near the conduction band, 621 00:31:52,277 --> 00:31:53,578 and that's the key. 622 00:31:53,578 --> 00:31:57,248 So now we've got the valence band, 623 00:31:57,248 --> 00:32:00,551 and we've got the conduction band. 624 00:32:00,551 --> 00:32:04,622 And what's happened is there's a new level here 625 00:32:04,622 --> 00:32:06,291 that is called the donor level. 626 00:32:11,663 --> 00:32:21,306 That level is where the extra, extra key electron goes. 627 00:32:21,306 --> 00:32:22,674 It can't go in here, remember. 628 00:32:22,674 --> 00:32:24,876 This is all filled. 629 00:32:24,876 --> 00:32:32,917 So now, I've doped with P. But look, 630 00:32:32,917 --> 00:32:37,021 if I've got an electron here, now this difference in energy 631 00:32:37,021 --> 00:32:38,923 is really small. 632 00:32:38,923 --> 00:32:39,791 It's really small. 633 00:32:39,791 --> 00:32:40,992 I've engineered it this way. 634 00:32:40,992 --> 00:32:42,093 I've thought about it. 635 00:32:42,093 --> 00:32:44,929 So if I put phosphorus in here, that extra electron 636 00:32:44,929 --> 00:32:48,132 isn't sitting far away anymore from the conduction band. 637 00:32:48,132 --> 00:32:52,537 In fact, now it's so close that room temperature just 638 00:32:52,537 --> 00:32:53,438 kicks it right on up. 639 00:32:53,438 --> 00:32:57,475 So effectively, it's going to go up here, 640 00:32:57,475 --> 00:33:01,312 because that's a small delta e between the donor 641 00:33:01,312 --> 00:33:03,014 level and the conduction band. 642 00:33:03,014 --> 00:33:05,516 This is how doping works. 643 00:33:05,516 --> 00:33:07,518 This is how doping works. 644 00:33:07,518 --> 00:33:08,853 So I put a phosphorus atom in. 645 00:33:08,853 --> 00:33:10,888 There's an extra electron that comes out of that. 646 00:33:10,888 --> 00:33:12,290 The extra electron needs a state. 647 00:33:12,290 --> 00:33:13,458 It gets a state. 648 00:33:13,458 --> 00:33:14,759 That's called a donor state. 649 00:33:14,759 --> 00:33:16,494 Donor makes sense, right, because it's 650 00:33:16,494 --> 00:33:20,932 donating an electron into the conduction band. 651 00:33:25,403 --> 00:33:28,740 Once I get the electron into the conduction band, I'm home free. 652 00:33:28,740 --> 00:33:31,609 Because now, I've done what temperature was doing before, 653 00:33:31,609 --> 00:33:34,345 but I did it with chemistry. 654 00:33:34,345 --> 00:33:36,581 And so you could ask questions like this. 655 00:33:36,581 --> 00:33:40,585 How much phosphorus do you need to substitutionally dope? 656 00:33:40,585 --> 00:33:42,587 Substitution meant just what you-- 657 00:33:42,587 --> 00:33:44,422 substitution was I took a silicon atom 658 00:33:44,422 --> 00:33:45,957 and I substituted it. 659 00:33:45,957 --> 00:33:48,860 That's substitutional doping. 660 00:33:48,860 --> 00:33:51,129 To substitutionally dope a mole of silicon 661 00:33:51,129 --> 00:33:54,899 and get a free electron density of 5 times 10 to the 17. 662 00:33:54,899 --> 00:33:56,300 I'm going big here. 663 00:33:56,300 --> 00:33:59,804 Because look, temperature-- gesundheit. 664 00:33:59,804 --> 00:34:03,975 OK, maybe I'm willing to run my semiconductor in a really hot 665 00:34:03,975 --> 00:34:06,744 room, my phone at 600 kelvin. 666 00:34:06,744 --> 00:34:09,013 I'm still only at 10 to the 15. 667 00:34:09,013 --> 00:34:11,049 I want 10 to the 17 now. 668 00:34:11,049 --> 00:34:13,418 How much phosphorus do I need? 669 00:34:13,418 --> 00:34:14,552 You can solve that problem. 670 00:34:17,155 --> 00:34:19,757 I'll just write down a couple of the steps. 671 00:34:19,757 --> 00:34:24,962 So the volume of one mole of silicon 672 00:34:24,962 --> 00:34:32,670 is one mole times 28.1 grams per mole. 673 00:34:32,670 --> 00:34:35,406 Oh, and I got the density on there, too, right? 674 00:34:35,406 --> 00:34:41,411 Divided by 2.33 grams per centimeter cubed. 675 00:34:41,411 --> 00:34:42,713 How did I get the density? 676 00:34:42,713 --> 00:34:46,184 I looked it up in the periodic table. 677 00:34:46,184 --> 00:34:47,918 And so one mole of silicon is going 678 00:34:47,918 --> 00:34:53,157 to give me 12 centimeters cubed of silicon. 679 00:34:53,157 --> 00:34:57,094 One mole of silicon is 12 centimeters cubed. 680 00:34:57,094 --> 00:35:03,000 I need 5 times 10 to the 17 electrons in the conduction 681 00:35:03,000 --> 00:35:06,370 band per centimeter cubed. 682 00:35:06,370 --> 00:35:09,574 You see why per centimeter cubed is a good measure here. 683 00:35:09,574 --> 00:35:13,277 So that means I need 12 times that total. 684 00:35:13,277 --> 00:35:14,512 So I need 12 times that. 685 00:35:14,512 --> 00:35:20,618 So I need 5 times 10 to the 17 P atoms. 686 00:35:20,618 --> 00:35:23,054 Why do I need that many P atoms, times 12? 687 00:35:27,792 --> 00:35:30,828 Let me just write my units here to be very careful. 688 00:35:30,828 --> 00:35:36,667 P atoms per centimeter cubed times 12 centimeters cubed. 689 00:35:36,667 --> 00:35:41,506 That's how P atoms I need in this mole of silicon 690 00:35:41,506 --> 00:35:43,007 to get what? 691 00:35:43,007 --> 00:35:44,175 It's one to one. 692 00:35:44,175 --> 00:35:48,312 Because each P atom had one extra electron. 693 00:35:48,312 --> 00:35:51,082 Those other electrons are in the bonds. 694 00:35:51,082 --> 00:35:54,252 They're not going into the conduction band. 695 00:35:54,252 --> 00:35:56,120 It had one for one. 696 00:35:56,120 --> 00:35:59,056 One electron went to this donor state, went into the conduction 697 00:35:59,056 --> 00:36:00,358 band per phosphorus atom. 698 00:36:00,358 --> 00:36:02,860 So if I want that many carriers, if I 699 00:36:02,860 --> 00:36:06,364 want that many free electrons, I need that many atoms. 700 00:36:09,367 --> 00:36:12,003 Well, you guys can look up the phosphorus grams per mole, 701 00:36:12,003 --> 00:36:19,810 and you can get that this is 0.0003 grams of phosphorus. 702 00:36:19,810 --> 00:36:21,512 That's really not much. 703 00:36:21,512 --> 00:36:24,048 You see why it's called an impurity, right? 704 00:36:24,048 --> 00:36:25,516 You see why it's called an impurity. 705 00:36:25,516 --> 00:36:26,350 That's not much. 706 00:36:26,350 --> 00:36:29,921 I have all this silicon, and I only 707 00:36:29,921 --> 00:36:33,758 need 0.0003 grams of phosphorus, and I've 708 00:36:33,758 --> 00:36:39,197 bumped up the number of carriers by orders of magnitude. 709 00:36:39,197 --> 00:36:41,365 Not only that, I've done something really important, 710 00:36:41,365 --> 00:36:42,934 as well. 711 00:36:42,934 --> 00:36:44,869 And you can see this, because now, 712 00:36:44,869 --> 00:36:51,442 if I plot something like temperature 713 00:36:51,442 --> 00:36:53,644 versus number of carriers-- 714 00:36:58,049 --> 00:37:02,453 well, you saw the graph for temperature before, right? 715 00:37:02,453 --> 00:37:05,623 It was like this. 716 00:37:05,623 --> 00:37:08,626 That's the graph from a couple sides ago. 717 00:37:08,626 --> 00:37:13,197 But now, if I do it with chemistry, it's flat. 718 00:37:15,800 --> 00:37:20,204 Until the temperature gets really hot, I could-- 719 00:37:20,204 --> 00:37:22,373 give myself more room here, because that's 720 00:37:22,373 --> 00:37:24,075 kind of the point, right? 721 00:37:24,075 --> 00:37:24,942 Number of carriers. 722 00:37:27,578 --> 00:37:32,550 I can make this now flat. 723 00:37:35,286 --> 00:37:42,426 From doping, from temperature. 724 00:37:42,426 --> 00:37:47,331 And so you can see, OK, at a certain point, 725 00:37:47,331 --> 00:37:50,468 the temperature goes up, up, up. 726 00:37:50,468 --> 00:37:52,103 And at a certain point, the temperature 727 00:37:52,103 --> 00:37:55,706 is going to be so hot that I'm adding electrons, even 728 00:37:55,706 --> 00:37:58,676 beyond this. 729 00:37:58,676 --> 00:38:01,445 But you saw the temperatures there, 1,000 degrees kelvin. 730 00:38:01,445 --> 00:38:06,017 No, this allows me to have a predictable, flat number 731 00:38:06,017 --> 00:38:09,520 of carriers in the conduction band no matter the temperature. 732 00:38:09,520 --> 00:38:13,324 Just think about how important that is. 733 00:38:13,324 --> 00:38:16,093 Semiconductors are kind of discovered in the 1800s. 734 00:38:16,093 --> 00:38:19,897 But it wasn't until physicists and chemists 735 00:38:19,897 --> 00:38:22,733 were able to control the band gap 736 00:38:22,733 --> 00:38:27,104 and how to put carriers in and out of it until they could 737 00:38:27,104 --> 00:38:29,273 really work on the semiconductor revolution, which 738 00:38:29,273 --> 00:38:32,476 is what led to Snapchat. 739 00:38:32,476 --> 00:38:33,044 Did I get it? 740 00:38:33,044 --> 00:38:35,913 Snapchat is still used. 741 00:38:35,913 --> 00:38:36,847 I knew that. 742 00:38:36,847 --> 00:38:38,983 Slack. 743 00:38:38,983 --> 00:38:43,621 Now, you can do the same thing going the other way. 744 00:38:43,621 --> 00:38:46,957 You can do the same thing going the other way. 745 00:38:46,957 --> 00:38:52,963 If I now put gallium, so if I dope with gallium, well, 746 00:38:52,963 --> 00:39:02,640 you see, gallium has one too few electrons. 747 00:39:02,640 --> 00:39:06,610 And so if I dope with gallium, what I have-- 748 00:39:06,610 --> 00:39:08,913 so the gallium is there. 749 00:39:08,913 --> 00:39:09,814 Where is it? 750 00:39:09,814 --> 00:39:11,282 It's on the other side. 751 00:39:11,282 --> 00:39:12,917 Where's silicon? 752 00:39:12,917 --> 00:39:14,719 Silicon. 753 00:39:14,719 --> 00:39:17,488 Phosphorus is over there, group 15. 754 00:39:17,488 --> 00:39:18,823 Silicon is group 14. 755 00:39:18,823 --> 00:39:21,292 Gallium is group 13. 756 00:39:21,292 --> 00:39:22,893 One fewer electrons, but it really 757 00:39:22,893 --> 00:39:25,496 wants to make those four bonds. 758 00:39:25,496 --> 00:39:28,332 The material isn't happy if you break one. 759 00:39:28,332 --> 00:39:29,900 And so what does it do it? 760 00:39:29,900 --> 00:39:31,068 It steals an electron. 761 00:39:31,068 --> 00:39:32,636 It takes it. 762 00:39:32,636 --> 00:39:36,407 It says, I need an electron to be happy, so it takes one out. 763 00:39:36,407 --> 00:39:45,049 And that's called an accepter level, where what's happened 764 00:39:45,049 --> 00:39:47,952 is the gallium has actually pulled 765 00:39:47,952 --> 00:39:50,054 an electron out of there. 766 00:39:50,054 --> 00:39:55,126 And that leaves behind a positive charge. 767 00:39:55,126 --> 00:39:56,594 This is called a hole. 768 00:39:59,463 --> 00:40:02,099 That's called a hole. 769 00:40:02,099 --> 00:40:02,900 Think about it. 770 00:40:02,900 --> 00:40:06,537 If I take an electron off of an atom, it's positively charged. 771 00:40:06,537 --> 00:40:08,839 If I take an electron out of the VBM, 772 00:40:08,839 --> 00:40:11,442 there's a positive charge in there. 773 00:40:11,442 --> 00:40:15,646 That's really important, because these positive charges 774 00:40:15,646 --> 00:40:19,283 effectively are like electrons. 775 00:40:19,283 --> 00:40:21,752 They're like negative charges, but they're positive. 776 00:40:21,752 --> 00:40:25,556 So they also can conduct. 777 00:40:25,556 --> 00:40:28,926 They also can conduct, right? 778 00:40:28,926 --> 00:40:30,094 And that's really important. 779 00:40:30,094 --> 00:40:33,197 So these are two different types. 780 00:40:33,197 --> 00:40:36,000 And you can imagine the brilliance of the naming. 781 00:40:36,000 --> 00:40:40,204 These are P type, because it's a positive charge. 782 00:40:40,204 --> 00:40:44,775 And these are N type, because it's a negative charge. 783 00:40:44,775 --> 00:40:46,277 Those are N type semiconductors. 784 00:40:46,277 --> 00:40:47,111 What does that mean? 785 00:40:47,111 --> 00:40:49,847 I've used a little chemistry, sprinkled a little something 786 00:40:49,847 --> 00:40:50,948 with extra electrons. 787 00:40:50,948 --> 00:40:53,651 It's got negative charge in the conduction band. 788 00:40:53,651 --> 00:40:57,455 P type, P means positive. 789 00:40:57,455 --> 00:41:00,324 It means that I have introduced states here, 790 00:41:00,324 --> 00:41:01,692 because I needed an electron. 791 00:41:01,692 --> 00:41:02,660 I say, I need an extra one. 792 00:41:02,660 --> 00:41:04,128 I'm going to grab it from somebody. 793 00:41:04,128 --> 00:41:05,196 I don't care who. 794 00:41:05,196 --> 00:41:06,764 And so you create a positive charge 795 00:41:06,764 --> 00:41:09,333 in the valence band that can conduct electricity, 796 00:41:09,333 --> 00:41:13,404 just like a negative charge in the conduction band can. 797 00:41:13,404 --> 00:41:16,607 This is what the entire semiconductor revolution 798 00:41:16,607 --> 00:41:17,775 has been based on. 799 00:41:17,775 --> 00:41:19,610 And really, so much of the focus was 800 00:41:19,610 --> 00:41:21,846 on simply taking these elements-- in particular, 801 00:41:21,846 --> 00:41:23,047 silicon and germanium. 802 00:41:23,047 --> 00:41:26,250 But then, many, many more, as I showed you in the LED graph, 803 00:41:26,250 --> 00:41:30,387 many, many more have been used to make, 804 00:41:30,387 --> 00:41:33,691 to engineer, these simple-- 805 00:41:33,691 --> 00:41:37,027 what are seemingly simple properties, the band gap 806 00:41:37,027 --> 00:41:38,596 and the doping. 807 00:41:38,596 --> 00:41:40,731 And so I'm not going to go through this in detail. 808 00:41:40,731 --> 00:41:42,399 I'm just leaving it here so you have it. 809 00:41:42,399 --> 00:41:44,768 But you get charts like this. 810 00:41:44,768 --> 00:41:49,940 Here, you have, OK, carbon is up there. 811 00:41:49,940 --> 00:41:53,143 Well, if you dope it with boron, you can see that it's P type. 812 00:41:53,143 --> 00:41:53,711 You see that? 813 00:41:53,711 --> 00:41:57,147 Because I've got one fewer electron than carbon. 814 00:41:57,147 --> 00:41:59,149 So I'm going to grab that from the valence band, 815 00:41:59,149 --> 00:42:01,719 create a positive charge P type. 816 00:42:01,719 --> 00:42:04,421 I could also dope silicon and germanium. 817 00:42:04,421 --> 00:42:06,423 I'd say carbon, silicon, germanium. 818 00:42:06,423 --> 00:42:07,958 So I'm looking at this middle column, 819 00:42:07,958 --> 00:42:09,460 doping it with either side. 820 00:42:13,564 --> 00:42:16,500 Why can't I put aluminum in carbon? 821 00:42:16,500 --> 00:42:17,601 Why didn't they list that? 822 00:42:17,601 --> 00:42:20,538 Well, because if I try to put an aluminum inside the carbon 823 00:42:20,538 --> 00:42:22,706 network, the network gets all messed up. 824 00:42:22,706 --> 00:42:24,008 Doesn't fit. 825 00:42:24,008 --> 00:42:25,843 So that's also important. 826 00:42:25,843 --> 00:42:27,912 Can it fit? 827 00:42:27,912 --> 00:42:31,882 But it's through this that the semiconductor revolution 828 00:42:31,882 --> 00:42:32,683 started. 829 00:42:32,683 --> 00:42:35,653 It's only through this, this kind of control 830 00:42:35,653 --> 00:42:38,122 and this knowledge of atomic orbitals, 831 00:42:38,122 --> 00:42:43,093 really, if you think about it, and the structure of the atom. 832 00:42:43,093 --> 00:42:44,995 Now, I'm not going to talk about transistors, 833 00:42:44,995 --> 00:42:50,134 but this did lead to the development of the transistor. 834 00:42:50,134 --> 00:42:51,735 There's a really nice video there. 835 00:42:51,735 --> 00:42:53,070 It's, like, eight, nine minutes. 836 00:42:53,070 --> 00:42:56,840 I suggest you wait until your Friday night social. 837 00:42:56,840 --> 00:43:01,879 But if I take a P type and I take an N type 838 00:43:01,879 --> 00:43:03,914 and I take a P type and I put them together, 839 00:43:03,914 --> 00:43:07,718 some really important things happen. 840 00:43:07,718 --> 00:43:10,421 So important that it led to this, which 841 00:43:10,421 --> 00:43:12,957 is the very first transistor. 842 00:43:12,957 --> 00:43:14,625 That's a transistor. 843 00:43:14,625 --> 00:43:18,162 It's a dope semiconductor, one type, next to a dope 844 00:43:18,162 --> 00:43:21,231 semiconductor, another type. 845 00:43:21,231 --> 00:43:23,000 Now, those are the three people-- 846 00:43:23,000 --> 00:43:25,002 Bardeen, Shockley, and Brattain-- 847 00:43:25,002 --> 00:43:27,605 who won the Nobel Prize for this work. 848 00:43:27,605 --> 00:43:30,040 And that's the first transistor. 849 00:43:30,040 --> 00:43:34,678 Does anybody know how many transistors we make today? 850 00:43:34,678 --> 00:43:37,581 Per second. 851 00:43:37,581 --> 00:43:40,751 That's the only time metric we can use. 852 00:43:40,751 --> 00:43:43,721 Yeah, it's something around 10 trillion. 853 00:43:43,721 --> 00:43:47,992 We make 10 trillion transistors per second today. 854 00:43:47,992 --> 00:43:48,859 This is a big deal. 855 00:43:48,859 --> 00:43:51,462 This started it all, and it's all about chemistry 856 00:43:51,462 --> 00:43:55,165 and the physics of this device. 857 00:43:55,165 --> 00:43:58,068 This led to diodes and photodiodes. 858 00:43:58,068 --> 00:44:01,805 This led to the whole revolution. 859 00:44:01,805 --> 00:44:09,313 And what I want to point out here is that this also led-- 860 00:44:09,313 --> 00:44:11,415 it called on chemistry. 861 00:44:11,415 --> 00:44:12,449 So I love this chart. 862 00:44:12,449 --> 00:44:13,984 Unfortunately, they didn't update it, 863 00:44:13,984 --> 00:44:18,322 but this is an Intel chart that they used to show. 864 00:44:18,322 --> 00:44:22,092 And what they're showing is how are they making chips. 865 00:44:22,092 --> 00:44:24,395 How much of the periodic table do they 866 00:44:24,395 --> 00:44:26,263 need to make the current chip? 867 00:44:26,263 --> 00:44:28,899 Well, in the '80s, there's almost nothing lit up here. 868 00:44:28,899 --> 00:44:31,335 There's a little bit over here that you can't see, 869 00:44:31,335 --> 00:44:32,436 stuff we just talked about. 870 00:44:32,436 --> 00:44:34,471 But look at the '90s and look at the 2000s. 871 00:44:34,471 --> 00:44:38,942 And today, it's 75% of this. 872 00:44:38,942 --> 00:44:42,046 It's literally 75% of this is in your phone. 873 00:44:42,046 --> 00:44:42,546 Yeah. 874 00:44:42,546 --> 00:44:44,114 Why? 875 00:44:44,114 --> 00:44:47,251 The reason is exactly what we've talked about today, 876 00:44:47,251 --> 00:44:50,120 because they need more and more and more 877 00:44:50,120 --> 00:44:53,991 flexibility and ways to tune the band gap 878 00:44:53,991 --> 00:44:57,127 and the semiconducting properties of these materials 879 00:44:57,127 --> 00:44:57,828 and the doping. 880 00:44:57,828 --> 00:44:58,929 Why do they need new ways? 881 00:44:58,929 --> 00:45:01,365 Because they're making them so darn small. 882 00:45:01,365 --> 00:45:03,600 They're so small, it gets harder to figure out 883 00:45:03,600 --> 00:45:05,803 how to do it right, how to do it in a way that's also 884 00:45:05,803 --> 00:45:09,106 stable over time, for example. 885 00:45:09,106 --> 00:45:11,108 So they need new chemistry. 886 00:45:11,108 --> 00:45:14,078 This is a call to action to the field of chemistry, 887 00:45:14,078 --> 00:45:17,948 and chemistry responded. 888 00:45:17,948 --> 00:45:19,983 And there's the data on the cost. 889 00:45:19,983 --> 00:45:21,452 I thought that was kind of cool. 890 00:45:21,452 --> 00:45:26,457 So these are orders of magnitude of cost and number 891 00:45:26,457 --> 00:45:28,125 of transistors. 892 00:45:28,125 --> 00:45:33,664 And I'll just say one more why this matters. 893 00:45:33,664 --> 00:45:36,533 Because the semiconductor is also the same thing 894 00:45:36,533 --> 00:45:40,471 we use to take electricity from the sun, 895 00:45:40,471 --> 00:45:42,439 to generate electricity from the sun. 896 00:45:42,439 --> 00:45:48,746 And you can imagine, you are doing that in your goody bag. 897 00:45:48,746 --> 00:45:53,217 You're literally using this semiconductor 898 00:45:53,217 --> 00:45:58,589 to generate electricity by shining light on it. 899 00:45:58,589 --> 00:45:59,490 Why is this important? 900 00:45:59,490 --> 00:46:00,891 Well, I like this comparison. 901 00:46:00,891 --> 00:46:03,794 All the coal, oil, and gas known to humans 902 00:46:03,794 --> 00:46:07,364 is what you get from the sun in about 20 days. 903 00:46:07,364 --> 00:46:08,132 This is the sun. 904 00:46:08,132 --> 00:46:10,567 Now, we've seen the sun before. 905 00:46:10,567 --> 00:46:13,070 This is how we see it in our class. 906 00:46:13,070 --> 00:46:16,874 The sun is a spectrum of different wavelengths 907 00:46:16,874 --> 00:46:18,008 and intensities. 908 00:46:18,008 --> 00:46:20,377 And this is already on planet Earth, 909 00:46:20,377 --> 00:46:22,513 because you can see those chemistries that 910 00:46:22,513 --> 00:46:25,149 are in the atmosphere have already absorbed. 911 00:46:25,149 --> 00:46:28,485 Remember ozone down here, helping us with UV radiation? 912 00:46:28,485 --> 00:46:31,455 And out here, you've got a lot of water and other things, CO2. 913 00:46:31,455 --> 00:46:32,289 Those are absorbing. 914 00:46:32,289 --> 00:46:35,592 That's why it doesn't look smooth. 915 00:46:35,592 --> 00:46:39,096 But the point is, I want to semiconductor to absorb as much 916 00:46:39,096 --> 00:46:40,164 of this as possible. 917 00:46:40,164 --> 00:46:43,367 If I want a good solar cell, I should absorb as much 918 00:46:43,367 --> 00:46:46,036 of this as possible. 919 00:46:46,036 --> 00:46:48,906 But the problem is that it's a constrained optimization 920 00:46:48,906 --> 00:46:50,007 problem. 921 00:46:50,007 --> 00:46:52,242 So let's see, if I-- 922 00:46:52,242 --> 00:46:53,043 I'll just use this. 923 00:46:57,548 --> 00:47:00,284 This goes back to Bohr, by the way. 924 00:47:00,284 --> 00:47:01,952 Remember, Bohr, I'm absorbing light. 925 00:47:01,952 --> 00:47:03,620 It's just now, I've got an actual solid. 926 00:47:03,620 --> 00:47:06,423 I don't have an atom. 927 00:47:06,423 --> 00:47:08,392 I've got a solid, which is what you need if you 928 00:47:08,392 --> 00:47:09,526 want to generate a current. 929 00:47:09,526 --> 00:47:12,329 I've got to hook leads up to it. 930 00:47:12,329 --> 00:47:14,531 But my solid is a semiconductor. 931 00:47:14,531 --> 00:47:18,802 And you can imagine, say, well, if my gap were really, really 932 00:47:18,802 --> 00:47:23,707 tiny, then any amount-- 933 00:47:23,707 --> 00:47:27,945 almost any amount of this spectrum 934 00:47:27,945 --> 00:47:31,915 would excite electrons. 935 00:47:31,915 --> 00:47:34,952 And I might grab most of that spectrum. 936 00:47:34,952 --> 00:47:36,787 I might absorb most of it. 937 00:47:36,787 --> 00:47:39,790 But the problem with that is that, then, all of these 938 00:47:39,790 --> 00:47:43,560 will thermalize, like I said in the beginning. 939 00:47:43,560 --> 00:47:44,428 Loss to heat. 940 00:47:47,664 --> 00:47:48,432 Loss to heat. 941 00:47:48,432 --> 00:47:50,500 So if my band gap is really small, 942 00:47:50,500 --> 00:47:56,406 I absorb a lot of the light, but I lose most of it as heat. 943 00:47:56,406 --> 00:48:00,677 If my band gap is really big, then there's so much of this 944 00:48:00,677 --> 00:48:02,112 light that I cannot absorb. 945 00:48:05,849 --> 00:48:07,751 By the way, also, the voltage that you get out 946 00:48:07,751 --> 00:48:10,387 of your solar cell is essentially this band gap. 947 00:48:10,387 --> 00:48:12,289 So if I get to really, really small band gaps, 948 00:48:12,289 --> 00:48:13,724 I have almost no voltage. 949 00:48:13,724 --> 00:48:15,626 That's bad, too. 950 00:48:15,626 --> 00:48:17,027 But if my band gap is too big, you 951 00:48:17,027 --> 00:48:18,128 think, oh, I'll get a high voltage. 952 00:48:18,128 --> 00:48:18,762 No. 953 00:48:18,762 --> 00:48:21,665 You won't absorb any photons. 954 00:48:21,665 --> 00:48:23,867 So it's a constraint problem. 955 00:48:23,867 --> 00:48:24,968 It's a constraint problem. 956 00:48:24,968 --> 00:48:28,739 You can actually solve this, and you can plot-- 957 00:48:28,739 --> 00:48:31,308 in fact, here's a little animation. 958 00:48:31,308 --> 00:48:33,176 Energy comes in from the sun. 959 00:48:33,176 --> 00:48:34,278 It excites an electron. 960 00:48:34,278 --> 00:48:35,779 This is how PowerPoint sees it. 961 00:48:35,779 --> 00:48:37,848 Leaves behind a hole, and you get them out. 962 00:48:37,848 --> 00:48:40,284 That's a solar cell. 963 00:48:40,284 --> 00:48:44,121 And this is the chart I want to show you. 964 00:48:44,121 --> 00:48:47,557 Because you see, if I take this constraint into account, 965 00:48:47,557 --> 00:48:49,893 that I don't absorb light if the gap is too big, 966 00:48:49,893 --> 00:48:52,062 but I do absorb light and it all goes 967 00:48:52,062 --> 00:48:53,864 to heat if the gap is too small, it 968 00:48:53,864 --> 00:48:55,933 means there's some sweet spot. 969 00:48:55,933 --> 00:48:57,634 There's some sweet spot. 970 00:48:57,634 --> 00:49:00,170 And that's what is plotted here. 971 00:49:00,170 --> 00:49:02,806 This is the band gap of a semiconductor, 972 00:49:02,806 --> 00:49:05,342 and this is the maximum that that solar cell 973 00:49:05,342 --> 00:49:07,144 efficiency could be. 974 00:49:07,144 --> 00:49:09,379 That's the maximum that it could be for that gap. 975 00:49:09,379 --> 00:49:12,649 So you can see the sweet spot is right there. 976 00:49:12,649 --> 00:49:14,551 That's a thermodynamic derivation 977 00:49:14,551 --> 00:49:16,720 called Shockley-Queisser of the maximum efficiency 978 00:49:16,720 --> 00:49:18,689 you could ever get out of a single material. 979 00:49:18,689 --> 00:49:20,457 And notice, if you put the materials here, 980 00:49:20,457 --> 00:49:23,360 silicon is 90% of the solar cells you buy today. 981 00:49:23,360 --> 00:49:26,964 And notice that it's not quite at its maximum potential. 982 00:49:26,964 --> 00:49:29,666 It's also not quite in the middle, where you'd want. 983 00:49:29,666 --> 00:49:31,568 It should have a slightly higher gap, 984 00:49:31,568 --> 00:49:34,004 and you'd get to higher efficiency. 985 00:49:34,004 --> 00:49:35,405 But these materials out of gallium 986 00:49:35,405 --> 00:49:36,907 arsenide, they do have the-- 987 00:49:36,907 --> 00:49:38,709 what is GS? 988 00:49:38,709 --> 00:49:41,078 That's not an element. 989 00:49:41,078 --> 00:49:44,748 Gallium arsenide, it does have a better gap, 990 00:49:44,748 --> 00:49:47,484 but it's much more expensive. 991 00:49:47,484 --> 00:49:48,251 And so we go. 992 00:49:48,251 --> 00:49:50,587 And a lot of solar cell research is 993 00:49:50,587 --> 00:49:53,557 on getting as close to this point as you can. 994 00:49:53,557 --> 00:49:54,725 See you guys on Friday.