1 00:00:00,030 --> 00:00:01,980 NARRATOR: The following content is provided under a 2 00:00:01,980 --> 00:00:03,830 Creative Commons License. 3 00:00:03,830 --> 00:00:06,860 Your support will help MIT OpenCourseWare continue to 4 00:00:06,860 --> 00:00:10,510 offer high-quality educational resources for free. 5 00:00:10,510 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:17,190 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,190 --> 00:00:18,440 ocw.mit.edu. 8 00:00:20,940 --> 00:00:25,670 PROFESSOR: OK, so this takes us into the paper by Heitler 9 00:00:25,670 --> 00:00:30,030 and London, where, by using the concept of linear 10 00:00:30,030 --> 00:00:34,410 combination of atomic orbitals into molecular orbitals for a 11 00:00:34,410 --> 00:00:38,660 large number of atoms, instead of splitting one plus one 12 00:00:38,660 --> 00:00:42,690 atoms, making a bond into two energy levels of bonding and 13 00:00:42,690 --> 00:00:46,430 AN antibonding, we take a large number of atoms, bring 14 00:00:46,430 --> 00:00:49,640 them together, and we get a large number of bonding 15 00:00:49,640 --> 00:00:52,370 orbitals and a large number of antibonding orbitals. 16 00:00:52,370 --> 00:00:58,410 And they have to lie within a zone of about 5 to 10 electron 17 00:00:58,410 --> 00:01:00,840 volts, which means if you put Avogadro's number of these 18 00:01:00,840 --> 00:01:04,550 things together, you're going to end up with an energy 19 00:01:04,550 --> 00:01:07,950 difference between successive energy levels on the order of 20 00:01:07,950 --> 00:01:11,530 about 10 to the minus 20 electron volts, or 10 to the 21 00:01:11,530 --> 00:01:12,890 minus 40 joules. 22 00:01:12,890 --> 00:01:16,610 And for all intents and purposes, that is a continuum, 23 00:01:16,610 --> 00:01:18,730 and hence, the term band. 24 00:01:18,730 --> 00:01:22,040 And now we start populating this with electrons, and each 25 00:01:22,040 --> 00:01:24,050 one of these is a separate state. 26 00:01:24,050 --> 00:01:27,110 And electrons go in two by two, just like Noah's Ark, all 27 00:01:27,110 --> 00:01:30,950 the way up-- either halfway up or all the way up. 28 00:01:30,950 --> 00:01:33,820 But now the energy difference is very, very tiny. 29 00:01:33,820 --> 00:01:37,240 And a second instance, we looked at insulators where-- 30 00:01:37,240 --> 00:01:38,950 for example, in diamond-- 31 00:01:38,950 --> 00:01:41,070 where the bonds are really strong. 32 00:01:41,070 --> 00:01:44,890 So that means if the atomic orbital is roughly at the 33 00:01:44,890 --> 00:01:48,550 middle here, the depression to make the bonding orbital is 34 00:01:48,550 --> 00:01:50,870 very, very great, and very negative. 35 00:01:50,870 --> 00:01:54,330 And therefore, the elevation to the antibonding orbital is 36 00:01:54,330 --> 00:01:56,300 great and relatively positive. 37 00:01:56,300 --> 00:01:58,650 And when we start putting Avogadro's number of these 38 00:01:58,650 --> 00:02:00,980 things together, we still end up with the 10 to 39 00:02:00,980 --> 00:02:02,440 the minus 40 joules. 40 00:02:02,440 --> 00:02:06,590 But when we get to the top of the bonding orbitals, we have 41 00:02:06,590 --> 00:02:10,990 still got 3 or 5 or 5 electron volts to get to the bottom of 42 00:02:10,990 --> 00:02:13,600 the antibonding orbitals, hence the formation of the 43 00:02:13,600 --> 00:02:15,700 band gap with an energy of-- 44 00:02:15,700 --> 00:02:16,420 as I mentioned. 45 00:02:16,420 --> 00:02:19,110 So up here, we have the conduction band where 46 00:02:19,110 --> 00:02:20,950 electrons are free to move about. 47 00:02:20,950 --> 00:02:24,060 And this is derived from the antibonding orbitals. 48 00:02:24,060 --> 00:02:27,130 And down here, we have the valence band, which consists 49 00:02:27,130 --> 00:02:30,720 of the bonding orbitals derived from sigma and pi. 50 00:02:30,720 --> 00:02:34,160 And then the semiconductor is sort of like an insulator-- 51 00:02:34,160 --> 00:02:37,820 as they say in California, it's like an insulator-- but 52 00:02:37,820 --> 00:02:40,140 the band gap isn't quite so severe. 53 00:02:40,140 --> 00:02:43,560 It's down on the order of 1 to 3 electron volts, and that 54 00:02:43,560 --> 00:02:45,300 gives it unique properties. 55 00:02:45,300 --> 00:02:45,760 Why? 56 00:02:45,760 --> 00:02:48,590 What's magical about 1 to 3 electron volts? 57 00:02:48,590 --> 00:02:50,410 Number one, visible light. 58 00:02:50,410 --> 00:02:52,980 Visible light is 2 to 3 electron volts. 59 00:02:52,980 --> 00:02:57,790 So visible light shines right through an insulator, because 60 00:02:57,790 --> 00:03:02,510 visible light has an energy of about 2 to 3 electron volts. 61 00:03:02,510 --> 00:03:06,390 If that's the energy of 2 to 3 electron volts, and this is 6, 62 00:03:06,390 --> 00:03:08,540 it zooms right through. 63 00:03:08,540 --> 00:03:13,200 But if it's 2 electron volts and this is 1 electron volt, 64 00:03:13,200 --> 00:03:15,390 we're going to get thermal excitation. 65 00:03:15,390 --> 00:03:17,760 I know Professor Ballinger talked about thermal 66 00:03:17,760 --> 00:03:21,270 excitation the last day and what happens, and it's very 67 00:03:21,270 --> 00:03:26,220 reminiscent of excitation in the case of the Bohr model. 68 00:03:26,220 --> 00:03:28,680 Photoexcitation across the band gap. 69 00:03:31,200 --> 00:03:37,940 Incident photon with energy greater than the 70 00:03:37,940 --> 00:03:39,220 energy of the band gap. 71 00:03:39,220 --> 00:03:41,100 And it's the same drill as you've seen before. 72 00:03:41,100 --> 00:03:44,260 That's why those early lessons on-- 73 00:03:44,260 --> 00:03:47,410 photon comes in or electron comes in, strikes the Bohr 74 00:03:47,410 --> 00:03:51,390 atom, electron rises up, momentarily sits there, falls 75 00:03:51,390 --> 00:03:53,440 back down, photon emitted. 76 00:03:53,440 --> 00:03:56,060 It's the same set of ideas. 77 00:03:56,060 --> 00:03:59,470 Only instead of moving from n equals 1 to n equals 2 in the 78 00:03:59,470 --> 00:04:02,150 Bohr atom, you're moving from the valence band to the 79 00:04:02,150 --> 00:04:04,810 conduction band, sitting in the conduction band 80 00:04:04,810 --> 00:04:07,170 momentarily, you fall back down, and you get a 81 00:04:07,170 --> 00:04:07,990 photoemission. 82 00:04:07,990 --> 00:04:10,320 So that was covered last day. 83 00:04:10,320 --> 00:04:13,590 And I know towards the end of the lesson, he started talking 84 00:04:13,590 --> 00:04:15,750 about thermal excitation. 85 00:04:15,750 --> 00:04:18,560 So let's look at that in a little more detail. 86 00:04:18,560 --> 00:04:20,090 Thermal excitation. 87 00:04:20,090 --> 00:04:22,370 So thermal excitation of what? 88 00:04:22,370 --> 00:04:30,670 Thermal excitation of electrons across the band gap. 89 00:04:30,670 --> 00:04:33,400 So this is matter energy interaction, only in this 90 00:04:33,400 --> 00:04:35,360 case, it's thermally inspired. 91 00:04:35,360 --> 00:04:37,590 So let's draw our cartoon again. 92 00:04:37,590 --> 00:04:42,890 Up here, we have the conduction band, and below we 93 00:04:42,890 --> 00:04:44,880 have the valence band. 94 00:04:44,880 --> 00:04:47,200 So in the conduction band we have free electrons. 95 00:04:47,200 --> 00:04:50,180 In the valence band is where all the bonds live. 96 00:04:50,180 --> 00:04:54,470 And we've got an energy gap here of some value. 97 00:04:54,470 --> 00:04:56,270 Could be semiconductor, could be insulator. 98 00:04:56,270 --> 00:04:58,720 In this case, we're going to use visible light. 99 00:04:58,720 --> 00:05:04,580 And we've gone through the analysis with incident photon 100 00:05:04,580 --> 00:05:06,270 and the emission. 101 00:05:06,270 --> 00:05:09,060 In this case, I want to look at thermal excitation. 102 00:05:09,060 --> 00:05:12,860 So with thermal excitation, I start with an electron down 103 00:05:12,860 --> 00:05:14,360 here in a bond. 104 00:05:14,360 --> 00:05:16,480 This electron lives in a bond. 105 00:05:16,480 --> 00:05:19,790 And with thermal excitation, the electron jumps out of the 106 00:05:19,790 --> 00:05:23,160 bond and up into the conduction band. 107 00:05:23,160 --> 00:05:26,050 So I'm going to designate the electron in the conduction 108 00:05:26,050 --> 00:05:29,210 band with an e minus and a circle around it. 109 00:05:29,210 --> 00:05:30,880 And it leaves behind a broken bond. 110 00:05:30,880 --> 00:05:33,630 As you know, every bond has two electrons in it. 111 00:05:33,630 --> 00:05:39,080 Well, one of the electrons left the bond, leaving a hole. 112 00:05:39,080 --> 00:05:41,480 Little h with a plus sign. 113 00:05:41,480 --> 00:05:45,560 This is a broken bond, and a broken bond is highly unstable 114 00:05:45,560 --> 00:05:46,870 and very mobile. 115 00:05:46,870 --> 00:05:49,130 If I put a potential across here. 116 00:05:49,130 --> 00:05:53,070 If I put this material-- and I'm doing a mixed metaphor-- 117 00:05:53,070 --> 00:05:55,090 this is an energy level diagram. 118 00:05:55,090 --> 00:05:57,780 But now I'm going to put a couple of plates across an 119 00:05:57,780 --> 00:05:58,855 energy level diagram. 120 00:05:58,855 --> 00:06:00,020 But you're smart. 121 00:06:00,020 --> 00:06:01,020 You can understand this. 122 00:06:01,020 --> 00:06:02,240 So this is not energy. 123 00:06:02,240 --> 00:06:06,070 Now I'm going to make the right electrode negative and 124 00:06:06,070 --> 00:06:08,540 I'm going to make the left electrode positive. 125 00:06:08,540 --> 00:06:09,650 What would happen? 126 00:06:09,650 --> 00:06:12,380 Well, the electrons in the conduction band are going to 127 00:06:12,380 --> 00:06:15,150 be attracted to the positive electrode or repelled by the 128 00:06:15,150 --> 00:06:19,300 negative electrode, but the complementary situation occurs 129 00:06:19,300 --> 00:06:20,600 in the valence band. 130 00:06:20,600 --> 00:06:24,100 This broken bond is like a hot potato, and it has an 131 00:06:24,100 --> 00:06:24,970 effective charge. 132 00:06:24,970 --> 00:06:28,290 This is a zero in a land of minus one. 133 00:06:28,290 --> 00:06:31,370 A broken bond is a zero in a land of minus one. 134 00:06:31,370 --> 00:06:36,000 So therefore, if I make the right side negative, this hole 135 00:06:36,000 --> 00:06:37,350 is going to be drawn. 136 00:06:37,350 --> 00:06:40,340 So I have two forms of electronic conduction. 137 00:06:40,340 --> 00:06:43,660 I have electrons moving to the left in the conduction band 138 00:06:43,660 --> 00:06:47,150 and I have holes moving to the right in the valence band. 139 00:06:47,150 --> 00:06:52,600 So for every thermal excitation I get two carriers. 140 00:06:52,600 --> 00:07:03,200 Every excitation of electron from valence band to 141 00:07:03,200 --> 00:07:09,880 conduction band generates two carriers. 142 00:07:09,880 --> 00:07:10,830 Carriers of what? 143 00:07:10,830 --> 00:07:11,920 Water? 144 00:07:11,920 --> 00:07:16,680 Carriers of electrical charge. 145 00:07:16,680 --> 00:07:18,600 Two carriers of electrical charge. 146 00:07:18,600 --> 00:07:19,680 And what are they? 147 00:07:19,680 --> 00:07:24,810 The electron in the conduction band and the hole-- 148 00:07:24,810 --> 00:07:26,730 little h with a plus sign-- 149 00:07:26,730 --> 00:07:28,790 in the valence band. 150 00:07:28,790 --> 00:07:31,330 So that's how thermal excitation works. 151 00:07:31,330 --> 00:07:34,410 And you can see that the numbers have to be equal. 152 00:07:34,410 --> 00:07:38,590 So we write, therefore, that the populations are equal. 153 00:07:38,590 --> 00:07:43,180 The number of electrons in the conduction band equals the 154 00:07:43,180 --> 00:07:46,860 number of holes in the valence band. 155 00:07:46,860 --> 00:07:52,340 Now electrical engineers have a similar expression, but they 156 00:07:52,340 --> 00:07:57,470 don't care about numbers and electrons and holes, they care 157 00:07:57,470 --> 00:07:59,210 about the functionality. 158 00:07:59,210 --> 00:08:03,380 And the electron is a carrier of negative charge and the 159 00:08:03,380 --> 00:08:06,070 hole is a carrier of positive charge. 160 00:08:06,070 --> 00:08:09,040 So the electrical engineering books will write, thermal 161 00:08:09,040 --> 00:08:15,410 excitation gives rise to pair generation. 162 00:08:15,410 --> 00:08:16,070 Pair of what? 163 00:08:16,070 --> 00:08:17,720 Pair of charge carriers. 164 00:08:17,720 --> 00:08:20,400 And the population of negative charge carriers equals the 165 00:08:20,400 --> 00:08:24,310 population of positive charge carriers, which in chemistry 166 00:08:24,310 --> 00:08:28,030 is the number of electrons equals the number of holes, or 167 00:08:28,030 --> 00:08:31,070 the number of broken bonds. 168 00:08:31,070 --> 00:08:36,020 So that's the way it works, but there's a conundrum here. 169 00:08:36,020 --> 00:08:39,200 Thermal excitation is based upon the thermal energy, and 170 00:08:39,200 --> 00:08:43,430 we know that the average thermal energy in an 171 00:08:43,430 --> 00:08:45,220 environment is roughly given-- 172 00:08:45,220 --> 00:08:47,720 I mean there are fancier calculations-- 173 00:08:47,720 --> 00:08:50,240 but to a first order, I can approximate it as the product 174 00:08:50,240 --> 00:08:53,130 of the Boltzmann constant and absolute temperature. 175 00:08:58,040 --> 00:09:00,850 So at room temperature-- 176 00:09:00,850 --> 00:09:04,450 room temperature, I like to say, about 300 Kelvin. 177 00:09:04,450 --> 00:09:06,620 300 Kelvin is 27 Celsius. 178 00:09:06,620 --> 00:09:09,575 That's kind of a warm room, but 300 is a nice number. 179 00:09:09,575 --> 00:09:10,440 All right? 180 00:09:10,440 --> 00:09:15,900 So if you take 300 Kelvin, you get on the order of about 1/40 181 00:09:15,900 --> 00:09:17,520 of an electron volt. 182 00:09:17,520 --> 00:09:22,190 1/40 of an electron volt, which is a lot less than one 183 00:09:22,190 --> 00:09:24,820 electron volt, which is roughly the band gap of a 184 00:09:24,820 --> 00:09:26,550 semiconductor. 185 00:09:26,550 --> 00:09:29,920 So how is it that we get any thermal excitation of data 186 00:09:29,920 --> 00:09:33,940 indicate that there is some thermal excitation even at 187 00:09:33,940 --> 00:09:34,870 room temperature? 188 00:09:34,870 --> 00:09:38,620 So the question is, if the average thermal energy is a 189 00:09:38,620 --> 00:09:41,410 fortieth of electron volt according to this-- and this 190 00:09:41,410 --> 00:09:42,550 is correct-- 191 00:09:42,550 --> 00:09:46,030 and the band gap is one eV, then it should be no thermal 192 00:09:46,030 --> 00:09:47,780 excitation. 193 00:09:47,780 --> 00:09:49,160 But we know what happens. 194 00:09:49,160 --> 00:09:53,210 So, one eV, which I'm going to say is Eg. 195 00:09:53,210 --> 00:09:54,120 All right? 196 00:09:54,120 --> 00:10:02,900 So how do we get any thermal excitation under these 197 00:10:02,900 --> 00:10:04,460 conditions? 198 00:10:04,460 --> 00:10:08,470 So there's an answer to this. 199 00:10:08,470 --> 00:10:13,410 And for this we go to merry old England and James Clerk 200 00:10:13,410 --> 00:10:18,810 Maxwell, that you know or will come to know in 8.02 as the 201 00:10:18,810 --> 00:10:21,480 annunciator of Maxwell's equations of 202 00:10:21,480 --> 00:10:22,800 electricity and magnetism. 203 00:10:22,800 --> 00:10:26,530 He also thought about physical chemistry, and in particular 204 00:10:26,530 --> 00:10:30,350 he thought about the physical chemistry of gases. 205 00:10:30,350 --> 00:10:32,100 And what did he teach us about gases? 206 00:10:32,100 --> 00:10:36,310 He said, if you look here in this room, you see nitrogen 207 00:10:36,310 --> 00:10:38,420 and oxygen and all the other constituents of air. 208 00:10:38,420 --> 00:10:41,530 But to a first approximation, we have four parts nitrogen, 209 00:10:41,530 --> 00:10:42,950 one part oxygen. 210 00:10:42,950 --> 00:10:45,430 The room is roughly 300 Kelvin. 211 00:10:45,430 --> 00:10:51,340 What Maxwell taught us is that velocities of the gas species 212 00:10:51,340 --> 00:10:54,720 zooming around in this room are not all equal. 213 00:10:54,720 --> 00:10:58,100 Some of the gas species are moving around as though 214 00:10:58,100 --> 00:11:00,350 they're at 500 Kelvin. 215 00:11:00,350 --> 00:11:03,860 And some of them are moving around very slowly as though 216 00:11:03,860 --> 00:11:05,650 they're at 100 Kelvin. 217 00:11:05,650 --> 00:11:08,440 On average, it's 300 Kelvin, because we can 218 00:11:08,440 --> 00:11:10,060 feel it as 300 Kelvin. 219 00:11:10,060 --> 00:11:11,970 But some of them are zooming around. 220 00:11:11,970 --> 00:11:13,945 Some are really lazy and they're just moving along 221 00:11:13,945 --> 00:11:15,340 really slowly. 222 00:11:15,340 --> 00:11:17,950 And furthermore, he was quantitative about it. 223 00:11:17,950 --> 00:11:21,020 He said, I'm going to tell you what the distribution of 224 00:11:21,020 --> 00:11:22,850 energies is. 225 00:11:22,850 --> 00:11:25,510 So let's get that on the board for starters. 226 00:11:25,510 --> 00:11:38,290 That in any ensemble of gas species, could be gas atoms or 227 00:11:38,290 --> 00:11:41,870 it could be gas molecules or gas compounds, in any ensemble 228 00:11:41,870 --> 00:11:49,610 of gas species, that all molecules-- 229 00:11:49,610 --> 00:11:54,560 because you can always say the atom is a degenerate form-- 230 00:11:54,560 --> 00:12:02,465 all molecules do not have the same velocity. 231 00:12:05,200 --> 00:12:08,000 And furthermore, he gave us the distribution. 232 00:12:08,000 --> 00:12:17,480 He calculated the distribution of velocities. 233 00:12:17,480 --> 00:12:20,340 So that was about 1859. 234 00:12:20,340 --> 00:12:21,100 Forgive me here. 235 00:12:21,100 --> 00:12:22,350 Velocities. 236 00:12:25,570 --> 00:12:26,340 OK. 237 00:12:26,340 --> 00:12:35,990 And then Boltzmann came along in 1872. 238 00:12:35,990 --> 00:12:38,480 And Boltzmann generalized this idea. 239 00:12:38,480 --> 00:12:42,870 He made the link between gas velocity and temperature. 240 00:12:42,870 --> 00:12:46,120 So, he took the idea and he said, if the gas molecules 241 00:12:46,120 --> 00:12:49,300 move at different velocities, that means they 242 00:12:49,300 --> 00:12:50,920 have different energies. 243 00:12:50,920 --> 00:12:53,600 And why do we call this the Boltzmann constant? 244 00:12:53,600 --> 00:12:56,730 Because Boltzmann made the link between particle energy 245 00:12:56,730 --> 00:12:57,850 and temperature. 246 00:12:57,850 --> 00:13:01,140 So he said there's a variation of instant temperature. 247 00:13:01,140 --> 00:13:02,200 All right? 248 00:13:02,200 --> 00:13:13,700 So Boltzmann generalized Maxwell's idea to energy and 249 00:13:13,700 --> 00:13:17,360 then ultimately temperature. 250 00:13:17,360 --> 00:13:21,430 And so I'm going to show you, instead of the Maxwell 251 00:13:21,430 --> 00:13:25,440 distribution, I'm going to give you the Maxwell-Boltzmann 252 00:13:25,440 --> 00:13:26,630 distribution. 253 00:13:26,630 --> 00:13:28,480 But before I do, I want to make sure you understand the 254 00:13:28,480 --> 00:13:32,510 math and appreciate what I'm going to plot for you. 255 00:13:32,510 --> 00:13:34,790 So we just had a test, right? 256 00:13:34,790 --> 00:13:38,560 In fact, we can go back to the slide. 257 00:13:38,560 --> 00:13:39,400 All right. 258 00:13:39,400 --> 00:13:40,790 So what do we have here? 259 00:13:40,790 --> 00:13:45,010 I could plot on this axis, the abscissa, the grade-- 260 00:13:45,010 --> 00:13:46,200 g-- 261 00:13:46,200 --> 00:13:50,320 and on the ordinate, I'll plot the number of people who have 262 00:13:50,320 --> 00:13:51,730 any given grade-- 263 00:13:51,730 --> 00:13:52,700 n of g. 264 00:13:52,700 --> 00:13:57,520 Now the class av was 66, all right? 265 00:13:57,520 --> 00:14:00,350 This is going to go from 0 to 100. 266 00:14:00,350 --> 00:14:02,400 Now what we see here is-- and by the way, I'm going to 267 00:14:02,400 --> 00:14:03,150 normalize it. 268 00:14:03,150 --> 00:14:06,670 Instead of dealing with 463 or whatever, I'm going to divide 269 00:14:06,670 --> 00:14:08,100 by the total class. 270 00:14:08,100 --> 00:14:10,855 So the number is going to go from 0 to 1. 271 00:14:10,855 --> 00:14:13,060 So this a normalized distribution. 272 00:14:13,060 --> 00:14:15,450 What I'm teaching you applies all through science. 273 00:14:15,450 --> 00:14:17,400 As I told you, this is the most important class. 274 00:14:17,400 --> 00:14:20,100 Not because I'm teaching, but because the subject matter is 275 00:14:20,100 --> 00:14:22,160 general, just as Boltzmann did. 276 00:14:22,160 --> 00:14:24,820 So let's look at the normalized distribution. 277 00:14:24,820 --> 00:14:28,100 Now the class av was 66. 278 00:14:28,100 --> 00:14:30,910 Now we didn't have everybody getting 66. 279 00:14:30,910 --> 00:14:32,560 That was not the distribution. 280 00:14:32,560 --> 00:14:35,160 That's one solution to the problem, isn't it? 281 00:14:35,160 --> 00:14:37,930 Instead, what we got was we got that. 282 00:14:37,930 --> 00:14:41,280 Now one possibility would be this one, 283 00:14:41,280 --> 00:14:43,610 the bell-shaped curve. 284 00:14:43,610 --> 00:14:45,600 Goes like this. 285 00:14:45,600 --> 00:14:46,450 That's bell-shaped. 286 00:14:46,450 --> 00:14:49,230 This is Gaussian. 287 00:14:49,230 --> 00:14:52,240 This is a Gaussian distribution, and its 288 00:14:52,240 --> 00:14:57,410 functionality is y equals e to the minus x minus x average, 289 00:14:57,410 --> 00:15:00,670 quantity squared. 290 00:15:00,670 --> 00:15:03,570 Now, to have a normal distribution, you have to have 291 00:15:03,570 --> 00:15:07,560 a class of normal people, so that didn't happen on this 292 00:15:07,560 --> 00:15:10,320 test. That's a joke. 293 00:15:10,320 --> 00:15:13,500 God, you're so serious. 294 00:15:13,500 --> 00:15:15,380 Have you no fun in your lives? 295 00:15:15,380 --> 00:15:16,580 Have you ever laughed? 296 00:15:16,580 --> 00:15:19,550 AUDIENCE: [LAUGHTER] 297 00:15:19,550 --> 00:15:21,460 PROFESSOR: Overachievers, you. 298 00:15:21,460 --> 00:15:21,860 OK. 299 00:15:21,860 --> 00:15:24,132 So we're not going to have a Gaussian distribution. 300 00:15:24,132 --> 00:15:25,560 We're going to have that one there. 301 00:15:25,560 --> 00:15:29,830 It's kind of a skewed Gaussian with a long tail. 302 00:15:29,830 --> 00:15:32,130 All right, so that's the one thing. 303 00:15:32,130 --> 00:15:39,310 But what Boltzmann gave us, instead of the number of atoms 304 00:15:39,310 --> 00:15:42,780 of a given grade, he plotted it as a function of energy. 305 00:15:42,780 --> 00:15:45,690 So instead, the Maxwell-Boltzmann distribution 306 00:15:45,690 --> 00:15:49,070 has energy as the ordinate instead of the grade, and up 307 00:15:49,070 --> 00:15:50,890 here, the number of atoms-- 308 00:15:50,890 --> 00:15:52,530 or more importantly-- 309 00:15:52,530 --> 00:15:53,790 the atom fraction. 310 00:15:53,790 --> 00:15:56,660 The fraction of atoms in the distribution 311 00:15:56,660 --> 00:16:00,890 that have that energy. 312 00:16:00,890 --> 00:16:02,695 And it doesn't look like a normal distribution. 313 00:16:02,695 --> 00:16:04,810 It looks sort of off-normal. 314 00:16:04,810 --> 00:16:05,480 Skewed, like this. 315 00:16:05,480 --> 00:16:10,420 It rises to a peak and it has a long tail that 316 00:16:10,420 --> 00:16:12,450 moves off to the right. 317 00:16:12,450 --> 00:16:14,820 So this is the Maxwell-Boltzmann 318 00:16:14,820 --> 00:16:16,500 distribution. 319 00:16:16,500 --> 00:16:19,960 It's not y equals x minus x bar squared. 320 00:16:19,960 --> 00:16:29,730 So this is Maxwell-Boltzmann distribution of energies. 321 00:16:29,730 --> 00:16:35,010 And furthermore, what we see here is that the area under 322 00:16:35,010 --> 00:16:37,030 this line has to equal 1. 323 00:16:37,030 --> 00:16:40,710 If you integrate the fraction from 0 to infinity, because 324 00:16:40,710 --> 00:16:45,490 this asymptotically goes out to infinity, the integral 325 00:16:45,490 --> 00:16:47,040 under this line is 1. 326 00:16:47,040 --> 00:16:47,560 OK. 327 00:16:47,560 --> 00:16:53,570 Area equals 1, which is the integral of ndE. 328 00:16:53,570 --> 00:16:57,830 Now, because of the asymmetry here, clearly this is the 329 00:16:57,830 --> 00:16:58,730 average energy. 330 00:16:58,730 --> 00:17:01,450 The average energy isn't the maximum energy. 331 00:17:01,450 --> 00:17:03,860 Whereas in the Gaussian-- 332 00:17:03,860 --> 00:17:06,090 let's keep the Gaussian over here, just for grins and 333 00:17:06,090 --> 00:17:08,520 chuckles-- so the Gaussian looks like this. 334 00:17:08,520 --> 00:17:09,650 It's symmetric. 335 00:17:09,650 --> 00:17:21,550 And this is the n of g max and also a g average, whereas 336 00:17:21,550 --> 00:17:25,610 here, the average is a little bit to the right. 337 00:17:25,610 --> 00:17:27,160 A little bit higher. 338 00:17:27,160 --> 00:17:28,160 OK. 339 00:17:28,160 --> 00:17:32,590 So now, if this is the distribution, and this at room 340 00:17:32,590 --> 00:17:37,810 temperature is 1/40 of an electron volt, and way, way up 341 00:17:37,810 --> 00:17:43,210 here is the band gap energy, there's a tiny but non-zero 342 00:17:43,210 --> 00:17:47,910 fraction of this distribution that has energy in excess of 343 00:17:47,910 --> 00:17:49,580 the band gap energy. 344 00:17:49,580 --> 00:17:54,930 And so this tiny fraction of the total distribution has the 345 00:17:54,930 --> 00:17:57,660 thermal energy to allow this excitation and pair 346 00:17:57,660 --> 00:18:00,300 generation to occur. 347 00:18:00,300 --> 00:18:02,842 And furthermore, this is a function of temperature. 348 00:18:02,842 --> 00:18:04,510 This is a function of temperature. 349 00:18:04,510 --> 00:18:08,365 So E average is related to temperature. 350 00:18:08,365 --> 00:18:13,055 So, I'll say E average 1 at T1. 351 00:18:13,055 --> 00:18:15,210 And then what I'm going to do is I'm going to heat this to a 352 00:18:15,210 --> 00:18:17,330 higher temperature, so I'll use red chalk to 353 00:18:17,330 --> 00:18:18,740 indicate it's hotter. 354 00:18:18,740 --> 00:18:22,250 And what happens to the distribution under an increase 355 00:18:22,250 --> 00:18:23,110 in temperature? 356 00:18:23,110 --> 00:18:25,780 Well, the average had better move to the right, and that's 357 00:18:25,780 --> 00:18:26,530 what happens. 358 00:18:26,530 --> 00:18:28,990 But it doesn't just move to the right, it skews a little 359 00:18:28,990 --> 00:18:30,360 bit and broadens. 360 00:18:30,360 --> 00:18:32,660 So in point of fact, at a higher temperature, 361 00:18:32,660 --> 00:18:33,910 it looks like this. 362 00:18:37,680 --> 00:18:37,850 OK. 363 00:18:37,850 --> 00:18:44,930 So this is now E average 2 at T2 where T2 is 364 00:18:44,930 --> 00:18:46,900 greater than T1. 365 00:18:46,900 --> 00:18:49,360 T2 is greater than T1. 366 00:18:49,360 --> 00:18:51,450 OK, so that's the Maxwell-Boltzmann 367 00:18:51,450 --> 00:18:52,320 distribution. 368 00:18:52,320 --> 00:18:54,330 But here's where the interesting stuff occurs. 369 00:18:54,330 --> 00:19:00,790 So I'm going to blow up this high energy end of the 370 00:19:00,790 --> 00:19:02,040 distribution. 371 00:19:02,040 --> 00:19:05,040 So again, this is going to be n of E 372 00:19:05,040 --> 00:19:08,390 normalized, and this is E. 373 00:19:08,390 --> 00:19:13,360 And what we're going to find here is that at T1-- 374 00:19:13,360 --> 00:19:17,930 this is the curve at T1, and the area under the line is 375 00:19:17,930 --> 00:19:19,370 shown here-- 376 00:19:19,370 --> 00:19:22,410 and then-- 377 00:19:22,410 --> 00:19:26,050 not to scale-- 378 00:19:26,050 --> 00:19:27,550 we're going to put a break in this. 379 00:19:27,550 --> 00:19:30,550 And I'll show you how much of a break is needed. 380 00:19:30,550 --> 00:19:35,960 And then, at T2 I'm going to have this come down. 381 00:19:35,960 --> 00:19:37,450 This is T2. 382 00:19:37,450 --> 00:19:41,640 And the area under the line T2 captures the 383 00:19:41,640 --> 00:19:43,690 T1 plus all of this. 384 00:19:48,350 --> 00:19:51,930 And so what we see, is that for a modest increase in 385 00:19:51,930 --> 00:19:56,790 temperature, this maximum shifts modestly, but the area 386 00:19:56,790 --> 00:19:59,800 under the line in excess of this critical 387 00:19:59,800 --> 00:20:02,850 energy increases radically. 388 00:20:02,850 --> 00:20:06,460 And that's the powerful leveraging factor of increase 389 00:20:06,460 --> 00:20:06,850 in temperature. 390 00:20:06,850 --> 00:20:10,620 And I've done some calculations just to show you 391 00:20:10,620 --> 00:20:12,840 what this does. 392 00:20:12,840 --> 00:20:17,920 The functionality of the Maxwell-Boltzmann distribution 393 00:20:17,920 --> 00:20:29,800 is e to the minus some critical energy divided by the 394 00:20:29,800 --> 00:20:32,220 product of Boltzmann constant temperature. 395 00:20:32,220 --> 00:20:35,100 So we can put in a value here-- eg-- 396 00:20:35,100 --> 00:20:36,330 what have you. 397 00:20:36,330 --> 00:20:36,620 All right. 398 00:20:36,620 --> 00:20:39,180 So I chose for silicon-- 399 00:20:39,180 --> 00:20:43,780 for silicon, I know the band gap energy is 1.1 eV-- 400 00:20:43,780 --> 00:20:49,340 and I have it at room temperature-- 401 00:20:49,340 --> 00:20:51,380 when I go through the calculation-- 402 00:20:51,380 --> 00:20:55,750 the fraction underneath that line is 10 to the minus 19. 403 00:20:55,750 --> 00:20:58,350 One part in 10 to the minus 19. 404 00:20:58,350 --> 00:21:00,370 This is the area. 405 00:21:00,370 --> 00:21:07,200 Area under the curve is greater than the band gap 406 00:21:07,200 --> 00:21:10,810 energy of 1.1 eV. 407 00:21:10,810 --> 00:21:14,440 So then I said, let's go up to the melting point. 408 00:21:14,440 --> 00:21:16,390 I'm not going to melt the silicon, I'm just going to 409 00:21:16,390 --> 00:21:18,580 bring it up to its melting point but not melt it. 410 00:21:18,580 --> 00:21:20,830 So it's like ice cubes at 0 Celsius. 411 00:21:20,830 --> 00:21:22,330 It's still solid. 412 00:21:22,330 --> 00:21:22,630 OK? 413 00:21:22,630 --> 00:21:24,710 The melting point of silicon, you can look in your Periodic 414 00:21:24,710 --> 00:21:26,880 Table, it's over 1400 degrees C. 415 00:21:26,880 --> 00:21:30,240 And this is 10 to the minus 4. 416 00:21:30,240 --> 00:21:32,460 10 to the minus 4. 417 00:21:32,460 --> 00:21:34,880 Area under curve: da da da da. 418 00:21:34,880 --> 00:21:37,360 So that means that the red area-- 419 00:21:37,360 --> 00:21:38,760 A2, the red. 420 00:21:38,760 --> 00:21:42,240 Actually, let's use red chalk so that everybody is in tune. 421 00:21:42,240 --> 00:21:52,970 A2 to A1 is equal to 10 to the 15, whereas T2 over T1-- 422 00:21:52,970 --> 00:21:54,752 well, red chalk. 423 00:21:54,752 --> 00:21:57,160 It's my chance to use red chalk and I'm not going to 424 00:21:57,160 --> 00:21:58,100 squander it. 425 00:21:58,100 --> 00:22:01,510 T2 divided by T1-- 426 00:22:01,510 --> 00:22:05,140 it's about 1700 Kelvin divided by 300 Kelvin-- 427 00:22:05,140 --> 00:22:07,240 is about 6. 428 00:22:07,240 --> 00:22:10,570 So for a change in temperature by a factor of 6, I get a 429 00:22:10,570 --> 00:22:14,265 change in population of 10 to the 15. 430 00:22:14,265 --> 00:22:17,410 So you can see how modest increases in temperature have 431 00:22:17,410 --> 00:22:22,340 a huge impact on thermal excitation. 432 00:22:22,340 --> 00:22:27,650 So now you say, if we wanted to make a device, we can't 433 00:22:27,650 --> 00:22:33,350 heat our computers up to 1600 degrees, 1500 degrees C in 434 00:22:33,350 --> 00:22:35,970 order to get an adequate number of charge carriers. 435 00:22:35,970 --> 00:22:37,980 There has to be another way to get charge carriers. 436 00:22:37,980 --> 00:22:39,750 I'm going to show you a third way that's 437 00:22:39,750 --> 00:22:43,430 called chemical promotion. 438 00:22:43,430 --> 00:22:48,470 So now I want to talk about charge carrier generation. 439 00:22:48,470 --> 00:22:57,670 Charge carrier generation by change of chemistry, and it's 440 00:22:57,670 --> 00:23:03,810 going to be specifically by the introduction of 441 00:23:03,810 --> 00:23:06,140 impurities. 442 00:23:06,140 --> 00:23:09,410 Charge carrier generation by introduction of impurities. 443 00:23:09,410 --> 00:23:12,800 You might say, gee, aren't impurities bad for a system? 444 00:23:12,800 --> 00:23:14,950 Well, I want to tell you, there are two kinds of 445 00:23:14,950 --> 00:23:16,750 impurities in this world. 446 00:23:16,750 --> 00:23:21,630 There are bad impurities which we call contaminants, and 447 00:23:21,630 --> 00:23:25,150 that's what you're commonly taught to think about. 448 00:23:25,150 --> 00:23:26,060 That's bad. 449 00:23:26,060 --> 00:23:30,230 But there are good impurities, and these are called dopants. 450 00:23:30,230 --> 00:23:33,880 Dopants are impurities that we are happy 451 00:23:33,880 --> 00:23:37,330 to have in our system. 452 00:23:37,330 --> 00:23:42,280 And so by the introduction of impurities of value, we can 453 00:23:42,280 --> 00:23:47,020 lead to engineered materials. 454 00:23:49,980 --> 00:23:52,700 So I'm giving you the introduction to high 455 00:23:52,700 --> 00:23:56,660 technology, where we're going to control the engineering 456 00:23:56,660 --> 00:24:00,960 properties of a material through control of chemistry. 457 00:24:00,960 --> 00:24:10,780 So that's chemical composition tailored-- 458 00:24:10,780 --> 00:24:12,030 for specific-- 459 00:24:18,040 --> 00:24:24,240 for targeted values of properties. 460 00:24:24,240 --> 00:24:27,210 And that's the essence of material science. 461 00:24:27,210 --> 00:24:28,840 We control the chemistry. 462 00:24:28,840 --> 00:24:33,670 We control the properties by controlling the chemistry. 463 00:24:33,670 --> 00:24:37,750 So what I want to do is give a vivid example of this, and 464 00:24:37,750 --> 00:24:39,130 it's not going to be an isolated example. 465 00:24:39,130 --> 00:24:41,910 It's going to be the example that pertains to all of the 466 00:24:41,910 --> 00:24:44,080 microelectronic devices in our world. 467 00:24:44,080 --> 00:24:45,340 So that's silicon. 468 00:24:45,340 --> 00:24:49,700 So let's look at how doping works in silicon. 469 00:24:49,700 --> 00:24:52,810 It also applies to germanium, but we don't use much 470 00:24:52,810 --> 00:24:53,970 germanium in devices. 471 00:24:53,970 --> 00:24:55,960 It's dominantly silicon. 472 00:24:55,960 --> 00:24:58,910 So what we're going to do is dope. 473 00:24:58,910 --> 00:25:02,030 The gambit here is to dope-- 474 00:25:02,030 --> 00:25:03,470 that's introduce an impurity-- 475 00:25:03,470 --> 00:25:08,880 with aliovalent impurity. 476 00:25:08,880 --> 00:25:10,450 What do I mean by aliovalent? 477 00:25:10,450 --> 00:25:13,100 You know the word alias? 478 00:25:13,100 --> 00:25:14,080 It's another name. 479 00:25:14,080 --> 00:25:15,690 Alio in Latin means other. 480 00:25:15,690 --> 00:25:18,300 So we're going to dope silicon with something that has a 481 00:25:18,300 --> 00:25:19,980 different valence from that of silicon. 482 00:25:19,980 --> 00:25:21,400 Can't before. 483 00:25:21,400 --> 00:25:24,770 So let's look at the simplest example. 484 00:25:24,770 --> 00:25:28,840 And I'm going to put phosphorus into silicon. 485 00:25:28,840 --> 00:25:31,760 I'm going to dope phosphorus into silicon, and phosphorus 486 00:25:31,760 --> 00:25:35,740 is Group 5, or more properly, IUPAC calls it Group 15. 487 00:25:35,740 --> 00:25:39,290 So we're going to put Group 15 element into silicon, which is 488 00:25:39,290 --> 00:25:40,330 Group 14 element. 489 00:25:40,330 --> 00:25:43,920 So we call phosphorus a supervalent dopant, meaning it 490 00:25:43,920 --> 00:25:49,390 has a valence higher than that of the silicon. 491 00:25:49,390 --> 00:25:53,090 So it's a supervalent dopant. 492 00:25:53,090 --> 00:25:54,830 Supervalent dopant. 493 00:25:54,830 --> 00:25:57,450 So now let's look at how that supervalent dopant works. 494 00:25:57,450 --> 00:26:01,730 I'm going to show you some silicon here, and I'm going to 495 00:26:01,730 --> 00:26:03,290 give you the silicon. 496 00:26:03,290 --> 00:26:07,340 This is sp3 hybridized. 497 00:26:07,340 --> 00:26:12,110 it's sitting here as a single crystal. 498 00:26:18,240 --> 00:26:18,960 Here are three silicons. 499 00:26:18,960 --> 00:26:20,100 So it's a single crystal. 500 00:26:20,100 --> 00:26:22,620 All these silicons on the bottom row line up. 501 00:26:22,620 --> 00:26:24,860 All the silicons in the center line up. 502 00:26:24,860 --> 00:26:28,220 And there are silicons at the top and they all line up. 503 00:26:28,220 --> 00:26:31,390 So that if I look at it on the edge, it's a perfectly, 504 00:26:31,390 --> 00:26:33,440 atomically smooth system. 505 00:26:33,440 --> 00:26:35,220 And I have one of these. 506 00:26:35,220 --> 00:26:38,110 I know Professor Ballinger made reference to it last day. 507 00:26:38,110 --> 00:26:39,990 This is last-generation technology. 508 00:26:39,990 --> 00:26:41,640 It's only eight-inch diameter. 509 00:26:41,640 --> 00:26:45,440 But this is an eight-inch diameter silicon wafer. 510 00:26:45,440 --> 00:26:48,070 So this started as a giant salami, eight inches in 511 00:26:48,070 --> 00:26:50,460 diameter-- probably two meters long. 512 00:26:50,460 --> 00:26:52,040 Single crystal. 513 00:26:52,040 --> 00:26:56,710 Every atom here is adjacent to the next atom according to the 514 00:26:56,710 --> 00:26:59,220 rules of atomic arrangement. 515 00:26:59,220 --> 00:27:01,320 And when this thing is cut and polished, 516 00:27:01,320 --> 00:27:03,680 it's flat to one atom. 517 00:27:03,680 --> 00:27:05,390 It is atomically flat. 518 00:27:05,390 --> 00:27:09,600 And it makes a fantastic shaving mirror. 519 00:27:09,600 --> 00:27:11,510 Actually Dave, can you cut to this? 520 00:27:11,510 --> 00:27:12,550 Yeah, here we go. 521 00:27:12,550 --> 00:27:14,250 Here's the penny. 522 00:27:14,250 --> 00:27:15,430 And this is silicon here. 523 00:27:15,430 --> 00:27:19,080 It's going to drive this thing nuts because it can't focus on 524 00:27:19,080 --> 00:27:21,400 this thing, because it's so-- 525 00:27:21,400 --> 00:27:22,500 there we are. 526 00:27:22,500 --> 00:27:26,850 So this was a part of a giant salami, and now it's been cut. 527 00:27:26,850 --> 00:27:29,560 And obviously you can't cut it one-atom thick. 528 00:27:29,560 --> 00:27:32,380 It's some submillimeter thickness, because you need to 529 00:27:32,380 --> 00:27:34,580 have some mechanical strength to it. 530 00:27:34,580 --> 00:27:37,740 But the surface is absolutely flat to one atom. 531 00:27:37,740 --> 00:27:38,470 All right. 532 00:27:38,470 --> 00:27:40,060 And that's what we're going to dope into. 533 00:27:40,060 --> 00:27:42,290 We're going to dope into this thing, and I'll show you how 534 00:27:42,290 --> 00:27:43,350 we're going to dope it later. 535 00:27:43,350 --> 00:27:45,710 Actually, why don't we cut to that. 536 00:27:45,710 --> 00:27:49,190 Here's something that's already been doped and made 537 00:27:49,190 --> 00:27:50,310 into devices. 538 00:27:50,310 --> 00:27:52,500 So there's the plain old silicon, which you're having a 539 00:27:52,500 --> 00:27:54,600 hard time seeing anything except a little bit of 540 00:27:54,600 --> 00:27:55,590 reflection. 541 00:27:55,590 --> 00:27:58,290 And now here's the thing that's been processed, so 542 00:27:58,290 --> 00:28:00,190 let's zoom. 543 00:28:00,190 --> 00:28:01,440 Zoom. 544 00:28:03,630 --> 00:28:04,250 OK. 545 00:28:04,250 --> 00:28:06,600 So now you can see all the features. 546 00:28:06,600 --> 00:28:11,480 So these features involved gas phase reaction to introduce 547 00:28:11,480 --> 00:28:14,740 dopant atoms into the silicon lattice. 548 00:28:14,740 --> 00:28:16,630 And then we're going to chop these little things up and put 549 00:28:16,630 --> 00:28:20,280 them in your cell phones and in your laptops and whatever 550 00:28:20,280 --> 00:28:22,210 other devices are out there. 551 00:28:22,210 --> 00:28:22,500 OK. 552 00:28:22,500 --> 00:28:24,770 So this is what we're talking about, and if we live long 553 00:28:24,770 --> 00:28:26,320 enough, we'll see one of these. 554 00:28:26,320 --> 00:28:28,330 This is a Pentium chip. 555 00:28:28,330 --> 00:28:28,520 OK. 556 00:28:28,520 --> 00:28:29,920 So where's the chip? 557 00:28:29,920 --> 00:28:32,640 The chip is underneath this piece of gold. 558 00:28:32,640 --> 00:28:33,890 Where did I put my pointer? 559 00:28:36,490 --> 00:28:37,780 Ah, it's over here. 560 00:28:37,780 --> 00:28:38,520 All right. 561 00:28:38,520 --> 00:28:43,610 So the actual silicon device is underneath this. 562 00:28:43,610 --> 00:28:47,120 And all of these are this spider's web of leads. 563 00:28:47,120 --> 00:28:49,700 It's trying to access all the tiny devices. 564 00:28:49,700 --> 00:28:52,870 It doesn't do you any good to have a device density that's 565 00:28:52,870 --> 00:28:55,110 greater than your access density. 566 00:28:55,110 --> 00:28:58,010 So the technology that goes into this is phenomenal. 567 00:28:58,010 --> 00:29:01,400 Plus, these things all generate heat. 568 00:29:01,400 --> 00:29:05,260 When you put all these tens of thousands of devices into 569 00:29:05,260 --> 00:29:07,230 something the size of your fingernail, you've got a 570 00:29:07,230 --> 00:29:12,660 toaster oven working here, and you have to get that heat out. 571 00:29:12,660 --> 00:29:15,560 And this is several generations old. 572 00:29:15,560 --> 00:29:17,500 What you have in your machines today is 573 00:29:17,500 --> 00:29:19,760 even denser than this. 574 00:29:19,760 --> 00:29:20,880 And supercomputers? 575 00:29:20,880 --> 00:29:21,440 Forget it. 576 00:29:21,440 --> 00:29:24,830 You have to have those things so aggressively cooled or else 577 00:29:24,830 --> 00:29:27,200 they'll heat up and it'll be just like a 578 00:29:27,200 --> 00:29:29,530 light bulb, just bursting. 579 00:29:29,530 --> 00:29:30,920 So that's what's going on inside. 580 00:29:30,920 --> 00:29:32,720 So let's see how that happens. 581 00:29:32,720 --> 00:29:34,560 Let's cut back to-- well, you can leave that up. 582 00:29:34,560 --> 00:29:37,053 It's a pretty image and will probably soothe the nerves of 583 00:29:37,053 --> 00:29:38,590 the students. 584 00:29:38,590 --> 00:29:40,515 So now I'm going to put phosphorus in here. 585 00:29:40,515 --> 00:29:43,570 I'll put phosphorus in here, but where does phosphorus go? 586 00:29:43,570 --> 00:29:46,490 Phosphorus goes onto a silicon site. 587 00:29:46,490 --> 00:29:49,260 So it actually comes in and sits here. 588 00:29:49,260 --> 00:29:52,000 Phosphorus comes and sits at a silicon site. 589 00:29:52,000 --> 00:29:54,170 Now what do we know about the number of bonds that 590 00:29:54,170 --> 00:29:56,110 phosphorus likes to form? 591 00:29:56,110 --> 00:29:58,340 It has five valence electrons. 592 00:29:58,340 --> 00:30:01,500 So it forms one, two, three, four bonds, and 593 00:30:01,500 --> 00:30:03,650 it has a fifth electron. 594 00:30:03,650 --> 00:30:07,500 And that fifth electron is sitting there somewhere. 595 00:30:07,500 --> 00:30:13,860 It's sitting there somewhere in the lattice. 596 00:30:13,860 --> 00:30:15,130 All right. 597 00:30:15,130 --> 00:30:16,970 It's sitting somewhere in the lattice because it has no 598 00:30:16,970 --> 00:30:18,070 place to go. 599 00:30:18,070 --> 00:30:20,370 Now in energy space, I know where it goes. 600 00:30:20,370 --> 00:30:24,220 So here's the conduction band of silicon, and this is the 601 00:30:24,220 --> 00:30:25,850 valence band. 602 00:30:25,850 --> 00:30:31,700 And this is all of the silicon host crystal, because the 603 00:30:31,700 --> 00:30:34,750 dopant is in a tiny, tiny amount. 604 00:30:34,750 --> 00:30:36,540 We're talking parts per million. 605 00:30:36,540 --> 00:30:38,120 So for all intents and purposes, it's 606 00:30:38,120 --> 00:30:39,310 still a silicon crystal. 607 00:30:39,310 --> 00:30:41,700 It has tiny amounts of phosphorus in it. 608 00:30:41,700 --> 00:30:47,090 So this is the band gap of silicon, where this is about 609 00:30:47,090 --> 00:30:48,700 1.1 electron volts. 610 00:30:48,700 --> 00:30:50,640 And where does this fifth electron go? 611 00:30:50,640 --> 00:30:53,220 This fifth electron sits up in here in the conduction band, 612 00:30:53,220 --> 00:30:54,440 doesn't it? 613 00:30:54,440 --> 00:30:57,050 And every time I introduce a phosphorus, I have a fifth 614 00:30:57,050 --> 00:31:00,220 electron that goes in the conduction band. 615 00:31:00,220 --> 00:31:03,240 But I don't have to generate a hole. 616 00:31:03,240 --> 00:31:06,490 I don't need to break bonds in order to put electrons in the 617 00:31:06,490 --> 00:31:07,860 conduction band. 618 00:31:07,860 --> 00:31:11,060 Because the fifth electron is like the fifth wheel. 619 00:31:11,060 --> 00:31:11,790 You know? 620 00:31:11,790 --> 00:31:13,810 It goes in the conduction band. 621 00:31:13,810 --> 00:31:16,045 So there's no generation of holes here. 622 00:31:16,045 --> 00:31:16,980 All right. 623 00:31:16,980 --> 00:31:20,575 And furthermore, I can control the conductivity. 624 00:31:20,575 --> 00:31:23,030 At the end of last lecture, Professor Ballinger showed you 625 00:31:23,030 --> 00:31:26,480 that the conductivity of a substance is related to the 626 00:31:26,480 --> 00:31:28,000 number of charge carriers. 627 00:31:28,000 --> 00:31:31,500 So if I want to double the number of phosphoruses, I will 628 00:31:31,500 --> 00:31:34,740 double the number of electrons in the conduction band, 629 00:31:34,740 --> 00:31:36,260 independent of temperature. 630 00:31:36,260 --> 00:31:37,090 All right. 631 00:31:37,090 --> 00:31:48,920 So for every phosphorus dopant atom, we get one electron in 632 00:31:48,920 --> 00:31:51,070 the conduction band. 633 00:31:51,070 --> 00:31:54,425 We get one electron in the conduction band and no holes. 634 00:31:58,980 --> 00:32:04,140 No holes in the valence band. 635 00:32:04,140 --> 00:32:05,520 It's direct. 636 00:32:05,520 --> 00:32:06,770 It's direct. 637 00:32:06,770 --> 00:32:07,880 All right. 638 00:32:07,880 --> 00:32:12,260 Now, electrical engineers would look at this and they'd 639 00:32:12,260 --> 00:32:13,840 say, I don't care if it's phosphorus. 640 00:32:13,840 --> 00:32:15,880 They don't care about the chemistry, they care about the 641 00:32:15,880 --> 00:32:17,390 functionality. 642 00:32:17,390 --> 00:32:20,990 What kind of carriers am I throwing into this crystal? 643 00:32:20,990 --> 00:32:22,490 For an electrical engineer, there are only 644 00:32:22,490 --> 00:32:23,740 two kinds of carriers. 645 00:32:23,740 --> 00:32:25,730 Positive carriers and negative carriers. 646 00:32:25,730 --> 00:32:28,280 For every phosphorus, what's the outcome? 647 00:32:28,280 --> 00:32:29,230 A negative carrier. 648 00:32:29,230 --> 00:32:33,250 So this is now doped silicon. 649 00:32:33,250 --> 00:32:35,520 It generated negative carriers, so 650 00:32:35,520 --> 00:32:38,300 this is called n-type. 651 00:32:38,300 --> 00:32:40,990 This is now n-type silicon. 652 00:32:40,990 --> 00:32:45,850 And its properties are governed by the population of 653 00:32:45,850 --> 00:32:47,630 these-- because I'm going to show you in a second that the 654 00:32:47,630 --> 00:32:51,210 number of these far exceeds the number that are thermally 655 00:32:51,210 --> 00:32:51,940 generated-- 656 00:32:51,940 --> 00:32:54,585 so the properties here are called extrinsic. 657 00:32:54,585 --> 00:32:59,600 So now we have a crystal that is exhibiting it's extrinsic 658 00:32:59,600 --> 00:33:03,550 behavior, thanks to the doping with the supervalent impurity. 659 00:33:06,280 --> 00:33:07,440 One more thing. 660 00:33:07,440 --> 00:33:09,090 One more thing. 661 00:33:09,090 --> 00:33:11,180 Something very, very cool here. 662 00:33:11,180 --> 00:33:13,690 You see this electron? 663 00:33:13,690 --> 00:33:15,390 It's sitting here somewhere in the-- 664 00:33:15,390 --> 00:33:18,310 now this is Cartesian map. 665 00:33:18,310 --> 00:33:20,540 I'm looking through a scanning electron microscope. 666 00:33:20,540 --> 00:33:21,400 I see all the silicons. 667 00:33:21,400 --> 00:33:22,580 I get the phosphorus. 668 00:33:22,580 --> 00:33:25,120 And there's an electron in here somewhere. 669 00:33:25,120 --> 00:33:27,610 And this has 15, right? 670 00:33:27,610 --> 00:33:28,670 This has 15 protons. 671 00:33:28,670 --> 00:33:30,690 This has 14 protons. 672 00:33:30,690 --> 00:33:36,110 So in a land of 14 plus, 15 plus is relatively 673 00:33:36,110 --> 00:33:37,630 positive, isn't it? 674 00:33:37,630 --> 00:33:40,480 The phosphorus is locally positive in comparison with 675 00:33:40,480 --> 00:33:42,800 the rest of the silicon lattice. 676 00:33:42,800 --> 00:33:45,690 And it's pinned, because it's covalently bonded. 677 00:33:45,690 --> 00:33:47,360 And there's an electron sitting here 678 00:33:47,360 --> 00:33:49,620 with no place to go. 679 00:33:49,620 --> 00:33:53,570 Do you know of a model that describes the behavior of a 680 00:33:53,570 --> 00:33:58,380 one-electron system around a pinned positive nucleus? 681 00:33:58,380 --> 00:33:59,510 AUDIENCE: The Bohr model. 682 00:33:59,510 --> 00:34:00,470 PROFESSOR: Bohr model? 683 00:34:00,470 --> 00:34:03,330 Just for grins and chuckles, what if we were to use the 684 00:34:03,330 --> 00:34:07,260 Bohr model to describe the behavior of that electron? 685 00:34:07,260 --> 00:34:09,080 You can say it's crazy. 686 00:34:09,080 --> 00:34:11,910 That doesn't make any sense, because that's not a 687 00:34:11,910 --> 00:34:12,700 one-electron system. 688 00:34:12,700 --> 00:34:17,880 But what if we modeled it as though it were? 689 00:34:17,880 --> 00:34:20,130 I'm going to-- just for grins and chuckles-- get a sense of 690 00:34:20,130 --> 00:34:22,210 what that ground state value is. 691 00:34:22,210 --> 00:34:29,900 And recall that in hydrogen, the ground state-- 692 00:34:29,900 --> 00:34:32,160 E1, ground state of the electron-- 693 00:34:32,160 --> 00:34:34,780 is equal to minus k. 694 00:34:34,780 --> 00:34:41,400 Which is minus me to the fourth over 8 epsilon naught 695 00:34:41,400 --> 00:34:44,640 squared times Planck constant squared. 696 00:34:44,640 --> 00:34:49,880 Which is minus 13.6 electron volts 697 00:34:49,880 --> 00:34:54,530 So what is the energy of that electron there if we use the 698 00:34:54,530 --> 00:34:55,160 Bohr model? 699 00:34:55,160 --> 00:34:57,800 Well, we have to modify it a little bit, because the 700 00:34:57,800 --> 00:35:00,220 electron isn't moving in a vacuum. 701 00:35:00,220 --> 00:35:02,970 Depending on how far this electron is from the center, 702 00:35:02,970 --> 00:35:05,300 it could be moving around, and there are all kinds of silicon 703 00:35:05,300 --> 00:35:07,160 atoms and bonds and whatnot. 704 00:35:07,160 --> 00:35:10,022 So there are all kinds of stuff between the electron and 705 00:35:10,022 --> 00:35:10,860 the center here. 706 00:35:10,860 --> 00:35:12,460 So I have to use a modified form. 707 00:35:12,460 --> 00:35:15,260 I don't use the permittivity of vacuum. 708 00:35:15,260 --> 00:35:17,620 I map the permittivity of vacuum into 709 00:35:17,620 --> 00:35:19,350 the dielectric constant. 710 00:35:19,350 --> 00:35:27,360 This is the dielectric constant of silicon. 711 00:35:27,360 --> 00:35:30,730 Remember there's so little phosphorus there that it 712 00:35:30,730 --> 00:35:31,910 doesn't alter the properties. 713 00:35:31,910 --> 00:35:34,400 And then for reasons I can't go in to here, I have to 714 00:35:34,400 --> 00:35:37,560 change the mass of the electron into 715 00:35:37,560 --> 00:35:41,690 the effective mass-- 716 00:35:41,690 --> 00:35:46,310 we saw this when Bohr did the calculation about the lines of 717 00:35:46,310 --> 00:35:47,390 helium plus-- 718 00:35:47,390 --> 00:35:54,440 effective mass of electron in the conduction band. 719 00:35:54,440 --> 00:35:56,380 So if you put both of those in-- 720 00:35:56,380 --> 00:35:59,270 and I've got numbers for this-- 721 00:35:59,270 --> 00:36:06,150 this value is 11.7 and the second one is about 1/5 of the 722 00:36:06,150 --> 00:36:07,800 rest mass of the electron. 723 00:36:07,800 --> 00:36:12,720 So if you put all of that in, you end up with the energy of 724 00:36:12,720 --> 00:36:18,610 this ground state electron equal to minus k times 0.2 725 00:36:18,610 --> 00:36:23,340 divided by 11.7 squared, which equals minus 726 00:36:23,340 --> 00:36:26,490 0.02 electron volts. 727 00:36:26,490 --> 00:36:28,240 0.02 electron volts. 728 00:36:28,240 --> 00:36:33,070 So this is 2/100 of an electron volt below something. 729 00:36:33,070 --> 00:36:34,450 What's it below? 730 00:36:34,450 --> 00:36:36,760 It's below the conduction band. 731 00:36:36,760 --> 00:36:38,180 It's right here. 732 00:36:38,180 --> 00:36:43,700 This is the ground state of the electron from phosphorus. 733 00:36:43,700 --> 00:36:46,650 It's the ground state of the electron from phosphorus. 734 00:36:46,650 --> 00:36:53,040 E1 of electron from phosphorus. 735 00:36:53,040 --> 00:36:56,595 And phosphorus, the electrical engineers call a donor. 736 00:36:56,595 --> 00:36:58,210 A donor of what? 737 00:36:58,210 --> 00:36:59,530 It's a donor of electrons. 738 00:36:59,530 --> 00:37:05,340 So this thing here is called the donor level. 739 00:37:05,340 --> 00:37:07,330 And that's the ground state. 740 00:37:07,330 --> 00:37:08,740 So the electron should be sitting. 741 00:37:08,740 --> 00:37:10,900 Isn't the ground state here lower than the bottom of the 742 00:37:10,900 --> 00:37:12,210 conduction band? 743 00:37:12,210 --> 00:37:12,960 Sure it is. 744 00:37:12,960 --> 00:37:15,790 So the electron really should be down in here. 745 00:37:15,790 --> 00:37:17,130 There's the electron. 746 00:37:17,130 --> 00:37:19,160 Now you're saying, how are you going to get conductivity? 747 00:37:19,160 --> 00:37:25,020 Well, we just figured out that the energy level of the ground 748 00:37:25,020 --> 00:37:26,540 state of the donor-- 749 00:37:26,540 --> 00:37:33,280 so I'm going to call this the energy of the donor level, 750 00:37:33,280 --> 00:37:34,350 ground state-- 751 00:37:34,350 --> 00:37:35,600 is 0.02. 752 00:37:35,600 --> 00:37:37,730 How does that compare with thermal energy at room 753 00:37:37,730 --> 00:37:39,220 temperature? 754 00:37:39,220 --> 00:37:40,140 It's comparable. 755 00:37:40,140 --> 00:37:44,030 So at room temperature with 1/40 of an electron volt, 756 00:37:44,030 --> 00:37:48,790 there's enough energy to promote this electron up into 757 00:37:48,790 --> 00:37:52,270 the conduction band by thermal excitation 758 00:37:52,270 --> 00:37:54,170 from the donor level. 759 00:37:54,170 --> 00:37:56,080 Thermal excitation from the donor level. 760 00:37:56,080 --> 00:37:58,870 And in fact, if we want to do something really, really-- 761 00:37:58,870 --> 00:38:01,090 I want to use an adverb here-- really, really cool. 762 00:38:01,090 --> 00:38:02,600 If that's the ground state-- 763 00:38:02,600 --> 00:38:05,000 I'm going to blow this up. 764 00:38:05,000 --> 00:38:07,810 So this is the bottom of the conduction band. 765 00:38:07,810 --> 00:38:10,010 And now this is the ground state. 766 00:38:10,010 --> 00:38:12,990 This is the donor level. 767 00:38:12,990 --> 00:38:15,360 This is the donor level, which I was calling E1. 768 00:38:18,650 --> 00:38:22,210 Is it just the donor level here and the conduction band, 769 00:38:22,210 --> 00:38:27,630 or can you see that there's an E2 and an E3 and an E4? 770 00:38:27,630 --> 00:38:30,320 And I have a whole set of quantum states from the donor 771 00:38:30,320 --> 00:38:33,590 level right up to the conduction band. 772 00:38:33,590 --> 00:38:35,550 And if I have enough energy-- 773 00:38:35,550 --> 00:38:43,410 if E thermal is on the order of E donor-- 774 00:38:43,410 --> 00:38:46,030 I get promotion of these up in here. 775 00:38:46,030 --> 00:38:48,780 Now what would we say if this were the Bohr model? 776 00:38:48,780 --> 00:38:51,840 You'd have an electron loose in a ground state up in here 777 00:38:51,840 --> 00:38:54,410 where it's free to move. 778 00:38:54,410 --> 00:38:57,330 What's that process called? 779 00:38:57,330 --> 00:38:58,280 Ionization. 780 00:38:58,280 --> 00:39:00,220 And you know what the electrical engineers call 781 00:39:00,220 --> 00:39:01,450 these electrons? 782 00:39:01,450 --> 00:39:04,370 They call them ionized electrons. 783 00:39:04,370 --> 00:39:07,290 But they're referring to the ionization of the electron out 784 00:39:07,290 --> 00:39:10,160 of the donor level into the conduction band, not out of 785 00:39:10,160 --> 00:39:12,270 the silicon crystal. 786 00:39:12,270 --> 00:39:23,800 So these are ionized electrons out of donor level. 787 00:39:23,800 --> 00:39:25,440 So we've come full circle. 788 00:39:25,440 --> 00:39:27,480 By the way, this is a calculation. 789 00:39:27,480 --> 00:39:30,940 You know what the measured value is? 790 00:39:30,940 --> 00:39:37,630 It was measured as minus 0.045 electron volts. 791 00:39:37,630 --> 00:39:39,340 You might look at that and say, whoa, that's about two 792 00:39:39,340 --> 00:39:39,970 times this. 793 00:39:39,970 --> 00:39:40,560 Hey, wait a minute. 794 00:39:40,560 --> 00:39:42,650 We started at 13.6. 795 00:39:42,650 --> 00:39:47,160 We went from 13.6 to this, and the real value is this, and so 796 00:39:47,160 --> 00:39:50,590 we are in good shape. 797 00:39:50,590 --> 00:39:57,490 Now, what happens if I put another phosphorus in here? 798 00:39:57,490 --> 00:40:00,960 Another phosphorus, it's also going to sit at this-- 799 00:40:00,960 --> 00:40:02,110 I'm going to do it over here. 800 00:40:02,110 --> 00:40:03,990 If I put another phosphorus, it also has 801 00:40:03,990 --> 00:40:05,220 the same donor level. 802 00:40:05,220 --> 00:40:07,920 And another phosphorus, it has the same donor level. 803 00:40:07,920 --> 00:40:09,345 How can I justify this? 804 00:40:09,345 --> 00:40:12,810 Am I not violating the Pauli exclusion principle? 805 00:40:12,810 --> 00:40:16,120 How come all the phosphorus donor states 806 00:40:16,120 --> 00:40:18,240 are at the same level? 807 00:40:18,240 --> 00:40:21,110 Or put another way, under what circumstances is 808 00:40:21,110 --> 00:40:23,910 this diagram accurate? 809 00:40:23,910 --> 00:40:27,310 If the number of phosphorus atoms that I 810 00:40:27,310 --> 00:40:29,270 introduce is tiny-- 811 00:40:29,270 --> 00:40:30,530 parts per million-- 812 00:40:30,530 --> 00:40:34,010 the separation, the physical separation of this phosphorus 813 00:40:34,010 --> 00:40:37,190 from its nearest phosphorus neighbor is so great, that for 814 00:40:37,190 --> 00:40:40,660 all intents and purposes, they are at infinite separation. 815 00:40:40,660 --> 00:40:44,320 And therefore, all of the phosphorus donor atoms 816 00:40:44,320 --> 00:40:47,190 establish a donor level at the same value. 817 00:40:47,190 --> 00:40:52,990 And if you dope to very, very high levels, you see this 818 00:40:52,990 --> 00:40:54,000 break down. 819 00:40:54,000 --> 00:40:56,390 If you go to very, very high concentrations of phosphorus 820 00:40:56,390 --> 00:41:00,060 dopant, you will discover what happens if these two energy 821 00:41:00,060 --> 00:41:04,490 levels get close enough together in real space. 822 00:41:04,490 --> 00:41:06,030 They have to split. 823 00:41:06,030 --> 00:41:08,770 And so you'll see all of that happening down here at the 824 00:41:08,770 --> 00:41:09,570 miniature level. 825 00:41:09,570 --> 00:41:13,420 The last thing I wanted to do was to push the Bohr model 826 00:41:13,420 --> 00:41:15,170 just a little bit harder. 827 00:41:15,170 --> 00:41:18,180 And so I've given you an energy, and the energy seems 828 00:41:18,180 --> 00:41:18,870 to make sense. 829 00:41:18,870 --> 00:41:20,110 Even though you might say, this is the crazy. 830 00:41:20,110 --> 00:41:22,580 It's not a one-electron system, but it gave us a 831 00:41:22,580 --> 00:41:24,210 reasonable number. 832 00:41:24,210 --> 00:41:27,780 Let's just for interest's sake determine: what's this radius? 833 00:41:27,780 --> 00:41:33,240 I wonder how far this electron is away from the donor 834 00:41:33,240 --> 00:41:35,290 phosphorus? 835 00:41:35,290 --> 00:41:37,260 So I plug into the r1. 836 00:41:37,260 --> 00:41:40,330 That's the radius of the ground state electron. 837 00:41:40,330 --> 00:41:42,900 And that's the Bohr radius, right? 838 00:41:42,900 --> 00:41:47,440 0.529 angstroms in elemental hydrogen, but now this has to 839 00:41:47,440 --> 00:41:52,870 be modified by adding the dielectric constant and the 840 00:41:52,870 --> 00:41:54,330 effective mass. 841 00:41:54,330 --> 00:42:02,590 And the number is 30 angstroms, or 3 nanometers, if 842 00:42:02,590 --> 00:42:04,170 you must. All right? 843 00:42:04,170 --> 00:42:09,710 And compare that to silicon-silicon bond distance. 844 00:42:09,710 --> 00:42:15,210 The silicon-silicon bond distance is 2.35 angstroms. So 845 00:42:15,210 --> 00:42:19,200 clearly this electron is very far removed from the central 846 00:42:19,200 --> 00:42:20,310 phosphorus. 847 00:42:20,310 --> 00:42:21,790 It's not as I depicted. 848 00:42:21,790 --> 00:42:24,505 It has to be way over here, going way, way around. 849 00:42:27,400 --> 00:42:31,960 This is really, really something. 850 00:42:31,960 --> 00:42:37,590 So now you understand how you can get extrinsic properties 851 00:42:37,590 --> 00:42:42,650 and the behavior of the system governed by the introduction 852 00:42:42,650 --> 00:42:44,040 of impurities. 853 00:42:44,040 --> 00:42:47,220 What I'm going to do next day, is to show you that at typical 854 00:42:47,220 --> 00:42:52,470 doping levels, when you dope, dope at about 10 855 00:42:52,470 --> 00:42:53,330 to the minus 6-- 856 00:42:53,330 --> 00:42:54,410 1 part per million-- 857 00:42:54,410 --> 00:42:58,020 10 to the minus 6 phosphorus per silicon. 858 00:42:58,020 --> 00:43:03,540 It turns out that the number of electrons from this 859 00:43:03,540 --> 00:43:11,120 operation is much greater than the number of electrons from 860 00:43:11,120 --> 00:43:14,780 thermal excitation, which is tiny. 861 00:43:14,780 --> 00:43:17,570 And therefore, we argue that the properties are governed by 862 00:43:17,570 --> 00:43:20,070 the dopant atom, and so we have extrinsic 863 00:43:20,070 --> 00:43:22,060 behavior that we see. 864 00:43:22,060 --> 00:43:25,520 OK, well that's a day's work. 865 00:43:25,520 --> 00:43:27,430 David, may we go to the slides, please? 866 00:43:40,920 --> 00:43:44,140 OK, so you saw all that last day, and this, this, this. 867 00:43:44,140 --> 00:43:46,330 All right, there's the insulator, and that. 868 00:43:46,330 --> 00:43:49,730 So I'm just doing the lecture again and fast. You can read. 869 00:43:49,730 --> 00:43:51,150 You can parse visual images. 870 00:43:51,150 --> 00:43:51,980 See? 871 00:43:51,980 --> 00:43:54,120 There's the n-type semiconductor. 872 00:43:54,120 --> 00:43:56,710 We're going to look at p-type next day, quickly. 873 00:43:56,710 --> 00:43:57,830 There's a silicon crystal. 874 00:43:57,830 --> 00:43:58,790 There's the salamis-- 875 00:43:58,790 --> 00:44:00,890 there's the little wafers that are cut. 876 00:44:00,890 --> 00:44:03,926 And there's the spectrum, the x-ray spectrum indicating you 877 00:44:03,926 --> 00:44:05,200 have a single crystal. 878 00:44:05,200 --> 00:44:06,910 There's the first transistor-- 879 00:44:06,910 --> 00:44:08,720 this was a single crystal of germanium 880 00:44:08,720 --> 00:44:10,450 lying here on its side-- 881 00:44:10,450 --> 00:44:15,440 the point transistor in the fall of 1947. 882 00:44:15,440 --> 00:44:18,610 Three gentleman at the Bell Labs that demonstrated the 883 00:44:18,610 --> 00:44:20,010 rectification. 884 00:44:20,010 --> 00:44:23,250 And they won the Nobel Prize for this in 1956. 885 00:44:23,250 --> 00:44:24,080 Now, you can also make 886 00:44:24,080 --> 00:44:26,032 semiconductors that have compounds. 887 00:44:26,032 --> 00:44:28,620 So these are compound semiconductors-- 888 00:44:28,620 --> 00:44:31,590 Professor Ballinger showed you last day-- tin, germanium, 889 00:44:31,590 --> 00:44:32,980 silicon, carbon. 890 00:44:32,980 --> 00:44:33,850 And look at all of these. 891 00:44:33,850 --> 00:44:36,100 This is a Group 3 element with a Group 5 element. 892 00:44:36,100 --> 00:44:37,830 5 plus 3 is 8. 893 00:44:37,830 --> 00:44:38,730 Group 3 and 5. 894 00:44:38,730 --> 00:44:41,220 This is Group 2 and 6. 895 00:44:41,220 --> 00:44:42,495 2 plus 6 is 8. 896 00:44:42,495 --> 00:44:44,720 It's always about octet stability. 897 00:44:44,720 --> 00:44:48,410 But they make strong covalent bonds that give band gaps all 898 00:44:48,410 --> 00:44:50,470 over the map. 899 00:44:50,470 --> 00:44:55,320 So suppose I wanted to have something like a stoplight. 900 00:44:55,320 --> 00:44:57,630 Suppose I wanted a stoplight, and I wanted 901 00:44:57,630 --> 00:44:58,740 to make a red light. 902 00:44:58,740 --> 00:44:59,660 Well, I need-- 903 00:44:59,660 --> 00:45:03,057 I can go backwards from 660 nanometers, and I can go e 904 00:45:03,057 --> 00:45:05,270 equals hc over lambda and calculate-- 905 00:45:05,270 --> 00:45:10,000 I need a material with 1.97 electron volts band gap, and I 906 00:45:10,000 --> 00:45:13,180 look on here and there's nothing that's exactly 1.97. 907 00:45:13,180 --> 00:45:15,510 Well, I can mix these things. 908 00:45:15,510 --> 00:45:16,570 I can mix them. 909 00:45:16,570 --> 00:45:23,280 I can mix something that has 1.52 with 2.3 and get 1.97. 910 00:45:23,280 --> 00:45:25,460 That's called band gap engineering. 911 00:45:25,460 --> 00:45:27,920 And there's more than one mix here, so why would I choose 912 00:45:27,920 --> 00:45:29,960 one mix over another? 913 00:45:29,960 --> 00:45:33,530 It's cheaper, or it's easier to process, or it's stable in 914 00:45:33,530 --> 00:45:34,790 the atmosphere. 915 00:45:34,790 --> 00:45:36,750 You don't want a semiconductor that can't 916 00:45:36,750 --> 00:45:38,470 stand rain and snow. 917 00:45:38,470 --> 00:45:41,710 And so I'm showing you here a variety of compound 918 00:45:41,710 --> 00:45:44,810 semiconductors, and this is the basis of things like-- 919 00:45:44,810 --> 00:45:50,970 the LED, the CD reader, the DVD reader is based on light 920 00:45:50,970 --> 00:45:53,070 that's generated from these. 921 00:45:53,070 --> 00:45:54,960 What was the big deal about Blu-ray? 922 00:45:54,960 --> 00:45:57,410 Why is Blu-ray so cool? 923 00:45:57,410 --> 00:46:00,480 Because the original reader was red. 924 00:46:00,480 --> 00:46:03,400 And what's the wavelength of red light? 925 00:46:03,400 --> 00:46:06,070 Red light is around 600 nanometers. 926 00:46:06,070 --> 00:46:08,205 And what's the wavelength of blue light? 927 00:46:08,205 --> 00:46:10,870 It's down around 300 nanometers. 928 00:46:10,870 --> 00:46:15,540 So all other things being equal, my stylus is half the 929 00:46:15,540 --> 00:46:19,480 size, which means for a given area, I can get double the 930 00:46:19,480 --> 00:46:25,390 density of information without changing the size of the disc. 931 00:46:25,390 --> 00:46:29,560 But it wasn't trivial to find a blue laser. 932 00:46:29,560 --> 00:46:33,080 And the person who found the right mix of compounds that 933 00:46:33,080 --> 00:46:36,690 could give blue in an efficient manner became a very 934 00:46:36,690 --> 00:46:37,940 wealthy individual. 935 00:46:40,090 --> 00:46:41,570 So this is our stoplight now. 936 00:46:41,570 --> 00:46:45,720 These are the materials that go into the stoplights. 937 00:46:45,720 --> 00:46:50,060 No more do you have that giant lens with a 150-watt 938 00:46:50,060 --> 00:46:51,110 incandescent bulb. 939 00:46:51,110 --> 00:46:54,450 Now you have the array of these LEDs that are designed 940 00:46:54,450 --> 00:46:57,350 to be in this band gap. 941 00:46:57,350 --> 00:46:59,070 So I think at this point, we've 942 00:46:59,070 --> 00:47:00,940 probably run out of time. 943 00:47:00,940 --> 00:47:03,780 So we'll resume the discussion tomorrow. 944 00:47:03,780 --> 00:47:06,060 Same time, same place.