1 00:00:17,666 --> 00:00:22,737 We are going to be leaving the territory of-- 2 00:00:22,737 --> 00:00:24,539 some of you have had high school chemistry. 3 00:00:24,539 --> 00:00:27,208 We're going to be starting to leave that territory 4 00:00:27,208 --> 00:00:32,447 and get into some of the things I've talked about before, 5 00:00:32,447 --> 00:00:33,848 that you may have never seen. 6 00:00:33,848 --> 00:00:38,920 So for example, today we'll be talking about semiconductors 7 00:00:38,920 --> 00:00:42,824 and what happens when you take all these atomic orbitals 8 00:00:42,824 --> 00:00:45,293 and you put them into a solid. 9 00:00:45,293 --> 00:00:49,197 And then, by the end of the week, we'll talk about metals. 10 00:00:49,197 --> 00:00:51,633 And then next week, we're going to talk about crystals. 11 00:00:51,633 --> 00:00:53,001 So that's what's coming. 12 00:00:53,001 --> 00:00:53,068 OK, now there's one type of bonding-- 13 00:00:53,068 --> 00:01:00,075 Before we get into semiconductors and solids, 14 00:01:00,075 --> 00:01:02,210 there's one type of bonding we covered but I didn't 15 00:01:02,210 --> 00:01:04,745 put the stats up on the column. 16 00:01:04,745 --> 00:01:08,683 So I just wanted to kind of make sure that we finish that, 17 00:01:08,683 --> 00:01:10,885 and that was hydrogen bonding. 18 00:01:10,885 --> 00:01:12,420 And there's a little video-- 19 00:01:12,420 --> 00:01:15,023 you know, water, we're not going to go 20 00:01:15,023 --> 00:01:17,125 into all the amazing properties of water. 21 00:01:17,125 --> 00:01:19,828 But if you're interested, this is a really cool website 22 00:01:19,828 --> 00:01:23,064 that talks about all the anomalies of water. 23 00:01:23,064 --> 00:01:28,269 And many of water's properties are anomalous. 24 00:01:28,269 --> 00:01:32,039 And much of the reason for that is the last type of bonding 25 00:01:32,039 --> 00:01:34,109 we talked about, intermolecular bonds 26 00:01:34,109 --> 00:01:37,846 we talked about last Friday, which is the hydrogen bond. 27 00:01:37,846 --> 00:01:41,649 So remember our table, I just wanted to fill out the table 28 00:01:41,649 --> 00:01:43,651 because I didn't fill out the table, right. 29 00:01:43,651 --> 00:01:45,019 That's the type of bond. 30 00:01:45,019 --> 00:01:48,890 And the model was some kind of electronegative-- 31 00:01:51,493 --> 00:01:54,429 it was some kind of highly electronegative atom. 32 00:01:54,429 --> 00:01:59,768 Like a was oxygen or nitrogen or fluorine. 33 00:01:59,768 --> 00:02:03,338 So that you drew a lot of charge off of that hydrogen 34 00:02:03,338 --> 00:02:07,509 and you left it with a really strong delta plus 35 00:02:07,509 --> 00:02:12,013 so that it could then bond to some other atom. 36 00:02:12,013 --> 00:02:13,581 It might be the same, by the way. 37 00:02:13,581 --> 00:02:16,851 It was in the cases that we talked about. 38 00:02:16,851 --> 00:02:20,355 Actually, I'll just use the same atom because we use HF and H2O, 39 00:02:20,355 --> 00:02:22,257 so then it would be the O or the F. 40 00:02:22,257 --> 00:02:26,361 But it's to a lone pair on that atom. 41 00:02:26,361 --> 00:02:28,663 That was the hydrogen bond. 42 00:02:28,663 --> 00:02:37,572 And the range of attraction is in kilojoules per mole of bonds 43 00:02:37,572 --> 00:02:42,143 is something like, let's see, 10 to 40. 44 00:02:42,143 --> 00:02:44,045 So it's pretty strong, you know, compared 45 00:02:44,045 --> 00:02:46,247 to some of the weaker things like London, 46 00:02:46,247 --> 00:02:49,017 the hydrogen bond can be pretty strong. 47 00:02:49,017 --> 00:02:52,120 And one of the examples that is the classic example 48 00:02:52,120 --> 00:02:54,289 would be 49 00:02:54,289 --> 00:02:59,727 Hydrogen, hydrogen, there's the hydrogen bond right there, 50 00:02:59,727 --> 00:03:00,428 you see? 51 00:03:00,428 --> 00:03:05,834 Hydrogen bond between another oxygen with its hydrogens 52 00:03:05,834 --> 00:03:06,367 as well. 53 00:03:06,367 --> 00:03:10,939 Now, we talked about how water is so special 54 00:03:10,939 --> 00:03:15,677 because in the case of water, not only do I have exactly two 55 00:03:15,677 --> 00:03:19,514 hydrogens in each molecule that have caused this strong delta 56 00:03:19,514 --> 00:03:22,317 plus, but I've also got two lone pairs. 57 00:03:22,317 --> 00:03:24,252 So the numbers work. 58 00:03:24,252 --> 00:03:27,989 In HF, that's also a hydrogen bonded-- 59 00:03:27,989 --> 00:03:30,692 it can hydrogen bond to itself, but I've 60 00:03:30,692 --> 00:03:33,228 got three lone pairs on each F and only one hydrogen 61 00:03:33,228 --> 00:03:34,796 that I've taken that charge away from. 62 00:03:34,796 --> 00:03:36,397 So you still get the hydrogen bonding, 63 00:03:36,397 --> 00:03:39,367 but this is the beautiful balance. 64 00:03:39,367 --> 00:03:43,905 And there's a video showing water bonded to each other. 65 00:03:43,905 --> 00:03:45,473 Oh, there it is. 66 00:03:45,473 --> 00:03:48,409 Because there's nothing like just imagining what a hydrogen 67 00:03:48,409 --> 00:03:49,477 bond looks like. 68 00:03:49,477 --> 00:03:52,513 And so of course, a hydrogen bond will-- 69 00:03:52,513 --> 00:03:53,448 OK, charges. 70 00:03:53,448 --> 00:03:54,482 Oh, it's French. 71 00:03:54,482 --> 00:03:58,186 [SPEAKING FRENCH] OK. 72 00:03:58,186 --> 00:03:59,754 Oh, that's what it looks like. 73 00:03:59,754 --> 00:04:01,256 Really, if you could get down there, 74 00:04:01,256 --> 00:04:05,159 it would be a ray of a laser beam light. 75 00:04:05,159 --> 00:04:08,396 It's a liaison hydrogene. 76 00:04:08,396 --> 00:04:11,132 And there it is. 77 00:04:11,132 --> 00:04:13,368 And this is what's going on in the liquid. 78 00:04:13,368 --> 00:04:14,802 They're kind of seeing each other. 79 00:04:14,802 --> 00:04:15,837 And they're talking. 80 00:04:15,837 --> 00:04:20,575 But they feel this strong, strong hydrogen bond. 81 00:04:20,575 --> 00:04:22,243 And that's happening all over the place. 82 00:04:22,243 --> 00:04:26,881 And in a liquid, they are making and breaking all the time. 83 00:04:26,881 --> 00:04:28,249 Question? 84 00:04:28,249 --> 00:04:30,752 STUDENT: Why do they separate? 85 00:04:30,752 --> 00:04:31,419 Yeah. 86 00:04:31,419 --> 00:04:33,554 Yeah, because-- well, it depends. 87 00:04:33,554 --> 00:04:34,155 It depends. 88 00:04:34,155 --> 00:04:35,623 It's a great question. 89 00:04:35,623 --> 00:04:38,092 Why do they separate? 90 00:04:38,092 --> 00:04:40,662 Well, they don't in ice. 91 00:04:40,662 --> 00:04:43,298 So in ice, I mean, you know, they can. 92 00:04:43,298 --> 00:04:47,302 But in ice, it's a solid, so they're sort of locked in. 93 00:04:47,302 --> 00:04:50,805 And so in there, you're going to have pretty much each water 94 00:04:50,805 --> 00:04:52,206 molecule has four-- 95 00:04:52,206 --> 00:04:53,374 look at this. 96 00:04:53,374 --> 00:04:55,510 It's you know from VESPR, right? 97 00:04:55,510 --> 00:04:58,313 Four possible bonds. 98 00:04:58,313 --> 00:05:00,548 You can make tetrahedral. 99 00:05:00,548 --> 00:05:01,916 But there's actually lots of ways 100 00:05:01,916 --> 00:05:03,584 you can orient them in a solid. 101 00:05:03,584 --> 00:05:06,554 There's many forms of ice, 12 different ways 102 00:05:06,554 --> 00:05:08,723 to make a solid of ice. 103 00:05:08,723 --> 00:05:12,994 But see, here-- gesundheit. 104 00:05:12,994 --> 00:05:16,097 So here in the liquid at room temperature, 105 00:05:16,097 --> 00:05:20,268 with the laser beams, they're coming in and they're bonding, 106 00:05:20,268 --> 00:05:23,438 but they have enough energy to break the bond, too. 107 00:05:23,438 --> 00:05:25,773 So they stick and they unstick because there's 108 00:05:25,773 --> 00:05:29,510 enough thermal energy in the system to continuously break 109 00:05:29,510 --> 00:05:30,445 them and remake them. 110 00:05:30,445 --> 00:05:33,281 That's when it's a liquid. 111 00:05:33,281 --> 00:05:35,850 When is it a liquid versus a gas? 112 00:05:35,850 --> 00:05:37,752 Right, the boiling point, remember, 113 00:05:37,752 --> 00:05:40,421 that is a proxy we talked about last Friday. 114 00:05:40,421 --> 00:05:43,124 That is a proxy for the bonding strength 115 00:05:43,124 --> 00:05:45,426 between these molecules. 116 00:05:45,426 --> 00:05:48,363 If it's a stronger bonding, then the boiling point 117 00:05:48,363 --> 00:05:49,964 will be higher and higher. 118 00:05:49,964 --> 00:05:53,735 Oh, water should have boiled at a much lower temperature 119 00:05:53,735 --> 00:05:56,604 if it didn't have this very special hydrogen bond, which 120 00:05:56,604 --> 00:05:58,740 is not a dipole-dipole. 121 00:05:58,740 --> 00:06:02,243 People try to write the physics of the hydrogen bond as 1 122 00:06:02,243 --> 00:06:03,011 over r cubed. 123 00:06:03,011 --> 00:06:04,245 That is not true. 124 00:06:04,245 --> 00:06:08,383 That is not just as simple as, it's another dipole-dipole type 125 00:06:08,383 --> 00:06:09,050 interaction. 126 00:06:09,050 --> 00:06:11,452 It's complicated. 127 00:06:11,452 --> 00:06:14,155 Complicated. 128 00:06:14,155 --> 00:06:18,326 Remember, we had covalent bonds were complicated too. 129 00:06:18,326 --> 00:06:21,062 So we're not going to put a simple one 130 00:06:21,062 --> 00:06:24,932 over r something dependence for the hydrogen bond. 131 00:06:24,932 --> 00:06:26,401 OK, good question. 132 00:06:26,401 --> 00:06:29,637 OK now, all right, so that's an intermolecular-- now 133 00:06:29,637 --> 00:06:31,372 we're going to move on to solids. 134 00:06:31,372 --> 00:06:34,142 So that was our last intermolecular interaction. 135 00:06:34,142 --> 00:06:35,777 Oh, before I do, there's actually 136 00:06:35,777 --> 00:06:40,882 an example question I put there that you could now answer, 137 00:06:40,882 --> 00:06:42,082 which this is actually-- 138 00:06:42,082 --> 00:06:43,985 I just want to show you the type of-- 139 00:06:43,985 --> 00:06:46,387 so we covered all these intermolecular bonds. 140 00:06:46,387 --> 00:06:48,890 Here's a question from a quiz last year. 141 00:06:48,890 --> 00:06:52,460 List the intermolecular forces in each substance, methane, 142 00:06:52,460 --> 00:06:54,829 and then you've got that CH3OH. 143 00:06:54,829 --> 00:06:57,965 And then you've got the CH3CL. 144 00:06:57,965 --> 00:07:01,035 And so you can do this now because for methane 145 00:07:01,035 --> 00:07:03,071 all you've got is London. 146 00:07:03,071 --> 00:07:04,272 It's not a polar molecule. 147 00:07:04,272 --> 00:07:05,373 All you've got is London. 148 00:07:05,373 --> 00:07:08,443 There's no hydrogen bond. 149 00:07:08,443 --> 00:07:14,682 But for CH3OH, do you have hydrogen bonding? 150 00:07:14,682 --> 00:07:15,817 Yeah, you do. 151 00:07:15,817 --> 00:07:17,018 Because if you draw-- 152 00:07:17,018 --> 00:07:20,888 because you've got an H that's had the charge taken 153 00:07:20,888 --> 00:07:25,827 from it by oxygen, a highly electronegative atom, and then 154 00:07:25,827 --> 00:07:28,262 and then you've got lone pairs on that same oxygen. 155 00:07:28,262 --> 00:07:32,600 So you can hydrogen bond and you've also got London. 156 00:07:32,600 --> 00:07:33,868 All right, now is that it? 157 00:07:33,868 --> 00:07:35,970 Is there anything else? 158 00:07:35,970 --> 00:07:37,138 CH3OH. 159 00:07:37,138 --> 00:07:37,638 What else? 160 00:07:37,638 --> 00:07:41,542 Is there any other type of bond? 161 00:07:41,542 --> 00:07:43,311 Well, the last question you need to ask 162 00:07:43,311 --> 00:07:46,447 is, is there a dipole moment in the molecule? 163 00:07:46,447 --> 00:07:49,217 Because if that molecule had a permanent dipole, 164 00:07:49,217 --> 00:07:51,719 then there is another type of intermolecular interaction, 165 00:07:51,719 --> 00:07:53,821 like we talked about, dipole-dipole. 166 00:07:53,821 --> 00:07:57,091 So you'd have three. 167 00:07:57,091 --> 00:08:03,231 And for CH3CO, well there, you also-- you know that for CH3CO, 168 00:08:03,231 --> 00:08:04,765 you're going to have a dipole moment. 169 00:08:04,765 --> 00:08:08,002 Remember, we compared dipole moments of molecules. 170 00:08:08,002 --> 00:08:09,904 And if you have a diaper moment in a molecule, 171 00:08:09,904 --> 00:08:13,074 then that dipole moment can talk to another dipole moment 172 00:08:13,074 --> 00:08:14,709 and be interacting with it. 173 00:08:14,709 --> 00:08:16,711 So that's a kind of bond. 174 00:08:16,711 --> 00:08:17,879 And is that it? 175 00:08:21,149 --> 00:08:24,385 London, London is always there. 176 00:08:24,385 --> 00:08:25,453 It's always there. 177 00:08:25,453 --> 00:08:27,421 We've also got London, don't forget. 178 00:08:27,421 --> 00:08:30,892 So you'd have dipole-dipole plus London here. 179 00:08:30,892 --> 00:08:35,696 Dipole-dipole London and hydrogen, just London. 180 00:08:35,696 --> 00:08:37,698 So this is the kind of way I want-- 181 00:08:37,698 --> 00:08:39,500 and you might be able to think about, well, 182 00:08:39,500 --> 00:08:41,434 would a trend-- if you think about, 183 00:08:41,434 --> 00:08:43,236 like, OK well, if a molecule just 184 00:08:43,236 --> 00:08:47,742 has London, then what does London depend on? 185 00:08:47,742 --> 00:08:51,479 All right, well, it depends on the polarizability 186 00:08:51,479 --> 00:08:52,180 of the charge. 187 00:08:52,180 --> 00:08:53,748 So that can be something [INAUDIBLE].. 188 00:08:53,748 --> 00:08:56,417 It depends on the size because that tells you how much-- 189 00:08:56,417 --> 00:09:01,889 if I say, well, what about SIH4 compared to CH4? 190 00:09:01,889 --> 00:09:05,092 Which is going to be more strongly bonded? 191 00:09:05,092 --> 00:09:06,861 You can answer that because you know 192 00:09:06,861 --> 00:09:08,629 the only force there is London. 193 00:09:08,629 --> 00:09:12,333 And you know for London, it's how much contact area you have 194 00:09:12,333 --> 00:09:13,768 is going to be one of the factors. 195 00:09:13,768 --> 00:09:16,037 The more contact area, the more chances these things 196 00:09:16,037 --> 00:09:18,573 can get close enough and polarize. 197 00:09:18,573 --> 00:09:22,443 And then polarizability would be the other. 198 00:09:22,443 --> 00:09:24,745 All right, now we're going on to solids. 199 00:09:24,745 --> 00:09:29,817 Now, the big picture is pretty awesome. 200 00:09:29,817 --> 00:09:31,319 If you look at the big picture, we 201 00:09:31,319 --> 00:09:33,588 have done the electronic structure 202 00:09:33,588 --> 00:09:35,990 of atoms and molecules. 203 00:09:35,990 --> 00:09:38,226 So we've gone through and we've worked our way 204 00:09:38,226 --> 00:09:41,862 through the Bohr atom, the atomic model, quantum numbers, 205 00:09:41,862 --> 00:09:44,765 Aufbau, what happens when you go from one electron 206 00:09:44,765 --> 00:09:49,637 to many, and octet stability, which is Lewis and Vesper. 207 00:09:49,637 --> 00:09:53,274 We have also now talked about how molecules come together 208 00:09:53,274 --> 00:09:55,910 in different ways, how the atoms come together in the molecule, 209 00:09:55,910 --> 00:09:58,346 and how the molecules come together in different ways. 210 00:09:58,346 --> 00:10:02,416 Dipole-dipole, London dispersion, hydrogen bonding. 211 00:10:02,416 --> 00:10:04,285 And then there's these forms of aggregation, 212 00:10:04,285 --> 00:10:05,319 gas, liquid, and solid. 213 00:10:05,319 --> 00:10:07,722 And of course, we're excited about this. 214 00:10:07,722 --> 00:10:11,726 So I put my little emoji there, because that's 215 00:10:11,726 --> 00:10:13,027 what we're going to do now. 216 00:10:13,027 --> 00:10:14,729 We're actually going to take-- 217 00:10:14,729 --> 00:10:16,564 we talked a little bit about solids already, 218 00:10:16,564 --> 00:10:20,301 but now we're going to take the electronic structure that we've 219 00:10:20,301 --> 00:10:23,137 built up, these orbitals. 220 00:10:23,137 --> 00:10:25,806 And we're going to make solids out of them. 221 00:10:25,806 --> 00:10:30,878 So this is the week where these are the next two weeks, right, 222 00:10:30,878 --> 00:10:34,115 where we're going to talk a lot about solids. 223 00:10:34,115 --> 00:10:41,722 And this week, this week we're going 224 00:10:41,722 --> 00:10:45,226 to do the electronic structure. 225 00:10:45,226 --> 00:10:50,931 And next week, we're going to do atoms. 226 00:10:50,931 --> 00:10:54,001 So that's our plan. 227 00:10:54,001 --> 00:10:56,470 And next week Friday, we're going to break a bunch of stuff 228 00:10:56,470 --> 00:10:57,705 with parents. 229 00:10:57,705 --> 00:10:59,373 So this week we're [INAUDIBLE]. 230 00:10:59,373 --> 00:11:01,375 What do electrons do in solids? 231 00:11:01,375 --> 00:11:03,577 Next week, how do atoms arrange in solids? 232 00:11:03,577 --> 00:11:06,447 And together, that gives us so much understanding 233 00:11:06,447 --> 00:11:11,519 of how chemistry effects properties in solids. 234 00:11:11,519 --> 00:11:12,753 So that's the big picture. 235 00:11:12,753 --> 00:11:15,289 Now, here's the thing, why does that matter? 236 00:11:15,289 --> 00:11:20,461 Well, because so many properties can vary by so much 237 00:11:20,461 --> 00:11:22,330 depending on what I just said. 238 00:11:22,330 --> 00:11:25,333 How does chemistry affect properties in solids? 239 00:11:25,333 --> 00:11:29,337 Well, it's complicated, but look at this variation. 240 00:11:29,337 --> 00:11:32,440 28 orders of magnitude of connectivity, electrical 241 00:11:32,440 --> 00:11:34,040 conductivity. 242 00:11:34,040 --> 00:11:39,013 28 orders of magnitude, that's a lot of zeros. 243 00:11:39,013 --> 00:11:39,513 [INAUDIBLE] 244 00:11:39,513 --> 00:11:41,115 These are the electrical conductivities 245 00:11:41,115 --> 00:11:45,953 of different atoms, different materials. 246 00:11:45,953 --> 00:11:50,191 And you can see that it's going to depend on what you have, 247 00:11:50,191 --> 00:11:52,927 but it's also going to depend on-- so that's the chemistry. 248 00:11:52,927 --> 00:11:55,129 But it's also going to depend on the bonding. 249 00:11:55,129 --> 00:11:58,299 It's going to depend on how the electronic structure comes 250 00:11:58,299 --> 00:11:58,999 together. 251 00:11:58,999 --> 00:12:01,435 And it's going to depend on how the atoms come together. 252 00:12:01,435 --> 00:12:05,873 That is what will explain 28 orders of magnitude. 253 00:12:05,873 --> 00:12:08,943 That is a lot of variation. 254 00:12:08,943 --> 00:12:13,614 So we start by thinking about how electrons see these solids. 255 00:12:13,614 --> 00:12:15,349 That's how we're going to start. 256 00:12:15,349 --> 00:12:18,719 Now, the thing is that these good old days 257 00:12:18,719 --> 00:12:23,023 of molecular orbital theory are going to end. 258 00:12:23,023 --> 00:12:24,458 They're going to have to end today. 259 00:12:24,458 --> 00:12:28,162 No, they're not ending for like quizzes and exams. 260 00:12:28,162 --> 00:12:29,397 Don't forget about them. 261 00:12:29,397 --> 00:12:31,966 But we've got to move on because this is just 262 00:12:31,966 --> 00:12:36,604 two atoms, two atoms. 263 00:12:36,604 --> 00:12:40,641 But what happens when we have like a solid? 264 00:12:40,641 --> 00:12:42,710 How many atoms do we have? 265 00:12:42,710 --> 00:12:43,811 We've got a lot. 266 00:12:43,811 --> 00:12:44,545 We've got a lot. 267 00:12:44,545 --> 00:12:47,281 So let's go-- we'll go here. 268 00:12:47,281 --> 00:12:52,253 OK, now, if you think about that picture, that was our-- 269 00:12:52,253 --> 00:12:55,356 I'm going to take 1s orbitals. 270 00:12:55,356 --> 00:12:59,827 And let's just think about this for a second. 271 00:12:59,827 --> 00:13:02,797 If we take 1s orbitals and you have 272 00:13:02,797 --> 00:13:06,434 two atoms that come together, well, they're 273 00:13:06,434 --> 00:13:12,640 going to do just what you see there where 274 00:13:12,640 --> 00:13:15,075 you've got your 1s and your 1s. 275 00:13:15,075 --> 00:13:16,644 I'm not even going to fill these out, 276 00:13:16,644 --> 00:13:19,747 and they're sigma and sigma star. 277 00:13:19,747 --> 00:13:24,452 And so that would be like two 1s orbitals that I have either-- 278 00:13:24,452 --> 00:13:27,354 OK, so up here, I took one. 279 00:13:27,354 --> 00:13:30,257 It was a positive and I subtracted one. 280 00:13:30,257 --> 00:13:35,229 And here, I took one and I added one. 281 00:13:35,229 --> 00:13:38,899 And remember, this gave us this and this. 282 00:13:38,899 --> 00:13:42,803 And this gave us the bonding orbital, right? 283 00:13:42,803 --> 00:13:44,805 Bonding, anti-bonding. 284 00:13:44,805 --> 00:13:46,807 It all came from LCAO. 285 00:13:46,807 --> 00:13:49,677 LCAO is the linear combination of atomic orbitals. 286 00:13:49,677 --> 00:13:51,111 That's the theory we use to build 287 00:13:51,111 --> 00:13:52,947 up our [INAUDIBLE] theory. 288 00:13:52,947 --> 00:13:56,283 But now, we've got to go a lot further. 289 00:13:56,283 --> 00:13:58,486 So I'm going to-- because I don't 290 00:13:58,486 --> 00:14:02,556 want to keep adding things here and here, it gets complicated. 291 00:14:02,556 --> 00:14:08,295 I'm trying to find the MOs for more, and more, and more atoms 292 00:14:08,295 --> 00:14:12,132 because I've got to put a whole lot into my solid. 293 00:14:12,132 --> 00:14:14,301 So I'm going to write them just on one side. 294 00:14:14,301 --> 00:14:19,139 If I write the two here like that, 295 00:14:19,139 --> 00:14:21,308 and that would be sigma and sigma star, 296 00:14:21,308 --> 00:14:22,843 then you know what I'm talking about. 297 00:14:22,843 --> 00:14:24,378 I'm taking the two and I'm combining them 298 00:14:24,378 --> 00:14:25,412 in two different ways. 299 00:14:25,412 --> 00:14:27,014 But what if I had three? 300 00:14:27,014 --> 00:14:29,550 Well see, if I had three-- 301 00:14:29,550 --> 00:14:32,486 so I've got three s orbitals now. 302 00:14:32,486 --> 00:14:38,392 So if I've got three s orbitals, then if you think about it, 303 00:14:38,392 --> 00:14:43,330 I could also add them like that. 304 00:14:43,330 --> 00:14:45,966 That would be a very nice bonding orbital. 305 00:14:45,966 --> 00:14:47,668 If you add them, you see that they're 306 00:14:47,668 --> 00:14:50,204 going to have the same kind of really nice bonding. 307 00:14:50,204 --> 00:14:52,940 But I can also subtract one in the middle. 308 00:14:52,940 --> 00:14:55,075 And if I did that-- 309 00:14:55,075 --> 00:14:59,480 so I had a plus, minus, plus there. 310 00:14:59,480 --> 00:15:03,784 So those are the signs, plus s, minus s, plus s. 311 00:15:03,784 --> 00:15:07,288 Then you can see that in-between those, as I add these together, 312 00:15:07,288 --> 00:15:09,023 you have nodes. 313 00:15:09,023 --> 00:15:12,760 So this is not going to look like a very happy bonding 314 00:15:12,760 --> 00:15:13,427 situation. 315 00:15:13,427 --> 00:15:15,195 I'm going to have something in there 316 00:15:15,195 --> 00:15:16,964 and then something in there. 317 00:15:16,964 --> 00:15:19,466 That's what that's going to look like as I bring them closer 318 00:15:19,466 --> 00:15:20,701 and try to add them. 319 00:15:20,701 --> 00:15:23,671 I made two nodes here. 320 00:15:23,671 --> 00:15:26,140 Well, there's one other way you could do this. 321 00:15:26,140 --> 00:15:29,276 And we know that the number of molecular orbitals 322 00:15:29,276 --> 00:15:32,279 has to equal the number of atomic orbitals. 323 00:15:32,279 --> 00:15:33,013 We know that. 324 00:15:33,013 --> 00:15:34,982 So there's one more that we mean, 325 00:15:34,982 --> 00:15:37,217 because I started with three s's. 326 00:15:37,217 --> 00:15:39,019 And you can kind of see that. 327 00:15:39,019 --> 00:15:44,325 You can see that because if I had a plus and a plus, 328 00:15:44,325 --> 00:15:47,394 if I had done it that way or maybe the other way, 329 00:15:47,394 --> 00:15:49,597 maybe this was over there, but you 330 00:15:49,597 --> 00:15:52,499 see I got a little bonding going on in here between them. 331 00:15:52,499 --> 00:15:54,835 And I got an anti-bonding there. 332 00:15:54,835 --> 00:15:56,837 It's almost like it kind of cancels out. 333 00:15:56,837 --> 00:16:00,674 So you can imagine that that combination of s 334 00:16:00,674 --> 00:16:02,710 orbitals, if I add and subtract them this way, 335 00:16:02,710 --> 00:16:05,913 it's going to be somewhere right in the middle. 336 00:16:05,913 --> 00:16:08,549 Maybe not so bonding, maybe not so anti-bonding. 337 00:16:08,549 --> 00:16:11,018 OK, good. 338 00:16:11,018 --> 00:16:13,053 All right, well let's do four. 339 00:16:13,053 --> 00:16:16,624 So if I had four, if I started with four-- 340 00:16:16,624 --> 00:16:18,859 this is like four hydrogen atoms, let's say, 341 00:16:18,859 --> 00:16:20,361 although I'm not filling it yet. 342 00:16:20,361 --> 00:16:23,263 But so four 1s orbitals. 343 00:16:23,263 --> 00:16:26,767 Well now you see, I could do this. 344 00:16:26,767 --> 00:16:30,004 I can add them all up and get this super awesome bonding 345 00:16:30,004 --> 00:16:30,504 state. 346 00:16:33,674 --> 00:16:39,813 I could also alternate them so that everything 347 00:16:39,813 --> 00:16:41,649 is anti-bonding. 348 00:16:41,649 --> 00:16:42,716 Look at that. 349 00:16:42,716 --> 00:16:45,252 These are going to cancel as you bring them together 350 00:16:45,252 --> 00:16:48,288 and you're going to get anti-bonding, anti-bonding. 351 00:16:48,288 --> 00:16:53,027 But there's also two other options that are in between. 352 00:16:53,027 --> 00:16:58,132 Right here, I can add 2 and then subtract 2. 353 00:16:58,132 --> 00:17:00,868 And you can see, these are both negative. 354 00:17:00,868 --> 00:17:02,269 And as they come together, they're 355 00:17:02,269 --> 00:17:04,704 going to overlap constructively, so will these. 356 00:17:04,704 --> 00:17:06,406 But in the middle here, they're going 357 00:17:06,406 --> 00:17:10,277 to be kind of destructive interference. 358 00:17:10,277 --> 00:17:13,614 And so you're going to have this one node in between. 359 00:17:13,614 --> 00:17:15,182 But in general, you can imagine, this 360 00:17:15,182 --> 00:17:17,617 will be more bonding than anti-bonding, 361 00:17:17,617 --> 00:17:19,853 so we draw it down below the middle. 362 00:17:19,853 --> 00:17:23,156 Whereas up here, you could also imagine something 363 00:17:23,156 --> 00:17:26,026 like this, where you start with a plus 364 00:17:26,026 --> 00:17:29,830 and you put two minuses in there and a plus over there. 365 00:17:29,830 --> 00:17:31,498 I'm just adding and subtracting. 366 00:17:31,498 --> 00:17:34,334 I'm just taking LCAO theory and moving it 367 00:17:34,334 --> 00:17:37,171 to more than two orbitals. 368 00:17:37,171 --> 00:17:40,340 OK, so now you can actually understand this 369 00:17:40,340 --> 00:17:41,742 from a number of nodes, right? 370 00:17:41,742 --> 00:17:45,079 This is like three nodes. 371 00:17:45,079 --> 00:17:49,883 This is two nodes over there. 372 00:17:49,883 --> 00:17:53,287 This is one node. 373 00:17:53,287 --> 00:17:55,456 And zero nodes. 374 00:17:55,456 --> 00:17:57,458 This is exactly the kind of thing 375 00:17:57,458 --> 00:17:59,893 we talked about already, but for only two orbitals. 376 00:17:59,893 --> 00:18:02,396 Now we're just continuing it along. 377 00:18:02,396 --> 00:18:07,000 OK, you can see why the good old days are over, because see, 378 00:18:07,000 --> 00:18:10,370 now we've got to jump this up a level. 379 00:18:10,370 --> 00:18:12,840 And we've got to think, how many s orbitals 380 00:18:12,840 --> 00:18:16,243 do I have in a typical piece of matter? 381 00:18:16,243 --> 00:18:19,680 How many do you think? 382 00:18:19,680 --> 00:18:20,347 Take a guess. 383 00:18:23,851 --> 00:18:25,552 Roughly? 384 00:18:25,552 --> 00:18:28,222 Take a chunk of hydrogen this big. 385 00:18:28,222 --> 00:18:31,825 How many atoms do I have? 386 00:18:31,825 --> 00:18:33,494 A mole, exactly. 387 00:18:33,494 --> 00:18:36,430 That's why we invented the mole, so 388 00:18:36,430 --> 00:18:41,568 that we could count big numbers by just saying 1, 1 mole. 389 00:18:41,568 --> 00:18:43,403 But if I have a mole, then I've got like 10 390 00:18:43,403 --> 00:18:45,272 to the 24th of these. 391 00:18:45,272 --> 00:18:47,474 I just went to four. 392 00:18:47,474 --> 00:18:49,777 I just went to four. 393 00:18:49,777 --> 00:18:51,378 But it just keeps on going. 394 00:18:51,378 --> 00:18:52,713 So [INAUDIBLE]. 395 00:18:52,713 --> 00:18:57,785 So here is like, OK, 1, orbital of atom. 396 00:18:57,785 --> 00:18:59,553 Boy, I labeled that well. 397 00:18:59,553 --> 00:19:02,756 2, bonding, anti-bonding orbitals of molecules. 398 00:19:02,756 --> 00:19:04,992 And then you see, OK, there's 3. 399 00:19:04,992 --> 00:19:06,760 There's 4, 5. 400 00:19:06,760 --> 00:19:08,362 Then you keep on going. 401 00:19:08,362 --> 00:19:09,863 OK, they got a little tired and then 402 00:19:09,863 --> 00:19:15,135 they wrote 30, 30 orbitals. 403 00:19:15,135 --> 00:19:17,971 30 is still way, way far away. 404 00:19:17,971 --> 00:19:21,175 But if you had 30s orbitals, you might still 405 00:19:21,175 --> 00:19:24,178 be able to kind of see these lines discretely. 406 00:19:24,178 --> 00:19:25,512 Remember, this is energy space. 407 00:19:25,512 --> 00:19:27,080 There might actually-- remember, like, 408 00:19:27,080 --> 00:19:28,749 these energies are really important, 409 00:19:28,749 --> 00:19:30,250 the lines between the deltas. 410 00:19:30,250 --> 00:19:35,055 But if you have a mole, if you have a mole, 411 00:19:35,055 --> 00:19:37,424 it looks like one continuous set of lines. 412 00:19:37,424 --> 00:19:41,562 These don't really look discrete anymore. 413 00:19:41,562 --> 00:19:44,131 These don't look discrete. 414 00:19:44,131 --> 00:19:49,369 And so if you have a mole of atoms, so if you have a solid, 415 00:19:49,369 --> 00:19:54,441 we call that collection of orbitals that 416 00:19:54,441 --> 00:19:56,977 are all stuck in here a band. 417 00:19:56,977 --> 00:19:59,213 We call that a band. 418 00:19:59,213 --> 00:20:01,348 OK, so if I take-- 419 00:20:01,348 --> 00:20:07,054 Now, I'm not going to draw 10 to the 24th. 420 00:20:07,054 --> 00:20:09,790 10 to the 24th s orbitals. 421 00:20:09,790 --> 00:20:14,628 But pretend, pretend that that's what I have here. 422 00:20:14,628 --> 00:20:16,029 Then what happens? 423 00:20:18,866 --> 00:20:23,136 What I do is I form a continuum of states, a continuum 424 00:20:23,136 --> 00:20:25,172 of levels for those electrons. 425 00:20:25,172 --> 00:20:28,041 And this, they're so packed together, 426 00:20:28,041 --> 00:20:29,409 we don't even draw them as lines. 427 00:20:29,409 --> 00:20:30,978 We can't. 428 00:20:30,978 --> 00:20:35,249 So this is called the 1s band. 429 00:20:35,249 --> 00:20:37,417 Oh, band. 430 00:20:37,417 --> 00:20:38,752 It's a band. 431 00:20:38,752 --> 00:20:40,754 It's a band of states. 432 00:20:40,754 --> 00:20:42,723 It's a band of states. 433 00:20:42,723 --> 00:20:45,492 It's the 1s band. 434 00:20:45,492 --> 00:20:49,029 Now, there are some important rules 435 00:20:49,029 --> 00:20:53,100 that are really just the same but we follow them here too. 436 00:20:53,100 --> 00:20:55,035 And so I want to emphasize them. 437 00:20:55,035 --> 00:20:57,070 We've already learned them for molecules. 438 00:20:57,070 --> 00:20:59,840 They holds for bands and solids. 439 00:20:59,840 --> 00:21:05,545 All right, so now, for example, let's think about this. 440 00:21:05,545 --> 00:21:11,919 Each of these orbitals could occupy how many electrons? 441 00:21:11,919 --> 00:21:13,220 Two. 442 00:21:13,220 --> 00:21:21,929 So I have two electrons for each s orbital, s orb. 443 00:21:21,929 --> 00:21:28,168 Well, you know, if you think about that, then for n atoms, 444 00:21:28,168 --> 00:21:30,871 and here what did I say, 10 to the 24. 445 00:21:30,871 --> 00:21:34,241 Because there is one s orbital that comes from each atom. 446 00:21:34,241 --> 00:21:42,883 So for n atoms, then I would have 2n electrons 447 00:21:42,883 --> 00:21:49,289 can go into the one s band. 448 00:21:49,289 --> 00:21:51,091 So if I have-- 449 00:21:51,091 --> 00:21:52,192 that makes sense, right? 450 00:21:52,192 --> 00:21:54,628 Because I had two for each orbital, and I had that many. 451 00:21:54,628 --> 00:22:00,233 So if I know how many atoms I have that make up this solid, 452 00:22:00,233 --> 00:22:03,136 then that's how many electrons that band can have in it. 453 00:22:03,136 --> 00:22:07,007 All we did is go from the atomic orbital picture to the solid 454 00:22:07,007 --> 00:22:08,675 to the mole. 455 00:22:08,675 --> 00:22:10,978 OK, why am I saying that? 456 00:22:10,978 --> 00:22:17,818 Because filling is incredibly important 457 00:22:17,818 --> 00:22:19,920 And it happens in the same way-- just like it 458 00:22:19,920 --> 00:22:22,389 was so important for molecular orbitals, 459 00:22:22,389 --> 00:22:24,424 it's also critical for bands. 460 00:22:24,424 --> 00:22:29,896 So filling is like MOs. 461 00:22:29,896 --> 00:22:39,639 It's just like in MOs, start from lowest energy. 462 00:22:43,777 --> 00:22:44,911 Then fill up. 463 00:22:48,081 --> 00:22:50,584 So you know, if you think about this, 464 00:22:50,584 --> 00:22:53,020 if I had-- now I'm going to actually say, 465 00:22:53,020 --> 00:22:56,390 well, OK, I made the one s band by combining these orbitals. 466 00:22:56,390 --> 00:22:58,592 Now I'm going to see what I have, 467 00:22:58,592 --> 00:23:00,060 which tells me how to fill it. 468 00:23:00,060 --> 00:23:08,668 Now I have hydrogen. So if this is the one s band 469 00:23:08,668 --> 00:23:17,944 and I have hydrogen, hydrogen has, for each hydrogen, 470 00:23:17,944 --> 00:23:20,180 I've got one electron. 471 00:23:20,180 --> 00:23:22,682 But I just said that in the one band, 472 00:23:22,682 --> 00:23:24,885 for each atom I could have put two electrons. 473 00:23:24,885 --> 00:23:28,522 So you know if this is made of hydrogen, it's half filled, 474 00:23:28,522 --> 00:23:32,292 which is exactly what that picture shows. 475 00:23:32,292 --> 00:23:33,093 That's the filling. 476 00:23:33,093 --> 00:23:34,728 You see it's filled half way. 477 00:23:34,728 --> 00:23:36,530 The band is filled halfway. 478 00:23:36,530 --> 00:23:43,103 It's like the MO picture, but it's not 479 00:23:43,103 --> 00:23:45,372 because I've made a continuous band out of it. 480 00:23:45,372 --> 00:23:47,874 So instead of putting lines here, lines there, 481 00:23:47,874 --> 00:23:50,143 and then occupying them with arrows, 482 00:23:50,143 --> 00:23:55,682 I fill them up with 10 to the 24-ish electrons. 483 00:23:55,682 --> 00:23:56,983 So we fill bands up like that. 484 00:23:56,983 --> 00:23:58,351 And we know that it's half filled 485 00:23:58,351 --> 00:24:01,188 because it's hydrogen. Another thing 486 00:24:01,188 --> 00:24:05,492 that we know is that the energy-- 487 00:24:05,492 --> 00:24:08,228 remember this? 488 00:24:08,228 --> 00:24:12,599 This is also important. 489 00:24:12,599 --> 00:24:20,707 That energy is related to interaction and overlap. 490 00:24:20,707 --> 00:24:26,446 This is something we talked about, interaction and overlap 491 00:24:26,446 --> 00:24:27,547 of the orbitals. 492 00:24:27,547 --> 00:24:33,253 How much does that band go up and down in energy? 493 00:24:33,253 --> 00:24:34,788 This is something we've talked about. 494 00:24:34,788 --> 00:24:36,490 How much that band goes up and in energy, 495 00:24:36,490 --> 00:24:41,228 it's just like in the H2 molecule. 496 00:24:41,228 --> 00:24:43,396 One s, one s, sigma, sigma, star. 497 00:24:43,396 --> 00:24:45,899 How far apart are sigma star and energy? 498 00:24:45,899 --> 00:24:48,268 Well, it depends on the interaction strength 499 00:24:48,268 --> 00:24:51,004 and the overlap between those orbitals. 500 00:24:51,004 --> 00:24:53,507 The same is true in solids. 501 00:24:53,507 --> 00:24:54,541 Same is true in solids. 502 00:24:54,541 --> 00:24:59,212 So what is the width of that band? 503 00:24:59,212 --> 00:25:02,182 How spread out over energy is it? 504 00:25:02,182 --> 00:25:05,619 OK, so those are some ground rules. 505 00:25:05,619 --> 00:25:08,054 Now, what else can we say? 506 00:25:08,054 --> 00:25:10,457 OK, so there's the absolute least bonding 507 00:25:10,457 --> 00:25:13,560 state, anti-bonding, all the way up there, the most bonding. 508 00:25:13,560 --> 00:25:16,029 And then you've got almost infinite number 509 00:25:16,029 --> 00:25:17,297 of possibilities in between. 510 00:25:19,900 --> 00:25:27,073 But the thing is that filling determines the properties. 511 00:25:27,073 --> 00:25:31,745 You can't just know the bands or the band structure, 512 00:25:31,745 --> 00:25:33,813 as it's called. 513 00:25:33,813 --> 00:25:35,549 But you have to know the filling. 514 00:25:35,549 --> 00:25:39,386 And when you have a situation like this-- 515 00:25:39,386 --> 00:25:40,820 so let's write this down. 516 00:25:43,490 --> 00:25:50,096 When you have partial filling, partially 517 00:25:50,096 --> 00:25:55,535 filled band is a metal. 518 00:25:59,339 --> 00:26:02,742 And I will talk about metals on Friday. 519 00:26:02,742 --> 00:26:04,978 So we will come back to that concept 520 00:26:04,978 --> 00:26:09,249 and the electronic structure of metals on Friday. 521 00:26:09,249 --> 00:26:13,053 But today, I want to talk about something else that happens, 522 00:26:13,053 --> 00:26:18,325 which is when you fill not in the middle of a band, 523 00:26:18,325 --> 00:26:20,860 not in the middle, but maybe all the way up to the top. 524 00:26:20,860 --> 00:26:22,562 And there's a gap. 525 00:26:22,562 --> 00:26:25,098 That's a different kind of material. 526 00:26:25,098 --> 00:26:27,400 So if filling stops somewhere partially in the band, 527 00:26:27,400 --> 00:26:29,202 in the middle of a band, if you're filling, 528 00:26:29,202 --> 00:26:32,772 you're counting, and you didn't go all the way up, 529 00:26:32,772 --> 00:26:35,508 then you have a metal. 530 00:26:35,508 --> 00:26:36,876 But the thing is, here we've only 531 00:26:36,876 --> 00:26:39,045 talked about one kind of band. 532 00:26:39,045 --> 00:26:40,547 This is the s band. 533 00:26:40,547 --> 00:26:44,718 But every single one of these-- 534 00:26:44,718 --> 00:26:48,221 look at this, I can take a mole of orbitals 535 00:26:48,221 --> 00:26:51,458 and make an s band, like that. 536 00:26:51,458 --> 00:26:53,159 And then, oh, that was 1s. 537 00:26:53,159 --> 00:26:55,262 Here's 2s. 538 00:26:55,262 --> 00:27:01,935 And look at this, I can take the p electrons and make a p band. 539 00:27:01,935 --> 00:27:03,236 2p band. 540 00:27:03,236 --> 00:27:05,972 I can do this with every single-- 541 00:27:05,972 --> 00:27:09,175 2s, 1s, right? 542 00:27:09,175 --> 00:27:16,349 So depending on a bunch of factors, 543 00:27:16,349 --> 00:27:20,053 these bands could look different. 544 00:27:20,053 --> 00:27:21,221 What does it depend on? 545 00:27:21,221 --> 00:27:26,693 So this is-- the way these bands are organized, right, 546 00:27:26,693 --> 00:27:30,230 we know now that these orbitals will 547 00:27:30,230 --> 00:27:35,068 come together like I've drawn there and there and form bands. 548 00:27:35,068 --> 00:27:38,038 What is the difference between these? 549 00:27:38,038 --> 00:27:40,874 Did they overlap, maybe? 550 00:27:40,874 --> 00:27:43,243 Are they very far in energy? 551 00:27:43,243 --> 00:27:46,880 These things depend on atom-- 552 00:27:50,050 --> 00:28:01,728 depends on the atom and the bonding and the structure. 553 00:28:08,368 --> 00:28:10,870 How do those bands look? 554 00:28:10,870 --> 00:28:12,339 Well, it depends. 555 00:28:12,339 --> 00:28:14,808 And we'll be talking about some examples. 556 00:28:14,808 --> 00:28:20,847 But for now, I want to focus on that filling thing again. 557 00:28:20,847 --> 00:28:25,051 What happens if I-- 558 00:28:25,051 --> 00:28:28,488 if I fill this 1s up to half way, it's a metal. 559 00:28:28,488 --> 00:28:30,657 If I keep filling, keep adding electrons, 560 00:28:30,657 --> 00:28:34,728 and I fill this up halfway, it's a metal. 561 00:28:34,728 --> 00:28:39,432 But if I stop filling, you know, if I fill this 562 00:28:39,432 --> 00:28:43,970 and then I fill this, and then there's some space in energy 563 00:28:43,970 --> 00:28:46,940 and I didn't fill any more, that's not a metal. 564 00:28:46,940 --> 00:28:48,408 That's not a metal. 565 00:28:48,408 --> 00:28:49,542 So if there's a gap-- 566 00:28:49,542 --> 00:28:52,879 so there can be gaps between bands, which I just showed you. 567 00:28:52,879 --> 00:28:56,149 That's between an s and a p band. 568 00:28:56,149 --> 00:28:58,118 And then the filling determines the properties. 569 00:28:58,118 --> 00:28:59,886 And they're so important. 570 00:28:59,886 --> 00:29:01,354 They're so important. 571 00:29:01,354 --> 00:29:02,422 So let's talk about that. 572 00:29:02,422 --> 00:29:03,857 I want to talk about these. 573 00:29:03,857 --> 00:29:05,959 What we're going to do is we're talking 574 00:29:05,959 --> 00:29:12,031 about semiconductors today and Wednesday, and metals 575 00:29:12,031 --> 00:29:13,600 on Friday. 576 00:29:13,600 --> 00:29:15,969 And we're going to see it through the vantage point 577 00:29:15,969 --> 00:29:17,604 of these electronic levels. 578 00:29:17,604 --> 00:29:19,773 And then next week, we'll see it through the vantage 579 00:29:19,773 --> 00:29:21,074 point of atoms. 580 00:29:24,444 --> 00:29:29,182 So, if you have a gap between-- 581 00:29:29,182 --> 00:29:30,850 well, you always have gaps, the question, 582 00:29:30,850 --> 00:29:33,086 again, comes to filling. 583 00:29:33,086 --> 00:29:34,154 If the filling stops-- 584 00:29:39,192 --> 00:29:42,228 I want to define this very important-- so 585 00:29:42,228 --> 00:29:47,066 if the filling stops, then you have this highest 586 00:29:47,066 --> 00:29:48,101 occupied level. 587 00:29:48,101 --> 00:29:51,371 So let's suppose I have filling-- 588 00:29:51,371 --> 00:29:53,740 this is some band. 589 00:29:53,740 --> 00:29:55,408 And this is some band. 590 00:29:55,408 --> 00:29:58,311 And this is unoccupied. 591 00:29:58,311 --> 00:30:02,348 So unoccupied by electrons. 592 00:30:02,348 --> 00:30:06,486 This is fully occupied by electrons. 593 00:30:09,489 --> 00:30:11,157 So what's going to happen? 594 00:30:11,157 --> 00:30:14,494 Well, first of all, let's just get some terms. 595 00:30:14,494 --> 00:30:18,531 The last band that I filled, the last band that I filled, 596 00:30:18,531 --> 00:30:19,899 is called the valence band. 597 00:30:24,037 --> 00:30:26,306 Valence band. 598 00:30:26,306 --> 00:30:29,609 And we use vb for short. 599 00:30:29,609 --> 00:30:33,246 And the first band that I don't fill 600 00:30:33,246 --> 00:30:35,215 is called the conduction band. 601 00:30:35,215 --> 00:30:40,353 And as we talk more about these materials, 602 00:30:40,353 --> 00:30:42,755 you will see why they're called that. 603 00:30:42,755 --> 00:30:43,423 Conduction band. 604 00:30:46,759 --> 00:30:50,029 But for now, just trust me in the labeling. 605 00:30:50,029 --> 00:30:53,233 So the conduction band and the valence band 606 00:30:53,233 --> 00:30:55,235 depend on the filling. 607 00:30:55,235 --> 00:30:58,805 Because again, it's, you know, it's where I filled to. 608 00:30:58,805 --> 00:31:02,842 Now, the top level, the very, very top level out of these 10 609 00:31:02,842 --> 00:31:07,046 to the 24 level, that very top one has a special name. 610 00:31:07,046 --> 00:31:10,383 It's the vb maximum. 611 00:31:10,383 --> 00:31:11,384 That makes sense, right? 612 00:31:11,384 --> 00:31:15,321 It's the top valence band, or the vbn. 613 00:31:15,321 --> 00:31:18,224 And the one down here also has a special name, 614 00:31:18,224 --> 00:31:27,000 it's the cb minimum, or cbm. 615 00:31:27,000 --> 00:31:30,236 So the valence band maximum and the conduction band minimum 616 00:31:30,236 --> 00:31:32,572 are, you know, it tells you, if you think about it, 617 00:31:32,572 --> 00:31:35,508 it tells you if you subtracted those energies 618 00:31:35,508 --> 00:31:38,111 between those parts of the band, you'd 619 00:31:38,111 --> 00:31:40,380 get the distance and energy between the two bands. 620 00:31:43,550 --> 00:31:46,085 So the conduction band minimum is this energy level 621 00:31:46,085 --> 00:31:48,721 here and the valence band maximum energy is-- 622 00:31:48,721 --> 00:31:51,424 Now remember, valence electro-- it's called the valence band. 623 00:31:51,424 --> 00:31:53,760 It makes sense because valence electrons, remember, 624 00:31:53,760 --> 00:31:56,896 are those ones, as we talked about with Louis, where you've 625 00:31:56,896 --> 00:31:59,232 got kind of the bonding and the action and the chemistry 626 00:31:59,232 --> 00:32:00,166 happening. 627 00:32:00,166 --> 00:32:03,236 And so this is that top most state 628 00:32:03,236 --> 00:32:05,972 of the top most valence band. 629 00:32:05,972 --> 00:32:07,640 This is the valence band top most state. 630 00:32:10,343 --> 00:32:12,912 And there's one more definition we got to know about. 631 00:32:12,912 --> 00:32:14,347 This is why we're setting this up, 632 00:32:14,347 --> 00:32:17,984 which is that that energy difference here, oh, that 633 00:32:17,984 --> 00:32:20,320 is really important. 634 00:32:20,320 --> 00:32:25,258 So the energy of the conduction band minimum, 635 00:32:25,258 --> 00:32:29,228 minus the energy of the valence band maximum, 636 00:32:29,228 --> 00:32:35,735 is equal to something called the bandgap, energy gap. 637 00:32:35,735 --> 00:32:36,469 It's the band gap. 638 00:32:40,540 --> 00:32:46,346 This is an extremely important property of materials, 639 00:32:46,346 --> 00:32:47,814 the electronic band gap. 640 00:32:50,750 --> 00:32:53,019 What is the energy difference between the highest 641 00:32:53,019 --> 00:32:58,224 occupied electrons and the lowest unoccupied electrons? 642 00:32:58,224 --> 00:33:01,327 That's what we're talking about. 643 00:33:01,327 --> 00:33:07,800 So if that filling, if that distance-- 644 00:33:07,800 --> 00:33:10,637 OK, so here's an element, carbon, 645 00:33:10,637 --> 00:33:12,505 in the diamond structure. 646 00:33:12,505 --> 00:33:17,443 And just-- purple is filled and not purple is not filled. 647 00:33:17,443 --> 00:33:19,846 So you know that that's the connection band. 648 00:33:19,846 --> 00:33:21,114 And that's the valence band. 649 00:33:21,114 --> 00:33:24,817 And the band gap, which we've just defined here, 650 00:33:24,817 --> 00:33:29,122 is the energy difference between those. 651 00:33:29,122 --> 00:33:31,124 And for diamond, it's really large. 652 00:33:31,124 --> 00:33:33,459 For diamond, it's really large. 653 00:33:33,459 --> 00:33:37,797 So you can see that, in fact, the gap is over-- 654 00:33:37,797 --> 00:33:39,432 if we converted this to electron-volts, 655 00:33:39,432 --> 00:33:42,468 is more than five electron-volts. 656 00:33:45,505 --> 00:33:49,175 Now, I mentioned thermal energy in answer 657 00:33:49,175 --> 00:33:52,345 to the question about water. 658 00:33:52,345 --> 00:33:58,651 And room temperature-- so room temperature, 659 00:33:58,651 --> 00:34:02,021 the energy of room temperature, if you think about temperature 660 00:34:02,021 --> 00:34:07,927 as an energy of like vibrational motion, and you can do that. 661 00:34:07,927 --> 00:34:11,496 You use something called the Boltzmann constant 662 00:34:11,496 --> 00:34:14,033 and you can get what the room temperature energy is. 663 00:34:14,033 --> 00:34:19,038 And it's something like 0.025 electron-volts. 664 00:34:19,038 --> 00:34:20,672 Seems pretty small. 665 00:34:20,672 --> 00:34:25,143 So the point is, if that's the energy, the thermal energy I 666 00:34:25,143 --> 00:34:30,616 have at room temperature, then if my bandgap is so much 667 00:34:30,616 --> 00:34:33,152 larger than that, is so much larger than 668 00:34:33,152 --> 00:34:37,056 that, it means those electrons are always going to be stuck. 669 00:34:37,056 --> 00:34:40,293 They're never going to, even in some accident, 670 00:34:40,293 --> 00:34:44,630 have enough thermal energy to come up and be excited. 671 00:34:44,630 --> 00:34:48,601 We'll talk about this later. 672 00:34:48,601 --> 00:34:49,902 So they're really stuck. 673 00:34:49,902 --> 00:34:53,072 And if an electron is in the valence band, 674 00:34:53,072 --> 00:34:55,108 it can't move very well. 675 00:34:55,108 --> 00:34:58,377 It can't move-- it's kind of stuck in those bonds. 676 00:34:58,377 --> 00:35:00,179 It's kind of stuck in those bonds. 677 00:35:00,179 --> 00:35:04,317 And so here, if there is electrons all stuck here, 678 00:35:04,317 --> 00:35:06,319 and they never have a chance to go up here 679 00:35:06,319 --> 00:35:09,222 where they can travel freely, this 680 00:35:09,222 --> 00:35:10,857 is really going to be an insulator. 681 00:35:10,857 --> 00:35:15,194 This is not going to carry electrons through the material. 682 00:35:15,194 --> 00:35:16,162 So that's an insulator. 683 00:35:16,162 --> 00:35:18,731 When you have a very large bandgap like that, 684 00:35:18,731 --> 00:35:21,768 we call that an insulator. 685 00:35:21,768 --> 00:35:23,269 OK, but see if we compare-- 686 00:35:23,269 --> 00:35:24,771 and this is interesting, you're just 687 00:35:24,771 --> 00:35:28,508 going down in the periodic table if you compare diamond 688 00:35:28,508 --> 00:35:32,645 to silicon to germanium. 689 00:35:32,645 --> 00:35:35,848 Well, see, what happens is the bandgap gets smaller. 690 00:35:35,848 --> 00:35:39,886 I'm still filling them all the way up to the top of a band. 691 00:35:39,886 --> 00:35:42,688 So I'm not a metal. 692 00:35:42,688 --> 00:35:45,258 If I'm a metal, it's because my filling stopped somewhere 693 00:35:45,258 --> 00:35:46,793 in the middle of the band. 694 00:35:46,793 --> 00:35:48,294 I'm not a metal. 695 00:35:48,294 --> 00:35:51,430 I'm a semi conductor and not an insulator. 696 00:35:51,430 --> 00:35:53,332 And the reason I'm a semi conductor 697 00:35:53,332 --> 00:35:55,368 is that my bandgap is kind of small 698 00:35:55,368 --> 00:35:59,172 enough so that electrons can kind of jump from here 699 00:35:59,172 --> 00:36:03,409 up to there, sometimes. 700 00:36:03,409 --> 00:36:05,411 Sometimes. 701 00:36:05,411 --> 00:36:09,615 That's why it's called a semi conductor. 702 00:36:09,615 --> 00:36:12,051 They kind of conduct electrons. 703 00:36:12,051 --> 00:36:15,988 So the electron can get up to the conduction 704 00:36:15,988 --> 00:36:19,659 band in a semiconductor more easily than an insulator. 705 00:36:19,659 --> 00:36:22,862 And that's why it can conduct electricity much better 706 00:36:22,862 --> 00:36:27,366 than an insulator, many, many, many orders of magnitude. 707 00:36:27,366 --> 00:36:29,368 But the way that we have talked about getting 708 00:36:29,368 --> 00:36:33,239 electrons excited, getting electrons excited, 709 00:36:33,239 --> 00:36:34,807 is with light. 710 00:36:34,807 --> 00:36:37,443 And we can do that for solids, too. 711 00:36:37,443 --> 00:36:40,179 We can do the same thing for solids. 712 00:36:40,179 --> 00:36:48,221 And so if I plot the absorption, if I take a solid 713 00:36:48,221 --> 00:36:51,290 and I shine a light on it, there's 714 00:36:51,290 --> 00:36:59,332 something called the absorption coefficient, which is really 715 00:36:59,332 --> 00:37:06,005 just a measure of how far down into the solid 716 00:37:06,005 --> 00:37:10,776 did that light have to go before some electron got excited 717 00:37:10,776 --> 00:37:12,478 by it? 718 00:37:12,478 --> 00:37:14,881 How well does it-- well, OK, different solids 719 00:37:14,881 --> 00:37:16,949 can absorb electrons differently. 720 00:37:16,949 --> 00:37:21,220 But the main point is, if I plot that versus energy 721 00:37:21,220 --> 00:37:27,827 for something like silicon, the bandgap of silicon is 1.1 ev, 722 00:37:27,827 --> 00:37:29,695 so that's what it would look like for silicon 723 00:37:29,695 --> 00:37:33,399 because you know-- 724 00:37:33,399 --> 00:37:34,967 this should be wavelength. 725 00:37:38,905 --> 00:37:44,911 Because you know-- because as you get to lower-- 726 00:37:44,911 --> 00:37:48,447 so you know that above-- 727 00:37:48,447 --> 00:37:50,449 it's exactly like for atoms. 728 00:37:50,449 --> 00:37:53,519 If I shine light, like remember the Bohr model, 729 00:37:53,519 --> 00:37:57,890 if I shine light on an atom that has enough energy to promote it 730 00:37:57,890 --> 00:38:01,560 up, then it can go. 731 00:38:01,560 --> 00:38:08,067 But the difference here is that for silicon, for silicon, 732 00:38:08,067 --> 00:38:09,869 that's right there, for silicon there's 733 00:38:09,869 --> 00:38:12,171 this big empty space with no bands. 734 00:38:12,171 --> 00:38:13,673 It's just like the atom. 735 00:38:13,673 --> 00:38:18,811 When there's no states, I cannot have an electron there. 736 00:38:18,811 --> 00:38:20,112 I'm stuck. 737 00:38:20,112 --> 00:38:22,682 So the electron can be here or it can be here. 738 00:38:22,682 --> 00:38:24,417 And so the light, the energy of the light, 739 00:38:24,417 --> 00:38:28,454 has to be at least the bandgap to get it up. 740 00:38:28,454 --> 00:38:32,058 At least the bandgap to get it up. 741 00:38:32,058 --> 00:38:34,994 So what that means is that if I had-- 742 00:38:34,994 --> 00:38:39,332 so, why does this go to zero with increasing wavelength? 743 00:38:39,332 --> 00:38:43,869 What it means is that if my valence band looks like this 744 00:38:43,869 --> 00:38:46,906 and my conduction band looks like this, 745 00:38:46,906 --> 00:38:50,409 and now my light is coming and I want to take an electron 746 00:38:50,409 --> 00:38:52,511 and promote it up. 747 00:38:52,511 --> 00:38:54,613 Well, it cannot be-- 748 00:38:54,613 --> 00:39:04,790 the electron cannot exist inside the band gap. 749 00:39:04,790 --> 00:39:06,459 There is no states there. 750 00:39:06,459 --> 00:39:08,227 It's just like we talked about with atoms. 751 00:39:08,227 --> 00:39:11,197 But now we've got almost infinite states here, 752 00:39:11,197 --> 00:39:12,365 no states there. 753 00:39:12,365 --> 00:39:14,200 And then again we start with infinite places 754 00:39:14,200 --> 00:39:14,900 where it can be. 755 00:39:17,670 --> 00:39:19,872 What that means is that if I shine light on it, 756 00:39:19,872 --> 00:39:24,577 the only way silicon, the only way it can absorb this light 757 00:39:24,577 --> 00:39:29,081 is if the light has energy greater than the band gap, 758 00:39:29,081 --> 00:39:31,917 or wavelength less than the bandgap. 759 00:39:31,917 --> 00:39:34,086 That's why I drew it that way. 760 00:39:34,086 --> 00:39:35,521 So it goes to zero-- so it's going 761 00:39:35,521 --> 00:39:37,790 to absorb in wavelength up to a certain point. 762 00:39:37,790 --> 00:39:39,592 And then if I go higher in wavelength, 763 00:39:39,592 --> 00:39:41,193 those are energies that are too small. 764 00:39:41,193 --> 00:39:43,763 It's going to try to absorb here but there's nowhere to absorb 765 00:39:43,763 --> 00:39:46,999 to, so it can't. 766 00:39:46,999 --> 00:39:49,368 But if it has enough energy, oh, look at this. 767 00:39:49,368 --> 00:39:50,603 This is also different. 768 00:39:50,603 --> 00:39:54,306 I could absorb here or here or here. 769 00:39:54,306 --> 00:39:57,009 I can take all those higher energies 770 00:39:57,009 --> 00:40:01,247 and absorb light kind of continuously, 771 00:40:01,247 --> 00:40:03,082 unlike in the atom where it could only 772 00:40:03,082 --> 00:40:07,086 be the level to hop you from n equals 2 to n equals 4. 773 00:40:07,086 --> 00:40:11,190 But here I have an almost continuous set of states, 774 00:40:11,190 --> 00:40:15,428 except in the band gap, where I have no states. 775 00:40:15,428 --> 00:40:19,098 So that's what the absorption would look like for silicon. 776 00:40:19,098 --> 00:40:22,601 And if you look at the bandgap, this very, very important 777 00:40:22,601 --> 00:40:24,403 quantity, there is carbon. 778 00:40:24,403 --> 00:40:25,838 There's diamond. 779 00:40:25,838 --> 00:40:27,039 There's silicon. 780 00:40:27,039 --> 00:40:29,075 There's germanium. 781 00:40:29,075 --> 00:40:32,978 And you can see that as you go to heavier and heavier 782 00:40:32,978 --> 00:40:38,017 elements, you change the gap. 783 00:40:38,017 --> 00:40:39,585 And you can understand this from what 784 00:40:39,585 --> 00:40:42,488 you know about the electron levels in atoms. 785 00:40:42,488 --> 00:40:50,930 Because in an atom, remember, if I get heavier and heavier, 786 00:40:50,930 --> 00:40:55,334 those electrons all the way on the outer edges of the atom, 787 00:40:55,334 --> 00:40:58,537 they're more weakly bonded to the atom. 788 00:40:58,537 --> 00:41:02,575 They're weaker and weaker and weaker. 789 00:41:02,575 --> 00:41:05,411 So the energy is higher and higher. 790 00:41:05,411 --> 00:41:09,014 Remember, so instead of being these deeper energy levels that 791 00:41:09,014 --> 00:41:12,318 have more bonding, more energy in them, lower in energy, 792 00:41:12,318 --> 00:41:15,688 they're less and less energy. 793 00:41:15,688 --> 00:41:19,158 So you can imagine, now, that those 794 00:41:19,158 --> 00:41:20,826 are what you're starting with. 795 00:41:20,826 --> 00:41:22,928 Those are what you're starting with, these. 796 00:41:22,928 --> 00:41:25,397 Right these are the atom levels that you're starting with. 797 00:41:25,397 --> 00:41:28,167 So if you're going to make your atom have electrons that 798 00:41:28,167 --> 00:41:32,938 are more weakly bound with energies that are higher, 799 00:41:32,938 --> 00:41:35,174 that aren't as deep and don't have as much distance 800 00:41:35,174 --> 00:41:39,078 between them in the energy landscape, 801 00:41:39,078 --> 00:41:41,013 then the gaps will get smaller. 802 00:41:41,013 --> 00:41:45,618 Now, that is a very simple picture 803 00:41:45,618 --> 00:41:46,886 of why the gaps get smaller. 804 00:41:46,886 --> 00:41:49,522 It happens to work for this column. 805 00:41:49,522 --> 00:41:51,790 So if you look at this-- and some people 806 00:41:51,790 --> 00:41:54,527 would even call this a metal because that's 807 00:41:54,527 --> 00:41:58,564 such a small gap, but I like to call it a semiconductor. 808 00:41:58,564 --> 00:42:02,168 But if your gap is zero, if you're band gap is zero, 809 00:42:02,168 --> 00:42:04,537 it means there is no gap. 810 00:42:04,537 --> 00:42:08,474 So by definition, you're in the middle of a band. 811 00:42:08,474 --> 00:42:10,209 You're somewhere in the middle of a band. 812 00:42:10,209 --> 00:42:13,579 And if you're in the middle of a band, you're a metal. 813 00:42:13,579 --> 00:42:16,582 You didn't fill that band all the way up. 814 00:42:16,582 --> 00:42:18,217 But if you filled it up and then there's 815 00:42:18,217 --> 00:42:20,653 a little gap between you and the next level, 816 00:42:20,653 --> 00:42:21,854 then you're a semiconductor. 817 00:42:21,854 --> 00:42:25,191 Or if it's much greater, like greater than three 818 00:42:25,191 --> 00:42:28,060 electron volts, 3 and 1/2 electron volts, 819 00:42:28,060 --> 00:42:31,730 then you're an insulator. 820 00:42:31,730 --> 00:42:34,500 Now, so you can imagine now why-- 821 00:42:34,500 --> 00:42:37,369 so as the interactions get stronger, 822 00:42:37,369 --> 00:42:41,040 you can imagine those distances can get larger. 823 00:42:41,040 --> 00:42:44,143 And so you could have larger and larger gaps, 824 00:42:44,143 --> 00:42:45,678 which can explain this trend. 825 00:42:45,678 --> 00:42:48,480 But as I said before, where did I put it, 826 00:42:48,480 --> 00:42:53,886 it depends, not just on the atom and the original energy levels, 827 00:42:53,886 --> 00:42:56,222 but on how those bond together. 828 00:42:56,222 --> 00:42:58,357 And we'll talk about that on Wednesday. 829 00:42:58,357 --> 00:43:00,492 And it also depends on the structure, which 830 00:43:00,492 --> 00:43:01,994 we'll talk about next week. 831 00:43:01,994 --> 00:43:03,696 So it's not just as simple as that 832 00:43:03,696 --> 00:43:07,233 but you can understand basic trends this way 833 00:43:07,233 --> 00:43:09,568 for some of the columns. 834 00:43:09,568 --> 00:43:14,373 OK, we'll get to that on Friday. 835 00:43:14,373 --> 00:43:17,443 Now, the goodie bag gives you a way to probe this. 836 00:43:17,443 --> 00:43:18,877 So what's in the goodie bag? 837 00:43:18,877 --> 00:43:24,450 The goodie bag has a way of measuring conductivity. 838 00:43:24,450 --> 00:43:27,453 Now, I just told you that you cannot get connectivity unless 839 00:43:27,453 --> 00:43:32,725 you have electrons that are able to make this jump, 840 00:43:32,725 --> 00:43:34,360 to make this jump. 841 00:43:34,360 --> 00:43:37,997 They've got to be able to go up from the valence band 842 00:43:37,997 --> 00:43:39,531 to the conduction band. 843 00:43:39,531 --> 00:43:41,967 If they don't do that, they're not free. 844 00:43:41,967 --> 00:43:44,503 They're stuck in these bonds. 845 00:43:44,503 --> 00:43:48,641 You've got to get them free so they can roam around and not 846 00:43:48,641 --> 00:43:51,844 be stuck in this bond or that bond. 847 00:43:51,844 --> 00:43:53,078 This measures that. 848 00:43:53,078 --> 00:43:54,179 This measures that. 849 00:43:54,179 --> 00:43:57,950 This measures whether electrons are in the conduction band. 850 00:43:57,950 --> 00:44:01,287 You've also got some LEDs and some LEDs. 851 00:44:01,287 --> 00:44:04,156 And this is a critical piece here. 852 00:44:04,156 --> 00:44:08,127 Why do you have two kinds of LEDs? 853 00:44:08,127 --> 00:44:11,196 Because on the one hand, what you're doing, 854 00:44:11,196 --> 00:44:13,999 I'm giving you a way to excite electrons. 855 00:44:13,999 --> 00:44:19,972 So I'm giving you a way to actually promote electrons. 856 00:44:19,972 --> 00:44:23,676 So you've got 10 to the 24 electrons in this valence band. 857 00:44:23,676 --> 00:44:27,079 This would be the vb and this would be the cb. 858 00:44:27,079 --> 00:44:31,817 And what you're doing is you're shining light 859 00:44:31,817 --> 00:44:36,822 with different frequencies, which means different energies. 860 00:44:36,822 --> 00:44:38,590 That's what the right hand side gives you. 861 00:44:38,590 --> 00:44:42,661 It gives you different energies of the photons. 862 00:44:42,661 --> 00:44:45,564 So you have a way, now, of shining energy 863 00:44:45,564 --> 00:44:46,965 on a semiconductor. 864 00:44:46,965 --> 00:44:49,401 And that's the second piece. 865 00:44:49,401 --> 00:44:52,604 The semiconductor is what an LED is. 866 00:44:52,604 --> 00:44:55,374 It's a semiconductor. 867 00:44:55,374 --> 00:44:57,509 If LEDs were insulators, they wouldn't work. 868 00:44:57,509 --> 00:45:00,012 And if they were metals, they wouldn't work. 869 00:45:00,012 --> 00:45:04,883 Because the way an LED works is actually just the opposite. 870 00:45:04,883 --> 00:45:09,054 Here, I'm shining light so that an electron gets promoted 871 00:45:09,054 --> 00:45:12,124 and I can measure that with my voltmeter. 872 00:45:12,124 --> 00:45:16,161 But I could also put electrons in with a current. 873 00:45:16,161 --> 00:45:17,996 That gets them up here and then they 874 00:45:17,996 --> 00:45:20,032 drop down and emit a photon. 875 00:45:20,032 --> 00:45:22,434 That's what an LED is. 876 00:45:22,434 --> 00:45:24,770 That's what an LED is, it's just the reverse. 877 00:45:24,770 --> 00:45:27,272 And so what I've given you on the left 878 00:45:27,272 --> 00:45:30,809 are different semiconductors. 879 00:45:30,809 --> 00:45:34,146 Because you see, just like a different-- you know, 880 00:45:34,146 --> 00:45:37,182 if I'm running current through like I am on the right, 881 00:45:37,182 --> 00:45:39,251 you see, those are different colors. 882 00:45:39,251 --> 00:45:44,590 That means that I must have different gaps. 883 00:45:44,590 --> 00:45:45,224 You know that. 884 00:45:45,224 --> 00:45:46,658 You know that already from the work 885 00:45:46,658 --> 00:45:50,362 we did with Bohr and the color or frequency of light 886 00:45:50,362 --> 00:45:52,564 that you can get out of different transitions. 887 00:45:52,564 --> 00:45:54,166 But it's the same here. 888 00:45:54,166 --> 00:45:57,169 Did an electron-- you know, did I put an electron up here 889 00:45:57,169 --> 00:46:02,441 and then it fell down and gave off some lambda? 890 00:46:02,441 --> 00:46:08,847 That lambda has to equal the difference between the-- 891 00:46:08,847 --> 00:46:10,849 it just equals the band gap. 892 00:46:10,849 --> 00:46:15,020 It equals the band gap because the electron was put up 893 00:46:15,020 --> 00:46:17,856 to here in the cbm and then it drops down to the vbm 894 00:46:17,856 --> 00:46:18,824 and it emits a photon. 895 00:46:18,824 --> 00:46:20,759 That's what's happening on the right hand side. 896 00:46:20,759 --> 00:46:23,228 But see, you've also got, on the left hand side, 897 00:46:23,228 --> 00:46:29,268 you've got sensors because it's just LEDs on the left. 898 00:46:29,268 --> 00:46:33,305 But if I hook those up, if I hook those up 899 00:46:33,305 --> 00:46:37,009 to the volt meter, well, I'm hooking up 900 00:46:37,009 --> 00:46:39,011 a semiconductor to a voltmeter. 901 00:46:39,011 --> 00:46:44,183 So I'm hooking this up and I'm reading, is there any current. 902 00:46:44,183 --> 00:46:46,985 And the answer in a dark room is no, 903 00:46:46,985 --> 00:46:48,854 unless you make it really, really hot. 904 00:46:48,854 --> 00:46:51,557 Don't, because you have to go to very high temperatures. 905 00:46:51,557 --> 00:46:54,827 Well, what if I shine light on this now? 906 00:46:54,827 --> 00:46:58,030 Well, if I shine light that has the right energy 907 00:46:58,030 --> 00:47:02,334 to put electrons up in the cbm from the vbm, 908 00:47:02,334 --> 00:47:04,803 then I'll read something on the voltmeter. 909 00:47:04,803 --> 00:47:07,806 So by giving you different LEDs on the left, 910 00:47:07,806 --> 00:47:09,575 I'm giving you different band gaps. 911 00:47:09,575 --> 00:47:13,545 You have in your hands different semiconductor band gaps. 912 00:47:13,545 --> 00:47:16,615 And by reading whether there are electrons in here or not, 913 00:47:16,615 --> 00:47:19,785 you can tell what frequency of light I shined on them. 914 00:47:19,785 --> 00:47:23,522 So they're both emitters of photons and detectors 915 00:47:23,522 --> 00:47:24,990 of photons. 916 00:47:24,990 --> 00:47:27,693 And it all comes together because you 917 00:47:27,693 --> 00:47:31,196 have a semiconductor, which happens because you took 10 918 00:47:31,196 --> 00:47:33,832 to the 24 states, you put them together, 919 00:47:33,832 --> 00:47:36,502 you had gaps between them, and you filled all the way up 920 00:47:36,502 --> 00:47:40,806 to one of those gaps, and that gap was around 1 or 2 electron 921 00:47:40,806 --> 00:47:42,241 volts. 922 00:47:42,241 --> 00:47:46,478 We will pick this up on Friday and go further-- 923 00:47:46,478 --> 00:47:48,080 I mean on Wednesday, on Wednesday.