WEBVTT 00:00:00.000 --> 00:00:02.070 - [Teacher] To figure out how we use semiconductors 00:00:02.070 --> 00:00:04.530 to build all these awesome computing devices, 00:00:04.530 --> 00:00:06.210 we're going to start from scratch, 00:00:06.210 --> 00:00:08.620 all the way down to even understanding 00:00:08.620 --> 00:00:11.520 why semiconductors are semiconductors. 00:00:11.520 --> 00:00:13.070 I mean, why is it that certain materials 00:00:13.070 --> 00:00:13.990 behave like conductors, 00:00:13.990 --> 00:00:16.530 which are very good at passing electricity 00:00:16.530 --> 00:00:18.870 through them while others are not? 00:00:18.870 --> 00:00:23.570 To understand this, we need to look at the atomic level. 00:00:23.570 --> 00:00:26.490 Now we might have some intuition about these atoms, 00:00:26.490 --> 00:00:27.323 but guess what? 00:00:27.323 --> 00:00:28.420 Turns out that our knowledge 00:00:28.420 --> 00:00:30.900 of the atomic structure is not enough. 00:00:30.900 --> 00:00:32.850 And so in this video, we're just gonna recapitulate 00:00:32.850 --> 00:00:34.650 all the stuff that we might already know 00:00:34.650 --> 00:00:35.830 from the previous videos. 00:00:35.830 --> 00:00:38.620 And we'll see why the current knowledge 00:00:38.620 --> 00:00:39.830 or the current theory of the atoms 00:00:39.830 --> 00:00:44.000 is not sufficient to talk about solids in general, 00:00:44.000 --> 00:00:45.450 which we'll be interested in. 00:00:46.620 --> 00:00:48.890 For starters, you may already have some intuition. 00:00:48.890 --> 00:00:53.160 For example, you may know that all matter is made of atoms. 00:00:53.160 --> 00:00:56.900 And if you were to pick any one of them and zoom in, 00:00:56.900 --> 00:00:59.100 then you might know that the atoms themselves 00:00:59.100 --> 00:01:01.110 are made of even smaller things. 00:01:01.110 --> 00:01:03.370 At the center, we have this thing called as the nucleus, 00:01:03.370 --> 00:01:05.000 which have a positive charge, 00:01:05.000 --> 00:01:07.660 and the electrons which are negatively charged 00:01:07.660 --> 00:01:08.990 are attracted by the nucleus 00:01:08.990 --> 00:01:12.210 and end up going around the nucleus in different orbits 00:01:12.210 --> 00:01:13.620 just like the solar system 00:01:13.620 --> 00:01:15.460 and how the planets go around the sun. 00:01:15.460 --> 00:01:17.290 Now this is not a very accurate model, 00:01:17.290 --> 00:01:18.850 we'll get back to that. 00:01:18.850 --> 00:01:20.650 But as of now, let's use this model. 00:01:20.650 --> 00:01:23.490 But the important thing is there are some electrons 00:01:23.490 --> 00:01:26.690 like these, which are tightly bound to the nucleus. 00:01:26.690 --> 00:01:28.603 We call them as bound electrons. 00:01:29.620 --> 00:01:31.750 Bound electrons, and these are not responsible 00:01:31.750 --> 00:01:33.070 for conduction. 00:01:33.070 --> 00:01:35.300 Whereas there are other electrons 00:01:35.300 --> 00:01:37.740 which are not strongly attracted by the nucleus 00:01:37.740 --> 00:01:41.210 and they are free, as in, they're free to move 00:01:41.210 --> 00:01:43.280 from one atom to another. 00:01:43.280 --> 00:01:45.800 And it's these electrons which we call 00:01:45.800 --> 00:01:47.580 as conduction electrons or free electrons, 00:01:47.580 --> 00:01:50.590 which are really responsible for conduction. 00:01:50.590 --> 00:01:51.710 And in some materials, 00:01:51.710 --> 00:01:54.640 it's very easy to get these free electrons. 00:01:54.640 --> 00:01:56.840 And so they end up having a lot of them, 00:01:56.840 --> 00:01:59.440 and we call these materials as good conductors 00:01:59.440 --> 00:02:00.610 or conductors. 00:02:00.610 --> 00:02:02.140 On the other hand, some materials, 00:02:02.140 --> 00:02:04.690 well, it's extremely difficult to get these free electrons. 00:02:04.690 --> 00:02:07.900 And as a result, you have extremely negligible amount. 00:02:07.900 --> 00:02:11.340 And as a result, they are bad conductors or insulators. 00:02:11.340 --> 00:02:13.150 And of course we have the intermediate ones 00:02:13.150 --> 00:02:15.280 which we end up calling semiconductors. 00:02:15.280 --> 00:02:16.600 So I think the most important question 00:02:16.600 --> 00:02:18.540 that we have to ask ourselves over here, 00:02:18.540 --> 00:02:21.060 is how does an electron become free? 00:02:21.060 --> 00:02:23.330 I mean, what makes it free and what does that depend on? 00:02:23.330 --> 00:02:25.120 That's the thing that we need to figure out. 00:02:25.120 --> 00:02:27.800 And we have to look at, look at this whole thing 00:02:27.800 --> 00:02:31.610 for a solid, because our semiconductors are solids. 00:02:31.610 --> 00:02:33.650 So we need to find out, or we need to figure out 00:02:33.650 --> 00:02:37.080 what makes an electron free in solids. 00:02:37.080 --> 00:02:39.850 And to do that, we need to get past this 00:02:39.850 --> 00:02:43.110 solar system model of the atom, as I mentioned before, 00:02:43.110 --> 00:02:44.300 it's not very accurate. 00:02:44.300 --> 00:02:47.280 And we need to look at a more accurate model 00:02:47.280 --> 00:02:49.510 of the atomic structure. 00:02:49.510 --> 00:02:50.970 So let's do that. 00:02:50.970 --> 00:02:53.680 Now, you may have already learned about this in chemistry. 00:02:53.680 --> 00:02:55.380 It turns out that instead of thinking 00:02:55.380 --> 00:02:58.440 of where the electrons are and what orbits 00:02:58.440 --> 00:02:59.850 or what path they take, 00:02:59.850 --> 00:03:03.340 it's much better to think about them in terms of energies. 00:03:03.340 --> 00:03:05.450 It's better think about what are the energies 00:03:05.450 --> 00:03:07.000 that the electrons can take up. 00:03:07.000 --> 00:03:09.280 And you may have already studied in chemistry 00:03:09.280 --> 00:03:11.200 that the inside of any atoms, 00:03:11.200 --> 00:03:14.940 so if I draw over here energies, 00:03:14.940 --> 00:03:18.140 inside any atom, electrons can have only some 00:03:18.140 --> 00:03:20.095 specific energy values, 00:03:20.095 --> 00:03:22.880 only some specific energy values. 00:03:22.880 --> 00:03:24.720 And so maybe the lowest energy 00:03:24.720 --> 00:03:26.970 that electron can have maybe somewhere over here. 00:03:26.970 --> 00:03:29.310 We're not gonna write down the numbers over here. 00:03:29.310 --> 00:03:30.960 We're not gonna look at it very quantitatively, 00:03:30.960 --> 00:03:32.010 don't worry about it. 00:03:32.010 --> 00:03:33.450 So maybe this is the lowest energy 00:03:33.450 --> 00:03:35.000 that an electron can possess. 00:03:35.000 --> 00:03:36.730 The next higher energy an electron can possess 00:03:36.730 --> 00:03:38.450 might be somewhere over here, 00:03:38.450 --> 00:03:41.240 and maybe next higher might be somewhere over here, 00:03:41.240 --> 00:03:42.290 and so on and so forth. 00:03:42.290 --> 00:03:44.550 And we give names to these energy levels. 00:03:44.550 --> 00:03:48.570 We call the lowest one as the 1S energy level. 00:03:48.570 --> 00:03:50.120 The next higher one becomes 2S, 00:03:51.170 --> 00:03:54.230 the one that comes above that would be 2P. 00:03:54.230 --> 00:03:58.984 Then we have 3S and 3P and so on and so forth. 00:03:58.984 --> 00:04:01.780 And again, if this looks very new to you 00:04:01.780 --> 00:04:03.800 and you have no idea what S and P are, 00:04:03.800 --> 00:04:06.650 it would be a great idea to pause this over here, 00:04:06.650 --> 00:04:09.360 go back and watch the electron configuration videos 00:04:09.360 --> 00:04:13.180 on chemistry, and then come back over here. 00:04:13.180 --> 00:04:15.760 But anyways, it turns out electrons cannot take up 00:04:15.760 --> 00:04:17.700 these energy levels randomly. 00:04:17.700 --> 00:04:20.340 There's a particular rule using which electrons 00:04:20.340 --> 00:04:23.310 sort of fill up these energy levels. 00:04:23.310 --> 00:04:25.540 And that rule, again, you may have studied about them. 00:04:25.540 --> 00:04:28.980 We call that as the Pauli's exclusion principle. 00:04:28.980 --> 00:04:31.683 Pauli's exclusion, 00:04:33.380 --> 00:04:35.930 exclusion principle, or rule. 00:04:35.930 --> 00:04:39.150 And it simply says that no two electrons, 00:04:39.150 --> 00:04:41.210 no two electrons 00:04:42.190 --> 00:04:44.870 can have identical, 00:04:44.870 --> 00:04:48.950 can have identical energies. 00:04:48.950 --> 00:04:51.670 Now, again, this is not the accurate statement of Pauli, 00:04:51.670 --> 00:04:54.320 but this will help us, this is enough for us. 00:04:54.320 --> 00:04:56.230 So let's take a concrete example. 00:04:56.230 --> 00:04:59.590 Suppose we take, say, a sodium atom, 00:04:59.590 --> 00:05:03.600 then it has, it has 11 electrons inside it. 00:05:03.600 --> 00:05:05.393 There are 11 electrons. 00:05:07.040 --> 00:05:08.850 And now these 11 electrons 00:05:08.850 --> 00:05:11.480 can only have these specific energy levels. 00:05:11.480 --> 00:05:13.560 And the way these electrons 00:05:13.560 --> 00:05:15.200 are going to fill up the energy levels 00:05:15.200 --> 00:05:17.700 will be using the exclusion principle. 00:05:17.700 --> 00:05:21.250 So the first electron, well, remember, 00:05:21.250 --> 00:05:23.580 electrons always want to take the lowest energy possible. 00:05:23.580 --> 00:05:26.960 So the first electron would go over here, over here, 00:05:26.960 --> 00:05:28.610 and then you might think, well, the next electron 00:05:28.610 --> 00:05:31.050 can't go over here because that's what Pauli's telling us. 00:05:31.050 --> 00:05:32.410 No arguing with Pauli. 00:05:32.410 --> 00:05:34.110 Second electron, if it comes over here, 00:05:34.110 --> 00:05:37.260 it might have identical energy, but not really, 00:05:37.260 --> 00:05:40.700 because it turns out that electrons can have 00:05:40.700 --> 00:05:42.380 up spin and down spins. 00:05:42.380 --> 00:05:45.360 So if the first electron goes into the 1S tier, 00:05:45.360 --> 00:05:47.920 and suppose it takes up the up spin, 00:05:47.920 --> 00:05:50.370 then another electron can actually take up 00:05:50.370 --> 00:05:53.590 the same energy level and now be down spin 00:05:53.590 --> 00:05:54.950 because turns out these two spins 00:05:54.950 --> 00:05:57.100 have slightly different energy. 00:05:57.100 --> 00:05:59.240 So these two electrons are strictly speaking, 00:05:59.240 --> 00:06:02.140 still being Pauli, because they're not exactly identical 00:06:02.140 --> 00:06:03.740 because of their spins. 00:06:03.740 --> 00:06:05.640 But the next electron, the third electron, 00:06:05.640 --> 00:06:08.650 well, it cannot take up the 1S energy level anymore, 00:06:08.650 --> 00:06:10.640 because if it does and then up spin, 00:06:10.640 --> 00:06:11.880 then it'll be identical to this one. 00:06:11.880 --> 00:06:13.120 If it does with a down spin, 00:06:13.120 --> 00:06:15.100 then it'll be identical to this one. 00:06:15.100 --> 00:06:16.680 So it can't take the that up anywhere. 00:06:16.680 --> 00:06:18.150 So it has to take up now 00:06:18.150 --> 00:06:20.850 the next higher energy level available that's over here. 00:06:20.850 --> 00:06:22.730 It can take up anywhere in between as well. 00:06:22.730 --> 00:06:24.960 The energy levels in between are inaccessible 00:06:24.960 --> 00:06:25.793 to these electrons. 00:06:25.793 --> 00:06:28.280 So the next energy it will take up would be 2S, 00:06:28.280 --> 00:06:30.300 again, it might take up with an up spin. 00:06:30.300 --> 00:06:33.580 The fourth electron might go over with a down spin. 00:06:33.580 --> 00:06:36.910 The next electron will take up over here, up spin, 00:06:36.910 --> 00:06:38.763 and the next one will be down spin. 00:06:39.700 --> 00:06:40.850 Now here's the thing. 00:06:40.850 --> 00:06:44.060 It turns out that in P, in P energy level, 00:06:44.060 --> 00:06:46.630 there are three ways in which electrons 00:06:46.630 --> 00:06:48.420 can occupy that energy level. 00:06:48.420 --> 00:06:50.830 We call them as orbitals, right? 00:06:50.830 --> 00:06:52.960 It turns out that in the S energy levels, 00:06:52.960 --> 00:06:53.920 there's only one way. 00:06:53.920 --> 00:06:55.710 So there's only one orbital, 00:06:55.710 --> 00:06:57.900 but in P there are three orbitals. 00:06:57.900 --> 00:07:01.761 So another electron can take up the 2P energy level 00:07:01.761 --> 00:07:04.450 by being in a different orbital. 00:07:04.450 --> 00:07:05.910 So this electron and this electron 00:07:05.910 --> 00:07:07.660 will be in different orbitals, 00:07:07.660 --> 00:07:09.450 or different configuration, we could say, 00:07:09.450 --> 00:07:10.970 don't have to worry about it too much. 00:07:10.970 --> 00:07:12.930 And so they'll still not be identical. 00:07:12.930 --> 00:07:15.320 And so another electron can take up that same orbital 00:07:15.320 --> 00:07:16.750 with a down spin. 00:07:16.750 --> 00:07:21.170 Another electron, the third orbital of P with an up spin, 00:07:21.170 --> 00:07:22.880 and then down spin. 00:07:22.880 --> 00:07:25.040 And now the 2P is completely filled. 00:07:25.040 --> 00:07:28.170 There are no more orbitals available. 00:07:28.170 --> 00:07:29.190 And so the last electron, 00:07:29.190 --> 00:07:31.120 we're down to one, two, three, four, five, six, seven, 00:07:31.120 --> 00:07:35.090 eight, nine, 10, the last electron will be over here 00:07:35.090 --> 00:07:37.810 in the 3S up spin. 00:07:37.810 --> 00:07:41.540 But this is for a single atom of sodium. 00:07:41.540 --> 00:07:44.970 What if we have say, two atoms of sodium, 00:07:44.970 --> 00:07:47.413 very close to each other, what happens then? 00:07:49.090 --> 00:07:49.923 Somewhat like this, 00:07:49.923 --> 00:07:52.060 what if they form some kind of a molecule? 00:07:52.060 --> 00:07:54.990 How would the electrons of this molecule 00:07:54.990 --> 00:07:56.310 fill up the energy levels? 00:07:56.310 --> 00:07:59.600 Can we say that now each atom will have something like this. 00:07:59.600 --> 00:08:03.610 Each atom will have electrons filled up accordingly. 00:08:03.610 --> 00:08:06.160 Well, that won't work, that can't be possible. 00:08:06.160 --> 00:08:07.290 And the way we can think about it, 00:08:07.290 --> 00:08:09.370 is we can say that, if you do it this way, 00:08:09.370 --> 00:08:11.360 Pauli's rule will be violated. 00:08:11.360 --> 00:08:13.850 Remember, Pauli says no two electrons, 00:08:13.850 --> 00:08:15.490 and when we say no two electrons, 00:08:15.490 --> 00:08:17.740 it can be no two electrons inside an atom, 00:08:17.740 --> 00:08:20.370 or no two electrons inside a molecule, 00:08:20.370 --> 00:08:23.960 or maybe no two electrons inside an entire solid. 00:08:23.960 --> 00:08:26.490 No two electrons can have identical energies. 00:08:26.490 --> 00:08:30.040 So if the two atoms have these electron configurations 00:08:30.040 --> 00:08:32.390 then I hope you can see that this electron 00:08:32.390 --> 00:08:35.430 and this electron will, they will be identical. 00:08:35.430 --> 00:08:38.720 This one, and this one will be absolutely identical. 00:08:38.720 --> 00:08:40.960 And so all of them will have identical pairs 00:08:40.960 --> 00:08:45.360 and Pauli will be very, very sad, so that can't be possible. 00:08:45.360 --> 00:08:48.080 And if we have an entire solid, 00:08:48.080 --> 00:08:51.710 which is made of sodium, where we have like 10 to the 23 00:08:51.710 --> 00:08:53.870 atoms packed very close to each other, 00:08:53.870 --> 00:08:57.520 and if we used this model for each atom, 00:08:57.520 --> 00:09:00.835 then there would be about 10 to the 23 identical copies 00:09:00.835 --> 00:09:03.340 of electrons in each level. 00:09:03.340 --> 00:09:08.020 And that would make Pauli extremely sad, extremely sad. 00:09:08.020 --> 00:09:11.370 So the key takeaway is that this structure 00:09:11.370 --> 00:09:15.400 that we have learned for a single atom cannot be extended 00:09:15.400 --> 00:09:16.830 when we go all the way to the solids. 00:09:16.830 --> 00:09:19.700 We require a new theory to understand what's going on 00:09:19.700 --> 00:09:22.233 and how electrons are arranged or how to think about them 00:09:22.233 --> 00:09:24.040 when it comes to solids. 00:09:24.040 --> 00:09:26.583 And we'll explore them in the future videos.