WEBVTT 00:00:00.000 --> 00:00:02.420 align:middle line:84% The following content is provided under a Creative 00:00:02.420 --> 00:00:03.600 align:middle line:90% Commons license. 00:00:03.600 --> 00:00:06.050 align:middle line:84% Your support will help MIT OpenCourseWare 00:00:06.050 --> 00:00:09.650 align:middle line:84% continue to offer high quality educational resources for free. 00:00:09.650 --> 00:00:12.620 align:middle line:84% To make a donation or to view additional materials 00:00:12.620 --> 00:00:16.520 align:middle line:84% from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.520 --> 00:00:20.300 align:middle line:90% at ocw.mit.edu. 00:00:20.300 --> 00:00:23.870 align:middle line:84% GANG CHEN: OK, well, let me start talking. 00:00:23.870 --> 00:00:30.860 align:middle line:84% And I ran out of my slides, I mean, since last week. 00:00:30.860 --> 00:00:33.510 align:middle line:90% I was making this a new topic. 00:00:33.510 --> 00:00:38.330 align:middle line:84% And you will see, I thought I'm pretty familiar with this, 00:00:38.330 --> 00:00:41.460 align:middle line:90% but I still struggle a lot. 00:00:41.460 --> 00:00:48.060 align:middle line:84% And there is one place I will show where I'm still confused. 00:00:48.060 --> 00:00:51.590 align:middle line:90% Maybe you can help me. 00:00:51.590 --> 00:00:56.030 align:middle line:84% And then, that's always related to this electron negative charge 00:00:56.030 --> 00:00:57.360 align:middle line:90% that always confuse me. 00:00:57.360 --> 00:00:58.880 align:middle line:90% So I struggle a lot. 00:00:58.880 --> 00:01:02.330 align:middle line:90% 00:01:02.330 --> 00:01:07.400 align:middle line:84% So today, in the first few lectures, 00:01:07.400 --> 00:01:11.840 align:middle line:84% we discussed the thermal electric effect. 00:01:11.840 --> 00:01:17.940 align:middle line:84% And now we move on to talk about the thermionic engines. 00:01:17.940 --> 00:01:21.860 align:middle line:84% And also, I hope we will have time 00:01:21.860 --> 00:01:27.650 align:middle line:84% to discuss related topics from the discussion 00:01:27.650 --> 00:01:32.090 align:middle line:84% on thermionic engines, and also hoping to actually jump in 00:01:32.090 --> 00:01:36.980 align:middle line:84% to introduce you to really how pin junction works. 00:01:36.980 --> 00:01:42.920 align:middle line:84% And in terms of Schottky barrier and Schottky 00:01:42.920 --> 00:01:49.400 align:middle line:84% diode, that's really just a metal semiconductor interface. 00:01:49.400 --> 00:01:53.990 align:middle line:84% Again, I think from the vacuum thermionics, 00:01:53.990 --> 00:01:58.500 align:middle line:84% we can probably appreciate the evolution. 00:01:58.500 --> 00:02:00.200 align:middle line:84% I hope you will see the evolution. 00:02:00.200 --> 00:02:04.580 align:middle line:84% And then, in the mathematical formulation-- 00:02:04.580 --> 00:02:07.160 align:middle line:84% formula, the expression for current voltage 00:02:07.160 --> 00:02:07.945 align:middle line:90% are very similar. 00:02:07.945 --> 00:02:11.820 align:middle line:90% 00:02:11.820 --> 00:02:13.050 align:middle line:90% But let me-- 00:02:13.050 --> 00:02:17.070 align:middle line:84% I need something that we showed before. 00:02:17.070 --> 00:02:23.520 align:middle line:84% So this is the first, the Fermi-Dirac statistics. 00:02:23.520 --> 00:02:27.660 align:middle line:84% This was what we did in probably the first lecture, 00:02:27.660 --> 00:02:33.420 align:middle line:84% the occupation of electrons in a quantum state. 00:02:33.420 --> 00:02:37.950 align:middle line:84% And here you can see, it's a very-- this is the electron 00:02:37.950 --> 00:02:40.120 align:middle line:90% volts, 0.051. 00:02:40.120 --> 00:02:45.900 align:middle line:84% So the Fermi-Dirac distribution is very narrowly focused 00:02:45.900 --> 00:02:48.330 align:middle line:90% near the chemical potential. 00:02:48.330 --> 00:02:51.540 align:middle line:84% And if you are away from the chemical potential, 00:02:51.540 --> 00:02:57.240 align:middle line:84% the function-- either its state is fully filled or almost empty. 00:02:57.240 --> 00:03:00.570 align:middle line:90% And let me just make a remark. 00:03:00.570 --> 00:03:06.660 align:middle line:84% Typically, when we talk about thermionic emission, e minus mu, 00:03:06.660 --> 00:03:08.550 align:middle line:90% is u weight. 00:03:08.550 --> 00:03:12.430 align:middle line:84% So what we-- really, at the tail end, 00:03:12.430 --> 00:03:15.610 align:middle line:84% are for the Fermi-Dirac distribution. 00:03:15.610 --> 00:03:18.760 align:middle line:84% And the e minus mu is still u weight, 00:03:18.760 --> 00:03:23.160 align:middle line:84% kb is a 26 milli electron volts at room temperature. 00:03:23.160 --> 00:03:26.920 align:middle line:84% You can see that factor of 1 will drop out 00:03:26.920 --> 00:03:28.510 align:middle line:90% because it's insignificant. 00:03:28.510 --> 00:03:35.780 align:middle line:84% So use this when we derive the Richardson formula. 00:03:35.780 --> 00:03:42.290 align:middle line:84% And the other point that I will use in the discussion 00:03:42.290 --> 00:03:45.800 align:middle line:90% is the electron number density. 00:03:45.800 --> 00:03:48.710 align:middle line:84% So this is, again, we did before. 00:03:48.710 --> 00:03:53.690 align:middle line:84% We did the content of number of electrons counting 00:03:53.690 --> 00:03:55.790 align:middle line:90% all the quantum states. 00:03:55.790 --> 00:03:59.900 align:middle line:84% Each quantum state have two electron spin-up, spin-down. 00:03:59.900 --> 00:04:04.640 align:middle line:84% And this is the average number of electrons, two states, 00:04:04.640 --> 00:04:05.760 align:middle line:90% spin-up, spin-down. 00:04:05.760 --> 00:04:11.330 align:middle line:84% And from there, if we do the exponential, drop the 1, 00:04:11.330 --> 00:04:16.230 align:middle line:84% we get the electron number density is proportional. 00:04:16.230 --> 00:04:21.200 align:middle line:84% Here is, I want to point out t 3/2. 00:04:21.200 --> 00:04:23.960 align:middle line:84% So we group all this factor into nc. 00:04:23.960 --> 00:04:28.010 align:middle line:84% And then it's the difference of the conduction 00:04:28.010 --> 00:04:30.840 align:middle line:84% band to the chemical potential exponential. 00:04:30.840 --> 00:04:37.910 align:middle line:84% So that's what we had before in terms of electron density. 00:04:37.910 --> 00:04:46.710 align:middle line:84% And the other point is to make-- is to, again, review that we 00:04:46.710 --> 00:04:51.600 align:middle line:84% say, what's the difference between metals, semiconductors? 00:04:51.600 --> 00:04:57.350 align:middle line:84% In metal, we have the chemical potential for into the band. 00:04:57.350 --> 00:05:00.080 align:middle line:90% And semiconductor has bandgap. 00:05:00.080 --> 00:05:04.550 align:middle line:84% We dope it either n type or we dope the t type. 00:05:04.550 --> 00:05:07.760 align:middle line:84% Depends on what kind of atoms, for example, 00:05:07.760 --> 00:05:11.570 align:middle line:84% we put theta either boron, which is a t type, 00:05:11.570 --> 00:05:14.270 align:middle line:90% or phosphorus, which is n type. 00:05:14.270 --> 00:05:19.940 align:middle line:84% And that way we're shifting the Fermi level 00:05:19.940 --> 00:05:21.300 align:middle line:90% or the chemical potential. 00:05:21.300 --> 00:05:23.870 align:middle line:90% 00:05:23.870 --> 00:05:30.800 align:middle line:84% So those were what we covered previously. 00:05:30.800 --> 00:05:36.620 align:middle line:84% And now let's think about, if I have a material, meta, 00:05:36.620 --> 00:05:39.097 align:middle line:90% for example, I pull the-- 00:05:39.097 --> 00:05:40.430 align:middle line:90% I want to pull out the electron. 00:05:40.430 --> 00:05:43.220 align:middle line:90% 00:05:43.220 --> 00:05:49.100 align:middle line:84% And if I pull out the electron, the ion background, in metal 00:05:49.100 --> 00:05:50.660 align:middle line:90% attract the electron. 00:05:50.660 --> 00:05:54.950 align:middle line:84% So I have to do some work to pull it out. 00:05:54.950 --> 00:05:59.840 align:middle line:84% So the minimal amount of work that I pull electrons 00:05:59.840 --> 00:06:05.490 align:middle line:84% from inside immediately to outside, vacuum, 00:06:05.490 --> 00:06:07.790 align:middle line:90% is the work function. 00:06:07.790 --> 00:06:12.935 align:middle line:84% So from the Fermi level, this is a metal, from Fermi level, 00:06:12.935 --> 00:06:14.630 align:middle line:90% I pull electron. 00:06:14.630 --> 00:06:16.880 align:middle line:90% I pull it out to vacuum level. 00:06:16.880 --> 00:06:22.200 align:middle line:84% But this vacuum is immediately outside the metal. 00:06:22.200 --> 00:06:26.910 align:middle line:84% And then why I emphasize that, if you think about the-- 00:06:26.910 --> 00:06:28.290 align:middle line:90% I have a vacuum. 00:06:28.290 --> 00:06:31.470 align:middle line:84% I have positive charge, a negative charge. 00:06:31.470 --> 00:06:35.940 align:middle line:84% Even both positive and negative charge in vacuum, 00:06:35.940 --> 00:06:38.700 align:middle line:84% then the electrical potential at these two points, 00:06:38.700 --> 00:06:44.430 align:middle line:84% even in vacuum, are different because there is a potential 00:06:44.430 --> 00:06:47.040 align:middle line:90% from the [INAUDIBLE]. 00:06:47.040 --> 00:06:51.750 align:middle line:84% So I say, this is immediately outside the surface of how 00:06:51.750 --> 00:06:54.593 align:middle line:90% we define the work function. 00:06:54.593 --> 00:06:55.860 align:middle line:90% AUDIENCE: For metals, right? 00:06:55.860 --> 00:06:56.800 align:middle line:90% GANG CHEN: Yes. 00:06:56.800 --> 00:07:03.020 align:middle line:84% Semiconductor we have to use a different terminology. 00:07:03.020 --> 00:07:06.602 align:middle line:84% And that's how Einstein got the Nobel Prize. 00:07:06.602 --> 00:07:13.610 align:middle line:84% So he explained the photoconductivity effect, where 00:07:13.610 --> 00:07:17.690 align:middle line:84% the effect was you shine light on a metal, 00:07:17.690 --> 00:07:20.990 align:middle line:84% and then you get electricity, you get the electron out. 00:07:20.990 --> 00:07:23.210 align:middle line:90% So you can measure current. 00:07:23.210 --> 00:07:25.940 align:middle line:84% But what was puzzling at the time 00:07:25.940 --> 00:07:28.100 align:middle line:84% was that the number of the current 00:07:28.100 --> 00:07:32.540 align:middle line:84% not just depend on intensity, but depend on the wavelengths 00:07:32.540 --> 00:07:34.550 align:middle line:90% of the light. 00:07:34.550 --> 00:07:39.810 align:middle line:84% And see, so there was no explanation. 00:07:39.810 --> 00:07:43.790 align:middle line:84% And Einstein then explained, you have 00:07:43.790 --> 00:07:50.030 align:middle line:84% to have the photon energy larger than the work function 00:07:50.030 --> 00:07:53.360 align:middle line:84% to leave the electron on the metal surface. 00:07:53.360 --> 00:07:57.110 align:middle line:84% So the photon energy, of course, is inversely 00:07:57.110 --> 00:07:58.700 align:middle line:90% proportional to wavelength. 00:07:58.700 --> 00:08:01.700 align:middle line:84% So long wavelength full time not effective there. 00:08:01.700 --> 00:08:05.810 align:middle line:84% So not-- you know Einstein's Nobel Prize is not 00:08:05.810 --> 00:08:09.530 align:middle line:84% because of relativity, which was too radical. 00:08:09.530 --> 00:08:11.850 align:middle line:84% And this were more or less controversial. 00:08:11.850 --> 00:08:14.600 align:middle line:90% 00:08:14.600 --> 00:08:19.490 align:middle line:84% And then, in semiconductor, the Fermi level, 00:08:19.490 --> 00:08:21.260 align:middle line:90% there's no electron there. 00:08:21.260 --> 00:08:26.270 align:middle line:84% When we dope, it such that Fermi level fall inside the bandgap. 00:08:26.270 --> 00:08:30.590 align:middle line:84% So there are no electron between the conduction and valence band. 00:08:30.590 --> 00:08:32.780 align:middle line:90% The Fermi level is in between. 00:08:32.780 --> 00:08:37.610 align:middle line:84% So the way-- you could lift the electron, 00:08:37.610 --> 00:08:39.110 align:middle line:84% but then when you lift the electron, 00:08:39.110 --> 00:08:41.659 align:middle line:84% usually you lift from the bottom conduction 00:08:41.659 --> 00:08:44.690 align:middle line:84% band, which is ec to the vacuum level, 00:08:44.690 --> 00:08:46.760 align:middle line:90% and we give a different name. 00:08:46.760 --> 00:08:50.720 align:middle line:84% And in that case, we call it affinity. 00:08:50.720 --> 00:08:54.350 align:middle line:84% So semiconductor, because the chemical 00:08:54.350 --> 00:08:57.970 align:middle line:84% potential level can be changed by doping. 00:08:57.970 --> 00:09:02.230 align:middle line:84% But how much energy you need to lift an electron 00:09:02.230 --> 00:09:06.780 align:middle line:84% from the bottom conduction band to vacuum level, that's fixed. 00:09:06.780 --> 00:09:10.520 align:middle line:84% So this is a number you can look into tables, 00:09:10.520 --> 00:09:17.390 align:middle line:84% the affinity of semiconductors, and typically counted 00:09:17.390 --> 00:09:19.800 align:middle line:90% from conduction band edge. 00:09:19.800 --> 00:09:23.250 align:middle line:90% So those are the basics. 00:09:23.250 --> 00:09:30.120 align:middle line:84% And now, of course, if I think about the Fermi-Dirac 00:09:30.120 --> 00:09:34.410 align:middle line:84% statistics, there are some electrons with energy 00:09:34.410 --> 00:09:36.990 align:middle line:90% higher than w. 00:09:36.990 --> 00:09:42.730 align:middle line:84% Even though that f is very small, but it's not 0. 00:09:42.730 --> 00:09:47.500 align:middle line:84% So what I want to talk now is how much 00:09:47.500 --> 00:09:52.210 align:middle line:84% energy-- how many electrons is flowing out of the surface. 00:09:52.210 --> 00:09:54.760 align:middle line:84% And of course, you put a piece of metal there. 00:09:54.760 --> 00:09:55.620 align:middle line:90% You flow out. 00:09:55.620 --> 00:09:58.790 align:middle line:84% There are also ones that come back in randomly. 00:09:58.790 --> 00:10:01.450 align:middle line:84% And then, at the end, there may be some electron 00:10:01.450 --> 00:10:03.520 align:middle line:90% flying around the surface. 00:10:03.520 --> 00:10:08.720 align:middle line:84% I'm just looking into the flux coming out. 00:10:08.720 --> 00:10:12.440 align:middle line:90% So the flux comes out. 00:10:12.440 --> 00:10:16.435 align:middle line:90% e is the electron energy-- 00:10:16.435 --> 00:10:19.694 align:middle line:90% 00:10:19.694 --> 00:10:23.780 align:middle line:90% and say, outside. 00:10:23.780 --> 00:10:27.620 align:middle line:90% And I probably should not-- 00:10:27.620 --> 00:10:28.970 align:middle line:90% so this is where-- 00:10:28.970 --> 00:10:29.690 align:middle line:90% OK. 00:10:29.690 --> 00:10:32.570 align:middle line:90% Mu, this is one of the-- 00:10:32.570 --> 00:10:40.160 align:middle line:84% if you look at how we derive the chemical potential, 00:10:40.160 --> 00:10:42.560 align:middle line:84% you will see the derivation process 00:10:42.560 --> 00:10:49.700 align:middle line:84% is really mu is relative to the bottom of conduction band. 00:10:49.700 --> 00:10:51.750 align:middle line:84% And when I talk about work function 00:10:51.750 --> 00:10:54.200 align:middle line:90% is relative to the vacuum level. 00:10:54.200 --> 00:10:57.210 align:middle line:84% So there are some difference in the reference point. 00:10:57.210 --> 00:11:00.380 align:middle line:84% So that's the one place that can cause confusion. 00:11:00.380 --> 00:11:06.890 align:middle line:84% So I'm looking at, really, for those electrons with an energy 00:11:06.890 --> 00:11:10.260 align:middle line:90% above the vacuum level. 00:11:10.260 --> 00:11:14.220 align:middle line:84% And those energy, you can think of this kinetic energy 00:11:14.220 --> 00:11:17.715 align:middle line:84% inside in the vacuum here, that's the-- 00:11:17.715 --> 00:11:21.750 align:middle line:84% when I write this more, hk is the momentum. 00:11:21.750 --> 00:11:27.360 align:middle line:84% p squared divided by 2m is the kinetic energy, 00:11:27.360 --> 00:11:35.260 align:middle line:84% So those electrons, here, that's the kinetic energy. 00:11:35.260 --> 00:11:40.460 align:middle line:84% And I want to calculate the flux of the particle. 00:11:40.460 --> 00:11:42.520 align:middle line:84% I'm not putting charge there yet. 00:11:42.520 --> 00:11:45.400 align:middle line:90% I don't like that negative e. 00:11:45.400 --> 00:11:49.720 align:middle line:84% So just a particle flux coming out. 00:11:49.720 --> 00:11:53.560 align:middle line:84% So here, because it's coming out with kx, 00:11:53.560 --> 00:11:57.190 align:middle line:84% the wave vector, which is the momentum, 00:11:57.190 --> 00:11:59.500 align:middle line:90% it is the positive x direction. 00:11:59.500 --> 00:12:03.580 align:middle line:84% I don't do both from negative infinite to positive infinite. 00:12:03.580 --> 00:12:06.430 align:middle line:90% So now I do this summation. 00:12:06.430 --> 00:12:08.710 align:middle line:84% Because I'm looking at flux, so vx 00:12:08.710 --> 00:12:14.020 align:middle line:84% is the velocity in the x direction coming out. 00:12:14.020 --> 00:12:16.450 align:middle line:90% And then f is [INAUDIBLE] state. 00:12:16.450 --> 00:12:18.810 align:middle line:90% So I'm still doing my counting. 00:12:18.810 --> 00:12:23.130 align:middle line:84% The number of electrons, each electron has a velocity, 00:12:23.130 --> 00:12:26.210 align:middle line:84% and that gives me the flux there. 00:12:26.210 --> 00:12:33.950 align:middle line:84% So if you start from here, you do your normal way of converting 00:12:33.950 --> 00:12:36.960 align:middle line:84% this weight, because this is a flux, 00:12:36.960 --> 00:12:39.440 align:middle line:90% we should already be divided. 00:12:39.440 --> 00:12:41.180 align:middle line:90% That's a typo here. 00:12:41.180 --> 00:12:44.750 align:middle line:84% So if you do your normal conversion of the summation 00:12:44.750 --> 00:12:49.210 align:middle line:84% into integration, that's what we do here. 00:12:49.210 --> 00:12:57.550 align:middle line:84% And then, in reality, because the electron is-- 00:12:57.550 --> 00:13:01.010 align:middle line:84% or in terms of weight vector, it's not very large. 00:13:01.010 --> 00:13:05.200 align:middle line:84% So you actually can extend this integration really rather than 0 00:13:05.200 --> 00:13:08.440 align:middle line:90% to pi or a 0 to infinite. 00:13:08.440 --> 00:13:12.220 align:middle line:90% So what's the vx? 00:13:12.220 --> 00:13:16.240 align:middle line:84% vx here is a p divided by momentum. 00:13:16.240 --> 00:13:19.030 align:middle line:84% So I'm doing that because, at the end, 00:13:19.030 --> 00:13:23.740 align:middle line:84% you can do either energy integration or momentum 00:13:23.740 --> 00:13:24.560 align:middle line:90% integration. 00:13:24.560 --> 00:13:30.310 align:middle line:84% And in this case, you can say k, I integrate over k is easier. 00:13:30.310 --> 00:13:36.300 align:middle line:84% Because if I put this, drop the 1, 00:13:36.300 --> 00:13:42.150 align:middle line:84% and e minus mu is work function plus the kinetic energy. 00:13:42.150 --> 00:13:45.510 align:middle line:84% And you can see, if I do this integration, 00:13:45.510 --> 00:13:48.960 align:middle line:84% I can actually, because of the summation here, 00:13:48.960 --> 00:13:54.540 align:middle line:84% I can split each term and do integration kx, dky, dkz. 00:13:54.540 --> 00:13:58.170 align:middle line:84% So that's an easier integration than I convert it into energy. 00:13:58.170 --> 00:14:01.350 align:middle line:84% I show this because, like I said, the density of states 00:14:01.350 --> 00:14:03.660 align:middle line:90% is just a mathematical tool. 00:14:03.660 --> 00:14:08.650 align:middle line:84% If you use-- it's sometimes convenient to use it in energy, 00:14:08.650 --> 00:14:13.930 align:middle line:84% sometimes convenient to use just as momentum itself. 00:14:13.930 --> 00:14:19.420 align:middle line:84% So if I do this, go rather than 0 to pi over a, 0 to infinite, 00:14:19.420 --> 00:14:23.160 align:middle line:84% because this exponential function drops out quickly, 00:14:23.160 --> 00:14:24.250 align:middle line:90% this is what I get. 00:14:24.250 --> 00:14:27.274 align:middle line:90% 00:14:27.274 --> 00:14:31.680 align:middle line:84% And the exponential here, w, is the work function. 00:14:31.680 --> 00:14:32.480 align:middle line:90% it's the energy. 00:14:32.480 --> 00:14:33.965 align:middle line:90% kbt is also energy. 00:14:33.965 --> 00:14:36.940 align:middle line:90% 00:14:36.940 --> 00:14:41.640 align:middle line:84% This is a very small number because w is a few electron 00:14:41.640 --> 00:14:42.490 align:middle line:90% volts. 00:14:42.490 --> 00:14:46.080 align:middle line:84% kbt is 0.026 at room temperature. 00:14:46.080 --> 00:14:50.500 align:middle line:84% So that's a big negative exponent. 00:14:50.500 --> 00:14:54.910 align:middle line:84% But the front side, this term you can see 00:14:54.910 --> 00:14:56.530 align:middle line:90% is temperature-dependent. 00:14:56.530 --> 00:15:02.370 align:middle line:84% And we could write it in terms of t squared times a constant. 00:15:02.370 --> 00:15:05.090 align:middle line:90% So now I put it-- 00:15:05.090 --> 00:15:07.400 align:middle line:84% before I said it's particle flux. 00:15:07.400 --> 00:15:09.590 align:middle line:84% Now I put the charge, because each particle 00:15:09.590 --> 00:15:10.910 align:middle line:90% carries a negative e. 00:15:10.910 --> 00:15:14.690 align:middle line:90% So this is my current flux. 00:15:14.690 --> 00:15:18.440 align:middle line:84% So the current flux, now I have a t squared. 00:15:18.440 --> 00:15:24.420 align:middle line:84% And whatever in the front, I group it into a, so a t 00:15:24.420 --> 00:15:26.940 align:middle line:90% squared dot exponential. 00:15:26.940 --> 00:15:30.880 align:middle line:84% And this is the Richardson formula. 00:15:30.880 --> 00:15:35.080 align:middle line:84% And Richardson got, say, did a lot of experiment, 00:15:35.080 --> 00:15:39.400 align:middle line:84% and he was awarded a Nobel Prize for this work 00:15:39.400 --> 00:15:42.280 align:middle line:90% in the thermionic emission. 00:15:42.280 --> 00:15:45.550 align:middle line:84% But there are also, if you go to check the literature, in fact, 00:15:45.550 --> 00:15:49.840 align:middle line:84% the Dushman had a paper before him. 00:15:49.840 --> 00:15:54.340 align:middle line:84% So sometimes people call Richardson-Dushman formula 00:15:54.340 --> 00:15:56.590 align:middle line:84% rather than just Richardson formula. 00:15:56.590 --> 00:16:00.730 align:middle line:84% But the point is, we have a t square, 00:16:00.730 --> 00:16:08.950 align:middle line:84% we have exponential function for the flux of electrons coming out 00:16:08.950 --> 00:16:09.630 align:middle line:90% of the surface. 00:16:09.630 --> 00:16:12.790 align:middle line:90% 00:16:12.790 --> 00:16:19.870 align:middle line:84% And this is a constant a is called the Richardson constant. 00:16:19.870 --> 00:16:24.210 align:middle line:84% But, say, in more general form, because the quantum reflection, 00:16:24.210 --> 00:16:27.490 align:middle line:84% so this is, in fact, not just an a, 00:16:27.490 --> 00:16:29.610 align:middle line:90% there is a factor in the front. 00:16:29.610 --> 00:16:32.370 align:middle line:84% That's the electron get reflected 00:16:32.370 --> 00:16:35.620 align:middle line:84% even though its energy is larger than the work function. 00:16:35.620 --> 00:16:40.110 align:middle line:84% But the waves has always a possibility to get reflected. 00:16:40.110 --> 00:16:45.120 align:middle line:84% So that's a 1 minus r shows the transmission. 00:16:45.120 --> 00:16:47.670 align:middle line:90% And the rest is the-- 00:16:47.670 --> 00:16:52.890 align:middle line:84% what's the-- this one sometimes we use w, sometimes you use phi. 00:16:52.890 --> 00:16:54.110 align:middle line:90% It's all work function. 00:16:54.110 --> 00:16:56.858 align:middle line:90% 00:16:56.858 --> 00:17:00.770 align:middle line:90% So any question here? 00:17:00.770 --> 00:17:01.320 align:middle line:90% Yes. 00:17:01.320 --> 00:17:03.830 align:middle line:84% AUDIENCE: How did he measure that? 00:17:03.830 --> 00:17:05.930 align:middle line:84% GANG CHEN: How did he measure that? 00:17:05.930 --> 00:17:12.410 align:middle line:84% You put the voltage or, in fact, Edison did a lot of work too. 00:17:12.410 --> 00:17:16.220 align:middle line:84% This is this-- the beginning, so you see 00:17:16.220 --> 00:17:18.680 align:middle line:90% people develop vacuum tubes. 00:17:18.680 --> 00:17:22.700 align:middle line:84% So you can, in this case, you change the temperature, 00:17:22.700 --> 00:17:27.319 align:middle line:84% you measure the current that come out of the electrode. 00:17:27.319 --> 00:17:30.350 align:middle line:84% And what Richardson did different 00:17:30.350 --> 00:17:33.920 align:middle line:84% is before, if you go to read the literature, 00:17:33.920 --> 00:17:40.460 align:middle line:84% and people do the charge, this kind of thermionic emission, 00:17:40.460 --> 00:17:46.340 align:middle line:84% not in vacuum, just in air, in a, say, gas environment. 00:17:46.340 --> 00:17:50.510 align:middle line:84% And sometimes the surface is negative, sometimes is positive. 00:17:50.510 --> 00:17:53.420 align:middle line:84% So it made the explanation very difficult. 00:17:53.420 --> 00:17:57.230 align:middle line:84% What Richardson did was do it in vacuum. 00:17:57.230 --> 00:18:00.880 align:middle line:84% And that made the explanation much more cleaner. 00:18:00.880 --> 00:18:03.640 align:middle line:84% AUDIENCE: This is just for metal or everything? 00:18:03.640 --> 00:18:07.096 align:middle line:84% GANG CHEN: This is just for metal. 00:18:07.096 --> 00:18:09.090 align:middle line:84% And the w is for the work function. 00:18:09.090 --> 00:18:14.700 align:middle line:90% 00:18:14.700 --> 00:18:20.230 align:middle line:84% Now, next, this is where my confusion starts kicking in. 00:18:20.230 --> 00:18:24.630 align:middle line:84% And I mean, let's talk about two metals. 00:18:24.630 --> 00:18:26.830 align:middle line:84% They have different work functions. 00:18:26.830 --> 00:18:29.434 align:middle line:90% 00:18:29.434 --> 00:18:35.350 align:middle line:90% And you connect them together. 00:18:35.350 --> 00:18:39.610 align:middle line:84% And once you connect them, let's say, the charge 00:18:39.610 --> 00:18:42.810 align:middle line:90% will flow from one to the other. 00:18:42.810 --> 00:18:44.540 align:middle line:90% This is a mass diffusion. 00:18:44.540 --> 00:18:48.946 align:middle line:84% If the chemical potential are different, 00:18:48.946 --> 00:18:52.450 align:middle line:84% they always at the end will pull together 00:18:52.450 --> 00:18:53.960 align:middle line:90% equal chemical potential. 00:18:53.960 --> 00:18:55.490 align:middle line:84% You don't have any driving force. 00:18:55.490 --> 00:18:58.840 align:middle line:84% You just connect and put a wire in between them. 00:18:58.840 --> 00:19:05.710 align:middle line:84% So of course, two pieces of metal lie in contact, far away, 00:19:05.710 --> 00:19:09.690 align:middle line:84% each has a local vacuum level, no torque. 00:19:09.690 --> 00:19:13.090 align:middle line:84% But if I connect a piece of wire between the two, 00:19:13.090 --> 00:19:16.810 align:middle line:84% then the chemical potential is flat. 00:19:16.810 --> 00:19:19.630 align:middle line:84% So that means initially there is a current flow 00:19:19.630 --> 00:19:23.470 align:middle line:90% from one side to the other. 00:19:23.470 --> 00:19:25.030 align:middle line:90% And I was trying to think-- 00:19:25.030 --> 00:19:26.970 align:middle line:90% you can tell me now-- 00:19:26.970 --> 00:19:28.860 align:middle line:84% I was trying to think, now, what's 00:19:28.860 --> 00:19:30.610 align:middle line:84% the direction of this current flow? 00:19:30.610 --> 00:19:33.540 align:middle line:90% 00:19:33.540 --> 00:19:34.770 align:middle line:90% What do you think? 00:19:34.770 --> 00:19:36.900 align:middle line:84% What's the direction of the current flow? 00:19:36.900 --> 00:19:40.080 align:middle line:84% Sometimes we're forced to think, ask questions, 00:19:40.080 --> 00:19:41.580 align:middle line:90% try to explain to you. 00:19:41.580 --> 00:19:44.490 align:middle line:84% Even though I can't make it clear, but maybe 00:19:44.490 --> 00:19:47.680 align:middle line:84% I can make it clear when we all talk and think. 00:19:47.680 --> 00:19:55.640 align:middle line:84% So now I have one piece of metal at larger chemical potential-- 00:19:55.640 --> 00:20:01.160 align:middle line:84% larger work function, a piece of metal smaller work function. 00:20:01.160 --> 00:20:05.040 align:middle line:90% And I connected them together. 00:20:05.040 --> 00:20:08.190 align:middle line:84% If I don't connect them together, I think, 00:20:08.190 --> 00:20:10.447 align:middle line:84% when I put them very close to each other, 00:20:10.447 --> 00:20:11.780 align:middle line:90% I know the direction of current. 00:20:11.780 --> 00:20:16.180 align:middle line:90% 00:20:16.180 --> 00:20:18.410 align:middle line:90% When connected, I don't know. 00:20:18.410 --> 00:20:19.460 align:middle line:90% If I don't connect-- 00:20:19.460 --> 00:20:20.280 align:middle line:90% let me tell you. 00:20:20.280 --> 00:20:23.030 align:middle line:84% If I don't connect them, but I put 00:20:23.030 --> 00:20:26.660 align:middle line:84% them very close to each other, I think 00:20:26.660 --> 00:20:30.080 align:middle line:84% the electron will go from the high work function side 00:20:30.080 --> 00:20:33.340 align:middle line:84% to the lower work function side through the vacuum again. 00:20:33.340 --> 00:20:39.580 align:middle line:90% 00:20:39.580 --> 00:20:41.688 align:middle line:90% Do you agree? 00:20:41.688 --> 00:20:42.980 align:middle line:90% Or you have different argument? 00:20:42.980 --> 00:20:45.840 align:middle line:90% 00:20:45.840 --> 00:20:48.810 align:middle line:84% But when I connect them together, my question was, 00:20:48.810 --> 00:20:53.310 align:middle line:84% will the electron flow from the other way? 00:20:53.310 --> 00:20:57.570 align:middle line:90% 00:20:57.570 --> 00:21:01.290 align:middle line:84% Because that means, the question is, which one is positive, 00:21:01.290 --> 00:21:03.190 align:middle line:84% which one is negative at the end? 00:21:03.190 --> 00:21:09.320 align:middle line:90% 00:21:09.320 --> 00:21:12.840 align:middle line:84% I don't have-- I still don't have a good answer. 00:21:12.840 --> 00:21:18.620 align:middle line:84% AUDIENCE: When electron travels from the left to the right, then 00:21:18.620 --> 00:21:23.020 align:middle line:84% doesn't it increase the Fermi level of the right side? 00:21:23.020 --> 00:21:23.650 align:middle line:90% Then if you-- 00:21:23.650 --> 00:21:28.360 align:middle line:84% GANG CHEN: If the electrons go from left to right, 00:21:28.360 --> 00:21:31.670 align:middle line:90% it increased the Fermi level-- 00:21:31.670 --> 00:21:36.120 align:middle line:84% well, so this is another thing there. 00:21:36.120 --> 00:21:42.640 align:middle line:84% What's really increased is furthermore, 00:21:42.640 --> 00:21:44.820 align:middle line:84% it depends on how you measure it. 00:21:44.820 --> 00:21:47.830 align:middle line:84% I said that the way we calculate from Fermi level 00:21:47.830 --> 00:21:50.860 align:middle line:84% before is relative conduction band. 00:21:50.860 --> 00:21:53.590 align:middle line:84% Fermi level chemical potential is a measure 00:21:53.590 --> 00:21:57.230 align:middle line:90% of number of electrons. 00:21:57.230 --> 00:21:58.260 align:middle line:90% Maybe you're right. 00:21:58.260 --> 00:22:01.040 align:middle line:84% Maybe this is the way we should think about it. 00:22:01.040 --> 00:22:12.900 align:middle line:84% And maybe I should say, far away for the vacuum is the same. 00:22:12.900 --> 00:22:17.940 align:middle line:90% And then, so this is the-- 00:22:17.940 --> 00:22:20.910 align:middle line:84% because here I have a larger work function. 00:22:20.910 --> 00:22:24.574 align:middle line:84% Here I have smaller work function. 00:22:24.574 --> 00:22:25.885 align:middle line:90% Far away. 00:22:25.885 --> 00:22:31.080 align:middle line:84% So when I connected it together, so electron 00:22:31.080 --> 00:22:37.730 align:middle line:90% should go this way, the wire. 00:22:37.730 --> 00:22:41.240 align:middle line:84% But that's different from what I was saying. 00:22:41.240 --> 00:22:43.430 align:middle line:84% If I put the vacuum, the electron 00:22:43.430 --> 00:22:45.590 align:middle line:90% probably will go this way. 00:22:45.590 --> 00:22:46.680 align:middle line:90% AUDIENCE: Why? 00:22:46.680 --> 00:22:48.496 align:middle line:90% GANG CHEN: Huh? 00:22:48.496 --> 00:22:51.155 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:22:51.155 --> 00:22:51.780 align:middle line:90% GANG CHEN: Why? 00:22:51.780 --> 00:22:59.680 align:middle line:84% Because I was thinking somehow those electrons-- 00:22:59.680 --> 00:23:01.240 align:middle line:90% OK, this are they-- 00:23:01.240 --> 00:23:04.540 align:middle line:84% here is the energy, and this is the kinetic energy. 00:23:04.540 --> 00:23:07.060 align:middle line:84% Of course, you have to-- this kinetic energy 00:23:07.060 --> 00:23:09.410 align:middle line:90% must overcome the work function. 00:23:09.410 --> 00:23:13.820 align:middle line:84% So what's left over here is still 0. 00:23:13.820 --> 00:23:17.490 align:middle line:84% Just those kinetic energy just above the chemical-- 00:23:17.490 --> 00:23:22.120 align:middle line:84% the work vacuum is still 0, because the rest is used 00:23:22.120 --> 00:23:27.520 align:middle line:90% to overcome this work function. 00:23:27.520 --> 00:23:32.020 align:middle line:84% But anyway, so if I think this way, if I connect with the wire, 00:23:32.020 --> 00:23:35.960 align:middle line:84% then the electrons should flow this way. 00:23:35.960 --> 00:23:39.230 align:middle line:84% And that's what they were saying. 00:23:39.230 --> 00:23:41.600 align:middle line:90% In that way, maybe your reason-- 00:23:41.600 --> 00:23:45.080 align:middle line:84% so electron now, the chemical potential is raised, 00:23:45.080 --> 00:23:47.340 align:middle line:84% but you don't change the work function. 00:23:47.340 --> 00:23:50.660 align:middle line:84% So the vacuum level is raised here local. 00:23:50.660 --> 00:23:56.530 align:middle line:84% And then you have a, say, so this is the-- 00:23:56.530 --> 00:24:00.480 align:middle line:84% if I draw, that might be the local-- 00:24:00.480 --> 00:24:02.670 align:middle line:84% this is the vacuum, local vacuum level, 00:24:02.670 --> 00:24:04.790 align:middle line:90% this is local vacuum level. 00:24:04.790 --> 00:24:10.700 align:middle line:84% And then, my question then, so if the electron is 00:24:10.700 --> 00:24:18.110 align:middle line:84% flowing this way, how should I think which one is the positive? 00:24:18.110 --> 00:24:18.770 align:middle line:90% Yes. 00:24:18.770 --> 00:24:21.270 align:middle line:84% AUDIENCE: Does it depend on the difference between the Fermi 00:24:21.270 --> 00:24:23.390 align:middle line:84% level and the work functions, how 00:24:23.390 --> 00:24:24.852 align:middle line:90% they interact with each other? 00:24:24.852 --> 00:24:26.810 align:middle line:84% Because in this diagram, when you connect them, 00:24:26.810 --> 00:24:29.060 align:middle line:84% the Fermi levels become the same. 00:24:29.060 --> 00:24:30.980 align:middle line:84% GANG CHEN: Well, after you connect, 00:24:30.980 --> 00:24:32.570 align:middle line:90% the Fermi level has to be same. 00:24:32.570 --> 00:24:33.237 align:middle line:90% AUDIENCE: Right. 00:24:33.237 --> 00:24:36.920 align:middle line:84% So the work functions, depending on their differences, they can-- 00:24:36.920 --> 00:24:40.090 align:middle line:84% that you can have no flow or flow in either direction-- 00:24:40.090 --> 00:24:42.540 align:middle line:90% GANG CHEN: Yes. 00:24:42.540 --> 00:24:44.700 align:middle line:84% But see, I'm drawing a schematic where 00:24:44.700 --> 00:24:48.060 align:middle line:84% I have one side is a larger work function. 00:24:48.060 --> 00:24:50.910 align:middle line:84% So now with this work function is really relative to Fermi 00:24:50.910 --> 00:24:52.560 align:middle line:90% level to vacuum level, right? 00:24:52.560 --> 00:24:56.700 align:middle line:84% So my question is, which side is flowing? 00:24:56.700 --> 00:25:05.780 align:middle line:84% AUDIENCE: So-- looking at the Richardson formula, the smaller 00:25:05.780 --> 00:25:08.340 align:middle line:90% the w, the bigger the current. 00:25:08.340 --> 00:25:12.560 align:middle line:90% 00:25:12.560 --> 00:25:14.220 align:middle line:90% GANG CHEN: OK, so you're right. 00:25:14.220 --> 00:25:15.678 align:middle line:90% So the smaller-- 00:25:15.678 --> 00:25:17.720 align:middle line:84% OK, that's a good way to think about it, I think. 00:25:17.720 --> 00:25:18.803 align:middle line:90% AUDIENCE: That's kind of-- 00:25:18.803 --> 00:25:21.680 align:middle line:84% GANG CHEN: So the larger is the w. 00:25:21.680 --> 00:25:22.810 align:middle line:90% OK, good. 00:25:22.810 --> 00:25:26.570 align:middle line:84% So maybe this will be consistent. 00:25:26.570 --> 00:25:29.990 align:middle line:84% The larger is-- smaller w, more flux going 00:25:29.990 --> 00:25:33.590 align:middle line:90% this way and higher, less flux. 00:25:33.590 --> 00:25:36.900 align:middle line:84% So at the end, you will have more electrons on this side. 00:25:36.900 --> 00:25:39.650 align:middle line:84% So this will be positive, this will be negative. 00:25:39.650 --> 00:25:43.940 align:middle line:84% And that's consistent with my connecting wire. 00:25:43.940 --> 00:25:46.830 align:middle line:90% OK, now I agree. 00:25:46.830 --> 00:25:48.990 align:middle line:90% Thank you. 00:25:48.990 --> 00:25:51.810 align:middle line:84% AUDIENCE: The local vacuum level is shifted 00:25:51.810 --> 00:25:54.220 align:middle line:90% by the electrical potential. 00:25:54.220 --> 00:25:56.320 align:middle line:84% GANG CHEN: Well, that's the-- so, OK. 00:25:56.320 --> 00:26:02.670 align:middle line:84% Once you get more electrons here, now you think about, 00:26:02.670 --> 00:26:08.100 align:middle line:84% this is the-- electric field, the direction is this way. 00:26:08.100 --> 00:26:10.350 align:middle line:84% That's your electric field direction. 00:26:10.350 --> 00:26:16.320 align:middle line:84% And you will resist the further going to the other side. 00:26:16.320 --> 00:26:19.620 align:middle line:84% And then you draw your potential. 00:26:19.620 --> 00:26:22.500 align:middle line:84% Now, if you say, electrostatic field 00:26:22.500 --> 00:26:27.720 align:middle line:84% equals the energy, which is the potential divided by charge, 00:26:27.720 --> 00:26:32.310 align:middle line:84% which is negative, so when I fill 00:26:32.310 --> 00:26:34.710 align:middle line:84% this way, that means this flag here is higher, 00:26:34.710 --> 00:26:38.730 align:middle line:84% this flag is lower, that means the energy is higher, 00:26:38.730 --> 00:26:39.880 align:middle line:90% and this is lower. 00:26:39.880 --> 00:26:41.400 align:middle line:90% That's consistent. 00:26:41.400 --> 00:26:45.480 align:middle line:84% It's just this e, you have to think about the voltage opposite 00:26:45.480 --> 00:26:52.250 align:middle line:84% to e, to the local energies because of the negative charge. 00:26:52.250 --> 00:26:54.730 align:middle line:84% That's the part I really don't like. 00:26:54.730 --> 00:26:57.820 align:middle line:84% Every time I draw this diagram, I have to say, 00:26:57.820 --> 00:26:59.275 align:middle line:90% ah, electron is a negative. 00:26:59.275 --> 00:27:00.580 align:middle line:90% How I'm going to draw? 00:27:00.580 --> 00:27:02.940 align:middle line:84% Whether I'm drawing a potential here, 00:27:02.940 --> 00:27:05.230 align:middle line:90% here, here, OK, they're really-- 00:27:05.230 --> 00:27:06.550 align:middle line:90% OK. 00:27:06.550 --> 00:27:10.600 align:middle line:90% Here we have an energy or e. 00:27:10.600 --> 00:27:15.970 align:middle line:84% When that's talked about the electron energy or local energy. 00:27:15.970 --> 00:27:18.620 align:middle line:84% I say, when I talk about voltage, 00:27:18.620 --> 00:27:21.440 align:middle line:84% I talk about electrostatic potential. 00:27:21.440 --> 00:27:24.260 align:middle line:84% And electrostatic potential is really 00:27:24.260 --> 00:27:28.270 align:middle line:84% divided by charge, u divided by q. 00:27:28.270 --> 00:27:34.300 align:middle line:84% This q electron is [INAUDIBLE] to reverse the sign. 00:27:34.300 --> 00:27:41.300 align:middle line:84% So when I draw this way, as the potential, 00:27:41.300 --> 00:27:42.780 align:middle line:90% I'm drawing this work function. 00:27:42.780 --> 00:27:44.210 align:middle line:90% That's an energy unit. 00:27:44.210 --> 00:27:46.970 align:middle line:84% So when I draw the electrostatic, 00:27:46.970 --> 00:27:50.950 align:middle line:90% I have to reverse this way. 00:27:50.950 --> 00:27:51.450 align:middle line:90% See? 00:27:51.450 --> 00:27:55.200 align:middle line:84% This has a higher electrostatic than this side 00:27:55.200 --> 00:27:56.482 align:middle line:90% because the [INAUDIBLE]. 00:27:56.482 --> 00:28:00.740 align:middle line:90% 00:28:00.740 --> 00:28:03.130 align:middle line:84% That's where the confusion every time I have. 00:28:03.130 --> 00:28:06.050 align:middle line:90% But I do want to mention this. 00:28:06.050 --> 00:28:10.220 align:middle line:90% So now, clarify the question. 00:28:10.220 --> 00:28:15.860 align:middle line:84% So you get a w, so that's the w minus w prime. 00:28:15.860 --> 00:28:18.500 align:middle line:90% So really, this negative e is-- 00:28:18.500 --> 00:28:20.750 align:middle line:84% because I did w on this side, if I 00:28:20.750 --> 00:28:23.660 align:middle line:84% put the positive electrode, negative electrode, 00:28:23.660 --> 00:28:25.580 align:middle line:84% and I should mention negative voltage, 00:28:25.580 --> 00:28:29.060 align:middle line:84% that means this positive this negative. 00:28:29.060 --> 00:28:31.910 align:middle line:84% AUDIENCE: What does the dotted line mean? 00:28:31.910 --> 00:28:33.080 align:middle line:90% GANG CHEN: Huh? 00:28:33.080 --> 00:28:36.030 align:middle line:84% AUDIENCE: In the figure, we have a line in the middle. 00:28:36.030 --> 00:28:37.860 align:middle line:84% GANG CHEN: Oh, that's not my figure. 00:28:37.860 --> 00:28:39.140 align:middle line:90% I should have cited this. 00:28:39.140 --> 00:28:43.746 align:middle line:84% I got some-- this one was from [INAUDIBLE]. 00:28:43.746 --> 00:28:44.990 align:middle line:90% 00:28:44.990 --> 00:28:47.560 align:middle line:84% So what he's saying is that you are checking 00:28:47.560 --> 00:28:51.710 align:middle line:90% the electrostatic energy. 00:28:51.710 --> 00:28:54.860 align:middle line:84% Because this is a chemical potential, and there is also 00:28:54.860 --> 00:28:56.150 align:middle line:90% electrostatics. 00:28:56.150 --> 00:28:59.750 align:middle line:84% So here, the voltage is a positive here, 00:28:59.750 --> 00:29:03.996 align:middle line:84% but for electron, the electrostatic can move up. 00:29:03.996 --> 00:29:07.560 align:middle line:84% AUDIENCE: But in the upper figure, 00:29:07.560 --> 00:29:11.910 align:middle line:84% isn't it true that the right side should go up 00:29:11.910 --> 00:29:15.250 align:middle line:84% so that the work function level should be the same? 00:29:15.250 --> 00:29:15.750 align:middle line:90% I mean-- 00:29:15.750 --> 00:29:17.417 align:middle line:84% GANG CHEN: Work function doesn't change. 00:29:17.417 --> 00:29:20.587 align:middle line:84% Work function is that you pull electrons from metal-- 00:29:20.587 --> 00:29:21.420 align:middle line:90% AUDIENCE: Yeah, so-- 00:29:21.420 --> 00:29:23.910 align:middle line:84% GANG CHEN: --immediately out to the local vacuum. 00:29:23.910 --> 00:29:27.540 align:middle line:84% AUDIENCE: So when electrons are out from the metal, 00:29:27.540 --> 00:29:30.327 align:middle line:84% then the energy of the two electrons should be the same. 00:29:30.327 --> 00:29:31.660 align:middle line:90% GANG CHEN: No, that's the point. 00:29:31.660 --> 00:29:33.370 align:middle line:84% That's what I say at the beginning. 00:29:33.370 --> 00:29:36.790 align:middle line:90% You have a local vacuum. 00:29:36.790 --> 00:29:41.950 align:middle line:84% Once you see-- once the electron goes from this side 00:29:41.950 --> 00:29:45.031 align:middle line:90% to the other side, right? 00:29:45.031 --> 00:29:46.000 align:middle line:90% So here is positive. 00:29:46.000 --> 00:29:47.170 align:middle line:90% We got a negative. 00:29:47.170 --> 00:29:50.770 align:middle line:84% So the local vacuum locally on the surface 00:29:50.770 --> 00:29:57.560 align:middle line:84% here, a metal surface, there is a higher electrostatic potential 00:29:57.560 --> 00:29:58.170 align:middle line:90% than here. 00:29:58.170 --> 00:30:01.640 align:middle line:90% 00:30:01.640 --> 00:30:06.050 align:middle line:84% So the local vacuum level varies. 00:30:06.050 --> 00:30:09.080 align:middle line:84% AUDIENCE: But in your figure, in the middle-- 00:30:09.080 --> 00:30:09.860 align:middle line:90% GANG CHEN: Yeah? 00:30:09.860 --> 00:30:13.430 align:middle line:84% AUDIENCE: --the highest level that is the work function 00:30:13.430 --> 00:30:15.050 align:middle line:90% level is the same. 00:30:15.050 --> 00:30:16.310 align:middle line:90% It's different from-- 00:30:16.310 --> 00:30:19.220 align:middle line:84% GANG CHEN: No, what I put there is thinking at the beginning, 00:30:19.220 --> 00:30:19.980 align:middle line:90% far away. 00:30:19.980 --> 00:30:21.950 align:middle line:90% No talk to each other. 00:30:21.950 --> 00:30:25.050 align:middle line:84% If you put together, they start talking, 00:30:25.050 --> 00:30:27.990 align:middle line:84% you have local electrostatic influence, 00:30:27.990 --> 00:30:34.152 align:middle line:84% you will create an imbalance in the field, electrostatic field. 00:30:34.152 --> 00:30:34.985 align:middle line:90% AUDIENCE: OK, I see. 00:30:34.985 --> 00:30:38.723 align:middle line:84% So the upper figure does it mean that the two-- 00:30:38.723 --> 00:30:39.890 align:middle line:90% GANG CHEN: There is no talk. 00:30:39.890 --> 00:30:43.170 align:middle line:84% This is just a random, because you really can't align it. 00:30:43.170 --> 00:30:46.070 align:middle line:90% 00:30:46.070 --> 00:30:49.460 align:middle line:84% But this is where contact potential is-- 00:30:49.460 --> 00:30:53.700 align:middle line:84% this is actually defined as the contact potential. 00:30:53.700 --> 00:30:57.240 align:middle line:84% And I say this because, if it turns out 00:30:57.240 --> 00:31:01.522 align:middle line:84% that very often we want to measure the work function. 00:31:01.522 --> 00:31:02.730 align:middle line:90% And this is when I realized-- 00:31:02.730 --> 00:31:05.940 align:middle line:84% I suddenly realized this is an easy way to-- relatively easy 00:31:05.940 --> 00:31:08.540 align:middle line:90% way to measure work function. 00:31:08.540 --> 00:31:13.100 align:middle line:84% And one way to measure work function 00:31:13.100 --> 00:31:15.360 align:middle line:84% is just to measure the contact potential. 00:31:15.360 --> 00:31:17.180 align:middle line:84% You take a standard piece of material 00:31:17.180 --> 00:31:18.980 align:middle line:84% where you know the work function. 00:31:18.980 --> 00:31:22.670 align:middle line:84% And then you come close to the other piece, 00:31:22.670 --> 00:31:25.680 align:middle line:84% and you start to have current flow. 00:31:25.680 --> 00:31:30.180 align:middle line:84% Because when you close it, and your potential is the same, 00:31:30.180 --> 00:31:33.270 align:middle line:84% but when you change distance, your current-- 00:31:33.270 --> 00:31:35.310 align:middle line:84% because they used to think of capacitor, 00:31:35.310 --> 00:31:37.530 align:middle line:90% you still have current flow. 00:31:37.530 --> 00:31:40.740 align:middle line:84% And that's the so-called Kelvin probe. 00:31:40.740 --> 00:31:43.290 align:middle line:84% Kelvin probe, Kelvin method actually 00:31:43.290 --> 00:31:45.630 align:middle line:90% measure the contact potential. 00:31:45.630 --> 00:31:48.180 align:middle line:84% And using that, if you have a standard piece, 00:31:48.180 --> 00:31:51.090 align:middle line:84% you can measure the other contact potential. 00:31:51.090 --> 00:31:54.870 align:middle line:84% And I think Kelvin probe is standard [INAUDIBLE] rate if you 00:31:54.870 --> 00:31:57.540 align:middle line:90% buy atomic force microscope. 00:31:57.540 --> 00:32:02.220 align:middle line:84% You can add a few thousand and it will have a Kelvin probe 00:32:02.220 --> 00:32:03.386 align:middle line:90% software with it. 00:32:03.386 --> 00:32:06.850 align:middle line:90% 00:32:06.850 --> 00:32:08.600 align:middle line:90% So let's move on. 00:32:08.600 --> 00:32:11.240 align:middle line:90% Now I'm talking-- 00:32:11.240 --> 00:32:16.370 align:middle line:84% I'm thinking about, really, the diode. 00:32:16.370 --> 00:32:20.270 align:middle line:90% That's what I drew on the board. 00:32:20.270 --> 00:32:29.786 align:middle line:84% And again, I draw a higher and anode 00:32:29.786 --> 00:32:32.240 align:middle line:90% and a lower function cathode. 00:32:32.240 --> 00:32:37.700 align:middle line:84% So in this case, just as we discussed, 00:32:37.700 --> 00:32:40.130 align:middle line:84% you have a local vacuum level higher 00:32:40.130 --> 00:32:42.970 align:middle line:84% and then eventually the chemical potential is flat. 00:32:42.970 --> 00:32:46.332 align:middle line:90% 00:32:46.332 --> 00:32:51.340 align:middle line:84% And at the equilibrium, at the transient, 00:32:51.340 --> 00:32:52.750 align:middle line:90% they will have current. 00:32:52.750 --> 00:32:55.510 align:middle line:84% But eventually, you establish equilibrium. 00:32:55.510 --> 00:32:57.880 align:middle line:90% So this is the-- 00:32:57.880 --> 00:33:02.350 align:middle line:84% normally, this is the cathode current 00:33:02.350 --> 00:33:03.970 align:middle line:90% going from left to right. 00:33:03.970 --> 00:33:08.620 align:middle line:84% And this is the anode current from right to left. 00:33:08.620 --> 00:33:17.100 align:middle line:84% And you can say, I do not just do wc, I do a wc plus ec. 00:33:17.100 --> 00:33:20.450 align:middle line:84% This is because I'm thinking about the static state. 00:33:20.450 --> 00:33:24.030 align:middle line:84% I'm not thinking about the transient initial establishing 00:33:24.030 --> 00:33:24.990 align:middle line:90% equilibrium. 00:33:24.990 --> 00:33:27.990 align:middle line:84% So you can see, once you got a potential, 00:33:27.990 --> 00:33:32.050 align:middle line:84% the electron from here cannot really go here anymore. 00:33:32.050 --> 00:33:34.410 align:middle line:84% So only the electron with the energy 00:33:34.410 --> 00:33:37.350 align:middle line:84% u on this side, with the energy higher than this point 00:33:37.350 --> 00:33:40.380 align:middle line:90% can go to the other side. 00:33:40.380 --> 00:33:44.510 align:middle line:90% So at the end you get the-- 00:33:44.510 --> 00:33:49.060 align:middle line:84% at the equilibrium, the difference of the two is 0. 00:33:49.060 --> 00:33:51.490 align:middle line:90% There is no net current flux. 00:33:51.490 --> 00:33:56.490 align:middle line:84% You put the two pieces of metal together, you connect them. 00:33:56.490 --> 00:33:59.220 align:middle line:84% Rather than just the initial current, at the end, 00:33:59.220 --> 00:34:01.920 align:middle line:90% it should be no current flow. 00:34:01.920 --> 00:34:05.280 align:middle line:84% Otherwise you get a perpetual motor. 00:34:05.280 --> 00:34:08.440 align:middle line:90% 00:34:08.440 --> 00:34:12.750 align:middle line:84% So that's the vacuum at equilibrium. 00:34:12.750 --> 00:34:14.880 align:middle line:84% Now I'm going to put a temperature difference 00:34:14.880 --> 00:34:17.380 align:middle line:90% across it. 00:34:17.380 --> 00:34:20.710 align:middle line:84% One side is hotter cathode, I made it hotter, 00:34:20.710 --> 00:34:23.380 align:middle line:90% and one is colder. 00:34:23.380 --> 00:34:30.070 align:middle line:84% And of course, I still have the current. 00:34:30.070 --> 00:34:35.380 align:middle line:84% And if I write the Richardson expression-- 00:34:35.380 --> 00:34:36.040 align:middle line:90% OK. 00:34:36.040 --> 00:34:42.850 align:middle line:84% Now, in this case, if you think about it, when you heat it up, 00:34:42.850 --> 00:34:45.610 align:middle line:84% there should be more electrons gaining 00:34:45.610 --> 00:34:50.080 align:middle line:84% kinetic energy, higher kinetic energy, higher temperature. 00:34:50.080 --> 00:34:55.400 align:middle line:84% So the electron will go from cathode to anode. 00:34:55.400 --> 00:34:59.570 align:middle line:84% So electron, there are some current go here. 00:34:59.570 --> 00:35:05.810 align:middle line:84% And so, eventually, relative to speaking, 00:35:05.810 --> 00:35:09.830 align:middle line:84% the chemical potential will no longer be the same. 00:35:09.830 --> 00:35:11.750 align:middle line:84% And really, this chemical potential 00:35:11.750 --> 00:35:14.300 align:middle line:84% is the electrochemical potential. 00:35:14.300 --> 00:35:19.610 align:middle line:84% Because what I added here, the voltage that's generated 00:35:19.610 --> 00:35:21.480 align:middle line:90% added to the chemical potential. 00:35:21.480 --> 00:35:25.820 align:middle line:84% So this level is the electrochemical potential. 00:35:25.820 --> 00:35:27.470 align:middle line:90% And that's what I can measure. 00:35:27.470 --> 00:35:28.940 align:middle line:84% When I put the two electrodes, I'll 00:35:28.940 --> 00:35:30.710 align:middle line:90% measure a voltage difference. 00:35:30.710 --> 00:35:33.620 align:middle line:84% And that voltage difference is these two points, 00:35:33.620 --> 00:35:35.086 align:middle line:90% voltage difference. 00:35:35.086 --> 00:35:37.856 align:middle line:90% 00:35:37.856 --> 00:35:46.880 align:middle line:84% So because of that, my current, cathode current, now-- 00:35:46.880 --> 00:35:50.290 align:middle line:84% and this is what I originally had. 00:35:50.290 --> 00:35:52.660 align:middle line:90% And this is the additional. 00:35:52.660 --> 00:35:57.750 align:middle line:84% And again, this is where I don't like it because I put a-- 00:35:57.750 --> 00:36:00.701 align:middle line:90% I should put a negative sign. 00:36:00.701 --> 00:36:07.140 align:middle line:84% Because if you think about, the electron here now, 00:36:07.140 --> 00:36:08.940 align:middle line:84% the electron that needs to go over 00:36:08.940 --> 00:36:12.360 align:middle line:84% this, so from electrochemical potential mu c 00:36:12.360 --> 00:36:15.540 align:middle line:90% to the maximum point is-- 00:36:15.540 --> 00:36:18.610 align:middle line:90% the distance is shorter. 00:36:18.610 --> 00:36:21.820 align:middle line:90% And I put a positive sign here. 00:36:21.820 --> 00:36:26.110 align:middle line:84% So ideally, I should get the negative solution v0. 00:36:26.110 --> 00:36:27.705 align:middle line:90% That's my open circuit voltage. 00:36:27.705 --> 00:36:31.486 align:middle line:90% 00:36:31.486 --> 00:36:34.330 align:middle line:90% And I don't think I get that. 00:36:34.330 --> 00:36:36.460 align:middle line:90% I still don't know why. 00:36:36.460 --> 00:36:40.434 align:middle line:84% My sign doesn't seem to be right. 00:36:40.434 --> 00:36:43.000 align:middle line:90% So I give you the challenge. 00:36:43.000 --> 00:36:45.990 align:middle line:84% You go back to sort it out and come back and teach me. 00:36:45.990 --> 00:36:51.040 align:middle line:90% And this is the cathode. 00:36:51.040 --> 00:36:53.190 align:middle line:90% This is the anode. 00:36:53.190 --> 00:36:56.610 align:middle line:84% And of course, at steady state, if I 00:36:56.610 --> 00:36:59.670 align:middle line:84% don't put any connectors there, I 00:36:59.670 --> 00:37:02.430 align:middle line:84% have a voltage difference between these-- 00:37:02.430 --> 00:37:06.060 align:middle line:90% real voltage that I can measure. 00:37:06.060 --> 00:37:14.280 align:middle line:84% So again, this doesn't relate to the negative charge, 00:37:14.280 --> 00:37:18.190 align:middle line:84% but at the equilibrium, I should not 00:37:18.190 --> 00:37:21.298 align:middle line:84% say at equilibrium, at steady state, not equilibrium. 00:37:21.298 --> 00:37:22.840 align:middle line:84% When you have temperature difference, 00:37:22.840 --> 00:37:24.760 align:middle line:84% you have chemical potential difference, 00:37:24.760 --> 00:37:26.080 align:middle line:90% you don't have equilibrium. 00:37:26.080 --> 00:37:30.100 align:middle line:84% Accurate way to say is at steady state. 00:37:30.100 --> 00:37:34.390 align:middle line:84% At steady state, there is no net current flow 00:37:34.390 --> 00:37:37.390 align:middle line:84% because I didn't connect it to any load. 00:37:37.390 --> 00:37:39.010 align:middle line:90% I have open circuit. 00:37:39.010 --> 00:37:42.370 align:middle line:90% So current is 0. 00:37:42.370 --> 00:37:45.640 align:middle line:84% So if I go through this steps, put 00:37:45.640 --> 00:37:52.225 align:middle line:84% this two expressions, this one minus this one is 0. 00:37:52.225 --> 00:37:55.570 align:middle line:90% So I'm going to do that. 00:37:55.570 --> 00:37:56.830 align:middle line:90% This are the two terms. 00:37:56.830 --> 00:38:01.480 align:middle line:90% 00:38:01.480 --> 00:38:08.180 align:middle line:84% And I take the ratio, I take a log, get rid of my exponential. 00:38:08.180 --> 00:38:10.890 align:middle line:90% 00:38:10.890 --> 00:38:15.010 align:middle line:84% Second step, I was hoping I'd get a negative sign, 00:38:15.010 --> 00:38:16.060 align:middle line:90% but I don't get it. 00:38:16.060 --> 00:38:19.270 align:middle line:84% So tell me where I should get it. 00:38:19.270 --> 00:38:21.495 align:middle line:84% I didn't see, I get a negative sign. 00:38:21.495 --> 00:38:26.800 align:middle line:90% 00:38:26.800 --> 00:38:29.050 align:middle line:90% I still don't know why. 00:38:29.050 --> 00:38:34.260 align:middle line:84% But anyway, the magnitude is correct. 00:38:34.260 --> 00:38:37.990 align:middle line:90% The sign somehow, I don't know. 00:38:37.990 --> 00:38:45.730 align:middle line:84% But let me also look at this and point out 00:38:45.730 --> 00:38:48.250 align:middle line:84% that if you think about before, when 00:38:48.250 --> 00:38:54.460 align:middle line:84% we talk about Seebeck effect, is a voltage divided by delta t. 00:38:54.460 --> 00:38:58.390 align:middle line:84% So if I do a voltage divided by delta t, not delta t, 00:38:58.390 --> 00:39:01.970 align:middle line:84% just an order of magnitude, this term I put it here. 00:39:01.970 --> 00:39:05.410 align:middle line:90% And here is kb divided by e. 00:39:05.410 --> 00:39:09.370 align:middle line:84% 2kb divided by e, that's of the same order of Seebeck 00:39:09.370 --> 00:39:10.850 align:middle line:90% coefficient. 00:39:10.850 --> 00:39:13.650 align:middle line:84% So this term actually come from-- 00:39:13.650 --> 00:39:17.360 align:middle line:84% is a very similar to the thermoelectric. 00:39:17.360 --> 00:39:22.480 align:middle line:84% And this term is the thermionic term here 00:39:22.480 --> 00:39:25.750 align:middle line:84% because it depends on the barrier height of the anode-- 00:39:25.750 --> 00:39:26.860 align:middle line:90% anode barrier height. 00:39:26.860 --> 00:39:30.195 align:middle line:90% 00:39:30.195 --> 00:39:33.710 align:middle line:84% So that's the open circuit voltage. 00:39:33.710 --> 00:39:37.390 align:middle line:90% 00:39:37.390 --> 00:39:41.690 align:middle line:84% And of course, open circuit is useless. 00:39:41.690 --> 00:39:43.520 align:middle line:90% You don't generate any power. 00:39:43.520 --> 00:39:46.750 align:middle line:84% You have maximal voltage, but you don't generate power. 00:39:46.750 --> 00:39:49.990 align:middle line:84% This is the same for photovoltaic cell, 00:39:49.990 --> 00:39:52.690 align:middle line:90% So you need to put a load here. 00:39:52.690 --> 00:39:55.990 align:middle line:84% Once your current start flow, you 00:39:55.990 --> 00:39:59.540 align:middle line:84% don't get that high open circuit voltage anymore. 00:39:59.540 --> 00:40:02.230 align:middle line:90% You get your actual voltage. 00:40:02.230 --> 00:40:04.690 align:middle line:90% That's the actual voltage. 00:40:04.690 --> 00:40:09.280 align:middle line:84% And you can change this voltage by changing your load 00:40:09.280 --> 00:40:10.520 align:middle line:90% resistance. 00:40:10.520 --> 00:40:11.950 align:middle line:90% That's a load matching. 00:40:11.950 --> 00:40:15.220 align:middle line:84% That's for all solid state device, solar cells, 00:40:15.220 --> 00:40:20.320 align:middle line:84% thermoelectrics, thermionic, you have to optimize your load 00:40:20.320 --> 00:40:25.150 align:middle line:84% or optimize the device itself to match the internal and external. 00:40:25.150 --> 00:40:26.120 align:middle line:90% That's load matching. 00:40:26.120 --> 00:40:28.650 align:middle line:90% 00:40:28.650 --> 00:40:32.010 align:middle line:90% So if I write-- 00:40:32.010 --> 00:40:35.070 align:middle line:84% I rewrite the expression because the contact potential 00:40:35.070 --> 00:40:37.440 align:middle line:90% is the same as wa. 00:40:37.440 --> 00:40:42.250 align:middle line:84% And you can say my current depends on the voltage. 00:40:42.250 --> 00:40:47.130 align:middle line:84% And of course, power is just current times the voltage. 00:40:47.130 --> 00:40:49.780 align:middle line:90% 00:40:49.780 --> 00:40:56.260 align:middle line:84% So that's my unit volume power, unit surface, I think, 00:40:56.260 --> 00:40:59.050 align:middle line:90% because j is the surface. 00:40:59.050 --> 00:41:01.390 align:middle line:90% And so, that's the power. 00:41:01.390 --> 00:41:07.120 align:middle line:84% Now, for thermionic generator, I have to do the efficiency. 00:41:07.120 --> 00:41:10.630 align:middle line:84% So I have to look at how much heat transfer happen. 00:41:10.630 --> 00:41:13.840 align:middle line:84% I have now electrical power output. 00:41:13.840 --> 00:41:17.040 align:middle line:84% I have to look at how much heat transfer. 00:41:17.040 --> 00:41:19.690 align:middle line:84% So what are the mode of heat transfer 00:41:19.690 --> 00:41:21.390 align:middle line:90% here if you look at this? 00:41:21.390 --> 00:41:24.900 align:middle line:90% 00:41:24.900 --> 00:41:26.600 align:middle line:90% First, this side is hot. 00:41:26.600 --> 00:41:27.530 align:middle line:90% This side is cold. 00:41:27.530 --> 00:41:28.980 align:middle line:90% There is a radiation. 00:41:28.980 --> 00:41:33.072 align:middle line:90% Any other heat transfer? 00:41:33.072 --> 00:41:35.100 align:middle line:90% AUDIENCE: Electron carries heat. 00:41:35.100 --> 00:41:37.930 align:middle line:90% GANG CHEN: That's right. 00:41:37.930 --> 00:41:42.490 align:middle line:84% Just, we don't forget electrons also carry heat. 00:41:42.490 --> 00:41:47.410 align:middle line:84% So first, let's look at-- that's a fundamental site. 00:41:47.410 --> 00:41:50.470 align:middle line:84% Radiation is not necessarily due to electrons. 00:41:50.470 --> 00:41:51.910 align:middle line:90% It could be due to lattice. 00:41:51.910 --> 00:41:54.690 align:middle line:84% But electron, when you have charge flow, 00:41:54.690 --> 00:41:56.110 align:middle line:90% always carry the heat. 00:41:56.110 --> 00:41:58.870 align:middle line:84% So I have to count that part of heat. 00:41:58.870 --> 00:42:00.650 align:middle line:90% So this is the first step. 00:42:00.650 --> 00:42:02.480 align:middle line:90% What's the kinetic energy? 00:42:02.480 --> 00:42:07.630 align:middle line:84% That's the-- just the 1/2 mv squared. 00:42:07.630 --> 00:42:10.240 align:middle line:84% So this is a p squared divided by 2m. 00:42:10.240 --> 00:42:13.810 align:middle line:84% That's the kinetic energy above the barrier. 00:42:13.810 --> 00:42:17.250 align:middle line:84% So I do my integration in the same way 00:42:17.250 --> 00:42:21.900 align:middle line:84% I did before as I do particle flux. 00:42:21.900 --> 00:42:23.740 align:middle line:84% I didn't start from beginning here. 00:42:23.740 --> 00:42:25.970 align:middle line:90% I just write the expression. 00:42:25.970 --> 00:42:28.710 align:middle line:90% And I do my integration. 00:42:28.710 --> 00:42:35.100 align:middle line:84% And it turns out the heat flux, kinetic part of the heat flux is 00:42:35.100 --> 00:42:38.490 align:middle line:84% proportional to current flux then 2k be, 00:42:38.490 --> 00:42:40.740 align:middle line:90% That's the Seebeck coefficient-- 00:42:40.740 --> 00:42:41.470 align:middle line:90% times t. 00:42:41.470 --> 00:42:43.320 align:middle line:84% So Peltier coefficient, remember, 00:42:43.320 --> 00:42:47.250 align:middle line:84% in the thermoelectrics, Peltier coefficient equal Seebeck 00:42:47.250 --> 00:42:49.405 align:middle line:90% times t. 00:42:49.405 --> 00:42:53.530 align:middle line:84% So you can see, this is very much the Seebeck part. 00:42:53.530 --> 00:42:58.670 align:middle line:84% This is the Peltier coefficient, Seebeck times t, times part. 00:42:58.670 --> 00:43:04.100 align:middle line:84% So this is the [INAUDIBLE] carried by electrons 00:43:04.100 --> 00:43:06.550 align:middle line:90% from cathode to anode. 00:43:06.550 --> 00:43:08.325 align:middle line:90% But then heat is more than this. 00:43:08.325 --> 00:43:10.920 align:middle line:90% 00:43:10.920 --> 00:43:15.000 align:middle line:84% Because, remember, when we define the heat 00:43:15.000 --> 00:43:18.540 align:middle line:84% is the energy minus chemical potential, 00:43:18.540 --> 00:43:24.410 align:middle line:84% e minus mu, relative to chemical potential. 00:43:24.410 --> 00:43:27.360 align:middle line:84% So relative to chemical potential, 00:43:27.360 --> 00:43:30.060 align:middle line:84% I have this part is kinetic energy. 00:43:30.060 --> 00:43:34.560 align:middle line:84% Then I have really from here to here. 00:43:34.560 --> 00:43:37.170 align:middle line:90% This is a cathode site. 00:43:37.170 --> 00:43:38.910 align:middle line:84% The energy, the one that really go 00:43:38.910 --> 00:43:43.830 align:middle line:84% over the barrier, the rest of it from here to here. 00:43:43.830 --> 00:43:50.940 align:middle line:90% So that's my w 4 e minus v here. 00:43:50.940 --> 00:43:53.970 align:middle line:90% So this is from here to here. 00:43:53.970 --> 00:44:00.810 align:middle line:84% That's my potential part, and this is the 1/2 mv squared 00:44:00.810 --> 00:44:02.560 align:middle line:90% kinetic. 00:44:02.560 --> 00:44:04.610 align:middle line:84% So that's all the heat it carries. 00:44:04.610 --> 00:44:08.370 align:middle line:90% 00:44:08.370 --> 00:44:11.860 align:middle line:84% What is this in terms of resemblance? 00:44:11.860 --> 00:44:14.050 align:middle line:84% If you're a mechanical engineer, think of this. 00:44:14.050 --> 00:44:15.730 align:middle line:90% Give me an analogy. 00:44:15.730 --> 00:44:20.000 align:middle line:90% 00:44:20.000 --> 00:44:20.500 align:middle line:90% Huh? 00:44:20.500 --> 00:44:23.650 align:middle line:90% 00:44:23.650 --> 00:44:25.575 align:middle line:90% This is evaporation of water. 00:44:25.575 --> 00:44:28.840 align:middle line:90% 00:44:28.840 --> 00:44:34.790 align:middle line:84% The water molecule coming out of the surface 00:44:34.790 --> 00:44:40.790 align:middle line:84% carry a lot more energy because you have to say the energy is-- 00:44:40.790 --> 00:44:49.380 align:middle line:84% say every other-- so if you think about the water, 00:44:49.380 --> 00:44:59.260 align:middle line:84% and there are some molecules flying around. 00:44:59.260 --> 00:45:04.650 align:middle line:84% If I take all the molecule away, and then there's 00:45:04.650 --> 00:45:06.900 align:middle line:84% another molecule we created behind. 00:45:06.900 --> 00:45:09.090 align:middle line:84% And the creation of this molecule 00:45:09.090 --> 00:45:13.150 align:middle line:84% from the liquid phase to the vapor phase, this 00:45:13.150 --> 00:45:15.050 align:middle line:90% is the lock and key. 00:45:15.050 --> 00:45:23.130 align:middle line:84% Essentially, those terms, this and the heat of the 00:45:23.130 --> 00:45:28.460 align:middle line:84% electrons when you come out of the surface. 00:45:28.460 --> 00:45:32.020 align:middle line:90% And this is the kinetic part. 00:45:32.020 --> 00:45:35.980 align:middle line:90% But at the end, also I see this. 00:45:35.980 --> 00:45:40.090 align:middle line:84% I still have a little bit of trouble thinking 00:45:40.090 --> 00:45:43.600 align:middle line:84% this as a evaporation process, because I'm 00:45:43.600 --> 00:45:47.860 align:middle line:84% trying to think of an analogy of, OK, here 00:45:47.860 --> 00:45:53.650 align:middle line:90% is a potential, the bottom. 00:45:53.650 --> 00:45:56.570 align:middle line:84% You come out here, so that's the minimum. 00:45:56.570 --> 00:45:59.680 align:middle line:90% So each molecule carry out this. 00:45:59.680 --> 00:46:02.860 align:middle line:84% I say, that's an evaporation process. 00:46:02.860 --> 00:46:06.530 align:middle line:84% But what about suddenly a bottle-- 00:46:06.530 --> 00:46:08.650 align:middle line:90% OK. 00:46:08.650 --> 00:46:10.550 align:middle line:90% What about this process? 00:46:10.550 --> 00:46:12.910 align:middle line:84% If I have a high energy electron, 00:46:12.910 --> 00:46:18.050 align:middle line:84% and the potential here suddenly fall off a cliff? 00:46:18.050 --> 00:46:22.550 align:middle line:84% And then that's excess energy, potential energy. 00:46:22.550 --> 00:46:26.020 align:middle line:84% Do I consider that as a evaporation process also? 00:46:26.020 --> 00:46:34.700 align:middle line:84% Then I'm a little bit confused whether to think of mechanical. 00:46:34.700 --> 00:46:38.410 align:middle line:90% I don't know what's the-- 00:46:38.410 --> 00:46:43.180 align:middle line:84% whether I can give an analogy of this two different processes 00:46:43.180 --> 00:46:44.950 align:middle line:90% in terms of evaporation. 00:46:44.950 --> 00:46:50.480 align:middle line:84% And this one is more, to me, somehow, to me, 00:46:50.480 --> 00:46:56.510 align:middle line:84% is I have a container of liquid, I open a hole. 00:46:56.510 --> 00:46:58.170 align:middle line:90% This is a high temperature. 00:46:58.170 --> 00:47:02.540 align:middle line:84% When the liquid come out here to the other side, the vacuum, 00:47:02.540 --> 00:47:07.730 align:middle line:84% it suddenly evaporate, change from a liquid phase 00:47:07.730 --> 00:47:11.580 align:middle line:90% to vapor phase. 00:47:11.580 --> 00:47:15.693 align:middle line:84% I'm making this to this and this to this. 00:47:15.693 --> 00:47:19.080 align:middle line:90% 00:47:19.080 --> 00:47:21.060 align:middle line:84% You can tell me whether you agree. 00:47:21.060 --> 00:47:23.370 align:middle line:84% But at the end, I'll give you one example 00:47:23.370 --> 00:47:25.920 align:middle line:84% where I struggle on this question-- 00:47:25.920 --> 00:47:29.234 align:middle line:90% why I struggle on this question. 00:47:29.234 --> 00:47:32.130 align:middle line:90% So that's the electron heat. 00:47:32.130 --> 00:47:37.320 align:middle line:84% And of course, there's also another side from a-- 00:47:37.320 --> 00:47:39.860 align:middle line:90% I can reverse this. 00:47:39.860 --> 00:47:42.020 align:middle line:90% This is from anode to cathode. 00:47:42.020 --> 00:47:46.370 align:middle line:90% This is from cathode to anode. 00:47:46.370 --> 00:47:48.320 align:middle line:90% And the difference give me-- 00:47:48.320 --> 00:47:51.130 align:middle line:84% this is the electronic part of the heat. 00:47:51.130 --> 00:47:52.940 align:middle line:90% That's the first two. 00:47:52.940 --> 00:47:56.930 align:middle line:90% And then we have radiation part. 00:47:56.930 --> 00:48:01.240 align:middle line:84% And then you have a lead, that lead conduct heat. 00:48:01.240 --> 00:48:03.170 align:middle line:84% So that's a conduction heat loss. 00:48:03.170 --> 00:48:04.940 align:middle line:84% So if you have a real device, you 00:48:04.940 --> 00:48:06.595 align:middle line:84% have to consider all those heat losses. 00:48:06.595 --> 00:48:10.356 align:middle line:90% 00:48:10.356 --> 00:48:15.910 align:middle line:84% And of course, the efficiency is defined 00:48:15.910 --> 00:48:20.560 align:middle line:84% as the power out divided heat in, always what 00:48:20.560 --> 00:48:24.380 align:middle line:90% we do when we do efficiency. 00:48:24.380 --> 00:48:29.900 align:middle line:84% And if I do most ideal situation, I neglect radiation. 00:48:29.900 --> 00:48:31.100 align:middle line:90% Why you can neglect? 00:48:31.100 --> 00:48:35.930 align:middle line:84% I say, well, I have my perfect photonic crystal, no radiation. 00:48:35.930 --> 00:48:37.120 align:middle line:90% It's impossible. 00:48:37.120 --> 00:48:40.810 align:middle line:84% But let's say, I make this small. 00:48:40.810 --> 00:48:44.380 align:middle line:84% So if I neglect all other heat, just for the electronic part, 00:48:44.380 --> 00:48:46.840 align:middle line:90% I cannot neglect it-- 00:48:46.840 --> 00:48:47.970 align:middle line:90% intrinsic. 00:48:47.970 --> 00:48:50.665 align:middle line:84% And that's the curve you will get. 00:48:50.665 --> 00:48:54.460 align:middle line:84% And this time, I remember to cite the reference. 00:48:54.460 --> 00:48:58.630 align:middle line:84% And you can see, in terms of the efficiency you can get, 00:48:58.630 --> 00:49:00.700 align:middle line:90% it's very much a e v a. 00:49:00.700 --> 00:49:02.800 align:middle line:90% That's wa, e v a. 00:49:02.800 --> 00:49:04.240 align:middle line:90% v is the voltage. 00:49:04.240 --> 00:49:09.010 align:middle line:84% So it's w work function of the anode side divided by kta. 00:49:09.010 --> 00:49:11.590 align:middle line:90% So that's one parameter. 00:49:11.590 --> 00:49:15.880 align:middle line:90% And you optimize this parameter. 00:49:15.880 --> 00:49:19.330 align:middle line:84% And this is the ratio of the hot to the cold-- 00:49:19.330 --> 00:49:23.050 align:middle line:84% the cold to hot side temperature. 00:49:23.050 --> 00:49:24.690 align:middle line:90% So that's the ratio. 00:49:24.690 --> 00:49:27.460 align:middle line:84% So you can see the heat efficiency, 00:49:27.460 --> 00:49:30.850 align:middle line:84% pretty impressive, very high efficiency. 00:49:30.850 --> 00:49:33.580 align:middle line:84% Of course, this is when you neglect the radiation. 00:49:33.580 --> 00:49:35.950 align:middle line:84% You can't get rid of the radiation part. 00:49:35.950 --> 00:49:38.830 align:middle line:84% You also have additional heat loss. 00:49:38.830 --> 00:49:40.990 align:middle line:84% But compared to thermal electric, 00:49:40.990 --> 00:49:43.540 align:middle line:84% because you're using vacuum, so you don't 00:49:43.540 --> 00:49:46.000 align:middle line:90% have full-on heat conduction. 00:49:46.000 --> 00:49:49.658 align:middle line:84% That's why this can give you a high efficiency theoretically. 00:49:49.658 --> 00:49:52.800 align:middle line:90% 00:49:52.800 --> 00:49:57.320 align:middle line:84% And the first experiment was done by [INAUDIBLE]. 00:49:57.320 --> 00:49:59.180 align:middle line:90% Some of you are from that lab. 00:49:59.180 --> 00:50:01.970 align:middle line:90% 00:50:01.970 --> 00:50:04.520 align:middle line:90% He was a-- he did the-- 00:50:04.520 --> 00:50:06.650 align:middle line:90% this was in the '50s. 00:50:06.650 --> 00:50:10.670 align:middle line:90% So he came from-- 00:50:10.670 --> 00:50:11.630 align:middle line:90% he told his story. 00:50:11.630 --> 00:50:14.780 align:middle line:84% He came from Greek and trying to get a topic, 00:50:14.780 --> 00:50:20.870 align:middle line:84% and he were able, at the time-- it was since, didn't have really 00:50:20.870 --> 00:50:22.580 align:middle line:90% research government funding. 00:50:22.580 --> 00:50:26.600 align:middle line:84% But somehow he was able to get some funding to do the thesis. 00:50:26.600 --> 00:50:29.030 align:middle line:90% And he did a thesis. 00:50:29.030 --> 00:50:32.030 align:middle line:90% He went out and open company. 00:50:32.030 --> 00:50:36.470 align:middle line:84% He had a very nice book, Thermionic Energy Conversion, 00:50:36.470 --> 00:50:38.000 align:middle line:90% two volumes. 00:50:38.000 --> 00:50:40.230 align:middle line:90% I was reading some of it. 00:50:40.230 --> 00:50:43.970 align:middle line:84% I couldn't read all of this, but very detailed. 00:50:43.970 --> 00:50:46.260 align:middle line:84% He actually talk about the detailed electron-- 00:50:46.260 --> 00:50:48.500 align:middle line:90% I'm very impressed. 00:50:48.500 --> 00:50:52.430 align:middle line:84% So he talk about from basic quantum mechanics 00:50:52.430 --> 00:50:53.600 align:middle line:90% to work function. 00:50:53.600 --> 00:50:56.270 align:middle line:90% 00:50:56.270 --> 00:51:03.020 align:middle line:84% But that's Hatsopoulos and Gyftopoulos. 00:51:03.020 --> 00:51:07.970 align:middle line:84% Gyftopoulos is still professor emeritus in nuclear engineering. 00:51:07.970 --> 00:51:10.240 align:middle line:90% So they wrote a book together. 00:51:10.240 --> 00:51:13.870 align:middle line:84% And you can see, they did an experiment, 00:51:13.870 --> 00:51:19.960 align:middle line:84% 2,300 F per high temperature, hot side. 00:51:19.960 --> 00:51:24.400 align:middle line:84% And cold side, 1,000 F. That's the challenge with thermionics, 00:51:24.400 --> 00:51:28.250 align:middle line:84% it's a very high-temperature device. 00:51:28.250 --> 00:51:32.960 align:middle line:84% And the efficiency was, at the time, 1958, it was pretty good, 00:51:32.960 --> 00:51:39.240 align:middle line:84% 13%, 13%, 14%, pretty good efficiency. 00:51:39.240 --> 00:51:45.160 align:middle line:84% And so, they were very ambitious here. 00:51:45.160 --> 00:51:48.990 align:middle line:84% He also put his voltage negative. 00:51:48.990 --> 00:51:51.820 align:middle line:90% And you should read this paper. 00:51:51.820 --> 00:51:54.390 align:middle line:90% I'll send it as a reading. 00:51:54.390 --> 00:51:58.230 align:middle line:84% So his story is, he started-- he was a faculty 00:51:58.230 --> 00:52:00.600 align:middle line:90% member in our department. 00:52:00.600 --> 00:52:03.060 align:middle line:84% And he went out to start the company-- 00:52:03.060 --> 00:52:07.570 align:middle line:84% assistant professor at MIT started a company that's 00:52:07.570 --> 00:52:10.060 align:middle line:90% called a Thermo Electron. 00:52:10.060 --> 00:52:15.220 align:middle line:84% You go 128, 95, you will see the signs, Thermo Electron. 00:52:15.220 --> 00:52:17.960 align:middle line:90% Now it's called Thermo Fisher. 00:52:17.960 --> 00:52:24.310 align:middle line:84% And I believe they were trying to commercialize this. 00:52:24.310 --> 00:52:27.970 align:middle line:84% The story is, he said, he told me 00:52:27.970 --> 00:52:30.190 align:middle line:84% he went to Washington on Washington trade, 00:52:30.190 --> 00:52:32.950 align:middle line:90% and then he realized NASA-- 00:52:32.950 --> 00:52:36.670 align:middle line:84% the business really depends on whether NASA flies or not. 00:52:36.670 --> 00:52:39.520 align:middle line:90% And so he changed direction. 00:52:39.520 --> 00:52:40.570 align:middle line:90% Good for him, I think. 00:52:40.570 --> 00:52:43.150 align:middle line:84% Otherwise, I can't really say something. 00:52:43.150 --> 00:52:44.920 align:middle line:84% And the company, Thermo Electron, 00:52:44.920 --> 00:52:47.710 align:middle line:84% really does a lot of instrumentation. 00:52:47.710 --> 00:52:52.450 align:middle line:84% So it's no longer doing really thermionic energy conversion. 00:52:52.450 --> 00:52:55.910 align:middle line:84% And the recent merger is now with Fisher. 00:52:55.910 --> 00:53:00.160 align:middle line:84% Fisher is another big, I'd say, company name. 00:53:00.160 --> 00:53:01.982 align:middle line:90% So now it's Thermo Electron-- 00:53:01.982 --> 00:53:02.940 align:middle line:90% Fisher Thermo Electron. 00:53:02.940 --> 00:53:06.830 align:middle line:90% 00:53:06.830 --> 00:53:11.180 align:middle line:90% That's a good story. 00:53:11.180 --> 00:53:14.705 align:middle line:84% And the real device was not as simple 00:53:14.705 --> 00:53:17.130 align:middle line:84% as I draw, of course, the high temperature. 00:53:17.130 --> 00:53:20.930 align:middle line:84% But also there is really a fundamental problem. 00:53:20.930 --> 00:53:23.480 align:middle line:84% This is the fundamental problem is charging. 00:53:23.480 --> 00:53:28.600 align:middle line:84% If you have an electron in the vacuum, 00:53:28.600 --> 00:53:31.930 align:middle line:84% So any electron, any charge, surrounding charge, 00:53:31.930 --> 00:53:35.570 align:middle line:84% there is a field, a charge there will free the field. 00:53:35.570 --> 00:53:38.020 align:middle line:84% So when you've got a lot of electrons, 00:53:38.020 --> 00:53:41.720 align:middle line:84% they will create electrostatic potential. 00:53:41.720 --> 00:53:45.290 align:middle line:84% And this potential distribution, you can see now, 00:53:45.290 --> 00:53:51.150 align:middle line:84% I draw rather than a linear one, and really depends on the gap, 00:53:51.150 --> 00:53:53.270 align:middle line:90% depends on the charge number. 00:53:53.270 --> 00:53:58.100 align:middle line:84% But the point is, now your barrier is higher 00:53:58.100 --> 00:53:59.510 align:middle line:90% than just work function. 00:53:59.510 --> 00:54:03.230 align:middle line:84% You got an additional barrier to overcome 00:54:03.230 --> 00:54:05.330 align:middle line:90% due to space charge effect. 00:54:05.330 --> 00:54:07.100 align:middle line:90% So this is a big problem. 00:54:07.100 --> 00:54:10.080 align:middle line:90% Space charge is a big problem. 00:54:10.080 --> 00:54:16.290 align:middle line:84% And in addition to this, there are also many other problems. 00:54:16.290 --> 00:54:20.590 align:middle line:84% Of course, the most mature work functions are very large. 00:54:20.590 --> 00:54:23.640 align:middle line:84% That means you have to operate at higher temperature, 00:54:23.640 --> 00:54:24.760 align:middle line:90% few electron volts. 00:54:24.760 --> 00:54:27.450 align:middle line:84% So if you check most material, metals 00:54:27.450 --> 00:54:29.130 align:middle line:90% is about four electron volts. 00:54:29.130 --> 00:54:32.290 align:middle line:84% There are some materials like [INAUDIBLE], two electron volts. 00:54:32.290 --> 00:54:37.530 align:middle line:84% So if you use a cesium, cesium is actually-- 00:54:37.530 --> 00:54:40.290 align:middle line:84% you can first, you can generate cesium 00:54:40.290 --> 00:54:43.590 align:middle line:84% to neutralize the positive charge system vapor, 00:54:43.590 --> 00:54:46.410 align:middle line:84% to neutralize the negative electrons. 00:54:46.410 --> 00:54:49.800 align:middle line:90% So they reduce the space charge. 00:54:49.800 --> 00:54:53.010 align:middle line:84% But cesium is very corrosive, so there's 00:54:53.010 --> 00:54:56.060 align:middle line:90% problems at high temperature. 00:54:56.060 --> 00:55:01.580 align:middle line:84% And you can use either vacuum, or there are other modes where 00:55:01.580 --> 00:55:03.980 align:middle line:90% you just put a gas in between. 00:55:03.980 --> 00:55:06.630 align:middle line:84% When you put the gas, there's a plasma formation. 00:55:06.630 --> 00:55:08.900 align:middle line:84% So there's this vacuum mode or plasma 00:55:08.900 --> 00:55:11.350 align:middle line:84% mode of operation thermionic devices. 00:55:11.350 --> 00:55:14.280 align:middle line:90% 00:55:14.280 --> 00:55:19.310 align:middle line:84% But historically, think about this, the transistor, the diode, 00:55:19.310 --> 00:55:22.220 align:middle line:84% the solid state were invented in the '50s. 00:55:22.220 --> 00:55:27.960 align:middle line:84% And before that, computers were built on vacuum diodes. 00:55:27.960 --> 00:55:29.670 align:middle line:84% The vacuum diode is essentially this, 00:55:29.670 --> 00:55:32.810 align:middle line:84% except they operate in a near room temperature. 00:55:32.810 --> 00:55:35.662 align:middle line:84% And this is just a one site to operate the high temperature 00:55:35.662 --> 00:55:36.985 align:middle line:90% outside the room. 00:55:36.985 --> 00:55:42.990 align:middle line:84% Problem is, we go to 1,000 degrees. 00:55:42.990 --> 00:55:44.930 align:middle line:90% What are the recent trends? 00:55:44.930 --> 00:55:48.570 align:middle line:84% The research in this is relatively small, I would say. 00:55:48.570 --> 00:55:52.350 align:middle line:84% A Russian actually put this in space station. 00:55:52.350 --> 00:55:54.690 align:middle line:84% I tried to dig out a picture, I couldn't find one. 00:55:54.690 --> 00:55:56.610 align:middle line:90% But they call it the Topaz. 00:55:56.610 --> 00:56:00.000 align:middle line:84% And so Russia had a few space station, 00:56:00.000 --> 00:56:04.710 align:middle line:84% space missions that use thermionic engines rather than 00:56:04.710 --> 00:56:07.080 align:middle line:90% thermoelectric engines. 00:56:07.080 --> 00:56:09.810 align:middle line:84% You can search whether you can find more information 00:56:09.810 --> 00:56:11.910 align:middle line:90% if you're interested. 00:56:11.910 --> 00:56:16.920 align:middle line:84% And so, some of the idea people explore, one 00:56:16.920 --> 00:56:20.040 align:middle line:84% is the negative electron affinity. 00:56:20.040 --> 00:56:21.660 align:middle line:90% So if you let-- 00:56:21.660 --> 00:56:23.640 align:middle line:84% maybe electron just jump off itself. 00:56:23.640 --> 00:56:26.790 align:middle line:84% Negative electron affinity, vacuum level 00:56:26.790 --> 00:56:30.460 align:middle line:90% is lower than what's inside. 00:56:30.460 --> 00:56:35.710 align:middle line:84% And so that's one, people still look at this. 00:56:35.710 --> 00:56:37.750 align:middle line:90% And the other is a small gap. 00:56:37.750 --> 00:56:41.090 align:middle line:84% And this small gap, there were actually some programs, 00:56:41.090 --> 00:56:44.330 align:middle line:90% so the gap goes to angstroms. 00:56:44.330 --> 00:56:47.000 align:middle line:90% It's crazy in the sense-- 00:56:47.000 --> 00:56:48.710 align:middle line:84% of course, in that case, what happens 00:56:48.710 --> 00:56:50.960 align:middle line:84% is the electron can tunnel quantum mechanically 00:56:50.960 --> 00:56:52.670 align:middle line:90% from high side to low side. 00:56:52.670 --> 00:56:56.180 align:middle line:84% So you don't have this space charge limitation anymore. 00:56:56.180 --> 00:56:58.700 align:middle line:84% The electron don't have to be having an energy 00:56:58.700 --> 00:57:03.140 align:middle line:84% higher than the top of the electrostatic. 00:57:03.140 --> 00:57:05.540 align:middle line:84% So you can really just zip through, 00:57:05.540 --> 00:57:08.570 align:middle line:84% when this one is of the order of angstroms, 00:57:08.570 --> 00:57:10.880 align:middle line:84% that's a scanning tunneling microscope principle. 00:57:10.880 --> 00:57:15.070 align:middle line:84% Electron can go from one side to the other tunnel. 00:57:15.070 --> 00:57:18.820 align:middle line:84% But say, like I said, that's pretty-- 00:57:18.820 --> 00:57:20.980 align:middle line:84% technologically, it's too challenging, 00:57:20.980 --> 00:57:26.660 align:middle line:84% because think about the maintain hundreds of degrees 00:57:26.660 --> 00:57:27.730 align:middle line:90% at angstrom level. 00:57:27.730 --> 00:57:30.902 align:middle line:90% 00:57:30.902 --> 00:57:36.100 align:middle line:84% And then, the most recent is solid state thermionic 00:57:36.100 --> 00:57:40.900 align:middle line:84% where you run into still the heat conduction problem. 00:57:40.900 --> 00:57:43.780 align:middle line:84% Once you got a solid, everything solid state, 00:57:43.780 --> 00:57:45.530 align:middle line:90% then you have heat conduction. 00:57:45.530 --> 00:57:49.930 align:middle line:84% So that's the same as thermal electrics operation. 00:57:49.930 --> 00:57:57.620 align:middle line:84% But I just want to give you one sketch on what does 00:57:57.620 --> 00:58:01.090 align:middle line:90% the electron affinity means? 00:58:01.090 --> 00:58:07.760 align:middle line:84% Because normally you can see, the work function 00:58:07.760 --> 00:58:11.540 align:middle line:84% is between chemical potential and vacuum level. 00:58:11.540 --> 00:58:12.940 align:middle line:90% That's a work function. 00:58:12.940 --> 00:58:16.540 align:middle line:84% And of course, the space charge created a higher. 00:58:16.540 --> 00:58:20.290 align:middle line:84% And the negative electron affinity still 00:58:20.290 --> 00:58:23.500 align:middle line:84% doesn't mean the electron will all-- for other metal, 00:58:23.500 --> 00:58:27.250 align:middle line:90% you don't get the metal anymore. 00:58:27.250 --> 00:58:33.050 align:middle line:84% Here is the bottom of conduction band. 00:58:33.050 --> 00:58:36.470 align:middle line:84% But this is a, say, in negative electron affinity, which 00:58:36.470 --> 00:58:40.970 align:middle line:84% is typically semiconductors, very wide gap semiconductors, 00:58:40.970 --> 00:58:43.580 align:middle line:84% the electron actually sits in here, 00:58:43.580 --> 00:58:45.830 align:middle line:90% more the Fermi level is here. 00:58:45.830 --> 00:58:48.240 align:middle line:90% So it does not come out. 00:58:48.240 --> 00:58:55.080 align:middle line:84% So you still need to overcome the space charge 00:58:55.080 --> 00:58:57.170 align:middle line:90% to [INAUDIBLE] come out. 00:58:57.170 --> 00:59:01.970 align:middle line:84% So that's the liquid [INAUDIBLE] affinity material. 00:59:01.970 --> 00:59:05.300 align:middle line:84% So people have interest in this, not only 00:59:05.300 --> 00:59:07.680 align:middle line:84% for thermoelectrics and thermionics. 00:59:07.680 --> 00:59:11.700 align:middle line:90% 00:59:11.700 --> 00:59:16.200 align:middle line:84% So that's a discussion on thermionics, which is 00:59:16.200 --> 00:59:17.560 align:middle line:90% in formula, what's important. 00:59:17.560 --> 00:59:18.060 align:middle line:90% Yes. 00:59:18.060 --> 00:59:20.950 align:middle line:90% 00:59:20.950 --> 00:59:23.483 align:middle line:84% AUDIENCE: You said that [INAUDIBLE] is very [INAUDIBLE]. 00:59:23.483 --> 00:59:24.250 align:middle line:90% GANG CHEN: Right. 00:59:24.250 --> 00:59:27.860 align:middle line:84% AUDIENCE: What happens if you just put some [INAUDIBLE]? 00:59:27.860 --> 00:59:29.570 align:middle line:84% GANG CHEN: Dielectric material is-- 00:59:29.570 --> 00:59:31.884 align:middle line:84% the problem now you got a heat conduction. 00:59:31.884 --> 00:59:32.426 align:middle line:90% AUDIENCE: Oh. 00:59:32.426 --> 00:59:35.116 align:middle line:90% 00:59:35.116 --> 00:59:37.380 align:middle line:84% GANG CHEN: So run into this classical thermoelectrical 00:59:37.380 --> 00:59:37.880 align:middle line:90% problem. 00:59:37.880 --> 00:59:41.550 align:middle line:90% 00:59:41.550 --> 00:59:46.350 align:middle line:90% And what are we-- 00:59:46.350 --> 00:59:51.230 align:middle line:84% now somebody ask, say, semiconductors? 00:59:51.230 --> 00:59:53.945 align:middle line:84% And let's think about now we have 00:59:53.945 --> 00:59:57.800 align:middle line:90% a metal and a semiconductor. 00:59:57.800 --> 01:00:01.370 align:middle line:84% You always have that in any microelectronic device. 01:00:01.370 --> 01:00:04.082 align:middle line:84% Because, at the end, you want to make a count. 01:00:04.082 --> 01:00:06.460 align:middle line:84% You put the metal on the semiconductor. 01:00:06.460 --> 01:00:09.580 align:middle line:84% So that's a typical classical situation. 01:00:09.580 --> 01:00:12.380 align:middle line:90% And now let's see what happens. 01:00:12.380 --> 01:00:15.480 align:middle line:84% And now, of course, here is the Fermi level. 01:00:15.480 --> 01:00:17.330 align:middle line:84% Here is the semiconductor Fermi level. 01:00:17.330 --> 01:00:19.445 align:middle line:84% I'm talking about the along degenerate. 01:00:19.445 --> 01:00:21.440 align:middle line:90% So Fermi level is in the gap. 01:00:21.440 --> 01:00:25.200 align:middle line:84% This is really where electron sits in. 01:00:25.200 --> 01:00:30.850 align:middle line:84% And when I put these two together, 01:00:30.850 --> 01:00:33.220 align:middle line:90% I still got the same problem. 01:00:33.220 --> 01:00:36.280 align:middle line:84% If I collect them electrically or put them in contact 01:00:36.280 --> 01:00:40.570 align:middle line:84% with the shutter, the chemical potential difference 01:00:40.570 --> 01:00:42.430 align:middle line:90% will drive the charge flow. 01:00:42.430 --> 01:00:45.670 align:middle line:84% So eventually, the chemical potential on the two sides 01:00:45.670 --> 01:00:47.560 align:middle line:90% will be the same. 01:00:47.560 --> 01:00:53.260 align:middle line:84% That is always the driving force for diffusion, mass transfer, 01:00:53.260 --> 01:00:54.160 align:middle line:90% charges of mass. 01:00:54.160 --> 01:00:56.650 align:middle line:84% Mass transfer is chemical position. 01:00:56.650 --> 01:00:58.540 align:middle line:90% Heat transfer is temperature. 01:00:58.540 --> 01:01:01.300 align:middle line:90% Mechanical is pressure. 01:01:01.300 --> 01:01:05.540 align:middle line:90% So the thermodynamic quantities. 01:01:05.540 --> 01:01:08.770 align:middle line:84% And then, when I put them together, 01:01:08.770 --> 01:01:12.700 align:middle line:84% so the Fermi level will align to each other, chemical potential 01:01:12.700 --> 01:01:17.450 align:middle line:90% align to each other eventually. 01:01:17.450 --> 01:01:21.160 align:middle line:84% That's a driving force for charge flow. 01:01:21.160 --> 01:01:28.270 align:middle line:84% And here the work function here is the affinity. 01:01:28.270 --> 01:01:31.300 align:middle line:84% And then at the point of all the contact, 01:01:31.300 --> 01:01:34.720 align:middle line:84% you can think that they have to have the local same vacuum 01:01:34.720 --> 01:01:38.230 align:middle line:90% level, same vacuum level. 01:01:38.230 --> 01:01:41.680 align:middle line:84% At that point, if I put these two pieces together locally, 01:01:41.680 --> 01:01:44.590 align:middle line:84% I pull electrons out to vacuum, that's 01:01:44.590 --> 01:01:47.260 align:middle line:84% the same point as the metal side. 01:01:47.260 --> 01:01:50.770 align:middle line:84% So there is a mismatch between the work 01:01:50.770 --> 01:01:52.690 align:middle line:90% function and the affinity. 01:01:52.690 --> 01:01:58.370 align:middle line:84% And this mismatch is delta here, which you can check. 01:01:58.370 --> 01:02:00.860 align:middle line:84% For different material you can always define-- 01:02:00.860 --> 01:02:01.620 align:middle line:90% not always. 01:02:01.620 --> 01:02:04.260 align:middle line:84% Sometimes people have measured it. 01:02:04.260 --> 01:02:07.810 align:middle line:84% But in theory, you can find this. 01:02:07.810 --> 01:02:10.120 align:middle line:90% So there's delta. 01:02:10.120 --> 01:02:17.590 align:middle line:84% That's the-- this delta is the Schottky barrier height. 01:02:17.590 --> 01:02:18.710 align:middle line:90% That's the barrier height. 01:02:18.710 --> 01:02:24.250 align:middle line:84% There is a potential difference of the electrons 01:02:24.250 --> 01:02:28.790 align:middle line:84% in the semiconductor and metal side. 01:02:28.790 --> 01:02:32.510 align:middle line:84% Now, of course, if you think about this, 01:02:32.510 --> 01:02:39.260 align:middle line:84% electrons here, so this electron will fall into the lower-- 01:02:39.260 --> 01:02:42.320 align:middle line:90% the metal side. 01:02:42.320 --> 01:02:44.560 align:middle line:84% Electron go from high energy to lower energy. 01:02:44.560 --> 01:02:48.480 align:middle line:84% Anything go higher energy to lower energy. 01:02:48.480 --> 01:02:52.470 align:middle line:84% So once they fall, there is less-- 01:02:52.470 --> 01:02:54.850 align:middle line:84% there are positive charge, less electron here. 01:02:54.850 --> 01:02:59.820 align:middle line:84% So chemical potential is measured between ec and here, 01:02:59.820 --> 01:03:02.500 align:middle line:84% and less electron means larger distance. 01:03:02.500 --> 01:03:06.850 align:middle line:84% So you can see here, I'm going far away from the interface. 01:03:06.850 --> 01:03:08.490 align:middle line:90% That's my bulk region. 01:03:08.490 --> 01:03:11.490 align:middle line:84% Interfacial region, the semiconductor side, 01:03:11.490 --> 01:03:12.930 align:middle line:90% there is a band bending. 01:03:12.930 --> 01:03:15.850 align:middle line:90% ec is no longer flat. 01:03:15.850 --> 01:03:18.460 align:middle line:90% 01:03:18.460 --> 01:03:22.420 align:middle line:84% And that's because intuitively electron 01:03:22.420 --> 01:03:28.330 align:middle line:84% fall on this side, less electron, so bigger separation 01:03:28.330 --> 01:03:28.830 align:middle line:90% there. 01:03:28.830 --> 01:03:29.810 align:middle line:90% Yes. 01:03:29.810 --> 01:03:31.650 align:middle line:90% AUDIENCE: Are the Fermi levels-- 01:03:31.650 --> 01:03:32.615 align:middle line:90% GANG CHEN: Same. 01:03:32.615 --> 01:03:33.490 align:middle line:90% AUDIENCE: Same level? 01:03:33.490 --> 01:03:34.210 align:middle line:90% GANG CHEN: Yes. 01:03:34.210 --> 01:03:36.700 align:middle line:90% I didn't draw it level. 01:03:36.700 --> 01:03:40.600 align:middle line:84% AUDIENCE: So the vacuums are different? 01:03:40.600 --> 01:03:42.438 align:middle line:90% GANG CHEN: Vacuum now-- 01:03:42.438 --> 01:03:43.480 align:middle line:90% AUDIENCE: It's different. 01:03:43.480 --> 01:03:44.520 align:middle line:90% GANG CHEN: Vacuum-- 01:03:44.520 --> 01:03:45.100 align:middle line:90% AUDIENCE: It's three levels. 01:03:45.100 --> 01:03:45.990 align:middle line:90% GANG CHEN: Yes. 01:03:45.990 --> 01:03:48.520 align:middle line:84% Yes, thank you for telling me that. 01:03:48.520 --> 01:03:50.200 align:middle line:90% Vacuum level is different. 01:03:50.200 --> 01:03:51.940 align:middle line:84% AUDIENCE: So is the drop the same 01:03:51.940 --> 01:03:56.270 align:middle line:84% on the other side because the ec will go down [INAUDIBLE]? 01:03:56.270 --> 01:03:59.450 align:middle line:84% GANG CHEN: So locally, the vacuum level also changing. 01:03:59.450 --> 01:04:04.940 align:middle line:84% So this is where, again, you have to really think, 01:04:04.940 --> 01:04:07.370 align:middle line:84% this is defined really, really low quality. 01:04:07.370 --> 01:04:12.950 align:middle line:84% This rule is actually sometimes violated, 01:04:12.950 --> 01:04:16.520 align:middle line:84% particularly when you put two different semiconductors. 01:04:16.520 --> 01:04:19.070 align:middle line:84% You first think about the lack of vacuum level, 01:04:19.070 --> 01:04:21.850 align:middle line:84% then look at the affinity, and that's the [INAUDIBLE]. 01:04:21.850 --> 01:04:24.120 align:middle line:90% It doesn't always work. 01:04:24.120 --> 01:04:26.870 align:middle line:84% AUDIENCE: Because I'm trying to tell-- so if delta, 01:04:26.870 --> 01:04:29.690 align:middle line:84% before you bring into contact, you have ec between-- 01:04:29.690 --> 01:04:30.992 align:middle line:90% ec and the Fermi level. 01:04:30.992 --> 01:04:31.700 align:middle line:90% GANG CHEN: Right. 01:04:31.700 --> 01:04:32.270 align:middle line:90% AUDIENCE: The level, right? 01:04:32.270 --> 01:04:32.700 align:middle line:90% GANG CHEN: Right. 01:04:32.700 --> 01:04:34.325 align:middle line:84% AUDIENCE: So that's the original level. 01:04:34.325 --> 01:04:37.460 align:middle line:84% When you bring it together, ef and the vacuum 01:04:37.460 --> 01:04:39.890 align:middle line:84% drops down for the semiconductor, 01:04:39.890 --> 01:04:41.790 align:middle line:90% then ec drops down as well. 01:04:41.790 --> 01:04:43.460 align:middle line:90% Is that correct? 01:04:43.460 --> 01:04:46.445 align:middle line:84% So that's why that's why [INAUDIBLE] 01:04:46.445 --> 01:04:47.330 align:middle line:90% 01:04:47.330 --> 01:04:49.850 align:middle line:84% GANG CHEN: Does the vacuum level change? 01:04:49.850 --> 01:04:51.260 align:middle line:90% Let me draw the vacuum level. 01:04:51.260 --> 01:04:56.405 align:middle line:84% What I saw with the vacuum level here, this is a vacuum. 01:04:56.405 --> 01:04:57.030 align:middle line:90% Let me draw it. 01:04:57.030 --> 01:04:58.760 align:middle line:90% This is the metal side. 01:04:58.760 --> 01:05:02.450 align:middle line:84% And this seems to be the semiconductor side. 01:05:02.450 --> 01:05:04.910 align:middle line:90% And this is the ec. 01:05:04.910 --> 01:05:07.820 align:middle line:90% And here is the-- 01:05:07.820 --> 01:05:11.990 align:middle line:90% so here is the work function. 01:05:11.990 --> 01:05:16.700 align:middle line:84% Here is my electron going into vacuum. 01:05:16.700 --> 01:05:20.140 align:middle line:90% So this is my affinity. 01:05:20.140 --> 01:05:23.026 align:middle line:84% The difference can be the [INAUDIBLE]. 01:05:23.026 --> 01:05:25.360 align:middle line:90% 01:05:25.360 --> 01:05:29.560 align:middle line:84% So I didn't have that jump in the vacuum. 01:05:29.560 --> 01:05:31.360 align:middle line:90% Locally I put the same. 01:05:31.360 --> 01:05:34.732 align:middle line:90% 01:05:34.732 --> 01:05:37.420 align:middle line:90% So this is the-- 01:05:37.420 --> 01:05:44.380 align:middle line:84% this kind of interface here, is often 01:05:44.380 --> 01:05:47.950 align:middle line:90% between metal and semiconductor. 01:05:47.950 --> 01:05:49.740 align:middle line:90% And this is a Schottky barrier. 01:05:49.740 --> 01:05:52.270 align:middle line:90% 01:05:52.270 --> 01:05:58.102 align:middle line:84% And now if I think about the flying flow electron, I put a-- 01:05:58.102 --> 01:05:59.420 align:middle line:90% I talk about contact. 01:05:59.420 --> 01:06:04.795 align:middle line:84% You apply a voltage, how the electron flows? 01:06:04.795 --> 01:06:09.536 align:middle line:90% 01:06:09.536 --> 01:06:12.530 align:middle line:84% And of course, you can always say, again, 01:06:12.530 --> 01:06:17.460 align:middle line:84% from left to right, right to left, same kind of thinking 01:06:17.460 --> 01:06:17.960 align:middle line:90% there. 01:06:17.960 --> 01:06:20.815 align:middle line:90% 01:06:20.815 --> 01:06:23.590 align:middle line:90% And now here is a p type. 01:06:23.590 --> 01:06:28.270 align:middle line:84% So before I draw an electron, and here is a pulse. 01:06:28.270 --> 01:06:32.690 align:middle line:84% Pulse is a-- this from here to here is barrier. 01:06:32.690 --> 01:06:34.510 align:middle line:90% This is a positive charge-- 01:06:34.510 --> 01:06:35.260 align:middle line:90% [INAUDIBLE] holes. 01:06:35.260 --> 01:06:38.830 align:middle line:84% And here there are less holes because the electron 01:06:38.830 --> 01:06:42.744 align:middle line:90% fall into here neutralize-- 01:06:42.744 --> 01:06:45.040 align:middle line:90% make less hole really. 01:06:45.040 --> 01:06:46.490 align:middle line:90% Because electron fall into-- 01:06:46.490 --> 01:06:48.080 align:middle line:90% wait. 01:06:48.080 --> 01:06:52.510 align:middle line:90% Where I'm confusing? 01:06:52.510 --> 01:06:59.170 align:middle line:84% Think about-- so positive, so really, so electron 01:06:59.170 --> 01:07:04.080 align:middle line:84% should fall into this side, from here to here, 01:07:04.080 --> 01:07:09.420 align:middle line:84% because the electron is at a higher energy than here. 01:07:09.420 --> 01:07:12.270 align:middle line:90% So electron fall into this side. 01:07:12.270 --> 01:07:15.990 align:middle line:84% There's less hole here because the electron 01:07:15.990 --> 01:07:17.890 align:middle line:90% fell in the empty state. 01:07:17.890 --> 01:07:21.120 align:middle line:84% And the holes are just what's left over, 01:07:21.120 --> 01:07:22.750 align:middle line:90% the empty states of electrons. 01:07:22.750 --> 01:07:25.496 align:middle line:90% 01:07:25.496 --> 01:07:26.610 align:middle line:90% So what's hole? 01:07:26.610 --> 01:07:28.170 align:middle line:90% There's really no hole. 01:07:28.170 --> 01:07:31.230 align:middle line:90% 01:07:31.230 --> 01:07:36.680 align:middle line:84% In the [INAUDIBLE] span, this is the ev, 01:07:36.680 --> 01:07:40.040 align:middle line:84% the electron field over here, and left 01:07:40.040 --> 01:07:41.810 align:middle line:90% behind the few empty space. 01:07:41.810 --> 01:07:43.730 align:middle line:90% Those are the empty area. 01:07:43.730 --> 01:07:50.960 align:middle line:84% Now the metal, electron from the metal, electron from the metal 01:07:50.960 --> 01:07:55.370 align:middle line:84% fall into this side, fill in some of those empty states. 01:07:55.370 --> 01:07:59.210 align:middle line:84% So this is no longer available for full. 01:07:59.210 --> 01:08:02.900 align:middle line:90% So this is less holes space. 01:08:02.900 --> 01:08:05.250 align:middle line:90% So there are less holes here. 01:08:05.250 --> 01:08:06.530 align:middle line:90% This is less hole. 01:08:06.530 --> 01:08:12.800 align:middle line:84% So the Fermi level return, the chemical potential, and the span 01:08:12.800 --> 01:08:14.300 align:middle line:90% becomes larger. 01:08:14.300 --> 01:08:17.790 align:middle line:84% So this is the Schottky barrier for the p type. 01:08:17.790 --> 01:08:21.370 align:middle line:90% 01:08:21.370 --> 01:08:22.444 align:middle line:90% AUDIENCE: Professor. 01:08:22.444 --> 01:08:23.069 align:middle line:90% GANG CHEN: Yes. 01:08:23.069 --> 01:08:25.550 align:middle line:84% AUDIENCE: So in the p type, [INAUDIBLE], 01:08:25.550 --> 01:08:27.585 align:middle line:84% so you are bigger actually [INAUDIBLE] 01:08:27.585 --> 01:08:32.009 align:middle line:84% p type [INAUDIBLE] level will go up. 01:08:32.009 --> 01:08:34.950 align:middle line:84% But it seems like in the vacuum-- 01:08:34.950 --> 01:08:38.470 align:middle line:84% GANG CHEN: Vacuum level, I didn't draw a vacuum level here. 01:08:38.470 --> 01:08:39.806 align:middle line:90% AUDIENCE: The green region. 01:08:39.806 --> 01:08:40.764 align:middle line:90% GANG CHEN: Where is it? 01:08:40.764 --> 01:08:41.539 align:middle line:90% Where do you mean? 01:08:41.539 --> 01:08:42.956 align:middle line:84% AUDIENCE: I mean, the [INAUDIBLE], 01:08:42.956 --> 01:08:46.942 align:middle line:84% the ec and the [INAUDIBLE] is the [INAUDIBLE]. 01:08:46.942 --> 01:08:47.859 align:middle line:90% GANG CHEN: No, no, no. 01:08:47.859 --> 01:08:50.109 align:middle line:90% The p type has to be-- 01:08:50.109 --> 01:08:53.020 align:middle line:90% you have to look at the-- 01:08:53.020 --> 01:08:57.495 align:middle line:84% I think this is your w on the other side. 01:08:57.495 --> 01:08:58.120 align:middle line:90% AUDIENCE: Yeah. 01:08:58.120 --> 01:09:05.340 align:middle line:84% GANG CHEN: And you have to think about this will be here. 01:09:05.340 --> 01:09:08.922 align:middle line:90% 01:09:08.922 --> 01:09:13.189 align:middle line:84% And so, from here, vacuum level-- 01:09:13.189 --> 01:09:14.680 align:middle line:90% AUDIENCE: Yeah. 01:09:14.680 --> 01:09:16.260 align:middle line:90% GANG CHEN: --vacuum level here. 01:09:16.260 --> 01:09:19.319 align:middle line:84% And now electrons start to fill in, 01:09:19.319 --> 01:09:21.630 align:middle line:84% because the electrons go from high energy states 01:09:21.630 --> 01:09:22.593 align:middle line:90% to lower energy states. 01:09:22.593 --> 01:09:24.510 align:middle line:84% AUDIENCE: Yes, you mentioned that [INAUDIBLE]. 01:09:24.510 --> 01:09:25.080 align:middle line:90% That's why. 01:09:25.080 --> 01:09:27.420 align:middle line:84% GANG CHEN: So the Fermi level will 01:09:27.420 --> 01:09:30.270 align:middle line:90% be-- because this is p type. 01:09:30.270 --> 01:09:33.750 align:middle line:84% So the p type will be going here. 01:09:33.750 --> 01:09:34.890 align:middle line:90% This is the Fermi level. 01:09:34.890 --> 01:09:37.086 align:middle line:90% So this is the-- 01:09:37.086 --> 01:09:38.615 align:middle line:90% this will be the-- 01:09:38.615 --> 01:09:42.125 align:middle line:90% 01:09:42.125 --> 01:09:43.750 align:middle line:84% AUDIENCE: Do the ec all the way around? 01:09:43.750 --> 01:09:44.297 align:middle line:90% [INAUDIBLE] 01:09:44.297 --> 01:09:45.630 align:middle line:90% GANG CHEN: No, ec doesn't go in. 01:09:45.630 --> 01:09:47.910 align:middle line:84% This one, ec the background has to be the same. 01:09:47.910 --> 01:09:50.877 align:middle line:84% So between here and here, this it hasn't been done. 01:09:50.877 --> 01:09:51.960 align:middle line:90% AUDIENCE: Oh, [INAUDIBLE]. 01:09:51.960 --> 01:09:54.690 align:middle line:90% GANG CHEN: Yeah. 01:09:54.690 --> 01:09:59.230 align:middle line:84% But there are not much electrons in the p type. 01:09:59.230 --> 01:10:02.650 align:middle line:84% So you say, why the electron doesn't flow. 01:10:02.650 --> 01:10:04.630 align:middle line:84% AUDIENCE: And the vacuum he has right now too. 01:10:04.630 --> 01:10:05.380 align:middle line:90% GANG CHEN: Huh? 01:10:05.380 --> 01:10:07.088 align:middle line:84% AUDIENCE: The vacuum he has right now too 01:10:07.088 --> 01:10:08.300 align:middle line:90% are the semiconductor side. 01:10:08.300 --> 01:10:13.630 align:middle line:84% GANG CHEN: Vacuum also has to bend down, yeah. 01:10:13.630 --> 01:10:15.270 align:middle line:90% So this is your vacuum level. 01:10:15.270 --> 01:10:17.378 align:middle line:90% 01:10:17.378 --> 01:10:18.420 align:middle line:90% AUDIENCE: So [INAUDIBLE]. 01:10:18.420 --> 01:10:19.045 align:middle line:90% GANG CHEN: Huh? 01:10:19.045 --> 01:10:21.431 align:middle line:90% 01:10:21.431 --> 01:10:23.806 align:middle line:84% AUDIENCE: That's exactly what I was telling, [INAUDIBLE]. 01:10:23.806 --> 01:10:25.550 align:middle line:90% GANG CHEN: Oh, vacuum, I see. 01:10:25.550 --> 01:10:27.100 align:middle line:90% Yeah, vacuum is [INAUDIBLE]. 01:10:27.100 --> 01:10:29.415 align:middle line:84% I thought you were asking the ec. 01:10:29.415 --> 01:10:36.090 align:middle line:90% 01:10:36.090 --> 01:10:36.760 align:middle line:90% Very tricky. 01:10:36.760 --> 01:10:40.070 align:middle line:90% 01:10:40.070 --> 01:10:41.510 align:middle line:90% Now let's check. 01:10:41.510 --> 01:10:42.880 align:middle line:90% I'm giving you the formula. 01:10:42.880 --> 01:10:43.920 align:middle line:90% I'm not deriving. 01:10:43.920 --> 01:10:50.050 align:middle line:84% But the point is, it's a Richardson formula. 01:10:50.050 --> 01:10:52.850 align:middle line:84% Negative what we wrote for vacuum. 01:10:52.850 --> 01:10:56.730 align:middle line:84% And when I-- but there is some difference also. 01:10:56.730 --> 01:11:02.480 align:middle line:84% So the first factor here is the same Richardson factor. 01:11:02.480 --> 01:11:07.580 align:middle line:84% And then I have this exponential ev kvt. 01:11:07.580 --> 01:11:09.410 align:middle line:84% And then you can see, that depends on 01:11:09.410 --> 01:11:12.670 align:middle line:84% whether my voltage is positive or negative. 01:11:12.670 --> 01:11:17.700 align:middle line:84% So when I see positive, is I raise 01:11:17.700 --> 01:11:21.960 align:middle line:84% the Fermi level on this side, on the semiconductor side. 01:11:21.960 --> 01:11:26.070 align:middle line:84% So the voltage is applied, so this will be, in this case, 01:11:26.070 --> 01:11:29.010 align:middle line:84% this will be positive electrode, negative electrode, 01:11:29.010 --> 01:11:33.000 align:middle line:90% raise the electron on this side. 01:11:33.000 --> 01:11:36.960 align:middle line:84% And of course, the electron raised, 01:11:36.960 --> 01:11:39.660 align:middle line:84% so there is more chance for this electron going 01:11:39.660 --> 01:11:42.630 align:middle line:90% from left to right-- 01:11:42.630 --> 01:11:43.870 align:middle line:90% from right to left. 01:11:43.870 --> 01:11:47.078 align:middle line:90% 01:11:47.078 --> 01:11:53.060 align:middle line:84% So that's where my ev kvt comes from exponentially. 01:11:53.060 --> 01:11:57.860 align:middle line:84% So I have-- this is a forward bias. 01:11:57.860 --> 01:12:04.290 align:middle line:84% Now, when I reverse bias it, let's 01:12:04.290 --> 01:12:05.790 align:middle line:84% say when the electrons go this way, 01:12:05.790 --> 01:12:07.250 align:middle line:90% it really tried to go this way. 01:12:07.250 --> 01:12:08.170 align:middle line:90% That's what I draw. 01:12:08.170 --> 01:12:11.100 align:middle line:84% This is a positive metal, positive semiconductor, 01:12:11.100 --> 01:12:14.600 align:middle line:90% and it's [INAUDIBLE], right? 01:12:14.600 --> 01:12:19.040 align:middle line:84% And when we reverse pass it this direction, 01:12:19.040 --> 01:12:23.160 align:middle line:84% the Fahrenheit is fixed, didn't change. 01:12:23.160 --> 01:12:27.000 align:middle line:84% So this current is always the first-- 01:12:27.000 --> 01:12:31.370 align:middle line:90% this saturation current here. 01:12:31.370 --> 01:12:33.990 align:middle line:84% Now there is less going this way. 01:12:33.990 --> 01:12:39.840 align:middle line:84% But that's not much less because you see here, 01:12:39.840 --> 01:12:41.370 align:middle line:90% that difference is small. 01:12:41.370 --> 01:12:46.710 align:middle line:84% So now, this is the same as a diode. 01:12:46.710 --> 01:12:51.030 align:middle line:84% Biased differently, you have, say, 01:12:51.030 --> 01:12:53.240 align:middle line:84% different current characteristics. 01:12:53.240 --> 01:12:58.670 align:middle line:84% So that's similar to a diode, typical diode. 01:12:58.670 --> 01:13:03.410 align:middle line:84% And this is a Schottky diode, positive bias, negative bias, 01:13:03.410 --> 01:13:06.680 align:middle line:90% saturation current here, not 0. 01:13:06.680 --> 01:13:09.890 align:middle line:84% And this is if we invest too much, it break down. 01:13:09.890 --> 01:13:14.780 align:middle line:84% So you can just punch over this barrier 01:13:14.780 --> 01:13:16.980 align:middle line:90% and under not reverse bias. 01:13:16.980 --> 01:13:21.635 align:middle line:90% 01:13:21.635 --> 01:13:29.520 align:middle line:84% And you can see, a metal semiconductor interface, 01:13:29.520 --> 01:13:33.240 align:middle line:84% and if you make a contact like this, it's not good. 01:13:33.240 --> 01:13:36.440 align:middle line:84% Typically, you don't want to make a Schottky contact. 01:13:36.440 --> 01:13:41.120 align:middle line:90% 01:13:41.120 --> 01:13:45.380 align:middle line:90% And how you solve that problem? 01:13:45.380 --> 01:13:48.050 align:middle line:84% And the way people solve this problem 01:13:48.050 --> 01:13:51.210 align:middle line:90% is they dope it very heavily. 01:13:51.210 --> 01:13:55.770 align:middle line:84% So let's say, when you dope heavy, this becomes-- 01:13:55.770 --> 01:14:00.630 align:middle line:84% say, so basically, when you dope very heavy, few electrons come 01:14:00.630 --> 01:14:03.030 align:middle line:90% over, this is very narrow. 01:14:03.030 --> 01:14:04.560 align:middle line:90% This is very sharp. 01:14:04.560 --> 01:14:17.730 align:middle line:84% So when we draw, this becomes very sharp when you dope heavy. 01:14:17.730 --> 01:14:21.790 align:middle line:84% And when it becomes very sharp, so the electron tunnel 01:14:21.790 --> 01:14:26.060 align:middle line:84% through rather than have to go over the barrier. 01:14:26.060 --> 01:14:28.810 align:middle line:90% 01:14:28.810 --> 01:14:34.960 align:middle line:84% So that's one way to overcome the Schottky resistance here. 01:14:34.960 --> 01:14:38.800 align:middle line:84% Otherwise you'll see, so this is how 01:14:38.800 --> 01:14:42.040 align:middle line:84% people make [INAUDIBLE] contact is you 01:14:42.040 --> 01:14:45.340 align:middle line:90% dope the region very heavily. 01:14:45.340 --> 01:14:50.130 align:middle line:84% And of course, you want to use the right metal 01:14:50.130 --> 01:14:54.230 align:middle line:84% to start with so that the work function, 01:14:54.230 --> 01:14:55.720 align:middle line:90% the delta here is not large. 01:14:55.720 --> 01:14:59.220 align:middle line:90% 01:14:59.220 --> 01:15:03.020 align:middle line:84% So that's why, if you want to make a metal-- a contact, 01:15:03.020 --> 01:15:04.610 align:middle line:84% you want to know your work function, 01:15:04.610 --> 01:15:08.930 align:middle line:84% you want to know your electron affinity, [INAUDIBLE]. 01:15:08.930 --> 01:15:12.530 align:middle line:84% And of course, there are many other reasons 01:15:12.530 --> 01:15:15.380 align:middle line:84% where you do make a good contact and other than this. 01:15:15.380 --> 01:15:20.490 align:middle line:84% You may have a physical long contact, a vacuum gap here 01:15:20.490 --> 01:15:21.900 align:middle line:90% that could also-- 01:15:21.900 --> 01:15:27.466 align:middle line:84% vacuum gap is essentially a very high barrier. 01:15:27.466 --> 01:15:29.110 align:middle line:90% You have to power through that. 01:15:29.110 --> 01:15:30.730 align:middle line:90% You can power through that. 01:15:30.730 --> 01:15:33.961 align:middle line:84% Or if it's too wide, there's no chance you can go through. 01:15:33.961 --> 01:15:37.780 align:middle line:90% 01:15:37.780 --> 01:15:40.040 align:middle line:90% Schottky diode. 01:15:40.040 --> 01:15:43.670 align:middle line:84% Since we're talking about diode, I'll continue. 01:15:43.670 --> 01:15:47.540 align:middle line:90% This is a metal semiconductor. 01:15:47.540 --> 01:15:51.760 align:middle line:84% A regular diode is not a metal semiconductor. 01:15:51.760 --> 01:15:53.630 align:middle line:84% It is a semiconductor-semiconductor 01:15:53.630 --> 01:15:54.980 align:middle line:90% diode. 01:15:54.980 --> 01:15:58.610 align:middle line:84% So let's look at semiconductor-semiconductor. 01:15:58.610 --> 01:16:04.960 align:middle line:84% So we make a semiconductor n type, semiconductor p type. 01:16:04.960 --> 01:16:09.880 align:middle line:84% And I put the two pieces together, contact, same thing 01:16:09.880 --> 01:16:11.380 align:middle line:90% happened. 01:16:11.380 --> 01:16:16.860 align:middle line:84% The chemical potential must align each other. 01:16:16.860 --> 01:16:22.660 align:middle line:84% So what that align looking like, what it really means 01:16:22.660 --> 01:16:26.740 align:middle line:84% is, here, n type got a lot of electrons. 01:16:26.740 --> 01:16:28.870 align:middle line:90% So electrons go this side. 01:16:28.870 --> 01:16:30.580 align:middle line:90% P type I got a lot of hole. 01:16:30.580 --> 01:16:32.060 align:middle line:90% Hole go the other side. 01:16:32.060 --> 01:16:36.520 align:middle line:90% 01:16:36.520 --> 01:16:41.500 align:middle line:84% And so, when electrons go from this side to this side, 01:16:41.500 --> 01:16:42.390 align:middle line:90% what's left behind? 01:16:42.390 --> 01:16:45.770 align:middle line:90% 01:16:45.770 --> 01:16:48.924 align:middle line:90% Positive atoms there. 01:16:48.924 --> 01:16:52.620 align:middle line:84% So what do you have here is positive atom. 01:16:52.620 --> 01:16:55.390 align:middle line:90% This atom do not move. 01:16:55.390 --> 01:16:59.040 align:middle line:84% Those atoms are just charged there. 01:16:59.040 --> 01:17:01.710 align:middle line:90% They don't move. 01:17:01.710 --> 01:17:07.410 align:middle line:84% On this side, holes left, so they left behind-- really, 01:17:07.410 --> 01:17:12.495 align:middle line:84% just get a holes left is, you get an excess electron to-- 01:17:12.495 --> 01:17:15.240 align:middle line:90% 01:17:15.240 --> 01:17:19.400 align:middle line:90% for this case, p type or boron. 01:17:19.400 --> 01:17:25.700 align:middle line:84% Say you get an excess electron, not called the neutral now 01:17:25.700 --> 01:17:27.390 align:middle line:90% in this region. 01:17:27.390 --> 01:17:32.740 align:middle line:84% So those, when I draw this, is the ions, positive ions, 01:17:32.740 --> 01:17:37.950 align:middle line:84% negative ions on the two sides of the interface. 01:17:37.950 --> 01:17:41.480 align:middle line:84% That's a space charge region, not 01:17:41.480 --> 01:17:46.260 align:middle line:90% a mobile ion, mobile electrons. 01:17:46.260 --> 01:17:48.630 align:middle line:90% And if I draw the bandgap-- 01:17:48.630 --> 01:17:49.690 align:middle line:90% band alignment. 01:17:49.690 --> 01:17:52.620 align:middle line:90% So if I-- oops, I forgot-- 01:17:52.620 --> 01:17:54.210 align:middle line:90% ec should be mu. 01:17:54.210 --> 01:17:57.160 align:middle line:90% 01:17:57.160 --> 01:18:00.580 align:middle line:84% No, this one, there should be a line here. 01:18:00.580 --> 01:18:02.020 align:middle line:90% That's a ef. 01:18:02.020 --> 01:18:04.900 align:middle line:90% I disappear. 01:18:04.900 --> 01:18:06.370 align:middle line:90% This is a ef. 01:18:06.370 --> 01:18:10.100 align:middle line:84% And this ef and this ef will have to align each other. 01:18:10.100 --> 01:18:15.290 align:middle line:84% So it's easy to think about the connection. 01:18:15.290 --> 01:18:22.820 align:middle line:84% If I have far away from the interface, I have n type. 01:18:22.820 --> 01:18:27.160 align:middle line:84% And far away from the interface, I have p type. 01:18:27.160 --> 01:18:30.040 align:middle line:84% And now p type Fermi level is close to eb, 01:18:30.040 --> 01:18:32.740 align:middle line:84% and type of Fermi level is close to ec. 01:18:32.740 --> 01:18:34.175 align:middle line:90% And then connect in between. 01:18:34.175 --> 01:18:40.730 align:middle line:90% 01:18:40.730 --> 01:18:44.830 align:middle line:90% And at the end it's equilibrium. 01:18:44.830 --> 01:18:46.900 align:middle line:90% That's equilibrium. 01:18:46.900 --> 01:18:50.620 align:middle line:84% And in between this region, a space 01:18:50.620 --> 01:18:53.700 align:middle line:90% charge region, no charge there. 01:18:53.700 --> 01:19:00.420 align:middle line:84% No free carrier, no electron, no holes, just a positively ion, 01:19:00.420 --> 01:19:01.135 align:middle line:90% negative ions. 01:19:01.135 --> 01:19:05.260 align:middle line:90% 01:19:05.260 --> 01:19:12.980 align:middle line:84% And that means I got that now I have positive ion, negative ion. 01:19:12.980 --> 01:19:18.050 align:middle line:84% I have a potential pointing from positive negative. 01:19:18.050 --> 01:19:21.620 align:middle line:84% So that potential is building potential point 01:19:21.620 --> 01:19:23.960 align:middle line:90% negative to positive. 01:19:23.960 --> 01:19:28.010 align:middle line:84% And this potential will resist further diffusion. 01:19:28.010 --> 01:19:31.660 align:middle line:84% So at the end, you've got the equilibrium. 01:19:31.660 --> 01:19:35.470 align:middle line:84% So this is the view of the input picture 01:19:35.470 --> 01:19:40.384 align:middle line:84% that resists diffusion of charge from one side to other. 01:19:40.384 --> 01:19:42.900 align:middle line:90% Change junction. 01:19:42.900 --> 01:19:47.640 align:middle line:84% Now let's look at what's the current voltage characteristics. 01:19:47.640 --> 01:19:50.580 align:middle line:84% Very similar to Richardson's formula. 01:19:50.580 --> 01:19:53.130 align:middle line:90% So I'm going through this. 01:19:53.130 --> 01:19:54.690 align:middle line:90% That's what you learned before. 01:19:54.690 --> 01:19:57.231 align:middle line:90% So this is a-- 01:19:57.231 --> 01:20:00.780 align:middle line:90% I threw at you. 01:20:00.780 --> 01:20:05.060 align:middle line:84% Electron number density, hole number density, 01:20:05.060 --> 01:20:09.050 align:middle line:84% and the electron in any semiconductor, if you 01:20:09.050 --> 01:20:12.170 align:middle line:84% [INAUDIBLE] the electron, you can also derive similar hole. 01:20:12.170 --> 01:20:14.900 align:middle line:84% And then you take the product, you found out 01:20:14.900 --> 01:20:15.940 align:middle line:90% the product is constant. 01:20:15.940 --> 01:20:18.780 align:middle line:90% 01:20:18.780 --> 01:20:23.290 align:middle line:84% This p and n, so if you dope the electron, dope for n type, 01:20:23.290 --> 01:20:26.030 align:middle line:84% there are less hole because p times n is constant. 01:20:26.030 --> 01:20:29.840 align:middle line:90% 01:20:29.840 --> 01:20:33.080 align:middle line:84% p times n here is a relative band structure, 01:20:33.080 --> 01:20:36.650 align:middle line:84% effective mass conduction, effective mass balance, bandgap, 01:20:36.650 --> 01:20:39.310 align:middle line:90% and kvt, right? 01:20:39.310 --> 01:20:41.360 align:middle line:90% So p times n is constant. 01:20:41.360 --> 01:20:50.290 align:middle line:84% That's the-- now, how I calculate building potential? 01:20:50.290 --> 01:20:54.100 align:middle line:84% From on this side, I can say, because I 01:20:54.100 --> 01:20:57.400 align:middle line:84% know this is a constant, so I just need to calculate this. 01:20:57.400 --> 01:20:59.180 align:middle line:90% I need to calculate this. 01:20:59.180 --> 01:21:01.030 align:middle line:90% And the difference is this. 01:21:01.030 --> 01:21:02.832 align:middle line:90% That's the building potential. 01:21:02.832 --> 01:21:05.445 align:middle line:90% 01:21:05.445 --> 01:21:09.960 align:middle line:90% So from-- or look at this side. 01:21:09.960 --> 01:21:11.670 align:middle line:90% I have ec minus n. 01:21:11.670 --> 01:21:15.420 align:middle line:84% That's ecn minus mu, that's this distance. 01:21:15.420 --> 01:21:18.150 align:middle line:90% So I can start from the-- 01:21:18.150 --> 01:21:21.570 align:middle line:84% let's suppose each of the donor, each phosphor, for example, 01:21:21.570 --> 01:21:24.970 align:middle line:90% I put in give me a electron. 01:21:24.970 --> 01:21:28.420 align:middle line:90% And I reverse it, I get this. 01:21:28.420 --> 01:21:33.430 align:middle line:84% And I can do the same on this side. 01:21:33.430 --> 01:21:37.000 align:middle line:84% Given the number of the acceptor, 01:21:37.000 --> 01:21:39.485 align:middle line:84% that's the number of phosphor I-- 01:21:39.485 --> 01:21:40.940 align:middle line:90% boron I put here. 01:21:40.940 --> 01:21:43.480 align:middle line:90% Each boron create a one hole. 01:21:43.480 --> 01:21:46.990 align:middle line:84% So I find the distance between here and here. 01:21:46.990 --> 01:21:51.730 align:middle line:84% This is from-- oh, well, I already converted it into ec. 01:21:51.730 --> 01:21:54.220 align:middle line:90% That's from here to here. 01:21:54.220 --> 01:21:57.910 align:middle line:84% And now this, from here to here, that's here, that's here. 01:21:57.910 --> 01:22:02.800 align:middle line:84% The difference of these two give me the building potential. 01:22:02.800 --> 01:22:05.470 align:middle line:84% So this is the building potential. 01:22:05.470 --> 01:22:12.328 align:middle line:84% And it's the acceptor/donor, acceptor on this side, donor 01:22:12.328 --> 01:22:12.870 align:middle line:90% on this side. 01:22:12.870 --> 01:22:16.090 align:middle line:84% How much I dope it, because the more I dope it, 01:22:16.090 --> 01:22:18.494 align:middle line:84% the higher is the building potential. 01:22:18.494 --> 01:22:24.360 align:middle line:90% 01:22:24.360 --> 01:22:28.770 align:middle line:84% How wide is the space charge region? 01:22:28.770 --> 01:22:30.913 align:middle line:84% Now that you can solve this equation. 01:22:30.913 --> 01:22:31.580 align:middle line:90% I'm not solving. 01:22:31.580 --> 01:22:34.320 align:middle line:90% I'm just agreeing [INAUDIBLE]. 01:22:34.320 --> 01:22:37.160 align:middle line:90% But I want you to look at this. 01:22:37.160 --> 01:22:41.304 align:middle line:84% If it's just an electrostatic, that's the-- 01:22:41.304 --> 01:22:43.715 align:middle line:84% this is the width of the space charge region. 01:22:43.715 --> 01:22:47.941 align:middle line:90% 01:22:47.941 --> 01:22:51.820 align:middle line:84% And it depends on the dielectric constant. 01:22:51.820 --> 01:22:58.600 align:middle line:84% Larger dielectric constant, wider is the, say, space 01:22:58.600 --> 01:23:00.100 align:middle line:90% charge region. 01:23:00.100 --> 01:23:04.120 align:middle line:84% So if I look at this one side, either acceptor, donor, 01:23:04.120 --> 01:23:07.150 align:middle line:90% that's roughly how wide it is. 01:23:07.150 --> 01:23:14.740 align:middle line:84% And that's why I said I want to dope heavily to make a-- 01:23:14.740 --> 01:23:18.490 align:middle line:84% to reduce the Schottky effect for contact. 01:23:18.490 --> 01:23:22.090 align:middle line:84% If you can see that if I dope heavier, 01:23:22.090 --> 01:23:24.380 align:middle line:84% the width of the space charge region is narrower. 01:23:24.380 --> 01:23:28.805 align:middle line:90% 01:23:28.805 --> 01:23:34.700 align:middle line:84% And this is where you will talk to people with intelligence. 01:23:34.700 --> 01:23:36.820 align:middle line:84% They say, oh, what's the bi-length? 01:23:36.820 --> 01:23:39.140 align:middle line:84% That's essentially a measure of the weight, 01:23:39.140 --> 01:23:41.670 align:middle line:90% the intrinsic weight. 01:23:41.670 --> 01:23:46.793 align:middle line:84% And then the bi-length is essentially what we have here, 01:23:46.793 --> 01:23:48.210 align:middle line:84% replaced by the building potential 01:23:48.210 --> 01:23:51.590 align:middle line:84% by kvt, this spread, thermal spread. 01:23:51.590 --> 01:23:54.342 align:middle line:90% 01:23:54.342 --> 01:24:01.260 align:middle line:84% So heavier doping, shorter is the space charge region. 01:24:01.260 --> 01:24:04.220 align:middle line:90% 01:24:04.220 --> 01:24:06.990 align:middle line:84% Some people do nanowire surface effect, 01:24:06.990 --> 01:24:09.770 align:middle line:84% depends on you can see whether surface effect [INAUDIBLE] 01:24:09.770 --> 01:24:13.310 align:middle line:90% or not, depends on your doping. 01:24:13.310 --> 01:24:14.612 align:middle line:90% So bi-length. 01:24:14.612 --> 01:24:16.900 align:middle line:90% 01:24:16.900 --> 01:24:18.430 align:middle line:90% Finally, this is a-- 01:24:18.430 --> 01:24:22.560 align:middle line:84% I want to show you this because it's the same as Richardson 01:24:22.560 --> 01:24:23.060 align:middle line:90% formula. 01:24:23.060 --> 01:24:25.755 align:middle line:90% 01:24:25.755 --> 01:24:33.250 align:middle line:84% That's a pn junction, i times v, current voltage relation, 01:24:33.250 --> 01:24:36.040 align:middle line:90% except js-- 01:24:36.040 --> 01:24:38.110 align:middle line:90% except js. 01:24:38.110 --> 01:24:41.240 align:middle line:84% And that has a lovely price there. 01:24:41.240 --> 01:24:44.200 align:middle line:90% The js is no longer a t square. 01:24:44.200 --> 01:24:47.480 align:middle line:90% 01:24:47.480 --> 01:24:52.820 align:middle line:84% That exponential barrier, no longer the Richardson form. 01:24:52.820 --> 01:24:56.510 align:middle line:84% And the one we have here is the diffusivity of hole, 01:24:56.510 --> 01:25:01.790 align:middle line:84% diffusivity of electron, recombination time of hole 01:25:01.790 --> 01:25:05.830 align:middle line:84% on each side with the electron on each side. 01:25:05.830 --> 01:25:09.900 align:middle line:84% So this is a complete different mechanism. 01:25:09.900 --> 01:25:14.532 align:middle line:90% And so, this are the definition. 01:25:14.532 --> 01:25:18.480 align:middle line:84% Here I'm going there quickly, but I want you to chew on it 01:25:18.480 --> 01:25:20.450 align:middle line:90% and come back I will do-- 01:25:20.450 --> 01:25:22.020 align:middle line:90% I will explain more. 01:25:22.020 --> 01:25:24.690 align:middle line:84% And basically, this is a different-- 01:25:24.690 --> 01:25:27.170 align:middle line:84% here you can see, the formula is the same. 01:25:27.170 --> 01:25:30.580 align:middle line:90% 01:25:30.580 --> 01:25:34.490 align:middle line:84% Saturation current js is different. 01:25:34.490 --> 01:25:41.480 align:middle line:84% But it's a complete different mechanism in terms of transport. 01:25:41.480 --> 01:25:47.840 align:middle line:84% Because in a pin junction, the electron will go from this side 01:25:47.840 --> 01:25:49.280 align:middle line:90% to this other side. 01:25:49.280 --> 01:25:52.896 align:middle line:90% There are no electron anymore. 01:25:52.896 --> 01:25:55.870 align:middle line:84% p side, there are not much electron there. 01:25:55.870 --> 01:25:59.170 align:middle line:90% So how the transfer happened? 01:25:59.170 --> 01:26:04.500 align:middle line:84% And it turns out, there's really the hole 01:26:04.500 --> 01:26:07.770 align:middle line:90% recombined with the electron. 01:26:07.770 --> 01:26:13.080 align:middle line:84% So the holes here recombine with the electron. 01:26:13.080 --> 01:26:15.220 align:middle line:90% And then hole has to supply-- 01:26:15.220 --> 01:26:17.220 align:middle line:90% keep supplying. 01:26:17.220 --> 01:26:18.870 align:middle line:90% So there is a-- 01:26:18.870 --> 01:26:23.240 align:middle line:84% so in a pin junction is a recompilation that's important, 01:26:23.240 --> 01:26:25.400 align:middle line:90% that drives the current flow. 01:26:25.400 --> 01:26:33.690 align:middle line:84% While in a Schottky diode, it's just electron go this side, 01:26:33.690 --> 01:26:35.150 align:middle line:90% electron go this side. 01:26:35.150 --> 01:26:37.860 align:middle line:90% There's no supply issue there. 01:26:37.860 --> 01:26:40.320 align:middle line:84% So one is a majority carrier device. 01:26:40.320 --> 01:26:42.670 align:middle line:84% The other is a minority carrier device-- 01:26:42.670 --> 01:26:45.360 align:middle line:90% very different. 01:26:45.360 --> 01:26:46.830 align:middle line:90% Formula is the same-- 01:26:46.830 --> 01:26:49.860 align:middle line:90% almost the same. 01:26:49.860 --> 01:26:53.800 align:middle line:90% So just the last slide. 01:26:53.800 --> 01:26:57.350 align:middle line:90% And again, I want to show us a-- 01:26:57.350 --> 01:26:59.640 align:middle line:84% I'll come back to do a little review. 01:26:59.640 --> 01:27:00.960 align:middle line:90% But to go think about this. 01:27:00.960 --> 01:27:05.970 align:middle line:84% So this is the electron current, hole current. 01:27:05.970 --> 01:27:10.440 align:middle line:84% And they add up to the total current must be continuous. 01:27:10.440 --> 01:27:13.340 align:middle line:90% That's a pin junction. 01:27:13.340 --> 01:27:16.460 align:middle line:84% And what most people do not know, 01:27:16.460 --> 01:27:19.040 align:middle line:84% even electrical engineer, I'm pretty sure, 01:27:19.040 --> 01:27:23.450 align:middle line:84% is that inside of the just space charge region, there's no heat. 01:27:23.450 --> 01:27:24.540 align:middle line:90% In fact, it's cooling. 01:27:24.540 --> 01:27:27.065 align:middle line:90% 01:27:27.065 --> 01:27:30.710 align:middle line:84% You look at the Peltier effect, you 01:27:30.710 --> 01:27:33.980 align:middle line:84% go to analyze the thermoelectric effect in the semiconductor 01:27:33.980 --> 01:27:37.460 align:middle line:84% device, you'll find out that in the space charge 01:27:37.460 --> 01:27:39.200 align:middle line:90% region, the cooling effect. 01:27:39.200 --> 01:27:43.140 align:middle line:84% And this is really the recombination 01:27:43.140 --> 01:27:47.050 align:middle line:84% outside the space charge region that created the cooling-- 01:27:47.050 --> 01:27:47.550 align:middle line:90% heating. 01:27:47.550 --> 01:27:53.410 align:middle line:84% Of course, heating is a big issue in microelectronics. 01:27:53.410 --> 01:27:56.830 align:middle line:84% But in a diode, the center, the interface 01:27:56.830 --> 01:27:58.077 align:middle line:90% is actually cooling type. 01:27:58.077 --> 01:28:01.000 align:middle line:90% 01:28:01.000 --> 01:28:04.630 align:middle line:90% OK, I'll stop here. 01:28:04.630 --> 01:28:08.620 align:middle line:84% And I'm thinking about the same topic. 01:28:08.620 --> 01:28:12.500 align:middle line:90% Again, a lot of materials. 01:28:12.500 --> 01:28:13.000 align:middle line:90%