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 --> 00:00:18.700 align:middle line:90% at ocw.mit.edu. 00:00:18.700 --> 00:00:22.365 align:middle line:90% 00:00:22.365 --> 00:00:24.240 align:middle line:84% GANG CHEN: --not a question, I will continue. 00:00:24.240 --> 00:00:29.630 align:middle line:84% So, again, I think what you're saying is exactly-- 00:00:29.630 --> 00:00:33.140 align:middle line:84% that we start-- so it's a very steep dive. 00:00:33.140 --> 00:00:37.880 align:middle line:84% We start from very basic thinking. 00:00:37.880 --> 00:00:41.900 align:middle line:84% And then we're trying to understand 00:00:41.900 --> 00:00:46.160 align:middle line:84% the materials-- what determines the material properties. 00:00:46.160 --> 00:00:52.970 align:middle line:84% And this lecture-- after I told some of you 00:00:52.970 --> 00:00:57.410 align:middle line:84% this is topic of thermal conductivity, what I'm hoping 00:00:57.410 --> 00:01:02.810 align:middle line:84% is to real [INAUDIBLE] from here, what people are thinking 00:01:02.810 --> 00:01:06.266 align:middle line:90% in making materials better. 00:01:06.266 --> 00:01:15.920 align:middle line:84% But let me start with a very brief review of last lecture. 00:01:15.920 --> 00:01:19.580 align:middle line:90% We showed what is a simple-- 00:01:19.580 --> 00:01:22.180 align:middle line:84% remember, my picture is always simple. 00:01:22.180 --> 00:01:25.080 align:middle line:84% It goes from left to right and right to left. 00:01:25.080 --> 00:01:28.320 align:middle line:84% And the difference gives you the flux. 00:01:28.320 --> 00:01:31.235 align:middle line:84% So from there, we show the general relation. 00:01:31.235 --> 00:01:35.970 align:middle line:90% 00:01:35.970 --> 00:01:42.120 align:middle line:84% The current flux is related to electrostatic potential. 00:01:42.120 --> 00:01:45.630 align:middle line:84% So that's the charged driving force for charge flow. 00:01:45.630 --> 00:01:47.720 align:middle line:84% And then we will have a temperature gradient 00:01:47.720 --> 00:01:50.130 align:middle line:84% that is comparable to the [INAUDIBLE] gradient. 00:01:50.130 --> 00:01:55.980 align:middle line:84% So now you see the electricity to heat properly. 00:01:55.980 --> 00:02:00.750 align:middle line:84% And then this one shows the peak current. 00:02:00.750 --> 00:02:04.350 align:middle line:84% So really, now, electron is carrying the heat, 00:02:04.350 --> 00:02:07.830 align:middle line:84% and the heat current is the electric current. 00:02:07.830 --> 00:02:10.770 align:middle line:84% Heat current is, again, coupled, in this case, 00:02:10.770 --> 00:02:14.130 align:middle line:84% not just to parameter gradient, but also 00:02:14.130 --> 00:02:17.820 align:middle line:84% to the actual potential gradient. 00:02:17.820 --> 00:02:22.730 align:middle line:84% And this is a very general [INAUDIBLE] relation. 00:02:22.730 --> 00:02:24.320 align:middle line:90% If I have written-- 00:02:24.320 --> 00:02:28.970 align:middle line:84% really, this gradient in terms of generalized force, 00:02:28.970 --> 00:02:31.610 align:middle line:84% and this coefficient-- across coefficients are equal. 00:02:31.610 --> 00:02:37.280 align:middle line:84% And this is what the [INAUDIBLE] before. 00:02:37.280 --> 00:02:41.150 align:middle line:90% And then I gave some-- 00:02:41.150 --> 00:02:44.810 align:middle line:84% we use some of the concept we learned before-- 00:02:44.810 --> 00:02:49.610 align:middle line:84% for example, density of states and the-- 00:02:49.610 --> 00:02:52.940 align:middle line:84% we have expression for this coefficient. 00:02:52.940 --> 00:02:56.480 align:middle line:84% So one is the electric conductivity. 00:02:56.480 --> 00:03:00.140 align:middle line:84% And this other coefficient from this other coefficient, 00:03:00.140 --> 00:03:06.050 align:middle line:84% called the Seebeck coefficient, and the [INAUDIBLE] equations. 00:03:06.050 --> 00:03:12.110 align:middle line:84% Let me just make one remark that those expressions are not 00:03:12.110 --> 00:03:13.880 align:middle line:90% the most general. 00:03:13.880 --> 00:03:16.920 align:middle line:84% You can have different transport regimes. 00:03:16.920 --> 00:03:19.920 align:middle line:84% This is the regime that most people do-- 00:03:19.920 --> 00:03:21.970 align:middle line:84% the most common transport regime. 00:03:21.970 --> 00:03:24.150 align:middle line:90% So those expression-- you can-- 00:03:24.150 --> 00:03:27.210 align:middle line:84% rather than [INAUDIBLE] derivation, 00:03:27.210 --> 00:03:29.850 align:middle line:84% you can access from Boltzmann equation 00:03:29.850 --> 00:03:32.280 align:middle line:90% to derive those coefficients. 00:03:32.280 --> 00:03:37.860 align:middle line:90% And I show examples. 00:03:37.860 --> 00:03:42.060 align:middle line:84% One thing that I want to emphasize 00:03:42.060 --> 00:03:45.720 align:middle line:84% is that the properties depends on temperature. 00:03:45.720 --> 00:03:48.990 align:middle line:84% So different temperature-- you can see 00:03:48.990 --> 00:03:51.390 align:middle line:90% the property [? attribute. ?] 00:03:51.390 --> 00:03:53.730 align:middle line:84% For electric conductivity, if you 00:03:53.730 --> 00:03:57.750 align:middle line:84% follow these simple Boltzmann statistics, 00:03:57.750 --> 00:04:00.160 align:middle line:84% you actually get the electric conductivity. 00:04:00.160 --> 00:04:05.100 align:middle line:84% In semiconductor, we know typical microelectronics type 00:04:05.100 --> 00:04:06.540 align:middle line:90% of doping. 00:04:06.540 --> 00:04:09.060 align:middle line:84% The electric conductivity increases with temperature. 00:04:09.060 --> 00:04:11.820 align:middle line:84% But for thermoelectric material-- 00:04:11.820 --> 00:04:15.130 align:middle line:84% so this is not quite right for thermoelectric materials. 00:04:15.130 --> 00:04:17.100 align:middle line:84% You can see the thermal conductivity, 00:04:17.100 --> 00:04:20.070 align:middle line:84% electric conductivity increases with temperature. 00:04:20.070 --> 00:04:23.310 align:middle line:84% And that's because of the doping, very heavily-- 00:04:23.310 --> 00:04:25.580 align:middle line:90% metals like this. 00:04:25.580 --> 00:04:27.740 align:middle line:84% Metal-- the electric conductivity 00:04:27.740 --> 00:04:32.570 align:middle line:84% decreases because when you get hot, they are not more photons. 00:04:32.570 --> 00:04:36.020 align:middle line:84% The atoms are vibrating more violently, 00:04:36.020 --> 00:04:37.520 align:middle line:90% and that's scattered electron. 00:04:37.520 --> 00:04:41.960 align:middle line:84% And that's why the electric conductivity will decrease. 00:04:41.960 --> 00:04:48.350 align:middle line:84% And they see that this typically will have a peak. 00:04:48.350 --> 00:04:52.460 align:middle line:84% And if you just talk simply, one-band transport. 00:04:52.460 --> 00:04:56.960 align:middle line:84% So one-band means if I have a conduction band and each 00:04:56.960 --> 00:05:01.040 align:middle line:84% electron only go one to one conduction band, 00:05:01.040 --> 00:05:05.330 align:middle line:84% then the series say it should increase with temperature 00:05:05.330 --> 00:05:07.550 align:middle line:84% because as the temperature increases, 00:05:07.550 --> 00:05:11.870 align:middle line:84% the separation of the chemical potential from the bottom-- 00:05:11.870 --> 00:05:14.750 align:middle line:84% so the [INAUDIBLE] chemical potential [? from ?] the center 00:05:14.750 --> 00:05:16.040 align:middle line:90% of the band. 00:05:16.040 --> 00:05:20.900 align:middle line:84% But in almost all materials, the behavior 00:05:20.900 --> 00:05:23.750 align:middle line:84% is you will pick some temperature 00:05:23.750 --> 00:05:25.580 align:middle line:90% and start to decrease. 00:05:25.580 --> 00:05:30.140 align:middle line:84% And the reason is, as the temperature increase, 00:05:30.140 --> 00:05:32.210 align:middle line:90% you excite-- 00:05:32.210 --> 00:05:36.260 align:middle line:84% intrinsically, you leave the thermal energy and the electron 00:05:36.260 --> 00:05:40.940 align:middle line:84% from the valence band through the hole behind the electron 00:05:40.940 --> 00:05:42.050 align:middle line:90% conduction band. 00:05:42.050 --> 00:05:46.190 align:middle line:84% So in this case, now, you have both electron and hole. 00:05:46.190 --> 00:05:48.830 align:middle line:90% So when you flow current-- 00:05:48.830 --> 00:05:50.990 align:middle line:84% electron current energy in one direction, 00:05:50.990 --> 00:05:53.370 align:middle line:84% flow current energy in the opposite direction-- 00:05:53.370 --> 00:05:55.790 align:middle line:90% so they cancel each other. 00:05:55.790 --> 00:05:58.220 align:middle line:84% In this case, you actually could get a higher 00:05:58.220 --> 00:06:02.030 align:middle line:84% electric conductivity, but the Seebecks cancel each other. 00:06:02.030 --> 00:06:05.600 align:middle line:84% So this is-- when you look at experimental data, 00:06:05.600 --> 00:06:08.300 align:middle line:84% it turns out that [INAUDIBLE] we do that and say, 00:06:08.300 --> 00:06:09.992 align:middle line:90% we cannot calculate exactly. 00:06:09.992 --> 00:06:12.200 align:middle line:84% So we look at experiments, and this is what happened. 00:06:12.200 --> 00:06:13.940 align:middle line:90% This is why it died. 00:06:13.940 --> 00:06:15.230 align:middle line:90% And this is where-- 00:06:15.230 --> 00:06:20.520 align:middle line:84% OK, how you can move this to higher temperature? 00:06:20.520 --> 00:06:24.050 align:middle line:84% If you have more electron, you dope it more heavily-- 00:06:24.050 --> 00:06:26.210 align:middle line:84% you will go to higher temperature. 00:06:26.210 --> 00:06:29.690 align:middle line:84% And if you have larger bandgap, it's 00:06:29.690 --> 00:06:33.740 align:middle line:84% more difficult to generate the thermal electron-hole pairs, 00:06:33.740 --> 00:06:36.260 align:middle line:84% and then you can move this to higher. 00:06:36.260 --> 00:06:39.540 align:middle line:84% So that's how you look at the different configurations 00:06:39.540 --> 00:06:42.480 align:middle line:90% with different materials. 00:06:42.480 --> 00:06:47.820 align:middle line:84% So that's where we were in the last lecture, 00:06:47.820 --> 00:06:51.660 align:middle line:84% and those were mainly discussion on electrons. 00:06:51.660 --> 00:06:57.090 align:middle line:84% And we also talked about the whole concept 00:06:57.090 --> 00:06:58.710 align:middle line:90% of lattice vibration. 00:06:58.710 --> 00:07:02.520 align:middle line:84% And we gave a very simple expression, before, 00:07:02.520 --> 00:07:04.860 align:middle line:84% on the phonon thermal conductivity. 00:07:04.860 --> 00:07:08.780 align:middle line:84% And again, my picture is left to right, right to left. 00:07:08.780 --> 00:07:12.210 align:middle line:84% So when I want to find out the heat flux going 00:07:12.210 --> 00:07:14.820 align:middle line:84% through any band, I say, how much heat 00:07:14.820 --> 00:07:18.450 align:middle line:84% is going in from one side to the other without scattering? 00:07:18.450 --> 00:07:21.120 align:middle line:90% So this is one relaxation time. 00:07:21.120 --> 00:07:23.560 align:middle line:90% And how much from left to right? 00:07:23.560 --> 00:07:25.320 align:middle line:90% [INAUDIBLE] one relaxation time. 00:07:25.320 --> 00:07:27.990 align:middle line:84% So difference gave me the heat flux. 00:07:27.990 --> 00:07:30.840 align:middle line:84% And what I want to do is a little bit more-- 00:07:30.840 --> 00:07:34.370 align:middle line:84% better [INAUDIBLE] meaning before-- 00:07:34.370 --> 00:07:36.120 align:middle line:84% I will just say this is the number density 00:07:36.120 --> 00:07:38.190 align:middle line:90% n per unit volume. 00:07:38.190 --> 00:07:44.406 align:middle line:84% Now, I'm going to do modes, so I'm going to sum up-- so this-- 00:07:44.406 --> 00:07:47.820 align:middle line:84% it's the same as what I drew here. 00:07:47.820 --> 00:07:51.390 align:middle line:90% But here is more rigorous. 00:07:51.390 --> 00:07:57.490 align:middle line:84% So this is the energy of one Coulomb lattice vibration-- 00:07:57.490 --> 00:08:01.200 align:middle line:84% [INAUDIBLE] of lattice vibration, so one phonon. 00:08:01.200 --> 00:08:02.580 align:middle line:90% And then this is-- 00:08:02.580 --> 00:08:06.390 align:middle line:84% per Coulomb mechanical modes, the Boltzmann-Einstein 00:08:06.390 --> 00:08:13.740 align:middle line:84% distribution Per state, quantum state, how many phonon you have? 00:08:13.740 --> 00:08:17.520 align:middle line:90% And this is the velocity. 00:08:17.520 --> 00:08:22.500 align:middle line:84% So this is really telling me, for quantum mechanical modes, 00:08:22.500 --> 00:08:28.770 align:middle line:84% how many phonons is moving to the forward, positive x 00:08:28.770 --> 00:08:29.320 align:middle line:90% direction? 00:08:29.320 --> 00:08:31.140 align:middle line:90% The one path gives me path-- 00:08:31.140 --> 00:08:32.110 align:middle line:90% random motion. 00:08:32.110 --> 00:08:35.640 align:middle line:84% So the idea is the same, but now I'm 00:08:35.640 --> 00:08:40.830 align:middle line:84% trying to do a better job counting-- better counting job. 00:08:40.830 --> 00:08:43.630 align:middle line:90% And here, what do we have-- 00:08:43.630 --> 00:08:46.020 align:middle line:84% this is-- remember, in the second lecture, 00:08:46.020 --> 00:08:48.820 align:middle line:84% I was doing blackbody counting-- blackbody radiation. 00:08:48.820 --> 00:08:51.690 align:middle line:84% So this is counting all the quantum 00:08:51.690 --> 00:08:55.710 align:middle line:84% mechanical allowed modes, kx wave vector. 00:08:55.710 --> 00:08:58.540 align:middle line:84% It's a [? phonon ?] wave. kx, ky, kz. 00:08:58.540 --> 00:09:01.170 align:middle line:84% So I'm summing up all those modes. 00:09:01.170 --> 00:09:05.370 align:middle line:84% And that's from left to right, minus from right 00:09:05.370 --> 00:09:07.650 align:middle line:84% to left, giving me the left flux. 00:09:07.650 --> 00:09:11.370 align:middle line:84% So that's what I showed before in simpler form. 00:09:11.370 --> 00:09:14.730 align:middle line:90% But if I do this-- 00:09:14.730 --> 00:09:18.420 align:middle line:90% and I will get the integral-- 00:09:18.420 --> 00:09:22.170 align:middle line:84% no longer just a simple one third of cv gamma. 00:09:22.170 --> 00:09:24.120 align:middle line:90% That's what we had before. 00:09:24.120 --> 00:09:29.280 align:middle line:84% And now it's the integration of all the frequency, 00:09:29.280 --> 00:09:30.150 align:middle line:90% each frequency. 00:09:30.150 --> 00:09:34.350 align:middle line:84% Remember, [? phonon-- ?] so the acoustic wave-- 00:09:34.350 --> 00:09:37.410 align:middle line:84% for example, low-frequency acoustic wave-- 00:09:37.410 --> 00:09:39.010 align:middle line:90% that's what you hear. 00:09:39.010 --> 00:09:45.120 align:middle line:84% And they have the different mean-free path, 00:09:45.120 --> 00:09:49.020 align:middle line:84% different group velocity, the higher frequency ones. 00:09:49.020 --> 00:09:52.220 align:middle line:84% So this can all change as a function of frequency. 00:09:52.220 --> 00:09:55.290 align:middle line:84% So what we're writing now is a more rigorous form 00:09:55.290 --> 00:09:59.340 align:middle line:84% for the thermal conductivity carrying heat conduction 00:09:59.340 --> 00:10:00.930 align:middle line:90% by the last waves. 00:10:00.930 --> 00:10:02.440 align:middle line:90% That's really important. 00:10:02.440 --> 00:10:04.720 align:middle line:90% 00:10:04.720 --> 00:10:09.000 align:middle line:84% So this is a typical [INAUDIBLE] bulk material. 00:10:09.000 --> 00:10:11.680 align:middle line:84% And people have measured the thermal conductivity. 00:10:11.680 --> 00:10:15.240 align:middle line:84% And this is a typical curve of thermal conductivity, 00:10:15.240 --> 00:10:18.370 align:middle line:90% of material versus temperature. 00:10:18.370 --> 00:10:22.540 align:middle line:84% And this is specific example of gallium arsenide. 00:10:22.540 --> 00:10:26.620 align:middle line:90% And you can say there is a peak. 00:10:26.620 --> 00:10:30.010 align:middle line:84% So there's a-- in bulk material, its peak is typically 00:10:30.010 --> 00:10:32.230 align:middle line:90% between 10 to 20 kelvin. 00:10:32.230 --> 00:10:35.370 align:middle line:84% And then after the peak [INAUDIBLE] 00:10:35.370 --> 00:10:38.560 align:middle line:90% it drops below, it increases. 00:10:38.560 --> 00:10:42.130 align:middle line:84% And this actually reflects different physics. 00:10:42.130 --> 00:10:50.260 align:middle line:84% So at a very high temperature, each mode is carrying energy kt. 00:10:50.260 --> 00:10:58.180 align:middle line:84% So the number of phonons is also proportional to t, temperature. 00:10:58.180 --> 00:11:00.530 align:middle line:90% And in this case, what happens-- 00:11:00.530 --> 00:11:02.530 align:middle line:84% because as the temperature increases, 00:11:02.530 --> 00:11:07.090 align:middle line:84% you excite more phonons, and they scatter each other. 00:11:07.090 --> 00:11:09.100 align:middle line:84% They scatter each other, and they 00:11:09.100 --> 00:11:11.090 align:middle line:90% drop the thermal conductivity. 00:11:11.090 --> 00:11:14.020 align:middle line:84% So that's why the thermal conductivity is dropping. 00:11:14.020 --> 00:11:18.370 align:middle line:84% And in fact, if you follow the [INAUDIBLE] same, 00:11:18.370 --> 00:11:21.970 align:middle line:84% the number is proportional to t, the thermal conductivity 00:11:21.970 --> 00:11:24.120 align:middle line:84% is typically inversely proportional 00:11:24.120 --> 00:11:26.760 align:middle line:90% to [INAUDIBLE] temperature. 00:11:26.760 --> 00:11:28.610 align:middle line:84% But see, that's a simple picture. 00:11:28.610 --> 00:11:32.200 align:middle line:84% And then in reality, this exponent is not 1. 00:11:32.200 --> 00:11:35.170 align:middle line:84% It's typically, depending on the material, between 1 and 1.5. 00:11:35.170 --> 00:11:37.210 align:middle line:84% People still are trying to figure out 00:11:37.210 --> 00:11:40.810 align:middle line:90% why it's not exactly 1. 00:11:40.810 --> 00:11:44.660 align:middle line:84% So this is a higher temperature range. 00:11:44.660 --> 00:11:48.710 align:middle line:84% And as you go to lower temperature, 00:11:48.710 --> 00:11:52.730 align:middle line:84% the phonon-phonon scattering-- the lattice wave interaction 00:11:52.730 --> 00:11:54.200 align:middle line:90% with itself-- 00:11:54.200 --> 00:11:56.090 align:middle line:90% becomes weaker. 00:11:56.090 --> 00:11:57.650 align:middle line:90% So in this case-- 00:11:57.650 --> 00:12:01.880 align:middle line:84% so the thermal conductivity will increase, even though-- 00:12:01.880 --> 00:12:04.130 align:middle line:84% if you go to check specific heat-- 00:12:04.130 --> 00:12:09.290 align:middle line:84% specific heat of-- which, in this dielectric 00:12:09.290 --> 00:12:10.880 align:middle line:90% is due to phonons. 00:12:10.880 --> 00:12:14.150 align:middle line:84% Specifically, this is typically this curve. 00:12:14.150 --> 00:12:15.590 align:middle line:90% I forgot to show one. 00:12:15.590 --> 00:12:18.020 align:middle line:90% And it's not a constant. 00:12:18.020 --> 00:12:19.760 align:middle line:84% It increases from low temperature 00:12:19.760 --> 00:12:20.990 align:middle line:90% to the high temperature. 00:12:20.990 --> 00:12:23.540 align:middle line:84% But thermal conductivity-- so even though there are less 00:12:23.540 --> 00:12:24.650 align:middle line:90% energy-- 00:12:24.650 --> 00:12:26.570 align:middle line:84% specifically the measure of phonon energy-- 00:12:26.570 --> 00:12:29.120 align:middle line:84% less energy in this region compared to this region-- 00:12:29.120 --> 00:12:32.510 align:middle line:84% but because less scattering, the phonon goes longer. 00:12:32.510 --> 00:12:34.800 align:middle line:84% So the thermal conductivity actually increases. 00:12:34.800 --> 00:12:37.468 align:middle line:90% 00:12:37.468 --> 00:12:41.260 align:middle line:84% So in this region it's typically phonon-phonon 00:12:41.260 --> 00:12:44.350 align:middle line:84% scattering-- no longer dominant [INAUDIBLE] you've 00:12:44.350 --> 00:12:46.180 align:middle line:90% got an [INAUDIBLE] atoms. 00:12:46.180 --> 00:12:52.240 align:middle line:84% So for example, in silicon, if you have a phosphor or boron, 00:12:52.240 --> 00:12:55.210 align:middle line:90% you dope it, they are lighter. 00:12:55.210 --> 00:12:57.400 align:middle line:84% So you think about that-- you have a string. 00:12:57.400 --> 00:13:00.640 align:middle line:84% Again, phonon is the lattice vibration. 00:13:00.640 --> 00:13:02.860 align:middle line:84% You have the same mass [INAUDIBLE] 00:13:02.860 --> 00:13:06.840 align:middle line:84% And suddenly, you put a different mass that created 00:13:06.840 --> 00:13:09.660 align:middle line:90% some scattering of the waves. 00:13:09.660 --> 00:13:13.650 align:middle line:84% And so this is the region where the limit-- 00:13:13.650 --> 00:13:17.100 align:middle line:84% the peak here is very much limited by these impurities 00:13:17.100 --> 00:13:18.900 align:middle line:90% in the material. 00:13:18.900 --> 00:13:23.340 align:middle line:84% And then when you go to very low temperature-- 00:13:23.340 --> 00:13:26.610 align:middle line:84% so the mean-free path becomes very long. 00:13:26.610 --> 00:13:29.280 align:middle line:90% In fact, even you can measure-- 00:13:29.280 --> 00:13:32.610 align:middle line:84% make a fault material, the mean-free path 00:13:32.610 --> 00:13:35.320 align:middle line:90% is longer than your sample size. 00:13:35.320 --> 00:13:39.340 align:middle line:84% So in this case, the boundary scattering becomes dominant. 00:13:39.340 --> 00:13:43.480 align:middle line:84% And the mean-free path is no longer 00:13:43.480 --> 00:13:47.320 align:middle line:84% dependent on the frequency, but dependent on-- is 00:13:47.320 --> 00:13:49.390 align:middle line:90% limited by the sample size. 00:13:49.390 --> 00:13:53.060 align:middle line:84% So in this region, the thermal conductivity 00:13:53.060 --> 00:13:59.350 align:middle line:84% is exactly due to the specific heat. 00:13:59.350 --> 00:14:03.920 align:middle line:84% So the behavior-- just specific heat and sample size. 00:14:03.920 --> 00:14:06.047 align:middle line:90% So-- yes. 00:14:06.047 --> 00:14:07.880 align:middle line:84% AUDIENCE: No question because I just think-- 00:14:07.880 --> 00:14:10.550 align:middle line:84% because of [INAUDIBLE] the power. 00:14:10.550 --> 00:14:11.360 align:middle line:90% That's why t-- 00:14:11.360 --> 00:14:13.600 align:middle line:84% GANG CHEN: That's exactly the reason. 00:14:13.600 --> 00:14:17.030 align:middle line:84% So, by the way, this is why blackbody radiation 00:14:17.030 --> 00:14:19.280 align:middle line:90% to the fourth power. 00:14:19.280 --> 00:14:21.170 align:middle line:90% Specifically, the third power-- 00:14:21.170 --> 00:14:24.380 align:middle line:90% the energy is dU dt. 00:14:24.380 --> 00:14:28.490 align:middle line:84% So if you integrate, the energy is the temperature fourth power. 00:14:28.490 --> 00:14:31.460 align:middle line:84% And the [? phonon-phonon-- ?] this is a regime. 00:14:31.460 --> 00:14:33.980 align:middle line:84% Unfortunately, it's a very low-temperature regime. 00:14:33.980 --> 00:14:38.240 align:middle line:84% But this regime, phonon behave almost identically to photon. 00:14:38.240 --> 00:14:41.870 align:middle line:84% Now, scatter-- very weak scatter. 00:14:41.870 --> 00:14:48.660 align:middle line:84% So you can see the temperature-- the power is the same. 00:14:48.660 --> 00:14:53.250 align:middle line:84% So that's a typical behavior of lattice thermal conductivity 00:14:53.250 --> 00:14:54.210 align:middle line:90% in crystals. 00:14:54.210 --> 00:14:57.240 align:middle line:90% And just give one example. 00:14:57.240 --> 00:15:00.650 align:middle line:84% The highest thermal conductivity material is diamond. 00:15:00.650 --> 00:15:05.150 align:middle line:84% And if you purify the diamond, you can change this peak by-- 00:15:05.150 --> 00:15:06.920 align:middle line:90% from this peak. 00:15:06.920 --> 00:15:09.560 align:middle line:84% Diamond-- [INAUDIBLE] temperature is about 2,000. 00:15:09.560 --> 00:15:11.670 align:middle line:90% And that peak go very high. 00:15:11.670 --> 00:15:16.190 align:middle line:84% And if you purify it-- just to say even isotopes-- 00:15:16.190 --> 00:15:18.965 align:middle line:90% carbon 12 versus carbon 13-- 00:15:18.965 --> 00:15:22.610 align:middle line:84% you can significantly limit this peak. 00:15:22.610 --> 00:15:26.450 align:middle line:84% [INAUDIBLE] room temperature, the thermal conductivity 00:15:26.450 --> 00:15:29.910 align:middle line:84% will be influenced by the [INAUDIBLE] of isotopes. 00:15:29.910 --> 00:15:32.860 align:middle line:90% 00:15:32.860 --> 00:15:38.080 align:middle line:84% So now if I combine the thermal conductivity, 00:15:38.080 --> 00:15:42.510 align:middle line:84% it turns out lattice has a contribution. 00:15:42.510 --> 00:15:44.430 align:middle line:90% The electron also carry heat. 00:15:44.430 --> 00:15:48.060 align:middle line:84% So if I have an electron and I have four-- 00:15:48.060 --> 00:15:52.170 align:middle line:84% four [INAUDIBLE] So I have electron hole. 00:15:52.170 --> 00:15:55.506 align:middle line:90% And then I mentioned-- 00:15:55.506 --> 00:16:00.550 align:middle line:84% when they move-- when the electron hole or diffuse, 00:16:00.550 --> 00:16:04.573 align:middle line:84% the higher temperature region-- you may get more electron hole. 00:16:04.573 --> 00:16:06.240 align:middle line:84% When you go to lower temperature region, 00:16:06.240 --> 00:16:07.800 align:middle line:90% they have less electron hole. 00:16:07.800 --> 00:16:09.150 align:middle line:90% What happens? 00:16:09.150 --> 00:16:13.470 align:middle line:84% The electron hole will combine each with each other 00:16:13.470 --> 00:16:14.860 align:middle line:90% and give off heat. 00:16:14.860 --> 00:16:18.840 align:middle line:84% So in that case, they carry the potential energy 00:16:18.840 --> 00:16:20.620 align:middle line:90% from one place to other. 00:16:20.620 --> 00:16:22.860 align:middle line:84% And this is the bipolar contribution, 00:16:22.860 --> 00:16:25.980 align:middle line:84% which is a really bad for thermoelectric. 00:16:25.980 --> 00:16:31.830 align:middle line:84% So this is an example of-- most people 00:16:31.830 --> 00:16:35.730 align:middle line:84% who do thermoelectrics don't pay attention to this, 00:16:35.730 --> 00:16:39.720 align:middle line:90% and that's wrong. 00:16:39.720 --> 00:16:43.150 align:middle line:84% For example, the electronic contribution-- 00:16:43.150 --> 00:16:47.370 align:middle line:84% you can calculate it from Wiedemann-Franz law, 00:16:47.370 --> 00:16:50.310 align:middle line:84% The electric conductivity divided by thermal conductivity 00:16:50.310 --> 00:16:52.060 align:middle line:84% is proportional to temperature [INAUDIBLE] 00:16:52.060 --> 00:16:53.830 align:middle line:84% constant mentioned in Wiedemann-Franz law. 00:16:53.830 --> 00:16:55.580 align:middle line:90% So many people will do this. 00:16:55.580 --> 00:16:58.900 align:middle line:84% They will calculate this term and this term, 00:16:58.900 --> 00:17:02.170 align:middle line:84% and they measure this term, and they subtract the difference, 00:17:02.170 --> 00:17:03.730 align:middle line:90% gives you the lattice. 00:17:03.730 --> 00:17:06.369 align:middle line:84% But they don't calculate this term. 00:17:06.369 --> 00:17:10.089 align:middle line:84% And this is actually difficult to calculate, 00:17:10.089 --> 00:17:11.890 align:middle line:90% and that's the reason. 00:17:11.890 --> 00:17:16.960 align:middle line:84% But you can see that the thermal conductivity at a higher 00:17:16.960 --> 00:17:20.750 align:middle line:90% temperature goes up. 00:17:20.750 --> 00:17:24.430 align:middle line:84% The lattice thermal conductivity always goes down. 00:17:24.430 --> 00:17:28.420 align:middle line:84% And the reason for this goes up is due to this term-- 00:17:28.420 --> 00:17:33.520 align:middle line:84% a very strong signature of bipolar thermal conductivity 00:17:33.520 --> 00:17:36.310 align:middle line:90% from electrons and the holes. 00:17:36.310 --> 00:17:40.570 align:middle line:84% And correspondingly, the Seebeck goes down-- 00:17:40.570 --> 00:17:43.840 align:middle line:84% the Seebeck-- because the electron hole cancel that. 00:17:43.840 --> 00:17:47.170 align:middle line:84% But the thermal conductivity is still 00:17:47.170 --> 00:17:49.640 align:middle line:90% getting both terms, [INAUDIBLE]. 00:17:49.640 --> 00:17:53.161 align:middle line:90% 00:17:53.161 --> 00:17:54.800 align:middle line:90% So now let's go back. 00:17:54.800 --> 00:17:59.650 align:middle line:84% I've talked a long time on this [INAUDIBLE] which parameters-- 00:17:59.650 --> 00:18:02.200 align:middle line:84% electrical, Seebeck, thermal conductivity. 00:18:02.200 --> 00:18:04.540 align:middle line:84% And we see that the thermal conductivity 00:18:04.540 --> 00:18:08.140 align:middle line:84% in the electronic part and phonon part. 00:18:08.140 --> 00:18:15.580 align:middle line:84% And now if I divide it by the electric conductivity-- 00:18:15.580 --> 00:18:18.850 align:middle line:90% so here, I have Lorenz number. 00:18:18.850 --> 00:18:22.600 align:middle line:84% And here, I have phonon divided by [INAUDIBLE], so sigma t. 00:18:22.600 --> 00:18:26.800 align:middle line:84% That's just the simple manipulation. 00:18:26.800 --> 00:18:30.490 align:middle line:90% And the Lorenz number in metal-- 00:18:30.490 --> 00:18:32.620 align:middle line:90% that's the exact number. 00:18:32.620 --> 00:18:34.480 align:middle line:84% But when you go to semiconductor, 00:18:34.480 --> 00:18:36.100 align:middle line:90% this depends on doping. 00:18:36.100 --> 00:18:40.870 align:middle line:84% So that's why I read it out as a function of n. 00:18:40.870 --> 00:18:45.160 align:middle line:84% But see, if you look at it, in metal Seebeck cancel each other. 00:18:45.160 --> 00:18:47.740 align:middle line:84% The electron above the Fermi level, 00:18:47.740 --> 00:18:50.290 align:middle line:84% electron below the Fermi level cancel each other. 00:18:50.290 --> 00:18:52.390 align:middle line:84% You will get a Seebeck [INAUDIBLE]. 00:18:52.390 --> 00:18:56.050 align:middle line:84% So you plug in those letters, and the best you get-- 00:18:56.050 --> 00:18:59.680 align:middle line:90% the most metal is about 0.01. 00:18:59.680 --> 00:19:02.620 align:middle line:84% When I first got into the thermoelectric proposal, 00:19:02.620 --> 00:19:08.770 align:middle line:84% I didn't know whether metal was good or bad, or semiconductor. 00:19:08.770 --> 00:19:12.730 align:middle line:84% Well, now you take a good thermal [INAUDIBLE]-- 00:19:12.730 --> 00:19:15.910 align:middle line:84% Bismuth telluride-- that's a typical example. 00:19:15.910 --> 00:19:20.740 align:middle line:84% And Seebeck is about 200 microwatt per kelvin. 00:19:20.740 --> 00:19:23.910 align:middle line:84% And [? phonon ?] thermal conductivity is about 1. 00:19:23.910 --> 00:19:27.940 align:middle line:84% Electrical conductivity is essentially 57 per meter. 00:19:27.940 --> 00:19:32.530 align:middle line:84% So Seebeck is just the inverse of [INAUDIBLE]. 00:19:32.530 --> 00:19:35.380 align:middle line:84% So that's the unit of electric conductivity. 00:19:35.380 --> 00:19:39.100 align:middle line:84% And you plug all those numbers, and then you 00:19:39.100 --> 00:19:41.110 align:middle line:90% find that's of the order of 1. 00:19:41.110 --> 00:19:48.760 align:middle line:84% So from 1950s to 1990s, the best thermoelectric materials have 00:19:48.760 --> 00:19:51.250 align:middle line:90% a figure of about 1. 00:19:51.250 --> 00:19:53.470 align:middle line:84% People have-- because experimentally, 00:19:53.470 --> 00:19:54.740 align:middle line:90% you can't get better. 00:19:54.740 --> 00:19:57.400 align:middle line:84% So people are reading a lot of papers 00:19:57.400 --> 00:20:01.400 align:middle line:84% on why we can't break-- this is the absolute maximum. 00:20:01.400 --> 00:20:05.420 align:middle line:84% So they're questioning whether their theory-- trying to say, 00:20:05.420 --> 00:20:08.470 align:middle line:90% why this is the maximum. 00:20:08.470 --> 00:20:12.350 align:middle line:90% So this is the-- 00:20:12.350 --> 00:20:14.730 align:middle line:84% really the theoretical foundation. 00:20:14.730 --> 00:20:20.660 align:middle line:84% We've talked-- and the last slide on this is a mature-- 00:20:20.660 --> 00:20:23.780 align:middle line:84% I said sometimes, you can get a really good one, 00:20:23.780 --> 00:20:27.530 align:middle line:84% or you throw away because the doping isn't right. 00:20:27.530 --> 00:20:29.430 align:middle line:90% You can say that-- 00:20:29.430 --> 00:20:31.820 align:middle line:84% say, because the doping determine where 00:20:31.820 --> 00:20:34.130 align:middle line:90% is the chemical potential, 00:20:34.130 --> 00:20:39.780 align:middle line:84% So the properties are so intertwined with each other-- 00:20:39.780 --> 00:20:42.710 align:middle line:84% Seebeck coefficient as a function of doping. 00:20:42.710 --> 00:20:46.160 align:middle line:90% Here is a bipolar effect. 00:20:46.160 --> 00:20:48.830 align:middle line:84% In fact, this one-- why it goes down? 00:20:48.830 --> 00:20:50.810 align:middle line:90% I have to check. 00:20:50.810 --> 00:20:53.100 align:middle line:84% The electric conductivity-- this looks better. 00:20:53.100 --> 00:20:55.490 align:middle line:84% The electric conductivity increases, 00:20:55.490 --> 00:20:58.610 align:middle line:84% and the thermal conductivity-- and you 00:20:58.610 --> 00:21:02.770 align:middle line:90% pick your zt at a certain value, 00:21:02.770 --> 00:21:04.600 align:middle line:90% So this is clearly-- 00:21:04.600 --> 00:21:08.710 align:middle line:84% so you have to really increase your doping. 00:21:08.710 --> 00:21:11.560 align:middle line:84% That's adding other materials or creating-- 00:21:11.560 --> 00:21:14.320 align:middle line:84% there are different ways, creating doping carriers. 00:21:14.320 --> 00:21:20.740 align:middle line:84% So this is the difficulty with thermoelectric optimization. 00:21:20.740 --> 00:21:22.560 align:middle line:90% A lot of work one has to do. 00:21:22.560 --> 00:21:25.160 align:middle line:90% 00:21:25.160 --> 00:21:30.170 align:middle line:84% Now we're going to really just say, what are the materials? 00:21:30.170 --> 00:21:31.130 align:middle line:90% Yes. 00:21:31.130 --> 00:21:32.720 align:middle line:84% AUDIENCE: That graph was actually 00:21:32.720 --> 00:21:34.150 align:middle line:90% measured experimentally? 00:21:34.150 --> 00:21:35.150 align:middle line:90% GANG CHEN: These curves? 00:21:35.150 --> 00:21:35.690 align:middle line:90% AUDIENCE: Yeah. 00:21:35.690 --> 00:21:37.357 align:middle line:84% GANG CHEN: These curves were calculated. 00:21:37.357 --> 00:21:38.730 align:middle line:90% AUDIENCE: So they're calculated, 00:21:38.730 --> 00:21:40.790 align:middle line:90% GANG CHEN: Yeah. 00:21:40.790 --> 00:21:43.100 align:middle line:84% Typically, when you see, like, two dots, 00:21:43.100 --> 00:21:46.810 align:middle line:90% that's mostly experimental. 00:21:46.810 --> 00:21:47.310 align:middle line:90% OK. 00:21:47.310 --> 00:21:48.930 align:middle line:84% Those are experimental-- what are 00:21:48.930 --> 00:21:50.820 align:middle line:90% you seeing here in this frame. 00:21:50.820 --> 00:21:55.560 align:middle line:90% So this is the summary. 00:21:55.560 --> 00:21:59.130 align:middle line:84% Not always updated, and people always are reporting progresses 00:21:59.130 --> 00:21:59.960 align:middle line:90% most days. 00:21:59.960 --> 00:22:07.380 align:middle line:84% So here is a summary of zt of different materials. 00:22:07.380 --> 00:22:10.320 align:middle line:84% And what people have traditionally been using-- 00:22:10.320 --> 00:22:11.400 align:middle line:90% this one's tenorite. 00:22:11.400 --> 00:22:14.220 align:middle line:90% That's in all the modules-- 00:22:14.220 --> 00:22:15.960 align:middle line:90% commercial module-- [INAUDIBLE]. 00:22:15.960 --> 00:22:18.480 align:middle line:84% And this is the function of temperature, 00:22:18.480 --> 00:22:23.790 align:middle line:84% So this commercial zt takes around room temperature-- 00:22:23.790 --> 00:22:25.140 align:middle line:90% 1. 00:22:25.140 --> 00:22:30.150 align:middle line:84% And [INAUDIBLE] tenorite is in the intermediate temperature-- 00:22:30.150 --> 00:22:32.110 align:middle line:90% 400 degree, 500 degree. 00:22:32.110 --> 00:22:35.210 align:middle line:90% And the peak is less than 1-- 00:22:35.210 --> 00:22:38.130 align:middle line:90% 0.8, 0.9. 00:22:38.130 --> 00:22:43.360 align:middle line:84% And the silicon-germanium-- this is what NASA has been using. 00:22:43.360 --> 00:22:46.300 align:middle line:90% NASA used it for space missions. 00:22:46.300 --> 00:22:50.110 align:middle line:84% They use nuclear as a heat source. 00:22:50.110 --> 00:22:52.870 align:middle line:84% But they build their system so they operate 00:22:52.870 --> 00:22:54.190 align:middle line:90% at a very high temperature. 00:22:54.190 --> 00:22:58.420 align:middle line:84% So silicon-germanium is what NASA used in the past. 00:22:58.420 --> 00:23:02.440 align:middle line:84% And remember, if you want to build a device, 00:23:02.440 --> 00:23:06.640 align:middle line:84% you have to have both n-type and p-type materials. 00:23:06.640 --> 00:23:11.860 align:middle line:84% So it's not all shown whether it's p-type or n-type. 00:23:11.860 --> 00:23:14.710 align:middle line:84% But for each type, you build a device-- 00:23:14.710 --> 00:23:16.840 align:middle line:90% you need both n and p. 00:23:16.840 --> 00:23:20.680 align:middle line:84% And also, ideally, if we go back to look 00:23:20.680 --> 00:23:24.100 align:middle line:84% at the notes in the device section, when 00:23:24.100 --> 00:23:27.340 align:middle line:84% we talk about device, you want these two materials closed-- 00:23:27.340 --> 00:23:28.540 align:middle line:90% properties closed. 00:23:28.540 --> 00:23:32.810 align:middle line:84% Otherwise, it's not the material that determine your efficiency. 00:23:32.810 --> 00:23:37.030 align:middle line:84% So you look at-- let's say the same temperature range-- 00:23:37.030 --> 00:23:39.640 align:middle line:90% what materials are available? 00:23:39.640 --> 00:23:45.190 align:middle line:84% And like I said, zt has been 1 most of the time, 00:23:45.190 --> 00:23:47.110 align:middle line:84% and there are some recent progress. 00:23:47.110 --> 00:23:49.340 align:middle line:90% We'll discuss these progresses. 00:23:49.340 --> 00:23:52.420 align:middle line:90% 00:23:52.420 --> 00:23:56.020 align:middle line:84% This is a more traditional material. 00:23:56.020 --> 00:23:58.285 align:middle line:84% Like I said, bismuth telluride, then tenorite, 00:23:58.285 --> 00:24:03.990 align:middle line:84% silicon-germanium, n-type and p-type materials. 00:24:03.990 --> 00:24:07.710 align:middle line:84% And skutterudite is a newer material. 00:24:07.710 --> 00:24:12.150 align:middle line:84% So the commercialized bismuth telluride-- 00:24:12.150 --> 00:24:14.500 align:middle line:84% bismuth telluride-- go to periodic table. 00:24:14.500 --> 00:24:16.590 align:middle line:84% I can't remember all those positions, 00:24:16.590 --> 00:24:19.650 align:middle line:84% every time I'm in my office I look at the periodic table. 00:24:19.650 --> 00:24:22.230 align:middle line:90% But those are heavy. 00:24:22.230 --> 00:24:25.980 align:middle line:84% So bismuth, [INAUDIBLE] are heavy elements. 00:24:25.980 --> 00:24:29.940 align:middle line:84% And why we want heavy elements in this case? 00:24:29.940 --> 00:24:31.150 align:middle line:90% Why is it good? 00:24:31.150 --> 00:24:32.250 align:middle line:90% So you look at it-- 00:24:32.250 --> 00:24:37.690 align:middle line:84% as it becomes heavier, the bandgap decreases here. 00:24:37.690 --> 00:24:38.910 align:middle line:90% This is the bandgap. 00:24:38.910 --> 00:24:43.440 align:middle line:84% The bandgap decrease is typically about-- you need-- 00:24:43.440 --> 00:24:47.460 align:middle line:84% for the bandgap versus temperature range-- 00:24:47.460 --> 00:24:49.770 align:middle line:90% around 10 kg. 00:24:49.770 --> 00:24:52.620 align:middle line:90% 10 times kdt-- kt. 00:24:52.620 --> 00:24:58.110 align:middle line:84% So at room temperature, the kt is 26 million electron volts. 00:24:58.110 --> 00:25:00.960 align:middle line:90% So 10 is the 0.26. 00:25:00.960 --> 00:25:02.940 align:middle line:84% Turns out the bismuth telluride-- 00:25:02.940 --> 00:25:07.870 align:middle line:90% the bandgap is about 0.15 range. 00:25:07.870 --> 00:25:12.610 align:middle line:84% So you go to, say, heavier material-- 00:25:12.610 --> 00:25:15.070 align:middle line:90% your band gap decreases. 00:25:15.070 --> 00:25:19.510 align:middle line:84% And now you think about thermal conductivity. 00:25:19.510 --> 00:25:23.290 align:middle line:84% Recall that when I say the vibrational frequency, 00:25:23.290 --> 00:25:27.040 align:middle line:84% vibrational frequency is the spring constant divided 00:25:27.040 --> 00:25:28.930 align:middle line:90% mass square root. 00:25:28.930 --> 00:25:30.760 align:middle line:90% So we have our mass-- 00:25:30.760 --> 00:25:34.660 align:middle line:84% you got the lower vibrational frequency. 00:25:34.660 --> 00:25:39.670 align:middle line:84% Lower vibrational frequency-- you look at the group velocity-- 00:25:39.670 --> 00:25:41.140 align:middle line:90% it travels slower. 00:25:41.140 --> 00:25:47.050 align:middle line:84% So the phonon [INAUDIBLE] to go more slowly than lighter atoms. 00:25:47.050 --> 00:25:51.460 align:middle line:84% So that's why the thermal conductivity is lower when 00:25:51.460 --> 00:25:53.830 align:middle line:90% you go to a heavier material. 00:25:53.830 --> 00:25:58.240 align:middle line:84% So bismuth telluride has a very complicated unit cell. 00:25:58.240 --> 00:26:01.900 align:middle line:84% This is really-- in terms of full periodicity, 00:26:01.900 --> 00:26:05.170 align:middle line:84% when you consider a hexagonal unit cell, 00:26:05.170 --> 00:26:10.750 align:middle line:84% it's really 30.7 angstrom-- many atoms here. 00:26:10.750 --> 00:26:15.160 align:middle line:90% And it's interesting. 00:26:15.160 --> 00:26:18.440 align:middle line:84% This is where you really want to understand the material. 00:26:18.440 --> 00:26:24.340 align:middle line:84% So it's a polaron bismuth terms of linear structure, 00:26:24.340 --> 00:26:26.320 align:middle line:90% And this is the polaron. 00:26:26.320 --> 00:26:28.840 align:middle line:90% This is the bismuth polaron. 00:26:28.840 --> 00:26:32.560 align:middle line:90% And in between the layers-- 00:26:32.560 --> 00:26:34.270 align:middle line:90% you got you see here-- 00:26:34.270 --> 00:26:36.820 align:middle line:90% this [INAUDIBLE] was bonded. 00:26:36.820 --> 00:26:43.570 align:middle line:84% And here is more a mixture of covalent and ionic bonding. 00:26:43.570 --> 00:26:45.430 align:middle line:90% And there are a lot of study-- 00:26:45.430 --> 00:26:48.430 align:middle line:84% people look at which layer is conducting electron, 00:26:48.430 --> 00:26:50.830 align:middle line:90% which layer is conducting hole. 00:26:50.830 --> 00:26:57.130 align:middle line:84% And it's really-- we're still working on bismuth telluride. 00:26:57.130 --> 00:27:00.970 align:middle line:84% And it's important to understand those details 00:27:00.970 --> 00:27:03.680 align:middle line:84% because people have been working this for many years. 00:27:03.680 --> 00:27:06.310 align:middle line:84% You want to do something, you need to look at detail. 00:27:06.310 --> 00:27:06.950 align:middle line:90% Where are they? 00:27:06.950 --> 00:27:09.400 align:middle line:84% Which are the layers of electrons? 00:27:09.400 --> 00:27:11.740 align:middle line:84% Think about something that you can-- 00:27:11.740 --> 00:27:15.860 align:middle line:84% example-- still got the electron transport well in this layer, 00:27:15.860 --> 00:27:19.730 align:middle line:84% but screw up the phonon, kill the phonon propagation 00:27:19.730 --> 00:27:21.240 align:middle line:90% in the materials. 00:27:21.240 --> 00:27:23.950 align:middle line:84% So people calculate the band structure. 00:27:23.950 --> 00:27:24.950 align:middle line:90% I'm not going to detail. 00:27:24.950 --> 00:27:28.260 align:middle line:84% This is really-- [? obviously, ?] you do this. 00:27:28.260 --> 00:27:31.490 align:middle line:84% This band structure calculation is also relative standard. 00:27:31.490 --> 00:27:34.250 align:middle line:84% You do a density functional theory calculation. 00:27:34.250 --> 00:27:39.440 align:middle line:84% And this is a pure-- bismuth telluride-- 00:27:39.440 --> 00:27:42.380 align:middle line:84% If you just do a pure bismuth telluride, 00:27:42.380 --> 00:27:45.980 align:middle line:84% [INAUDIBLE] the best is about 0.6. 00:27:45.980 --> 00:27:50.630 align:middle line:84% And how you get the 1 is really by alloying. 00:27:50.630 --> 00:27:53.990 align:middle line:84% Alloying-- so you can further reduce thermal conductivity 00:27:53.990 --> 00:27:54.990 align:middle line:90% by alloying. 00:27:54.990 --> 00:27:58.220 align:middle line:84% So bismuth telluride is a compound semiconductor. 00:27:58.220 --> 00:28:02.300 align:middle line:84% And you look at the same column of the periodic table. 00:28:02.300 --> 00:28:05.930 align:middle line:84% When we are thinking alloys, same column, periodic table. 00:28:05.930 --> 00:28:10.580 align:middle line:84% And then you substitute, for example, bismuth by antimony. 00:28:10.580 --> 00:28:15.530 align:middle line:84% And that way, you could reduce thermal conductivity. 00:28:15.530 --> 00:28:20.300 align:middle line:84% And the best example of alloying reduced thermal connectivity 00:28:20.300 --> 00:28:23.450 align:middle line:90% is silicon-germanium. 00:28:23.450 --> 00:28:29.690 align:middle line:84% And silicon-germanium-- this is not a thermal conductivity unit. 00:28:29.690 --> 00:28:33.860 align:middle line:84% The inverse thermal conductivity unit. 00:28:33.860 --> 00:28:38.420 align:middle line:84% So here is the silicon [INAUDIBLE] conducting. 00:28:38.420 --> 00:28:40.400 align:middle line:84% The thermal conductivity of silicon 00:28:40.400 --> 00:28:45.890 align:middle line:84% is about 150 watt per meter per kelvin. 00:28:45.890 --> 00:28:49.330 align:middle line:84% And the germanium is also very conductive-- 00:28:49.330 --> 00:28:53.300 align:middle line:84% about 60 watt per meter per kelvin. 00:28:53.300 --> 00:28:54.840 align:middle line:90% Now, you mix a little bit. 00:28:54.840 --> 00:28:57.470 align:middle line:84% You can see this is not a linear curve, 00:28:57.470 --> 00:29:00.590 align:middle line:84% You mix a little bit of silicon with germanium. 00:29:00.590 --> 00:29:03.970 align:middle line:84% Your thermal conductivity drops sharply. 00:29:03.970 --> 00:29:07.030 align:middle line:84% And the lowest thermal conductivity here-- 00:29:07.030 --> 00:29:11.740 align:middle line:84% your [INAUDIBLE] is about 67 watt per meter kelvin. 00:29:11.740 --> 00:29:16.720 align:middle line:84% So you drop from 100 to about 67 by alloying. 00:29:16.720 --> 00:29:18.220 align:middle line:90% And this is because-- 00:29:18.220 --> 00:29:21.980 align:middle line:84% again, if you think about it, you have an [INAUDIBLE]. 00:29:21.980 --> 00:29:25.610 align:middle line:84% First thing you do-- you can try with pure atoms there. 00:29:25.610 --> 00:29:29.050 align:middle line:84% Secondly, you mess up the atom periodicity. 00:29:29.050 --> 00:29:31.750 align:middle line:90% The wave becomes frustrated. 00:29:31.750 --> 00:29:36.430 align:middle line:84% And so the thermal conductivity will drop. 00:29:36.430 --> 00:29:39.040 align:middle line:84% So this is one way of scattering. 00:29:39.040 --> 00:29:44.080 align:middle line:84% And that's-- all thermoelectric materials that are made 00:29:44.080 --> 00:29:45.370 align:middle line:90% of alloys. 00:29:45.370 --> 00:29:50.560 align:middle line:84% And the typical [INAUDIBLE] of the alloy 00:29:50.560 --> 00:29:54.220 align:middle line:84% is in terms of scattering-- the additional scattering. 00:29:54.220 --> 00:29:58.360 align:middle line:84% And you can see here, this is a Rayleigh scattering relation. 00:29:58.360 --> 00:30:00.460 align:middle line:90% What is Rayleigh scattering? 00:30:00.460 --> 00:30:02.680 align:middle line:90% You go outside on a sunny day. 00:30:02.680 --> 00:30:05.220 align:middle line:90% You see blue skies. 00:30:05.220 --> 00:30:09.390 align:middle line:84% And the blue sky is-- the blue light gets scattered. 00:30:09.390 --> 00:30:12.720 align:middle line:84% And high-frequency blue light compared to red-- 00:30:12.720 --> 00:30:14.340 align:middle line:90% solar radiation. 00:30:14.340 --> 00:30:16.440 align:middle line:90% The high-frequency scatter more. 00:30:16.440 --> 00:30:19.780 align:middle line:84% So here is the Rayleigh scatter regime. 00:30:19.780 --> 00:30:22.450 align:middle line:84% That's the Rayleigh scattering, high-frequency. 00:30:22.450 --> 00:30:24.420 align:middle line:84% And the sound wave is the typical-- 00:30:24.420 --> 00:30:26.910 align:middle line:90% that's a typical model. 00:30:26.910 --> 00:30:31.300 align:middle line:84% High-frequency is the inverse time to scatter time. 00:30:31.300 --> 00:30:33.180 align:middle line:90% Relaxation time is shorter. 00:30:33.180 --> 00:30:34.860 align:middle line:90% So that's a Rayleigh scatter. 00:30:34.860 --> 00:30:39.120 align:middle line:84% And then this depends on the mass contrast, 00:30:39.120 --> 00:30:42.780 align:middle line:84% and also it depends on lattice parameter, 00:30:42.780 --> 00:30:45.430 align:middle line:90% lattice constant contrast. 00:30:45.430 --> 00:30:47.750 align:middle line:84% Those series were done in the '50s. 00:30:47.750 --> 00:30:49.840 align:middle line:84% And in fact, I have a lot of suspicion 00:30:49.840 --> 00:30:52.330 align:middle line:84% whether they are truly valid or not. 00:30:52.330 --> 00:30:56.740 align:middle line:90% And I say that's what people do. 00:30:56.740 --> 00:31:00.560 align:middle line:90% This is just the current status. 00:31:00.560 --> 00:31:04.930 align:middle line:84% The problem is you go to think about thermal conductivity-- 00:31:04.930 --> 00:31:10.420 align:middle line:84% I showed k equals one third cv gamma integration. 00:31:10.420 --> 00:31:14.560 align:middle line:84% And integration is very forgiving in the sense-- 00:31:14.560 --> 00:31:16.540 align:middle line:84% if you make the error in one place, 00:31:16.540 --> 00:31:18.290 align:middle line:90% you make up the other place. 00:31:18.290 --> 00:31:21.490 align:middle line:84% And when you don't have exact theory there 00:31:21.490 --> 00:31:23.710 align:middle line:84% and you got a lot of [INAUDIBLE] parameter, 00:31:23.710 --> 00:31:28.450 align:middle line:84% and that integration can help you publish your papers. 00:31:28.450 --> 00:31:32.235 align:middle line:84% But the details, very often, are missing. 00:31:32.235 --> 00:31:34.840 align:middle line:90% 00:31:34.840 --> 00:31:37.090 align:middle line:90% Like I said, this is-- 00:31:37.090 --> 00:31:40.840 align:middle line:84% typically, that's how people make the material-- 00:31:40.840 --> 00:31:44.180 align:middle line:84% bismuth in [INAUDIBLE] bismuth, antimony. 00:31:44.180 --> 00:31:46.820 align:middle line:90% And this x is about 0.3-- 00:31:46.820 --> 00:31:48.530 align:middle line:90% 0.3 to 0.5. 00:31:48.530 --> 00:31:54.230 align:middle line:84% And then the impact material, bismuth, antimony, and selenium. 00:31:54.230 --> 00:31:59.450 align:middle line:84% And if any of you, actually, are in front of physics department, 00:31:59.450 --> 00:32:00.560 align:middle line:90% you probably went to-- 00:32:00.560 --> 00:32:03.200 align:middle line:84% I remember a few weeks ago there was a seminar 00:32:03.200 --> 00:32:04.700 align:middle line:90% on topological conductor. 00:32:04.700 --> 00:32:07.950 align:middle line:84% Turns out that this material is very hot in the physics-- 00:32:07.950 --> 00:32:10.700 align:middle line:84% people are looking at antimony, telluride 00:32:10.700 --> 00:32:13.730 align:middle line:90% and its topological conductor. 00:32:13.730 --> 00:32:15.800 align:middle line:90% So very hot topic there. 00:32:15.800 --> 00:32:19.130 align:middle line:84% But see, we don't know whether that has any implication 00:32:19.130 --> 00:32:21.470 align:middle line:90% of thermodynamics or not. 00:32:21.470 --> 00:32:26.420 align:middle line:84% And doping-- you can always add other materials as doping. 00:32:26.420 --> 00:32:30.350 align:middle line:84% But say, here, typically, is by defects-- 00:32:30.350 --> 00:32:32.150 align:middle line:90% the so-called anti-site. 00:32:32.150 --> 00:32:34.970 align:middle line:84% So if you look at it, it's possible 00:32:34.970 --> 00:32:37.040 align:middle line:84% that bismuth go to tellurium site. 00:32:37.040 --> 00:32:41.810 align:middle line:84% And this is a particularly-- because bismuth and tellurium, 00:32:41.810 --> 00:32:44.420 align:middle line:90% their so-called char-- 00:32:44.420 --> 00:32:48.530 align:middle line:84% electronegativity is very similar. 00:32:48.530 --> 00:32:55.800 align:middle line:84% So when they exchange positions, the disturbance 00:32:55.800 --> 00:32:57.200 align:middle line:90% will increase very small. 00:32:57.200 --> 00:32:59.450 align:middle line:84% But the number of charge is different, 00:32:59.450 --> 00:33:03.720 align:middle line:84% so that create either holes or electrons. 00:33:03.720 --> 00:33:07.530 align:middle line:90% 00:33:07.530 --> 00:33:09.220 align:middle line:84% So that's the traditional material. 00:33:09.220 --> 00:33:14.370 align:middle line:84% We're now moving to more current materials people are talking. 00:33:14.370 --> 00:33:18.720 align:middle line:90% This is a oxide-- 00:33:18.720 --> 00:33:21.730 align:middle line:90% sodium cobalt oxide. 00:33:21.730 --> 00:33:26.730 align:middle line:84% And these were originally started in Japan. 00:33:26.730 --> 00:33:30.100 align:middle line:84% Terasaki made a lot of contribution to this. 00:33:30.100 --> 00:33:34.545 align:middle line:84% And it turns out people are interested in oxide since 1980s. 00:33:34.545 --> 00:33:35.045 align:middle line:90% Why? 00:33:35.045 --> 00:33:38.600 align:middle line:90% 00:33:38.600 --> 00:33:41.030 align:middle line:84% That's because the high-temperature superconductor 00:33:41.030 --> 00:33:42.960 align:middle line:90% was discovered out of oxide. 00:33:42.960 --> 00:33:45.070 align:middle line:84% It's a surprising amount [INAUDIBLE] 00:33:45.070 --> 00:33:52.430 align:middle line:84% BCO, boron, C, copper, oxygen. And that got lower [INAUDIBLE] 00:33:52.430 --> 00:33:55.970 align:middle line:84% So the transitional temperature, now 00:33:55.970 --> 00:33:58.130 align:middle line:84% in this high-temperature superconductor, 00:33:58.130 --> 00:34:02.030 align:middle line:84% has reached probably around 130 kelvin or 140 kelvin 00:34:02.030 --> 00:34:03.500 align:middle line:90% [INAUDIBLE]. 00:34:03.500 --> 00:34:07.970 align:middle line:84% But the superconductor itself is not 00:34:07.970 --> 00:34:10.040 align:middle line:90% interesting for thermoelectrics. 00:34:10.040 --> 00:34:10.730 align:middle line:90% Why? 00:34:10.730 --> 00:34:14.330 align:middle line:84% This is because there's only one quantum state. 00:34:14.330 --> 00:34:16.770 align:middle line:90% So the entropy is 0. 00:34:16.770 --> 00:34:18.949 align:middle line:90% Log of quantum state. 00:34:18.949 --> 00:34:22.699 align:middle line:90% That's the Boltzmann relation. 00:34:22.699 --> 00:34:25.040 align:middle line:90% Entropy carried by as a-- 00:34:25.040 --> 00:34:27.679 align:middle line:90% is a log state. 00:34:27.679 --> 00:34:30.530 align:middle line:84% So superconductor is not interesting. 00:34:30.530 --> 00:34:33.020 align:middle line:84% But this one is not a superconductor, 00:34:33.020 --> 00:34:37.620 align:middle line:84% and people have achieved about [INAUDIBLE] one. 00:34:37.620 --> 00:34:40.770 align:middle line:84% I think this is around 800 degrees Celsius, 00:34:40.770 --> 00:34:43.330 align:middle line:84% so it's a high-temperature application. 00:34:43.330 --> 00:34:46.449 align:middle line:90% 00:34:46.449 --> 00:34:52.810 align:middle line:84% [INAUDIBLE] I mentioned this material because if you go 00:34:52.810 --> 00:34:53.620 align:middle line:90% to Japan-- 00:34:53.620 --> 00:34:58.660 align:middle line:84% I talk a lot to Japan thermoelectric guys, 00:34:58.660 --> 00:35:01.570 align:middle line:90% and also, from company. 00:35:01.570 --> 00:35:06.230 align:middle line:84% Whenever you work on-- you look at the bismuth telluride-- 00:35:06.230 --> 00:35:09.040 align:middle line:90% Japan is very sensitive to-- 00:35:09.040 --> 00:35:14.170 align:middle line:84% because they have limited amount of materials. 00:35:14.170 --> 00:35:17.860 align:middle line:84% It's a small country, and the resources are limited. 00:35:17.860 --> 00:35:20.320 align:middle line:84% So they don't want-- they always say, 00:35:20.320 --> 00:35:23.140 align:middle line:84% can you make, out of this abundant material-- what 00:35:23.140 --> 00:35:24.320 align:middle line:90% are the abundant materials? 00:35:24.320 --> 00:35:27.820 align:middle line:90% Silicon and aluminum. 00:35:27.820 --> 00:35:29.590 align:middle line:90% So those type of materials. 00:35:29.590 --> 00:35:32.800 align:middle line:84% And so this is the one example where 00:35:32.800 --> 00:35:38.080 align:middle line:84% the material is called abundant-- nickel, tin, 00:35:38.080 --> 00:35:39.910 align:middle line:90% and titanium. 00:35:39.910 --> 00:35:43.870 align:middle line:84% And it has reached a reasonable figure of merit. 00:35:43.870 --> 00:35:45.640 align:middle line:90% And this is where-- 00:35:45.640 --> 00:35:47.260 align:middle line:84% for example, you look at [INAUDIBLE] 00:35:47.260 --> 00:35:51.130 align:middle line:84% this figure [INAUDIBLE] thermal conductivity is still very high. 00:35:51.130 --> 00:35:52.580 align:middle line:90% Why it's still very high? 00:35:52.580 --> 00:35:53.840 align:middle line:90% Why is it very high? 00:35:53.840 --> 00:35:55.780 align:middle line:84% Because you always think of bismuth telluride. 00:35:55.780 --> 00:35:57.690 align:middle line:84% That's a good number to remember. 00:35:57.690 --> 00:36:01.530 align:middle line:84% Thermal conductivity is about 1 or 1.5. 00:36:01.530 --> 00:36:05.520 align:middle line:84% Seebeck is about 200 microwatts per kelvin and electrical 00:36:05.520 --> 00:36:06.550 align:middle line:90% [INAUDIBLE]. 00:36:06.550 --> 00:36:09.550 align:middle line:84% So if you look at this, the thermal conductivity 00:36:09.550 --> 00:36:11.170 align:middle line:90% is in the denominator. 00:36:11.170 --> 00:36:14.170 align:middle line:90% And you get this good zt-- 00:36:14.170 --> 00:36:16.660 align:middle line:84% that means the electron is really good. 00:36:16.660 --> 00:36:20.140 align:middle line:84% x square sigma-- that's the power vector-- 00:36:20.140 --> 00:36:22.150 align:middle line:90% it's pretty good. 00:36:22.150 --> 00:36:24.200 align:middle line:90% Do you [? kill ?] this guy? 00:36:24.200 --> 00:36:25.250 align:middle line:90% Do you [? kill ?] it? 00:36:25.250 --> 00:36:27.310 align:middle line:90% Thermal conductivity, reducing. 00:36:27.310 --> 00:36:30.820 align:middle line:84% Particularly, Can you reduce the phonon pump. 00:36:30.820 --> 00:36:33.520 align:middle line:84% You don't just want to reduce it-- because the electronics are 00:36:33.520 --> 00:36:36.730 align:middle line:84% also part of the thermal conductivity-- this is 00:36:36.730 --> 00:36:40.970 align:middle line:90% part of thermal conductivity. 00:36:40.970 --> 00:36:43.910 align:middle line:90% So people are now looking into-- 00:36:43.910 --> 00:36:47.840 align:middle line:84% if you look at the pump materials, 00:36:47.840 --> 00:36:50.690 align:middle line:84% it's typically a bismuth telluride-- 00:36:50.690 --> 00:36:52.850 align:middle line:84% then telluride silicon-germanium. 00:36:52.850 --> 00:36:57.020 align:middle line:84% Those are simple structures-- simple compounds-- two atoms, 00:36:57.020 --> 00:36:58.520 align:middle line:90% binary. 00:36:58.520 --> 00:37:01.730 align:middle line:84% And now, people are looking-- going more 00:37:01.730 --> 00:37:04.610 align:middle line:90% into more complex structures. 00:37:04.610 --> 00:37:07.910 align:middle line:90% And why complex structure? 00:37:07.910 --> 00:37:09.740 align:middle line:84% From thermal conductivity point of view, 00:37:09.740 --> 00:37:13.250 align:middle line:90% there is a good reason there. 00:37:13.250 --> 00:37:15.810 align:middle line:90% This is a few lecture back. 00:37:15.810 --> 00:37:20.210 align:middle line:84% I was talking about the modes, in terms of optical phonon, 00:37:20.210 --> 00:37:21.980 align:middle line:90% acoustic phonons. 00:37:21.980 --> 00:37:26.270 align:middle line:84% Optical phonon is very flat, and acoustic phonon is really 00:37:26.270 --> 00:37:28.220 align:middle line:90% the one that carries heat. 00:37:28.220 --> 00:37:32.520 align:middle line:84% So when you got a lot of atoms in the unit cell, 00:37:32.520 --> 00:37:35.430 align:middle line:84% you have a lot of upper branches. 00:37:35.430 --> 00:37:38.400 align:middle line:84% So those upper branches don't carry much heat. 00:37:38.400 --> 00:37:43.500 align:middle line:84% So that's-- the more complex the crystal, typically, 00:37:43.500 --> 00:37:47.010 align:middle line:84% the lower is their thermal conductivity. 00:37:47.010 --> 00:37:53.310 align:middle line:84% And that's the only very simple hand-waving way of saying it. 00:37:53.310 --> 00:37:56.490 align:middle line:84% And of course, you can see some of this material 00:37:56.490 --> 00:37:59.310 align:middle line:84% has really low thermal conductivity. 00:37:59.310 --> 00:38:02.190 align:middle line:90% Bismuth telluride is here. 00:38:02.190 --> 00:38:05.820 align:middle line:84% And it's a particularly [INAUDIBLE] now. 00:38:05.820 --> 00:38:10.080 align:middle line:84% This [INAUDIBLE], zinc, pyrithione. 00:38:10.080 --> 00:38:11.530 align:middle line:90% Zinc is abundant. 00:38:11.530 --> 00:38:13.530 align:middle line:90% If you can make zinc-- 00:38:13.530 --> 00:38:17.625 align:middle line:84% zinc is a good one if you can make it work. 00:38:17.625 --> 00:38:20.070 align:middle line:84% And it has a very low thermal conductivity. 00:38:20.070 --> 00:38:23.790 align:middle line:84% And in fact, I think the antimony thermoelectric figure 00:38:23.790 --> 00:38:25.680 align:middle line:90% of merit, now has reached-- 00:38:25.680 --> 00:38:28.290 align:middle line:90% I think it's about 1.4. 00:38:28.290 --> 00:38:31.500 align:middle line:84% Pretty good, except that there are also issues-- 00:38:31.500 --> 00:38:32.950 align:middle line:90% material stability. 00:38:32.950 --> 00:38:38.110 align:middle line:84% And when you heat up to high temperature, zinc speed up. 00:38:38.110 --> 00:38:43.570 align:middle line:84% I have some pictures showing that under temperature gradient, 00:38:43.570 --> 00:38:46.420 align:middle line:90% the material grew here. 00:38:46.420 --> 00:38:48.820 align:middle line:90% Here are zinc coming out. 00:38:48.820 --> 00:38:51.735 align:middle line:84% So you've got a lot of material reliability issues. 00:38:51.735 --> 00:38:55.000 align:middle line:90% 00:38:55.000 --> 00:38:57.880 align:middle line:84% But generally, there are a lot of people looking 00:38:57.880 --> 00:39:02.110 align:middle line:84% into a lot more complex structures, crystal structures, 00:39:02.110 --> 00:39:04.540 align:middle line:84% and the broader-- a much broader range 00:39:04.540 --> 00:39:07.000 align:middle line:90% of thermoelectric materials. 00:39:07.000 --> 00:39:12.580 align:middle line:84% I mentioned this already, but now let's look at the ideas. 00:39:12.580 --> 00:39:15.190 align:middle line:90% We said that complex structure-- 00:39:15.190 --> 00:39:18.490 align:middle line:84% and this is another idea that's really 00:39:18.490 --> 00:39:22.600 align:middle line:90% interesting because the alloy-- 00:39:22.600 --> 00:39:25.840 align:middle line:84% if you think about silicon-germanium alloy-- 00:39:25.840 --> 00:39:31.120 align:middle line:84% and it's really-- germanium go to silicon atomic site. 00:39:31.120 --> 00:39:35.680 align:middle line:84% So you can think of that as a substitution, So 00:39:35.680 --> 00:39:39.970 align:middle line:84% silicon-germanium substitute silicon atom. 00:39:39.970 --> 00:39:42.655 align:middle line:84% The lattice-- if you think of a cube. 00:39:42.655 --> 00:39:44.500 align:middle line:84% Like, let's take a crystal [INAUDIBLE]. 00:39:44.500 --> 00:39:45.640 align:middle line:90% Think about cube. 00:39:45.640 --> 00:39:49.840 align:middle line:84% And the silicon sits in the corner of the cube. 00:39:49.840 --> 00:39:51.790 align:middle line:84% And now you take out the one off the corner, 00:39:51.790 --> 00:39:53.260 align:middle line:90% and you put in germanium. 00:39:53.260 --> 00:39:58.900 align:middle line:84% And so this is the substitutional type of-- 00:39:58.900 --> 00:40:02.570 align:middle line:84% I pulled that-- you can think of the impurities. 00:40:02.570 --> 00:40:07.910 align:middle line:84% And skutterudite is a simple, interesting material. 00:40:07.910 --> 00:40:10.010 align:middle line:84% This is a skutterudite that is cobalt 00:40:10.010 --> 00:40:14.680 align:middle line:84% antimonide, or rubidium antimonide, iron antimonide, 00:40:14.680 --> 00:40:16.760 align:middle line:90% that type of structure. 00:40:16.760 --> 00:40:22.250 align:middle line:84% And what is interesting is that it has a very large unit cell. 00:40:22.250 --> 00:40:24.500 align:middle line:90% A lot of atoms there. 00:40:24.500 --> 00:40:31.415 align:middle line:84% And also, in those unit cells-- so here, we got two [INAUDIBLE]. 00:40:31.415 --> 00:40:39.110 align:middle line:84% And so you can see this-- each is a square, But in this eight-- 00:40:39.110 --> 00:40:39.620 align:middle line:90% How many? 00:40:39.620 --> 00:40:41.930 align:middle line:90% We have eight cubes. 00:40:41.930 --> 00:40:46.040 align:middle line:84% Six of the square has atoms inside. 00:40:46.040 --> 00:40:50.360 align:middle line:84% Two of them don't have anything inside. 00:40:50.360 --> 00:40:54.020 align:middle line:90% So there is an open space there. 00:40:54.020 --> 00:40:56.470 align:middle line:84% The open space gives you an opportunity-- 00:40:56.470 --> 00:40:59.850 align:middle line:90% let's put another atom there. 00:40:59.850 --> 00:41:02.840 align:middle line:84% [INAUDIBLE] Another atom-- this atom has a very different 00:41:02.840 --> 00:41:07.040 align:middle line:84% [INAUDIBLE] from the host atom, cobalt antimonide. 00:41:07.040 --> 00:41:10.910 align:middle line:84% So the idea is like a rattlesnake. 00:41:10.910 --> 00:41:12.290 align:middle line:90% You put the atom-- 00:41:12.290 --> 00:41:13.790 align:middle line:90% the rattler on. 00:41:13.790 --> 00:41:19.340 align:middle line:84% And this rattler will disturb the normally periodical lattice 00:41:19.340 --> 00:41:22.340 align:middle line:84% strips in the surrounding material surrounding 00:41:22.340 --> 00:41:24.410 align:middle line:90% the lattice itself. 00:41:24.410 --> 00:41:27.800 align:middle line:84% So that was called phonon rattlers. 00:41:27.800 --> 00:41:36.020 align:middle line:84% And the next one-- is an example of-- 00:41:36.020 --> 00:41:38.570 align:middle line:90% you can see cobalt antimonide. 00:41:38.570 --> 00:41:44.450 align:middle line:84% And you fill this with other regular lanthanum. 00:41:44.450 --> 00:41:46.220 align:middle line:84% And people tried many different ways. 00:41:46.220 --> 00:41:51.260 align:middle line:84% This is-- I was in a meeting last week. 00:41:51.260 --> 00:41:53.540 align:middle line:90% And people are still putting-- 00:41:53.540 --> 00:41:57.560 align:middle line:84% first with one rattler, one atom, one type of atom. 00:41:57.560 --> 00:42:00.570 align:middle line:84% Now, people have gone to three rattlers. 00:42:00.570 --> 00:42:04.950 align:middle line:84% Well, the hope is each rattler have its own rattling frequency, 00:42:04.950 --> 00:42:12.150 align:middle line:84% and you kill the whole acoustic frequency of the whole lattice 00:42:12.150 --> 00:42:13.200 align:middle line:90% waves. 00:42:13.200 --> 00:42:20.430 align:middle line:84% So this is clearly a very dramatic decrease in the lattice 00:42:20.430 --> 00:42:22.270 align:middle line:90% thermal conductivity. 00:42:22.270 --> 00:42:25.890 align:middle line:84% And people have done neutron scattering 00:42:25.890 --> 00:42:31.090 align:middle line:84% to actually look at the atomic displacement in this material. 00:42:31.090 --> 00:42:38.290 align:middle line:84% So you can see here, this is a lanthanum cobalt antimonide. 00:42:38.290 --> 00:42:42.430 align:middle line:90% So here, you have iron, cobalt-- 00:42:42.430 --> 00:42:45.880 align:middle line:84% that's their atomic displacement. 00:42:45.880 --> 00:42:48.072 align:middle line:84% So inside, it's doing Brownian motion. 00:42:48.072 --> 00:42:49.780 align:middle line:84% And this is measurement that can actually 00:42:49.780 --> 00:42:52.990 align:middle line:84% measure what's the amplitude of the-- so the [INAUDIBLE] square 00:42:52.990 --> 00:42:54.280 align:middle line:90% is here. 00:42:54.280 --> 00:42:56.740 align:middle line:84% And what's the amplitude of that motion? 00:42:56.740 --> 00:43:00.110 align:middle line:84% And the lanthanum-- they put it into the cage 00:43:00.110 --> 00:43:06.760 align:middle line:84% there since we have a very large amplitude here, you can see. 00:43:06.760 --> 00:43:14.860 align:middle line:84% And the theory is that this scatter deforms, Again, 00:43:14.860 --> 00:43:16.490 align:middle line:90% the theory is still evolving. 00:43:16.490 --> 00:43:19.570 align:middle line:84% And the explanation-- people came up 00:43:19.570 --> 00:43:21.310 align:middle line:90% with different explanations. 00:43:21.310 --> 00:43:27.820 align:middle line:84% But you try to do the modeling experiment to really make 00:43:27.820 --> 00:43:31.040 align:middle line:90% this material [INAUDIBLE]. 00:43:31.040 --> 00:43:39.490 align:middle line:84% Here, I forgot whether this is a-- 00:43:39.490 --> 00:43:44.680 align:middle line:84% what type, n-type, but I do want to tell you a story. 00:43:44.680 --> 00:43:50.425 align:middle line:84% Many years ago, people reported the p-type skutterudites, 00:43:50.425 --> 00:43:54.800 align:middle line:84% cobalt antimonide, figure of merit for 1.4. 00:43:54.800 --> 00:43:59.500 align:middle line:90% And now nobody can get 1.4. 00:43:59.500 --> 00:44:04.210 align:middle line:84% Everybody-- the best they can get is 0.95. 00:44:04.210 --> 00:44:07.930 align:middle line:84% And the reason-- this will bring up a very important point. 00:44:07.930 --> 00:44:11.470 align:middle line:84% Thermoelectric research-- measuring this property 00:44:11.470 --> 00:44:13.300 align:middle line:90% is tricky. 00:44:13.300 --> 00:44:15.520 align:middle line:84% And you have three properties to measure-- 00:44:15.520 --> 00:44:18.580 align:middle line:84% electric conductivity, thermal conductivity, Seebeck. 00:44:18.580 --> 00:44:22.390 align:middle line:84% And even if you are very good, each property-- 00:44:22.390 --> 00:44:26.140 align:middle line:84% you say, OK, I have about 5% uncertainty, which I think 00:44:26.140 --> 00:44:28.570 align:middle line:90% is pretty good. 00:44:28.570 --> 00:44:34.240 align:middle line:84% And you go to [INAUDIBLE] and that's about 15%. 00:44:34.240 --> 00:44:37.870 align:middle line:84% And it turns out that many times, your system 00:44:37.870 --> 00:44:39.640 align:middle line:90% can take the same sample. 00:44:39.640 --> 00:44:41.230 align:middle line:90% So you do thermal conductivity. 00:44:41.230 --> 00:44:42.280 align:middle line:90% You take a sample. 00:44:42.280 --> 00:44:45.310 align:middle line:84% You go to pick another sample for electric conductivity. 00:44:45.310 --> 00:44:51.000 align:middle line:84% And you measure the wrong things. 00:44:51.000 --> 00:44:55.320 align:middle line:84% And sometimes, if you look at the-- 00:44:55.320 --> 00:44:57.660 align:middle line:84% telluride-- it's a layered structure. 00:44:57.660 --> 00:44:59.750 align:middle line:90% The property is very isotropic. 00:44:59.750 --> 00:45:02.770 align:middle line:84% So this will be really dangerous. 00:45:02.770 --> 00:45:05.200 align:middle line:84% You measure-- even the same sample. 00:45:05.200 --> 00:45:08.620 align:middle line:84% You measure properties-- thermal conductivity in one direction. 00:45:08.620 --> 00:45:10.950 align:middle line:84% You measure electrical in the other direction. 00:45:10.950 --> 00:45:13.620 align:middle line:90% And you can just get a good zt. 00:45:13.620 --> 00:45:14.700 align:middle line:90% That's not true. 00:45:14.700 --> 00:45:17.400 align:middle line:84% So this is-- every time you go to a meeting, 00:45:17.400 --> 00:45:19.170 align:middle line:90% people will be debating. 00:45:19.170 --> 00:45:22.025 align:middle line:84% And most of the time, people are skeptical of any report. 00:45:22.025 --> 00:45:24.670 align:middle line:90% 00:45:24.670 --> 00:45:30.700 align:middle line:84% It's just difficult because measurements are difficult. 00:45:30.700 --> 00:45:34.930 align:middle line:90% Now I turn to my favorite-- 00:45:34.930 --> 00:45:36.040 align:middle line:90% nanostructure. 00:45:36.040 --> 00:45:37.720 align:middle line:84% And I said that there are bulk material. 00:45:37.720 --> 00:45:40.720 align:middle line:84% People look at the different material, different crystal 00:45:40.720 --> 00:45:45.730 align:middle line:84% structures, phonon rattler, all working 00:45:45.730 --> 00:45:48.130 align:middle line:90% on crystalline materials. 00:45:48.130 --> 00:45:53.320 align:middle line:84% And there was-- say-- this nanostructure approach 00:45:53.320 --> 00:45:59.570 align:middle line:84% was really Millie Dresselhaus in the EE department at the time. 00:45:59.570 --> 00:46:04.870 align:middle line:84% And the story-- this is a really good story. 00:46:04.870 --> 00:46:08.080 align:middle line:90% Around the 1990-- 00:46:08.080 --> 00:46:12.700 align:middle line:84% US navy start to rethink thermoelectrics. 00:46:12.700 --> 00:46:15.070 align:middle line:84% So they went around-- asked around 00:46:15.070 --> 00:46:17.740 align:middle line:84% and they came to Millie, whether she had 00:46:17.740 --> 00:46:19.930 align:middle line:90% any idea on thermoelectrics. 00:46:19.930 --> 00:46:23.440 align:middle line:84% Millie didn't work on thermoelectrics before. 00:46:23.440 --> 00:46:26.140 align:middle line:90% And she thought about it. 00:46:26.140 --> 00:46:27.760 align:middle line:84% And there was a physics student who 00:46:27.760 --> 00:46:31.580 align:middle line:84% walked into her office, wanted to ask her 00:46:31.580 --> 00:46:33.440 align:middle line:90% whether she had a topic. 00:46:33.440 --> 00:46:37.540 align:middle line:84% So she said, oh, why don't you look at quantum 00:46:37.540 --> 00:46:40.085 align:middle line:84% well-- whether it can give better 00:46:40.085 --> 00:46:42.470 align:middle line:90% thermoelectric properties? 00:46:42.470 --> 00:46:44.990 align:middle line:90% So the student looked, and-- 00:46:44.990 --> 00:46:46.890 align:middle line:90% it's really a homework problem. 00:46:46.890 --> 00:46:48.680 align:middle line:90% I'll show you later. 00:46:48.680 --> 00:46:52.100 align:middle line:84% But the calculation turns out to be really interesting, 00:46:52.100 --> 00:46:54.110 align:middle line:84% and a lot of people started working on that. 00:46:54.110 --> 00:46:59.480 align:middle line:84% So sometimes a simple idea really stimulate the research. 00:46:59.480 --> 00:47:04.220 align:middle line:84% And here, this is a slide that I tried to make 00:47:04.220 --> 00:47:08.450 align:middle line:84% and seeing the potential of using metal. 00:47:08.450 --> 00:47:12.770 align:middle line:84% So you think about the electron and phonon. 00:47:12.770 --> 00:47:15.720 align:middle line:84% Electron is what carries the heat around. 00:47:15.720 --> 00:47:18.600 align:middle line:84% And of course, the quantum mechanics, they always-- 00:47:18.600 --> 00:47:21.240 align:middle line:84% we mentioned this [INAUDIBLE] before, 00:47:21.240 --> 00:47:23.040 align:middle line:84% but they have different wavelengths. 00:47:23.040 --> 00:47:25.190 align:middle line:90% And it turns out it's a spread. 00:47:25.190 --> 00:47:27.960 align:middle line:84% In real material, it's always a spread. 00:47:27.960 --> 00:47:31.440 align:middle line:84% And we need to look into the details. 00:47:31.440 --> 00:47:34.170 align:middle line:84% But in general, actually, electron movements 00:47:34.170 --> 00:47:38.220 align:middle line:84% can be longer, average speaking, than the phonon-- 00:47:38.220 --> 00:47:40.020 align:middle line:90% heat-carrying phonons. 00:47:40.020 --> 00:47:48.160 align:middle line:84% And so that's an order of magnitude that I often use. 00:47:48.160 --> 00:47:51.030 align:middle line:84% But again, each material is different, 00:47:51.030 --> 00:47:53.400 align:middle line:90% and each country is different. 00:47:53.400 --> 00:47:56.780 align:middle line:84% And the other is the mean-free path. 00:47:56.780 --> 00:48:00.350 align:middle line:84% That's the average distance in electron-phonon [INAUDIBLE]. 00:48:00.350 --> 00:48:03.770 align:middle line:90% So we look at-- 00:48:03.770 --> 00:48:09.200 align:middle line:84% one possibility is to look at the wavelength difference 00:48:09.200 --> 00:48:12.350 align:middle line:84% because the wavelength difference means-- 00:48:12.350 --> 00:48:16.190 align:middle line:84% an intuitive picture is if you have a surface, whether it's 00:48:16.190 --> 00:48:19.070 align:middle line:90% a smooth or rough-- 00:48:19.070 --> 00:48:22.850 align:middle line:84% really depends on the feature, on the surface 00:48:22.850 --> 00:48:27.430 align:middle line:90% versus the feature of the wave. 00:48:27.430 --> 00:48:32.110 align:middle line:84% If you have a visible light coming towards a surface 00:48:32.110 --> 00:48:33.400 align:middle line:90% like this, it look rough. 00:48:33.400 --> 00:48:35.720 align:middle line:90% You scatter light all direction. 00:48:35.720 --> 00:48:38.090 align:middle line:84% But if you have, really, a microwave 00:48:38.090 --> 00:48:41.060 align:middle line:84% coming in, very long wavelengths, the surface 00:48:41.060 --> 00:48:42.720 align:middle line:90% will be smooth. 00:48:42.720 --> 00:48:49.400 align:middle line:84% Much-- wavelengths larger than the roughness features. 00:48:49.400 --> 00:48:52.550 align:middle line:90% So while this idea was-- 00:48:52.550 --> 00:48:56.810 align:middle line:84% if you recall, the thermal conductivity-- the curve-- 00:48:56.810 --> 00:49:00.140 align:middle line:84% at a very low temperature, the thermal conductivity 00:49:00.140 --> 00:49:04.490 align:middle line:84% increases with the specific heat because the mean-free path 00:49:04.490 --> 00:49:06.230 align:middle line:90% equals the sample size. 00:49:06.230 --> 00:49:07.940 align:middle line:90% It's limited by sample size. 00:49:07.940 --> 00:49:13.130 align:middle line:84% So low temperature already have the size effect. 00:49:13.130 --> 00:49:17.420 align:middle line:84% And if I make the structure very small, that size effect-- 00:49:17.420 --> 00:49:19.370 align:middle line:84% I can shift to the high temperature, 00:49:19.370 --> 00:49:22.700 align:middle line:84% as long as it's small enough so that the-- 00:49:22.700 --> 00:49:26.140 align:middle line:90% let's take a wire or film-- 00:49:26.140 --> 00:49:29.080 align:middle line:84% if the diameter or thickness is comparable 00:49:29.080 --> 00:49:32.140 align:middle line:84% to the mean-free path, now, the phonon 00:49:32.140 --> 00:49:34.720 align:middle line:84% will no longer-- is a phonon-phonon collision. 00:49:34.720 --> 00:49:37.200 align:middle line:84% They will collide with the surface. 00:49:37.200 --> 00:49:42.320 align:middle line:84% And another simple intuitive picture is-- 00:49:42.320 --> 00:49:46.280 align:middle line:84% OK, what happens at the interface of the material? 00:49:46.280 --> 00:49:50.150 align:middle line:84% You have the lattice wave coming in and at the interface, 00:49:50.150 --> 00:49:52.990 align:middle line:90% you hear echoes. 00:49:52.990 --> 00:49:55.760 align:middle line:84% Well, we hear echoes for the visible-- 00:49:55.760 --> 00:49:56.750 align:middle line:90% audible range. 00:49:56.750 --> 00:50:02.160 align:middle line:84% But say-- and the peak current is [INAUDIBLE]. 00:50:02.160 --> 00:50:03.720 align:middle line:90% So those are high frequency. 00:50:03.720 --> 00:50:06.020 align:middle line:84% You still got the same phenomena happening. 00:50:06.020 --> 00:50:08.690 align:middle line:84% And the echo means some [INAUDIBLE] 00:50:08.690 --> 00:50:10.260 align:middle line:90% don't go forward anymore. 00:50:10.260 --> 00:50:13.280 align:middle line:84% So you could use those phenomena to [INAUDIBLE] 00:50:13.280 --> 00:50:15.770 align:middle line:90% the thermal conductivity. 00:50:15.770 --> 00:50:23.720 align:middle line:84% And Millie's idea at the time was squeeze electrons. 00:50:23.720 --> 00:50:26.180 align:middle line:84% So quantum effect-- which I'll talk more. 00:50:26.180 --> 00:50:29.630 align:middle line:84% But-- now, think about the quantum effect. 00:50:29.630 --> 00:50:31.610 align:middle line:90% Electron is a wave. 00:50:31.610 --> 00:50:33.770 align:middle line:90% Wave function is a function. 00:50:33.770 --> 00:50:38.000 align:middle line:84% The s orbital-- wave function is a ball. 00:50:38.000 --> 00:50:44.340 align:middle line:84% And let's say this is the size of the ball. 00:50:44.340 --> 00:50:47.634 align:middle line:90% Let's say [INAUDIBLE] angstrom. 00:50:47.634 --> 00:50:49.570 align:middle line:90% Now, you see this-- 00:50:49.570 --> 00:50:50.580 align:middle line:90% this is electron. 00:50:50.580 --> 00:50:54.890 align:middle line:84% You make a film only 10 angstrom or 50 angstrom. 00:50:54.890 --> 00:50:56.520 align:middle line:90% What happens? 00:50:56.520 --> 00:51:00.450 align:middle line:90% The ball is no longer a ball. 00:51:00.450 --> 00:51:03.180 align:middle line:84% I once-- when I was a student with [INAUDIBLE] 00:51:03.180 --> 00:51:07.000 align:middle line:84% there was an interesting analogy made by Professor [INAUDIBLE]. 00:51:07.000 --> 00:51:08.690 align:middle line:90% But think of this. 00:51:08.690 --> 00:51:12.740 align:middle line:84% You put a basketball into a piece of box. 00:51:12.740 --> 00:51:14.300 align:middle line:90% You squeeze the ball. 00:51:14.300 --> 00:51:17.480 align:middle line:90% You have energy quantization. 00:51:17.480 --> 00:51:22.180 align:middle line:84% So you have this wave, and then when your size is small, 00:51:22.180 --> 00:51:23.930 align:middle line:90% you quantize the wave. 00:51:23.930 --> 00:51:29.510 align:middle line:84% And ideally, what you want is this wave is-- 00:51:29.510 --> 00:51:33.080 align:middle line:84% under ideal quantization, you want this smooth surface, 00:51:33.080 --> 00:51:37.930 align:middle line:84% You don't want the interface-scattered electrons. 00:51:37.930 --> 00:51:42.370 align:middle line:84% And this is possible, again, using the wavelength range 00:51:42.370 --> 00:51:46.400 align:middle line:84% because whether the surface is smooth or rough 00:51:46.400 --> 00:51:47.650 align:middle line:90% depends on wavelength. 00:51:47.650 --> 00:51:52.300 align:middle line:84% For the case of electrons, the scatter is electrical potential. 00:51:52.300 --> 00:51:55.150 align:middle line:84% Your potential-- whether it's rough or not. 00:51:55.150 --> 00:51:58.510 align:middle line:84% And for the case of phonon lattice wave, 00:51:58.510 --> 00:52:01.510 align:middle line:84% fundamental or electrostatic-- but it's really-- 00:52:01.510 --> 00:52:06.070 align:middle line:84% you can think of mass spring, whether those-- 00:52:06.070 --> 00:52:09.920 align:middle line:90% the force is [INAUDIBLE] now. 00:52:09.920 --> 00:52:12.970 align:middle line:84% And so you actually have the potential-- 00:52:12.970 --> 00:52:16.010 align:middle line:84% if you think about the phonon and the electron-- 00:52:16.010 --> 00:52:21.010 align:middle line:84% your electron-- if you quantize it-- is the smooth. 00:52:21.010 --> 00:52:22.780 align:middle line:84% And because the wavelength difference-- 00:52:22.780 --> 00:52:24.280 align:middle line:84% you can potentially actually have 00:52:24.280 --> 00:52:28.660 align:middle line:84% the same surface will be rough for phonon, the acoustic wave. 00:52:28.660 --> 00:52:31.240 align:middle line:90% So this will be ideal. 00:52:31.240 --> 00:52:35.680 align:middle line:84% [INAUDIBLE] You want to screw up the atomic vibration, 00:52:35.680 --> 00:52:40.420 align:middle line:84% but electron can go as a waveguide. 00:52:40.420 --> 00:52:43.870 align:middle line:90% That will be one scenario. 00:52:43.870 --> 00:52:47.140 align:middle line:90% And the people started a lot-- 00:52:47.140 --> 00:52:49.690 align:middle line:90% 00:52:49.690 --> 00:52:53.170 align:middle line:84% and in fact, I should say at the same time, 00:52:53.170 --> 00:52:57.100 align:middle line:84% maybe go to other places, and people have a similar idea, 00:52:57.100 --> 00:53:02.050 align:middle line:84% although Millie did really a good calculation. 00:53:02.050 --> 00:53:10.420 align:middle line:84% This superlattice idea was from Rama, [INAUDIBLE]. 00:53:10.420 --> 00:53:12.550 align:middle line:90% And what he did is-- 00:53:12.550 --> 00:53:16.070 align:middle line:84% the perpendicular direction, the superlattice. 00:53:16.070 --> 00:53:18.950 align:middle line:90% And this is-- you can see-- 00:53:18.950 --> 00:53:26.420 align:middle line:84% the experiment-- thermal conductivity and the drop. 00:53:26.420 --> 00:53:32.000 align:middle line:84% So the bismuth skutterudite [INAUDIBLE] about 1.2, 00:53:32.000 --> 00:53:34.160 align:middle line:90% and they drop to 0.5. 00:53:34.160 --> 00:53:35.430 align:middle line:90% Very difficult measurement. 00:53:35.430 --> 00:53:38.200 align:middle line:84% And this is where I start getting into thermoelectrics. 00:53:38.200 --> 00:53:43.070 align:middle line:84% So my thesis-- my PhD, I was looking at the superlattice heat 00:53:43.070 --> 00:53:43.650 align:middle line:90% conduction. 00:53:43.650 --> 00:53:46.100 align:middle line:84% I was worried about lasers, not thermoelectric. 00:53:46.100 --> 00:53:48.730 align:middle line:84% I didn't know anything about thermoelectric. 00:53:48.730 --> 00:53:53.760 align:middle line:84% And the electron here decreased a little bit. 00:53:53.760 --> 00:53:55.910 align:middle line:90% This is s square sigma. 00:53:55.910 --> 00:53:59.390 align:middle line:84% The power factor, s square sigma, decreasing a little bit. 00:53:59.390 --> 00:54:04.190 align:middle line:84% And in the case of-- this is a [INAUDIBLE] map. 00:54:04.190 --> 00:54:08.720 align:middle line:90% He grew the telluride-- 00:54:08.720 --> 00:54:10.230 align:middle line:84% the [INAUDIBLE] on that telluride. 00:54:10.230 --> 00:54:14.120 align:middle line:84% And because the lattice constant is very different, 00:54:14.120 --> 00:54:16.920 align:middle line:84% the [? strain-- ?] so you grow certain thickness, 00:54:16.920 --> 00:54:20.250 align:middle line:84% the strain will break up the film and form dots. 00:54:20.250 --> 00:54:23.460 align:middle line:84% So he grew these multilayer structures. 00:54:23.460 --> 00:54:25.810 align:middle line:90% And this picture-- 00:54:25.810 --> 00:54:27.310 align:middle line:90% I don't think it is from him. 00:54:27.310 --> 00:54:28.270 align:middle line:90% I don't remember. 00:54:28.270 --> 00:54:33.810 align:middle line:84% But what he showed was, again, no thermal conductivity. 00:54:33.810 --> 00:54:35.400 align:middle line:84% And the power factor [INAUDIBLE]. 00:54:35.400 --> 00:54:40.140 align:middle line:84% So at the end, it turns out that, historically, 00:54:40.140 --> 00:54:42.720 align:middle line:90% the thermal conductivity alloy-- 00:54:42.720 --> 00:54:44.670 align:middle line:90% institutional. 00:54:44.670 --> 00:54:47.760 align:middle line:84% And now with this nanostructure, it 00:54:47.760 --> 00:54:49.620 align:middle line:84% turns out that the thermal conductivity 00:54:49.620 --> 00:54:53.780 align:middle line:84% seems to be a very effective strategy. 00:54:53.780 --> 00:54:57.710 align:middle line:90% But let me, again, caution-- 00:54:57.710 --> 00:55:02.880 align:middle line:84% almost now everybody questioned those results. 00:55:02.880 --> 00:55:06.030 align:middle line:84% It's a very interesting result-- very intriguing, 00:55:06.030 --> 00:55:09.120 align:middle line:84% but it's a very hard measurement. 00:55:09.120 --> 00:55:15.090 align:middle line:90% And [INAUDIBLE] retired. 00:55:15.090 --> 00:55:17.440 align:middle line:90% He's a very respected. 00:55:17.440 --> 00:55:19.770 align:middle line:90% And I talked to him a lot. 00:55:19.770 --> 00:55:21.630 align:middle line:90% [INAUDIBLE] He has a book. 00:55:21.630 --> 00:55:23.940 align:middle line:84% If you want to understand thermoelectric, 00:55:23.940 --> 00:55:25.450 align:middle line:90% he has a very good book. 00:55:25.450 --> 00:55:27.880 align:middle line:84% Not many people read because it's too difficult. 00:55:27.880 --> 00:55:29.070 align:middle line:90% [LAUGHTER] 00:55:29.070 --> 00:55:31.500 align:middle line:90% But very good if you read. 00:55:31.500 --> 00:55:33.060 align:middle line:90% And the first-- 00:55:33.060 --> 00:55:34.950 align:middle line:84% I remember the first two pages was talking 00:55:34.950 --> 00:55:36.558 align:middle line:90% about electrostatic computer. 00:55:36.558 --> 00:55:38.100 align:middle line:84% As a mechanical engineer, [INAUDIBLE] 00:55:38.100 --> 00:55:42.480 align:middle line:84% always been hard to understand, what's the electrical potential, 00:55:42.480 --> 00:55:45.120 align:middle line:90% what's the chemical potential? 00:55:45.120 --> 00:55:51.120 align:middle line:84% And Raman [INAUDIBLE] is from RTI. 00:55:51.120 --> 00:55:54.690 align:middle line:84% They have spin-off company trying 00:55:54.690 --> 00:55:58.387 align:middle line:84% to do the superlattices for microelectronics [INAUDIBLE]. 00:55:58.387 --> 00:56:00.720 align:middle line:84% And if you're interested, you can check the [INAUDIBLE]. 00:56:00.720 --> 00:56:03.450 align:middle line:84% They have [INAUDIBLE] start-ups [INAUDIBLE]. 00:56:03.450 --> 00:56:10.110 align:middle line:90% And the superlattice-- 00:56:10.110 --> 00:56:14.520 align:middle line:84% I guess the challenge is grew very thick, 00:56:14.520 --> 00:56:18.140 align:middle line:90% and also reduced the cost. 00:56:18.140 --> 00:56:20.990 align:middle line:90% So this is where my story is. 00:56:20.990 --> 00:56:25.130 align:middle line:84% I said I would be working on this for a long time. 00:56:25.130 --> 00:56:28.970 align:middle line:84% Since my [INAUDIBLE] was really useful leaders. 00:56:28.970 --> 00:56:34.790 align:middle line:90% And so those are experiments. 00:56:34.790 --> 00:56:37.410 align:middle line:84% In the along-the-field direction, 00:56:37.410 --> 00:56:38.790 align:middle line:90% you can see it's isotropic. 00:56:38.790 --> 00:56:41.000 align:middle line:90% This is the [INAUDIBLE]. 00:56:41.000 --> 00:56:44.300 align:middle line:84% But see-- the superlattice structure [INAUDIBLE]. 00:56:44.300 --> 00:56:46.730 align:middle line:84% So this is perpendicular to the [INAUDIBLE] plane 00:56:46.730 --> 00:56:49.400 align:middle line:84% direction-- parallel to the [INAUDIBLE] plane direction. 00:56:49.400 --> 00:56:54.800 align:middle line:84% And the problem is, if you think about this superlattice, 00:56:54.800 --> 00:56:58.970 align:middle line:84% basically, superlattice was invented 00:56:58.970 --> 00:57:02.240 align:middle line:90% by [INAUDIBLE] and Esaki. 00:57:02.240 --> 00:57:09.050 align:middle line:84% Esaki got the Nobel Prize for his work in resonant diode. 00:57:09.050 --> 00:57:12.440 align:middle line:84% That's before, even, the superlattice concept. 00:57:12.440 --> 00:57:18.540 align:middle line:84% And the name of superlattice means you have a super crystal. 00:57:18.540 --> 00:57:19.950 align:middle line:90% And so you see-- 00:57:19.950 --> 00:57:21.140 align:middle line:90% I say this is one layer. 00:57:21.140 --> 00:57:22.230 align:middle line:90% There's another layer. 00:57:22.230 --> 00:57:24.210 align:middle line:84% Now, you look at-- a unit cell is 00:57:24.210 --> 00:57:28.030 align:middle line:84% no longer cube, but the tetrahedral that 00:57:28.030 --> 00:57:30.240 align:middle line:90% cover from here to here. 00:57:30.240 --> 00:57:33.290 align:middle line:90% One period of a crystal. 00:57:33.290 --> 00:57:37.530 align:middle line:90% So that's what the name implies. 00:57:37.530 --> 00:57:40.360 align:middle line:84% According to the name, this is a new crystal. 00:57:40.360 --> 00:57:43.980 align:middle line:84% You can calculate a new energy phonon spectrum. 00:57:43.980 --> 00:57:45.690 align:middle line:90% You calculate group velocity. 00:57:45.690 --> 00:57:47.010 align:middle line:90% You have [INAUDIBLE] states. 00:57:47.010 --> 00:57:49.020 align:middle line:90% You do all this calculation. 00:57:49.020 --> 00:57:51.420 align:middle line:84% And then you do one third of cv gamma. 00:57:51.420 --> 00:57:52.470 align:middle line:90% I don't know gamma. 00:57:52.470 --> 00:57:55.180 align:middle line:84% But I know I can-- from that calculation. 00:57:55.180 --> 00:58:00.500 align:middle line:84% I know c, and I know v, from this state. 00:58:00.500 --> 00:58:02.340 align:middle line:90% [INAUDIBLE] That's the curve. 00:58:02.340 --> 00:58:04.380 align:middle line:84% You get as a function of thickness. 00:58:04.380 --> 00:58:06.900 align:middle line:90% Just-- it's not correct. 00:58:06.900 --> 00:58:11.730 align:middle line:84% So basically, the picture is not about forming 00:58:11.730 --> 00:58:13.380 align:middle line:90% a coherent structure. 00:58:13.380 --> 00:58:17.350 align:middle line:84% People are still debating, so I don't want to prejudice you. 00:58:17.350 --> 00:58:19.130 align:middle line:90% You should read literature. 00:58:19.130 --> 00:58:22.090 align:middle line:84% And that's my own prejudice because I've 00:58:22.090 --> 00:58:23.590 align:middle line:90% been doing research on that. 00:58:23.590 --> 00:58:25.030 align:middle line:84% But when you get into it and say, 00:58:25.030 --> 00:58:27.970 align:middle line:84% oh, [INAUDIBLE] look into the literature. 00:58:27.970 --> 00:58:29.815 align:middle line:84% Look at the different sides of the argument. 00:58:29.815 --> 00:58:32.410 align:middle line:90% 00:58:32.410 --> 00:58:36.970 align:middle line:84% And so when I go to look into the other picture, 00:58:36.970 --> 00:58:40.130 align:middle line:84% I just say, OK, now I got a surface. 00:58:40.130 --> 00:58:44.570 align:middle line:84% I only just consider not this supercell-- 00:58:44.570 --> 00:58:45.920 align:middle line:90% just two layers. 00:58:45.920 --> 00:58:47.750 align:middle line:84% And of course, periodic structure. 00:58:47.750 --> 00:58:49.220 align:middle line:90% We consider all that. 00:58:49.220 --> 00:58:52.400 align:middle line:84% And then we got an interface roughness. 00:58:52.400 --> 00:58:56.240 align:middle line:84% And that roughness scatter phonon diffusely. 00:58:56.240 --> 00:59:00.030 align:middle line:84% And that can cause the thermal conductivity reduction. 00:59:00.030 --> 00:59:02.410 align:middle line:84% And here, I got a fudging parameter. 00:59:02.410 --> 00:59:02.910 align:middle line:90% Yes. 00:59:02.910 --> 00:59:03.750 align:middle line:84% AUDIENCE: When you say, roughness, 00:59:03.750 --> 00:59:06.030 align:middle line:84% are you talking about just like obstacle spacing, 00:59:06.030 --> 00:59:08.610 align:middle line:84% like an electron diffraction or [INAUDIBLE] diffraction 00:59:08.610 --> 00:59:10.680 align:middle line:84% experiment, or you expect something 00:59:10.680 --> 00:59:13.210 align:middle line:84% to be scattered by something with spacing 00:59:13.210 --> 00:59:14.168 align:middle line:90% [INAUDIBLE] wavelength? 00:59:14.168 --> 00:59:14.877 align:middle line:90% GANG CHEN: Right. 00:59:14.877 --> 00:59:16.420 align:middle line:84% And so that's a very good question. 00:59:16.420 --> 00:59:20.040 align:middle line:84% And what's the mechanism of that roughness? 00:59:20.040 --> 00:59:25.080 align:middle line:84% And it turns out that when you grew superlattice, 00:59:25.080 --> 00:59:28.230 align:middle line:84% molecular beam epitaxy, and then you find out that 00:59:28.230 --> 00:59:29.137 align:middle line:90% they're in the 80s. 00:59:29.137 --> 00:59:29.970 align:middle line:90% There are a lot of-- 00:59:29.970 --> 00:59:32.610 align:middle line:84% gallium arsenide is the best studied system. 00:59:32.610 --> 00:59:35.730 align:middle line:84% And there are diffusion of atoms between the layers, 00:59:35.730 --> 00:59:39.450 align:middle line:84% about the one to three monoatomic layer. 00:59:39.450 --> 00:59:42.600 align:middle line:84% And they said the phonon weakness is very short. 00:59:42.600 --> 00:59:46.380 align:middle line:84% So my picture is really the atom-- 00:59:46.380 --> 00:59:50.010 align:middle line:84% if it's a perfect periodic, you see the atomic spacing 00:59:50.010 --> 00:59:52.410 align:middle line:90% is all periodic, the same atom. 00:59:52.410 --> 00:59:53.920 align:middle line:90% Then you should not have that. 00:59:53.920 --> 00:59:57.270 align:middle line:84% But now if you just have one atom [INAUDIBLE] and the random 00:59:57.270 --> 00:59:59.910 align:middle line:84% distance, later, another atom [INAUDIBLE], 00:59:59.910 --> 01:00:01.850 align:middle line:90% and that's the surface-- 01:00:01.850 --> 01:00:04.630 align:middle line:90% whether is rough or smooth-- 01:00:04.630 --> 01:00:07.810 align:middle line:90% is about 1/10 of the wavelength. 01:00:07.810 --> 01:00:09.840 align:middle line:90% So if you go to optics-- 01:00:09.840 --> 01:00:12.910 align:middle line:84% so here, again, we don't know exactly. 01:00:12.910 --> 01:00:14.080 align:middle line:90% So you go to optics. 01:00:14.080 --> 01:00:17.790 align:middle line:84% When people say whether surface is smooth or not-- 01:00:17.790 --> 01:00:20.220 align:middle line:90% it's about a 1/10 weakness. 01:00:20.220 --> 01:00:24.840 align:middle line:84% 1/10-- you look at the phase of the wave. 01:00:24.840 --> 01:00:28.350 align:middle line:84% So here-- because the wavelengths are falling, 01:00:28.350 --> 01:00:31.050 align:middle line:84% is about 1 nanometer to 10 nanometer range. 01:00:31.050 --> 01:00:35.400 align:middle line:84% So a little bit of atomic diffusion can cause that. 01:00:35.400 --> 01:00:38.440 align:middle line:84% But there are a lot of puzzles at this stage. 01:00:38.440 --> 01:00:42.570 align:middle line:84% You should read [INAUDIBLE] paper from UIUC, 01:00:42.570 --> 01:00:48.300 align:middle line:84% and they have done constant diselenide and some newer 01:00:48.300 --> 01:00:49.320 align:middle line:90% material system. 01:00:49.320 --> 01:00:50.880 align:middle line:84% And they found that they can have 01:00:50.880 --> 01:00:54.270 align:middle line:84% thermal conductivity really, really [INAUDIBLE]. 01:00:54.270 --> 01:00:59.220 align:middle line:84% The noise they have is twice [INAUDIBLE], solid, fully solid. 01:00:59.220 --> 01:01:05.920 align:middle line:84% Anyway-- so I say this is the picture I have, 01:01:05.920 --> 01:01:09.670 align:middle line:84% but I think there are probably more things that 01:01:09.670 --> 01:01:11.870 align:middle line:90% need to be done. 01:01:11.870 --> 01:01:15.770 align:middle line:84% So what I see from this picture-- what I conclude is, 01:01:15.770 --> 01:01:17.570 align:middle line:84% OK, we do need a periodic structure 01:01:17.570 --> 01:01:20.780 align:middle line:84% because if it's not a unit cell type of picture, 01:01:20.780 --> 01:01:22.700 align:middle line:90% then I don't need a periodicity. 01:01:22.700 --> 01:01:26.660 align:middle line:84% So that's why I need us to do this random composite 01:01:26.660 --> 01:01:30.050 align:middle line:84% structures, because that way, I can do [INAUDIBLE] lower cost. 01:01:30.050 --> 01:01:33.870 align:middle line:90% 01:01:33.870 --> 01:01:37.620 align:middle line:84% So we try this, and it works in some materials. 01:01:37.620 --> 01:01:43.590 align:middle line:90% This is [INAUDIBLE] telluride. 01:01:43.590 --> 01:01:45.960 align:middle line:84% This is about [INAUDIBLE] telluride. 01:01:45.960 --> 01:01:48.450 align:middle line:84% And this is-- this is skutterudite. 01:01:48.450 --> 01:01:52.260 align:middle line:84% This is skutterudite [INAUDIBLE] and nano. 01:01:52.260 --> 01:01:58.170 align:middle line:84% And [INAUDIBLE] I say what we do is just a [INAUDIBLE] material, 01:01:58.170 --> 01:02:01.410 align:middle line:84% and we contact them in nano form. 01:02:01.410 --> 01:02:05.430 align:middle line:84% Bismuth skutterudite works on [INAUDIBLE] geometric also. 01:02:05.430 --> 01:02:07.830 align:middle line:84% Didn't quite work on that telluride. 01:02:07.830 --> 01:02:09.840 align:middle line:90% That telluride grid growth. 01:02:09.840 --> 01:02:15.840 align:middle line:84% And skutterudite didn't work out either because of grid growth. 01:02:15.840 --> 01:02:19.470 align:middle line:84% So we're still trying to figure out how we can prevent-- 01:02:19.470 --> 01:02:22.470 align:middle line:84% stop that growth of the grid, and we 01:02:22.470 --> 01:02:24.640 align:middle line:90% drop the thermal connectivity. 01:02:24.640 --> 01:02:25.810 align:middle line:90% Yes. 01:02:25.810 --> 01:02:27.995 align:middle line:84% AUDIENCE: What about the quasicrystals? 01:02:27.995 --> 01:02:32.170 align:middle line:90% Is that [INAUDIBLE] 01:02:32.170 --> 01:02:35.540 align:middle line:84% GANG CHEN: That's a very good suggestion. 01:02:35.540 --> 01:02:38.330 align:middle line:84% And I didn't look at quasicrystals. 01:02:38.330 --> 01:02:42.550 align:middle line:84% But there are people looking for [INAUDIBLE]. 01:02:42.550 --> 01:02:45.260 align:middle line:84% Clustering is a very complicated-- 01:02:45.260 --> 01:02:48.430 align:middle line:84% like, you can have silicon [INAUDIBLE] 01:02:48.430 --> 01:02:50.200 align:middle line:90% germanium [INAUDIBLE]. 01:02:50.200 --> 01:02:53.680 align:middle line:90% So it's a-- it has a-- 01:02:53.680 --> 01:02:59.630 align:middle line:84% say, it has holes inside, and they have a little similar 01:02:59.630 --> 01:03:01.570 align:middle line:90% [INAUDIBLE]. 01:03:01.570 --> 01:03:03.410 align:middle line:90% But further crystal decay-- 01:03:03.410 --> 01:03:06.850 align:middle line:84% [INAUDIBLE] decay is whether you can make the electrons 01:03:06.850 --> 01:03:08.200 align:middle line:90% in your [INAUDIBLE]. 01:03:08.200 --> 01:03:10.690 align:middle line:84% Remember, you can kill a phonon if you just want 01:03:10.690 --> 01:03:12.700 align:middle line:90% to kill a phonon [INAUDIBLE]. 01:03:12.700 --> 01:03:15.340 align:middle line:84% But you also want to keep the electron moving. 01:03:15.340 --> 01:03:19.510 align:middle line:84% So the idea-- very good terminology 01:03:19.510 --> 01:03:21.640 align:middle line:90% came from Glen Slack. 01:03:21.640 --> 01:03:26.110 align:middle line:84% And he said, what you want is an electron crystal phonon 01:03:26.110 --> 01:03:31.330 align:middle line:84% glass in one material because the phonon in glass-- 01:03:31.330 --> 01:03:35.560 align:middle line:84% this glass here-- amorphous random atomic arrangement. 01:03:35.560 --> 01:03:39.370 align:middle line:84% So the phonon thermal conductivity is very poor. 01:03:39.370 --> 01:03:44.650 align:middle line:84% But this superlattice is different. 01:03:44.650 --> 01:03:47.070 align:middle line:90% It's still crystal. 01:03:47.070 --> 01:03:50.580 align:middle line:84% So you are-- where we can-- for example, 01:03:50.580 --> 01:03:53.520 align:middle line:84% we're looking into whether a randomized wave-- 01:03:53.520 --> 01:03:57.330 align:middle line:84% localized [INAUDIBLE] and localized wave. 01:03:57.330 --> 01:03:59.430 align:middle line:84% Very difficult, I think, but it's worth 01:03:59.430 --> 01:04:06.360 align:middle line:84% trying because you need this crystal structure to get 01:04:06.360 --> 01:04:09.000 align:middle line:90% the electron propagating. 01:04:09.000 --> 01:04:12.480 align:middle line:84% Very difficult because the short wavelengths. 01:04:12.480 --> 01:04:16.710 align:middle line:84% You can do photonic crystal, all that, for electromagnetic wave 01:04:16.710 --> 01:04:19.720 align:middle line:84% because the wavelength is pretty long. 01:04:19.720 --> 01:04:23.020 align:middle line:84% But it's very hard to do this for phonon 01:04:23.020 --> 01:04:25.360 align:middle line:84% because wavelengths are short, and they 01:04:25.360 --> 01:04:27.340 align:middle line:90% don't propagate very long. 01:04:27.340 --> 01:04:33.280 align:middle line:84% You need a long coherence to have the waves [? disrupt ?] 01:04:33.280 --> 01:04:34.100 align:middle line:90% each other. 01:04:34.100 --> 01:04:35.990 align:middle line:90% So those are the difficulties. 01:04:35.990 --> 01:04:38.830 align:middle line:90% 01:04:38.830 --> 01:04:41.530 align:middle line:84% So here are more detailed example. 01:04:41.530 --> 01:04:43.550 align:middle line:84% You can see the thermal conductivity dropped. 01:04:43.550 --> 01:04:47.830 align:middle line:84% So when I started this, everybody was saying, 01:04:47.830 --> 01:04:50.320 align:middle line:84% electron-- what are you going to do with the electron? 01:04:50.320 --> 01:04:51.600 align:middle line:90% I said, I don't know. 01:04:51.600 --> 01:04:53.980 align:middle line:90% I wish it would work out. 01:04:53.980 --> 01:04:56.230 align:middle line:84% But when I think back, you actually 01:04:56.230 --> 01:04:58.420 align:middle line:84% have good reason-- the general idea is, 01:04:58.420 --> 01:05:02.800 align:middle line:84% OK, let's don't get too much electrical potential offset 01:05:02.800 --> 01:05:06.610 align:middle line:84% at the interface, That's what the scatter electron 01:05:06.610 --> 01:05:08.950 align:middle line:90% [INAUDIBLE]. 01:05:08.950 --> 01:05:11.800 align:middle line:84% But see, it turns out in bismuth skutterudite, 01:05:11.800 --> 01:05:14.230 align:middle line:84% you can see the electron is better. 01:05:14.230 --> 01:05:16.630 align:middle line:84% When I first look at this, I couldn't believe it. 01:05:16.630 --> 01:05:20.360 align:middle line:84% And the reason is, of course, it's a semiconductor. 01:05:20.360 --> 01:05:22.930 align:middle line:84% The electric conductivity depends on the carrier 01:05:22.930 --> 01:05:27.250 align:middle line:84% concentration, It's the mobility times n, the carrier 01:05:27.250 --> 01:05:29.260 align:middle line:90% concentration, times charge. 01:05:29.260 --> 01:05:33.550 align:middle line:84% So turns out the bismuth telluride-- when you warm 01:05:33.550 --> 01:05:35.830 align:middle line:84% [INAUDIBLE], you generate defects 01:05:35.830 --> 01:05:37.510 align:middle line:90% that generate more electron. 01:05:37.510 --> 01:05:41.740 align:middle line:84% Or in this case, it's more holes because it's a positive Seebeck 01:05:41.740 --> 01:05:43.960 align:middle line:90% in the positive poles. 01:05:43.960 --> 01:05:46.610 align:middle line:84% Again, you can see that's the typical behavior. 01:05:46.610 --> 01:05:50.980 align:middle line:84% So at the end, if I plot the s square here-- 01:05:50.980 --> 01:05:57.520 align:middle line:84% so higher electron density, lower Seebeck. 01:05:57.520 --> 01:05:58.660 align:middle line:90% Higher electron density. 01:05:58.660 --> 01:06:02.290 align:middle line:84% Fermi level is closer to the [INAUDIBLE] edge, 01:06:02.290 --> 01:06:04.390 align:middle line:90% or you can get into the band. 01:06:04.390 --> 01:06:08.320 align:middle line:84% The Seebeck is the average distance thermal energy 01:06:08.320 --> 01:06:11.500 align:middle line:90% of electron [INAUDIBLE] 01:06:11.500 --> 01:06:15.310 align:middle line:84% So higher electric conductivity, lower sigma-- 01:06:15.310 --> 01:06:16.600 align:middle line:90% that's [INAUDIBLE]. 01:06:16.600 --> 01:06:19.570 align:middle line:84% But because you have higher carrier concentration, 01:06:19.570 --> 01:06:22.960 align:middle line:84% the bipolar decreases [INAUDIBLE] later, 01:06:22.960 --> 01:06:24.130 align:middle line:90% you can see here. 01:06:24.130 --> 01:06:27.130 align:middle line:90% It goes to higher temperature. 01:06:27.130 --> 01:06:29.980 align:middle line:84% And then-- so if you plot s square sigma, 01:06:29.980 --> 01:06:32.810 align:middle line:84% this is actually better than this. 01:06:32.810 --> 01:06:34.940 align:middle line:84% We try that very hard in superlattice. 01:06:34.940 --> 01:06:36.650 align:middle line:90% We didn't get a s square sigma. 01:06:36.650 --> 01:06:40.110 align:middle line:84% Both equally thermal conductivity increase 01:06:40.110 --> 01:06:43.970 align:middle line:84% [INAUDIBLE] factor, and this actually work. 01:06:43.970 --> 01:06:47.840 align:middle line:84% But we still don't know how exactly the model [INAUDIBLE] 01:06:47.840 --> 01:06:50.030 align:middle line:84% very difficult to model in random structure. 01:06:50.030 --> 01:06:52.830 align:middle line:90% 01:06:52.830 --> 01:06:54.850 align:middle line:90% We're doing that. 01:06:54.850 --> 01:06:57.430 align:middle line:90% And we're not the only one. 01:06:57.430 --> 01:07:02.860 align:middle line:84% In fact, [INAUDIBLE] has been working 01:07:02.860 --> 01:07:07.960 align:middle line:84% in this material system, which they call [INAUDIBLE]. 01:07:07.960 --> 01:07:11.500 align:middle line:90% And so [INAUDIBLE] telluride-- 01:07:11.500 --> 01:07:13.760 align:middle line:84% and the single crystal-- he grew single crystal. 01:07:13.760 --> 01:07:16.900 align:middle line:84% He spent several days growing single crystals, 01:07:16.900 --> 01:07:20.710 align:middle line:84% pulling heat in, and got the very good properties. 01:07:20.710 --> 01:07:24.175 align:middle line:90% And again, let me caution you-- 01:07:24.175 --> 01:07:28.150 align:middle line:84% you can't believe at this point because they extrapolate it. 01:07:28.150 --> 01:07:30.250 align:middle line:84% No, he doesn't show this anymore. 01:07:30.250 --> 01:07:33.700 align:middle line:84% And measurement is always a hard problem. 01:07:33.700 --> 01:07:34.990 align:middle line:90% One has to realize-- 01:07:34.990 --> 01:07:37.750 align:middle line:84% sometimes I scare people away by saying that, 01:07:37.750 --> 01:07:40.480 align:middle line:90% but that's reality of this. 01:07:40.480 --> 01:07:46.330 align:middle line:84% And what they found later on is that this material actually-- 01:07:46.330 --> 01:07:48.040 align:middle line:84% even though it's a single crystal, 01:07:48.040 --> 01:07:52.320 align:middle line:84% but a lot of precipitates out of nanodots. 01:07:52.320 --> 01:07:57.330 align:middle line:84% And with that, the thermal conductivity is also quite low. 01:07:57.330 --> 01:08:04.520 align:middle line:84% So we got a good figure of merit. 01:08:04.520 --> 01:08:06.580 align:middle line:84% This is a really interesting system. 01:08:06.580 --> 01:08:09.140 align:middle line:90% 01:08:09.140 --> 01:08:16.130 align:middle line:84% I've been talking to [INAUDIBLE] And I still can't really 01:08:16.130 --> 01:08:20.420 align:middle line:90% give you a very simple picture. 01:08:20.420 --> 01:08:24.380 align:middle line:84% Basically, I was asked give a very simple picture 01:08:24.380 --> 01:08:26.569 align:middle line:90% so I can explain to my students. 01:08:26.569 --> 01:08:30.649 align:middle line:84% And I don't think that I got a simple picture yet. 01:08:30.649 --> 01:08:35.930 align:middle line:84% But the idea it's looking at is-- 01:08:35.930 --> 01:08:42.649 align:middle line:84% here, is a silver [INAUDIBLE] It's a cubic structure. 01:08:42.649 --> 01:08:45.979 align:middle line:84% Silver antimony telluride [INAUDIBLE] similar. 01:08:45.979 --> 01:08:53.300 align:middle line:84% And what it's saying is the electron 01:08:53.300 --> 01:08:58.100 align:middle line:84% clouds between the atoms have overlap. 01:08:58.100 --> 01:09:01.220 align:middle line:84% And when one set of atoms moving that 01:09:01.220 --> 01:09:04.370 align:middle line:84% squeeze this flow of clouds, it's very significant. 01:09:04.370 --> 01:09:06.390 align:middle line:84% So the electron clouds are very significant. 01:09:06.390 --> 01:09:10.920 align:middle line:84% Squeezing cause the force anharmonicity. 01:09:10.920 --> 01:09:15.720 align:middle line:84% And this anharmonicity gives a very low-- so what you want is-- 01:09:15.720 --> 01:09:20.140 align:middle line:84% you want to make the atoms strongly scatter each other. 01:09:20.140 --> 01:09:22.920 align:middle line:90% 01:09:22.920 --> 01:09:25.740 align:middle line:84% High thermal conductivity-- if you just 01:09:25.740 --> 01:09:28.830 align:middle line:84% have a pure spring harmonic oscillator, 01:09:28.830 --> 01:09:31.920 align:middle line:84% you have infinite thermal conductivity. 01:09:31.920 --> 01:09:34.439 align:middle line:84% And the finite thermal conductivity 01:09:34.439 --> 01:09:38.340 align:middle line:84% really comes from the third term of the potential. 01:09:38.340 --> 01:09:41.100 align:middle line:90% It's not a f equals kx. 01:09:41.100 --> 01:09:46.020 align:middle line:84% For f equals kx plus a perturbation, kx squared. 01:09:46.020 --> 01:09:49.080 align:middle line:84% That square makes the two different frequency 01:09:49.080 --> 01:09:51.689 align:middle line:90% wave interact with each other. 01:09:51.689 --> 01:09:53.710 align:middle line:90% That's so hard for optical wave. 01:09:53.710 --> 01:09:55.170 align:middle line:90% It's much easier for phonon. 01:09:55.170 --> 01:10:00.480 align:middle line:84% But when you want to push to very low, very small limit, 01:10:00.480 --> 01:10:04.750 align:middle line:84% you got to [INAUDIBLE] get this anharmonicity very large. 01:10:04.750 --> 01:10:08.490 align:middle line:84% And one way to gauge that is this recent parameter, 01:10:08.490 --> 01:10:10.710 align:middle line:84% which is related to thermal expansion. 01:10:10.710 --> 01:10:12.840 align:middle line:84% And thermal expansion-- so higher 01:10:12.840 --> 01:10:14.940 align:middle line:84% [INAUDIBLE] thermal expansion material typically 01:10:14.940 --> 01:10:18.764 align:middle line:90% is more anharmonic. 01:10:18.764 --> 01:10:24.170 align:middle line:84% And what is showing is this minimum thermal conductivity 01:10:24.170 --> 01:10:25.550 align:middle line:90% theory. 01:10:25.550 --> 01:10:28.490 align:middle line:84% That's also another thing I never believe-- 01:10:28.490 --> 01:10:31.910 align:middle line:90% minimum thermal connectivity. 01:10:31.910 --> 01:10:33.440 align:middle line:90% The idea is one third-- 01:10:33.440 --> 01:10:36.270 align:middle line:90% k equals one third cv gamma. 01:10:36.270 --> 01:10:38.870 align:middle line:90% That's the kinetic theory. 01:10:38.870 --> 01:10:40.820 align:middle line:84% And the minimum thermal conductivity 01:10:40.820 --> 01:10:45.860 align:middle line:84% is replacing the mean-free path by the wavelength. 01:10:45.860 --> 01:10:50.990 align:middle line:84% So that's the minimum mean-free path you could have. 01:10:50.990 --> 01:10:54.420 align:middle line:84% And this was a Glen Slack original theory. 01:10:54.420 --> 01:11:00.530 align:middle line:84% And then David Cahill and Bobby Powell from Cornell 01:11:00.530 --> 01:11:05.490 align:middle line:84% said, oh, it should not be just a mean-free path wavelength. 01:11:05.490 --> 01:11:08.540 align:middle line:84% It should be mean free path equals plus wavelength. 01:11:08.540 --> 01:11:12.050 align:middle line:84% Einstein-- based on Einstein's argument. 01:11:12.050 --> 01:11:14.390 align:middle line:84% So that reduced thermal conductivity minimum 01:11:14.390 --> 01:11:15.890 align:middle line:90% by another half. 01:11:15.890 --> 01:11:20.550 align:middle line:84% And so very often, people will draw this thermal conductivity 01:11:20.550 --> 01:11:21.490 align:middle line:90% against the minimum. 01:11:21.490 --> 01:11:23.430 align:middle line:84% So this is the one example we say, OK, you've 01:11:23.430 --> 01:11:24.630 align:middle line:90% reached the minimum. 01:11:24.630 --> 01:11:27.120 align:middle line:90% You can't reduce anymore. 01:11:27.120 --> 01:11:31.230 align:middle line:84% But in fact, I said David Cahill because he 01:11:31.230 --> 01:11:32.740 align:middle line:90% measured layer structure. 01:11:32.740 --> 01:11:35.220 align:middle line:84% His thermal conductivity is twice the error. 01:11:35.220 --> 01:11:37.740 align:middle line:84% It's an order of magnitude smaller than the minimum. 01:11:37.740 --> 01:11:40.500 align:middle line:90% So his own minimum theory. 01:11:40.500 --> 01:11:41.730 align:middle line:90% There is a minimum-- 01:11:41.730 --> 01:11:45.030 align:middle line:84% his experiment, is an order of magnitude smaller. 01:11:45.030 --> 01:11:46.980 align:middle line:84% So that's why I say I don't believe 01:11:46.980 --> 01:11:53.260 align:middle line:84% in it because you should go look at their better formulation. 01:11:53.260 --> 01:11:57.345 align:middle line:84% When you have an [INAUDIBLE] you don't have one [INAUDIBLE] 01:11:57.345 --> 01:11:59.170 align:middle line:90% mean-free path. 01:11:59.170 --> 01:12:00.690 align:middle line:84% And if you're interested in this, 01:12:00.690 --> 01:12:02.542 align:middle line:84% I'll point you more to literature. 01:12:02.542 --> 01:12:06.430 align:middle line:90% 01:12:06.430 --> 01:12:10.770 align:middle line:84% This is something that I really want. 01:12:10.770 --> 01:12:15.330 align:middle line:84% [INAUDIBLE] OK, I bring you from the basics 01:12:15.330 --> 01:12:17.730 align:middle line:90% to, really, the forefront. 01:12:17.730 --> 01:12:27.450 align:middle line:84% Just a few months ago, there was a paper, indium [INAUDIBLE]. 01:12:27.450 --> 01:12:30.270 align:middle line:90% And what it's saying-- 01:12:30.270 --> 01:12:33.200 align:middle line:90% this is a charged density wave. 01:12:33.200 --> 01:12:36.600 align:middle line:90% And the [INAUDIBLE] instability. 01:12:36.600 --> 01:12:38.075 align:middle line:90% And this got really-- 01:12:38.075 --> 01:12:41.660 align:middle line:90% 01:12:41.660 --> 01:12:47.580 align:middle line:84% So what happens is this direction [INAUDIBLE] 01:12:47.580 --> 01:12:49.610 align:middle line:84% this is more like a layer structure. 01:12:49.610 --> 01:12:57.050 align:middle line:84% And then into the z-axis, that's the covalent bonding. 01:12:57.050 --> 01:13:04.010 align:middle line:84% But because the charge distortion-- so in the z-axis, 01:13:04.010 --> 01:13:06.800 align:middle line:84% actually, charge a strongly distorted 01:13:06.800 --> 01:13:10.080 align:middle line:84% and create a very large anharmonicity for the last wave 01:13:10.080 --> 01:13:11.150 align:middle line:90% scatter. 01:13:11.150 --> 01:13:15.020 align:middle line:84% So the thermal conductivity is really strange 01:13:15.020 --> 01:13:17.330 align:middle line:84% because when the [INAUDIBLE] direction, 01:13:17.330 --> 01:13:21.780 align:middle line:84% force weak force typically means low thermal conductivity. 01:13:21.780 --> 01:13:25.340 align:middle line:84% But in this case, what you have-- 01:13:25.340 --> 01:13:29.200 align:middle line:84% this is the z-axis for one direction. 01:13:29.200 --> 01:13:30.890 align:middle line:84% You have lower thermal conductivity 01:13:30.890 --> 01:13:33.780 align:middle line:90% in the [INAUDIBLE] direction. 01:13:33.780 --> 01:13:38.520 align:middle line:84% And very interesting, and definitely worth 01:13:38.520 --> 01:13:40.240 align:middle line:90% more study here. 01:13:40.240 --> 01:13:44.780 align:middle line:90% 01:13:44.780 --> 01:13:49.231 align:middle line:90% Now let me go to [INAUDIBLE]. 01:13:49.231 --> 01:13:52.570 align:middle line:84% This is the quantization I mentioned 01:13:52.570 --> 01:13:55.730 align:middle line:90% and the pizza box problem-- 01:13:55.730 --> 01:13:58.310 align:middle line:84% the possible [INAUDIBLE] in the box. 01:13:58.310 --> 01:14:02.590 align:middle line:90% So you have a simple-- 01:14:02.590 --> 01:14:04.130 align:middle line:90% this is a simple homework. 01:14:04.130 --> 01:14:08.870 align:middle line:84% I said before this is the z direction. 01:14:08.870 --> 01:14:10.780 align:middle line:90% Energy is quantized. 01:14:10.780 --> 01:14:15.280 align:middle line:84% And you can do the same standing wave argument I did before 01:14:15.280 --> 01:14:17.380 align:middle line:84% and see what's the wavelength and what's 01:14:17.380 --> 01:14:19.860 align:middle line:90% the corresponding energy. 01:14:19.860 --> 01:14:27.030 align:middle line:84% And so xy direction, is called the continuous wave vector. 01:14:27.030 --> 01:14:32.220 align:middle line:84% So now, for different n, we have the sub bands. 01:14:32.220 --> 01:14:37.950 align:middle line:84% So this energy quantized different energy levels in the-- 01:14:37.950 --> 01:14:41.340 align:middle line:84% due to the thickness in the z direction. 01:14:41.340 --> 01:14:45.090 align:middle line:84% So that's the basic [INAUDIBLE] idea. 01:14:45.090 --> 01:14:48.330 align:middle line:90% And now you go to do this. 01:14:48.330 --> 01:14:50.945 align:middle line:84% You calculate the density of states. 01:14:50.945 --> 01:14:54.018 align:middle line:90% 01:14:54.018 --> 01:14:55.560 align:middle line:84% I don't want to go through this math. 01:14:55.560 --> 01:14:59.130 align:middle line:84% But you can say this is the same thing we did before, 01:14:59.130 --> 01:15:01.520 align:middle line:90% except in the z direction. 01:15:01.520 --> 01:15:02.020 align:middle line:90% Now. 01:15:02.020 --> 01:15:03.540 align:middle line:90% I don't do-- 01:15:03.540 --> 01:15:07.770 align:middle line:84% I do not convert this summation into integration 01:15:07.770 --> 01:15:08.800 align:middle line:90% in the z direction. 01:15:08.800 --> 01:15:11.610 align:middle line:84% I convert the xy direction because the z direction-- 01:15:11.610 --> 01:15:15.390 align:middle line:84% that separation is too large, and the summation 01:15:15.390 --> 01:15:18.240 align:middle line:84% into integration-- that conversion is not a rigorous-- 01:15:18.240 --> 01:15:20.200 align:middle line:90% not mathematically accurate. 01:15:20.200 --> 01:15:22.690 align:middle line:84% So I still keep this summation here. 01:15:22.690 --> 01:15:27.010 align:middle line:84% And at the end, what you show is the density of states now is 01:15:27.010 --> 01:15:33.010 align:middle line:84% a staircase, or in typical parabolic band approximation, 01:15:33.010 --> 01:15:34.370 align:middle line:90% we got this 3D. 01:15:34.370 --> 01:15:36.420 align:middle line:90% This is 2D. 01:15:36.420 --> 01:15:41.220 align:middle line:84% And now, with that, there is advantage. 01:15:41.220 --> 01:15:43.620 align:middle line:90% Where is the advantage? 01:15:43.620 --> 01:15:46.680 align:middle line:84% Let's go back to the picture I showed before. 01:15:46.680 --> 01:15:51.870 align:middle line:84% Seebeck is a measure of the average energy of the electron 01:15:51.870 --> 01:15:53.380 align:middle line:90% relative to chemical potential. 01:15:53.380 --> 01:15:58.500 align:middle line:90% 01:15:58.500 --> 01:16:02.220 align:middle line:84% Electrical activity is really proportional to the number 01:16:02.220 --> 01:16:04.810 align:middle line:90% of electrons. 01:16:04.810 --> 01:16:08.680 align:middle line:90% So when I have this-- 01:16:08.680 --> 01:16:10.390 align:middle line:84% if you look at it, this [INAUDIBLE] 01:16:10.390 --> 01:16:14.800 align:middle line:84% says this is df Fermi-Dirac derivative. 01:16:14.800 --> 01:16:16.740 align:middle line:90% Now this is very small. 01:16:16.740 --> 01:16:18.340 align:middle line:90% This type of state-- 01:16:18.340 --> 01:16:23.680 align:middle line:84% that's the region where it's contributing to electrons. 01:16:23.680 --> 01:16:27.910 align:middle line:84% Because of the parabolic, this is a small number 01:16:27.910 --> 01:16:30.210 align:middle line:90% times small number. 01:16:30.210 --> 01:16:34.740 align:middle line:84% So the electric conduction-- the number of charges that carry 01:16:34.740 --> 01:16:37.650 align:middle line:90% the Seebeck-- most of them-- 01:16:37.650 --> 01:16:38.980 align:middle line:90% it's very low energy. 01:16:38.980 --> 01:16:40.360 align:middle line:90% The average energy is here. 01:16:40.360 --> 01:16:42.090 align:middle line:90% Those are low-energy electrons. 01:16:42.090 --> 01:16:46.110 align:middle line:84% They carry more electrical charge. 01:16:46.110 --> 01:16:49.290 align:middle line:84% So that's a problem with the [INAUDIBLE] band, 01:16:49.290 --> 01:16:50.490 align:middle line:90% with the density-- 01:16:50.490 --> 01:16:54.240 align:middle line:84% the [INAUDIBLE] density of states. 01:16:54.240 --> 01:17:01.230 align:middle line:84% OK, now you do the [INAUDIBLE] You have a sharp staircase. 01:17:01.230 --> 01:17:04.650 align:middle line:84% And you can put it-- and you see here-- you 01:17:04.650 --> 01:17:12.600 align:middle line:84% can put it in more charge or still have the same Seebeck. 01:17:12.600 --> 01:17:16.830 align:middle line:84% Or if you have similarity [INAUDIBLE], 01:17:16.830 --> 01:17:19.500 align:middle line:84% then you can increase your Seebeck 01:17:19.500 --> 01:17:23.940 align:middle line:84% At the end of what you want is for sigma to be larger, 01:17:23.940 --> 01:17:28.290 align:middle line:84% So that's why those quantum structures-- 01:17:28.290 --> 01:17:30.150 align:middle line:84% like, in the quantum wells, it can give you 01:17:30.150 --> 01:17:32.400 align:middle line:90% larger s square sigma. 01:17:32.400 --> 01:17:35.370 align:middle line:84% And then you look at the other quantum structures. 01:17:35.370 --> 01:17:38.100 align:middle line:84% The density of states-- this is the staircase 01:17:38.100 --> 01:17:40.740 align:middle line:90% for the two-dimensional. 01:17:40.740 --> 01:17:46.760 align:middle line:84% And then wires is a sharp peak here. 01:17:46.760 --> 01:17:50.070 align:middle line:84% And dots are just discrete lines. 01:17:50.070 --> 01:17:59.530 align:middle line:84% So progressively, going from 3D, 2D, to 1D, 0D, 01:17:59.530 --> 01:18:01.930 align:middle line:90% progressively better. 01:18:01.930 --> 01:18:04.690 align:middle line:90% So that's what the theory says. 01:18:04.690 --> 01:18:11.350 align:middle line:84% And at the time, Millie and [INAUDIBLE] in Lincoln Lab 01:18:11.350 --> 01:18:13.060 align:middle line:90% did the experiment. 01:18:13.060 --> 01:18:17.460 align:middle line:90% And they showed that-- 01:18:17.460 --> 01:18:20.560 align:middle line:84% I want, first, to show the trend is all right, 01:18:20.560 --> 01:18:23.600 align:middle line:90% except there is one caveat. 01:18:23.600 --> 01:18:24.360 align:middle line:90% You see there? 01:18:24.360 --> 01:18:28.940 align:middle line:90% 01:18:28.940 --> 01:18:30.570 align:middle line:90% This is not s square sigma. 01:18:30.570 --> 01:18:33.680 align:middle line:90% This is s square n. 01:18:33.680 --> 01:18:37.160 align:middle line:84% Electric conductivity is n times mobility times 01:18:37.160 --> 01:18:42.460 align:middle line:84% the carrier charge-- electron charge. 01:18:42.460 --> 01:18:48.700 align:middle line:84% And the reason is that the superlattice was not-- 01:18:48.700 --> 01:18:50.920 align:middle line:84% the quantum well was not very good-- 01:18:50.920 --> 01:18:53.890 align:middle line:90% interface scattered electrons. 01:18:53.890 --> 01:18:58.670 align:middle line:84% The electric conductivity-- if you plot-- 01:18:58.670 --> 01:19:01.420 align:middle line:84% I don't know the detail, but let's say 01:19:01.420 --> 01:19:05.755 align:middle line:84% there are still questions here because this is s square sigma 01:19:05.755 --> 01:19:07.870 align:middle line:84% and s squared n, not s square sigma. 01:19:07.870 --> 01:19:13.100 align:middle line:84% But the trend is there, and that generate a lot of interest. 01:19:13.100 --> 01:19:18.410 align:middle line:84% And this is just a more calculation I got from a book 01:19:18.410 --> 01:19:22.740 align:middle line:84% that [INAUDIBLE] and myself are writing and never have finished. 01:19:22.740 --> 01:19:25.360 align:middle line:90% I did not finish this. 01:19:25.360 --> 01:19:28.060 align:middle line:84% If anyone wants to read their draft. 01:19:28.060 --> 01:19:33.790 align:middle line:84% 3D, 2D, 1D, progressively, is better. 01:19:33.790 --> 01:19:35.110 align:middle line:90% That's a theory. 01:19:35.110 --> 01:19:38.740 align:middle line:84% And if you do an experiment, like I said, 01:19:38.740 --> 01:19:40.568 align:middle line:90% you can't scatter electrons. 01:19:40.568 --> 01:19:41.735 align:middle line:90% You have to be very careful. 01:19:41.735 --> 01:19:46.940 align:middle line:90% 01:19:46.940 --> 01:19:48.390 align:middle line:90% And there's another problem. 01:19:48.390 --> 01:19:51.720 align:middle line:84% So of course, superlattice-- the quantum well 01:19:51.720 --> 01:19:55.460 align:middle line:84% is just the [? film ?] that's conducting electron. 01:19:55.460 --> 01:20:00.740 align:middle line:84% And the problem is you have to sandwich this. 01:20:00.740 --> 01:20:06.590 align:middle line:84% Or you can use the air or vacuum or quantum wire in vacuum. 01:20:06.590 --> 01:20:08.990 align:middle line:90% Then there's no leakage. 01:20:08.990 --> 01:20:12.380 align:middle line:84% But normally, when you use another material to create 01:20:12.380 --> 01:20:14.870 align:middle line:84% a barrier to confine electron in the field, 01:20:14.870 --> 01:20:19.040 align:middle line:84% then you've got the phonons in the barrier. 01:20:19.040 --> 01:20:21.750 align:middle line:84% The phonons in this barrier will kill your conduction. 01:20:21.750 --> 01:20:23.840 align:middle line:90% So they'll kill your-- 01:20:23.840 --> 01:20:26.960 align:middle line:84% create a more [INAUDIBLE] leakage here. 01:20:26.960 --> 01:20:31.340 align:middle line:84% And there are solutions on this, theoretically. 01:20:31.340 --> 01:20:34.255 align:middle line:84% I've worked with Millie on this before. 01:20:34.255 --> 01:20:36.960 align:middle line:90% 01:20:36.960 --> 01:20:39.900 align:middle line:84% Just as a caveat, one has to pay attention. 01:20:39.900 --> 01:20:44.300 align:middle line:84% For example, there are also study by [INAUDIBLE] and others 01:20:44.300 --> 01:20:46.910 align:middle line:84% say if you reduce the thickness-- 01:20:46.910 --> 01:20:48.560 align:middle line:84% you want to reduce barrier [INAUDIBLE], 01:20:48.560 --> 01:20:50.000 align:middle line:90% you reduce thickness. 01:20:50.000 --> 01:20:54.390 align:middle line:84% And then you have another problem where these two 01:20:54.390 --> 01:20:56.610 align:middle line:84% [INAUDIBLE] will start talking to each other-- 01:20:56.610 --> 01:20:57.510 align:middle line:90% colony. 01:20:57.510 --> 01:20:59.530 align:middle line:84% And that colony, actually, is not good. 01:20:59.530 --> 01:21:02.510 align:middle line:90% 01:21:02.510 --> 01:21:07.740 align:middle line:84% The [INAUDIBLE] becomes less sharper than the pure quantum 01:21:07.740 --> 01:21:08.820 align:middle line:90% well. 01:21:08.820 --> 01:21:11.970 align:middle line:90% There are potential solutions. 01:21:11.970 --> 01:21:17.120 align:middle line:84% I encourage you to read the literature and work on this. 01:21:17.120 --> 01:21:20.780 align:middle line:84% But it turns out this general idea 01:21:20.780 --> 01:21:24.370 align:middle line:84% of [INAUDIBLE] featuring density of states 01:21:24.370 --> 01:21:30.410 align:middle line:84% is a universal, not only in thin films but in bulk materials. 01:21:30.410 --> 01:21:36.060 align:middle line:84% And there was one paper by [INAUDIBLE]. 01:21:36.060 --> 01:21:39.390 align:middle line:90% And he wrote a paper around '97. 01:21:39.390 --> 01:21:43.440 align:middle line:84% And he's a very good theoretician. 01:21:43.440 --> 01:21:46.470 align:middle line:84% He just took a simple math problem. 01:21:46.470 --> 01:21:49.680 align:middle line:84% He said, I'm going to optimize the density of states. 01:21:49.680 --> 01:21:52.060 align:middle line:84% Just write the expression I wrote before. 01:21:52.060 --> 01:21:54.810 align:middle line:84% Treat it as a function that d [INAUDIBLE] 01:21:54.810 --> 01:21:57.340 align:middle line:84% states as a function of mathematics. 01:21:57.340 --> 01:22:01.980 align:middle line:84% What's the function that will give you maximum s square sigma 01:22:01.980 --> 01:22:04.080 align:middle line:90% or give you maximum zt? 01:22:04.080 --> 01:22:09.020 align:middle line:84% And at the end, he concluded it's the delta function. 01:22:09.020 --> 01:22:11.360 align:middle line:90% So delta function is the best. 01:22:11.360 --> 01:22:15.680 align:middle line:84% And if you go back to what I showed here, 01:22:15.680 --> 01:22:17.270 align:middle line:90% quantum dot is best. 01:22:17.270 --> 01:22:20.570 align:middle line:84% Except the electron model-- how are you going to move quantum 01:22:20.570 --> 01:22:23.840 align:middle line:84% dots-- the electron going to [INAUDIBLE] delta t or quantum 01:22:23.840 --> 01:22:25.040 align:middle line:90% dots. 01:22:25.040 --> 01:22:27.800 align:middle line:90% So wire is also good. 01:22:27.800 --> 01:22:29.870 align:middle line:90% So this is a general principle. 01:22:29.870 --> 01:22:31.760 align:middle line:84% Another interesting comment I want to make 01:22:31.760 --> 01:22:35.060 align:middle line:84% is you go to check the Lorentz number. 01:22:35.060 --> 01:22:38.390 align:middle line:90% And that's what I suspected-- 01:22:38.390 --> 01:22:42.470 align:middle line:84% the Lorentz number in quantum dot can be 0. 01:22:42.470 --> 01:22:43.790 align:middle line:90% Very strange. 01:22:43.790 --> 01:22:45.860 align:middle line:90% Nobody demonstrated that. 01:22:45.860 --> 01:22:48.140 align:middle line:90% Very interesting experiment. 01:22:48.140 --> 01:22:51.590 align:middle line:84% Electrical activity is not 0, but 01:22:51.590 --> 01:22:54.710 align:middle line:84% the electronic thermal conductivity is 0. 01:22:54.710 --> 01:22:58.160 align:middle line:90% Very easy to check. 01:22:58.160 --> 01:23:00.250 align:middle line:90% Let me go here. 01:23:00.250 --> 01:23:06.570 align:middle line:84% So this is really the reason [INAUDIBLE] and he said-- 01:23:06.570 --> 01:23:12.710 align:middle line:84% we talk a lot, but very smart guy, and would say-- 01:23:12.710 --> 01:23:15.030 align:middle line:84% He worked on nanowires-- bismuth nanowires. 01:23:15.030 --> 01:23:16.310 align:middle line:90% Worked with Millie and-- 01:23:16.310 --> 01:23:19.940 align:middle line:84% And he say, I'm going to turn to bulk material. 01:23:19.940 --> 01:23:23.870 align:middle line:84% So one day-- he read Russian literature, 01:23:23.870 --> 01:23:26.400 align:middle line:84% and this is all, actually, in Russian literature. 01:23:26.400 --> 01:23:29.660 align:middle line:84% It turns out there is some doping. 01:23:29.660 --> 01:23:32.150 align:middle line:84% Particularly when we think about doping-- 01:23:32.150 --> 01:23:33.700 align:middle line:90% we think about doping-- 01:23:33.700 --> 01:23:39.680 align:middle line:84% the energy level is inside the band, in the bandgap. 01:23:39.680 --> 01:23:43.070 align:middle line:90% But there are some other atoms. 01:23:43.070 --> 01:23:47.960 align:middle line:84% The doping level is within the conduction of valence band. 01:23:47.960 --> 01:23:51.800 align:middle line:84% And in this case, is in the valence band. 01:23:51.800 --> 01:23:53.930 align:middle line:90% And this valence band-- 01:23:53.930 --> 01:23:56.630 align:middle line:84% the doping form additional energy states 01:23:56.630 --> 01:24:01.650 align:middle line:84% that create a sharp feature in the density of states. 01:24:01.650 --> 01:24:07.440 align:middle line:84% And this [INAUDIBLE] feature led to very good Seebeck coefficient 01:24:07.440 --> 01:24:10.930 align:middle line:90% and very high [INAUDIBLE]. 01:24:10.930 --> 01:24:12.520 align:middle line:90% Very nice idea. 01:24:12.520 --> 01:24:15.040 align:middle line:84% The question is whether you can replicate it in different 01:24:15.040 --> 01:24:18.530 align:middle line:84% materials because [INAUDIBLE] nobody wants to touch it 01:24:18.530 --> 01:24:24.210 align:middle line:84% because it's very poisonous because-- 01:24:24.210 --> 01:24:25.313 align:middle line:90% it's not that terrible. 01:24:25.313 --> 01:24:25.980 align:middle line:90% I have a friend. 01:24:25.980 --> 01:24:29.100 align:middle line:84% And he said, I focused on it for more than 50 years, 01:24:29.100 --> 01:24:32.700 align:middle line:84% superconductor, and nothing happened. 01:24:32.700 --> 01:24:37.200 align:middle line:90% But the person-- be careful. 01:24:37.200 --> 01:24:44.166 align:middle line:84% Now, this is another idea I think, again, come back to-- 01:24:44.166 --> 01:24:47.490 align:middle line:84% you can interpret the same intensity of state. 01:24:47.490 --> 01:24:51.210 align:middle line:90% This is Seebeck coefficient. 01:24:51.210 --> 01:24:55.390 align:middle line:84% If [INAUDIBLE] position is here in the band, this [INAUDIBLE] 01:24:55.390 --> 01:24:56.530 align:middle line:90% is a positive. 01:24:56.530 --> 01:24:58.440 align:middle line:90% So they cancel each other. 01:24:58.440 --> 01:25:01.000 align:middle line:90% Of course, this is larger. 01:25:01.000 --> 01:25:03.720 align:middle line:84% So you still have-- the cancellation is small. 01:25:03.720 --> 01:25:07.380 align:middle line:84% But if you put a potential-- so you have a particle, 01:25:07.380 --> 01:25:10.290 align:middle line:84% or you have an interface, that just happen 01:25:10.290 --> 01:25:14.010 align:middle line:84% to have this potential height, then those electrons 01:25:14.010 --> 01:25:14.710 align:middle line:90% are scattered. 01:25:14.710 --> 01:25:17.860 align:middle line:84% So that's for the energy field or thermionic emission. 01:25:17.860 --> 01:25:21.670 align:middle line:84% I'll talk about thermionic emission in the next lecture. 01:25:21.670 --> 01:25:23.820 align:middle line:84% We'll talk about thermionic engines. 01:25:23.820 --> 01:25:24.880 align:middle line:90% That's a different way. 01:25:24.880 --> 01:25:26.700 align:middle line:90% But this is a solid. 01:25:26.700 --> 01:25:29.100 align:middle line:84% So you scatter this low-energy electron, 01:25:29.100 --> 01:25:30.975 align:middle line:84% and then you only have high-energy electrons 01:25:30.975 --> 01:25:32.972 align:middle line:90% [INAUDIBLE]. 01:25:32.972 --> 01:25:37.410 align:middle line:84% And if I draw the [INAUDIBLE] state picture is-- 01:25:37.410 --> 01:25:40.350 align:middle line:84% although there [? are high ?] electrons in this region, 01:25:40.350 --> 01:25:43.120 align:middle line:84% but I scatter them-- they do not move. 01:25:43.120 --> 01:25:47.160 align:middle line:84% So now, in terms of this state, what's really moving 01:25:47.160 --> 01:25:49.800 align:middle line:84% is-- you still have a sharp picture. 01:25:49.800 --> 01:25:53.100 align:middle line:84% So that's my interpretation of this picture-- 01:25:53.100 --> 01:25:54.460 align:middle line:90% this different idea. 01:25:54.460 --> 01:25:57.870 align:middle line:84% So you can always think about the different states, features 01:25:57.870 --> 01:25:59.070 align:middle line:90% for electron. 01:25:59.070 --> 01:26:02.850 align:middle line:84% But really, the one that has win so far is-- 01:26:02.850 --> 01:26:08.250 align:middle line:84% the only successful example I know is this one. 01:26:08.250 --> 01:26:11.970 align:middle line:90% Truly work in materials. 01:26:11.970 --> 01:26:15.930 align:middle line:84% So most other approach that's successful is important. 01:26:15.930 --> 01:26:20.040 align:middle line:84% So with that, I [INAUDIBLE] will from the very simple things 01:26:20.040 --> 01:26:21.380 align:middle line:90% I don't know. 01:26:21.380 --> 01:26:23.690 align:middle line:90% And you can figure out. 01:26:23.690 --> 01:26:25.000 align:middle line:90%