WEBVTT 00:00:00.000 --> 00:00:02.458 align:middle line:84% SPEAKER: The following content is provided under a Creative 00:00:02.458 --> 00:00:03.600 align:middle line:90% Commons license. 00:00:03.600 --> 00:00:06.050 align:middle line:84% Your support will help MIT OpenCourseWare 00:00:06.050 --> 00:00:09.650 align:middle line:84% continue to offer high quality educational resources for free. 00:00:09.650 --> 00:00:12.620 align:middle line:84% To make a donation or to view additional materials 00:00:12.620 --> 00:00:16.520 align:middle line:84% from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.520 --> 00:00:20.240 align:middle line:90% at ocw.mit.edu. 00:00:20.240 --> 00:00:24.200 align:middle line:84% GANG CHEN: This course is for pass fail. 00:00:24.200 --> 00:00:29.910 align:middle line:84% You should turn in your weekly reading report. 00:00:29.910 --> 00:00:31.662 align:middle line:90% And I will give you-- 00:00:31.662 --> 00:00:32.495 align:middle line:90% I'll send the email. 00:00:32.495 --> 00:00:36.020 align:middle line:84% So I'll give you two buy-outs since I haven't said this 00:00:36.020 --> 00:00:37.430 align:middle line:90% before. 00:00:37.430 --> 00:00:45.740 align:middle line:84% Two buy-outs means you can skip two reports, but below that, 00:00:45.740 --> 00:00:48.260 align:middle line:90% you can't pass this course-- 00:00:48.260 --> 00:00:50.450 align:middle line:90% so pass fail, OK? 00:00:50.450 --> 00:00:52.463 align:middle line:90% So I'll send that out. 00:00:52.463 --> 00:00:55.850 align:middle line:90% 00:00:55.850 --> 00:01:00.230 align:middle line:84% I came back this morning from San Diego. 00:01:00.230 --> 00:01:02.030 align:middle line:90% And what I want to show you-- 00:01:02.030 --> 00:01:04.730 align:middle line:90% 00:01:04.730 --> 00:01:06.830 align:middle line:90% OK, this is my towel bag. 00:01:06.830 --> 00:01:13.130 align:middle line:84% And that's all I bring because now I feel one day, 00:01:13.130 --> 00:01:19.010 align:middle line:84% my son had a homework assignment-- carbon footprint. 00:01:19.010 --> 00:01:23.510 align:middle line:84% And he came back and said we will be below the average, 00:01:23.510 --> 00:01:25.940 align:middle line:90% except you travel too much. 00:01:25.940 --> 00:01:32.540 align:middle line:84% So my footprint is just a tremendous release of family 00:01:32.540 --> 00:01:34.940 align:middle line:90% carbon dioxide footprint. 00:01:34.940 --> 00:01:38.840 align:middle line:84% My way of trying to redeem a little bit 00:01:38.840 --> 00:01:43.220 align:middle line:90% is by traveling light. 00:01:43.220 --> 00:01:46.470 align:middle line:84% And I was at a meeting in San Diego. 00:01:46.470 --> 00:01:53.750 align:middle line:84% This meeting was on the application of thermoelectrics. 00:01:53.750 --> 00:02:00.380 align:middle line:84% So we actually, in the last two days, really-- 00:02:00.380 --> 00:02:03.840 align:middle line:84% the key people from thermoelectrics area 00:02:03.840 --> 00:02:09.360 align:middle line:84% around the world converged in San Diego discussing 00:02:09.360 --> 00:02:11.640 align:middle line:90% the application areas. 00:02:11.640 --> 00:02:18.360 align:middle line:84% I'll share some of the meeting findings. 00:02:18.360 --> 00:02:18.920 align:middle line:90% Let's see. 00:02:18.920 --> 00:02:21.190 align:middle line:90% I want to start by-- 00:02:21.190 --> 00:02:27.770 align:middle line:84% some of you read one or both of the papers-- 00:02:27.770 --> 00:02:31.040 align:middle line:90% the assignment. 00:02:31.040 --> 00:02:36.590 align:middle line:84% One is by crowning one in on the Inconvenient Truth. 00:02:36.590 --> 00:02:43.040 align:middle line:84% And the story is he attended one of those conferences organized 00:02:43.040 --> 00:02:45.710 align:middle line:90% by Al Gore. 00:02:45.710 --> 00:02:49.060 align:middle line:90% And so that was a good title-- 00:02:49.060 --> 00:02:51.200 align:middle line:90% Inconvenient Truth's title. 00:02:51.200 --> 00:02:55.760 align:middle line:84% And I know he called me at the time 00:02:55.760 --> 00:02:57.950 align:middle line:90% and was asking for some slides. 00:02:57.950 --> 00:03:03.410 align:middle line:84% So whether you have any thoughts-- 00:03:03.410 --> 00:03:07.860 align:middle line:84% the other the other review by Lambell is more optimistic. 00:03:07.860 --> 00:03:10.400 align:middle line:90% So one is the pessimistic one. 00:03:10.400 --> 00:03:14.180 align:middle line:84% The other is, I think, the more optimistic one. 00:03:14.180 --> 00:03:18.710 align:middle line:84% And I don't know which side you're in. 00:03:18.710 --> 00:03:25.000 align:middle line:84% Any thoughts on that, or anyone have any opinion? 00:03:25.000 --> 00:03:26.620 align:middle line:90% Yes? 00:03:26.620 --> 00:03:28.930 align:middle line:84% AUDIENCE: They were saying some of the same things 00:03:28.930 --> 00:03:31.930 align:middle line:84% with a different tone because they both were saying 00:03:31.930 --> 00:03:35.140 align:middle line:84% that if this is going to be useful, 00:03:35.140 --> 00:03:39.100 align:middle line:84% it's for low power, niche applications, 00:03:39.100 --> 00:03:42.010 align:middle line:90% maybe some covered applications. 00:03:42.010 --> 00:03:44.920 align:middle line:84% And then the difference was in terms of-- 00:03:44.920 --> 00:03:45.857 align:middle line:90% I think it was-- 00:03:45.857 --> 00:03:48.190 align:middle line:84% Bell was saying this is going to be a great impact if we 00:03:48.190 --> 00:03:50.210 align:middle line:90% can do these applications. 00:03:50.210 --> 00:03:54.790 align:middle line:84% And Cronin Vining was more like, you can do these applications, 00:03:54.790 --> 00:03:57.400 align:middle line:84% but it might not make that much of an impact overall. 00:03:57.400 --> 00:03:59.590 align:middle line:84% You're never going to touch the large scale energy 00:03:59.590 --> 00:04:01.167 align:middle line:90% sector with thermal objects. 00:04:01.167 --> 00:04:01.750 align:middle line:90% GANG CHEN: OK. 00:04:01.750 --> 00:04:02.530 align:middle line:90% Yeah. 00:04:02.530 --> 00:04:06.100 align:middle line:90% So I would buy into the-- 00:04:06.100 --> 00:04:08.410 align:middle line:90% but still, the two-- 00:04:08.410 --> 00:04:10.180 align:middle line:90% in terms of the impact-- 00:04:10.180 --> 00:04:13.930 align:middle line:84% conclusions seemed to be a little bit different, right? 00:04:13.930 --> 00:04:16.269 align:middle line:84% Probably the same no matter what you do. 00:04:16.269 --> 00:04:20.769 align:middle line:84% Thermoelectric won't make a difference in the larger scale. 00:04:20.769 --> 00:04:24.690 align:middle line:90% So who raised their hand? 00:04:24.690 --> 00:04:25.490 align:middle line:90% Who else? 00:04:25.490 --> 00:04:27.415 align:middle line:90% 00:04:27.415 --> 00:04:28.790 align:middle line:84% AUDIENCE: But there's an argument 00:04:28.790 --> 00:04:31.190 align:middle line:84% for doing a lot of little things, right? 00:04:31.190 --> 00:04:33.920 align:middle line:84% If you were to, for some reason, take over 00:04:33.920 --> 00:04:36.290 align:middle line:84% all of the low power applications, that's 00:04:36.290 --> 00:04:39.500 align:middle line:84% a lot of things you add efficiency for. 00:04:39.500 --> 00:04:42.320 align:middle line:90% It's not a large scale. 00:04:42.320 --> 00:04:45.080 align:middle line:84% So it's like, if you replaced every cell phone with something 00:04:45.080 --> 00:04:50.720 align:middle line:84% that saves 5%, that's a lot of cell phones that you 00:04:50.720 --> 00:04:52.490 align:middle line:90% [INAUDIBLE]. 00:04:52.490 --> 00:04:55.700 align:middle line:84% GANG CHEN: I guess the future is very uncertain. 00:04:55.700 --> 00:04:58.290 align:middle line:84% And it's very hard to see what technology will win. 00:04:58.290 --> 00:04:59.040 align:middle line:90% AUDIENCE: Exactly. 00:04:59.040 --> 00:05:04.520 align:middle line:84% GANG CHEN: So that's a good perspective. 00:05:04.520 --> 00:05:10.130 align:middle line:84% Well, I was asked to serve as a panelist in this meeting. 00:05:10.130 --> 00:05:13.460 align:middle line:84% I gave a talk, but they also asked me to serve as a panelist. 00:05:13.460 --> 00:05:15.650 align:middle line:84% So I thought of what I would say-- 00:05:15.650 --> 00:05:19.010 align:middle line:84% anything during the meeting different from what I was going 00:05:19.010 --> 00:05:21.830 align:middle line:90% to talk on the scientific side. 00:05:21.830 --> 00:05:23.660 align:middle line:84% I pulled out the Cronin Vining's paper. 00:05:23.660 --> 00:05:25.730 align:middle line:84% I read it again on the airplane and made 00:05:25.730 --> 00:05:29.000 align:middle line:84% a few slides I want to share with you. 00:05:29.000 --> 00:05:32.270 align:middle line:84% So let me-- this is not in the handout, 00:05:32.270 --> 00:05:38.240 align:middle line:90% but I can put it in the website. 00:05:38.240 --> 00:05:40.880 align:middle line:90% So I also try to use-- 00:05:40.880 --> 00:05:44.870 align:middle line:84% you can help me think about the last time. 00:05:44.870 --> 00:05:49.670 align:middle line:84% I say whether it's incorrect conclusion or inconvenient 00:05:49.670 --> 00:05:50.810 align:middle line:90% truth. 00:05:50.810 --> 00:05:56.060 align:middle line:84% So I think the erroneous argument is really 00:05:56.060 --> 00:05:57.590 align:middle line:90% based on here. 00:05:57.590 --> 00:06:02.210 align:middle line:84% This is the efficiency heat source. 00:06:02.210 --> 00:06:06.360 align:middle line:84% And they look at, of course, this is the maximum you can get. 00:06:06.360 --> 00:06:10.250 align:middle line:84% So there's no mistake in the scientific side. 00:06:10.250 --> 00:06:15.110 align:middle line:84% The question is, where do you place the dots? 00:06:15.110 --> 00:06:16.010 align:middle line:90% This is fine. 00:06:16.010 --> 00:06:19.490 align:middle line:90% This is a cold running cycle. 00:06:19.490 --> 00:06:24.650 align:middle line:84% You can even get the 60% if you do the coaching. 00:06:24.650 --> 00:06:31.490 align:middle line:84% And although we-- he has now put in there somewhere 00:06:31.490 --> 00:06:35.690 align:middle line:84% between around 25% internal combustion. 00:06:35.690 --> 00:06:40.620 align:middle line:84% And solar sturdy-- that's a mistake. 00:06:40.620 --> 00:06:46.220 align:middle line:84% Nobody has that kind of efficiency even demonstrated. 00:06:46.220 --> 00:06:50.390 align:middle line:84% Nuclear ranking, that's the esteemed solar ranking. 00:06:50.390 --> 00:06:55.660 align:middle line:84% So solar, these two dots accompanied [INAUDIBLE]. 00:06:55.660 --> 00:06:59.890 align:middle line:84% The solar, if you think about what's currently 00:06:59.890 --> 00:07:02.800 align:middle line:84% deployed in solar steam generation 00:07:02.800 --> 00:07:07.020 align:middle line:84% is between 15% to 18% efficiency. 00:07:07.020 --> 00:07:11.350 align:middle line:84% And, of course, in the lower target range for this argument 00:07:11.350 --> 00:07:13.200 align:middle line:90% here are competitive technology. 00:07:13.200 --> 00:07:16.260 align:middle line:84% This is an organic Rankine cycle, 00:07:16.260 --> 00:07:20.820 align:middle line:84% for example, where the organic has a lower evaporation 00:07:20.820 --> 00:07:21.360 align:middle line:90% temperature. 00:07:21.360 --> 00:07:25.440 align:middle line:84% So you can do the steam engine-based cycles. 00:07:25.440 --> 00:07:28.620 align:middle line:90% So that's his argument. 00:07:28.620 --> 00:07:32.970 align:middle line:84% Basically, you see the thermoelectrics, even 00:07:32.970 --> 00:07:39.360 align:middle line:84% [INAUDIBLE] too [INAUDIBLE] be much dense compared to, 00:07:39.360 --> 00:07:41.375 align:middle line:84% of course, if you compare with this talk. 00:07:41.375 --> 00:07:44.840 align:middle line:90% 00:07:44.840 --> 00:07:52.015 align:middle line:84% Let's say, I thought that the comparison was not on the mark. 00:07:52.015 --> 00:07:54.120 align:middle line:84% Because now, if you look at the PV, 00:07:54.120 --> 00:08:00.020 align:middle line:84% photovoltaic, and amorphous silicon is about 6% to 8%. 00:08:00.020 --> 00:08:03.800 align:middle line:84% The single crystalline silicon deploys about 18% 00:08:03.800 --> 00:08:05.360 align:middle line:90% In the real world. 00:08:05.360 --> 00:08:07.280 align:middle line:84% Of course, in the lab there has been 00:08:07.280 --> 00:08:10.760 align:middle line:90% higher efficiency demonstrated. 00:08:10.760 --> 00:08:15.950 align:middle line:84% And the first solar panels generate, 00:08:15.950 --> 00:08:22.440 align:middle line:84% that's the fastest growing solar sector is about 10% efficiency. 00:08:22.440 --> 00:08:27.960 align:middle line:84% So, of course, even PV you can make the same argument. 00:08:27.960 --> 00:08:29.940 align:middle line:90% Will it make a difference? 00:08:29.940 --> 00:08:33.330 align:middle line:84% Because they were at least 30 terawatts 00:08:33.330 --> 00:08:36.750 align:middle line:90% in the next 30, 40 years. 00:08:36.750 --> 00:08:39.330 align:middle line:84% And PV now the deployment annually 00:08:39.330 --> 00:08:42.240 align:middle line:90% is about six, seven gigawatt. 00:08:42.240 --> 00:08:47.340 align:middle line:84% You can go to see how much you have to have to catch that. 00:08:47.340 --> 00:08:49.440 align:middle line:84% Let's say, of course, today nobody 00:08:49.440 --> 00:08:53.190 align:middle line:90% would really argue against PV. 00:08:53.190 --> 00:08:58.260 align:middle line:84% In the long run, this could be a solution. 00:08:58.260 --> 00:09:04.710 align:middle line:84% So you look at the PV cell efficiency progress, 00:09:04.710 --> 00:09:05.950 align:middle line:90% this is the best. 00:09:05.950 --> 00:09:12.600 align:middle line:84% This is the best efficiency progress against the year. 00:09:12.600 --> 00:09:16.620 align:middle line:84% And as I said, amorphous silicon-- 00:09:16.620 --> 00:09:19.590 align:middle line:84% this is the amorphous silicon there 00:09:19.590 --> 00:09:22.920 align:middle line:90% where this is amorphous silicon. 00:09:22.920 --> 00:09:27.856 align:middle line:84% And then deployed [INAUDIBLE] 6% to 8% efficiency 00:09:27.856 --> 00:09:29.590 align:middle line:90% in the real world. 00:09:29.590 --> 00:09:36.310 align:middle line:84% And single crystalline silicon, 26% here, 00:09:36.310 --> 00:09:41.020 align:middle line:90% and deployed is about 8%. 00:09:41.020 --> 00:09:44.540 align:middle line:90% And part is [INAUDIBLE]. 00:09:44.540 --> 00:09:48.140 align:middle line:90% And so, this is a-- 00:09:48.140 --> 00:09:52.100 align:middle line:84% with this low efficiency, you are, of course, 00:09:52.100 --> 00:09:54.330 align:middle line:84% competing against the coal generation. 00:09:54.330 --> 00:09:56.130 align:middle line:84% And at this stage, it is not competitive. 00:09:56.130 --> 00:09:59.150 align:middle line:84% So the government is giving stimulus, trying 00:09:59.150 --> 00:10:02.750 align:middle line:90% to promote this technology. 00:10:02.750 --> 00:10:07.460 align:middle line:84% And let's see, I think my argument, 00:10:07.460 --> 00:10:13.430 align:middle line:84% if you think about why solar, even nobody probably really 00:10:13.430 --> 00:10:15.660 align:middle line:84% will think that in the near future 00:10:15.660 --> 00:10:20.870 align:middle line:84% you get a 40% solar cell in the deployed. 00:10:20.870 --> 00:10:23.030 align:middle line:84% Of course, concentrating is another option, 00:10:23.030 --> 00:10:27.890 align:middle line:84% but there are a lot of problems with multi-junction solar cells. 00:10:27.890 --> 00:10:31.700 align:middle line:84% So why solar can make a, say, come to the map 00:10:31.700 --> 00:10:33.560 align:middle line:90% and people accept it? 00:10:33.560 --> 00:10:36.200 align:middle line:84% I think fundamentally is heated-- 00:10:36.200 --> 00:10:37.740 align:middle line:90% solar energy is free. 00:10:37.740 --> 00:10:39.680 align:middle line:90% So it's not like coal. 00:10:39.680 --> 00:10:48.920 align:middle line:84% Coal, say, any petroleum-based, you have to put in more money 00:10:48.920 --> 00:10:50.330 align:middle line:90% to get the fuel. 00:10:50.330 --> 00:10:55.370 align:middle line:84% But in the case of solar, you have free fuel come in. 00:10:55.370 --> 00:11:00.440 align:middle line:84% So now you look at the thermal, how we use the energy now, 00:11:00.440 --> 00:11:05.270 align:middle line:84% you see, OK, mostly are fossil fuels. 00:11:05.270 --> 00:11:11.000 align:middle line:84% And the way we're using is conversion into heat and then 00:11:11.000 --> 00:11:14.000 align:middle line:84% into whatever mechanical electrical energy or just 00:11:14.000 --> 00:11:15.470 align:middle line:90% a simple heat. 00:11:15.470 --> 00:11:21.140 align:middle line:84% So heat is intrinsically connected in almost over 90% 00:11:21.140 --> 00:11:25.040 align:middle line:90% of the way we are using energy. 00:11:25.040 --> 00:11:27.920 align:middle line:84% So that's the one part, that's the input part. 00:11:27.920 --> 00:11:32.420 align:middle line:84% And now you look at the output part, 00:11:32.420 --> 00:11:36.530 align:middle line:90% useful energy is about 35%. 00:11:36.530 --> 00:11:40.340 align:middle line:90% That means 65% is thrown away. 00:11:40.340 --> 00:11:42.050 align:middle line:84% And of course, thermodynamics will tell 00:11:42.050 --> 00:11:44.240 align:middle line:90% you have to throw away some. 00:11:44.240 --> 00:11:48.260 align:middle line:84% Let's say, we threw away a lot more 00:11:48.260 --> 00:11:53.870 align:middle line:84% than what's need in terms of thermodynamics. 00:11:53.870 --> 00:11:57.920 align:middle line:84% Because if you think about combustion process, right, 00:11:57.920 --> 00:12:00.590 align:middle line:84% let's take a 2,000 degree Kelvin. 00:12:00.590 --> 00:12:03.920 align:middle line:84% In thermodynamics, most of this is a high temperature 00:12:03.920 --> 00:12:06.100 align:middle line:90% combustion. 00:12:06.100 --> 00:12:10.245 align:middle line:84% The carbon cycle is over 90% efficiency. 00:12:10.245 --> 00:12:12.490 align:middle line:90% And we're throwing away 60%-- 00:12:12.490 --> 00:12:14.080 align:middle line:90% more than 60%. 00:12:14.080 --> 00:12:19.030 align:middle line:84% So, in fact, if you think about your free energy, 00:12:19.030 --> 00:12:22.450 align:middle line:84% I said the solar is free, but you're throwing a lot of here 00:12:22.450 --> 00:12:23.210 align:middle line:90% also free. 00:12:23.210 --> 00:12:26.560 align:middle line:90% 00:12:26.560 --> 00:12:28.310 align:middle line:90% And if you can take that-- 00:12:28.310 --> 00:12:31.100 align:middle line:84% so, of course, you think of where it could be deployed. 00:12:31.100 --> 00:12:33.500 align:middle line:90% Is it here or is it here? 00:12:33.500 --> 00:12:37.970 align:middle line:84% I don't have a clear answer, but the gut feeling 00:12:37.970 --> 00:12:44.520 align:middle line:84% is probably this is where you will have this is a free energy. 00:12:44.520 --> 00:12:49.420 align:middle line:84% So you may have more, let's say, easier acceptance. 00:12:49.420 --> 00:12:52.010 align:middle line:84% And of course, there are a lot of you where a lot of heat 00:12:52.010 --> 00:12:52.750 align:middle line:90% is free. 00:12:52.750 --> 00:12:58.120 align:middle line:84% But let's say, even in the case of heat is not free, 00:12:58.120 --> 00:13:00.670 align:middle line:90% I add this into this generated. 00:13:00.670 --> 00:13:03.010 align:middle line:84% If you think about the household, and say 00:13:03.010 --> 00:13:06.580 align:middle line:84% you burn fuel, but you just take a hot shower, 00:13:06.580 --> 00:13:09.190 align:middle line:90% that's where you generate heat. 00:13:09.190 --> 00:13:13.930 align:middle line:84% So this is a, say now you're talking about combined heat 00:13:13.930 --> 00:13:16.210 align:middle line:90% and power in your household. 00:13:16.210 --> 00:13:20.890 align:middle line:84% And fundamentally, of course, the solar is also the heat. 00:13:20.890 --> 00:13:24.280 align:middle line:84% So whether we can use it, with thermoelectric, 00:13:24.280 --> 00:13:27.370 align:middle line:84% you have to, at the end, calculate the cost. 00:13:27.370 --> 00:13:29.920 align:middle line:84% In the real world, they say solar, 00:13:29.920 --> 00:13:32.770 align:middle line:84% even solar is still not competitive 00:13:32.770 --> 00:13:35.680 align:middle line:84% because it hasn't reached that cost level. 00:13:35.680 --> 00:13:38.980 align:middle line:84% So if you look at what's the solar cost. 00:13:38.980 --> 00:13:45.370 align:middle line:84% And per dollar watt, of course, it's progressively decreasing. 00:13:45.370 --> 00:13:49.630 align:middle line:84% And now the best, I think, the first solar 00:13:49.630 --> 00:13:55.400 align:middle line:84% is claiming they're about slightly below $1 per watt. 00:13:55.400 --> 00:14:00.680 align:middle line:84% So to reach the grid part, some people 00:14:00.680 --> 00:14:03.530 align:middle line:84% say already it depends on where you are. 00:14:03.530 --> 00:14:06.900 align:middle line:84% But I think, let's say, this is ideally equal. 00:14:06.900 --> 00:14:09.410 align:middle line:84% So ideally, you say this is where 00:14:09.410 --> 00:14:12.110 align:middle line:90% you want to reach the grid. 00:14:12.110 --> 00:14:14.210 align:middle line:84% When you say grid parity is really 00:14:14.210 --> 00:14:19.430 align:middle line:84% compete against the coal generation type of technology. 00:14:19.430 --> 00:14:22.190 align:middle line:90% So it's a factor of three. 00:14:22.190 --> 00:14:27.185 align:middle line:84% And it doesn't sound to be very far, but it is a lot there. 00:14:27.185 --> 00:14:30.530 align:middle line:84% Of course, there are a lot of challenges to get there. 00:14:30.530 --> 00:14:32.600 align:middle line:90% Let's see. 00:14:32.600 --> 00:14:35.420 align:middle line:84% Thermoelectrics, I give one example. 00:14:35.420 --> 00:14:37.430 align:middle line:90% I think it's not the-- 00:14:37.430 --> 00:14:40.880 align:middle line:84% actually it could have say, even in the large scale 00:14:40.880 --> 00:14:42.530 align:middle line:90% for the application. 00:14:42.530 --> 00:14:47.420 align:middle line:84% Because this is actually a measurement found in the lab. 00:14:47.420 --> 00:14:52.250 align:middle line:84% So it's just a two legs, one and two. 00:14:52.250 --> 00:14:57.270 align:middle line:84% Each leg is about 1.5 millimeter cube. 00:14:57.270 --> 00:15:04.680 align:middle line:84% And so, this two leg, you have about 190 degree delta t, 00:15:04.680 --> 00:15:07.890 align:middle line:90% you generate about 80 milliwatt. 00:15:07.890 --> 00:15:10.680 align:middle line:84% And 80 megawatt, so if I take that, 00:15:10.680 --> 00:15:14.400 align:middle line:84% I go to calculate the weight of the two legs and calculate 00:15:14.400 --> 00:15:19.270 align:middle line:84% the material price, and calculate the cost for this 80 00:15:19.270 --> 00:15:21.330 align:middle line:84% mega from a material perspective, 00:15:21.330 --> 00:15:25.650 align:middle line:84% and they got about $0.10 per watt materials. 00:15:25.650 --> 00:15:31.050 align:middle line:84% And that's just to say, this is almost like a bottom line. 00:15:31.050 --> 00:15:33.690 align:middle line:84% So you have to pay for the materials. 00:15:33.690 --> 00:15:35.700 align:middle line:84% And of course, you have to manufacturer it, 00:15:35.700 --> 00:15:38.310 align:middle line:84% you have many other things together. 00:15:38.310 --> 00:15:44.100 align:middle line:84% So the question is, do you go from here, 00:15:44.100 --> 00:15:50.160 align:middle line:84% say, to build anything that is cheap enough to be adopted? 00:15:50.160 --> 00:15:54.630 align:middle line:84% Of course, the efficiency, there are many constraints. 00:15:54.630 --> 00:15:58.230 align:middle line:84% In fact, the biggest constraint for thermoelectrics 00:15:58.230 --> 00:16:02.380 align:middle line:84% is, I think, of course, efficiency is the one. 00:16:02.380 --> 00:16:05.500 align:middle line:84% But the very different from solar is-- 00:16:05.500 --> 00:16:09.010 align:middle line:84% you have to have heat incoming and heat rejection. 00:16:09.010 --> 00:16:11.500 align:middle line:84% And those systems, of your systems, 00:16:11.500 --> 00:16:16.570 align:middle line:84% could be much more expensive than just a thermoelectric one. 00:16:16.570 --> 00:16:22.960 align:middle line:84% So again, this is where I think a lot of you engineers really 00:16:22.960 --> 00:16:27.370 align:middle line:84% think where it could be used, where there are 00:16:27.370 --> 00:16:31.270 align:middle line:90% a lot of room for innovation. 00:16:31.270 --> 00:16:37.360 align:middle line:84% And the workshop I went to was organized by the Department 00:16:37.360 --> 00:16:39.940 align:middle line:90% of Energy, energy efficiency. 00:16:39.940 --> 00:16:44.830 align:middle line:84% And the focus there is the automobile, 00:16:44.830 --> 00:16:49.480 align:middle line:84% because the automobile now is the biggest 00:16:49.480 --> 00:16:54.100 align:middle line:84% driver for thermoelectrics because there's 00:16:54.100 --> 00:16:57.130 align:middle line:90% the waste heat from the engine. 00:16:57.130 --> 00:17:02.080 align:middle line:84% And so, if you think about 40% of the heat 00:17:02.080 --> 00:17:04.730 align:middle line:84% actually goes through the exhaust. 00:17:04.730 --> 00:17:09.710 align:middle line:84% And it's a really government legislation. 00:17:09.710 --> 00:17:17.180 align:middle line:84% The government, particularly in Europe, there is legislation, 00:17:17.180 --> 00:17:22.670 align:middle line:84% I forgot the year, I have loads, that a few years down 00:17:22.670 --> 00:17:25.910 align:middle line:84% the road and the CO2 emission, there's 00:17:25.910 --> 00:17:30.090 align:middle line:90% a standard per 100 kilometer. 00:17:30.090 --> 00:17:35.160 align:middle line:84% And if you are one gram above that, 00:17:35.160 --> 00:17:38.790 align:middle line:90% it's a penalty of 95 euros. 00:17:38.790 --> 00:17:43.300 align:middle line:90% So with the 95 euros-- 00:17:43.300 --> 00:17:48.970 align:middle line:84% so if you-- roughly you need a 3% fuel saving to get there, 00:17:48.970 --> 00:17:53.230 align:middle line:90% to get that three grams. 00:17:53.230 --> 00:18:01.180 align:middle line:84% And so that means the system has to be around 300 euros 00:18:01.180 --> 00:18:06.730 align:middle line:84% to have a few hundred, watt of 300 watt, let's say, 00:18:06.730 --> 00:18:08.930 align:middle line:90% 300 watt of electric power. 00:18:08.930 --> 00:18:11.970 align:middle line:84% So roughly, you have a $1 per watt range 00:18:11.970 --> 00:18:13.220 align:middle line:90% they are calculating in there. 00:18:13.220 --> 00:18:15.850 align:middle line:90% 00:18:15.850 --> 00:18:17.500 align:middle line:90% I thought it's a-- 00:18:17.500 --> 00:18:21.010 align:middle line:84% automobile is the hardest problem. 00:18:21.010 --> 00:18:25.550 align:middle line:84% In fact, I was-- a BMW guy was saying the same thing. 00:18:25.550 --> 00:18:30.580 align:middle line:84% I was-- I agree with him, and I thought a lot of in the past. 00:18:30.580 --> 00:18:32.940 align:middle line:84% And if you can do automobile, you can do anywhere. 00:18:32.940 --> 00:18:35.500 align:middle line:84% So if that area is successful, I think 00:18:35.500 --> 00:18:37.390 align:middle line:90% there are a lot more impact. 00:18:37.390 --> 00:18:39.460 align:middle line:84% But unfortunately, that's also hardest 00:18:39.460 --> 00:18:46.810 align:middle line:84% because it has to be very space-constrained, very 00:18:46.810 --> 00:18:49.600 align:middle line:90% efficient, weight-constrained. 00:18:49.600 --> 00:18:51.550 align:middle line:84% When you add a weight to the system, 00:18:51.550 --> 00:18:55.450 align:middle line:90% you actually create a penalty. 00:18:55.450 --> 00:18:58.240 align:middle line:84% The efficiency of the automobile drops. 00:18:58.240 --> 00:19:00.550 align:middle line:84% So there are a lot of constraints, 00:19:00.550 --> 00:19:03.880 align:middle line:90% but see, the dynamics-- 00:19:03.880 --> 00:19:07.520 align:middle line:84% it's there where the government is putting money. 00:19:07.520 --> 00:19:09.710 align:middle line:84% So unfortunately, thermoelectrics 00:19:09.710 --> 00:19:13.280 align:middle line:84% is very dynamic in terms of dynamic situation 00:19:13.280 --> 00:19:16.640 align:middle line:84% where the money came from, automobile, is driving hardest 00:19:16.640 --> 00:19:18.620 align:middle line:90% application. 00:19:18.620 --> 00:19:22.040 align:middle line:84% And which is not quite sure whether it will be 00:19:22.040 --> 00:19:25.250 align:middle line:90% completely successful or not. 00:19:25.250 --> 00:19:28.100 align:middle line:84% You are tackling the hardest problem. 00:19:28.100 --> 00:19:31.520 align:middle line:84% But I thought that there are many other areas where 00:19:31.520 --> 00:19:33.590 align:middle line:90% you could innovate. 00:19:33.590 --> 00:19:35.600 align:middle line:90% Maybe it's not as hard, I think. 00:19:35.600 --> 00:19:38.630 align:middle line:84% Of course, the challenge is where the money is. 00:19:38.630 --> 00:19:42.900 align:middle line:90% So chicken-egg problem. 00:19:42.900 --> 00:19:47.220 align:middle line:84% But I think we need more success to stimulate 00:19:47.220 --> 00:19:53.530 align:middle line:84% the interest from both government and the public. 00:19:53.530 --> 00:19:55.720 align:middle line:84% And clearly, you see, I'm on the-- which 00:19:55.720 --> 00:19:58.950 align:middle line:84% side of the fence because I'm biased. 00:19:58.950 --> 00:20:02.610 align:middle line:90% 00:20:02.610 --> 00:20:06.180 align:middle line:90% Now let's come back to designs. 00:20:06.180 --> 00:20:08.850 align:middle line:90% 00:20:08.850 --> 00:20:14.730 align:middle line:84% So I know that for many of you, it's a very steep dive. 00:20:14.730 --> 00:20:18.720 align:middle line:90% We start from nothing. 00:20:18.720 --> 00:20:20.778 align:middle line:90% I assume that the-- 00:20:20.778 --> 00:20:24.810 align:middle line:84% I hear from the engineers is a lot of those concepts. 00:20:24.810 --> 00:20:31.260 align:middle line:84% I was reading your report, a lot of those concepts are foreign, 00:20:31.260 --> 00:20:33.240 align:middle line:90% and we should expect it. 00:20:33.240 --> 00:20:34.860 align:middle line:90% Let's see. 00:20:34.860 --> 00:20:36.900 align:middle line:84% What I'm going to do-- to hope is 00:20:36.900 --> 00:20:42.100 align:middle line:84% to bring you to where I was yesterday, in the least today 00:20:42.100 --> 00:20:45.330 align:middle line:84% and the next lecture-- will be part of the next lecture. 00:20:45.330 --> 00:20:47.820 align:middle line:84% And where I was yesterday, there was 00:20:47.820 --> 00:20:50.580 align:middle line:84% talking about the most current topic 00:20:50.580 --> 00:20:51.905 align:middle line:90% in thermoelectric research. 00:20:51.905 --> 00:20:54.870 align:middle line:90% 00:20:54.870 --> 00:21:01.980 align:middle line:84% So last time we're talking about the energy levels in solids. 00:21:01.980 --> 00:21:04.140 align:middle line:84% We talked about the lattice vibration, 00:21:04.140 --> 00:21:07.870 align:middle line:84% where the quantum of lattice vibration 00:21:07.870 --> 00:21:11.710 align:middle line:84% is a phonon, so basic energy [INAUDIBLE] of vibration. 00:21:11.710 --> 00:21:14.290 align:middle line:90% And of course, most of you-- 00:21:14.290 --> 00:21:19.090 align:middle line:84% I had a colleague when I was a UCLA faculty member. 00:21:19.090 --> 00:21:24.250 align:middle line:84% And he said in my course, three courses down the road, 00:21:24.250 --> 00:21:27.830 align:middle line:84% see, I don't still don't understand what is a phonon. 00:21:27.830 --> 00:21:30.110 align:middle line:90% It's not a real particle. 00:21:30.110 --> 00:21:32.690 align:middle line:84% Phonon is a collective vibration. 00:21:32.690 --> 00:21:39.800 align:middle line:84% And you have a lot more easier acceptance 00:21:39.800 --> 00:21:42.110 align:middle line:90% to the name of photon. 00:21:42.110 --> 00:21:45.650 align:middle line:84% But if you go to think about what is the photon, 00:21:45.650 --> 00:21:48.050 align:middle line:90% it's the same-- 00:21:48.050 --> 00:21:50.260 align:middle line:84% you must have the same confusion there. 00:21:50.260 --> 00:21:51.890 align:middle line:90% What is a photon? 00:21:51.890 --> 00:21:53.810 align:middle line:90% Photon is just people talk. 00:21:53.810 --> 00:21:56.570 align:middle line:84% It's the electromagnetic wave, the quantized form 00:21:56.570 --> 00:22:02.820 align:middle line:84% of electromagnetic wave, the quanta of the electron. 00:22:02.820 --> 00:22:06.300 align:middle line:84% And I took a course in quantum mechanics, 00:22:06.300 --> 00:22:08.820 align:middle line:84% and midway there was a substitute professor 00:22:08.820 --> 00:22:10.410 align:middle line:90% at Berkeley. 00:22:10.410 --> 00:22:13.510 align:middle line:84% And he asked the class, anybody understood? 00:22:13.510 --> 00:22:16.200 align:middle line:84% No student dared to raise their hand, 00:22:16.200 --> 00:22:17.740 align:middle line:84% understand the quantum mechanics. 00:22:17.740 --> 00:22:18.720 align:middle line:90% That's correct answer. 00:22:18.720 --> 00:22:20.280 align:middle line:90% Nobody else it. 00:22:20.280 --> 00:22:24.240 align:middle line:84% But see, what I think-- so take it-- let's go from there. 00:22:24.240 --> 00:22:28.830 align:middle line:84% The phonon spectra in solids, and what's important in solids 00:22:28.830 --> 00:22:31.510 align:middle line:90% is their crystal structure. 00:22:31.510 --> 00:22:34.680 align:middle line:84% So in each crystalline directions, 00:22:34.680 --> 00:22:39.120 align:middle line:84% there are different, say, mass springs 00:22:39.120 --> 00:22:42.780 align:middle line:84% because the spring constant is different, even 00:22:42.780 --> 00:22:45.540 align:middle line:90% though it's the same atoms. 00:22:45.540 --> 00:22:50.280 align:middle line:84% Say, electrons in solid in different crystallographic 00:22:50.280 --> 00:22:56.280 align:middle line:84% directions, there are different energy levels for the electrons. 00:22:56.280 --> 00:23:00.570 align:middle line:84% So we started with the simplest picture. 00:23:00.570 --> 00:23:03.290 align:middle line:84% But I said, I want you to get comfortable. 00:23:03.290 --> 00:23:06.100 align:middle line:84% If you read any papers, you'll see 00:23:06.100 --> 00:23:09.310 align:middle line:84% people show those complicated lines 00:23:09.310 --> 00:23:13.300 align:middle line:84% where in each crystallographic direction 00:23:13.300 --> 00:23:15.980 align:middle line:84% that's the different crystallographic direction. 00:23:15.980 --> 00:23:18.400 align:middle line:90% Very often use the symbols. 00:23:18.400 --> 00:23:23.980 align:middle line:84% And those are wave vectors, different wave vectors. 00:23:23.980 --> 00:23:26.670 align:middle line:90% Wave vector is 2 pi over lambda. 00:23:26.670 --> 00:23:29.500 align:middle line:84% So we think about the wavelengths, the waves. 00:23:29.500 --> 00:23:32.800 align:middle line:84% Different wavelengths have different-- 00:23:32.800 --> 00:23:36.100 align:middle line:84% each wavelength has a corresponding vibrational 00:23:36.100 --> 00:23:37.570 align:middle line:90% frequency. 00:23:37.570 --> 00:23:39.760 align:middle line:90% So that's the phonon spectrum. 00:23:39.760 --> 00:23:43.990 align:middle line:84% And also shown at the end here, this 00:23:43.990 --> 00:23:48.340 align:middle line:84% is another concept that we introduced, density of states. 00:23:48.340 --> 00:23:51.310 align:middle line:84% So it's a number of quantum mechanical modes 00:23:51.310 --> 00:23:55.640 align:middle line:84% or quantum mechanical states at, in this case, 00:23:55.640 --> 00:23:58.730 align:middle line:90% per frequency interval. 00:23:58.730 --> 00:24:01.070 align:middle line:90% So it's a differentiable. 00:24:01.070 --> 00:24:04.010 align:middle line:84% So you can integrate this density of states 00:24:04.010 --> 00:24:08.720 align:middle line:84% over all frequency to get how many quantum states you have. 00:24:08.720 --> 00:24:13.040 align:middle line:90% So that's the phonons. 00:24:13.040 --> 00:24:16.520 align:middle line:84% And the electron, again, you see here, 00:24:16.520 --> 00:24:19.430 align:middle line:84% different crystallographic direction, there 00:24:19.430 --> 00:24:25.160 align:middle line:84% is a different energy for the electrons, a different wave 00:24:25.160 --> 00:24:29.720 align:middle line:84% vector, which means the electron wave different wavelengths have 00:24:29.720 --> 00:24:30.950 align:middle line:90% different energy. 00:24:30.950 --> 00:24:37.760 align:middle line:84% And this is the case theta bandgap, not bandgap. 00:24:37.760 --> 00:24:42.710 align:middle line:84% In the case of silicon, the minimum of the conduction band 00:24:42.710 --> 00:24:47.300 align:middle line:84% and maximum of the valence band, the another safe spot, 00:24:47.300 --> 00:24:49.730 align:middle line:84% that's the indirect semiconductor. 00:24:49.730 --> 00:24:54.090 align:middle line:84% And it's really this whether you have gap 00:24:54.090 --> 00:24:58.830 align:middle line:84% or not that determine whether you are metal, semiconductor, 00:24:58.830 --> 00:24:59.880 align:middle line:90% insulator. 00:24:59.880 --> 00:25:02.520 align:middle line:84% The insulator is a much larger gap. 00:25:02.520 --> 00:25:09.300 align:middle line:84% Semiconductor is a gap that's in the less than 3 electron volts. 00:25:09.300 --> 00:25:13.240 align:middle line:84% And gallium arsenide is direct gap, minimum, 00:25:13.240 --> 00:25:17.490 align:middle line:84% maximum is at the same wave vector location. 00:25:17.490 --> 00:25:22.630 align:middle line:84% And they have very different optical properties. 00:25:22.630 --> 00:25:30.900 align:middle line:84% And then we give an example of how to calculate, again, 00:25:30.900 --> 00:25:32.220 align:middle line:90% [INAUDIBLE]. 00:25:32.220 --> 00:25:37.830 align:middle line:84% So how to calculate how many electrons we have in the-- so 00:25:37.830 --> 00:25:39.870 align:middle line:84% here is the most of those electron 00:25:39.870 --> 00:25:43.470 align:middle line:84% is in this region, the minimum of the conduction band. 00:25:43.470 --> 00:25:47.490 align:middle line:84% And when we do the calculation, we 00:25:47.490 --> 00:25:51.840 align:middle line:84% say this sub-states, that's the number of states per unit energy 00:25:51.840 --> 00:25:52.470 align:middle line:90% interval. 00:25:52.470 --> 00:25:55.500 align:middle line:84% Of course, we went through the summation 00:25:55.500 --> 00:25:58.290 align:middle line:84% to introduce the density of states. 00:25:58.290 --> 00:26:01.680 align:middle line:84% And then this is also the number of quantum states. 00:26:01.680 --> 00:26:04.540 align:middle line:84% And each quantum state, how many electrons we have, 00:26:04.540 --> 00:26:06.330 align:middle line:84% that's the Fermi-Dirac distribution. 00:26:06.330 --> 00:26:08.370 align:middle line:90% And they integrate. 00:26:08.370 --> 00:26:12.390 align:middle line:84% So if you do a parabolic event, that's the-- 00:26:12.390 --> 00:26:15.540 align:middle line:84% say parabola, we can approximate-- 00:26:15.540 --> 00:26:20.520 align:middle line:84% always approximate, not always, but as approximation, 00:26:20.520 --> 00:26:23.940 align:middle line:84% when I have a minimum or maximum, 00:26:23.940 --> 00:26:26.900 align:middle line:84% I can say the first order derivative is 0. 00:26:26.900 --> 00:26:29.670 align:middle line:84% So the Taylor expansion gave me the second order. 00:26:29.670 --> 00:26:30.960 align:middle line:90% That's a parabolic band. 00:26:30.960 --> 00:26:36.420 align:middle line:84% So with that parabolic band approximation I have-- 00:26:36.420 --> 00:26:41.190 align:middle line:84% I can do a [INAUDIBLE] statistics. 00:26:41.190 --> 00:26:44.790 align:middle line:84% I can do this integration to get the relation 00:26:44.790 --> 00:26:50.690 align:middle line:84% of how many electrons is determined by ec minus mu. 00:26:50.690 --> 00:26:53.920 align:middle line:90% That's this guy. 00:26:53.920 --> 00:26:57.380 align:middle line:84% It's this guy is really the [INAUDIBLE] potential. 00:26:57.380 --> 00:26:59.330 align:middle line:84% So [INAUDIBLE] potential determine 00:26:59.330 --> 00:27:03.270 align:middle line:84% how many the number of particles, electrons. 00:27:03.270 --> 00:27:09.720 align:middle line:84% And here is, say, the related to the effective mass, 00:27:09.720 --> 00:27:16.400 align:middle line:84% how flat this mass is, the curvature, how flat is this guy. 00:27:16.400 --> 00:27:20.970 align:middle line:84% So those are some of the key concepts that we 00:27:20.970 --> 00:27:25.160 align:middle line:90% learned in the last lecture. 00:27:25.160 --> 00:27:28.790 align:middle line:90% And today I'm going to-- 00:27:28.790 --> 00:27:31.670 align:middle line:90% we learn the phenomenon. 00:27:31.670 --> 00:27:36.620 align:middle line:84% You read also Goodsmith's chapter on Seebeck effect. 00:27:36.620 --> 00:27:40.970 align:middle line:84% And today we're going to have more mathematics, 00:27:40.970 --> 00:27:45.060 align:middle line:84% going to have expressions for those coefficients. 00:27:45.060 --> 00:27:47.960 align:middle line:84% What determine the electric conductivity? 00:27:47.960 --> 00:27:50.390 align:middle line:84% What determine the Seebeck coefficient? 00:27:50.390 --> 00:27:52.910 align:middle line:84% What determine the thermal conductivity? 00:27:52.910 --> 00:27:55.340 align:middle line:90% So that's the goal here. 00:27:55.340 --> 00:28:00.170 align:middle line:84% And I will still use the same picture 00:28:00.170 --> 00:28:05.960 align:middle line:84% I presented in the first class where I say, 00:28:05.960 --> 00:28:09.800 align:middle line:84% I look at how many particles are going from left to right 00:28:09.800 --> 00:28:12.260 align:middle line:84% and how many particles are from right to left, 00:28:12.260 --> 00:28:14.750 align:middle line:84% and the difference being the flux. 00:28:14.750 --> 00:28:17.660 align:middle line:84% And this flux could be heat flux. 00:28:17.660 --> 00:28:19.790 align:middle line:90% It could be charge flux. 00:28:19.790 --> 00:28:22.640 align:middle line:84% And so, with that, we will derive 00:28:22.640 --> 00:28:26.220 align:middle line:84% will have the mathematical expressions for all 00:28:26.220 --> 00:28:29.120 align:middle line:90% the transport coefficients. 00:28:29.120 --> 00:28:35.130 align:middle line:84% So let me start with the electrical conduction. 00:28:35.130 --> 00:28:39.510 align:middle line:84% And electric conduction, in the simplest picture, 00:28:39.510 --> 00:28:44.020 align:middle line:84% would consider an isothermal electrical conductor. 00:28:44.020 --> 00:28:48.120 align:middle line:84% So there's isothermal, there is no Seebeck effect, just 00:28:48.120 --> 00:28:50.680 align:middle line:90% a simple potential flow. 00:28:50.680 --> 00:28:57.510 align:middle line:84% I have an electric field, and the electric field here, this 00:28:57.510 --> 00:29:00.570 align:middle line:84% is the most, for mechanical engineering, including me, 00:29:00.570 --> 00:29:03.180 align:middle line:84% the most troublesome point is the electron 00:29:03.180 --> 00:29:05.250 align:middle line:90% has a negative charge. 00:29:05.250 --> 00:29:09.600 align:middle line:84% So when I draw a field and say and charge go that way, 00:29:09.600 --> 00:29:12.150 align:middle line:90% that's a talk about electron. 00:29:12.150 --> 00:29:17.610 align:middle line:84% And now, of course, under a field, 00:29:17.610 --> 00:29:19.530 align:middle line:90% electron experience a force. 00:29:19.530 --> 00:29:22.650 align:middle line:90% So F equals ma. 00:29:22.650 --> 00:29:29.670 align:middle line:84% Force of the charge experience is the charge 00:29:29.670 --> 00:29:31.110 align:middle line:90% times the electric field. 00:29:31.110 --> 00:29:33.000 align:middle line:84% Then you can charge for electrons. 00:29:33.000 --> 00:29:34.956 align:middle line:90% F equals ma. 00:29:34.956 --> 00:29:42.294 align:middle line:84% And so, that's the simple Newton's law of motion. 00:29:42.294 --> 00:29:45.640 align:middle line:84% But the electron will not travel very far 00:29:45.640 --> 00:29:47.710 align:middle line:90% because they will collide. 00:29:47.710 --> 00:29:49.430 align:middle line:90% They collide with each other. 00:29:49.430 --> 00:29:53.830 align:middle line:84% They collide with-- by the phonon, 00:29:53.830 --> 00:29:58.700 align:middle line:84% the lattice vibration also distort their motion. 00:29:58.700 --> 00:30:03.290 align:middle line:84% So once in a while, between the collision, they go straight. 00:30:03.290 --> 00:30:06.390 align:middle line:84% Under the field, due to one collision 00:30:06.390 --> 00:30:08.750 align:middle line:84% they will change direction, trajectory. 00:30:08.750 --> 00:30:15.440 align:middle line:84% So the terminal velocity, I can do a integration of this, 00:30:15.440 --> 00:30:17.390 align:middle line:90% So I do a integration. 00:30:17.390 --> 00:30:23.420 align:middle line:84% I say, OK, this is the collision part where the free acceleration 00:30:23.420 --> 00:30:24.960 align:middle line:90% time, you can think that way. 00:30:24.960 --> 00:30:28.790 align:middle line:84% And I say, this is the velocity the electron will 00:30:28.790 --> 00:30:32.660 align:middle line:84% get between each collision, the terminal velocity, 00:30:32.660 --> 00:30:34.820 align:middle line:84% that's also called the drift velocity. 00:30:34.820 --> 00:30:37.970 align:middle line:84% So you integrate that, you get drift velocity. 00:30:37.970 --> 00:30:45.710 align:middle line:84% And we can also write the e pi e tau divided by m as a mu. 00:30:45.710 --> 00:30:49.850 align:middle line:84% And the mu is called the mobility, it's [INAUDIBLE]. 00:30:49.850 --> 00:30:54.840 align:middle line:84% So we have velocity is proportional to electric field, 00:30:54.840 --> 00:30:57.770 align:middle line:84% drift velocity proportional to electric field 00:30:57.770 --> 00:31:02.290 align:middle line:84% through the proportionality constant the mobility. 00:31:02.290 --> 00:31:07.210 align:middle line:84% And now, once I have the each electron drift velocity, 00:31:07.210 --> 00:31:10.220 align:middle line:90% I can calculate current easily. 00:31:10.220 --> 00:31:10.720 align:middle line:90% Why? 00:31:10.720 --> 00:31:13.240 align:middle line:90% The current is just a-- 00:31:13.240 --> 00:31:15.980 align:middle line:90% so let me just add one more. 00:31:15.980 --> 00:31:21.490 align:middle line:84% The mean free path is the time between the collision times-- 00:31:21.490 --> 00:31:24.260 align:middle line:84% now I don't use this drift velocity. 00:31:24.260 --> 00:31:27.190 align:middle line:84% This way I put a thermal velocity. 00:31:27.190 --> 00:31:32.800 align:middle line:84% So what I mean is electron, they have two part velocity. 00:31:32.800 --> 00:31:36.580 align:middle line:84% One is they are doing thermal random motion. 00:31:36.580 --> 00:31:40.880 align:middle line:84% And in fact, that's a very high speed, 10 to the 6 meter 00:31:40.880 --> 00:31:42.350 align:middle line:90% per second. 00:31:42.350 --> 00:31:44.300 align:middle line:90% It is very fast. 00:31:44.300 --> 00:31:50.900 align:middle line:84% And so, and of course, so they do a random motion, 00:31:50.900 --> 00:31:52.890 align:middle line:84% that's a random thermal velocity. 00:31:52.890 --> 00:31:56.000 align:middle line:84% And then under field they have superimposed 00:31:56.000 --> 00:31:59.420 align:middle line:84% on that thermal velocity is a drift velocity. 00:31:59.420 --> 00:32:03.980 align:middle line:84% And for mechanical engineer, that's the same with convection. 00:32:03.980 --> 00:32:11.480 align:middle line:84% Molecules move about 300 meter per second in this room. 00:32:11.480 --> 00:32:14.030 align:middle line:84% Let's say, the average velocity is 0. 00:32:14.030 --> 00:32:17.870 align:middle line:84% The convection is when the average velocity is not 0. 00:32:17.870 --> 00:32:20.330 align:middle line:84% So this is the convection velocity. 00:32:20.330 --> 00:32:23.320 align:middle line:84% That's the molecule random velocity. 00:32:23.320 --> 00:32:27.610 align:middle line:84% And now, so this is the mean free path times-- 00:32:27.610 --> 00:32:29.680 align:middle line:84% so this is the collision, the distance 00:32:29.680 --> 00:32:32.150 align:middle line:90% between successive collision. 00:32:32.150 --> 00:32:34.445 align:middle line:90% That's the mean free path. 00:32:34.445 --> 00:32:35.320 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:32:35.320 --> 00:32:35.945 align:middle line:90% GANG CHEN: Yes. 00:32:35.945 --> 00:32:39.400 align:middle line:84% AUDIENCE: So this drift velocity is basically [INAUDIBLE]? 00:32:39.400 --> 00:32:40.130 align:middle line:90% 00:32:40.130 --> 00:32:40.870 align:middle line:90% GANG CHEN: Right. 00:32:40.870 --> 00:32:43.480 align:middle line:84% AUDIENCE: And the terminal velocity is already 00:32:43.480 --> 00:32:45.300 align:middle line:90% existing between [INAUDIBLE]? 00:32:45.300 --> 00:32:46.540 align:middle line:90% GANG CHEN: Right. 00:32:46.540 --> 00:32:50.440 align:middle line:84% So even typically drift velocity is much smaller 00:32:50.440 --> 00:32:51.950 align:middle line:90% than the thermal velocity. 00:32:51.950 --> 00:32:54.190 align:middle line:84% Just the same as when we do convection. 00:32:54.190 --> 00:32:56.290 align:middle line:84% You're electric engineer, so that's easier. 00:32:56.290 --> 00:32:58.180 align:middle line:84% Let's say when we do convection, it's 00:32:58.180 --> 00:33:01.780 align:middle line:84% a meter, 10 meter per second is pretty fast, wind. 00:33:01.780 --> 00:33:07.240 align:middle line:84% But the molecule is 300 meter per second is moving around. 00:33:07.240 --> 00:33:11.920 align:middle line:84% Of course, the electron thermal velocity could be 10 to the 6. 00:33:11.920 --> 00:33:12.440 align:middle line:90% Yes. 00:33:12.440 --> 00:33:14.350 align:middle line:84% AUDIENCE: Why is it the thermal velocity 0? 00:33:14.350 --> 00:33:15.560 align:middle line:90% GANG CHEN: Thermal velocity? 00:33:15.560 --> 00:33:15.880 align:middle line:90% AUDIENCE: Yeah. 00:33:15.880 --> 00:33:16.150 align:middle line:90% GANG CHEN: Ah. 00:33:16.150 --> 00:33:16.983 align:middle line:90% [INTERPOSING VOICES] 00:33:16.983 --> 00:33:19.420 align:middle line:84% GANG CHEN: Anything, unless you go to 0 Kelvin. 00:33:19.420 --> 00:33:21.400 align:middle line:84% AUDIENCE: But the average, not the repeat-- 00:33:21.400 --> 00:33:22.990 align:middle line:84% is that like the root mean squared? 00:33:22.990 --> 00:33:26.260 align:middle line:84% The average density has to be going in each direction, right? 00:33:26.260 --> 00:33:26.930 align:middle line:90% GANG CHEN: Yeah. 00:33:26.930 --> 00:33:32.815 align:middle line:84% So the average of velocity is 0, but the magnitude is not 0. 00:33:32.815 --> 00:33:33.315 align:middle line:90% Right? 00:33:33.315 --> 00:33:33.982 align:middle line:90% AUDIENCE: Right. 00:33:33.982 --> 00:33:35.590 align:middle line:84% But if any individual electrons use-- 00:33:35.590 --> 00:33:36.655 align:middle line:90% which one would that be? 00:33:36.655 --> 00:33:38.030 align:middle line:84% GANG CHEN: This is the magnitude. 00:33:38.030 --> 00:33:39.762 align:middle line:90% This is not the vector velocity. 00:33:39.762 --> 00:33:40.720 align:middle line:90% It's the magnitude of-- 00:33:40.720 --> 00:33:43.175 align:middle line:84% AUDIENCE: So of each, it's not an ensemble property? 00:33:43.175 --> 00:33:44.300 align:middle line:90% GANG CHEN: It's an average. 00:33:44.300 --> 00:33:45.580 align:middle line:90% It's a rough thing. 00:33:45.580 --> 00:33:47.005 align:middle line:90% So it's an ensemble property. 00:33:47.005 --> 00:33:48.880 align:middle line:84% AUDIENCE: So it's like the root mean squared? 00:33:48.880 --> 00:33:49.588 align:middle line:90% GANG CHEN: Right. 00:33:49.588 --> 00:33:57.850 align:middle line:84% So, OK, how you estimate it is 1/2 kvt, we said before, 00:33:57.850 --> 00:34:00.970 align:middle line:90% roughly 1/2 mv squared. 00:34:00.970 --> 00:34:05.170 align:middle line:84% So that's your thermal, because this is the thermal energy. 00:34:05.170 --> 00:34:07.960 align:middle line:84% And the kinetic energy, that's the kinetic velocity. 00:34:07.960 --> 00:34:08.739 align:middle line:90% AUDIENCE: OK. 00:34:08.739 --> 00:34:11.620 align:middle line:84% GANG CHEN: And the mass of electron very small. 00:34:11.620 --> 00:34:15.330 align:middle line:84% That's why it's much faster than the molecules. 00:34:15.330 --> 00:34:19.045 align:middle line:90% 00:34:19.045 --> 00:34:24.940 align:middle line:84% So now it's easy, because the current-- 00:34:24.940 --> 00:34:25.940 align:middle line:90% what's a current? 00:34:25.940 --> 00:34:30.219 align:middle line:84% Current is the left motion of a charge. 00:34:30.219 --> 00:34:36.130 align:middle line:84% So the electron coulomb number density 00:34:36.130 --> 00:34:40.980 align:middle line:84% per unit volume, number of electrons per unit volume, 00:34:40.980 --> 00:34:44.409 align:middle line:90% times here the drift velocity. 00:34:44.409 --> 00:34:47.409 align:middle line:90% This is the convection current. 00:34:47.409 --> 00:34:50.170 align:middle line:90% That's the electric current. 00:34:50.170 --> 00:34:52.780 align:middle line:84% And you go to check the unit, you should-- 00:34:52.780 --> 00:34:55.102 align:middle line:90% I should have a unit here. 00:34:55.102 --> 00:34:56.570 align:middle line:90% I didn't put it there. 00:34:56.570 --> 00:34:58.740 align:middle line:84% That's the amp per meter squared. 00:34:58.740 --> 00:35:01.270 align:middle line:90% 00:35:01.270 --> 00:35:05.960 align:middle line:84% If you do a heat transfer, you will be watt per meter squared. 00:35:05.960 --> 00:35:07.060 align:middle line:90% This is a flux. 00:35:07.060 --> 00:35:08.890 align:middle line:90% You go to look at the unit. 00:35:08.890 --> 00:35:12.010 align:middle line:90% So this is a coulomb per second. 00:35:12.010 --> 00:35:14.110 align:middle line:90% Seconds come from here-- 00:35:14.110 --> 00:35:15.580 align:middle line:90% gives you amp. 00:35:15.580 --> 00:35:20.820 align:middle line:84% Here is a meter cubit, one more meter cubit, here is one meter, 00:35:20.820 --> 00:35:22.780 align:middle line:90% so give you a meter squared. 00:35:22.780 --> 00:35:26.830 align:middle line:84% So m per meter squared, that's a unit of current. 00:35:26.830 --> 00:35:27.920 align:middle line:90% What is that? 00:35:27.920 --> 00:35:29.590 align:middle line:90% That's Ohm's law. 00:35:29.590 --> 00:35:33.730 align:middle line:90% So here is a few steps. 00:35:33.730 --> 00:35:35.180 align:middle line:90% You get the picture. 00:35:35.180 --> 00:35:39.263 align:middle line:84% You learn from high school, this is the Ohm's law. 00:35:39.263 --> 00:35:40.180 align:middle line:90% You have your current. 00:35:40.180 --> 00:35:42.520 align:middle line:84% It's proportional electric conductivity 00:35:42.520 --> 00:35:44.880 align:middle line:90% times the electric potential. 00:35:44.880 --> 00:35:48.500 align:middle line:84% The electric potential, if you do electric field, 00:35:48.500 --> 00:35:51.590 align:middle line:84% electric field is the electrostatic potential 00:35:51.590 --> 00:35:53.840 align:middle line:90% gradient. 00:35:53.840 --> 00:35:56.130 align:middle line:84% So that's right into differential form. 00:35:56.130 --> 00:35:59.246 align:middle line:90% 00:35:59.246 --> 00:36:01.610 align:middle line:84% And in fact, this is a very similar-- 00:36:01.610 --> 00:36:04.760 align:middle line:84% if you take and replace this with a temperature, 00:36:04.760 --> 00:36:06.650 align:middle line:90% that's a Fourier law. 00:36:06.650 --> 00:36:11.600 align:middle line:84% So even though one is seems like a convection picture, 00:36:11.600 --> 00:36:13.910 align:middle line:84% the other seems diffusion picture. 00:36:13.910 --> 00:36:19.170 align:middle line:84% But they all collision dominate transport process. 00:36:19.170 --> 00:36:22.440 align:middle line:84% It's all collision laws, the diffusion phenomena. 00:36:22.440 --> 00:36:25.560 align:middle line:90% 00:36:25.560 --> 00:36:29.970 align:middle line:90% So that's the Ohm's law. 00:36:29.970 --> 00:36:35.500 align:middle line:84% And now let's go to the isothermal in the previous case, 00:36:35.500 --> 00:36:37.350 align:middle line:84% now I'm putting a temperature gradient. 00:36:37.350 --> 00:36:40.660 align:middle line:84% I want to consider coupled transport. 00:36:40.660 --> 00:36:43.690 align:middle line:84% Thermoelectric is a heat and charge coupling. 00:36:43.690 --> 00:36:47.110 align:middle line:84% And of course, when I have a guilty-- 00:36:47.110 --> 00:36:50.325 align:middle line:84% say, a potential, I still got that convection drift part. 00:36:50.325 --> 00:36:53.030 align:middle line:90% 00:36:53.030 --> 00:36:57.410 align:middle line:84% What's different now is that I have a temperature gradient. 00:36:57.410 --> 00:37:01.640 align:middle line:84% So the molecule or the electrons-- 00:37:01.640 --> 00:37:05.480 align:middle line:84% and I'm used to talk to mechanical molecule. 00:37:05.480 --> 00:37:12.350 align:middle line:84% So electrons here go faster than electron here. 00:37:12.350 --> 00:37:17.030 align:middle line:84% Now there is also diffusion flux of charge. 00:37:17.030 --> 00:37:19.640 align:middle line:84% So to consider that diffusion flux, 00:37:19.640 --> 00:37:22.530 align:middle line:84% I have from left to right and right to left. 00:37:22.530 --> 00:37:25.070 align:middle line:84% That's what I did for heat conduction before. 00:37:25.070 --> 00:37:28.220 align:middle line:90% So the electron flux law-- 00:37:28.220 --> 00:37:30.800 align:middle line:90% 00:37:30.800 --> 00:37:37.310 align:middle line:84% so here I have previous one from previous slide, the Ohm's law. 00:37:37.310 --> 00:37:43.780 align:middle line:84% That's the drift part because I have an electrical potential. 00:37:43.780 --> 00:37:46.900 align:middle line:84% But also I have the diffusion part. 00:37:46.900 --> 00:37:50.170 align:middle line:84% This is going from left to right. 00:37:50.170 --> 00:37:52.750 align:middle line:90% This is from right to left. 00:37:52.750 --> 00:37:55.440 align:middle line:84% Again, I carry this negative sign, negative charge. 00:37:55.440 --> 00:37:59.990 align:middle line:90% 00:37:59.990 --> 00:38:04.140 align:middle line:84% This way should be thermal velocity. 00:38:04.140 --> 00:38:06.720 align:middle line:90% I should have been more careful. 00:38:06.720 --> 00:38:10.020 align:middle line:84% It should be thermal velocity because they are ranked randomly 00:38:10.020 --> 00:38:14.390 align:middle line:84% jiggling from left to right and right to left. 00:38:14.390 --> 00:38:18.290 align:middle line:84% And the left for density, and in this region one 00:38:18.290 --> 00:38:21.670 align:middle line:84% mean free path you can go zip through. 00:38:21.670 --> 00:38:23.670 align:middle line:84% Longer than one mean free path, it will collide, 00:38:23.670 --> 00:38:25.590 align:middle line:90% change directions. 00:38:25.590 --> 00:38:27.990 align:middle line:84% So I'm only considering those whizzing 00:38:27.990 --> 00:38:31.950 align:middle line:84% by mean free path that can zip through from left to right. 00:38:31.950 --> 00:38:35.850 align:middle line:84% And then on the right to left, one mean free path 00:38:35.850 --> 00:38:39.450 align:middle line:90% can go half of them only. 00:38:39.450 --> 00:38:45.330 align:middle line:84% Because it go equally go in all directions randomly. 00:38:45.330 --> 00:38:49.110 align:middle line:84% So this is the same way I did for Fourier law, the diffusion 00:38:49.110 --> 00:38:50.280 align:middle line:90% part. 00:38:50.280 --> 00:38:53.490 align:middle line:84% And now I do the Taylor expansion, the different-- 00:38:53.490 --> 00:38:56.250 align:middle line:90% expand over at x. 00:38:56.250 --> 00:39:00.640 align:middle line:90% So I do the Taylor expansion. 00:39:00.640 --> 00:39:05.900 align:middle line:90% I have e v x square tau even vx. 00:39:05.900 --> 00:39:09.620 align:middle line:84% And in this part, I'm just talking. 00:39:09.620 --> 00:39:13.360 align:middle line:90% I messed up a negative sign. 00:39:13.360 --> 00:39:15.260 align:middle line:90% See? 00:39:15.260 --> 00:39:18.830 align:middle line:84% That's what I say, I really don't like a negative sign 00:39:18.830 --> 00:39:20.450 align:middle line:90% in the electrons-- 00:39:20.450 --> 00:39:22.600 align:middle line:90% historical mistake. 00:39:22.600 --> 00:39:23.630 align:middle line:90% Can't have that. 00:39:23.630 --> 00:39:27.905 align:middle line:90% 00:39:27.905 --> 00:39:33.840 align:middle line:84% And you know that, we just showed before, n is related-- 00:39:33.840 --> 00:39:37.690 align:middle line:84% the electron density is related to the temperature 00:39:37.690 --> 00:39:40.450 align:middle line:84% and the local chemical potential. 00:39:40.450 --> 00:39:42.790 align:middle line:84% ec minus mu is the chemical potential. 00:39:42.790 --> 00:39:47.050 align:middle line:84% That's what I reviewed from last lecture. 00:39:47.050 --> 00:39:54.680 align:middle line:84% So now temperature depends on location, space. 00:39:54.680 --> 00:39:58.190 align:middle line:84% And ec minus mu, I can think of just mu, 00:39:58.190 --> 00:40:03.180 align:middle line:84% chemical potential depends on location. 00:40:03.180 --> 00:40:08.460 align:middle line:84% Because n really-- or say, mu determine n. 00:40:08.460 --> 00:40:11.890 align:middle line:90% So both depend on location. 00:40:11.890 --> 00:40:16.100 align:middle line:84% So if I take the dn, dx derivative, I have dx, 00:40:16.100 --> 00:40:19.902 align:middle line:90% dt, dx, give you many x. 00:40:19.902 --> 00:40:21.832 align:middle line:84% AUDIENCE: The velocity is also [INAUDIBLE]? 00:40:21.832 --> 00:40:23.160 align:middle line:90% 00:40:23.160 --> 00:40:25.380 align:middle line:90% GANG CHEN: Very good questions. 00:40:25.380 --> 00:40:27.990 align:middle line:90% I can't do that simply in here. 00:40:27.990 --> 00:40:32.850 align:middle line:90% So I just do 1/3 v square. 00:40:32.850 --> 00:40:35.910 align:middle line:84% Otherwise, I'll have to put it inside dm, dx. 00:40:35.910 --> 00:40:38.920 align:middle line:84% So that's why my coefficient will not be accurate. 00:40:38.920 --> 00:40:41.510 align:middle line:90% 00:40:41.510 --> 00:40:43.790 align:middle line:84% AUDIENCE: How much is the thermal velocity 00:40:43.790 --> 00:40:46.866 align:middle line:84% different from Fermi velocity, the temperature? 00:40:46.866 --> 00:40:48.910 align:middle line:84% GANG CHEN: Ah, thermal velocity is very 00:40:48.910 --> 00:40:51.010 align:middle line:90% different from Fermi velocity. 00:40:51.010 --> 00:40:52.450 align:middle line:90% This is-- OK. 00:40:52.450 --> 00:40:55.420 align:middle line:84% So some of you know all those concepts. 00:40:55.420 --> 00:41:04.930 align:middle line:84% But if you think about what's a Fermi level-- 00:41:04.930 --> 00:41:08.470 align:middle line:90% I briefly mentioned this before. 00:41:08.470 --> 00:41:09.120 align:middle line:90% In a metal-- 00:41:09.120 --> 00:41:13.000 align:middle line:90% 00:41:13.000 --> 00:41:14.630 align:middle line:90% I can take a simplest case. 00:41:14.630 --> 00:41:19.420 align:middle line:84% This is the electron energy level. 00:41:19.420 --> 00:41:21.865 align:middle line:84% In the metal, Fermi level is here. 00:41:21.865 --> 00:41:24.640 align:middle line:90% 00:41:24.640 --> 00:41:31.660 align:middle line:84% So the energy of the electron is close to Fermi level 00:41:31.660 --> 00:41:34.870 align:middle line:84% because only those electrons are moving. 00:41:34.870 --> 00:41:39.190 align:middle line:84% The electron deep inside don't have any free space to move. 00:41:39.190 --> 00:41:44.800 align:middle line:84% So this one is the Fermi velocity. 00:41:44.800 --> 00:41:47.170 align:middle line:90% So m vf squared. 00:41:47.170 --> 00:41:51.100 align:middle line:84% So that's also-- it turns out this also 00:41:51.100 --> 00:41:53.910 align:middle line:90% is the thermal velocity. 00:41:53.910 --> 00:41:57.300 align:middle line:84% Those are the electrons, because the electrons 00:41:57.300 --> 00:42:00.090 align:middle line:90% do have this much energy. 00:42:00.090 --> 00:42:03.090 align:middle line:84% They will move around with this energy. 00:42:03.090 --> 00:42:10.690 align:middle line:84% But in the semiconductor, that's the valence band, 00:42:10.690 --> 00:42:12.660 align:middle line:90% that's conduction band. 00:42:12.660 --> 00:42:17.760 align:middle line:84% And then you dope, and your ef may be here 00:42:17.760 --> 00:42:19.060 align:middle line:90% if you don't have it doped. 00:42:19.060 --> 00:42:22.200 align:middle line:84% That's what I was drawing before. 00:42:22.200 --> 00:42:27.430 align:middle line:84% So this ef, no electrons have this ef. 00:42:27.430 --> 00:42:29.950 align:middle line:90% Electrons only in this region-- 00:42:29.950 --> 00:42:34.120 align:middle line:84% because the thermally, a small fraction of electrons go there. 00:42:34.120 --> 00:42:36.790 align:middle line:90% So those energy is really-- 00:42:36.790 --> 00:42:40.424 align:middle line:90% this is just 1/2 [INAUDIBLE]. 00:42:40.424 --> 00:42:43.120 align:middle line:90% 00:42:43.120 --> 00:42:46.220 align:middle line:84% This is the relatively-- this kinetic potential is-- 00:42:46.220 --> 00:42:49.630 align:middle line:84% let's see, relative to the kinetic energy 00:42:49.630 --> 00:42:52.800 align:middle line:90% relative to here, 0. 00:42:52.800 --> 00:42:53.300 align:middle line:90% So. 00:42:53.300 --> 00:42:56.380 align:middle line:84% So the only is about the [INAUDIBLE] about the 1/2 00:42:56.380 --> 00:42:57.485 align:middle line:90% [INAUDIBLE]. 00:42:57.485 --> 00:42:58.970 align:middle line:90% 00:42:58.970 --> 00:43:01.420 align:middle line:84% AUDIENCE: The key is the difference 00:43:01.420 --> 00:43:03.910 align:middle line:84% between the energy of the electron 00:43:03.910 --> 00:43:05.440 align:middle line:90% and the chemical potential? 00:43:05.440 --> 00:43:07.420 align:middle line:84% GANG CHEN: No, not even chemical potential, 00:43:07.420 --> 00:43:10.648 align:middle line:84% only relative to the bottom of conduction band 00:43:10.648 --> 00:43:11.440 align:middle line:90% that you see there. 00:43:11.440 --> 00:43:12.780 align:middle line:90% AUDIENCE: Oh, OK. 00:43:12.780 --> 00:43:15.855 align:middle line:84% AUDIENCE: But can you [INAUDIBLE]? 00:43:15.855 --> 00:43:16.480 align:middle line:90% GANG CHEN: Yes. 00:43:16.480 --> 00:43:18.105 align:middle line:84% AUDIENCE: Yes, so it could be anything. 00:43:18.105 --> 00:43:20.330 align:middle line:90% It could be 0 degrees or like-- 00:43:20.330 --> 00:43:22.130 align:middle line:90% GANG CHEN: Yeah. 00:43:22.130 --> 00:43:25.840 align:middle line:84% Let's say, the average energy of those electrons near that 00:43:25.840 --> 00:43:29.698 align:middle line:84% conduction band bottom is about 1/2 [INAUDIBLE]. 00:43:29.698 --> 00:43:32.200 align:middle line:90% 00:43:32.200 --> 00:43:32.700 align:middle line:90% Yeah. 00:43:32.700 --> 00:43:36.090 align:middle line:90% 00:43:36.090 --> 00:43:39.690 align:middle line:84% So I'm going to clean this, take a derivative. 00:43:39.690 --> 00:43:42.240 align:middle line:90% My sign might be screwed up. 00:43:42.240 --> 00:43:43.980 align:middle line:90% Go to check. 00:43:43.980 --> 00:43:45.410 align:middle line:90% I mix it up again here. 00:43:45.410 --> 00:43:48.420 align:middle line:90% 00:43:48.420 --> 00:43:50.400 align:middle line:90% So here is what I have. 00:43:50.400 --> 00:43:52.620 align:middle line:90% I have this derivative. 00:43:52.620 --> 00:43:55.780 align:middle line:84% And also I have dt, dx derivative. 00:43:55.780 --> 00:44:00.330 align:middle line:90% 00:44:00.330 --> 00:44:03.780 align:middle line:84% So now I have the chemical potential derivative. 00:44:03.780 --> 00:44:07.980 align:middle line:84% Phi is the electrostatic potential derivative. 00:44:07.980 --> 00:44:10.440 align:middle line:84% And it turns out, this is when you 00:44:10.440 --> 00:44:14.550 align:middle line:84% do a detailed coefficient analysis, this coefficient 00:44:14.550 --> 00:44:17.740 align:middle line:84% and this coefficient is the same. 00:44:17.740 --> 00:44:18.995 align:middle line:90% So this is the fundamental. 00:44:18.995 --> 00:44:26.710 align:middle line:84% It is also called the Einstein relation, because here is the-- 00:44:26.710 --> 00:44:34.705 align:middle line:84% related to mobility, and here is related to the diffusivity. 00:44:34.705 --> 00:44:37.450 align:middle line:84% It's chemical potential gradient gives you 00:44:37.450 --> 00:44:40.300 align:middle line:90% the diffusion of the charge. 00:44:40.300 --> 00:44:42.820 align:middle line:90% And here is the motion. 00:44:42.820 --> 00:44:45.460 align:middle line:90% So Einstein didn't do electrons. 00:44:45.460 --> 00:44:50.770 align:middle line:84% Einstein did Brownian motion, hypotheses in molecules 00:44:50.770 --> 00:44:52.000 align:middle line:90% in liquid. 00:44:52.000 --> 00:44:57.070 align:middle line:84% And he derived the relation between the molecular diffusion 00:44:57.070 --> 00:45:02.320 align:middle line:84% coefficient and molecular mobility in the liquid. 00:45:02.320 --> 00:45:04.630 align:middle line:84% And that relation turns out also to be 00:45:04.630 --> 00:45:07.150 align:middle line:84% true between electric conductivity, 00:45:07.150 --> 00:45:12.390 align:middle line:84% and here you can think that as an electron diffusivity. 00:45:12.390 --> 00:45:15.090 align:middle line:84% So this is a general for the Einstein relations. 00:45:15.090 --> 00:45:17.857 align:middle line:84% And if you generalize even more it 00:45:17.857 --> 00:45:21.210 align:middle line:84% is the fluctuation dissipation theorem. 00:45:21.210 --> 00:45:24.990 align:middle line:84% So Einstein, that's his PhD thesis. 00:45:24.990 --> 00:45:26.730 align:middle line:84% If you were born at that year, you 00:45:26.730 --> 00:45:30.690 align:middle line:84% may be writing a paper say it's very important. 00:45:30.690 --> 00:45:34.090 align:middle line:90% He did the Brownian motion. 00:45:34.090 --> 00:45:40.060 align:middle line:84% And really, it's interesting to read that. 00:45:40.060 --> 00:45:43.750 align:middle line:84% He didn't even know there was an experiment on Brownian motion. 00:45:43.750 --> 00:45:47.740 align:middle line:84% So he studied statistical thermodynamics, the other branch 00:45:47.740 --> 00:45:49.630 align:middle line:90% of statistical thermodynamics. 00:45:49.630 --> 00:45:51.160 align:middle line:90% Before that it was Boltzmann. 00:45:51.160 --> 00:45:53.110 align:middle line:90% Boltzmann doing gas. 00:45:53.110 --> 00:45:55.300 align:middle line:90% Einstein tried to do liquid. 00:45:55.300 --> 00:45:57.400 align:middle line:90% And go to read. 00:45:57.400 --> 00:46:02.100 align:middle line:90% It's not that difficult. 00:46:02.100 --> 00:46:06.640 align:middle line:84% So there's-- I said, if you say the conductivity is the same 00:46:06.640 --> 00:46:09.830 align:middle line:90% here, there's a relationship. 00:46:09.830 --> 00:46:14.351 align:middle line:84% And if we combine these two terms-- 00:46:14.351 --> 00:46:20.100 align:middle line:84% and I have rewriting this here into this equation here. 00:46:20.100 --> 00:46:26.870 align:middle line:84% And the temperature gradient I write into the next term. 00:46:26.870 --> 00:46:32.390 align:middle line:84% So I have an electrostatic potential gradient, 00:46:32.390 --> 00:46:39.140 align:middle line:84% a chemical potential gradient, and a temperature reading. 00:46:39.140 --> 00:46:45.030 align:middle line:84% So that's-- and so this three term that drives my current flow 00:46:45.030 --> 00:46:49.320 align:middle line:84% in the case when I have a temperature gradient 00:46:49.320 --> 00:46:51.765 align:middle line:90% in a conductor or semiconductor. 00:46:51.765 --> 00:46:54.345 align:middle line:90% 00:46:54.345 --> 00:46:55.745 align:middle line:90% And I continue this. 00:46:55.745 --> 00:46:58.690 align:middle line:90% 00:46:58.690 --> 00:47:06.810 align:middle line:84% I combine some electrostatic potential 00:47:06.810 --> 00:47:09.197 align:middle line:90% with the chemical potential. 00:47:09.197 --> 00:47:12.400 align:middle line:90% 00:47:12.400 --> 00:47:16.210 align:middle line:84% That's called electrochemical potential. 00:47:16.210 --> 00:47:18.730 align:middle line:84% Some of you that do battery, you know 00:47:18.730 --> 00:47:21.850 align:middle line:84% the electrochemical potential in battery. 00:47:21.850 --> 00:47:25.380 align:middle line:84% And in fact, electrical engineers should also know that. 00:47:25.380 --> 00:47:27.600 align:middle line:84% It's not the electrostatic potential 00:47:27.600 --> 00:47:29.160 align:middle line:84% that drives the current flow, it's 00:47:29.160 --> 00:47:33.000 align:middle line:84% the combined electrochemical potential 00:47:33.000 --> 00:47:35.730 align:middle line:90% that drives current flow. 00:47:35.730 --> 00:47:38.040 align:middle line:84% And most-- of course, most electrical engineers 00:47:38.040 --> 00:47:39.510 align:middle line:90% deal with isothermal. 00:47:39.510 --> 00:47:46.210 align:middle line:84% So you don't consider this term, isothermal. 00:47:46.210 --> 00:47:48.790 align:middle line:84% But you have to consider this term. 00:47:48.790 --> 00:47:53.020 align:middle line:84% So there is always electrochemical potential 00:47:53.020 --> 00:47:55.670 align:middle line:84% gradient that drives the current flow. 00:47:55.670 --> 00:47:58.210 align:middle line:84% And so, it's a very important concept, 00:47:58.210 --> 00:48:02.070 align:middle line:84% and it's hard to understand to some extent. 00:48:02.070 --> 00:48:05.130 align:middle line:84% Where is this electrochemical potential? 00:48:05.130 --> 00:48:11.400 align:middle line:84% So I said, the ec, this separation here 00:48:11.400 --> 00:48:14.970 align:middle line:90% is the chemical potential. 00:48:14.970 --> 00:48:16.920 align:middle line:84% And electrostatic potential, this 00:48:16.920 --> 00:48:20.840 align:middle line:84% is when I'm drawing a conductor or semiconductor. 00:48:20.840 --> 00:48:24.930 align:middle line:84% And if I draw relative to an absolute reference here, 00:48:24.930 --> 00:48:28.370 align:middle line:90% this ec is parallel. 00:48:28.370 --> 00:48:31.130 align:middle line:84% So electrostatic potential depends on where 00:48:31.130 --> 00:48:32.930 align:middle line:90% you plot your reference. 00:48:32.930 --> 00:48:36.140 align:middle line:84% So I can always shift up and down 00:48:36.140 --> 00:48:37.880 align:middle line:84% because this is the gradient that 00:48:37.880 --> 00:48:40.550 align:middle line:90% determines really the current. 00:48:40.550 --> 00:48:42.920 align:middle line:84% So there's a constant reference point. 00:48:42.920 --> 00:48:47.410 align:middle line:84% So it's the gradient of this ec that gives you 00:48:47.410 --> 00:48:49.790 align:middle line:90% electrostatic potential. 00:48:49.790 --> 00:48:54.980 align:middle line:90% And so I have ec here minus e. 00:48:54.980 --> 00:48:59.110 align:middle line:90% The problem is, e energy-- 00:48:59.110 --> 00:49:00.500 align:middle line:90% ec is energy. 00:49:00.500 --> 00:49:04.900 align:middle line:84% Energy divided by charge is the electrostatic potential. 00:49:04.900 --> 00:49:08.145 align:middle line:84% This is always a historical problem, not my problem. 00:49:08.145 --> 00:49:10.930 align:middle line:90% 00:49:10.930 --> 00:49:15.800 align:middle line:90% So electrostatic is here. 00:49:15.800 --> 00:49:17.450 align:middle line:90% Chemical potential is here. 00:49:17.450 --> 00:49:21.390 align:middle line:84% So what's left is this electrochemical potential 00:49:21.390 --> 00:49:23.450 align:middle line:90% relative to absolute level. 00:49:23.450 --> 00:49:26.790 align:middle line:84% It's that gradient that drives current flow. 00:49:26.790 --> 00:49:32.298 align:middle line:90% 00:49:32.298 --> 00:49:37.660 align:middle line:84% So now I combine my electrical current. 00:49:37.660 --> 00:49:40.750 align:middle line:84% In the front, I just say this electroconductivity 00:49:40.750 --> 00:49:44.880 align:middle line:84% I generalized with the coefficient L11. 00:49:44.880 --> 00:49:48.300 align:middle line:90% And I combine all the two-- 00:49:48.300 --> 00:49:51.000 align:middle line:84% say, electrochemical potential gradient. 00:49:51.000 --> 00:49:54.520 align:middle line:84% So this is a typical-- the generalized Ohm's law, 00:49:54.520 --> 00:49:59.090 align:middle line:84% it should be this one, electric current proportional 00:49:59.090 --> 00:50:02.570 align:middle line:84% to electrochemical gradient is the electric conductivity 00:50:02.570 --> 00:50:05.390 align:middle line:90% as a proportionality constant. 00:50:05.390 --> 00:50:11.810 align:middle line:84% And when I have temperature gradient, I have L12, 00:50:11.810 --> 00:50:14.210 align:middle line:84% it's the extra term, the coupling 00:50:14.210 --> 00:50:17.310 align:middle line:90% between charge and heat. 00:50:17.310 --> 00:50:24.200 align:middle line:84% So that's the L12 here due to the temperature gradient. 00:50:24.200 --> 00:50:26.960 align:middle line:84% And it's really here what they created the diffusion. 00:50:26.960 --> 00:50:27.620 align:middle line:90% Yes. 00:50:27.620 --> 00:50:29.810 align:middle line:84% AUDIENCE: What is the electrostatic potential again? 00:50:29.810 --> 00:50:30.530 align:middle line:90% GANG CHEN: Ah? 00:50:30.530 --> 00:50:33.060 align:middle line:84% AUDIENCE: You're saying it's the same as the gradient of ec? 00:50:33.060 --> 00:50:33.920 align:middle line:90% GANG CHEN: Yeah. 00:50:33.920 --> 00:50:36.050 align:middle line:84% AUDIENCE: But then that cancel out [INAUDIBLE]. 00:50:36.050 --> 00:50:38.900 align:middle line:90% 00:50:38.900 --> 00:50:42.440 align:middle line:84% GANG CHEN: This one is the chemical potential. 00:50:42.440 --> 00:50:46.700 align:middle line:84% This is the electrostatic potential. 00:50:46.700 --> 00:50:51.510 align:middle line:84% The difference of these two give you the electrochemical. 00:50:51.510 --> 00:50:57.790 align:middle line:90% 00:50:57.790 --> 00:50:59.090 align:middle line:90% We can discuss more-- 00:50:59.090 --> 00:51:01.073 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:51:01.073 --> 00:51:05.030 align:middle line:84% GANG CHEN: He's the electrical engineer. 00:51:05.030 --> 00:51:07.520 align:middle line:90% OK. 00:51:07.520 --> 00:51:13.210 align:middle line:84% Now I'm combining everything together. 00:51:13.210 --> 00:51:17.640 align:middle line:84% And Seebeck is when there is no current flow. 00:51:17.640 --> 00:51:24.010 align:middle line:84% Seebeck voltage is an open circuit. 00:51:24.010 --> 00:51:28.090 align:middle line:84% When there is an open circuit, no current flow, 00:51:28.090 --> 00:51:31.390 align:middle line:84% you can say there is a temperature gradient, 00:51:31.390 --> 00:51:35.080 align:middle line:84% there is corresponding the electrochemical potential 00:51:35.080 --> 00:51:36.010 align:middle line:90% gradient. 00:51:36.010 --> 00:51:40.990 align:middle line:84% You put a probe there, you do measure electrostatic potential. 00:51:40.990 --> 00:51:44.150 align:middle line:84% You measure electrochemical potential. 00:51:44.150 --> 00:51:47.900 align:middle line:84% The metal is connected to a semiconductor. 00:51:47.900 --> 00:51:51.200 align:middle line:84% When you connect it, the metal, let's say, 00:51:51.200 --> 00:51:54.130 align:middle line:84% is a Fermi level connected to the electrochemical. 00:51:54.130 --> 00:51:57.950 align:middle line:84% So you measure-- you can only measure this. 00:51:57.950 --> 00:51:59.500 align:middle line:84% But when we are doing one experiment 00:51:59.500 --> 00:52:02.735 align:middle line:84% and we really want to measure electrostatic potential, what 00:52:02.735 --> 00:52:03.920 align:middle line:90% are we doing? 00:52:03.920 --> 00:52:07.370 align:middle line:84% So we are doing, for example, we're trying to do, 00:52:07.370 --> 00:52:11.790 align:middle line:84% OK, there is a green boundary, green one, green two. 00:52:11.790 --> 00:52:15.050 align:middle line:84% And the green boundary there is an electrostatic potential. 00:52:15.050 --> 00:52:18.080 align:middle line:84% We can't measure it with the contact method, 00:52:18.080 --> 00:52:19.130 align:middle line:90% but we're putting-- 00:52:19.130 --> 00:52:23.040 align:middle line:84% trying to put an atomic force microscope. 00:52:23.040 --> 00:52:25.320 align:middle line:84% And there, when they have-- there 00:52:25.320 --> 00:52:28.170 align:middle line:84% is electrostatic potential, it will 00:52:28.170 --> 00:52:30.940 align:middle line:84% be electrostatic potential determine the repulsion 00:52:30.940 --> 00:52:33.710 align:middle line:90% or attraction. 00:52:33.710 --> 00:52:35.180 align:middle line:90% And that's the coulomb's law. 00:52:35.180 --> 00:52:37.070 align:middle line:84% When you calculate use the coulomb's law, 00:52:37.070 --> 00:52:39.720 align:middle line:84% it's the electrostatic potential. 00:52:39.720 --> 00:52:42.930 align:middle line:84% So there's a-- still there are ways to-- 00:52:42.930 --> 00:52:45.120 align:middle line:84% I said the content method can't be distinguished, 00:52:45.120 --> 00:52:47.020 align:middle line:84% but there are ways to distinguish it. 00:52:47.020 --> 00:52:50.082 align:middle line:90% 00:52:50.082 --> 00:52:54.150 align:middle line:84% So that's where the Seebeck coefficient is. 00:52:54.150 --> 00:52:58.180 align:middle line:84% Seebeck coefficient is defined as they-- 00:52:58.180 --> 00:52:58.932 align:middle line:90% ah. 00:52:58.932 --> 00:53:05.040 align:middle line:84% It really should be negative d phi dx divided by dt, dx, 00:53:05.040 --> 00:53:05.700 align:middle line:90% should be. 00:53:05.700 --> 00:53:10.200 align:middle line:90% So here is negative d phi dx. 00:53:10.200 --> 00:53:13.290 align:middle line:84% Then it should be phi dash minus phi z. 00:53:13.290 --> 00:53:18.900 align:middle line:84% And you can say, it's related to the Seebeck coefficient 00:53:18.900 --> 00:53:22.940 align:middle line:84% now can be expressed in terms of ec minus mu. 00:53:22.940 --> 00:53:25.800 align:middle line:90% That's chemical potential. 00:53:25.800 --> 00:53:29.195 align:middle line:84% Three, kbt is the thermal energy. 00:53:29.195 --> 00:53:32.024 align:middle line:90% 00:53:32.024 --> 00:53:39.060 align:middle line:84% So the Seebeck coefficient has a very clear picture here. 00:53:39.060 --> 00:53:41.010 align:middle line:90% And this is the-- 00:53:41.010 --> 00:53:43.970 align:middle line:90% so you can set up two part. 00:53:43.970 --> 00:53:46.330 align:middle line:84% One is the chemical potential here. 00:53:46.330 --> 00:53:51.870 align:middle line:84% Between here and here, that's ec minus mu. 00:53:51.870 --> 00:53:58.080 align:middle line:84% And the electrons average is thermal energy in this region. 00:53:58.080 --> 00:54:02.610 align:middle line:84% But you ask me the vx is a random velocity. 00:54:02.610 --> 00:54:03.870 align:middle line:90% So that two-- 00:54:03.870 --> 00:54:06.600 align:middle line:90% 3/2 is not good. 00:54:06.600 --> 00:54:09.760 align:middle line:84% Because of vx I have to do integration averaging, 00:54:09.760 --> 00:54:13.770 align:middle line:84% and it turns out to 5/2 rather than 3/2. 00:54:13.770 --> 00:54:15.900 align:middle line:84% I'll show you more exact expressions. 00:54:15.900 --> 00:54:19.890 align:middle line:90% 00:54:19.890 --> 00:54:23.260 align:middle line:90% So now any question here? 00:54:23.260 --> 00:54:24.760 align:middle line:84% AUDIENCE: Can you go back one slide? 00:54:24.760 --> 00:54:26.590 align:middle line:90% GANG CHEN: Yeah. 00:54:26.590 --> 00:54:28.880 align:middle line:84% AUDIENCE: Why do we have, in the graph, 00:54:28.880 --> 00:54:33.040 align:middle line:84% why do we have the position dependent energy 00:54:33.040 --> 00:54:36.490 align:middle line:90% level or the potential energy-- 00:54:36.490 --> 00:54:37.910 align:middle line:90% GANG CHEN: Ah, here? 00:54:37.910 --> 00:54:38.670 align:middle line:90% AUDIENCE: Yeah. 00:54:38.670 --> 00:54:41.207 align:middle line:90% [INAUDIBLE] has a slope. 00:54:41.207 --> 00:54:42.040 align:middle line:90% [INTERPOSING VOICES] 00:54:42.040 --> 00:54:49.360 align:middle line:84% GANG CHEN: That's the potential of the electrons. 00:54:49.360 --> 00:54:54.580 align:middle line:84% Potential of electron is divided by electrical charge gives you 00:54:54.580 --> 00:54:57.720 align:middle line:90% electrostatic potential. 00:54:57.720 --> 00:55:02.810 align:middle line:84% Under current flow, your electron-- 00:55:02.810 --> 00:55:05.130 align:middle line:84% and so, the electrostatic potential 00:55:05.130 --> 00:55:07.692 align:middle line:90% is going downslope or upslope. 00:55:07.692 --> 00:55:08.650 align:middle line:90% AUDIENCE: OK, I think-- 00:55:08.650 --> 00:55:10.775 align:middle line:84% GANG CHEN: When I think about downslope or upslope, 00:55:10.775 --> 00:55:12.330 align:middle line:84% I always have to sit there thinking 00:55:12.330 --> 00:55:15.310 align:middle line:84% for a long time whether it's positive charge, negative charge 00:55:15.310 --> 00:55:17.400 align:middle line:90% so I can [INAUDIBLE]. 00:55:17.400 --> 00:55:19.960 align:middle line:84% That's why I don't like the charge, negative sign. 00:55:19.960 --> 00:55:24.180 align:middle line:90% 00:55:24.180 --> 00:55:24.970 align:middle line:90% By the way. 00:55:24.970 --> 00:55:28.290 align:middle line:84% I don't think, let me see, for a mechanical engineer, 00:55:28.290 --> 00:55:32.970 align:middle line:84% to understand this part, I have to sit there many, many times. 00:55:32.970 --> 00:55:35.610 align:middle line:84% And I think sometimes when you think 00:55:35.610 --> 00:55:38.370 align:middle line:84% you understand it, you have to ask the electric engineer, 00:55:38.370 --> 00:55:43.290 align:middle line:84% you understand it is problematic. 00:55:43.290 --> 00:55:46.025 align:middle line:84% But it's good to sit there and think through yourself. 00:55:46.025 --> 00:55:50.280 align:middle line:90% 00:55:50.280 --> 00:55:56.760 align:middle line:84% Now, I said in the previous part that was the electric current. 00:55:56.760 --> 00:56:00.060 align:middle line:84% Now I'm going to do heat current. 00:56:00.060 --> 00:56:02.490 align:middle line:84% Peltier coefficient is a heat current. 00:56:02.490 --> 00:56:07.860 align:middle line:84% So I have to think about the heat carried by the electrons. 00:56:07.860 --> 00:56:14.730 align:middle line:84% And again, we did this in the first lecture. 00:56:14.730 --> 00:56:17.280 align:middle line:84% When I think about the heat flow, 00:56:17.280 --> 00:56:24.280 align:middle line:84% Fourier law is from left to right, right to left, diffusion. 00:56:24.280 --> 00:56:27.410 align:middle line:84% Here you can see I put an equipotential conductor, 00:56:27.410 --> 00:56:32.240 align:middle line:84% low current flow, just a heat diffusion. 00:56:32.240 --> 00:56:33.530 align:middle line:90% That's a Fourier law. 00:56:33.530 --> 00:56:38.890 align:middle line:84% The Fourier law is valid for electrons and for phonons. 00:56:38.890 --> 00:56:41.080 align:middle line:84% I didn't say whether it's electron phonon here 00:56:41.080 --> 00:56:42.170 align:middle line:90% in this derivation. 00:56:42.170 --> 00:56:45.408 align:middle line:90% 00:56:45.408 --> 00:56:48.010 align:middle line:84% So I'm not going to this detail because we're 00:56:48.010 --> 00:56:49.540 align:middle line:90% writing down this before. 00:56:49.540 --> 00:56:52.420 align:middle line:84% And the thermal conductivity is 1, 0, 3, [INAUDIBLE]. 00:56:52.420 --> 00:56:56.270 align:middle line:84% So that's what we did before, diffusion. 00:56:56.270 --> 00:57:00.690 align:middle line:84% And now I'm going to do charge focused 00:57:00.690 --> 00:57:04.820 align:middle line:90% on heat carried by electron. 00:57:04.820 --> 00:57:08.172 align:middle line:84% And what's the heat carried by electron? 00:57:08.172 --> 00:57:12.110 align:middle line:84% And here you have to go back to a little bit of thermodynamics. 00:57:12.110 --> 00:57:21.830 align:middle line:84% And the first law tells you that du equals dq. 00:57:21.830 --> 00:57:24.530 align:middle line:84% Doesn't look typical thermodynamics. 00:57:24.530 --> 00:57:27.990 align:middle line:84% For mechanical engineering you do du dq-- 00:57:27.990 --> 00:57:31.442 align:middle line:90% du equals dq minus pv-- 00:57:31.442 --> 00:57:32.780 align:middle line:90% pd, pv. 00:57:32.780 --> 00:57:35.310 align:middle line:84% There we'll not talk about pdv work. 00:57:35.310 --> 00:57:38.020 align:middle line:90% There's no volume change. 00:57:38.020 --> 00:57:40.760 align:middle line:84% So we'll talk about chemical potential. 00:57:40.760 --> 00:57:45.170 align:middle line:84% So if you're a chemical engineer, this part is easier. 00:57:45.170 --> 00:57:50.020 align:middle line:90% So du equals dq plus mu pn. 00:57:50.020 --> 00:57:53.590 align:middle line:84% That's a chemical potential term. 00:57:53.590 --> 00:57:58.660 align:middle line:84% And what this tells you, because the du 00:57:58.660 --> 00:58:06.730 align:middle line:84% u is n times individual energy e if you have n electrons. 00:58:06.730 --> 00:58:12.700 align:middle line:90% So e minus mu is related to q. 00:58:12.700 --> 00:58:20.290 align:middle line:84% The heat-- so the energy of a charge consists of two parts. 00:58:20.290 --> 00:58:23.330 align:middle line:90% One is the chemical potential. 00:58:23.330 --> 00:58:24.750 align:middle line:90% The other is the heat. 00:58:24.750 --> 00:58:28.710 align:middle line:90% 00:58:28.710 --> 00:58:34.010 align:middle line:84% So e minus mu is the heat carried per charge. 00:58:34.010 --> 00:58:36.580 align:middle line:90% 00:58:36.580 --> 00:58:43.760 align:middle line:84% And now, if I take that, I say The heat carried per charge 00:58:43.760 --> 00:58:48.710 align:middle line:84% is e minus mu, again, applied to the same picture 00:58:48.710 --> 00:58:52.310 align:middle line:84% going from left to right and right to left. 00:58:52.310 --> 00:58:57.710 align:middle line:84% So this is a velocity, random velocity, thermal velocity, 00:58:57.710 --> 00:59:00.240 align:middle line:90% number density per unit volume. 00:59:00.240 --> 00:59:02.180 align:middle line:84% And again, you go to check here, it 00:59:02.180 --> 00:59:07.040 align:middle line:84% should be watt per meter squared, the unit. 00:59:07.040 --> 00:59:10.000 align:middle line:90% This is a jar. 00:59:10.000 --> 00:59:12.730 align:middle line:90% Per second gives you a watt. 00:59:12.730 --> 00:59:16.180 align:middle line:84% And then it's a meter and over meter cubed 00:59:16.180 --> 00:59:17.860 align:middle line:90% gives you a meter squared. 00:59:17.860 --> 00:59:25.910 align:middle line:84% So here I have left to right, right to left diffusion. 00:59:25.910 --> 00:59:28.970 align:middle line:90% I add an extra term here. 00:59:28.970 --> 00:59:34.460 align:middle line:84% Because when I do-- when I have a potential gradient, 00:59:34.460 --> 00:59:38.196 align:middle line:90% I'm looking at this case. 00:59:38.196 --> 00:59:41.780 align:middle line:90% Oh, I forgot to draw one. 00:59:41.780 --> 00:59:46.200 align:middle line:84% I should have electrical potential going down. 00:59:46.200 --> 00:59:48.110 align:middle line:90% I have current flow. 00:59:48.110 --> 00:59:50.850 align:middle line:84% I have temperature potential-- gradient. 00:59:50.850 --> 00:59:57.240 align:middle line:84% So that's the-- I'm considering coupled electron heat transport. 00:59:57.240 --> 01:00:00.810 align:middle line:90% So this is the diffusion term. 01:00:00.810 --> 01:00:04.230 align:middle line:90% And this is the drift term. 01:00:04.230 --> 01:00:11.270 align:middle line:84% Same as I consider, now I go back a few slides, here. 01:00:11.270 --> 01:00:15.960 align:middle line:84% Diffusion term for current flow, drift term for current flow. 01:00:15.960 --> 01:00:21.520 align:middle line:90% 01:00:21.520 --> 01:00:23.840 align:middle line:90% Diffusion and drift. 01:00:23.840 --> 01:00:27.860 align:middle line:90% So let's look at it again. 01:00:27.860 --> 01:00:31.580 align:middle line:90% Here is diffusion. 01:00:31.580 --> 01:00:37.430 align:middle line:84% And drift is-- this is a drift velocity times the charge 01:00:37.430 --> 01:00:38.270 align:middle line:90% density. 01:00:38.270 --> 01:00:40.920 align:middle line:84% And each one is carrying e minus mu. 01:00:40.920 --> 01:00:44.330 align:middle line:90% 01:00:44.330 --> 01:00:48.590 align:middle line:84% So this is the convection term there, 01:00:48.590 --> 01:00:51.230 align:middle line:84% convection of the electrons going 01:00:51.230 --> 01:00:55.280 align:middle line:90% through the surface we draw. 01:00:55.280 --> 01:00:58.100 align:middle line:90% And now, if I combine-- 01:00:58.100 --> 01:01:06.570 align:middle line:84% because this term will give me the same thing as I drew before, 01:01:06.570 --> 01:01:08.720 align:middle line:90% electrochemical potential. 01:01:08.720 --> 01:01:14.270 align:middle line:84% And the second term I will have also the temperature gradient. 01:01:14.270 --> 01:01:15.290 align:middle line:90% So here I draw-- 01:01:15.290 --> 01:01:16.520 align:middle line:90% I made some jump. 01:01:16.520 --> 01:01:18.860 align:middle line:84% I didn't go through each step derivation, 01:01:18.860 --> 01:01:23.380 align:middle line:84% and you can go through that yourself. 01:01:23.380 --> 01:01:27.940 align:middle line:84% And now the heat flux, what I have from this 01:01:27.940 --> 01:01:32.540 align:middle line:84% is the heat flux carried by the electron 01:01:32.540 --> 01:01:38.240 align:middle line:84% is temperature gradient terms but also 01:01:38.240 --> 01:01:40.750 align:middle line:90% is a potential gradient term. 01:01:40.750 --> 01:01:45.050 align:middle line:90% So I have, again a couple-- 01:01:45.050 --> 01:01:48.650 align:middle line:84% before I have a charge flux electric current, 01:01:48.650 --> 01:01:50.690 align:middle line:84% the potential gradient, temperature gradient. 01:01:50.690 --> 01:01:53.300 align:middle line:84% Now the heat carried by the charge 01:01:53.300 --> 01:01:56.960 align:middle line:84% is also proportional to the potential gradient 01:01:56.960 --> 01:01:59.740 align:middle line:90% and temperature gradient. 01:01:59.740 --> 01:02:08.920 align:middle line:84% So under equal, say, isothermal case, this is 0, 01:02:08.920 --> 01:02:09.740 align:middle line:90% but this is not. 01:02:09.740 --> 01:02:13.112 align:middle line:90% 01:02:13.112 --> 01:02:15.850 align:middle line:90% This is the Peltier coefficient. 01:02:15.850 --> 01:02:18.940 align:middle line:84% When I have heat flows through-- a charge flow 01:02:18.940 --> 01:02:22.950 align:middle line:84% through the current, the charge carries heat. 01:02:22.950 --> 01:02:28.790 align:middle line:84% So this is the L21 is the Peltier coefficient. 01:02:28.790 --> 01:02:33.480 align:middle line:90% And so, that's the-- 01:02:33.480 --> 01:02:37.550 align:middle line:84% now I have the coupled heat and charge flow, 01:02:37.550 --> 01:02:39.800 align:middle line:90% and I have the two expression. 01:02:39.800 --> 01:02:42.275 align:middle line:90% One, before I wrote the charge-- 01:02:42.275 --> 01:02:45.020 align:middle line:84% if you go back to the previous two slides, 01:02:45.020 --> 01:02:50.270 align:middle line:84% this jex equals L11 times this plus L12 times 01:02:50.270 --> 01:02:52.700 align:middle line:90% this for the current flux. 01:02:52.700 --> 01:02:55.860 align:middle line:84% And now, for the heat flux carried by charge, I have Two. 01:02:55.860 --> 01:02:58.640 align:middle line:84% 21, L22, and then we'll come back and rewrite 01:02:58.640 --> 01:03:00.360 align:middle line:90% this expression-later. 01:03:00.360 --> 01:03:04.190 align:middle line:90% 01:03:04.190 --> 01:03:08.330 align:middle line:90% So this is a kinetic. 01:03:08.330 --> 01:03:12.420 align:middle line:84% I have not considered the average. 01:03:12.420 --> 01:03:13.940 align:middle line:90% That's the question you ask. 01:03:13.940 --> 01:03:16.145 align:middle line:84% I cannot do that from this kind of picture. 01:03:16.145 --> 01:03:18.860 align:middle line:90% 01:03:18.860 --> 01:03:21.170 align:middle line:84% When you want to do the detail, you 01:03:21.170 --> 01:03:25.175 align:middle line:84% have to say each charge have different energies, 01:03:25.175 --> 01:03:26.900 align:middle line:90% slight different energy. 01:03:26.900 --> 01:03:30.080 align:middle line:84% So you have to count more carefully, 01:03:30.080 --> 01:03:35.000 align:middle line:84% just like we did before, counting all the modes, 01:03:35.000 --> 01:03:38.190 align:middle line:90% counting all the quantum modes. 01:03:38.190 --> 01:03:43.310 align:middle line:84% And each one is moving at a velocity-- 01:03:43.310 --> 01:03:45.930 align:middle line:84% local velocity, its own velocity. 01:03:45.930 --> 01:03:51.570 align:middle line:84% And each mode has this number of charge determined 01:03:51.570 --> 01:03:55.030 align:middle line:90% by Fermi-Dirac statistics. 01:03:55.030 --> 01:04:01.750 align:middle line:84% And of course, this e could be either e, minus e, 01:04:01.750 --> 01:04:07.800 align:middle line:84% that's when I do current, or E, capital E minus mu, 01:04:07.800 --> 01:04:09.780 align:middle line:90% that's when I do heat. 01:04:09.780 --> 01:04:17.400 align:middle line:84% So if I do that, I can get the more rigorous expressions. 01:04:17.400 --> 01:04:19.110 align:middle line:90% And this is what-- 01:04:19.110 --> 01:04:23.970 align:middle line:84% you still get the same format except the coefficient 01:04:23.970 --> 01:04:26.280 align:middle line:90% is a little bit different. 01:04:26.280 --> 01:04:35.280 align:middle line:84% So I have this relation I've written before, same format. 01:04:35.280 --> 01:04:43.750 align:middle line:84% And those cross-terms, these two terms depends on how you write. 01:04:43.750 --> 01:04:46.980 align:middle line:84% If you write generalized thermodynamic forces are equal, 01:04:46.980 --> 01:04:49.870 align:middle line:84% but this is not generalized thermodynamic force, 01:04:49.870 --> 01:04:52.540 align:middle line:90% so it's related. 01:04:52.540 --> 01:04:56.700 align:middle line:84% So that's the [INAUDIBLE] relation. 01:04:56.700 --> 01:04:59.580 align:middle line:84% And the course term always related. 01:04:59.580 --> 01:05:02.840 align:middle line:84% If you do piezoelectricity, there 01:05:02.840 --> 01:05:07.700 align:middle line:84% is also mechanical to electrical coupling coefficient in the case 01:05:07.700 --> 01:05:09.440 align:middle line:90% of mechanical motion. 01:05:09.440 --> 01:05:12.980 align:middle line:84% Or when you have current flow, quantum mechanical. 01:05:12.980 --> 01:05:16.700 align:middle line:84% So the reverse-- this coefficient, cross-coefficient 01:05:16.700 --> 01:05:21.140 align:middle line:84% is always related, and that's the also relation-- 01:05:21.140 --> 01:05:23.060 align:middle line:90% very fundamental. 01:05:23.060 --> 01:05:25.050 align:middle line:90% Also got a Nobel Prize for this. 01:05:25.050 --> 01:05:27.716 align:middle line:90% 01:05:27.716 --> 01:05:32.390 align:middle line:84% So that's the similar for the charge, 01:05:32.390 --> 01:05:36.660 align:middle line:84% flow, and for the charge carry the heat flow. 01:05:36.660 --> 01:05:39.490 align:middle line:90% And now I'm going to write this. 01:05:39.490 --> 01:05:45.390 align:middle line:84% You tend to think, this is a thermal conductivity. 01:05:45.390 --> 01:05:46.480 align:middle line:90% That's not right. 01:05:46.480 --> 01:05:49.440 align:middle line:90% 01:05:49.440 --> 01:05:54.840 align:middle line:84% Because when I write, I could write my potential, 01:05:54.840 --> 01:06:01.710 align:middle line:90% rewrite it into a jex L12. 01:06:01.710 --> 01:06:06.270 align:middle line:84% So I'm replacing my potential in terms of electric current 01:06:06.270 --> 01:06:08.490 align:middle line:84% because the electric here, potential 01:06:08.490 --> 01:06:10.290 align:middle line:84% is related to temperature gradient. 01:06:10.290 --> 01:06:16.520 align:middle line:84% And now if I substitute into here, 01:06:16.520 --> 01:06:21.740 align:middle line:84% I will say the electrical flux, heat flux 01:06:21.740 --> 01:06:25.070 align:middle line:84% carried by the charge is proportional to the electrical 01:06:25.070 --> 01:06:28.400 align:middle line:84% charge flux and with a proportionality 01:06:28.400 --> 01:06:29.790 align:middle line:90% that's a Peltier coefficient. 01:06:29.790 --> 01:06:33.140 align:middle line:84% I said this L21 is Peltier coefficient, that's not right, 01:06:33.140 --> 01:06:34.620 align:middle line:90% because this is a potential. 01:06:34.620 --> 01:06:37.670 align:middle line:84% But the Peltier is really current flux proportional 01:06:37.670 --> 01:06:39.740 align:middle line:90% to the charge flux. 01:06:39.740 --> 01:06:44.670 align:middle line:84% And this L21 divided by L11 is the Peltier coefficient. 01:06:44.670 --> 01:06:50.250 align:middle line:84% And the next term is the temperature gradient. 01:06:50.250 --> 01:06:52.920 align:middle line:84% So only when I write into this form 01:06:52.920 --> 01:06:56.700 align:middle line:84% I have the expression for the thermal conductivity. 01:06:56.700 --> 01:06:59.400 align:middle line:84% In terms of for electrons, the thermal conductivity 01:06:59.400 --> 01:07:03.980 align:middle line:90% involves all four coefficients. 01:07:03.980 --> 01:07:07.850 align:middle line:90% L11, L21, L 1.01. 01:07:07.850 --> 01:07:11.540 align:middle line:84% Of course, these two coefficients are related. 01:07:11.540 --> 01:07:17.350 align:middle line:84% So this is the thermal conductivity. 01:07:17.350 --> 01:07:23.380 align:middle line:84% And now if I write more clearly using the parabolic band 01:07:23.380 --> 01:07:26.380 align:middle line:84% approximation, again, here I'm not 01:07:26.380 --> 01:07:30.790 align:middle line:84% going to give the derivation, just say the same-- 01:07:30.790 --> 01:07:34.960 align:middle line:84% I follow those steps and do, in fact, 01:07:34.960 --> 01:07:36.470 align:middle line:84% I need to go forward to my equation. 01:07:36.470 --> 01:07:38.170 align:middle line:90% We're not going into that. 01:07:38.170 --> 01:07:41.980 align:middle line:90% And here is my final expression. 01:07:41.980 --> 01:07:44.800 align:middle line:84% This is a random velocity relaxation time, 01:07:44.800 --> 01:07:46.730 align:middle line:90% which could depend on energy. 01:07:46.730 --> 01:07:49.700 align:middle line:84% And before when we do it and we didn't say it depends on energy. 01:07:49.700 --> 01:07:53.290 align:middle line:84% So we have-- so this is a more rigorous expression. 01:07:53.290 --> 01:08:00.090 align:middle line:84% And density of states, and this is the other coefficient. 01:08:00.090 --> 01:08:05.400 align:middle line:84% So with that, you can actually, using those coefficients, 01:08:05.400 --> 01:08:09.680 align:middle line:84% you can actually go to model the solid. 01:08:09.680 --> 01:08:13.340 align:middle line:84% And what do you have, the solid is 01:08:13.340 --> 01:08:16.790 align:middle line:84% really different solid have different density of states. 01:08:16.790 --> 01:08:19.729 align:middle line:84% So the band structure is different. 01:08:19.729 --> 01:08:22.229 align:middle line:84% And sometimes it has multiple bands, 01:08:22.229 --> 01:08:25.250 align:middle line:84% so you have to consider multiple bands' effects. 01:08:25.250 --> 01:08:27.890 align:middle line:84% Electrons have holes is another-- 01:08:27.890 --> 01:08:30.590 align:middle line:84% so you can see electrons-- negative charge 01:08:30.590 --> 01:08:33.560 align:middle line:84% plus the positive charge, and those could all 01:08:33.560 --> 01:08:37.890 align:middle line:84% be taken into consideration using this formulations. 01:08:37.890 --> 01:08:40.350 align:middle line:84% Again, I don't expect that you'll fully 01:08:40.350 --> 01:08:44.840 align:middle line:90% say, be able to derive it. 01:08:44.840 --> 01:08:46.890 align:middle line:90% I didn't derive it. 01:08:46.890 --> 01:08:49.779 align:middle line:84% But this is where many people, when 01:08:49.779 --> 01:08:52.660 align:middle line:84% they try to interpret the experimental data, 01:08:52.660 --> 01:08:57.430 align:middle line:84% they go to those expressions and try to fit the expressions. 01:08:57.430 --> 01:09:01.870 align:middle line:84% I say they try to fit because you actually do not know 01:09:01.870 --> 01:09:03.880 align:middle line:90% exactly, for example, how to-- 01:09:03.880 --> 01:09:06.490 align:middle line:90% 01:09:06.490 --> 01:09:08.330 align:middle line:90% what's happening in the solid. 01:09:08.330 --> 01:09:12.689 align:middle line:90% 01:09:12.689 --> 01:09:16.290 align:middle line:84% I said the electric conductivity, thermal-- 01:09:16.290 --> 01:09:19.470 align:middle line:84% electronic thermal conductivity that's in the previous slide, 01:09:19.470 --> 01:09:24.439 align:middle line:84% so those are the electronic conductivity here, 01:09:24.439 --> 01:09:26.870 align:middle line:90% electronic thermal conductivity. 01:09:26.870 --> 01:09:31.510 align:middle line:84% And the L11 is the electrical conductivity sigma. 01:09:31.510 --> 01:09:34.840 align:middle line:90% 01:09:34.840 --> 01:09:42.130 align:middle line:84% And the ratio of this, if you go to do Fermi-Dirac statistics 01:09:42.130 --> 01:09:44.979 align:middle line:84% in metal, you can do this integral. 01:09:44.979 --> 01:09:50.800 align:middle line:84% And turns out the ratio for metal is a constant. 01:09:50.800 --> 01:09:54.690 align:middle line:84% And this is a so-called Wiedemann-Franz law. 01:09:54.690 --> 01:09:57.480 align:middle line:84% And so that means thermal conductivity 01:09:57.480 --> 01:09:59.550 align:middle line:90% is very hard to measure. 01:09:59.550 --> 01:10:04.260 align:middle line:84% So if you measure electric conductivity in metal, 01:10:04.260 --> 01:10:08.150 align:middle line:84% as long as the lattice contributions are large, 01:10:08.150 --> 01:10:09.500 align:middle line:90% you can roughly-- 01:10:09.500 --> 01:10:12.095 align:middle line:84% I say roughly because this is not always valid-- 01:10:12.095 --> 01:10:13.850 align:middle line:84% as we measure electric conductivity, 01:10:13.850 --> 01:10:17.250 align:middle line:84% you can go to estimate some of it just based 01:10:17.250 --> 01:10:19.920 align:middle line:84% on this interpolation Wiedemann-Franz law. 01:10:19.920 --> 01:10:25.910 align:middle line:84% So this L is the Lorentz constant, the Lawrence number. 01:10:25.910 --> 01:10:30.140 align:middle line:84% Let's say, if you do semiconductor, 01:10:30.140 --> 01:10:31.460 align:middle line:90% it's not a constant. 01:10:31.460 --> 01:10:35.120 align:middle line:84% So in thermoelectrics, if you go to actually read 01:10:35.120 --> 01:10:38.330 align:middle line:84% thermoelectric literature, many people just 01:10:38.330 --> 01:10:41.450 align:middle line:84% take this Lawrence number and say, OK, 01:10:41.450 --> 01:10:44.090 align:middle line:84% I measure electric conductivity, and I 01:10:44.090 --> 01:10:48.890 align:middle line:84% want to find out what's the electronic thermal conductivity, 01:10:48.890 --> 01:10:50.150 align:middle line:90% I calculate. 01:10:50.150 --> 01:10:52.160 align:middle line:84% They will take this constant number, 01:10:52.160 --> 01:10:54.990 align:middle line:84% and they subtract the total measured thermal conductivity 01:10:54.990 --> 01:10:59.100 align:middle line:84% so the rest is due to phonon lattice vibration. 01:10:59.100 --> 01:11:03.610 align:middle line:84% And that often leads to very, I say, varied result. 01:11:03.610 --> 01:11:05.650 align:middle line:84% You can't interpret those phonon, 01:11:05.650 --> 01:11:08.880 align:middle line:84% because they did a wrong calculation. 01:11:08.880 --> 01:11:13.440 align:middle line:84% In semiconductor, L actually depends on-- 01:11:13.440 --> 01:11:15.300 align:middle line:90% you have to calculate it. 01:11:15.300 --> 01:11:18.390 align:middle line:84% You have to go back to calculate the electronic thermal 01:11:18.390 --> 01:11:20.550 align:middle line:84% conductivity using this transport 01:11:20.550 --> 01:11:23.940 align:middle line:84% coefficient and the electrical thermal conductivity-- 01:11:23.940 --> 01:11:27.020 align:middle line:90% electrical conductivity. 01:11:27.020 --> 01:11:28.710 align:middle line:90% I'll give some examples later. 01:11:28.710 --> 01:11:32.185 align:middle line:90% 01:11:32.185 --> 01:11:37.210 align:middle line:84% And again, so let's go back to look at what it means. 01:11:37.210 --> 01:11:39.880 align:middle line:90% What's the Seebeck coefficient? 01:11:39.880 --> 01:11:45.400 align:middle line:84% So if you look at it, that's from the previous expression 01:11:45.400 --> 01:11:46.210 align:middle line:90% there. 01:11:46.210 --> 01:11:49.660 align:middle line:84% And it's really, the Seebeck coefficient 01:11:49.660 --> 01:11:55.540 align:middle line:84% is the weighted average of electron energy 01:11:55.540 --> 01:12:00.460 align:middle line:84% relative to ef. ef really is mu, chemical potential. 01:12:00.460 --> 01:12:03.430 align:middle line:84% In electrical engineering, the chemical potential 01:12:03.430 --> 01:12:08.980 align:middle line:84% and the Fermi level is typically mixed together. 01:12:08.980 --> 01:12:11.620 align:middle line:84% They don't distinguish very carefully. 01:12:11.620 --> 01:12:17.080 align:middle line:84% So ef weighed against the electric potential-- electric 01:12:17.080 --> 01:12:19.870 align:middle line:84% conductivity at each energy level. 01:12:19.870 --> 01:12:22.930 align:middle line:84% And that's really the average energy 01:12:22.930 --> 01:12:27.480 align:middle line:84% of the charge relative to the chemical potential. 01:12:27.480 --> 01:12:32.770 align:middle line:84% So that's still what I said before. 01:12:32.770 --> 01:12:41.740 align:middle line:84% And the electric conductivity is the density of states, velocity, 01:12:41.740 --> 01:12:44.990 align:middle line:84% electrical relaxation time, electron relaxation time, 01:12:44.990 --> 01:12:45.880 align:middle line:90% and efde. 01:12:45.880 --> 01:12:49.180 align:middle line:90% We'll show more later on. 01:12:49.180 --> 01:12:53.960 align:middle line:84% So with that, now you can see why metal is not good. 01:12:53.960 --> 01:12:56.810 align:middle line:90% 01:12:56.810 --> 01:13:03.620 align:middle line:84% Metal is not a good material for Seebeck, 01:13:03.620 --> 01:13:06.050 align:middle line:90% because Seebeck is too small. 01:13:06.050 --> 01:13:09.540 align:middle line:84% For wide metal, Seebeck is too small. 01:13:09.540 --> 01:13:15.332 align:middle line:84% And this is because in the metal, ef is an in [INAUDIBLE]. 01:13:15.332 --> 01:13:18.396 align:middle line:90% 01:13:18.396 --> 01:13:23.910 align:middle line:84% And the average energy of electron relative to ef-- 01:13:23.910 --> 01:13:29.730 align:middle line:84% so the electron in metal is about half is above, 01:13:29.730 --> 01:13:31.120 align:middle line:90% half is below ef. 01:13:31.120 --> 01:13:34.060 align:middle line:90% 01:13:34.060 --> 01:13:39.400 align:middle line:84% The electron below-- because the Fermi-Dirac distribution is 01:13:39.400 --> 01:13:40.090 align:middle line:90% over-- 01:13:40.090 --> 01:13:43.930 align:middle line:84% roughly over kt, that's the electrons. 01:13:43.930 --> 01:13:48.230 align:middle line:84% Only on this region kdt, in this region, 01:13:48.230 --> 01:13:50.500 align:middle line:90% there are multiple charge. 01:13:50.500 --> 01:13:52.210 align:middle line:90% And I draw too wide. 01:13:52.210 --> 01:13:55.720 align:middle line:84% It's really just this very narrow. 01:13:55.720 --> 01:14:00.700 align:middle line:84% Above is a positive heat, below is a negative heat. 01:14:00.700 --> 01:14:05.550 align:middle line:84% When they move together, the positive heat energy 01:14:05.550 --> 01:14:07.740 align:middle line:84% above the chemical potential move 01:14:07.740 --> 01:14:12.120 align:middle line:84% forward, energy below the-- electron below the chemical 01:14:12.120 --> 01:14:14.820 align:middle line:84% potential carry negative heat forward. 01:14:14.820 --> 01:14:17.160 align:middle line:90% At the end, they two cancel. 01:14:17.160 --> 01:14:20.360 align:middle line:84% So you've got a very small Seebeck coefficient. 01:14:20.360 --> 01:14:24.360 align:middle line:84% So metals have very small Seebeck coefficient. 01:14:24.360 --> 01:14:30.840 align:middle line:84% And if anybody has any idea to cut this part off, you can one-- 01:14:30.840 --> 01:14:34.020 align:middle line:90% I don't know how to do it. 01:14:34.020 --> 01:14:36.390 align:middle line:90% Or cut the upper part off. 01:14:36.390 --> 01:14:40.020 align:middle line:84% So in metal, do you have width-- think about width-- 01:14:40.020 --> 01:14:45.560 align:middle line:84% how I can place something to scatter potentially 01:14:45.560 --> 01:14:47.860 align:middle line:90% half of this. 01:14:47.860 --> 01:14:50.890 align:middle line:84% So if you scatter the bottom part, 01:14:50.890 --> 01:14:56.710 align:middle line:84% you get a positive Seebeck coefficient, current flow-- 01:14:56.710 --> 01:14:59.840 align:middle line:84% heat flow in the same direction as the current flow. 01:14:59.840 --> 01:15:04.280 align:middle line:84% You cut the positive part, you get a negative Seebeck 01:15:04.280 --> 01:15:08.403 align:middle line:84% coefficient, the heat flow [INAUDIBLE]. 01:15:08.403 --> 01:15:11.110 align:middle line:90% 01:15:11.110 --> 01:15:14.200 align:middle line:84% So this is where, if you do materials research, 01:15:14.200 --> 01:15:18.820 align:middle line:84% you have to think hard on this, how you could potentially 01:15:18.820 --> 01:15:22.490 align:middle line:84% manipulate the material to create 01:15:22.490 --> 01:15:28.820 align:middle line:84% this asymmetry in the current heat carried by each charge. 01:15:28.820 --> 01:15:33.508 align:middle line:90% 01:15:33.508 --> 01:15:38.410 align:middle line:84% Semiconductor is better for Seebeck 01:15:38.410 --> 01:15:44.260 align:middle line:84% because, of course, here what I'm draw is this [INAUDIBLE]. 01:15:44.260 --> 01:15:47.660 align:middle line:84% If you think about this, I said Seebeck is the average energy-- 01:15:47.660 --> 01:15:51.930 align:middle line:84% so semiconductor, for example, if I doped it 01:15:51.930 --> 01:15:55.480 align:middle line:84% so that Fermi level is here, and the average energy 01:15:55.480 --> 01:15:56.450 align:middle line:90% is rapid here. 01:15:56.450 --> 01:16:01.240 align:middle line:84% So there is no negative part to pass through. 01:16:01.240 --> 01:16:04.510 align:middle line:84% So each of this electron here is-- 01:16:04.510 --> 01:16:08.500 align:middle line:84% relative to the chemical potential is a carrier-- 01:16:08.500 --> 01:16:11.215 align:middle line:84% a positive heat relative to chemical 01:16:11.215 --> 01:16:14.910 align:middle line:90% potential-- no cancellation. 01:16:14.910 --> 01:16:18.000 align:middle line:84% Thermoelectrics are typically not here. 01:16:18.000 --> 01:16:21.510 align:middle line:90% They dope actually into here. 01:16:21.510 --> 01:16:24.360 align:middle line:84% So the bottom part is actually not good, 01:16:24.360 --> 01:16:27.290 align:middle line:90% only the top part is better. 01:16:27.290 --> 01:16:30.590 align:middle line:84% Why they want to dope it there is 01:16:30.590 --> 01:16:35.060 align:middle line:84% because, when you put your chemical potential here, 01:16:35.060 --> 01:16:37.330 align:middle line:84% the number of electrons here is very small. 01:16:37.330 --> 01:16:41.778 align:middle line:90% 01:16:41.778 --> 01:16:44.290 align:middle line:84% And the number of electrons is very small, 01:16:44.290 --> 01:16:46.800 align:middle line:84% so the electric conductivity here 01:16:46.800 --> 01:16:52.180 align:middle line:84% is, this is proportional to the number of electrons. 01:16:52.180 --> 01:16:54.250 align:middle line:90% So what do you want? 01:16:54.250 --> 01:16:57.910 align:middle line:84% Because at the end, the zt is s squared sigma. 01:16:57.910 --> 01:17:01.780 align:middle line:84% Remember, zt figure of merit is the-- 01:17:01.780 --> 01:17:04.840 align:middle line:84% s is the Seebeck coefficient, s squared, 01:17:04.840 --> 01:17:06.880 align:middle line:84% times the electric conductivity, because you 01:17:06.880 --> 01:17:10.375 align:middle line:84% want the enough electron to carry the heat. 01:17:10.375 --> 01:17:12.500 align:middle line:84% You just don't want the one electron to carry heat, 01:17:12.500 --> 01:17:14.670 align:middle line:84% it just doesn't carry enough heat. 01:17:14.670 --> 01:17:19.810 align:middle line:90% So you see here, this is a-- 01:17:19.810 --> 01:17:20.310 align:middle line:90% OK. 01:17:20.310 --> 01:17:23.560 align:middle line:90% If I look at this, what is df d? 01:17:23.560 --> 01:17:28.270 align:middle line:84% Fermi-Dirac is a very symmetric around the ef. 01:17:28.270 --> 01:17:30.400 align:middle line:90% A density of states is here. 01:17:30.400 --> 01:17:33.240 align:middle line:84% So it's really, in semiconductor, only this region. 01:17:33.240 --> 01:17:35.790 align:middle line:90% This two product is not 0. 01:17:35.790 --> 01:17:40.010 align:middle line:84% Only those regions is contributing 01:17:40.010 --> 01:17:44.320 align:middle line:84% to electric conduction if you look at this expression. 01:17:44.320 --> 01:17:47.408 align:middle line:90% 01:17:47.408 --> 01:17:51.330 align:middle line:84% And so, that meaning only this region of charge 01:17:51.330 --> 01:17:57.400 align:middle line:84% rather to the chemical potential is the Seebeck coefficient. 01:17:57.400 --> 01:18:01.250 align:middle line:84% So you, later on, we will-- when we talk about quantum structure, 01:18:01.250 --> 01:18:04.240 align:middle line:84% people want to say, how you can make 01:18:04.240 --> 01:18:08.260 align:middle line:90% this region carry more charge. 01:18:08.260 --> 01:18:10.480 align:middle line:90% So you create a peak here. 01:18:10.480 --> 01:18:13.600 align:middle line:84% The distance of these states is not good. 01:18:13.600 --> 01:18:18.680 align:middle line:84% d is a square root of e minus e, ef, we show-- 01:18:18.680 --> 01:18:20.260 align:middle line:90% well, you see before. 01:18:20.260 --> 01:18:23.800 align:middle line:84% This is a very small density of states. 01:18:23.800 --> 01:18:27.330 align:middle line:90% So don't give you many carriers. 01:18:27.330 --> 01:18:31.230 align:middle line:84% So that's where people do a lot of things when 01:18:31.230 --> 01:18:33.120 align:middle line:90% they try to improve electrons. 01:18:33.120 --> 01:18:36.900 align:middle line:84% They say, can I create something sharper in this region 01:18:36.900 --> 01:18:39.330 align:middle line:90% so I can put more electrons? 01:18:39.330 --> 01:18:43.950 align:middle line:84% So remember that, at the end, you want 01:18:43.950 --> 01:18:46.860 align:middle line:90% to optimize s square sigma. 01:18:46.860 --> 01:18:49.150 align:middle line:84% Not even optimal, just optimize that. 01:18:49.150 --> 01:18:51.240 align:middle line:84% You want to optimize ats so there are still 01:18:51.240 --> 01:18:54.460 align:middle line:90% some things were missing. 01:18:54.460 --> 01:19:02.920 align:middle line:84% So this is the material side, the basic material physics. 01:19:02.920 --> 01:19:06.810 align:middle line:84% And if I go, again, to enforce my statistics, 01:19:06.810 --> 01:19:09.450 align:middle line:84% I said that the electrical energy scattering 01:19:09.450 --> 01:19:12.000 align:middle line:84% relaxation time depends on electron energy. 01:19:12.000 --> 01:19:15.553 align:middle line:84% So there are a lot of different scattering mechanisms. 01:19:15.553 --> 01:19:16.720 align:middle line:90% We're not getting into that. 01:19:16.720 --> 01:19:19.140 align:middle line:84% You go to do material research, you read literature. 01:19:19.140 --> 01:19:25.140 align:middle line:84% But if I do a gamma here, this is a potential power. 01:19:25.140 --> 01:19:29.880 align:middle line:84% For example, due to lattice, due to acoustic phonon scattering, 01:19:29.880 --> 01:19:31.640 align:middle line:90% this gamma is negative 1/2. 01:19:31.640 --> 01:19:34.150 align:middle line:90% 01:19:34.150 --> 01:19:40.300 align:middle line:84% So what it means, negative 1/2 is a low energy electron, 01:19:40.300 --> 01:19:42.910 align:middle line:90% has a longer relaxation time. 01:19:42.910 --> 01:19:44.530 align:middle line:90% They travel further. 01:19:44.530 --> 01:19:47.470 align:middle line:84% High energy electron travel less. 01:19:47.470 --> 01:19:48.970 align:middle line:90% You don't like that. 01:19:48.970 --> 01:19:52.660 align:middle line:84% If you look at that, your Seebeck have a gamma here. 01:19:52.660 --> 01:19:53.860 align:middle line:90% And this is a-- 01:19:53.860 --> 01:19:55.120 align:middle line:90% not 3/2. 01:19:55.120 --> 01:19:57.680 align:middle line:84% If you do the before, that's 3/2. 01:19:57.680 --> 01:20:00.190 align:middle line:90% I said, it's five parts. 01:20:00.190 --> 01:20:04.020 align:middle line:90% That's due to this vx squared. 01:20:04.020 --> 01:20:07.320 align:middle line:84% This gamma is not good if it's negative, 01:20:07.320 --> 01:20:12.070 align:middle line:84% because if I think about acoustics phonon scatter, 01:20:12.070 --> 01:20:14.440 align:middle line:84% the high-energy electrons scatter. 01:20:14.440 --> 01:20:16.900 align:middle line:84% But I want the high-energy electron travel 01:20:16.900 --> 01:20:17.940 align:middle line:90% as far as possible. 01:20:17.940 --> 01:20:22.245 align:middle line:90% 01:20:22.245 --> 01:20:26.500 align:middle line:84% But the ionized impurity, it turns out that gamma can be 3/2. 01:20:26.500 --> 01:20:29.870 align:middle line:90% 01:20:29.870 --> 01:20:30.650 align:middle line:90% That's very good. 01:20:30.650 --> 01:20:34.640 align:middle line:84% Of course, ionized impurity, so that means you doped material 01:20:34.640 --> 01:20:38.270 align:middle line:84% very heavy, you can have ionized impurity dominant. 01:20:38.270 --> 01:20:42.330 align:middle line:84% The problem is your mean free path become very short. 01:20:42.330 --> 01:20:45.410 align:middle line:84% Your electric conductivity becomes small. 01:20:45.410 --> 01:20:48.220 align:middle line:84% Thermoelectric is always a struggle. 01:20:48.220 --> 01:20:51.890 align:middle line:84% You try to sell to one guy, the other guy is not happy. 01:20:51.890 --> 01:20:54.270 align:middle line:84% And that's why the material research is very hard. 01:20:54.270 --> 01:20:58.118 align:middle line:90% 01:20:58.118 --> 01:21:04.480 align:middle line:84% So and, of course, if I put the ec minus ef [INAUDIBLE] divided 01:21:04.480 --> 01:21:09.820 align:middle line:84% by n, and then you will see, because this depends 01:21:09.820 --> 01:21:14.780 align:middle line:84% on temperature-- so as the temperature increases, 01:21:14.780 --> 01:21:17.770 align:middle line:90% Seebeck coefficient increase. 01:21:17.770 --> 01:21:20.680 align:middle line:84% And the reason is that, if you look at this one, 01:21:20.680 --> 01:21:24.340 align:middle line:84% you go to check the reason, as you 01:21:24.340 --> 01:21:27.460 align:middle line:84% increase temperature, actually the Fermi level shift down. 01:21:27.460 --> 01:21:30.460 align:middle line:84% So the average energy now increases 01:21:30.460 --> 01:21:32.470 align:middle line:84% relative to the chemical potential-- 01:21:32.470 --> 01:21:34.200 align:middle line:90% Fermi level. 01:21:34.200 --> 01:21:37.680 align:middle line:84% So that's the reason why the Seebeck coefficient increases 01:21:37.680 --> 01:21:38.965 align:middle line:90% with temperature. 01:21:38.965 --> 01:21:44.140 align:middle line:90% 01:21:44.140 --> 01:21:50.500 align:middle line:84% Well, I gave you a very simple one-band picture, 01:21:50.500 --> 01:21:55.450 align:middle line:84% although I know many of you say, this 01:21:55.450 --> 01:21:59.310 align:middle line:90% is pretty complicated already. 01:21:59.310 --> 01:22:01.620 align:middle line:84% Let's say, if you want-- if you do materials, 01:22:01.620 --> 01:22:04.290 align:middle line:84% you go to look at the real material, 01:22:04.290 --> 01:22:10.350 align:middle line:84% this is still the among the simplest picture I can give you. 01:22:10.350 --> 01:22:15.430 align:middle line:84% But say, in real material, for example, I have electrons, 01:22:15.430 --> 01:22:19.716 align:middle line:90% I have holes, positive charge. 01:22:19.716 --> 01:22:23.960 align:middle line:84% It cancel each other, because when your electron mode see 01:22:23.960 --> 01:22:26.510 align:middle line:84% positive energy form of negative energy 01:22:26.510 --> 01:22:29.090 align:middle line:84% rather than chemical potential, they cancel each other. 01:22:29.090 --> 01:22:34.010 align:middle line:84% So Seebeck, for electron is negative, for hole is positive, 01:22:34.010 --> 01:22:37.160 align:middle line:84% and then you combine when you have 01:22:37.160 --> 01:22:40.610 align:middle line:84% two different electric conductivity or electron hole. 01:22:40.610 --> 01:22:45.240 align:middle line:84% And what's worse is this thermal conductivity. 01:22:45.240 --> 01:22:49.590 align:middle line:84% They just don't not only combine electron hole and lattice 01:22:49.590 --> 01:22:56.400 align:middle line:84% vibration, but the combined-- they carry a cluster. 01:22:56.400 --> 01:23:00.720 align:middle line:84% This is because when the electron and hole both diffuse 01:23:00.720 --> 01:23:03.720 align:middle line:84% from one place to the other, there 01:23:03.720 --> 01:23:05.730 align:middle line:84% is an extra energy across the bandgap. 01:23:05.730 --> 01:23:08.500 align:middle line:90% 01:23:08.500 --> 01:23:12.000 align:middle line:84% That extra energy-- so when electrons go from one diffuse 01:23:12.000 --> 01:23:15.450 align:middle line:84% to the next place, they combine with the hole in the next place, 01:23:15.450 --> 01:23:17.310 align:middle line:90% they carry a lot more energy. 01:23:17.310 --> 01:23:20.220 align:middle line:84% So this is a bipolar contribution 01:23:20.220 --> 01:23:25.500 align:middle line:84% of thermal conductivity-- very bad. 01:23:25.500 --> 01:23:30.190 align:middle line:84% And it took me several years to understand the bipolar. 01:23:30.190 --> 01:23:32.520 align:middle line:84% So even if you don't understand everything, 01:23:32.520 --> 01:23:34.025 align:middle line:90% you can still do research here. 01:23:34.025 --> 01:23:36.690 align:middle line:90% 01:23:36.690 --> 01:23:40.860 align:middle line:84% When I first wrote the thermoelectric proposal, 01:23:40.860 --> 01:23:43.320 align:middle line:84% I didn't know whether a metal was good 01:23:43.320 --> 01:23:46.460 align:middle line:84% or semiconductor was good, just to make 01:23:46.460 --> 01:23:48.195 align:middle line:90% you feel more comfortable. 01:23:48.195 --> 01:23:50.760 align:middle line:90% 01:23:50.760 --> 01:23:51.460 align:middle line:90% Look at this. 01:23:51.460 --> 01:23:53.640 align:middle line:90% This is the real material now. 01:23:53.640 --> 01:23:57.390 align:middle line:84% And this is actually out of an experiment. 01:23:57.390 --> 01:23:59.820 align:middle line:90% This is a Seebeck-- 01:23:59.820 --> 01:24:03.990 align:middle line:84% electric conductivity decreases with temperature. 01:24:03.990 --> 01:24:06.160 align:middle line:84% Seebeck increases with temperature. 01:24:06.160 --> 01:24:08.920 align:middle line:84% I wonder you start to appreciate-- look at the curve, 01:24:08.920 --> 01:24:11.400 align:middle line:84% see what the physics, what's [INAUDIBLE] physics? 01:24:11.400 --> 01:24:15.690 align:middle line:84% So I said, Seebeck typically increases with temperature. 01:24:15.690 --> 01:24:19.140 align:middle line:84% That's all fine, except that now finally start to drop. 01:24:19.140 --> 01:24:22.290 align:middle line:84% See, that's-- you said that was wrong. 01:24:22.290 --> 01:24:24.610 align:middle line:90% I'll say why. 01:24:24.610 --> 01:24:28.060 align:middle line:84% And if you look at the electrical number-- electron 01:24:28.060 --> 01:24:31.930 align:middle line:84% number density, then it will increase with temperature. 01:24:31.930 --> 01:24:33.940 align:middle line:84% So you think the electric conductivity 01:24:33.940 --> 01:24:37.110 align:middle line:84% should increase with temperature in semiconductor. 01:24:37.110 --> 01:24:42.026 align:middle line:84% But this is a completely wrong trend. 01:24:42.026 --> 01:24:44.800 align:middle line:84% If you think about n, go to check your n 01:24:44.800 --> 01:24:49.500 align:middle line:84% at the fourth slides, second slide I hand out, 01:24:49.500 --> 01:24:52.990 align:middle line:84% and that was a review from last lecture. 01:24:52.990 --> 01:24:58.990 align:middle line:84% The reason was that we dope this very heavily, and it's not-- 01:24:58.990 --> 01:25:00.910 align:middle line:90% almost like a metal. 01:25:00.910 --> 01:25:04.990 align:middle line:84% Metal, electric conductivity drop with temperature. 01:25:04.990 --> 01:25:08.410 align:middle line:84% So the carrier in the material is somewhere 01:25:08.410 --> 01:25:10.660 align:middle line:90% between semiconductor and metal. 01:25:10.660 --> 01:25:13.360 align:middle line:84% Microelectronics, you never dope that-- 01:25:13.360 --> 01:25:16.150 align:middle line:90% you seldom dope that. 01:25:16.150 --> 01:25:21.070 align:middle line:84% And so, in microelectronics and most semiconductor, 01:25:21.070 --> 01:25:25.220 align:middle line:84% the electric conductivity increases with temperature. 01:25:25.220 --> 01:25:29.690 align:middle line:84% And Seebeck, when I start to draw, 01:25:29.690 --> 01:25:33.770 align:middle line:84% so that's because when I go to higher temperature, 01:25:33.770 --> 01:25:35.330 align:middle line:90% I got a holes. 01:25:35.330 --> 01:25:40.310 align:middle line:84% Electrons go excited from valence band to conduction band 01:25:40.310 --> 01:25:42.260 align:middle line:84% and left behind the empty states, left 01:25:42.260 --> 01:25:44.630 align:middle line:84% behind this empty state of holes. 01:25:44.630 --> 01:25:48.260 align:middle line:84% So temperature increase, more excitation, more energy. 01:25:48.260 --> 01:25:51.680 align:middle line:84% You reject the electron from valence to the conduction band. 01:25:51.680 --> 01:25:52.890 align:middle line:90% You got holes. 01:25:52.890 --> 01:25:58.400 align:middle line:84% Holes is detrimental because they're canceling the electron. 01:25:58.400 --> 01:26:01.990 align:middle line:84% So when I go to high temperature, 01:26:01.990 --> 01:26:03.780 align:middle line:90% I start to drop there. 01:26:03.780 --> 01:26:07.400 align:middle line:90% The holes start to cancel. 01:26:07.400 --> 01:26:08.250 align:middle line:90% What do you do? 01:26:08.250 --> 01:26:10.160 align:middle line:90% You can dope it heavier. 01:26:10.160 --> 01:26:13.730 align:middle line:84% So this will have higher electron number, 01:26:13.730 --> 01:26:17.390 align:middle line:84% I shift to a higher temperature-- shift here. 01:26:17.390 --> 01:26:20.593 align:middle line:84% You can play with doping for different temperature. 01:26:20.593 --> 01:26:24.700 align:middle line:90% 01:26:24.700 --> 01:26:27.410 align:middle line:84% But here you see these pics here. 01:26:27.410 --> 01:26:29.500 align:middle line:90% You have to optimize it. 01:26:29.500 --> 01:26:32.110 align:middle line:84% And you can, if you do mature research, 01:26:32.110 --> 01:26:34.510 align:middle line:84% you can just miss the optimization. 01:26:34.510 --> 01:26:37.140 align:middle line:90% You may get a goal, throw away. 01:26:37.140 --> 01:26:39.940 align:middle line:90% That could happen. 01:26:39.940 --> 01:26:44.020 align:middle line:84% And so, there are a lot of details, of course, 01:26:44.020 --> 01:26:47.530 align:middle line:90% in doing the material research. 01:26:47.530 --> 01:26:52.260 align:middle line:90% OK, I think I will stop here.