WEBVTT 00:00:00.000 --> 00:00:01.976 align:middle line:90% [SQUEAKING] 00:00:01.976 --> 00:00:03.944 align:middle line:90% [RUSTLING] 00:00:03.944 --> 00:00:05.912 align:middle line:90% [CLICKING] 00:00:05.912 --> 00:00:17.060 align:middle line:90% 00:00:17.060 --> 00:00:18.860 align:middle line:84% JUEJUN HU: So in the last lecture, 00:00:18.860 --> 00:00:21.000 align:middle line:84% we discussed about the electronic structures 00:00:21.000 --> 00:00:22.400 align:middle line:90% in amorphous solids. 00:00:22.400 --> 00:00:24.100 align:middle line:84% We highlighted some differences here, 00:00:24.100 --> 00:00:26.600 align:middle line:84% one being that once you're introducing structure order, 00:00:26.600 --> 00:00:29.800 align:middle line:84% you inevitably create localized states, OK? 00:00:29.800 --> 00:00:33.500 align:middle line:84% And also, because of the presence of localized states, 00:00:33.500 --> 00:00:36.300 align:middle line:84% it means that you now no longer have a well-defined band gap, 00:00:36.300 --> 00:00:38.160 align:middle line:84% but instead, you have, essentially, 00:00:38.160 --> 00:00:40.120 align:middle line:84% a continuously distributed density 00:00:40.120 --> 00:00:42.740 align:middle line:84% of states across different energy energies. 00:00:42.740 --> 00:00:44.240 align:middle line:90% OK? 00:00:44.240 --> 00:00:47.360 align:middle line:84% What we will see next in this lecture 00:00:47.360 --> 00:00:50.160 align:middle line:84% is how the presence of these localized states 00:00:50.160 --> 00:00:51.880 align:middle line:84% will actually modify the transport 00:00:51.880 --> 00:00:54.320 align:middle line:90% properties of amorphous solids. 00:00:54.320 --> 00:00:55.820 align:middle line:90% OK? 00:00:55.820 --> 00:00:59.580 align:middle line:84% So as I mentioned, now, you have two kinds of states. 00:00:59.580 --> 00:01:02.980 align:middle line:84% You have extended states outside the mobility gap, localized 00:01:02.980 --> 00:01:05.019 align:middle line:90% states within the mobility gap. 00:01:05.019 --> 00:01:08.300 align:middle line:84% So when you're looking at the conduction, both kinds of states 00:01:08.300 --> 00:01:10.800 align:middle line:84% can actually contribute to electrical conduction. 00:01:10.800 --> 00:01:11.860 align:middle line:90% OK? 00:01:11.860 --> 00:01:14.020 align:middle line:84% So starting from the extended states, 00:01:14.020 --> 00:01:16.420 align:middle line:84% so for extended states in amorphous solids, 00:01:16.420 --> 00:01:19.500 align:middle line:84% the basic formalism describing the conductivity contributed 00:01:19.500 --> 00:01:21.980 align:middle line:84% by them are actually quite similar to that 00:01:21.980 --> 00:01:23.240 align:middle line:90% in crystalline solids. 00:01:23.240 --> 00:01:26.280 align:middle line:84% If you look at the equation here, it's really identical. 00:01:26.280 --> 00:01:30.420 align:middle line:84% The conductivity directly scales with mobility and the charge 00:01:30.420 --> 00:01:34.500 align:middle line:84% density or the density of the extended states. 00:01:34.500 --> 00:01:38.580 align:middle line:84% What's different, however, is in the expression for mobility 00:01:38.580 --> 00:01:39.660 align:middle line:90% here. 00:01:39.660 --> 00:01:40.540 align:middle line:90% OK? 00:01:40.540 --> 00:01:43.660 align:middle line:84% And this comes from the structure 00:01:43.660 --> 00:01:45.180 align:middle line:90% of the amorphous solids. 00:01:45.180 --> 00:01:48.033 align:middle line:84% So first thing is that in the amorphous solids, 00:01:48.033 --> 00:01:49.700 align:middle line:84% there are actually lots of, essentially, 00:01:49.700 --> 00:01:51.160 align:middle line:90% what we call the trapped states. 00:01:51.160 --> 00:01:53.860 align:middle line:84% Those are the states that's present in the band gap 00:01:53.860 --> 00:01:55.820 align:middle line:90% or in the mobility gap, OK? 00:01:55.820 --> 00:01:58.520 align:middle line:84% So when the electrons that are actually 00:01:58.520 --> 00:02:00.680 align:middle line:84% excited into the conduction valence band-- 00:02:00.680 --> 00:02:02.600 align:middle line:84% as they are moving along, there are 00:02:02.600 --> 00:02:05.800 align:middle line:84% chances that they may actually get trapped into those localized 00:02:05.800 --> 00:02:06.488 align:middle line:90% states. 00:02:06.488 --> 00:02:08.780 align:middle line:84% Now, once they get trapped into those localized states, 00:02:08.780 --> 00:02:10.520 align:middle line:84% obviously, they will stop contributing 00:02:10.520 --> 00:02:12.960 align:middle line:84% to the electrical conduction unless from an extended stay 00:02:12.960 --> 00:02:17.903 align:middle line:84% perspective, only till when they actually get released thermally 00:02:17.903 --> 00:02:19.820 align:middle line:84% back into the conduction band or valence band. 00:02:19.820 --> 00:02:22.030 align:middle line:84% Then they will contribute conduction once again. 00:02:22.030 --> 00:02:22.530 align:middle line:90% OK. 00:02:22.530 --> 00:02:26.120 align:middle line:84% So to account for the fact that these extended states-- 00:02:26.120 --> 00:02:28.520 align:middle line:84% the carriers do not always contribute 00:02:28.520 --> 00:02:30.680 align:middle line:84% to electrical conduction, we have 00:02:30.680 --> 00:02:32.280 align:middle line:84% to add this additional factor here. 00:02:32.280 --> 00:02:35.520 align:middle line:90% 1 minus f trap, OK? 00:02:35.520 --> 00:02:38.720 align:middle line:84% So f trap basically gives you the fraction of time 00:02:38.720 --> 00:02:40.680 align:middle line:84% when the carrier will be actually trapped 00:02:40.680 --> 00:02:45.600 align:middle line:90% in one of those trap states. 00:02:45.600 --> 00:02:49.460 align:middle line:84% So this will then decrease the effective mobility, 00:02:49.460 --> 00:02:51.160 align:middle line:90% you will see. 00:02:51.160 --> 00:02:52.660 align:middle line:90% OK? 00:02:52.660 --> 00:02:55.520 align:middle line:90% 00:02:55.520 --> 00:02:56.400 align:middle line:90% So that's one factor. 00:02:56.400 --> 00:02:58.525 align:middle line:84% Now, second is that if you look at this expression, 00:02:58.525 --> 00:03:05.060 align:middle line:84% mu 0 is what we call the free mobility. 00:03:05.060 --> 00:03:07.780 align:middle line:84% So this is assuming, if we ignore 00:03:07.780 --> 00:03:09.420 align:middle line:84% all these trapping events, what would 00:03:09.420 --> 00:03:12.760 align:middle line:84% be the apparent mobility we will observe for this extended state? 00:03:12.760 --> 00:03:15.900 align:middle line:90% 00:03:15.900 --> 00:03:19.380 align:middle line:84% I should mention that this mu 0 is also lower 00:03:19.380 --> 00:03:24.318 align:middle line:84% compared to the mobility in the crystalline counterpart. 00:03:24.318 --> 00:03:26.360 align:middle line:84% And the reason for that is pretty straightforward 00:03:26.360 --> 00:03:29.300 align:middle line:84% because in the amorphous solids, you get all this structure 00:03:29.300 --> 00:03:30.033 align:middle line:90% disorder. 00:03:30.033 --> 00:03:31.700 align:middle line:84% This structural disorder will contribute 00:03:31.700 --> 00:03:33.940 align:middle line:84% to scattering of carriers a lot more compared 00:03:33.940 --> 00:03:36.220 align:middle line:84% to in the case of crystalline solids. 00:03:36.220 --> 00:03:38.700 align:middle line:84% So as a result, the free mobility 00:03:38.700 --> 00:03:40.980 align:middle line:84% is also a lot lower compared to that 00:03:40.980 --> 00:03:42.760 align:middle line:84% in the case of crystalline material. 00:03:42.760 --> 00:03:50.940 align:middle line:90% 00:03:50.940 --> 00:03:54.680 align:middle line:84% So both factors combined together-- 00:03:54.680 --> 00:03:59.360 align:middle line:84% the apparent mobility you will see for the extended states 00:03:59.360 --> 00:04:01.040 align:middle line:90% in amorphous materials-- 00:04:01.040 --> 00:04:03.022 align:middle line:84% they will end up being orders of magnitude 00:04:03.022 --> 00:04:04.980 align:middle line:84% lower compared to the other crystalline solids. 00:04:04.980 --> 00:04:06.380 align:middle line:84% So if you look at, for example, in this example, 00:04:06.380 --> 00:04:08.255 align:middle line:84% what I'm showing on the right-hand side here, 00:04:08.255 --> 00:04:11.945 align:middle line:84% this is the electron drift mobility in amorphous silicon. 00:04:11.945 --> 00:04:13.320 align:middle line:84% If you look at the vertical axis, 00:04:13.320 --> 00:04:16.360 align:middle line:84% we are talking about drift mobility of the order of a few 00:04:16.360 --> 00:04:19.640 align:middle line:84% or even below 1 centimeters squared volts 00:04:19.640 --> 00:04:21.320 align:middle line:90% per second per volt per second. 00:04:21.320 --> 00:04:22.560 align:middle line:90% OK? 00:04:22.560 --> 00:04:27.480 align:middle line:84% So this is in contrast to the electron mobility in crystalline 00:04:27.480 --> 00:04:31.580 align:middle line:84% silicon, which is above 1,000 centimeters squared per volt per 00:04:31.580 --> 00:04:32.460 align:middle line:90% second, OK? 00:04:32.460 --> 00:04:35.640 align:middle line:90% 00:04:35.640 --> 00:04:38.240 align:middle line:84% So this huge difference means that essentially, 00:04:38.240 --> 00:04:41.580 align:middle line:84% the mobility in the amorphous solids tends to be a lot lower. 00:04:41.580 --> 00:04:44.840 align:middle line:84% The direct implication is that for mobility, 00:04:44.840 --> 00:04:47.380 align:middle line:84% if you are trying to use these materials, for example, 00:04:47.380 --> 00:04:50.177 align:middle line:84% for high speed electronic devices, for high speed 00:04:50.177 --> 00:04:51.760 align:middle line:84% electronic devices, you need a carrier 00:04:51.760 --> 00:04:55.220 align:middle line:84% to be quickly able to move in and out of the active region. 00:04:55.220 --> 00:04:59.180 align:middle line:84% And what this plot tells you is that these amorphous solids 00:04:59.180 --> 00:05:01.140 align:middle line:84% probably is a poor material if you're 00:05:01.140 --> 00:05:03.740 align:middle line:84% trying to use them for high speed applications. 00:05:03.740 --> 00:05:06.200 align:middle line:84% And again, if you look at the actual application 00:05:06.200 --> 00:05:08.120 align:middle line:84% people use these devices for-- for example, 00:05:08.120 --> 00:05:10.365 align:middle line:84% for display or maybe for solar cell-- 00:05:10.365 --> 00:05:11.740 align:middle line:84% none of those applications really 00:05:11.740 --> 00:05:13.200 align:middle line:90% require a gigahertz operation. 00:05:13.200 --> 00:05:13.700 align:middle line:90% OK? 00:05:13.700 --> 00:05:15.220 align:middle line:84% So that's a good reason why people are not using them 00:05:15.220 --> 00:05:16.660 align:middle line:90% for those applications. 00:05:16.660 --> 00:05:17.400 align:middle line:90% OK? 00:05:17.400 --> 00:05:18.442 align:middle line:90% The other thing. 00:05:18.442 --> 00:05:19.900 align:middle line:84% If you look at this plot here, this 00:05:19.900 --> 00:05:21.220 align:middle line:90% is basically an Arrhenius plot. 00:05:21.220 --> 00:05:24.080 align:middle line:84% Vertical axis is essentially logarithm of mobility. 00:05:24.080 --> 00:05:26.125 align:middle line:84% Horizontal axis is the inverse temperature. 00:05:26.125 --> 00:05:28.500 align:middle line:84% So you notice that it more or less follows this Arrhenius 00:05:28.500 --> 00:05:29.580 align:middle line:90% dependence. 00:05:29.580 --> 00:05:31.700 align:middle line:84% And as you go to higher temperature, 00:05:31.700 --> 00:05:34.593 align:middle line:84% the apparent mobility actually increases. 00:05:34.593 --> 00:05:36.260 align:middle line:84% And this comes from the fact that as you 00:05:36.260 --> 00:05:38.500 align:middle line:84% go to high temperature, the carriers essentially 00:05:38.500 --> 00:05:39.680 align:middle line:90% get more energy. 00:05:39.680 --> 00:05:42.700 align:middle line:84% It will stay less time being trapped in those localized 00:05:42.700 --> 00:05:43.240 align:middle line:90% states. 00:05:43.240 --> 00:05:43.740 align:middle line:90% OK? 00:05:43.740 --> 00:05:48.180 align:middle line:84% So if you look at the high temperature limit, 00:05:48.180 --> 00:05:49.920 align:middle line:84% if you go to infinite temperature, 00:05:49.920 --> 00:05:53.740 align:middle line:84% then what happens here is that essentially, the carriers, 00:05:53.740 --> 00:05:55.605 align:middle line:84% the, basically, f trap, the fraction 00:05:55.605 --> 00:05:57.980 align:middle line:84% of time staying in the trap, will essentially approach 0. 00:05:57.980 --> 00:06:00.400 align:middle line:84% And therefore, the mobility you're measuring here 00:06:00.400 --> 00:06:05.800 align:middle line:84% will then approach the free mobility, 00:06:05.800 --> 00:06:08.160 align:middle line:84% which, as you can tell, is still 3 orders of magnitude 00:06:08.160 --> 00:06:10.760 align:middle line:84% lower compared to what you get in a crystalline material. 00:06:10.760 --> 00:06:12.880 align:middle line:90% OK? 00:06:12.880 --> 00:06:15.920 align:middle line:84% All right, so for extended-stay conduction, 00:06:15.920 --> 00:06:18.420 align:middle line:84% basically, it still follows Arrhenius law, OK? 00:06:18.420 --> 00:06:21.320 align:middle line:84% It can be considered as a thermally activated process 00:06:21.320 --> 00:06:23.480 align:middle line:90% due to this detrapping process. 00:06:23.480 --> 00:06:27.495 align:middle line:84% Now, what about localized states? 00:06:27.495 --> 00:06:30.120 align:middle line:84% Now, unlike crystalline states, where the electrons essentially 00:06:30.120 --> 00:06:32.640 align:middle line:84% can freely roam across the entire material, 00:06:32.640 --> 00:06:34.760 align:middle line:84% in localized states, these electrons essentially 00:06:34.760 --> 00:06:38.960 align:middle line:84% only exist in a neighborhood of some defects, basically. 00:06:38.960 --> 00:06:39.680 align:middle line:90% OK? 00:06:39.680 --> 00:06:41.660 align:middle line:84% So if you want to have electrical conduction, 00:06:41.660 --> 00:06:43.820 align:middle line:84% you need these electrons to move around. 00:06:43.820 --> 00:06:46.680 align:middle line:90% 00:06:46.680 --> 00:06:49.800 align:middle line:84% So the only way to move around in the case of localized states 00:06:49.800 --> 00:06:51.620 align:middle line:84% is that they have to essentially hop 00:06:51.620 --> 00:06:54.358 align:middle line:84% from one localized state to another localized state. 00:06:54.358 --> 00:06:55.900 align:middle line:84% That's the only way they can actually 00:06:55.900 --> 00:06:58.620 align:middle line:84% move across the material, given the spatially confined 00:06:58.620 --> 00:07:00.740 align:middle line:90% nature of the wave function. 00:07:00.740 --> 00:07:02.660 align:middle line:90% OK? 00:07:02.660 --> 00:07:06.528 align:middle line:84% So the example of this hopping process-- it actually 00:07:06.528 --> 00:07:08.820 align:middle line:84% happens even in the case of crystallized semiconductive 00:07:08.820 --> 00:07:10.140 align:middle line:90% materials, OK? 00:07:10.140 --> 00:07:14.420 align:middle line:84% So for example, if you think about a crystalline material, 00:07:14.420 --> 00:07:16.700 align:middle line:84% if you put dopants in there, we mentioned 00:07:16.700 --> 00:07:22.920 align:middle line:84% that this is going to create states within the band gap. 00:07:22.920 --> 00:07:25.380 align:middle line:84% And then this will all create, essentially, 00:07:25.380 --> 00:07:27.780 align:middle line:84% localized states at each of the dopant atoms, 00:07:27.780 --> 00:07:29.660 align:middle line:90% around the dopant atoms, OK? 00:07:29.660 --> 00:07:32.100 align:middle line:84% So suppose, for example, what I'm plotting here-- this 00:07:32.100 --> 00:07:33.980 align:middle line:84% would be in the case of n type semiconductor 00:07:33.980 --> 00:07:35.740 align:middle line:90% with lots of donors. 00:07:35.740 --> 00:07:38.827 align:middle line:84% If you go to a really low temperature-- 00:07:38.827 --> 00:07:40.660 align:middle line:84% if you're a normal temperature, then because 00:07:40.660 --> 00:07:42.580 align:middle line:84% of the nature of these shallow dopants, 00:07:42.580 --> 00:07:44.173 align:middle line:84% all of the electrons on the carriers 00:07:44.173 --> 00:07:45.340 align:middle line:90% is going to get thermalized. 00:07:45.340 --> 00:07:47.590 align:middle line:84% They essentially release electrons into the conduction 00:07:47.590 --> 00:07:50.400 align:middle line:84% band, but if you go to cryogenic temperature, 00:07:50.400 --> 00:07:52.500 align:middle line:84% you can freeze out these carriers 00:07:52.500 --> 00:07:55.740 align:middle line:84% so that the dopants, or at least most of the dopants-- 00:07:55.740 --> 00:08:01.480 align:middle line:84% they will essentially be sitting at the donor atom. 00:08:01.480 --> 00:08:07.040 align:middle line:84% Now, this then creates a set of spatially separated localized 00:08:07.040 --> 00:08:08.720 align:middle line:90% states. 00:08:08.720 --> 00:08:11.160 align:middle line:84% If you apply electric field, then what happens 00:08:11.160 --> 00:08:13.760 align:middle line:84% is that these electrons can then hop 00:08:13.760 --> 00:08:17.240 align:middle line:84% from one of these dopant atoms to the next dopant 00:08:17.240 --> 00:08:22.280 align:middle line:84% atom and then so on and so forth, and in the process, 00:08:22.280 --> 00:08:24.220 align:middle line:84% contribute to electrical conduction. 00:08:24.220 --> 00:08:30.000 align:middle line:90% 00:08:30.000 --> 00:08:32.720 align:middle line:84% So this process, when from hopping 00:08:32.720 --> 00:08:35.240 align:middle line:84% from one atom to the other atom, this 00:08:35.240 --> 00:08:40.679 align:middle line:84% is basically a quantum mechanical tunneling process. 00:08:40.679 --> 00:08:43.396 align:middle line:90% OK? 00:08:43.396 --> 00:08:45.960 align:middle line:84% Now, in order for tunneling to take place, 00:08:45.960 --> 00:08:49.380 align:middle line:84% you need to have wave function overlap for the two 00:08:49.380 --> 00:08:51.060 align:middle line:90% neighboring localized states. 00:08:51.060 --> 00:08:52.532 align:middle line:90% OK? 00:08:52.532 --> 00:08:54.240 align:middle line:84% So more specifically, if you think about, 00:08:54.240 --> 00:08:56.032 align:middle line:84% for example, wave function for the electron 00:08:56.032 --> 00:08:57.907 align:middle line:84% at this one, because it's localized, 00:08:57.907 --> 00:08:59.740 align:middle line:84% what you're going to get-- the wave function 00:08:59.740 --> 00:09:02.100 align:middle line:84% is going to look something like this, if you 00:09:02.100 --> 00:09:03.600 align:middle line:90% think about the wave function. 00:09:03.600 --> 00:09:04.100 align:middle line:90% Psi. 00:09:04.100 --> 00:09:06.600 align:middle line:90% This is the x-axis. 00:09:06.600 --> 00:09:09.940 align:middle line:84% It's going to peak right at the dopant atom and then 00:09:09.940 --> 00:09:12.940 align:middle line:84% exponentially decay as you move away from the dopant atom. 00:09:12.940 --> 00:09:17.440 align:middle line:84% Same thing if you look at its neighbor dopant atom. 00:09:17.440 --> 00:09:19.940 align:middle line:84% You also get something like this. 00:09:19.940 --> 00:09:21.300 align:middle line:90% OK? 00:09:21.300 --> 00:09:24.420 align:middle line:84% So it is the overlap of the wave function 00:09:24.420 --> 00:09:27.820 align:middle line:84% that dictates the magnitude or the probability 00:09:27.820 --> 00:09:29.160 align:middle line:90% for this tunneling. 00:09:29.160 --> 00:09:32.100 align:middle line:90% 00:09:32.100 --> 00:09:36.820 align:middle line:84% So suppose you write the spacing between the two states, 00:09:36.820 --> 00:09:42.580 align:middle line:84% let's say, as R. Then mathematically, 00:09:42.580 --> 00:09:48.360 align:middle line:84% the wave function overlap will be given by exponential-- 00:09:48.360 --> 00:09:50.620 align:middle line:84% this wave function is exponentially decaying, 00:09:50.620 --> 00:09:58.020 align:middle line:84% so we can write it as exponential negative alpha R. 00:09:58.020 --> 00:09:58.520 align:middle line:90% OK? 00:09:58.520 --> 00:10:03.480 align:middle line:84% This will be what the wave function represents. 00:10:03.480 --> 00:10:09.280 align:middle line:84% So now, alpha is a constant we define to essentially gauge 00:10:09.280 --> 00:10:14.920 align:middle line:84% the spatial confinement of the localized wave function. 00:10:14.920 --> 00:10:17.800 align:middle line:84% In fact, mathematically, you can relate alpha directly 00:10:17.800 --> 00:10:22.180 align:middle line:84% to the imaginary part of your wave vector, OK? 00:10:22.180 --> 00:10:24.180 align:middle line:84% And that's pretty straightforward, actually. 00:10:24.180 --> 00:10:25.640 align:middle line:90% You can figure it out. 00:10:25.640 --> 00:10:28.480 align:middle line:90% OK? 00:10:28.480 --> 00:10:30.660 align:middle line:84% OK, then then if you define wave function this way, 00:10:30.660 --> 00:10:33.160 align:middle line:84% then the overlap here-- because you have two wave functions, 00:10:33.160 --> 00:10:34.920 align:middle line:84% you have to multiply them together. 00:10:34.920 --> 00:10:39.600 align:middle line:84% So essentially, it will become negative 2 alpha R. 00:10:39.600 --> 00:10:42.700 align:middle line:84% This will be effectively the wave function overlap. 00:10:42.700 --> 00:10:46.460 align:middle line:84% And we argue that the probability 00:10:46.460 --> 00:10:51.380 align:middle line:84% of tunneling within scales with this factor here. 00:10:51.380 --> 00:10:54.100 align:middle line:84% This is just for quantum mechanics, essentially. 00:10:54.100 --> 00:10:58.340 align:middle line:90% 00:10:58.340 --> 00:10:58.840 align:middle line:90% All right. 00:10:58.840 --> 00:11:00.840 align:middle line:84% So now, if you look at this vector, what it says 00:11:00.840 --> 00:11:03.100 align:middle line:90% is pretty clear. 00:11:03.100 --> 00:11:07.480 align:middle line:84% Assuming that, because in this case of a doped semiconductor, 00:11:07.480 --> 00:11:10.980 align:middle line:84% all the dopant atoms-- they are basically identical. 00:11:10.980 --> 00:11:12.980 align:middle line:84% So it means that the alpha is basically 00:11:12.980 --> 00:11:15.780 align:middle line:90% the same for all these states. 00:11:15.780 --> 00:11:22.243 align:middle line:84% Therefore, the larger the R, the smaller the hopping probability. 00:11:22.243 --> 00:11:24.160 align:middle line:84% And they actually decrease pretty drastically. 00:11:24.160 --> 00:11:25.452 align:middle line:90% It decreases exponentially, OK? 00:11:25.452 --> 00:11:29.420 align:middle line:84% So physically, what that means is that this kind of hopping 00:11:29.420 --> 00:11:34.015 align:middle line:84% will only take place between the nearest neighbors, practically. 00:11:34.015 --> 00:11:36.140 align:middle line:84% Anything further than that, the hopping probability 00:11:36.140 --> 00:11:39.580 align:middle line:84% drops exponentially, becomes negligible. 00:11:39.580 --> 00:11:41.826 align:middle line:90% OK. 00:11:41.826 --> 00:11:46.840 align:middle line:84% Now, this is what's known as fixed-range hopping. 00:11:46.840 --> 00:11:48.760 align:middle line:84% Essentially, fixed-range refers to the fact 00:11:48.760 --> 00:11:50.720 align:middle line:84% that this kind of hopping conduction only 00:11:50.720 --> 00:11:53.720 align:middle line:84% takes place between the two nearest neighbor localized 00:11:53.720 --> 00:11:55.220 align:middle line:90% states. 00:11:55.220 --> 00:11:55.720 align:middle line:90% OK? 00:11:55.720 --> 00:11:58.560 align:middle line:90% 00:11:58.560 --> 00:12:00.860 align:middle line:84% All right, so that's the case for localized states, 00:12:00.860 --> 00:12:03.040 align:middle line:84% for example, in a crystalline semiconductor. 00:12:03.040 --> 00:12:04.480 align:middle line:84% Now, in a mobile semiconductor, we 00:12:04.480 --> 00:12:06.280 align:middle line:84% expect something similar to take place. 00:12:06.280 --> 00:12:08.860 align:middle line:84% You get lots of localized states within the mobility gap. 00:12:08.860 --> 00:12:11.360 align:middle line:84% And therefore, you can have electrons essentially hop around 00:12:11.360 --> 00:12:12.840 align:middle line:90% between those localized states. 00:12:12.840 --> 00:12:15.420 align:middle line:84% Some important differences I want to mention here. 00:12:15.420 --> 00:12:18.420 align:middle line:84% First thing is that if you look at what I'm showing here, 00:12:18.420 --> 00:12:20.720 align:middle line:84% this is a very, very simplified schematic 00:12:20.720 --> 00:12:22.940 align:middle line:84% of the density of states within the mobility gap. 00:12:22.940 --> 00:12:26.080 align:middle line:84% There's essentially some density of states near the Fermi level. 00:12:26.080 --> 00:12:28.000 align:middle line:84% First thing we argue is that when 00:12:28.000 --> 00:12:29.660 align:middle line:84% we look at electrical conduction, 00:12:29.660 --> 00:12:32.520 align:middle line:84% we only need to consider localized states near the Fermi 00:12:32.520 --> 00:12:35.112 align:middle line:90% level. 00:12:35.112 --> 00:12:37.320 align:middle line:84% The argument for that is also pretty straightforward, 00:12:37.320 --> 00:12:39.875 align:middle line:84% similar to that in crystalline materials. 00:12:39.875 --> 00:12:42.500 align:middle line:84% If you think about, for example, metal, crystalline metal, when 00:12:42.500 --> 00:12:44.040 align:middle line:84% we talk about the electrical conduction, 00:12:44.040 --> 00:12:46.180 align:middle line:84% we said that only the states near the Fermi surface 00:12:46.180 --> 00:12:48.840 align:middle line:84% actually contribute to electrical conduction 00:12:48.840 --> 00:12:52.860 align:middle line:84% because if you look at states much above the Fermi level, 00:12:52.860 --> 00:12:54.015 align:middle line:90% they are all empty. 00:12:54.015 --> 00:12:56.140 align:middle line:84% There's no carrier to actually conduct electricity. 00:12:56.140 --> 00:12:58.840 align:middle line:84% If you look at states that's well below the Fermi level, 00:12:58.840 --> 00:13:00.060 align:middle line:90% then they're all filled. 00:13:00.060 --> 00:13:02.968 align:middle line:84% And because an electron is essentially a fermion, 00:13:02.968 --> 00:13:04.760 align:middle line:84% essentially, if you have all filled states, 00:13:04.760 --> 00:13:06.460 align:middle line:84% you cannot hop one to the other states. 00:13:06.460 --> 00:13:09.080 align:middle line:84% You need empty states in order for electrons to hop into. 00:13:09.080 --> 00:13:12.620 align:middle line:84% So that's why all the electrical conduction-- pretty much, they 00:13:12.620 --> 00:13:14.540 align:middle line:84% all take place around the Fermi level, where 00:13:14.540 --> 00:13:20.780 align:middle line:84% you get plenty of filled states and also empty states. 00:13:20.780 --> 00:13:23.380 align:middle line:84% So what we do-- let's label the density 00:13:23.380 --> 00:13:26.970 align:middle line:84% of states at the Fermi level with this letter g here. 00:13:26.970 --> 00:13:29.220 align:middle line:84% So g is basically a density of states of the localized 00:13:29.220 --> 00:13:31.140 align:middle line:90% states at the Fermi level. 00:13:31.140 --> 00:13:33.956 align:middle line:90% OK? 00:13:33.956 --> 00:13:36.020 align:middle line:90% OK, so that's the first thing. 00:13:36.020 --> 00:13:37.680 align:middle line:84% The hopping conduction only takes place 00:13:37.680 --> 00:13:38.820 align:middle line:90% around the Fermi level. 00:13:38.820 --> 00:13:40.525 align:middle line:90% OK. 00:13:40.525 --> 00:13:42.400 align:middle line:84% Now, second thing I also want to mention here 00:13:42.400 --> 00:13:43.580 align:middle line:84% is that if you look at this plot, 00:13:43.580 --> 00:13:45.040 align:middle line:84% you immediately realize that this 00:13:45.040 --> 00:13:48.200 align:middle line:84% is a bit different from the case of fixed-range hopping. 00:13:48.200 --> 00:13:52.560 align:middle line:84% The energy of those states that participate 00:13:52.560 --> 00:13:57.000 align:middle line:84% in the variable range hopping is not fixed. 00:13:57.000 --> 00:14:01.360 align:middle line:84% It's a distribution around the Fermi level. 00:14:01.360 --> 00:14:04.160 align:middle line:84% So it means that this hopping conduction can actually 00:14:04.160 --> 00:14:06.740 align:middle line:84% take place between two states with different energies. 00:14:06.740 --> 00:14:10.720 align:middle line:90% 00:14:10.720 --> 00:14:12.912 align:middle line:84% So when electrons want to hop from one state 00:14:12.912 --> 00:14:14.620 align:middle line:84% to another state with different energies, 00:14:14.620 --> 00:14:16.920 align:middle line:84% now, because of energy conservation, 00:14:16.920 --> 00:14:20.640 align:middle line:84% it means that it must involve another particle in the process 00:14:20.640 --> 00:14:23.040 align:middle line:84% just to fulfill the energy conservation condition. 00:14:23.040 --> 00:14:25.872 align:middle line:90% In this case, it's a phonon. 00:14:25.872 --> 00:14:28.080 align:middle line:84% So if you are hopping from one state with high energy 00:14:28.080 --> 00:14:29.680 align:middle line:84% to a state with low energy, you must 00:14:29.680 --> 00:14:31.865 align:middle line:84% emit the phonon to compensate for energy difference. 00:14:31.865 --> 00:14:33.240 align:middle line:84% Or alternatively, if you're going 00:14:33.240 --> 00:14:35.073 align:middle line:84% from a state with low energy to high energy, 00:14:35.073 --> 00:14:38.220 align:middle line:84% it must absorb a phonon in order to be able to actuate 00:14:38.220 --> 00:14:40.260 align:middle line:90% that kind of hopping. 00:14:40.260 --> 00:14:44.300 align:middle line:84% So in this case, hopping becomes a two-particle process. 00:14:44.300 --> 00:14:47.580 align:middle line:84% So if we still look at the probability of hopping, 00:14:47.580 --> 00:14:50.140 align:middle line:84% we are now the probability-- so this is basically 00:14:50.140 --> 00:14:53.060 align:middle line:84% hopping probability in the case of fixed-range hopping. 00:14:53.060 --> 00:14:57.020 align:middle line:84% In the case of amorphous solids, the probability 00:14:57.020 --> 00:14:59.900 align:middle line:84% will now be [INAUDIBLE] to two factors. 00:14:59.900 --> 00:15:03.780 align:middle line:84% The first factor is still the wave function overlap. 00:15:03.780 --> 00:15:05.180 align:middle line:90% Same. 00:15:05.180 --> 00:15:08.340 align:middle line:84% The second factor is the probability 00:15:08.340 --> 00:15:10.660 align:middle line:84% to find the phonon with the right energy 00:15:10.660 --> 00:15:12.700 align:middle line:84% to compensate the energy difference. 00:15:12.700 --> 00:15:14.820 align:middle line:84% Now, that probability is basically 00:15:14.820 --> 00:15:18.540 align:middle line:84% given by a Bose-Einstein distribution. 00:15:18.540 --> 00:15:21.700 align:middle line:84% But in this case, Boltzmann distribution 00:15:21.700 --> 00:15:23.780 align:middle line:84% is actually a very good approximation, OK? 00:15:23.780 --> 00:15:25.700 align:middle line:90% So what we have here-- 00:15:25.700 --> 00:15:26.840 align:middle line:90% then we have a-- 00:15:26.840 --> 00:15:30.300 align:middle line:90% 00:15:30.300 --> 00:15:41.640 align:middle line:84% let me just-- we will have negative kT delta E. OK? 00:15:41.640 --> 00:15:44.520 align:middle line:84% So here delta E is the energy difference 00:15:44.520 --> 00:15:46.400 align:middle line:84% between the two states that participate 00:15:46.400 --> 00:15:49.760 align:middle line:90% in this hopping process. 00:15:49.760 --> 00:15:50.260 align:middle line:90% OK? 00:15:50.260 --> 00:15:53.880 align:middle line:90% 00:15:53.880 --> 00:15:57.360 align:middle line:84% So next step, we need to maximize P, similar to the case 00:15:57.360 --> 00:15:58.480 align:middle line:90% here. 00:15:58.480 --> 00:16:00.737 align:middle line:84% For fixed-range hopping, maximizing P 00:16:00.737 --> 00:16:01.820 align:middle line:90% is really straightforward. 00:16:01.820 --> 00:16:05.480 align:middle line:84% It just means that you need to have the smallest R, nearest 00:16:05.480 --> 00:16:06.680 align:middle line:90% neighbors, OK? 00:16:06.680 --> 00:16:10.840 align:middle line:84% But in this case, the situation gets a bit more complicated. 00:16:10.840 --> 00:16:14.600 align:middle line:84% What we argue here is that this hopping process does not 00:16:14.600 --> 00:16:18.200 align:middle line:84% necessarily take place between the nearest neighbors. 00:16:18.200 --> 00:16:19.640 align:middle line:90% OK? 00:16:19.640 --> 00:16:22.140 align:middle line:84% Sometimes, if you're willing to travel a little bit further, 00:16:22.140 --> 00:16:23.890 align:middle line:84% go to a state that's a little bit further, 00:16:23.890 --> 00:16:26.960 align:middle line:84% you may be able to find a state that's actually closer in energy 00:16:26.960 --> 00:16:28.215 align:middle line:90% to the starting state. 00:16:28.215 --> 00:16:29.840 align:middle line:84% And therefore, the second term actually 00:16:29.840 --> 00:16:32.340 align:middle line:84% becomes bigger, which compensate for the decrease 00:16:32.340 --> 00:16:33.640 align:middle line:90% of the first term. 00:16:33.640 --> 00:16:34.140 align:middle line:90% OK? 00:16:34.140 --> 00:16:36.820 align:middle line:90% 00:16:36.820 --> 00:16:40.880 align:middle line:84% My analogy in everyday life is that, for example, 00:16:40.880 --> 00:16:45.380 align:middle line:84% if you ever want to refuel your car, and assuming your target 00:16:45.380 --> 00:16:48.460 align:middle line:84% is that you want to do this at the lowest cost, 00:16:48.460 --> 00:16:49.468 align:middle line:90% you have two options. 00:16:49.468 --> 00:16:51.760 align:middle line:84% You go to your nearest gas station and just fill it up, 00:16:51.760 --> 00:16:54.020 align:middle line:84% or you also realize that all the gas 00:16:54.020 --> 00:16:55.780 align:middle line:90% stations have different prices. 00:16:55.780 --> 00:16:58.480 align:middle line:84% If you're willing to drive maybe another extra half a mile, 00:16:58.480 --> 00:17:00.230 align:middle line:84% you may be able to find a gas station that 00:17:00.230 --> 00:17:02.580 align:middle line:84% actually has a lower price, which ends up being better. 00:17:02.580 --> 00:17:05.040 align:middle line:84% So then there goes this trade-off there. 00:17:05.040 --> 00:17:07.660 align:middle line:84% On one hand, you want to be able to search a larger distance 00:17:07.660 --> 00:17:10.700 align:middle line:84% range so that you find a gas station with a lower price. 00:17:10.700 --> 00:17:13.780 align:middle line:84% But at the same time, if you drive further, of course, 00:17:13.780 --> 00:17:14.922 align:middle line:90% you consume more gas. 00:17:14.922 --> 00:17:17.380 align:middle line:84% So eventually, that may actually increase the overall cost. 00:17:17.380 --> 00:17:19.980 align:middle line:84% So there's an optimized distance where 00:17:19.980 --> 00:17:23.700 align:middle line:84% you want to drive in order to get the lowest overall price. 00:17:23.700 --> 00:17:24.880 align:middle line:90% Same idea here. 00:17:24.880 --> 00:17:28.220 align:middle line:84% There's actually an optimal hopping distance 00:17:28.220 --> 00:17:31.520 align:middle line:84% to actually increase the overall probability 00:17:31.520 --> 00:17:32.940 align:middle line:90% of hopping between states. 00:17:32.940 --> 00:17:36.000 align:middle line:90% 00:17:36.000 --> 00:17:38.180 align:middle line:84% And this distance, as you'll see later, 00:17:38.180 --> 00:17:40.360 align:middle line:90% is a function of temperature. 00:17:40.360 --> 00:17:44.200 align:middle line:84% And that's why this hopping mechanism is called 00:17:44.200 --> 00:17:47.460 align:middle line:90% Variable Range Hopping, or VRH. 00:17:47.460 --> 00:17:50.000 align:middle line:90% 00:17:50.000 --> 00:17:52.200 align:middle line:84% So the hopping distance is not fixed. 00:17:52.200 --> 00:17:54.700 align:middle line:90% OK? 00:17:54.700 --> 00:18:00.720 align:middle line:84% So then what we do-- let's try to solve for this factor here. 00:18:00.720 --> 00:18:04.700 align:middle line:84% So let's try to maximize this function. 00:18:04.700 --> 00:18:06.340 align:middle line:84% Let's just put everything together, OK? 00:18:06.340 --> 00:18:17.960 align:middle line:84% It's going to be negative 2 alpha R negative kT delta E. 00:18:17.960 --> 00:18:21.840 align:middle line:84% So basically, in order to maximize this function, 00:18:21.840 --> 00:18:25.600 align:middle line:84% you need to minimize the exponent or the negative 00:18:25.600 --> 00:18:26.420 align:middle line:90% of the exponent. 00:18:26.420 --> 00:18:29.520 align:middle line:84% So you need to minimize this one. 00:18:29.520 --> 00:18:33.260 align:middle line:90% 00:18:33.260 --> 00:18:35.040 align:middle line:84% This is the fact that we want to minimize. 00:18:35.040 --> 00:18:35.540 align:middle line:90% OK? 00:18:35.540 --> 00:18:38.660 align:middle line:90% We want to make it smallest. 00:18:38.660 --> 00:18:42.140 align:middle line:90% So let me just write this as-- 00:18:42.140 --> 00:18:42.700 align:middle line:90% I don't know. 00:18:42.700 --> 00:18:47.360 align:middle line:84% Let me try to represent it with a letter. 00:18:47.360 --> 00:18:47.860 align:middle line:90% Tell me. 00:18:47.860 --> 00:18:49.600 align:middle line:90% What's your favorite letter? 00:18:49.600 --> 00:18:52.500 align:middle line:90% 00:18:52.500 --> 00:18:53.753 align:middle line:90% AUDIENCE: Beta? 00:18:53.753 --> 00:18:54.420 align:middle line:90% JUEJUN HU: Beta. 00:18:54.420 --> 00:18:54.920 align:middle line:90% All right. 00:18:54.920 --> 00:18:55.540 align:middle line:90% Sure. 00:18:55.540 --> 00:18:56.660 align:middle line:90% Sure. 00:18:56.660 --> 00:18:57.440 align:middle line:90% Greek letter. 00:18:57.440 --> 00:19:00.300 align:middle line:84% Surprised to learn that your favorite letter is a Greek one. 00:19:00.300 --> 00:19:00.880 align:middle line:90% That's OK. 00:19:00.880 --> 00:19:02.820 align:middle line:90% [CHUCKLES] Fine. 00:19:02.820 --> 00:19:03.960 align:middle line:90% Let's minimize that beta. 00:19:03.960 --> 00:19:04.460 align:middle line:90% OK? 00:19:04.460 --> 00:19:05.900 align:middle line:90% AUDIENCE: Alpha. 00:19:05.900 --> 00:19:06.898 align:middle line:90% JUEJUN HU: Alpha? 00:19:06.898 --> 00:19:07.940 align:middle line:90% I have omega alpha there. 00:19:07.940 --> 00:19:08.540 align:middle line:90% Sorry. 00:19:08.540 --> 00:19:10.300 align:middle line:90% No, your favorite is taken. 00:19:10.300 --> 00:19:13.620 align:middle line:84% That's why we go for the second favorite, beta. 00:19:13.620 --> 00:19:15.340 align:middle line:90% All right. 00:19:15.340 --> 00:19:18.500 align:middle line:84% So in order to get the minimum, what we need to do 00:19:18.500 --> 00:19:20.100 align:middle line:84% is that we need to essentially take 00:19:20.100 --> 00:19:22.860 align:middle line:84% the partial derivative of beta with respect to R 00:19:22.860 --> 00:19:24.820 align:middle line:90% and make it equal to 0. 00:19:24.820 --> 00:19:27.980 align:middle line:84% So if you do that, the first term is really straightforward. 00:19:27.980 --> 00:19:29.400 align:middle line:90% It's 2 alpha. 00:19:29.400 --> 00:19:34.880 align:middle line:84% The second term, we have to essentially look 00:19:34.880 --> 00:19:36.280 align:middle line:90% into it a little bit. 00:19:36.280 --> 00:19:39.160 align:middle line:84% We need to essentially establish a connection between delta E 00:19:39.160 --> 00:19:46.640 align:middle line:84% and R. So let's go back to the definition of delta E. Delta E 00:19:46.640 --> 00:19:48.932 align:middle line:84% essentially gives you the energy difference 00:19:48.932 --> 00:19:50.140 align:middle line:90% between the two states there. 00:19:50.140 --> 00:19:53.720 align:middle line:84% And if we want to find the states with a given energy 00:19:53.720 --> 00:19:56.160 align:middle line:84% difference, this has to do with abundance 00:19:56.160 --> 00:19:59.800 align:middle line:84% of the states in the surroundings. 00:19:59.800 --> 00:20:07.120 align:middle line:84% The abundance of states relates to the density of states. 00:20:07.120 --> 00:20:10.440 align:middle line:84% So density of states-- by definition, what it gives you 00:20:10.440 --> 00:20:14.500 align:middle line:84% is the number of states per unit volume per unit energy spacing. 00:20:14.500 --> 00:20:18.120 align:middle line:84% So for example, let's think about-- 00:20:18.120 --> 00:20:19.260 align:middle line:90% we have one particle. 00:20:19.260 --> 00:20:22.220 align:middle line:84% It won't hop to somewhere that's R distance away from it. 00:20:22.220 --> 00:20:26.140 align:middle line:84% If you make a sphere with a radius R, 00:20:26.140 --> 00:20:32.460 align:middle line:84% then the volume of the sphere is this one here, this vector, OK? 00:20:32.460 --> 00:20:39.460 align:middle line:84% Then you also times the energy spacing delta E. 00:20:39.460 --> 00:20:42.820 align:middle line:84% What this gives you-- density of states times volume times energy 00:20:42.820 --> 00:20:43.603 align:middle line:90% spacing-- 00:20:43.603 --> 00:20:45.020 align:middle line:84% gives you the number of states you 00:20:45.020 --> 00:20:47.820 align:middle line:84% can find within the sphere of radius R 00:20:47.820 --> 00:20:54.940 align:middle line:84% and also within the energy spacing of delta E. 00:20:54.940 --> 00:20:59.500 align:middle line:84% We argue that we want to set this to unity. 00:20:59.500 --> 00:21:02.180 align:middle line:84% We want to at least find one state that 00:21:02.180 --> 00:21:05.580 align:middle line:84% satisfies the condition that it's located to the center state 00:21:05.580 --> 00:21:07.660 align:middle line:84% within the sphere of distance R, and it's also 00:21:07.660 --> 00:21:15.560 align:middle line:84% within energy spacing of delta E. 00:21:15.560 --> 00:21:16.060 align:middle line:90% OK? 00:21:16.060 --> 00:21:17.860 align:middle line:84% This guarantees there exists one state that 00:21:17.860 --> 00:21:18.880 align:middle line:90% satisfies the condition. 00:21:18.880 --> 00:21:20.020 align:middle line:90% So they can hop over. 00:21:20.020 --> 00:21:21.540 align:middle line:90% OK? 00:21:21.540 --> 00:21:23.560 align:middle line:84% So if you take this condition, this actually 00:21:23.560 --> 00:21:27.600 align:middle line:84% relates delta E to R. So now, let's see what delta E is. 00:21:27.600 --> 00:21:32.840 align:middle line:90% Delta E now becomes-- 00:21:32.840 --> 00:21:40.320 align:middle line:90% this is 3 4 pi R cubed g. 00:21:40.320 --> 00:21:45.080 align:middle line:90% 00:21:45.080 --> 00:21:45.920 align:middle line:90% OK. 00:21:45.920 --> 00:21:48.720 align:middle line:90% Let's move over here. 00:21:48.720 --> 00:21:50.020 align:middle line:90% Now, what we have-- 00:21:50.020 --> 00:21:52.640 align:middle line:90% 00:21:52.640 --> 00:21:53.640 align:middle line:90% let's see. 00:21:53.640 --> 00:21:57.020 align:middle line:84% Let me write this beta term, simply start writing here. 00:21:57.020 --> 00:21:59.800 align:middle line:90% This is 2 alpha R plus-- 00:21:59.800 --> 00:22:02.640 align:middle line:84% let me just plug that in there-- delta E divided by kT. 00:22:02.640 --> 00:22:12.120 align:middle line:90% So you have 3 4 pi kT e. 00:22:12.120 --> 00:22:17.080 align:middle line:90% And then this is R to 3. 00:22:17.080 --> 00:22:21.580 align:middle line:84% So when you take the derivative with respect to R, 00:22:21.580 --> 00:22:23.400 align:middle line:90% now this is a negative. 00:22:23.400 --> 00:22:25.820 align:middle line:84% That's a negative 3 that comes up. 00:22:25.820 --> 00:22:40.360 align:middle line:84% So it becomes 9 4 pi kg T and then R negative 4. 00:22:40.360 --> 00:22:48.920 align:middle line:90% 00:22:48.920 --> 00:22:53.140 align:middle line:90% We let it equal to 0. 00:22:53.140 --> 00:22:55.760 align:middle line:84% And we can then solve for R, see what R is. 00:22:55.760 --> 00:23:00.700 align:middle line:90% 00:23:00.700 --> 00:23:03.060 align:middle line:90% Now, this gets more complicated. 00:23:03.060 --> 00:23:23.800 align:middle line:84% R becomes 9 8 pi alpha kg negative 1/4. 00:23:23.800 --> 00:23:24.920 align:middle line:90% OK? 00:23:24.920 --> 00:23:27.100 align:middle line:90% T is also negative 1/4. 00:23:27.100 --> 00:23:32.756 align:middle line:90% 00:23:32.756 --> 00:23:34.840 align:middle line:90% So what we are seeing here-- 00:23:34.840 --> 00:23:38.720 align:middle line:84% it basically says as you change temperature, 00:23:38.720 --> 00:23:41.680 align:middle line:84% the hopping distance is changing. 00:23:41.680 --> 00:23:46.720 align:middle line:84% The higher the temperature, the shorter the hopping distance. 00:23:46.720 --> 00:23:47.680 align:middle line:90% OK? 00:23:47.680 --> 00:23:49.680 align:middle line:84% This actually makes intuitive sense. 00:23:49.680 --> 00:23:53.440 align:middle line:84% The higher temperature means that you have more phonons 00:23:53.440 --> 00:23:55.000 align:middle line:90% available in the system. 00:23:55.000 --> 00:23:57.060 align:middle line:84% If you have more phonons available in the system, 00:23:57.060 --> 00:23:59.860 align:middle line:84% the importance of the second term actually decreases. 00:23:59.860 --> 00:24:02.160 align:middle line:84% It's a lot easier to find a state with energy close 00:24:02.160 --> 00:24:03.720 align:middle line:90% to the starting state. 00:24:03.720 --> 00:24:06.240 align:middle line:84% So then the system, or these mathematics, 00:24:06.240 --> 00:24:09.320 align:middle line:84% would then favor hopping between the nearest neighbors 00:24:09.320 --> 00:24:12.520 align:middle line:90% just to minimize beta. 00:24:12.520 --> 00:24:14.020 align:middle line:90% OK? 00:24:14.020 --> 00:24:17.020 align:middle line:90% 00:24:17.020 --> 00:24:19.558 align:middle line:84% So this is what we call the variable range hopping. 00:24:19.558 --> 00:24:21.100 align:middle line:84% Essentially, hopping distance becomes 00:24:21.100 --> 00:24:22.120 align:middle line:90% a function of temperature. 00:24:22.120 --> 00:24:24.578 align:middle line:84% The lower the temperature, the longer the hopping distance. 00:24:24.578 --> 00:24:26.820 align:middle line:84% The system will try to hop to a state that's 00:24:26.820 --> 00:24:31.020 align:middle line:84% further away in order to find the phonons, the right phonons. 00:24:31.020 --> 00:24:32.420 align:middle line:90% OK? 00:24:32.420 --> 00:24:32.920 align:middle line:90% All right. 00:24:32.920 --> 00:24:34.795 align:middle line:84% The last step is then we need to plug it back 00:24:34.795 --> 00:24:36.400 align:middle line:90% to the hopping probability. 00:24:36.400 --> 00:24:39.180 align:middle line:84% What we argue here is that the conductivity 00:24:39.180 --> 00:24:40.940 align:middle line:84% that you actually measured-- obviously, 00:24:40.940 --> 00:24:43.920 align:middle line:84% it should be proportional to hopping probability. 00:24:43.920 --> 00:24:49.940 align:middle line:84% And if you plug it back, it's actually pretty straightforward 00:24:49.940 --> 00:24:55.080 align:middle line:84% to see that eventually, it scales with an exponential-- 00:24:55.080 --> 00:24:55.580 align:middle line:90% no. 00:24:55.580 --> 00:25:10.500 align:middle line:90% 00:25:10.500 --> 00:25:11.040 align:middle line:90% OK? 00:25:11.040 --> 00:25:17.640 align:middle line:90% 00:25:17.640 --> 00:25:20.260 align:middle line:84% This is for variable range hopping. 00:25:20.260 --> 00:25:23.420 align:middle line:84% This is actually the well-known T to the negative 1/4 law. 00:25:23.420 --> 00:25:27.520 align:middle line:90% 00:25:27.520 --> 00:25:32.120 align:middle line:84% Some people also call this, essentially, Mott's law. 00:25:32.120 --> 00:25:35.240 align:middle line:84% Mott is the scientist who actually first proposed 00:25:35.240 --> 00:25:36.700 align:middle line:90% this theoretical formalism. 00:25:36.700 --> 00:25:41.160 align:middle line:90% 00:25:41.160 --> 00:25:44.243 align:middle line:84% Now, if you compare it with the Arrhenius law 00:25:44.243 --> 00:25:46.160 align:middle line:84% that you typically see for thermally activated 00:25:46.160 --> 00:25:49.320 align:middle line:84% process for extended states, Arrhenius law 00:25:49.320 --> 00:25:50.880 align:middle line:84% basically says that the conduction 00:25:50.880 --> 00:25:54.360 align:middle line:90% goes with T negative 1. 00:25:54.360 --> 00:25:56.840 align:middle line:84% This is the Arrhenius law, essentially. 00:25:56.840 --> 00:26:00.240 align:middle line:90% 00:26:00.240 --> 00:26:02.760 align:middle line:84% So if you try to plot, essentially, 00:26:02.760 --> 00:26:07.120 align:middle line:84% the electrical conduction in an amorphous solid or an Arrhenius 00:26:07.120 --> 00:26:09.080 align:middle line:84% plot, what we're going to see there 00:26:09.080 --> 00:26:13.040 align:middle line:84% is that the temperature dependence is actually less 00:26:13.040 --> 00:26:14.940 align:middle line:84% compared to the case of Arrhenius law. 00:26:14.940 --> 00:26:16.100 align:middle line:90% OK? 00:26:16.100 --> 00:26:19.980 align:middle line:84% Just to give you a-- let's look at-- 00:26:19.980 --> 00:26:22.300 align:middle line:84% so this is actually what it's going to be looking like. 00:26:22.300 --> 00:26:22.800 align:middle line:90% OK. 00:26:22.800 --> 00:26:24.920 align:middle line:84% This is an Arrhenius plot, typical Arrhenius plot. 00:26:24.920 --> 00:26:26.337 align:middle line:84% So if it's extended states, you're 00:26:26.337 --> 00:26:28.260 align:middle line:84% going to get, basically, just a straight line. 00:26:28.260 --> 00:26:30.860 align:middle line:84% And if it's variable range hopping, 00:26:30.860 --> 00:26:32.918 align:middle line:84% you have a curve looking something like this. 00:26:32.918 --> 00:26:34.460 align:middle line:84% As I said, the temperature dependence 00:26:34.460 --> 00:26:39.900 align:middle line:84% is less so that if you look at the high temperature, 00:26:39.900 --> 00:26:42.460 align:middle line:84% at high temperature, you get plenty of, essentially, 00:26:42.460 --> 00:26:44.980 align:middle line:84% extended states or plenty of free carriers in the conduction 00:26:44.980 --> 00:26:46.260 align:middle line:90% and now valence band. 00:26:46.260 --> 00:26:48.860 align:middle line:84% Now, in that case, extended state conduction always 00:26:48.860 --> 00:26:50.420 align:middle line:84% dominates because it's a lot easier 00:26:50.420 --> 00:26:52.913 align:middle line:84% to just move the carriers in these extended states 00:26:52.913 --> 00:26:55.580 align:middle line:84% rather than having to force them to hop from one localized state 00:26:55.580 --> 00:26:57.060 align:middle line:90% to another localized state. 00:26:57.060 --> 00:26:58.560 align:middle line:90% OK? 00:26:58.560 --> 00:27:02.900 align:middle line:84% However, when you go to low temperature, at low temperature, 00:27:02.900 --> 00:27:04.660 align:middle line:84% the number of free carriers essentially 00:27:04.660 --> 00:27:06.620 align:middle line:90% decreases exponentially. 00:27:06.620 --> 00:27:09.603 align:middle line:84% So at some point, there are so few extended states 00:27:09.603 --> 00:27:11.020 align:middle line:84% with free carrier populated that's 00:27:11.020 --> 00:27:13.040 align:middle line:84% available that electrical induction actually 00:27:13.040 --> 00:27:13.860 align:middle line:90% becomes very small. 00:27:13.860 --> 00:27:16.680 align:middle line:90% 00:27:16.680 --> 00:27:19.787 align:middle line:84% In that case, eventually, hopping 00:27:19.787 --> 00:27:22.120 align:middle line:84% is going to take over and become the dominant conduction 00:27:22.120 --> 00:27:24.360 align:middle line:84% mechanism at cryogenic temperature. 00:27:24.360 --> 00:27:26.920 align:middle line:90% 00:27:26.920 --> 00:27:29.280 align:middle line:84% This is very typical for any amorphous semiconductor. 00:27:29.280 --> 00:27:31.620 align:middle line:84% High temperature-- it behaves, essentially, linear. 00:27:31.620 --> 00:27:36.360 align:middle line:84% As you go to low temperature, Mott's T to the 1/4 law 00:27:36.360 --> 00:27:38.920 align:middle line:90% essentially takes over, OK? 00:27:38.920 --> 00:27:42.320 align:middle line:90% 00:27:42.320 --> 00:27:42.820 align:middle line:90% Yeah. 00:27:42.820 --> 00:27:44.480 align:middle line:84% So basically, if you measure the DC conductivity, 00:27:44.480 --> 00:27:46.340 align:middle line:84% it's going to be a combination of two terms. 00:27:46.340 --> 00:27:47.920 align:middle line:90% This is what it looks like. 00:27:47.920 --> 00:27:48.920 align:middle line:90% OK? 00:27:48.920 --> 00:27:52.430 align:middle line:84% So now, to show you that the science is correct, 00:27:52.430 --> 00:27:54.180 align:middle line:84% let's actually look at some real data, OK? 00:27:54.180 --> 00:27:56.160 align:middle line:84% In fact, by the way, this actually 00:27:56.160 --> 00:27:57.900 align:middle line:90% comes from my own PhD thesis. 00:27:57.900 --> 00:27:59.680 align:middle line:84% I was doing some conductivity measurement 00:27:59.680 --> 00:28:02.860 align:middle line:84% for these amorphous glass systems-- arsenic, selenium, 00:28:02.860 --> 00:28:03.840 align:middle line:90% tellurium, copper. 00:28:03.840 --> 00:28:05.080 align:middle line:90% OK. 00:28:05.080 --> 00:28:06.940 align:middle line:84% If you put copper into this glass there, 00:28:06.940 --> 00:28:08.982 align:middle line:84% turns out the copper actually forms a defect band 00:28:08.982 --> 00:28:09.963 align:middle line:90% within the band gap. 00:28:09.963 --> 00:28:11.380 align:middle line:84% And then the defect band obviously 00:28:11.380 --> 00:28:13.045 align:middle line:84% consists of lots of localized states. 00:28:13.045 --> 00:28:14.420 align:middle line:84% So those localized states is then 00:28:14.420 --> 00:28:17.700 align:middle line:84% going to promote this hopping conduction. 00:28:17.700 --> 00:28:19.820 align:middle line:84% At high temperature, on the other hand, 00:28:19.820 --> 00:28:22.940 align:middle line:84% this glass is actually a narrow band gap semiconductor, 00:28:22.940 --> 00:28:24.240 align:middle line:90% amorphous semiconductor. 00:28:24.240 --> 00:28:26.900 align:middle line:84% So you get electron electronic conduction. 00:28:26.900 --> 00:28:28.733 align:middle line:84% Copper, if you recall-- in the last lecture, 00:28:28.733 --> 00:28:30.150 align:middle line:84% we mentioned that this is actually 00:28:30.150 --> 00:28:32.340 align:middle line:84% one of the ions that has a very deformable electron 00:28:32.340 --> 00:28:33.300 align:middle line:90% cloud as well. 00:28:33.300 --> 00:28:36.082 align:middle line:84% So it can also contribute to ionic conduction, OK? 00:28:36.082 --> 00:28:38.540 align:middle line:84% But regardless of whether it's ionic conduction or extended 00:28:38.540 --> 00:28:41.900 align:middle line:84% state conduction, they all follow Arrhenius law. 00:28:41.900 --> 00:28:44.380 align:middle line:84% So that's why if you look at the high temperature 00:28:44.380 --> 00:28:46.960 align:middle line:84% regime on Arrhenius plot here-- this is Arrhenius plot. 00:28:46.960 --> 00:28:49.060 align:middle line:84% If you look at this range here, high temperature, 00:28:49.060 --> 00:28:52.280 align:middle line:84% you see that they more or less exhibit a linear trend. 00:28:52.280 --> 00:28:52.780 align:middle line:90% OK? 00:28:52.780 --> 00:28:55.100 align:middle line:84% But there's a very clear deviation 00:28:55.100 --> 00:28:56.520 align:middle line:90% as you go to lower temperature. 00:28:56.520 --> 00:28:57.220 align:middle line:90% OK? 00:28:57.220 --> 00:29:02.660 align:middle line:84% Now, instead, if you try to fit it with Mott's 1 over 4 law, 00:29:02.660 --> 00:29:04.480 align:middle line:90% you see the fitting coefficient. 00:29:04.480 --> 00:29:08.582 align:middle line:90% You get 0.99997. 00:29:08.582 --> 00:29:11.040 align:middle line:84% That's the moment you believe in science, when you actually 00:29:11.040 --> 00:29:12.040 align:middle line:90% look at those data. 00:29:12.040 --> 00:29:12.620 align:middle line:90% OK? 00:29:12.620 --> 00:29:14.160 align:middle line:84% So this is actually a very good example, 00:29:14.160 --> 00:29:16.535 align:middle line:84% where you see that you have almost perfect agreement with 00:29:16.535 --> 00:29:19.540 align:middle line:84% the Mott's negative 1/4 law, indicating that indeed, 00:29:19.540 --> 00:29:22.320 align:middle line:84% in this material system, there's very strong contribution coming 00:29:22.320 --> 00:29:24.940 align:middle line:84% from hopping at low temperatures. 00:29:24.940 --> 00:29:25.440 align:middle line:90% OK? 00:29:25.440 --> 00:29:28.840 align:middle line:90% 00:29:28.840 --> 00:29:29.800 align:middle line:90% OK? 00:29:29.800 --> 00:29:36.600 align:middle line:84% So the same dominance of this hopping at low temperature 00:29:36.600 --> 00:29:38.860 align:middle line:84% is quite significant for some other materials as well. 00:29:38.860 --> 00:29:42.888 align:middle line:84% For example, if you think about things like amorphous silicon, 00:29:42.888 --> 00:29:44.430 align:middle line:84% if you don't passivate it well, there 00:29:44.430 --> 00:29:46.480 align:middle line:84% are actually lots of states within the band gap. 00:29:46.480 --> 00:29:48.268 align:middle line:84% And as a result, this is then going 00:29:48.268 --> 00:29:50.560 align:middle line:84% to lead to a very strong contribution of variable range 00:29:50.560 --> 00:29:51.900 align:middle line:90% hopping at low temperature. 00:29:51.900 --> 00:29:56.380 align:middle line:84% And as a result, if you measure the conductivity, for example, 00:29:56.380 --> 00:29:58.795 align:middle line:84% for amorphous silicon versus crystalline silicon, 00:29:58.795 --> 00:30:00.920 align:middle line:84% at high temperature, obviously, crystalline silicon 00:30:00.920 --> 00:30:03.040 align:middle line:84% is going to be much higher because higher mobility, lots 00:30:03.040 --> 00:30:04.248 align:middle line:90% of carrier concentration, OK? 00:30:04.248 --> 00:30:06.008 align:middle line:84% But as you go to low temperature, 00:30:06.008 --> 00:30:08.300 align:middle line:84% it becomes possible that the amorphous silicon actually 00:30:08.300 --> 00:30:10.140 align:middle line:84% has higher electrical conductivity compared 00:30:10.140 --> 00:30:13.020 align:middle line:84% to the crystalline one because a crystalline semiconductor has 00:30:13.020 --> 00:30:15.100 align:middle line:84% very few contribution coming from hopping, 00:30:15.100 --> 00:30:17.060 align:middle line:90% unlike amorphous solids. 00:30:17.060 --> 00:30:18.020 align:middle line:90% OK? 00:30:18.020 --> 00:30:19.870 align:middle line:84% I'm basically giving you the answer to one 00:30:19.870 --> 00:30:21.120 align:middle line:90% of the [? Piazza ?] questions. 00:30:21.120 --> 00:30:23.520 align:middle line:90% [CHUCKLES] All right. 00:30:23.520 --> 00:30:26.340 align:middle line:84% So just to summarize what we have discussed here 00:30:26.340 --> 00:30:28.375 align:middle line:84% about the basic theory of electron conduction, 00:30:28.375 --> 00:30:30.500 align:middle line:84% we talked about two kinds of conduction mechanisms. 00:30:30.500 --> 00:30:31.875 align:middle line:84% We talked about ionic conduction. 00:30:31.875 --> 00:30:34.660 align:middle line:84% We talked about, essentially, electronic transport. 00:30:34.660 --> 00:30:38.040 align:middle line:84% For ionic conduction, everything boils down to this equation 00:30:38.040 --> 00:30:39.660 align:middle line:90% here. 00:30:39.660 --> 00:30:45.100 align:middle line:84% Conductivity scales with 1 over T times the Boltzmann factor, 00:30:45.100 --> 00:30:48.060 align:middle line:90% OK? 00:30:48.060 --> 00:30:51.740 align:middle line:84% And we mentioned that the main difference 00:30:51.740 --> 00:30:53.900 align:middle line:84% between amorphous system and crystalline system 00:30:53.900 --> 00:30:56.420 align:middle line:84% is that when you're trying to hop between those localized 00:30:56.420 --> 00:30:59.577 align:middle line:84% states for ions, the barrier height 00:30:59.577 --> 00:31:01.160 align:middle line:84% as well as the depth of the barriers-- 00:31:01.160 --> 00:31:04.320 align:middle line:84% those are actually statistically varying in amorphous solids. 00:31:04.320 --> 00:31:05.880 align:middle line:84% So as a result, when you actually 00:31:05.880 --> 00:31:09.200 align:middle line:84% plot them on an Arrhenius plot, the conductivity 00:31:09.200 --> 00:31:12.200 align:middle line:84% does exhibit a slight deviation from Arrhenius behavior. 00:31:12.200 --> 00:31:12.720 align:middle line:90% OK? 00:31:12.720 --> 00:31:14.640 align:middle line:84% That's the only difference there. 00:31:14.640 --> 00:31:18.120 align:middle line:84% For the electronic transport, you 00:31:18.120 --> 00:31:20.740 align:middle line:84% need to familiarize yourself with electronic structure, 00:31:20.740 --> 00:31:22.520 align:middle line:84% the band structure I'm showing here. 00:31:22.520 --> 00:31:23.800 align:middle line:90% OK? 00:31:23.800 --> 00:31:26.320 align:middle line:84% Unlike the case of crystalline solids, 00:31:26.320 --> 00:31:30.860 align:middle line:84% you don't have a k, crystal momentum or wave vector, 00:31:30.860 --> 00:31:32.080 align:middle line:90% whatever you call it. 00:31:32.080 --> 00:31:33.520 align:middle line:90% It's not a good quantum number. 00:31:33.520 --> 00:31:36.520 align:middle line:84% So that's why you can only represent the band structure 00:31:36.520 --> 00:31:39.060 align:middle line:84% in an amorphous material using density of states. 00:31:39.060 --> 00:31:41.520 align:middle line:84% You cannot plot the dispersion diagram or band diagram. 00:31:41.520 --> 00:31:42.188 align:middle line:90% OK? 00:31:42.188 --> 00:31:44.480 align:middle line:84% And you also have the presence of the localized states. 00:31:44.480 --> 00:31:46.120 align:middle line:84% They're giving rise to, essentially, a band tail 00:31:46.120 --> 00:31:46.980 align:middle line:90% in the gap states. 00:31:46.980 --> 00:31:50.703 align:middle line:84% And those also contribute to the variable range 00:31:50.703 --> 00:31:52.120 align:middle line:84% hopping conduction, which is again 00:31:52.120 --> 00:31:54.640 align:middle line:84% absent in the case of a crystalline semiconductor 00:31:54.640 --> 00:31:56.920 align:middle line:90% materials, OK? 00:31:56.920 --> 00:31:57.840 align:middle line:90% All right? 00:31:57.840 --> 00:32:02.520 align:middle line:84% So this is the basic theory chapter. 00:32:02.520 --> 00:32:11.140 align:middle line:84% Next, let me move on to the applications chapter. 00:32:11.140 --> 00:32:12.700 align:middle line:84% So for the applications, we are going 00:32:12.700 --> 00:32:16.300 align:middle line:84% to discuss amorphous silicon, which 00:32:16.300 --> 00:32:22.100 align:middle line:84% is one of the most important and most prevalent 00:32:22.100 --> 00:32:24.340 align:middle line:90% amorphous semiconductor systems. 00:32:24.340 --> 00:32:27.353 align:middle line:90% OK? 00:32:27.353 --> 00:32:29.020 align:middle line:84% And we are going to be talking about how 00:32:29.020 --> 00:32:32.860 align:middle line:84% to make macroelectronic devices out of amorphous silicon. 00:32:32.860 --> 00:32:38.620 align:middle line:84% I'm sure all of you have heard about microelectronic devices. 00:32:38.620 --> 00:32:40.460 align:middle line:84% In microelectronic devices, we all 00:32:40.460 --> 00:32:43.020 align:middle line:84% know that we have the Moore's law. 00:32:43.020 --> 00:32:44.820 align:middle line:84% What Moore's law says is that every 18 00:32:44.820 --> 00:32:46.420 align:middle line:84% months, the number of transistors 00:32:46.420 --> 00:32:48.020 align:middle line:90% will double on the chip. 00:32:48.020 --> 00:32:49.802 align:middle line:84% And then as a result, you can actually 00:32:49.802 --> 00:32:51.260 align:middle line:84% get more powerful and more powerful 00:32:51.260 --> 00:32:54.340 align:middle line:84% CPUs, making your computer smarter and smarter. 00:32:54.340 --> 00:32:56.780 align:middle line:84% And this is clearly shown in this plot here. 00:32:56.780 --> 00:32:58.580 align:middle line:84% Again, this one is a bit outdated. 00:32:58.580 --> 00:33:01.155 align:middle line:84% It was still showing 7-nanometer nodes. 00:33:01.155 --> 00:33:03.280 align:middle line:84% We know we are talking about 2-nanometer nodes now. 00:33:03.280 --> 00:33:07.040 align:middle line:84% So the Moore's law is actually continuing its trajectory 00:33:07.040 --> 00:33:11.160 align:middle line:84% in some sense, even till today, with the caveat 00:33:11.160 --> 00:33:12.582 align:middle line:90% that you probably know. 00:33:12.582 --> 00:33:14.540 align:middle line:84% Nowadays, when we're talking about 2-nanometer, 00:33:14.540 --> 00:33:18.400 align:middle line:84% 7-nanometer nodes, no longer refer to physical length 00:33:18.400 --> 00:33:20.940 align:middle line:84% or physical length of any of the structures on chip. 00:33:20.940 --> 00:33:23.120 align:middle line:84% Essentially, it's just a brand name. 00:33:23.120 --> 00:33:27.677 align:middle line:84% It's just, essentially, a marketing strategy, OK? 00:33:27.677 --> 00:33:29.760 align:middle line:84% In fact, if you look at, for example, 2-nanometer, 00:33:29.760 --> 00:33:33.420 align:middle line:84% 5-nanometer nodes, the actual length or size of the gate 00:33:33.420 --> 00:33:35.920 align:middle line:84% of the transistors in those structures is still of the order 00:33:35.920 --> 00:33:37.720 align:middle line:90% of 20 nanometers. 00:33:37.720 --> 00:33:38.807 align:middle line:90% It has stopped shrinking. 00:33:38.807 --> 00:33:40.640 align:middle line:84% People are actually going to different kinds 00:33:40.640 --> 00:33:41.720 align:middle line:90% of transistor architectures. 00:33:41.720 --> 00:33:43.400 align:middle line:84% They're starting from planar transistor. 00:33:43.400 --> 00:33:46.880 align:middle line:84% Then they go to FinFET, essentially a vertical thing. 00:33:46.880 --> 00:33:49.240 align:middle line:84% And then they go to so-called Gate-All-Around, GAA, 00:33:49.240 --> 00:33:49.740 align:middle line:90% essentially. 00:33:49.740 --> 00:33:51.940 align:middle line:84% But anyway, they changed the architectures there, 00:33:51.940 --> 00:33:54.080 align:middle line:84% but the feature size essentially, more or less, 00:33:54.080 --> 00:33:57.814 align:middle line:90% stays [? decadent. ?] OK? 00:33:57.814 --> 00:33:59.452 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:33:59.452 --> 00:34:00.160 align:middle line:90% JUEJUN HU: I saw. 00:34:00.160 --> 00:34:00.940 align:middle line:90% That's great. 00:34:00.940 --> 00:34:03.745 align:middle line:84% To some extent, there's a lot of innovation, new designs, 00:34:03.745 --> 00:34:05.120 align:middle line:84% new architectures, new materials. 00:34:05.120 --> 00:34:06.700 align:middle line:90% So there's new opportunities. 00:34:06.700 --> 00:34:08.631 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:34:08.631 --> 00:34:10.062 align:middle line:90% [LAUGHTER] 00:34:10.062 --> 00:34:12.047 align:middle line:90% AUDIENCE: They're lying to you. 00:34:12.047 --> 00:34:12.880 align:middle line:90% JUEJUN HU: Oh, yeah. 00:34:12.880 --> 00:34:14.320 align:middle line:84% True Yeah, all of them, all of them. 00:34:14.320 --> 00:34:14.820 align:middle line:90% Yeah. 00:34:14.820 --> 00:34:17.139 align:middle line:84% You talk to TSMC, Samsung, Intel? 00:34:17.139 --> 00:34:18.260 align:middle line:90% Yeah. 00:34:18.260 --> 00:34:18.760 align:middle line:90% No. 00:34:18.760 --> 00:34:21.560 align:middle line:84% [LAUGHS] There's no extra 2-nanometer transistor there, 00:34:21.560 --> 00:34:22.159 align:middle line:90% unfortunately. 00:34:22.159 --> 00:34:22.940 align:middle line:90% No. 00:34:22.940 --> 00:34:25.413 align:middle line:84% Anyway, but the bottom line for these microelectronics, 00:34:25.413 --> 00:34:27.580 align:middle line:84% we know that they are trying to make things smaller. 00:34:27.580 --> 00:34:29.480 align:middle line:84% The smaller you get, more devices 00:34:29.480 --> 00:34:31.739 align:middle line:84% you can pack there, something that gets more powerful. 00:34:31.739 --> 00:34:33.900 align:middle line:84% Now, macroelectronics-- we are talking 00:34:33.900 --> 00:34:36.739 align:middle line:84% about devices that follow completely different scaling 00:34:36.739 --> 00:34:37.280 align:middle line:90% laws. 00:34:37.280 --> 00:34:39.340 align:middle line:84% We're talking about devices such as displays, 00:34:39.340 --> 00:34:40.420 align:middle line:90% such as solar cells. 00:34:40.420 --> 00:34:44.980 align:middle line:84% In those cases, you actually need large area devices. 00:34:44.980 --> 00:34:47.340 align:middle line:84% And the figure of merit there essentially becomes 00:34:47.340 --> 00:34:52.199 align:middle line:84% the overall number of pixels or the cost per area. 00:34:52.199 --> 00:34:52.699 align:middle line:90% OK? 00:34:52.699 --> 00:34:55.380 align:middle line:84% Now, if you think about display, for example, 00:34:55.380 --> 00:34:59.000 align:middle line:84% when I was a little kid, the most fashionable gadget 00:34:59.000 --> 00:35:02.100 align:middle line:84% was a CRT display that's about maybe 8 inches in size. 00:35:02.100 --> 00:35:03.843 align:middle line:84% It's smaller than a pad you have, OK? 00:35:03.843 --> 00:35:05.760 align:middle line:84% And with a very low pixel count, so everything 00:35:05.760 --> 00:35:08.800 align:middle line:90% is very quantized, spatially. 00:35:08.800 --> 00:35:13.160 align:middle line:84% But now, we are talking about essentially huge micro-LED TVs 00:35:13.160 --> 00:35:16.020 align:middle line:90% with incredible resolution. 00:35:16.020 --> 00:35:17.000 align:middle line:90% OK? 00:35:17.000 --> 00:35:20.680 align:middle line:84% So these are what we call the macroelectronics. 00:35:20.680 --> 00:35:22.640 align:middle line:90% In this case, the scaling law-- 00:35:22.640 --> 00:35:25.400 align:middle line:84% I simply captured it as bigger is better. 00:35:25.400 --> 00:35:27.420 align:middle line:90% You want something that's huge. 00:35:27.420 --> 00:35:30.960 align:middle line:84% You can produce scalability with high quality. 00:35:30.960 --> 00:35:34.800 align:middle line:84% Well, that's where amorphous silicon comes in, OK? 00:35:34.800 --> 00:35:36.340 align:middle line:84% For those macroelectronic devices, 00:35:36.340 --> 00:35:39.240 align:middle line:84% you cannot use crystalline silicon out of the very simple 00:35:39.240 --> 00:35:42.068 align:middle line:84% reason that if you try to use crystalline silicon-- 00:35:42.068 --> 00:35:44.360 align:middle line:84% because single crystalline-- you have to either grow it 00:35:44.360 --> 00:35:46.080 align:middle line:84% on a single crystalline substrate, 00:35:46.080 --> 00:35:48.640 align:middle line:84% or you essentially have to cut it from a big single crystal 00:35:48.640 --> 00:35:49.360 align:middle line:90% boule. 00:35:49.360 --> 00:35:52.760 align:middle line:84% The largest size of wafer people are using nowadays 00:35:52.760 --> 00:35:54.580 align:middle line:84% in the industry is 300 millimeters. 00:35:54.580 --> 00:35:55.080 align:middle line:90% OK? 00:35:55.080 --> 00:35:56.620 align:middle line:90% 12 inches. 00:35:56.620 --> 00:36:00.700 align:middle line:84% While it sounds pretty big, it's smaller than your TV. 00:36:00.700 --> 00:36:01.260 align:middle line:90% OK? 00:36:01.260 --> 00:36:04.640 align:middle line:90% So that's why it doesn't work. 00:36:04.640 --> 00:36:05.260 align:middle line:90% OK? 00:36:05.260 --> 00:36:09.120 align:middle line:84% And also, for a lot of these macroelectronic devices, 00:36:09.120 --> 00:36:10.940 align:middle line:84% the figure of merit is quite different. 00:36:10.940 --> 00:36:13.620 align:middle line:84% For microelectronic devices, you want your computer to be fast. 00:36:13.620 --> 00:36:17.262 align:middle line:84% You want your transistors to respond at gigahertz speed. 00:36:17.262 --> 00:36:19.220 align:middle line:84% That's why you need single crystalline material 00:36:19.220 --> 00:36:20.980 align:middle line:90% with very high mobility. 00:36:20.980 --> 00:36:24.300 align:middle line:84% You don't care about your TV operating at gigahertz. 00:36:24.300 --> 00:36:27.540 align:middle line:84% Your eye cannot catch up to the high refresh rate, anyway. 00:36:27.540 --> 00:36:28.580 align:middle line:90% OK? 00:36:28.580 --> 00:36:31.660 align:middle line:84% So amorphous silicon turns out to be a pretty good material 00:36:31.660 --> 00:36:33.060 align:middle line:90% candidate. 00:36:33.060 --> 00:36:34.853 align:middle line:90% OK? 00:36:34.853 --> 00:36:37.520 align:middle line:84% So if you think about amorphous silicon, what I'm listing here-- 00:36:37.520 --> 00:36:39.360 align:middle line:84% these are the main advantage here, 00:36:39.360 --> 00:36:42.500 align:middle line:84% why they become attractive for macroelectronics. 00:36:42.500 --> 00:36:45.540 align:middle line:84% First one-- they can be deposited over a large area 00:36:45.540 --> 00:36:48.780 align:middle line:84% at low temperature in a monolithic manner. 00:36:48.780 --> 00:36:51.320 align:middle line:84% Large area-- obviously, if you can make it a large area, 00:36:51.320 --> 00:36:53.507 align:middle line:84% you can essentially scale down the cost per area. 00:36:53.507 --> 00:36:55.340 align:middle line:84% You can increase the fabrication throughput. 00:36:55.340 --> 00:36:56.320 align:middle line:90% OK? 00:36:56.320 --> 00:36:59.080 align:middle line:84% And this can be done essentially using a very mature so-called 00:36:59.080 --> 00:37:03.020 align:middle line:84% Plasma-Enhanced Chemical Vapor Deposition, or PECVD process. 00:37:03.020 --> 00:37:05.720 align:middle line:90% 00:37:05.720 --> 00:37:07.340 align:middle line:84% As I'll show you in a few minutes, 00:37:07.340 --> 00:37:10.620 align:middle line:84% people are now able to deposit on enormous glass substrates-- 00:37:10.620 --> 00:37:13.800 align:middle line:84% each one of them is several square meters-- 00:37:13.800 --> 00:37:16.240 align:middle line:84% in a continuous manner so that you 00:37:16.240 --> 00:37:18.160 align:middle line:84% can get extremely high fabrication throughput 00:37:18.160 --> 00:37:19.700 align:middle line:90% and that very, very low cost. 00:37:19.700 --> 00:37:24.240 align:middle line:90% 00:37:24.240 --> 00:37:26.410 align:middle line:90% Now, low temperature. 00:37:26.410 --> 00:37:28.920 align:middle line:84% The deposition temperature of amorphous silicon 00:37:28.920 --> 00:37:31.600 align:middle line:84% is also sufficiently low so that when you're actually 00:37:31.600 --> 00:37:33.580 align:middle line:84% putting the films on the substrate, 00:37:33.580 --> 00:37:36.080 align:middle line:84% you do not disrupt any of the existing devices 00:37:36.080 --> 00:37:38.265 align:middle line:84% or structures you already placed on substrate. 00:37:38.265 --> 00:37:39.640 align:middle line:84% And that's quite important coming 00:37:39.640 --> 00:37:40.900 align:middle line:90% from integration perspective. 00:37:40.900 --> 00:37:41.400 align:middle line:90% OK? 00:37:41.400 --> 00:37:44.200 align:middle line:90% Finally, monolithic. 00:37:44.200 --> 00:37:46.480 align:middle line:84% Monolithic essentially means that you can directly 00:37:46.480 --> 00:37:49.880 align:middle line:84% deposit these materials onto the target substrate 00:37:49.880 --> 00:37:51.620 align:middle line:90% versus hybrid approach. 00:37:51.620 --> 00:37:53.860 align:middle line:84% Hybrid means that you have to first deposit material 00:37:53.860 --> 00:37:55.000 align:middle line:90% on a foreign substrate. 00:37:55.000 --> 00:37:59.100 align:middle line:84% And then you can transfer it to the final target substrate. 00:37:59.100 --> 00:38:01.660 align:middle line:84% In lots of cases, monolithic integration 00:38:01.660 --> 00:38:04.360 align:middle line:84% is preferred because it simplifies the process, 00:38:04.360 --> 00:38:06.760 align:middle line:84% enhances yield, and enhances throughput. 00:38:06.760 --> 00:38:07.260 align:middle line:90% OK? 00:38:07.260 --> 00:38:10.637 align:middle line:84% And in that regard, because amorphous silicon is amorphous, 00:38:10.637 --> 00:38:12.220 align:middle line:84% it can really be deposited on any kind 00:38:12.220 --> 00:38:14.303 align:middle line:84% of substrate without having to worry about lattice 00:38:14.303 --> 00:38:15.235 align:middle line:90% matching constraints. 00:38:15.235 --> 00:38:16.860 align:middle line:84% It's actually advantageous specifically 00:38:16.860 --> 00:38:20.140 align:middle line:90% for monolithic integration. 00:38:20.140 --> 00:38:22.660 align:middle line:84% Finally, the last advantage I want to mention here 00:38:22.660 --> 00:38:26.660 align:middle line:84% is that in PECVD process, you can not only 00:38:26.660 --> 00:38:27.960 align:middle line:90% deposit amorphous silicon. 00:38:27.960 --> 00:38:31.780 align:middle line:84% You can also deposit passivation layers in the same process flow. 00:38:31.780 --> 00:38:33.260 align:middle line:90% OK? 00:38:33.260 --> 00:38:34.780 align:middle line:84% And passivation layers are actually 00:38:34.780 --> 00:38:36.980 align:middle line:84% extremely important for semiconductors. 00:38:36.980 --> 00:38:38.715 align:middle line:84% The reason people like silicon is 00:38:38.715 --> 00:38:41.340 align:middle line:84% because you get silicon dioxide, which is a perfect passivation 00:38:41.340 --> 00:38:42.020 align:middle line:90% layer. 00:38:42.020 --> 00:38:44.780 align:middle line:84% If you look back, in the 1960s, people were actually arguing 00:38:44.780 --> 00:38:47.540 align:middle line:84% about whether or not they should use germanium in silicon 00:38:47.540 --> 00:38:48.680 align:middle line:90% as a preferred material. 00:38:48.680 --> 00:38:50.460 align:middle line:84% Germanium does have many advantages with respect 00:38:50.460 --> 00:38:52.668 align:middle line:84% to silicon, like higher mobility, that kind of thing. 00:38:52.668 --> 00:38:55.880 align:middle line:84% The problem with germanium is that germanium oxide is not 00:38:55.880 --> 00:38:56.380 align:middle line:90% stable. 00:38:56.380 --> 00:38:58.360 align:middle line:90% It's actually soluble in water. 00:38:58.360 --> 00:39:01.420 align:middle line:84% So it's a terrible passivating material versus silicon dioxide. 00:39:01.420 --> 00:39:02.500 align:middle line:90% It's just great. 00:39:02.500 --> 00:39:03.620 align:middle line:90% Same thing here. 00:39:03.620 --> 00:39:06.360 align:middle line:84% For amorphous silicon, you can deposit the passivation layers, 00:39:06.360 --> 00:39:09.320 align:middle line:84% whether silicon dioxide or silicon nitride, 00:39:09.320 --> 00:39:11.720 align:middle line:84% in the same chamber where you deposit amorphous silicon 00:39:11.720 --> 00:39:13.760 align:middle line:84% without even having to actually break vacuum 00:39:13.760 --> 00:39:15.200 align:middle line:90% and remove the substrates. 00:39:15.200 --> 00:39:17.020 align:middle line:84% So it's a very convenient process. 00:39:17.020 --> 00:39:20.520 align:middle line:84% And you can do that continuously. 00:39:20.520 --> 00:39:21.020 align:middle line:90% All right. 00:39:21.020 --> 00:39:23.360 align:middle line:90% Next, doping capacity. 00:39:23.360 --> 00:39:25.020 align:middle line:90% You can dope amorphous silicon. 00:39:25.020 --> 00:39:28.140 align:middle line:84% While this may sound trivial, it's not. 00:39:28.140 --> 00:39:28.640 align:middle line:90% OK? 00:39:28.640 --> 00:39:32.880 align:middle line:84% As I will show you in the next slide, for a long time, 00:39:32.880 --> 00:39:35.760 align:middle line:84% people have thought amorphous silicon is a useless electronic 00:39:35.760 --> 00:39:39.060 align:middle line:84% material because they cannot dope it. 00:39:39.060 --> 00:39:39.560 align:middle line:90% OK? 00:39:39.560 --> 00:39:43.535 align:middle line:84% It's limited by a phenomenon called Fermi level pinning, 00:39:43.535 --> 00:39:46.160 align:middle line:84% that when you actually dope it, even if you put a lot of dopant 00:39:46.160 --> 00:39:48.460 align:middle line:84% in there, you do not shift the position of Fermi level. 00:39:48.460 --> 00:39:50.200 align:middle line:84% If you don't change the Fermi level position, 00:39:50.200 --> 00:39:51.560 align:middle line:84% you don't change the carrier concentration. 00:39:51.560 --> 00:39:53.352 align:middle line:84% You cannot make any, have junction devices. 00:39:53.352 --> 00:39:55.340 align:middle line:84% You cannot control the carrier concentration. 00:39:55.340 --> 00:39:56.588 align:middle line:90% It's a useless material. 00:39:56.588 --> 00:39:58.380 align:middle line:84% Now, the reason now people are able to dope 00:39:58.380 --> 00:40:01.580 align:middle line:84% it is because they were able to eliminate a lot of the defects 00:40:01.580 --> 00:40:04.860 align:middle line:84% in the material-- in particular, dangling bonds. 00:40:04.860 --> 00:40:05.580 align:middle line:90% OK? 00:40:05.580 --> 00:40:09.540 align:middle line:84% So dangling bonds-- these are the unsatisfied chemical bonds 00:40:09.540 --> 00:40:11.780 align:middle line:84% with essentially only one single electron. 00:40:11.780 --> 00:40:15.880 align:middle line:84% They are the dominant electron defects in amorphous silicon. 00:40:15.880 --> 00:40:19.740 align:middle line:90% 00:40:19.740 --> 00:40:23.860 align:middle line:84% So with plasma-enhanced CVD process, 00:40:23.860 --> 00:40:25.780 align:middle line:84% there's actually lots of hydrogen 00:40:25.780 --> 00:40:31.260 align:middle line:84% getting incorporated during the deposition of PECVD amorphously. 00:40:31.260 --> 00:40:33.480 align:middle line:84% And these hydrogen atoms-- they are quite small. 00:40:33.480 --> 00:40:35.300 align:middle line:90% They can move around. 00:40:35.300 --> 00:40:37.380 align:middle line:84% Hydrogen has one electron, so they can actually 00:40:37.380 --> 00:40:39.540 align:middle line:84% combine with a dangling bond to form 00:40:39.540 --> 00:40:41.780 align:middle line:90% a two-electron stable structure. 00:40:41.780 --> 00:40:44.380 align:middle line:84% And then as a result, this eliminates those electron 00:40:44.380 --> 00:40:45.180 align:middle line:90% defects. 00:40:45.180 --> 00:40:47.520 align:middle line:84% And now, amorphous silicon becomes 00:40:47.520 --> 00:40:50.280 align:middle line:90% amenable to actually doping. 00:40:50.280 --> 00:40:52.280 align:middle line:84% So the invention of PECVD amorphous silicon 00:40:52.280 --> 00:40:54.120 align:middle line:84% is what really opens up the door for all 00:40:54.120 --> 00:40:56.360 align:middle line:84% the electronic applications of amorphous silicon. 00:40:56.360 --> 00:40:59.764 align:middle line:90% OK? 00:40:59.764 --> 00:41:02.662 align:middle line:90% Now, finally, silicon. 00:41:02.662 --> 00:41:05.120 align:middle line:84% Even amorphous silicon is also compatible with all the CMOS 00:41:05.120 --> 00:41:06.420 align:middle line:90% process because it's silicon. 00:41:06.420 --> 00:41:10.320 align:middle line:84% So it's quite easy to use a lot of the existing infrastructure 00:41:10.320 --> 00:41:12.388 align:middle line:84% as well as technical know-how to develop process 00:41:12.388 --> 00:41:14.680 align:middle line:84% for amorphous silicon, leveraging what you already have 00:41:14.680 --> 00:41:16.040 align:middle line:90% for microelectronic industry. 00:41:16.040 --> 00:41:16.880 align:middle line:90% OK? 00:41:16.880 --> 00:41:17.480 align:middle line:90% OK. 00:41:17.480 --> 00:41:17.980 align:middle line:90% All right. 00:41:17.980 --> 00:41:20.392 align:middle line:84% So in the end, that's why I put this quote here. 00:41:20.392 --> 00:41:22.600 align:middle line:84% "The essence of being human is that one does not seek 00:41:22.600 --> 00:41:23.300 align:middle line:90% perfection." 00:41:23.300 --> 00:41:25.633 align:middle line:84% That's exactly the case in the case of macroelectronics. 00:41:25.633 --> 00:41:27.140 align:middle line:84% You do not need a perfect material. 00:41:27.140 --> 00:41:27.640 align:middle line:90% OK? 00:41:27.640 --> 00:41:29.505 align:middle line:84% As we'll see there, amorphous silicon still 00:41:29.505 --> 00:41:30.880 align:middle line:84% contains lots of defects compared 00:41:30.880 --> 00:41:32.800 align:middle line:84% to single crystalline silicon, but it's 00:41:32.800 --> 00:41:36.180 align:middle line:84% just adequate for macroelectronic applications. 00:41:36.180 --> 00:41:39.380 align:middle line:90% And that's why people use it. 00:41:39.380 --> 00:41:39.880 align:middle line:90% All right. 00:41:39.880 --> 00:41:41.760 align:middle line:84% So in this slide, I'm just basically showing 00:41:41.760 --> 00:41:44.040 align:middle line:84% you the structure of amorphous silicon. 00:41:44.040 --> 00:41:46.905 align:middle line:84% Left-hand side-- this is a unit cell of crystalline silicon. 00:41:46.905 --> 00:41:48.280 align:middle line:84% It has a diamond cubic structure. 00:41:48.280 --> 00:41:49.460 align:middle line:90% OK? 00:41:49.460 --> 00:41:52.780 align:middle line:84% If you look at the rings here, all 00:41:52.780 --> 00:41:55.710 align:middle line:84% of the rings in the crystalline silicon is six-membered rings. 00:41:55.710 --> 00:41:56.960 align:middle line:90% You can clearly see from here. 00:41:56.960 --> 00:42:00.260 align:middle line:84% This is a six-membered ring containing six silicon atoms. 00:42:00.260 --> 00:42:03.940 align:middle line:84% So in amorphous silicon, we have a more random distribution 00:42:03.940 --> 00:42:04.800 align:middle line:90% of the ring size. 00:42:04.800 --> 00:42:07.980 align:middle line:84% You can get five-membered ring, seven-membered rings, OK? 00:42:07.980 --> 00:42:10.880 align:middle line:84% As a result of this statistical nature of the structure, 00:42:10.880 --> 00:42:13.197 align:middle line:84% you also get lots of dangling bonds, as I said before. 00:42:13.197 --> 00:42:15.280 align:middle line:84% Not all the silicon becomes four-fold coordinated. 00:42:15.280 --> 00:42:17.700 align:middle line:84% Some of them have one extra electron hanging around. 00:42:17.700 --> 00:42:19.340 align:middle line:84% Those are the key electron defects 00:42:19.340 --> 00:42:21.740 align:middle line:90% that we have to address there. 00:42:21.740 --> 00:42:24.980 align:middle line:84% Now, what happens if you have lot of electron defects? 00:42:24.980 --> 00:42:27.900 align:middle line:90% Where's the-- OK. 00:42:27.900 --> 00:42:29.708 align:middle line:84% So if you have lots of electron defects, 00:42:29.708 --> 00:42:31.000 align:middle line:90% we can look at two things here. 00:42:31.000 --> 00:42:32.920 align:middle line:84% You can look at the density of states. 00:42:32.920 --> 00:42:34.940 align:middle line:90% This is what it looks like. 00:42:34.940 --> 00:42:39.260 align:middle line:84% These dangling bonds-- the defect associated with them 00:42:39.260 --> 00:42:41.700 align:middle line:84% is linked to this single atom layer. 00:42:41.700 --> 00:42:44.177 align:middle line:84% So spatially, they are very localized. 00:42:44.177 --> 00:42:45.760 align:middle line:84% What we have mentioned in last lecture 00:42:45.760 --> 00:42:48.360 align:middle line:84% is that if you have this kind of spatially localized defect 00:42:48.360 --> 00:42:51.560 align:middle line:84% states, it must have a very large imaginary part of the wave 00:42:51.560 --> 00:42:52.400 align:middle line:90% vector. 00:42:52.400 --> 00:42:53.520 align:middle line:90% OK? 00:42:53.520 --> 00:42:58.120 align:middle line:84% And as a result, it means that these states 00:42:58.120 --> 00:43:02.720 align:middle line:84% must be located near the center of the mobility gap. 00:43:02.720 --> 00:43:05.160 align:middle line:84% It's very far away from mobility edge. 00:43:05.160 --> 00:43:07.000 align:middle line:84% So they typically locate somewhere 00:43:07.000 --> 00:43:09.300 align:middle line:84% in the middle of the mobility gap, OK? 00:43:09.300 --> 00:43:12.440 align:middle line:90% So now, if you think about-- 00:43:12.440 --> 00:43:16.140 align:middle line:84% you essentially get lots of states 00:43:16.140 --> 00:43:21.000 align:middle line:84% right near the middle of the band gap or mobility gap. 00:43:21.000 --> 00:43:22.920 align:middle line:90% OK? 00:43:22.920 --> 00:43:25.000 align:middle line:84% So what happens if you try to dope it? 00:43:25.000 --> 00:43:26.760 align:middle line:84% If you try to dope it-- let's say you 00:43:26.760 --> 00:43:29.720 align:middle line:90% put some donors in there, OK? 00:43:29.720 --> 00:43:33.420 align:middle line:84% Normally, these electrons on these donors-- 00:43:33.420 --> 00:43:37.240 align:middle line:84% they will essentially thermalize and go to your conduction band. 00:43:37.240 --> 00:43:40.440 align:middle line:84% However, because of the presence of all 00:43:40.440 --> 00:43:43.820 align:middle line:84% of those states near the middle of the band gap, 00:43:43.820 --> 00:43:47.940 align:middle line:84% the electrons will instead try to fill the empty states 00:43:47.940 --> 00:43:50.340 align:middle line:90% near the middle of the gap. 00:43:50.340 --> 00:43:51.340 align:middle line:90% OK? 00:43:51.340 --> 00:43:54.740 align:middle line:84% So as a result, even if we're putting lots of dopant atoms, 00:43:54.740 --> 00:43:56.780 align:middle line:84% all of these electrons are just going 00:43:56.780 --> 00:44:00.300 align:middle line:84% to try to fill those mid-gap states. 00:44:00.300 --> 00:44:02.820 align:middle line:84% You need to essentially completely saturate 00:44:02.820 --> 00:44:04.260 align:middle line:90% all the mid-gap states. 00:44:04.260 --> 00:44:06.840 align:middle line:84% Then you can start to show the doping effect. 00:44:06.840 --> 00:44:10.700 align:middle line:90% 00:44:10.700 --> 00:44:13.620 align:middle line:84% So before you saturate all the states, then what you get 00:44:13.620 --> 00:44:16.700 align:middle line:84% is that essentially, you still have lots of empty 00:44:16.700 --> 00:44:21.780 align:middle line:84% and lots of filled states for those mid-gap defects. 00:44:21.780 --> 00:44:23.740 align:middle line:84% So the Fermi level, therefore, should also 00:44:23.740 --> 00:44:27.160 align:middle line:84% be located within the defect band. 00:44:27.160 --> 00:44:29.940 align:middle line:90% 00:44:29.940 --> 00:44:32.180 align:middle line:84% So effectively, what I'm saying here 00:44:32.180 --> 00:44:35.100 align:middle line:84% is that regardless of the dopant you put in there, if you don't 00:44:35.100 --> 00:44:37.340 align:middle line:84% saturate all these mid-gap states, 00:44:37.340 --> 00:44:39.020 align:middle line:84% the Fermi level will more or less 00:44:39.020 --> 00:44:43.120 align:middle line:84% be pinned near those mid-gap states. 00:44:43.120 --> 00:44:45.580 align:middle line:84% And that's why, when Fermi level position is fixed, 00:44:45.580 --> 00:44:47.900 align:middle line:84% you're not changing the carrier concentration. 00:44:47.900 --> 00:44:52.080 align:middle line:84% So you no longer get your doping effect. 00:44:52.080 --> 00:44:56.760 align:middle line:84% And this is known as Fermi level pinning, OK? 00:44:56.760 --> 00:45:01.200 align:middle line:84% So that's what I'm putting here on the slide. 00:45:01.200 --> 00:45:03.820 align:middle line:84% The Fermi level essentially gets pinned to the mid-gap state. 00:45:03.820 --> 00:45:06.760 align:middle line:90% 00:45:06.760 --> 00:45:08.638 align:middle line:84% Now, you may argue that-- well, simple. 00:45:08.638 --> 00:45:10.180 align:middle line:84% We just put lots of dopants in there. 00:45:10.180 --> 00:45:11.700 align:middle line:84% At some point, it's going to saturate all the defects. 00:45:11.700 --> 00:45:13.240 align:middle line:84% Then you start to get doping effect. 00:45:13.240 --> 00:45:16.060 align:middle line:84% It's actually quite difficult. Let's look at this plot here. 00:45:16.060 --> 00:45:18.102 align:middle line:84% What I'm showing you on the left-hand side here-- 00:45:18.102 --> 00:45:20.560 align:middle line:84% this is basically the conductivity in logarithm scale 00:45:20.560 --> 00:45:23.880 align:middle line:84% in the vertical axis as a function of inverse temperature 00:45:23.880 --> 00:45:25.340 align:middle line:90% to negative 1/4 power. 00:45:25.340 --> 00:45:28.280 align:middle line:84% So what you're seeing here is that at low temperature, 00:45:28.280 --> 00:45:30.960 align:middle line:84% you see that it follows pretty much a straight line, which 00:45:30.960 --> 00:45:33.580 align:middle line:84% indicates that you get variable range hopping. 00:45:33.580 --> 00:45:34.080 align:middle line:90% OK? 00:45:34.080 --> 00:45:37.880 align:middle line:84% Now, from the variable range hopping equation, 00:45:37.880 --> 00:45:41.860 align:middle line:84% you can actually infer what is the g here. 00:45:41.860 --> 00:45:44.460 align:middle line:84% That gives you the density of states near the Fermi level, 00:45:44.460 --> 00:45:46.180 align:middle line:84% which allows you to calculate what 00:45:46.180 --> 00:45:50.580 align:middle line:84% is the total number of defects within the mobility gap. 00:45:50.580 --> 00:45:51.460 align:middle line:90% OK? 00:45:51.460 --> 00:45:54.280 align:middle line:84% So according to that calculation, in this case, 00:45:54.280 --> 00:45:56.260 align:middle line:84% this is actually an amorphous silicon 00:45:56.260 --> 00:45:59.620 align:middle line:84% that's deposited using an electron beam evaporation. 00:45:59.620 --> 00:46:00.220 align:middle line:90% OK? 00:46:00.220 --> 00:46:02.500 align:middle line:84% If you do electron beam evaporation, 00:46:02.500 --> 00:46:03.880 align:middle line:90% essentially, you have a silicon. 00:46:03.880 --> 00:46:05.338 align:middle line:84% You heat it up at high temperature. 00:46:05.338 --> 00:46:07.460 align:middle line:84% They vaporize, condense to a cold substrate. 00:46:07.460 --> 00:46:08.600 align:middle line:90% It's a very high vacuum. 00:46:08.600 --> 00:46:09.612 align:middle line:90% So there's no impurity. 00:46:09.612 --> 00:46:11.820 align:middle line:84% What you end up getting is a very high purity silicon 00:46:11.820 --> 00:46:13.280 align:middle line:90% film only containing silicon. 00:46:13.280 --> 00:46:13.780 align:middle line:90% OK? 00:46:13.780 --> 00:46:16.660 align:middle line:84% So there's lots of dangling bonds that are not passivated 00:46:16.660 --> 00:46:20.340 align:middle line:84% by things like hydrogen. So the calculation tells you that 00:46:20.340 --> 00:46:22.460 align:middle line:84% in this pure amorphous silicon film, 00:46:22.460 --> 00:46:25.660 align:middle line:84% you get the mid-gap states with a concentration of 10 00:46:25.660 --> 00:46:29.820 align:middle line:90% to the 20th inverse centimeter. 00:46:29.820 --> 00:46:31.367 align:middle line:84% Now, typical semiconductor doping-- 00:46:31.367 --> 00:46:33.700 align:middle line:84% you're talking about doping concentration in order of 10 00:46:33.700 --> 00:46:35.530 align:middle line:90% to the 17th, 10 to the 18th. 00:46:35.530 --> 00:46:37.382 align:middle line:84% 10 to the 19th is considered high doping. 00:46:37.382 --> 00:46:39.340 align:middle line:84% 10 to the 20th-- that's like degenerate doping. 00:46:39.340 --> 00:46:40.960 align:middle line:90% It becomes practically metal. 00:46:40.960 --> 00:46:41.560 align:middle line:90% OK? 00:46:41.560 --> 00:46:43.580 align:middle line:84% So if you want to dope amorphous silicon, 00:46:43.580 --> 00:46:46.480 align:middle line:84% you need to put in at least 10 to the 20 carriers 00:46:46.480 --> 00:46:50.500 align:middle line:84% in order to then see any kind of a carrier concentration change. 00:46:50.500 --> 00:46:53.680 align:middle line:90% So that's not really practical. 00:46:53.680 --> 00:46:54.440 align:middle line:90% OK? 00:46:54.440 --> 00:46:58.040 align:middle line:84% So that's why, for a long time, if you don't passivate these 00:46:58.040 --> 00:46:59.880 align:middle line:84% dangling bone defects in amorphous silicon, 00:46:59.880 --> 00:47:03.380 align:middle line:84% this material is considered quite useless in the electronic 00:47:03.380 --> 00:47:04.880 align:middle line:84% industry because you cannot dope it. 00:47:04.880 --> 00:47:07.262 align:middle line:84% If you cannot dope it, you cannot make PN junctions. 00:47:07.262 --> 00:47:09.720 align:middle line:84% You cannot modulate the carrier concentration conductivity. 00:47:09.720 --> 00:47:11.600 align:middle line:90% It's of no use. 00:47:11.600 --> 00:47:14.952 align:middle line:90% OK. 00:47:14.952 --> 00:47:21.240 align:middle line:84% So what changes this picture is really the invention of a PECVD 00:47:21.240 --> 00:47:22.440 align:middle line:90% process, OK? 00:47:22.440 --> 00:47:25.920 align:middle line:84% In a PECVD process, the starting gas precursors 00:47:25.920 --> 00:47:28.820 align:middle line:84% are essentially silane, SiH4, typically. 00:47:28.820 --> 00:47:29.440 align:middle line:90% OK? 00:47:29.440 --> 00:47:32.077 align:middle line:84% And then you use hydrogen as a carrier gas. 00:47:32.077 --> 00:47:34.160 align:middle line:84% You then send it into a chamber where you actually 00:47:34.160 --> 00:47:35.860 align:middle line:90% get this active plasma. 00:47:35.860 --> 00:47:40.860 align:middle line:84% And this plasma is then going to split these precursor molecules 00:47:40.860 --> 00:47:42.940 align:middle line:90% into, essentially, radicals. 00:47:42.940 --> 00:47:44.140 align:middle line:90% OK? 00:47:44.140 --> 00:47:50.020 align:middle line:84% So you can get radicals, such as SiH3, SiH2, SiH, or even just 00:47:50.020 --> 00:47:51.640 align:middle line:90% hydrogen atom itself. 00:47:51.640 --> 00:47:56.020 align:middle line:84% Those precursors then condense onto the substrate 00:47:56.020 --> 00:47:58.645 align:middle line:84% to eventually form the amorphous silicon film. 00:47:58.645 --> 00:48:00.020 align:middle line:84% Now, you can see, in this process 00:48:00.020 --> 00:48:03.060 align:middle line:84% here, there's lots of hydrogen around. 00:48:03.060 --> 00:48:04.300 align:middle line:90% OK? 00:48:04.300 --> 00:48:06.540 align:middle line:84% First thing is that when you actually 00:48:06.540 --> 00:48:08.540 align:middle line:84% decompose the precursor, you still 00:48:08.540 --> 00:48:10.660 align:middle line:84% may have hydrogen attached to silicon. 00:48:10.660 --> 00:48:13.700 align:middle line:84% Also, because the carrier gas is hydrogen, 00:48:13.700 --> 00:48:17.780 align:middle line:84% this environment is really very much hydrogen-rich. 00:48:17.780 --> 00:48:20.180 align:middle line:84% So this abundance of hydrogen is what 00:48:20.180 --> 00:48:23.620 align:middle line:84% allows the passivation of those dangling node defects. 00:48:23.620 --> 00:48:25.180 align:middle line:90% OK. 00:48:25.180 --> 00:48:27.740 align:middle line:84% And with a reduced number of mid-gap states, 00:48:27.740 --> 00:48:30.620 align:middle line:84% then you'll be able to then effectively dope amorphous 00:48:30.620 --> 00:48:32.940 align:middle line:84% silicon together-- electronic devices. 00:48:32.940 --> 00:48:34.280 align:middle line:90% OK? 00:48:34.280 --> 00:48:34.780 align:middle line:90% All right. 00:48:34.780 --> 00:48:36.140 align:middle line:90% So that's the big picture. 00:48:36.140 --> 00:48:38.160 align:middle line:84% Now, on the right-hand side here, I'm 00:48:38.160 --> 00:48:41.200 align:middle line:84% showing you a schematic that illustrates how the deposition 00:48:41.200 --> 00:48:43.040 align:middle line:90% process actually takes place. 00:48:43.040 --> 00:48:44.440 align:middle line:90% OK? 00:48:44.440 --> 00:48:49.172 align:middle line:90% So basically, what do you have? 00:48:49.172 --> 00:48:50.880 align:middle line:84% On the top surface, what I'm showing here 00:48:50.880 --> 00:48:52.720 align:middle line:84% is a few layers of the silicon that's already 00:48:52.720 --> 00:48:53.845 align:middle line:90% deposited on the substrate. 00:48:53.845 --> 00:48:56.060 align:middle line:84% On the top layer, on the surface, 00:48:56.060 --> 00:48:58.560 align:middle line:84% you get both chemical bonds that are unsaturated, 00:48:58.560 --> 00:49:00.060 align:middle line:90% that essentially point upwards. 00:49:00.060 --> 00:49:03.240 align:middle line:84% So because there's tons of hydrogen around, 00:49:03.240 --> 00:49:06.680 align:middle line:84% normally, most of those chemical bonds would then have, 00:49:06.680 --> 00:49:08.860 align:middle line:84% essentially, hydrogen attached to them. 00:49:08.860 --> 00:49:10.760 align:middle line:84% So the surface is actually inert. 00:49:10.760 --> 00:49:14.960 align:middle line:84% It's passivated completely with hydrogen. OK? 00:49:14.960 --> 00:49:17.560 align:middle line:84% If you have new radicals coming onto the surface-- 00:49:17.560 --> 00:49:22.000 align:middle line:84% say SiH3 radical-- they would start by essentially adsorbing 00:49:22.000 --> 00:49:23.080 align:middle line:90% to the surface. 00:49:23.080 --> 00:49:24.600 align:middle line:84% It's not chemical attachment yet. 00:49:24.600 --> 00:49:25.100 align:middle line:90% OK? 00:49:25.100 --> 00:49:27.160 align:middle line:84% It's essentially physical adsorption. 00:49:27.160 --> 00:49:29.880 align:middle line:84% It will not be able to form the chemical bond with the surface 00:49:29.880 --> 00:49:31.963 align:middle line:84% because all the chemical bonds essentially are all 00:49:31.963 --> 00:49:34.680 align:middle line:90% saturated by hydrogen. OK? 00:49:34.680 --> 00:49:38.080 align:middle line:84% So what happens is that in some cases, 00:49:38.080 --> 00:49:41.460 align:middle line:84% sometimes, some of these SiH3, because there's 00:49:41.460 --> 00:49:43.580 align:middle line:84% one unsatisfied chemical bond, can 00:49:43.580 --> 00:49:46.570 align:middle line:84% combine with one of the hydrogen on the surface. 00:49:46.570 --> 00:49:48.820 align:middle line:84% And once it combines with the hydrogen on the surface, 00:49:48.820 --> 00:49:52.780 align:middle line:90% you form this SiH4 gas. 00:49:52.780 --> 00:49:53.800 align:middle line:90% It's a gas molecule. 00:49:53.800 --> 00:49:55.660 align:middle line:84% So it gets released to a surface. 00:49:55.660 --> 00:49:59.600 align:middle line:84% As you move into the free space you left behind, now, 00:49:59.600 --> 00:50:02.700 align:middle line:84% one unsatisfied dangling bond on the surface. 00:50:02.700 --> 00:50:06.180 align:middle line:90% The subsequent SiH3 radicals-- 00:50:06.180 --> 00:50:09.140 align:middle line:84% they can then diffuse on the surface through, essentially, 00:50:09.140 --> 00:50:12.200 align:middle line:84% surface diffusion onto this lattice size 00:50:12.200 --> 00:50:15.140 align:middle line:84% and then combine with that to essentially attach a new silicon 00:50:15.140 --> 00:50:16.060 align:middle line:90% atom. 00:50:16.060 --> 00:50:16.620 align:middle line:90% OK? 00:50:16.620 --> 00:50:19.220 align:middle line:84% So that's how the deposition process proceeds, essentially. 00:50:19.220 --> 00:50:21.940 align:middle line:84% So you have this extraction process of hydrogen 00:50:21.940 --> 00:50:23.780 align:middle line:84% from the surface by the radicals. 00:50:23.780 --> 00:50:26.180 align:middle line:84% And the other radicals then, through surface diffusion, 00:50:26.180 --> 00:50:28.700 align:middle line:84% come in, fill in the gap, and then form, essentially, 00:50:28.700 --> 00:50:30.180 align:middle line:90% the growth of the film. 00:50:30.180 --> 00:50:33.440 align:middle line:90% Does that make sense? 00:50:33.440 --> 00:50:34.920 align:middle line:84% You need to essentially remove some 00:50:34.920 --> 00:50:37.462 align:middle line:84% of the hydrogen from the surface to form these dangling bonds 00:50:37.462 --> 00:50:40.520 align:middle line:84% there so that you can have a continuous attachment of silicon 00:50:40.520 --> 00:50:41.960 align:middle line:90% onto those sites. 00:50:41.960 --> 00:50:44.000 align:middle line:90% AUDIENCE: So you're adding more? 00:50:44.000 --> 00:50:50.097 align:middle line:84% Was it not already satisfied or stable with hydrogen? 00:50:50.097 --> 00:50:51.180 align:middle line:90% JUEJUN HU: Initially, yes. 00:50:51.180 --> 00:50:52.480 align:middle line:84% Initially, it's all covered with hydrogen 00:50:52.480 --> 00:50:54.563 align:middle line:84% because there are lots of hydrogen on the surface. 00:50:54.563 --> 00:50:56.640 align:middle line:84% But the surface then becomes inert 00:50:56.640 --> 00:50:59.760 align:middle line:84% because there's no chemical bond to attach new atoms onto. 00:50:59.760 --> 00:51:01.560 align:middle line:84% So that's why you need some of the radicals 00:51:01.560 --> 00:51:03.498 align:middle line:84% to extract hydrogen from the surface-- 00:51:03.498 --> 00:51:04.040 align:middle line:90% AUDIENCE: Oh. 00:51:04.040 --> 00:51:04.820 align:middle line:90% JUEJUN HU: --to pull it away. 00:51:04.820 --> 00:51:05.720 align:middle line:90% AUDIENCE: Continue to add? 00:51:05.720 --> 00:51:07.740 align:middle line:84% JUEJUN HU: Yes, yeah, because it's a continuous process. 00:51:07.740 --> 00:51:08.782 align:middle line:90% You continue to flow gas. 00:51:08.782 --> 00:51:10.480 align:middle line:84% So there's always an abundance of supply 00:51:10.480 --> 00:51:13.440 align:middle line:90% for this surface adsorbed SiH3. 00:51:13.440 --> 00:51:14.540 align:middle line:90% And they will move around. 00:51:14.540 --> 00:51:16.840 align:middle line:84% Sometimes, they then remove a hydrogen from surface, 00:51:16.840 --> 00:51:19.680 align:middle line:84% go to a gas phase, leave behind the active site 00:51:19.680 --> 00:51:21.600 align:middle line:84% where the other can then diffuse onto that, 00:51:21.600 --> 00:51:23.000 align:middle line:90% attach to the surface. 00:51:23.000 --> 00:51:23.540 align:middle line:90% OK. 00:51:23.540 --> 00:51:25.280 align:middle line:84% So that's how the process goes on. 00:51:25.280 --> 00:51:29.140 align:middle line:84% Now, if you look at what I'm plotting down here, 00:51:29.140 --> 00:51:31.900 align:middle line:84% it's vertical axis is the defect density, basically dangling bond 00:51:31.900 --> 00:51:34.320 align:middle line:90% density in the silicon fuel. 00:51:34.320 --> 00:51:35.620 align:middle line:90% You deposit it. 00:51:35.620 --> 00:51:37.580 align:middle line:90% It's a function of temperature. 00:51:37.580 --> 00:51:39.940 align:middle line:84% There's some intermediate temperature that gives you 00:51:39.940 --> 00:51:42.460 align:middle line:90% the lowest defect density. 00:51:42.460 --> 00:51:43.280 align:middle line:90% OK? 00:51:43.280 --> 00:51:44.697 align:middle line:84% Now, the reason you have this kind 00:51:44.697 --> 00:51:47.940 align:middle line:84% of an intermediate temperature with optimal quality 00:51:47.940 --> 00:51:50.820 align:middle line:84% here is because if you go to low temperature, 00:51:50.820 --> 00:51:54.220 align:middle line:84% at low temperature, because the surface diffusion is essentially 00:51:54.220 --> 00:51:56.632 align:middle line:84% a thermally activated process, following Arrhenius law, 00:51:56.632 --> 00:51:58.340 align:middle line:84% at low temperature, the surface diffusion 00:51:58.340 --> 00:51:59.900 align:middle line:90% becomes very ineffective. 00:51:59.900 --> 00:52:04.540 align:middle line:84% These adsorbed SiH3 atoms hardly move on the surface. 00:52:04.540 --> 00:52:08.780 align:middle line:84% So then this extraction process becomes dominant process. 00:52:08.780 --> 00:52:11.500 align:middle line:84% You generate lots of surface dangling bonds. 00:52:11.500 --> 00:52:13.860 align:middle line:84% They are not adequately passivated 00:52:13.860 --> 00:52:16.300 align:middle line:90% by the subsequent SiH3 atoms. 00:52:16.300 --> 00:52:18.700 align:middle line:84% So then this essentially translates to a loss 00:52:18.700 --> 00:52:20.940 align:middle line:84% of surface defects, eventually, because 00:52:20.940 --> 00:52:23.820 align:middle line:84% of the unpassivated chemical bonds, OK? 00:52:23.820 --> 00:52:26.580 align:middle line:84% Now, if you go to a high temperature, 00:52:26.580 --> 00:52:29.840 align:middle line:84% this chemical reaction of SiH3 extraction 00:52:29.840 --> 00:52:32.520 align:middle line:84% of a hydrogen from surface and a release to free space 00:52:32.520 --> 00:52:34.520 align:middle line:84% is actually an endothermic reaction. 00:52:34.520 --> 00:52:37.165 align:middle line:84% Endothermic reaction means it actually absorbs heat. 00:52:37.165 --> 00:52:38.540 align:middle line:84% So if you go to high temperature, 00:52:38.540 --> 00:52:40.420 align:middle line:84% according to Le Chatelier's principle, 00:52:40.420 --> 00:52:43.000 align:middle line:84% the chemical equilibrium gets pushed along 00:52:43.000 --> 00:52:45.820 align:middle line:84% to essentially having this extraction there. 00:52:45.820 --> 00:52:49.240 align:middle line:84% So this will then also lead to, essentially, 00:52:49.240 --> 00:52:52.840 align:middle line:84% an inadequate passivation of the surface just because 00:52:52.840 --> 00:52:54.240 align:middle line:90% of the chemical equilibrium. 00:52:54.240 --> 00:52:58.320 align:middle line:84% So that's why there exists an optimal temperature window where 00:52:58.320 --> 00:53:01.600 align:middle line:84% you can have a minimal amount of this surface 00:53:01.600 --> 00:53:03.160 align:middle line:90% unpassivated chemical bond, OK? 00:53:03.160 --> 00:53:05.547 align:middle line:84% If you look at the temperature, also, you 00:53:05.547 --> 00:53:07.880 align:middle line:84% notice that the temperature is of the range of something 00:53:07.880 --> 00:53:10.980 align:middle line:84% like 250 degrees Celsius, 300 degrees Celsius. 00:53:10.980 --> 00:53:11.480 align:middle line:90% OK? 00:53:11.480 --> 00:53:13.647 align:middle line:84% That's also quite important because that temperature 00:53:13.647 --> 00:53:15.520 align:middle line:90% is actually adequately low. 00:53:15.520 --> 00:53:19.840 align:middle line:84% So it will not disrupt or damage any existing devices you already 00:53:19.840 --> 00:53:20.900 align:middle line:90% put on the substrate. 00:53:20.900 --> 00:53:21.400 align:middle line:90% OK? 00:53:21.400 --> 00:53:23.608 align:middle line:84% That's one advantage of using amorphous silicon here. 00:53:23.608 --> 00:53:26.080 align:middle line:84% You can do this low temperature processing. 00:53:26.080 --> 00:53:26.580 align:middle line:90% OK. 00:53:26.580 --> 00:53:30.260 align:middle line:90% 00:53:30.260 --> 00:53:30.760 align:middle line:90% All right. 00:53:30.760 --> 00:53:33.260 align:middle line:84% So that's about the deposition process. 00:53:33.260 --> 00:53:37.100 align:middle line:84% Next, in this table here, I'm summarizing 00:53:37.100 --> 00:53:39.940 align:middle line:84% the electronic properties of amorphous silicon in comparison 00:53:39.940 --> 00:53:42.700 align:middle line:84% to its bulk crystalline counterpart. 00:53:42.700 --> 00:53:44.200 align:middle line:90% OK. 00:53:44.200 --> 00:53:47.399 align:middle line:90% 00:53:47.399 --> 00:53:51.060 align:middle line:84% So what we are seeing here-- mobility. 00:53:51.060 --> 00:53:53.400 align:middle line:90% Again, mobility is way lower. 00:53:53.400 --> 00:53:55.440 align:middle line:84% This comes from two facts we have mentioned. 00:53:55.440 --> 00:53:57.940 align:middle line:84% One is that the free mobility is a lot lower 00:53:57.940 --> 00:54:00.780 align:middle line:84% because of the scattering of the disordered structure. 00:54:00.780 --> 00:54:03.580 align:middle line:84% Also, you get trapping effects, trapping and detrapping. 00:54:03.580 --> 00:54:06.300 align:middle line:84% So not all the carriers are always contributing 00:54:06.300 --> 00:54:07.600 align:middle line:90% to electrical conductivity. 00:54:07.600 --> 00:54:09.300 align:middle line:84% So both factors combined together-- 00:54:09.300 --> 00:54:11.540 align:middle line:84% you get mobility that's orders of magnitude 00:54:11.540 --> 00:54:14.460 align:middle line:90% lower compared to bulk silicon. 00:54:14.460 --> 00:54:15.700 align:middle line:90% OK? 00:54:15.700 --> 00:54:22.740 align:middle line:84% Now, this low mobility also means that the carrier diffusion 00:54:22.740 --> 00:54:25.840 align:middle line:84% length tends to be a lot smaller in amorphous silicon 00:54:25.840 --> 00:54:27.573 align:middle line:90% compared to crystalline silicon. 00:54:27.573 --> 00:54:29.240 align:middle line:84% The carrier diffusion length essentially 00:54:29.240 --> 00:54:32.840 align:middle line:84% gives you the average distance the carrier will move 00:54:32.840 --> 00:54:34.780 align:middle line:90% before they get recombined. 00:54:34.780 --> 00:54:35.280 align:middle line:90% OK? 00:54:35.280 --> 00:54:37.920 align:middle line:84% If you have a small mobility, the distance the carrier travels 00:54:37.920 --> 00:54:39.140 align:middle line:90% will get a lot smaller. 00:54:39.140 --> 00:54:42.360 align:middle line:84% And this accounts for the small carrier freelancing 00:54:42.360 --> 00:54:43.920 align:middle line:90% amorphous silicon. 00:54:43.920 --> 00:54:45.782 align:middle line:84% Now, what's the physical significance there? 00:54:45.782 --> 00:54:47.240 align:middle line:84% So if you're trying to make devices 00:54:47.240 --> 00:54:48.615 align:middle line:84% that rely on carrier collection-- 00:54:48.615 --> 00:54:50.040 align:middle line:90% for example, solar cells. 00:54:50.040 --> 00:54:52.480 align:middle line:84% Solar cells-- it operates like a PN junction. 00:54:52.480 --> 00:54:54.660 align:middle line:84% Light comes in, separates electrons on the host. 00:54:54.660 --> 00:54:57.800 align:middle line:84% They then move into the counted electrodes and get collected. 00:54:57.800 --> 00:55:00.640 align:middle line:84% So this process of those photoexcited carriers traveling 00:55:00.640 --> 00:55:03.640 align:middle line:84% to the context-- this relies on, essentially, carrier movement, 00:55:03.640 --> 00:55:05.320 align:middle line:90% diffusion and drift. 00:55:05.320 --> 00:55:09.280 align:middle line:84% So if you have a very small carrier diffusion length, 00:55:09.280 --> 00:55:11.760 align:middle line:84% it restricts, effectively, the thickness 00:55:11.760 --> 00:55:13.840 align:middle line:84% of the solar cell device you can make while still 00:55:13.840 --> 00:55:16.200 align:middle line:90% having high efficiency. 00:55:16.200 --> 00:55:18.840 align:middle line:84% What it means is that for amorphous silicon, 00:55:18.840 --> 00:55:21.080 align:middle line:84% the thickness of the solar cell probably 00:55:21.080 --> 00:55:24.580 align:middle line:84% is of the order of micron, 1 micron. 00:55:24.580 --> 00:55:25.220 align:middle line:90% OK? 00:55:25.220 --> 00:55:27.680 align:middle line:84% Anything thicker than that, you generate lots of carriers, 00:55:27.680 --> 00:55:29.620 align:middle line:84% but they will recombine before they reach your collection 00:55:29.620 --> 00:55:30.420 align:middle line:90% electrode. 00:55:30.420 --> 00:55:32.460 align:middle line:90% Then you get no current. 00:55:32.460 --> 00:55:33.020 align:middle line:90% OK? 00:55:33.020 --> 00:55:35.625 align:middle line:84% Versus crystalline silicon-- because of very large carrier 00:55:35.625 --> 00:55:37.500 align:middle line:84% diffusion lengths, you can make, essentially, 00:55:37.500 --> 00:55:40.540 align:middle line:84% crystalline silicon solar cells out of bulk wafers that's a few 00:55:40.540 --> 00:55:43.460 align:middle line:84% 10s or few 100s microns in thickness. 00:55:43.460 --> 00:55:44.060 align:middle line:90% OK? 00:55:44.060 --> 00:55:45.620 align:middle line:90% So that's the difference there. 00:55:45.620 --> 00:55:46.120 align:middle line:90% OK. 00:55:46.120 --> 00:55:48.620 align:middle line:84% Now, what we'll see in next slide is fortunately, 00:55:48.620 --> 00:55:51.020 align:middle line:84% amorphous silicon also has stronger light absorption. 00:55:51.020 --> 00:55:52.780 align:middle line:84% So this allows you to actually use a thinner film 00:55:52.780 --> 00:55:54.720 align:middle line:84% while still getting adequate light absorption. 00:55:54.720 --> 00:55:55.580 align:middle line:90% OK? 00:55:55.580 --> 00:55:56.080 align:middle line:90% All right. 00:55:56.080 --> 00:55:57.260 align:middle line:90% Now, next one. 00:55:57.260 --> 00:56:00.810 align:middle line:84% This is about doped conductivity and undoped conductivity. 00:56:00.810 --> 00:56:03.060 align:middle line:84% This is one aspect where amorphous silicon is actually 00:56:03.060 --> 00:56:03.980 align:middle line:90% pretty good. 00:56:03.980 --> 00:56:06.800 align:middle line:84% So if you look at the actual conductivity, absolute numbers, 00:56:06.800 --> 00:56:07.980 align:middle line:84% they tend to be a lot lower compared 00:56:07.980 --> 00:56:10.605 align:middle line:84% to the crystalline counterpart, again because of the much lower 00:56:10.605 --> 00:56:11.540 align:middle line:90% mobility there. 00:56:11.540 --> 00:56:15.100 align:middle line:84% But what really matters here is the contrast, 00:56:15.100 --> 00:56:18.580 align:middle line:84% the conductivity modulation between the doped material 00:56:18.580 --> 00:56:20.280 align:middle line:90% and undoped material. 00:56:20.280 --> 00:56:22.240 align:middle line:84% You can see that we still have nine 00:56:22.240 --> 00:56:24.800 align:middle line:84% orders of magnitude contrast between the dope, 00:56:24.800 --> 00:56:26.353 align:middle line:90% undoped states. 00:56:26.353 --> 00:56:28.520 align:middle line:84% That's actually really important for the application 00:56:28.520 --> 00:56:29.812 align:middle line:90% we're going to talk about here. 00:56:29.812 --> 00:56:31.530 align:middle line:84% For example, for display, people are 00:56:31.530 --> 00:56:33.280 align:middle line:84% using this amorphous silicon, essentially, 00:56:33.280 --> 00:56:36.480 align:middle line:84% to make thin film Transistors, essentially on/off switch, 00:56:36.480 --> 00:56:38.200 align:middle line:84% so they can turn the pixels on and off 00:56:38.200 --> 00:56:39.460 align:middle line:90% for display applications. 00:56:39.460 --> 00:56:42.080 align:middle line:84% In those cases, the figure of merit 00:56:42.080 --> 00:56:44.880 align:middle line:84% there is the contrast ratio, the on/off ratio. 00:56:44.880 --> 00:56:45.400 align:middle line:90% OK? 00:56:45.400 --> 00:56:49.020 align:middle line:84% And that actually directly relates to this ratio here. 00:56:49.020 --> 00:56:49.520 align:middle line:90% OK? 00:56:49.520 --> 00:56:51.467 align:middle line:84% So in that regard, amorphous silicon 00:56:51.467 --> 00:56:53.300 align:middle line:84% is pretty good for this kind of application. 00:56:53.300 --> 00:56:55.360 align:middle line:84% You can make very effective switches out 00:56:55.360 --> 00:56:57.320 align:middle line:90% of amorphous silicon. 00:56:57.320 --> 00:56:58.360 align:middle line:90% OK? 00:56:58.360 --> 00:56:59.080 align:middle line:90% Last one. 00:56:59.080 --> 00:57:01.280 align:middle line:90% Optical band gap. 00:57:01.280 --> 00:57:02.960 align:middle line:84% Amorphous silicon has a band gap that's 00:57:02.960 --> 00:57:06.120 align:middle line:84% actually much larger than crystalline silicon. 00:57:06.120 --> 00:57:10.680 align:middle line:84% The reason for that is because you put hydrogen in there, OK? 00:57:10.680 --> 00:57:13.380 align:middle line:84% In commercial-grade amorphous silicon, 00:57:13.380 --> 00:57:16.120 align:middle line:84% there's actually lots of hydrogen. Hydrogen is 00:57:16.120 --> 00:57:19.600 align:middle line:84% somewhere between 10% to 15% in amorphous silicon film. 00:57:19.600 --> 00:57:23.620 align:middle line:84% And that's why, if you look at this hydrogenated amorphous 00:57:23.620 --> 00:57:26.580 align:middle line:84% silicon field, it's customary that people write it 00:57:26.580 --> 00:57:27.340 align:middle line:90% in this form here. 00:57:27.340 --> 00:57:31.780 align:middle line:84% It's A silicon and then H, where the H represents 00:57:31.780 --> 00:57:34.020 align:middle line:84% that this is hydrogenated field with lots of hydrogen 00:57:34.020 --> 00:57:35.460 align:middle line:90% passivating defects. 00:57:35.460 --> 00:57:36.500 align:middle line:90% OK? 00:57:36.500 --> 00:57:39.760 align:middle line:84% So because of the large amount of hydrogen present in the film, 00:57:39.760 --> 00:57:41.600 align:middle line:84% it chemically modifies the structure. 00:57:41.600 --> 00:57:43.725 align:middle line:84% And therefore, this leads to a much larger band gap 00:57:43.725 --> 00:57:45.620 align:middle line:84% because hydrogen is a very light atom. 00:57:45.620 --> 00:57:49.300 align:middle line:84% So that's why amorphous silicon has a much larger band gap. 00:57:49.300 --> 00:57:50.800 align:middle line:90% OK? 00:57:50.800 --> 00:57:53.488 align:middle line:90% 00:57:53.488 --> 00:57:55.640 align:middle line:84% Now, this large band gap, of course, 00:57:55.640 --> 00:57:58.660 align:middle line:84% also impacts their optical absorption properties. 00:57:58.660 --> 00:58:00.983 align:middle line:84% So on this slide, I'm basically showing you 00:58:00.983 --> 00:58:03.400 align:middle line:84% this is basically absorption coefficient in vertical axis. 00:58:03.400 --> 00:58:07.500 align:middle line:84% Horizontal axis is the light energy, photon energy, OK? 00:58:07.500 --> 00:58:10.380 align:middle line:84% You see that for crystalline silicon, 00:58:10.380 --> 00:58:15.340 align:middle line:84% the absorption onset starts at about 1.1 eV, corresponding 00:58:15.340 --> 00:58:19.200 align:middle line:84% to its band gap, whereas amorphous silicon has a lot 00:58:19.200 --> 00:58:21.560 align:middle line:90% lower loss in this region here. 00:58:21.560 --> 00:58:24.660 align:middle line:84% But as soon as you move into the band gap of amorphous silicon-- 00:58:24.660 --> 00:58:26.505 align:middle line:90% as I said, it's about 1.7 eV-- 00:58:26.505 --> 00:58:27.380 align:middle line:90% there are two things. 00:58:27.380 --> 00:58:30.640 align:middle line:84% One is that you notice that the absorption is not 0, even below 00:58:30.640 --> 00:58:32.440 align:middle line:90% 1.7 eV. 00:58:32.440 --> 00:58:36.040 align:middle line:90% This comes from the back tail. 00:58:36.040 --> 00:58:38.200 align:middle line:84% You get those localized states that 00:58:38.200 --> 00:58:40.900 align:middle line:84% extend into the mobility gap or the band gap. 00:58:40.900 --> 00:58:43.060 align:middle line:84% So those states can still contribute to absorption. 00:58:43.060 --> 00:58:45.322 align:middle line:84% So that's why the absorption is nonzero 00:58:45.322 --> 00:58:47.780 align:middle line:84% even though you're looking at somewhere below the band gap. 00:58:47.780 --> 00:58:47.920 align:middle line:90% OK? 00:58:47.920 --> 00:58:49.040 align:middle line:84% That's one very important feature 00:58:49.040 --> 00:58:50.460 align:middle line:90% for amorphous semiconductors. 00:58:50.460 --> 00:58:53.520 align:middle line:84% The absorption does not go to 0 even below the band gap 00:58:53.520 --> 00:58:55.240 align:middle line:90% because of the localized state. 00:58:55.240 --> 00:58:56.200 align:middle line:90% OK? 00:58:56.200 --> 00:58:58.645 align:middle line:84% Second thing is once you go above the band gap, 00:58:58.645 --> 00:59:00.520 align:middle line:84% you see that absorption for amorphous silicon 00:59:00.520 --> 00:59:03.460 align:middle line:84% actually rises much quickly compared to crystalline silicon. 00:59:03.460 --> 00:59:06.400 align:middle line:84% It in fact quickly overtakes crystalline silicon 00:59:06.400 --> 00:59:08.780 align:middle line:84% as you go to the visible spectrum. 00:59:08.780 --> 00:59:11.680 align:middle line:90% 00:59:11.680 --> 00:59:13.555 align:middle line:84% Now, the reason for that is because if you 00:59:13.555 --> 00:59:15.055 align:middle line:84% think about crystalline silicon, you 00:59:15.055 --> 00:59:17.500 align:middle line:84% know that crystalline silicon is the indirect band gap 00:59:17.500 --> 00:59:19.460 align:middle line:90% semiconductor. 00:59:19.460 --> 00:59:21.080 align:middle line:84% In a direct band gap semiconductor, 00:59:21.080 --> 00:59:24.180 align:middle line:84% if you want to absorb a photon, it's a three-particle process. 00:59:24.180 --> 00:59:27.187 align:middle line:84% You need to have one electron in the valence band. 00:59:27.187 --> 00:59:29.520 align:middle line:84% You need to have one empty state in the conduction band. 00:59:29.520 --> 00:59:31.300 align:middle line:90% You need to also have a phonon. 00:59:31.300 --> 00:59:33.940 align:middle line:84% The phonon is used to compensate for the crystalline momentum 00:59:33.940 --> 00:59:36.460 align:middle line:84% mismatch between the states in the conduction 00:59:36.460 --> 00:59:38.700 align:middle line:84% and the valence band because you have k difference 00:59:38.700 --> 00:59:41.460 align:middle line:90% between those two states. 00:59:41.460 --> 00:59:43.705 align:middle line:84% And that's why the optical absorption is not 00:59:43.705 --> 00:59:45.580 align:middle line:84% very efficient in a crystalline semiconductor 00:59:45.580 --> 00:59:48.440 align:middle line:84% because you need the phonon to be involved in that process. 00:59:48.440 --> 00:59:48.940 align:middle line:90% OK. 00:59:48.940 --> 00:59:50.700 align:middle line:84% Now, what about amorphous silicon? 00:59:50.700 --> 00:59:53.860 align:middle line:84% In amorphous solids, we said that crystalline momentum is not 00:59:53.860 --> 00:59:55.380 align:middle line:90% a good quantum number. 00:59:55.380 --> 00:59:56.895 align:middle line:84% If it's not a good quantum number, 00:59:56.895 --> 00:59:59.020 align:middle line:84% you don't have to worry about momentum conservation 00:59:59.020 --> 01:00:02.420 align:middle line:90% in optical absorption process. 01:00:02.420 --> 01:00:06.420 align:middle line:84% So in this regard, amorphous solids behave somewhat more 01:00:06.420 --> 01:00:09.355 align:middle line:84% like a direct band gap semiconductor. 01:00:09.355 --> 01:00:10.980 align:middle line:84% You don't need the phonon participation 01:00:10.980 --> 01:00:15.040 align:middle line:84% in the optical absorption process 01:00:15.040 --> 01:00:17.320 align:middle line:84% because there's no momentum conservation whatsoever. 01:00:17.320 --> 01:00:18.220 align:middle line:90% Does that make sense? 01:00:18.220 --> 01:00:23.440 align:middle line:90% 01:00:23.440 --> 01:00:26.280 align:middle line:90% Thinking about it? 01:00:26.280 --> 01:00:28.460 align:middle line:84% AUDIENCE: [CHUCKLES] Say it again. 01:00:28.460 --> 01:00:29.460 align:middle line:90% JUEJUN HU: Say it again. 01:00:29.460 --> 01:00:30.360 align:middle line:90% OK. 01:00:30.360 --> 01:00:33.620 align:middle line:84% In a crystalline solid, in order to have optical absorption-- 01:00:33.620 --> 01:00:36.040 align:middle line:84% if you think about crystalline solid material, 01:00:36.040 --> 01:00:38.520 align:middle line:84% this is what the band structure looks like. 01:00:38.520 --> 01:00:40.320 align:middle line:90% This is your. 01:00:40.320 --> 01:00:41.720 align:middle line:90% This will be your k. 01:00:41.720 --> 01:00:42.980 align:middle line:90% This is crystalline momentum. 01:00:42.980 --> 01:00:44.240 align:middle line:90% This is energy. 01:00:44.240 --> 01:00:46.948 align:middle line:90% This is your valence band. 01:00:46.948 --> 01:00:47.740 align:middle line:90% Yeah, valence band. 01:00:47.740 --> 01:00:50.198 align:middle line:84% And then your conduction band-- if it's in direct band gap, 01:00:50.198 --> 01:00:53.200 align:middle line:84% the conduction band is located-- its minimum does not 01:00:53.200 --> 01:00:55.820 align:middle line:84% coincide with the maximum of the valence band. 01:00:55.820 --> 01:00:59.000 align:middle line:84% So now, if you want to have optical absorption, 01:00:59.000 --> 01:01:02.520 align:middle line:84% you are trying to promote, say, one electron from here to here. 01:01:02.520 --> 01:01:05.560 align:middle line:90% There's actually a k mismatch. 01:01:05.560 --> 01:01:08.400 align:middle line:84% So you also need a phonon with a k 01:01:08.400 --> 01:01:10.720 align:middle line:84% that corresponds to exactly this amount 01:01:10.720 --> 01:01:13.220 align:middle line:84% to compensate for this momentum difference 01:01:13.220 --> 01:01:15.880 align:middle line:84% in order to get momentum conservation. 01:01:15.880 --> 01:01:16.380 align:middle line:90% OK? 01:01:16.380 --> 01:01:20.220 align:middle line:84% So you need essentially one photon, one filled state, one 01:01:20.220 --> 01:01:22.860 align:middle line:84% empty state, and also a phonon with that k 01:01:22.860 --> 01:01:26.300 align:middle line:84% so that you can promote this hopping here. 01:01:26.300 --> 01:01:27.800 align:middle line:90% OK? 01:01:27.800 --> 01:01:32.220 align:middle line:84% Now, this whole concept of crystalline momentum 01:01:32.220 --> 01:01:36.100 align:middle line:84% is essentially a manifestation of the translational symmetry 01:01:36.100 --> 01:01:37.400 align:middle line:90% in crystalline lattice. 01:01:37.400 --> 01:01:37.900 align:middle line:90% OK? 01:01:37.900 --> 01:01:40.780 align:middle line:84% That whole thing just simply does not 01:01:40.780 --> 01:01:43.405 align:middle line:90% exist in amorphous solids. 01:01:43.405 --> 01:01:45.280 align:middle line:84% You can wipe this whole thing completely out. 01:01:45.280 --> 01:01:45.780 align:middle line:90% OK? 01:01:45.780 --> 01:01:48.980 align:middle line:84% So there's no crystalline momentum. 01:01:48.980 --> 01:01:51.700 align:middle line:84% You can essentially promote the carrier directly 01:01:51.700 --> 01:01:53.340 align:middle line:84% from valence band to conduction band 01:01:53.340 --> 01:01:57.260 align:middle line:84% without having to worry about momentum conservation. 01:01:57.260 --> 01:01:58.340 align:middle line:90% OK? 01:01:58.340 --> 01:02:00.980 align:middle line:84% So it behaves like a direct gap semiconductor, in that 01:02:00.980 --> 01:02:05.460 align:middle line:90% regard, the amorphous solid. 01:02:05.460 --> 01:02:07.800 align:middle line:90% You all took 3033, right? 01:02:07.800 --> 01:02:09.640 align:middle line:90% AUDIENCE: And it does-- it-- 01:02:09.640 --> 01:02:11.460 align:middle line:84% JUEJUN HU: I can see that it's a while ago. 01:02:11.460 --> 01:02:13.640 align:middle line:90% [LAUGHTER] 01:02:13.640 --> 01:02:15.160 align:middle line:84% I know things exponentially decay. 01:02:15.160 --> 01:02:17.680 align:middle line:90% The retention-- 01:02:17.680 --> 01:02:22.760 align:middle line:84% AUDIENCE: Particular reason on why it behaves just-- 01:02:22.760 --> 01:02:26.680 align:middle line:84% it doesn't need to keep the momentum? 01:02:26.680 --> 01:02:28.960 align:middle line:84% JUEJUN HU: Basically, just because this thing 01:02:28.960 --> 01:02:32.848 align:middle line:84% is just ill-defined in the amorphous solids. 01:02:32.848 --> 01:02:34.640 align:middle line:84% You don't have long-range structural order. 01:02:34.640 --> 01:02:35.360 align:middle line:90% AUDIENCE: OK, so there's-- 01:02:35.360 --> 01:02:36.080 align:middle line:90% JUEJUN HU: OK. 01:02:36.080 --> 01:02:37.840 align:middle line:84% So it just doesn't exist, the constraint. 01:02:37.840 --> 01:02:39.800 align:middle line:84% You don't have that constraint, essentially. 01:02:39.800 --> 01:02:41.400 align:middle line:84% There's additional constraint imposed 01:02:41.400 --> 01:02:42.817 align:middle line:84% in the crystalline solid, but it's 01:02:42.817 --> 01:02:44.920 align:middle line:84% absent in the case of amorphous solid. 01:02:44.920 --> 01:02:46.000 align:middle line:90% OK. 01:02:46.000 --> 01:02:49.580 align:middle line:84% AUDIENCE: So I guess the thing I was thinking about, 01:02:49.580 --> 01:02:51.200 align:middle line:84% why I had the blank look on my face, 01:02:51.200 --> 01:02:52.700 align:middle line:84% is I was thinking about when we were 01:02:52.700 --> 01:02:54.920 align:middle line:90% talking about localized states. 01:02:54.920 --> 01:02:58.182 align:middle line:84% And that requires a product for the-- 01:02:58.182 --> 01:02:59.640 align:middle line:84% JUEJUN HU: This is extended states. 01:02:59.640 --> 01:03:00.640 align:middle line:90% Yeah, this is extended states. 01:03:00.640 --> 01:03:03.000 align:middle line:84% We're talking about essentially siting of carriers from, 01:03:03.000 --> 01:03:05.640 align:middle line:84% essentially, across mobility edge or mobility gap, 01:03:05.640 --> 01:03:07.000 align:middle line:90% yeah, or across the band gap. 01:03:07.000 --> 01:03:07.740 align:middle line:90% OK? 01:03:07.740 --> 01:03:11.905 align:middle line:90% So yeah. 01:03:11.905 --> 01:03:13.280 align:middle line:84% For practical electronic devices, 01:03:13.280 --> 01:03:14.740 align:middle line:84% you rarely rely on the conduction 01:03:14.740 --> 01:03:18.420 align:middle line:84% for the hopping conduction because hopping conduction's 01:03:18.420 --> 01:03:19.760 align:middle line:90% actually fairly inefficient. 01:03:19.760 --> 01:03:20.620 align:middle line:90% It's slow. 01:03:20.620 --> 01:03:23.020 align:middle line:84% And it practically is only significant 01:03:23.020 --> 01:03:24.780 align:middle line:84% when you go to cryogenic temperature. 01:03:24.780 --> 01:03:26.640 align:middle line:84% So for normal device operating conditions, 01:03:26.640 --> 01:03:28.220 align:middle line:84% when you're trying to essentially send current 01:03:28.220 --> 01:03:30.340 align:middle line:84% through a device, those are all extended states 01:03:30.340 --> 01:03:31.540 align:middle line:90% contributing to that. 01:03:31.540 --> 01:03:32.057 align:middle line:90% Yeah. 01:03:32.057 --> 01:03:34.140 align:middle line:84% Yeah, so these are essentially from extended state 01:03:34.140 --> 01:03:35.300 align:middle line:90% to an extended state. 01:03:35.300 --> 01:03:36.220 align:middle line:90% OK. 01:03:36.220 --> 01:03:38.540 align:middle line:84% So that's what accounts for this absorption here, 01:03:38.540 --> 01:03:39.940 align:middle line:90% absorption above the band gap. 01:03:39.940 --> 01:03:43.480 align:middle line:84% Below the band gap, you can have excitation, for example, 01:03:43.480 --> 01:03:46.300 align:middle line:84% from a [INAUDIBLE] band tail to the above band tail 01:03:46.300 --> 01:03:49.160 align:middle line:84% or from a band tail to extended states. 01:03:49.160 --> 01:03:51.520 align:middle line:84% That's what contributes to this absorption here, 01:03:51.520 --> 01:03:54.060 align:middle line:90% this tail below the band gap. 01:03:54.060 --> 01:03:57.815 align:middle line:90% OK? 01:03:57.815 --> 01:03:59.860 align:middle line:90% Anyway, bottom line. 01:03:59.860 --> 01:04:01.700 align:middle line:84% You need to know that amorphous silicon-- 01:04:01.700 --> 01:04:03.180 align:middle line:84% once you go above the band gap gap, 01:04:03.180 --> 01:04:05.327 align:middle line:84% it's actually a lot more optically absorbing 01:04:05.327 --> 01:04:06.660 align:middle line:90% compared to crystalline silicon. 01:04:06.660 --> 01:04:07.600 align:middle line:90% You can see from here. 01:04:07.600 --> 01:04:11.440 align:middle line:84% So this also can be beneficial because it 01:04:11.440 --> 01:04:13.600 align:middle line:84% means that, as I have mentioned already before, 01:04:13.600 --> 01:04:16.800 align:middle line:84% while you have to make amorphous silicon cells, solar cells, 01:04:16.800 --> 01:04:20.080 align:middle line:84% very, very thin, you can absorb a sufficient amount of sunlight 01:04:20.080 --> 01:04:22.318 align:middle line:84% even within that micron-thick film because 01:04:22.318 --> 01:04:23.860 align:middle line:84% of a very high absorption coefficient 01:04:23.860 --> 01:04:25.340 align:middle line:90% on amorphous silicon. 01:04:25.340 --> 01:04:25.840 align:middle line:90% OK? 01:04:25.840 --> 01:04:29.200 align:middle line:84% So that compensates for the drawback in terms of low carrier 01:04:29.200 --> 01:04:30.160 align:middle line:90% mobility. 01:04:30.160 --> 01:04:31.960 align:middle line:90% OK? 01:04:31.960 --> 01:04:32.460 align:middle line:90% All right. 01:04:32.460 --> 01:04:34.720 align:middle line:84% Any more questions about this part? 01:04:34.720 --> 01:04:37.000 align:middle line:90% All good? 01:04:37.000 --> 01:04:37.800 align:middle line:90% All right. 01:04:37.800 --> 01:04:39.880 align:middle line:84% So now, next, I will show you, essentially 01:04:39.880 --> 01:04:42.968 align:middle line:84% talk a little bit more, about the deposition process. 01:04:42.968 --> 01:04:44.760 align:middle line:84% Instead of me talking about it, I will just 01:04:44.760 --> 01:04:47.000 align:middle line:90% show you a YouTube video. 01:04:47.000 --> 01:04:50.660 align:middle line:84% This is a fairly old YouTube video, and I'll tell you why. 01:04:50.660 --> 01:04:52.760 align:middle line:90% [VIDEO PLAYBACK] 01:04:52.760 --> 01:04:54.420 align:middle line:90% - Hi, I'm Charlie Gay. 01:04:54.420 --> 01:04:56.520 align:middle line:84% I'm the general manager of the Solar Business 01:04:56.520 --> 01:04:58.440 align:middle line:90% Group at Applied Materials. 01:04:58.440 --> 01:05:01.360 align:middle line:84% About 2 and 1/2 years ago, we had a vision for dramatically 01:05:01.360 --> 01:05:04.460 align:middle line:84% lowering the cost of manufacturing thin film solar 01:05:04.460 --> 01:05:05.460 align:middle line:90% panels. 01:05:05.460 --> 01:05:06.380 align:middle line:90% Today-- 01:05:06.380 --> 01:05:09.300 align:middle line:84% JUEJUN HU: That two years ago is 17 years ago, OK? 01:05:09.300 --> 01:05:09.900 align:middle line:90% [CHUCKLES] 01:05:09.900 --> 01:05:12.540 align:middle line:84% - --very site that was just a plot of land. 01:05:12.540 --> 01:05:16.020 align:middle line:84% Now, it's a full-scale SunFab production facility 01:05:16.020 --> 01:05:18.380 align:middle line:90% that is run by Signet Solar. 01:05:18.380 --> 01:05:20.340 align:middle line:90% Let's go take a look. 01:05:20.340 --> 01:05:23.820 align:middle line:84% - The SunFab is an automated blast module production line. 01:05:23.820 --> 01:05:26.460 align:middle line:84% The process begins with the front loader robot placing 01:05:26.460 --> 01:05:29.740 align:middle line:84% the 5.7-meter-square glass onto a conveyor. 01:05:29.740 --> 01:05:32.300 align:middle line:84% SunFab's sophisticated process, equipment, 01:05:32.300 --> 01:05:35.500 align:middle line:84% and factory automation software controls the various steps 01:05:35.500 --> 01:05:37.240 align:middle line:90% in the manufacturing operation. 01:05:37.240 --> 01:05:39.220 align:middle line:90% [MUSIC PLAYING] 01:05:39.220 --> 01:05:41.340 align:middle line:84% Next, the edges of the glass are rounded 01:05:41.340 --> 01:05:44.520 align:middle line:84% by a seamer and the glass washed to remove contaminants. 01:05:44.520 --> 01:05:47.480 align:middle line:90% [MUSIC PLAYING] 01:05:47.480 --> 01:05:51.420 align:middle line:90% 01:05:51.420 --> 01:05:54.340 align:middle line:84% The glass then enters a laser scribe, where the front contact 01:05:54.340 --> 01:05:57.960 align:middle line:84% layer is ablated to form lines for electrical cell isolation. 01:05:57.960 --> 01:06:00.580 align:middle line:90% [MUSIC PLAYING] 01:06:00.580 --> 01:06:04.320 align:middle line:84% After scribing, the glass is ready for silicon deposition. 01:06:04.320 --> 01:06:09.240 align:middle line:84% Because the PECVD 5.7 system is almost two stories high, 01:06:09.240 --> 01:06:11.560 align:middle line:84% the glass is transported to the deposition chamber 01:06:11.560 --> 01:06:12.580 align:middle line:90% by an elevator. 01:06:12.580 --> 01:06:15.580 align:middle line:90% [MUSIC PLAYING] 01:06:15.580 --> 01:06:16.080 align:middle line:90% 01:06:16.080 --> 01:06:19.760 align:middle line:84% The PECVD system is a plasma-enhanced chemical vapor 01:06:19.760 --> 01:06:21.020 align:middle line:90% deposition system. 01:06:21.020 --> 01:06:23.940 align:middle line:90% [MUSIC PLAYING] 01:06:23.940 --> 01:06:26.360 align:middle line:90% 01:06:26.360 --> 01:06:28.560 align:middle line:84% - We're here at the heart of the SunFab. 01:06:28.560 --> 01:06:31.400 align:middle line:84% This PECVD equipment is what's used 01:06:31.400 --> 01:06:34.880 align:middle line:84% to deposit the large area uniform semiconductor 01:06:34.880 --> 01:06:38.600 align:middle line:84% layers that make a solar panel electrically active. 01:06:38.600 --> 01:06:41.600 align:middle line:84% We developed this equipment by adapting tools 01:06:41.600 --> 01:06:44.080 align:middle line:84% from the flat panel display industry, 01:06:44.080 --> 01:06:47.440 align:middle line:84% where big screen TVs and flat panel monitors 01:06:47.440 --> 01:06:51.540 align:middle line:84% are routinely produced at a low cost, high yield, 01:06:51.540 --> 01:06:53.220 align:middle line:90% and predictable throughput. 01:06:53.220 --> 01:06:56.205 align:middle line:90% [MUSIC PLAYING] 01:06:56.205 --> 01:07:04.997 align:middle line:90% 01:07:04.997 --> 01:07:07.080 align:middle line:84% AUDIENCE: I feel like they're showing us all the-- 01:07:07.080 --> 01:07:09.780 align:middle line:84% - After the silicon deposition is complete, 01:07:09.780 --> 01:07:13.500 align:middle line:84% the deposit is scribed again before entering the inline 01:07:13.500 --> 01:07:17.220 align:middle line:84% sputter-down physical vapor deposition system. 01:07:17.220 --> 01:07:19.260 align:middle line:84% - We're here at the [INAUDIBLE] system. 01:07:19.260 --> 01:07:22.940 align:middle line:84% This is the back contact system on the SunFab line. 01:07:22.940 --> 01:07:25.340 align:middle line:84% It's designed along the same principles 01:07:25.340 --> 01:07:28.180 align:middle line:84% as our equipment that's used in the glass coating 01:07:28.180 --> 01:07:31.660 align:middle line:84% industry, where over 200 of these systems 01:07:31.660 --> 01:07:35.260 align:middle line:84% have been used in the field for the last 20 years. 01:07:35.260 --> 01:07:39.600 align:middle line:84% It's part of what makes the SunFab system so reliable. 01:07:39.600 --> 01:07:42.500 align:middle line:90% [MUSIC PLAYING] 01:07:42.500 --> 01:07:43.940 align:middle line:90% 01:07:43.940 --> 01:07:46.460 align:middle line:84% - Following back-contact layer deposition, 01:07:46.460 --> 01:07:49.340 align:middle line:84% the glass is scribed again and is then capable of generating 01:07:49.340 --> 01:07:50.200 align:middle line:90% electricity. 01:07:50.200 --> 01:07:53.125 align:middle line:90% [MUSIC PLAYING] 01:07:53.125 --> 01:07:54.100 align:middle line:90% 01:07:54.100 --> 01:07:57.100 align:middle line:84% - Next, the quality assurance and shunt removal system 01:07:57.100 --> 01:07:59.800 align:middle line:84% tests the glass and improves total power output 01:07:59.800 --> 01:08:01.620 align:middle line:90% by further isolating the cells. 01:08:01.620 --> 01:08:04.555 align:middle line:90% [MUSIC PLAYING] 01:08:04.555 --> 01:08:07.480 align:middle line:90% 01:08:07.480 --> 01:08:10.240 align:middle line:84% The SunFab line is designed to allow our customers 01:08:10.240 --> 01:08:13.640 align:middle line:84% the flexibility to make quarter, half, or full-size modules 01:08:13.640 --> 01:08:16.000 align:middle line:90% to serve unique market needs. 01:08:16.000 --> 01:08:17.888 align:middle line:84% Here you see the glass being scored and cut 01:08:17.888 --> 01:08:18.680 align:middle line:90% into the half-size. 01:08:18.680 --> 01:08:20.140 align:middle line:90% [CLACK] 01:08:20.140 --> 01:08:20.640 align:middle line:90% 01:08:20.640 --> 01:08:22.479 align:middle line:84% The process of edge deletion then 01:08:22.479 --> 01:08:26.560 align:middle line:84% removes the film from the glass edge for greater reliability. 01:08:26.560 --> 01:08:29.899 align:middle line:84% The bus line attach tool completes internal cell wiring. 01:08:29.899 --> 01:08:32.319 align:middle line:90% [MUSIC PLAYING] 01:08:32.319 --> 01:08:34.620 align:middle line:84% The glass is then ready for lamination. 01:08:34.620 --> 01:08:37.240 align:middle line:90% [MUSIC PLAYING] 01:08:37.240 --> 01:08:39.479 align:middle line:84% PVB foil is cut to the right size 01:08:39.479 --> 01:08:40.920 align:middle line:84% and placed on the glass, followed 01:08:40.920 --> 01:08:42.660 align:middle line:90% by a sheet of back glass. 01:08:42.660 --> 01:08:45.080 align:middle line:90% [MUSIC PLAYING] 01:08:45.080 --> 01:08:47.720 align:middle line:84% The laminator evenly spreads out the PVB foil 01:08:47.720 --> 01:08:50.279 align:middle line:84% between the front glass and the back glass, 01:08:50.279 --> 01:08:54.960 align:middle line:84% creating a uniform bond to secure glass PVE glass module. 01:08:54.960 --> 01:08:57.420 align:middle line:84% The module is then subjected to a high pressure 01:08:57.420 --> 01:09:00.100 align:middle line:84% and high temperature process within the autoclave, which 01:09:00.100 --> 01:09:02.260 align:middle line:84% removes trapped gases and anneals away 01:09:02.260 --> 01:09:05.420 align:middle line:84% physical stress for superior lamination. 01:09:05.420 --> 01:09:07.939 align:middle line:84% Overall, this lamination process is 01:09:07.939 --> 01:09:11.060 align:middle line:84% designed to enable the module to generate maximum power well 01:09:11.060 --> 01:09:13.040 align:middle line:84% beyond the typical warranty period. 01:09:13.040 --> 01:09:15.620 align:middle line:90% [MUSIC PLAYING] 01:09:15.620 --> 01:09:18.300 align:middle line:84% The SunFab line is also equipped with accumulators 01:09:18.300 --> 01:09:20.680 align:middle line:84% that buffer the line during system maintenance, 01:09:20.680 --> 01:09:22.279 align:middle line:90% preserving line productivity. 01:09:22.279 --> 01:09:25.269 align:middle line:90% [MUSIC PLAYING] 01:09:25.269 --> 01:09:28.260 align:middle line:90% 01:09:28.260 --> 01:09:31.240 align:middle line:84% Finally, the junction box is attached to the module. 01:09:31.240 --> 01:09:34.100 align:middle line:84% The junction box comes with built-in bypass diodes 01:09:34.100 --> 01:09:37.040 align:middle line:84% and standardized connectors to reduce install time. 01:09:37.040 --> 01:09:39.855 align:middle line:90% [MUSIC PLAYING] 01:09:39.855 --> 01:09:43.100 align:middle line:90% 01:09:43.100 --> 01:09:44.899 align:middle line:84% The solar simulator rates the module 01:09:44.899 --> 01:09:47.560 align:middle line:84% for power output and technical characteristics. 01:09:47.560 --> 01:09:50.560 align:middle line:90% [MUSIC PLAYING] 01:09:50.560 --> 01:09:51.060 align:middle line:90% 01:09:51.060 --> 01:09:54.860 align:middle line:84% SunFab is covered by an extensive 24-by-7 warranty, 01:09:54.860 --> 01:09:56.600 align:middle line:90% enabling faster-- 01:09:56.600 --> 01:10:00.440 align:middle line:84% JUEJUN HU: So basically, glass paneling, solar modules out. 01:10:00.440 --> 01:10:01.320 align:middle line:90% Fully automated. 01:10:01.320 --> 01:10:04.800 align:middle line:84% - --reduces operating expenses and increases factory output 01:10:04.800 --> 01:10:08.080 align:middle line:84% with the most comprehensive, lowest-cost support solution 01:10:08.080 --> 01:10:09.220 align:middle line:90% in the solar industry-- 01:10:09.220 --> 01:10:10.595 align:middle line:84% JUEJUN HU: That's pretty much it. 01:10:10.595 --> 01:10:12.640 align:middle line:90% [MUSIC PLAYING] 01:10:12.640 --> 01:10:15.120 align:middle line:84% - This is really, truly, the beginning 01:10:15.120 --> 01:10:18.920 align:middle line:84% of the major industrialization of solar power. 01:10:18.920 --> 01:10:22.320 align:middle line:84% The costs are coming down because a 5.7-square-meter 01:10:22.320 --> 01:10:26.960 align:middle line:84% module is able to be produced at a very low cost 01:10:26.960 --> 01:10:30.520 align:middle line:84% and because the cost to install this large area module out 01:10:30.520 --> 01:10:32.920 align:middle line:90% in the field is also very low. 01:10:32.920 --> 01:10:35.120 align:middle line:84% There's economies of scale at work here 01:10:35.120 --> 01:10:39.280 align:middle line:84% that are unprecedented in the history of solar manufacturing. 01:10:39.280 --> 01:10:40.500 align:middle line:90% Thank you for joining us. 01:10:40.500 --> 01:10:42.580 align:middle line:84% We look forward to seeing you again soon. 01:10:42.580 --> 01:10:43.800 align:middle line:90% [END PLAYBACK] 01:10:43.800 --> 01:10:45.368 align:middle line:90% JUEJUN HU: What do you think? 01:10:45.368 --> 01:10:46.160 align:middle line:90% AUDIENCE: I think-- 01:10:46.160 --> 01:10:46.560 align:middle line:90% JUEJUN HU: Sounds-- 01:10:46.560 --> 01:10:48.300 align:middle line:84% AUDIENCE: --have aesthetic complaints. 01:10:48.300 --> 01:10:48.800 align:middle line:90% [CHUCKLES] 01:10:48.800 --> 01:10:50.080 align:middle line:90% JUEJUN HU: Oh. 01:10:50.080 --> 01:10:51.660 align:middle line:90% I know it's a poor resolution. 01:10:51.660 --> 01:10:52.900 align:middle line:90% This is a 17-year-old video. 01:10:52.900 --> 01:10:53.780 align:middle line:90% What do you expect? 01:10:53.780 --> 01:10:55.580 align:middle line:90% AUDIENCE: [LAUGHS] 01:10:55.580 --> 01:11:00.140 align:middle line:84% JUEJUN HU: Now, why I decided to choose to do that-- 01:11:00.140 --> 01:11:02.320 align:middle line:84% you can no longer buy these systems anymore. 01:11:02.320 --> 01:11:03.252 align:middle line:90% [CHUCKLES] 01:11:03.252 --> 01:11:05.223 align:middle line:90% AUDIENCE: No. 01:11:05.223 --> 01:11:07.140 align:middle line:84% JUEJUN HU: It's certainly a technical triumph. 01:11:07.140 --> 01:11:10.300 align:middle line:84% If you look at this one here, each of these chambers 01:11:10.300 --> 01:11:13.020 align:middle line:90% is this little thing. 01:11:13.020 --> 01:11:16.580 align:middle line:84% This is the 5.7-square-meter deposition chamber. 01:11:16.580 --> 01:11:20.220 align:middle line:84% In each of the SunFab systems, you have 28. 01:11:20.220 --> 01:11:21.800 align:middle line:90% They have seven in each here. 01:11:21.800 --> 01:11:23.712 align:middle line:84% And then you have 28 individual chambers 01:11:23.712 --> 01:11:25.920 align:middle line:84% to ensure that you can have the potential throughput. 01:11:25.920 --> 01:11:28.080 align:middle line:90% So it's really quite remarkable. 01:11:28.080 --> 01:11:30.700 align:middle line:90% 01:11:30.700 --> 01:11:36.220 align:middle line:84% In fact, at some point, back in early 2011 or something, 01:11:36.220 --> 01:11:38.980 align:middle line:84% I was reading on the news that the UAE-- 01:11:38.980 --> 01:11:43.420 align:middle line:84% they tried to build a new technology city, Masdar City. 01:11:43.420 --> 01:11:45.820 align:middle line:84% And they purchased several-- not just 01:11:45.820 --> 01:11:48.420 align:middle line:84% one, several-- of these production lines. 01:11:48.420 --> 01:11:51.340 align:middle line:84% They ended up reselling it before even opening up 01:11:51.340 --> 01:11:52.160 align:middle line:90% the package. 01:11:52.160 --> 01:11:54.840 align:middle line:90% 01:11:54.840 --> 01:11:55.840 align:middle line:90% OK? 01:11:55.840 --> 01:11:56.920 align:middle line:90% Why? 01:11:56.920 --> 01:11:59.200 align:middle line:84% Because essentially, the whole business 01:11:59.200 --> 01:12:04.760 align:middle line:84% of amorphous silicon solar cell is gone in a few years. 01:12:04.760 --> 01:12:05.620 align:middle line:90% OK? 01:12:05.620 --> 01:12:06.840 align:middle line:90% Why is that? 01:12:06.840 --> 01:12:10.738 align:middle line:84% I guess I will leave that to the next lecture about why 01:12:10.738 --> 01:12:11.780 align:middle line:90% that's actually the case. 01:12:11.780 --> 01:12:12.780 align:middle line:90% AUDIENCE: Ugh. 01:12:12.780 --> 01:12:16.520 align:middle line:84% JUEJUN HU: [LAUGHS] That's the hanger. 01:12:16.520 --> 01:12:20.180 align:middle line:84% [LAUGHS] Yeah, but well, that's it. 01:12:20.180 --> 01:12:20.720 align:middle line:90% OK? 01:12:20.720 --> 01:12:23.420 align:middle line:84% Amorphous silicon is still important for many applications. 01:12:23.420 --> 01:12:24.440 align:middle line:90% OK? 01:12:24.440 --> 01:12:27.520 align:middle line:84% There are a few big applications we're talking about here. 01:12:27.520 --> 01:12:29.520 align:middle line:84% The two biggest ones are essentially 01:12:29.520 --> 01:12:30.777 align:middle line:90% display and solar cells. 01:12:30.777 --> 01:12:33.360 align:middle line:84% So even though solar cells is gone, I will still talk about it 01:12:33.360 --> 01:12:36.760 align:middle line:84% and talk about why it actually eventually ended up dissolving. 01:12:36.760 --> 01:12:38.820 align:middle line:84% It's still a very important material for display. 01:12:38.820 --> 01:12:39.320 align:middle line:90% OK? 01:12:39.320 --> 01:12:43.720 align:middle line:84% Some other smaller market-size applications-- for example, 01:12:43.720 --> 01:12:45.640 align:middle line:84% X-ray imaging-- when you go to hospital, 01:12:45.640 --> 01:12:47.900 align:middle line:84% you have this actually taking pictures there. 01:12:47.900 --> 01:12:50.300 align:middle line:84% You also need a very large area detector 01:12:50.300 --> 01:12:52.520 align:middle line:84% so that you can capture large-area images. 01:12:52.520 --> 01:12:54.040 align:middle line:84% And that's only possible with amorphous silicon. 01:12:54.040 --> 01:12:54.540 align:middle line:90% OK? 01:12:54.540 --> 01:12:57.132 align:middle line:84% You can also have a position-sensitive detector. 01:12:57.132 --> 01:12:59.340 align:middle line:84% It's a kind of detector that essentially can tell you 01:12:59.340 --> 01:13:01.440 align:middle line:84% where the light is actually coming in the location there. 01:13:01.440 --> 01:13:02.880 align:middle line:90% It's also a large area device. 01:13:02.880 --> 01:13:06.220 align:middle line:84% Finally, IR bolometer is basically a kind of IR imager 01:13:06.220 --> 01:13:07.940 align:middle line:90% that detects infrared light. 01:13:07.940 --> 01:13:10.500 align:middle line:84% The way that the IR bolometer works-- it's 01:13:10.500 --> 01:13:13.140 align:middle line:84% actually leveraged on one unique property of amorphous silicon. 01:13:13.140 --> 01:13:16.740 align:middle line:84% That has a very large Temperature Coefficient 01:13:16.740 --> 01:13:19.620 align:middle line:90% of Resistance, TCR. 01:13:19.620 --> 01:13:21.580 align:middle line:84% So when you actually change temperature, 01:13:21.580 --> 01:13:23.580 align:middle line:84% the electrical resistance of amorphous silicon 01:13:23.580 --> 01:13:25.700 align:middle line:84% actually changes quite dramatically. 01:13:25.700 --> 01:13:29.140 align:middle line:84% Basically, because when you change the temperature, as you 01:13:29.140 --> 01:13:31.260 align:middle line:84% go to high temperature, you excite more carriers 01:13:31.260 --> 01:13:34.020 align:middle line:90% into the conduction band. 01:13:34.020 --> 01:13:36.900 align:middle line:84% And you have, essentially, this extended-stay conduction 01:13:36.900 --> 01:13:39.340 align:middle line:84% that contributes to enhanced electrical conductivity. 01:13:39.340 --> 01:13:44.100 align:middle line:84% So by measuring the electrical resistance, 01:13:44.100 --> 01:13:46.180 align:middle line:84% you can actually know the temperature. 01:13:46.180 --> 01:13:48.020 align:middle line:84% So the way these devices are designed 01:13:48.020 --> 01:13:50.320 align:middle line:84% is that you have these suspended pixels. 01:13:50.320 --> 01:13:53.820 align:middle line:84% If infrared radiation comes in, it absorbs infrared light, 01:13:53.820 --> 01:13:55.600 align:middle line:84% converts it into heat, so then leads 01:13:55.600 --> 01:13:58.160 align:middle line:84% to a temperature rise locally, which then 01:13:58.160 --> 01:13:59.548 align:middle line:90% changes electrical resistance. 01:13:59.548 --> 01:14:01.340 align:middle line:84% So then by measuring electrical resistance, 01:14:01.340 --> 01:14:03.720 align:middle line:84% you can then use that to infer the intensity of light incident 01:14:03.720 --> 01:14:04.500 align:middle line:90% on the device. 01:14:04.500 --> 01:14:07.840 align:middle line:84% So that's why it's essentially used as night vision devices, 01:14:07.840 --> 01:14:08.460 align:middle line:90% basically. 01:14:08.460 --> 01:14:08.960 align:middle line:90% OK? 01:14:08.960 --> 01:14:10.920 align:middle line:84% So amorphous silicon is still quite important, 01:14:10.920 --> 01:14:14.640 align:middle line:84% even though the solar cell industry is basically gone. 01:14:14.640 --> 01:14:15.160 align:middle line:90% OK? 01:14:15.160 --> 01:14:19.120 align:middle line:84% And as I said, next lecture, we are going to just decipher 01:14:19.120 --> 01:14:22.160 align:middle line:84% why the whole amorphous silicon solar cell business 01:14:22.160 --> 01:14:25.310 align:middle line:90% just evaporated, OK? 01:14:25.310 --> 01:14:48.000 align:middle line:90%