1 00:00:15,966 --> 00:00:18,400 There are so many processes   2 00:00:18,400 --> 00:00:25,033 that are thermally activated. There are so many  processes that have Arrhenius-like behavior.   3 00:00:25,600 --> 00:00:30,716 That are Arrhenius-like. And if you go to  Dartmouth then they'll give you goodie bags   4 00:00:30,716 --> 00:00:35,683 with live crickets. And actually I really  hope not. But this is one of the labs that   5 00:00:35,683 --> 00:00:40,800 they have where they take crickets and they  measure the number of times a cricket chirps.   6 00:00:41,600 --> 00:00:47,283 And they're like, well okay. Let's measure the  cricket chirp over 13 seconds. We're gonna cool   7 00:00:47,283 --> 00:00:52,150 them down, hopefully not too cold, and then we're  going to heat them up, hopefully not too hot.   8 00:00:53,516 --> 00:00:58,550 Because crickets are nice, right? And so  then-- and they ca-- but look at that. And   9 00:00:58,550 --> 00:01:03,916 they count it. And then what do they do? Well they  didn't know about Arrhenius yet until somebody   10 00:01:03,916 --> 00:01:09,750 from MIT went and visited. So the first thing  they did is they plotted the data. Look at that.   11 00:01:09,750 --> 00:01:15,283 Chirps per 13 seconds plotted. And they're all  sitting there trying to fit a straight line to   12 00:01:15,283 --> 00:01:20,150 it. And then someone from this class is up  there visiting. They're like, you know what   13 00:01:20,150 --> 00:01:24,800 i think, this looks like a thermally activated  process. So i think it's probably exponential.   14 00:01:25,600 --> 00:01:31,200 And then they fit this nice exponential and  it fits the the cricket tripping beautifully.   15 00:01:32,233 --> 00:01:40,883 And you can go even further because you see  if you got this far. Well now you see this   16 00:01:40,883 --> 00:01:45,833 is a line. This is a line and we're going to do  that a lot when we go into reaction kinetics.   17 00:01:46,800 --> 00:01:53,683 If you have a exponential and you take a log,  that's a line versus 1 over T. Right? That's a   18 00:01:53,683 --> 00:01:58,483 line versus 1 over T. And so that's another way  you could look at data. They didn't do it there.   19 00:01:59,116 --> 00:02:09,916 But, you know, you could plot for example--  you could plot 1 over T versus the log of   20 00:02:10,633 --> 00:02:18,716 the number of vacancies. But the lattice-- the  number of vacancies is what we want. That ratio   21 00:02:18,716 --> 00:02:22,883 is the concentration. That concentration  is in equilibrium at some temperature.   22 00:02:23,600 --> 00:02:29,283 Okay. The lattice-- the number of lattice sites  is simply how many lattice sites you have,   23 00:02:29,283 --> 00:02:34,083 in whatever volume you have, for whatever crystal  structure you have, for whatever element you have.   24 00:02:34,633 --> 00:02:39,116 We'll see that in a few examples. So that's just  a concert-- it's the number of sites you have in   25 00:02:39,116 --> 00:02:43,750 the chunk of material. And then instead of-- The  question this equation tells you the answer to,   26 00:02:43,750 --> 00:02:48,633 is how many of those have a vacancy?  Because it's a thermally activated process.   27 00:02:49,600 --> 00:02:56,800 And if you plot that log in Nv versus  temperature you get this really nice   28 00:02:56,800 --> 00:03:05,283 linear line. And the slope of that  line is equal to minus E vacancy 29 00:03:07,600 --> 00:03:15,433 divided by R or it could be kB. R.  Let's write this again per mole. 30 00:03:18,950 --> 00:03:24,633 Or it could be kB if it's  per atom. You will see both.   31 00:03:25,350 --> 00:03:30,483 You will see both. And this  intercept-- intercept-- 32 00:03:33,600 --> 00:03:40,000 is equal to the-- let's see-- the intercept  is equal-- what do i have here? The   33 00:03:40,950 --> 00:03:44,316 log of n. Did i write it right? Log of n. 34 00:03:48,483 --> 00:03:50,483 Okay. Alright. 35 00:03:53,200 --> 00:03:58,550 Now, okay. Oh yeah. What else can you  do? Well before we go on to the defects,   36 00:03:58,550 --> 00:04:04,316 this explains the doping. I kept calling  the doping in semiconductors a thermally   37 00:04:04,316 --> 00:04:11,916 activated process. But look at what happens.  This is the carrier concentration in that   38 00:04:11,916 --> 00:04:14,716 conduction band. The thing you've  been you've been learning about,   39 00:04:14,716 --> 00:04:19,516 right? And thinking about. But look at it  now versus temperature. It's a straight line.   40 00:04:20,716 --> 00:04:24,400 It's a straight line. This is-- this  is experimentally what you observe.   41 00:04:25,350 --> 00:04:29,433 And the reason is because it's a thermally  activated process. And in fact, in this case,   42 00:04:30,483 --> 00:04:36,550 what is the activation energy? Right? The  activation energy for getting an electron into   43 00:04:36,550 --> 00:04:44,400 the conduction band is the gap. Right? And so now  you say germanium has a smaller gap than silicon,   44 00:04:44,400 --> 00:04:50,716 which has a smaller gap than gallium arsenide.  The slopes are different. The slopes are different   45 00:04:51,683 --> 00:04:58,082 because the energy that it takes in that activated  process is the gap. That's why the slopes are   46 00:04:58,082 --> 00:05:00,916 different. Right? Okay. Alright.