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PROFESSOR: OK.

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00:00:22,290 --> 00:00:27,140
Folks, I may not look like Don
Sadoway, but for today, I am

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00:00:27,140 --> 00:00:29,040
Don Sadoway.

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00:00:29,040 --> 00:00:31,810
So let's--

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00:00:31,810 --> 00:00:34,760
I guess you can hear me
pretty well, right?

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00:00:34,760 --> 00:00:36,210
OK.

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00:00:36,210 --> 00:00:41,470
Professor Sadoway is in a
faraway, terrible place.

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It's called Vienna.

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00:00:43,770 --> 00:00:44,800
Yeah, I know.

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We're here.

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00:00:46,260 --> 00:00:47,840
What can I say?

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00:00:47,840 --> 00:00:52,450
And he'll be back
next Tuesday.

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00:00:52,450 --> 00:00:55,100
And so my name is Ron
Ballinger, and

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00:00:55,100 --> 00:00:58,490
I'm taking his place.

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00:00:58,490 --> 00:01:00,380
Put a muffler on that.

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00:01:00,380 --> 00:01:01,920
OK, great.

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00:01:01,920 --> 00:01:03,960
I'm sure you're all anxious,
before we get

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00:01:03,960 --> 00:01:09,080
started, to see that.

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00:01:09,080 --> 00:01:10,330
Right.

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00:01:10,330 --> 00:01:11,380
The average--

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00:01:11,380 --> 00:01:17,520
it was about 66, which is about
10 points lower than the

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00:01:17,520 --> 00:01:22,490
last five or 10 quiz ones.

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00:01:22,490 --> 00:01:23,870
So it's a little bit lower.

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00:01:23,870 --> 00:01:28,440
It was a little bit harder
test. I'm sure Professor

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Sadoway will mention this when
he comes back, but for those

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00:01:32,330 --> 00:01:38,350
of you who are below the 50
mark, it's time to do

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00:01:38,350 --> 00:01:41,750
something about it, and when I
say do something about it, I'm

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00:01:41,750 --> 00:01:45,540
sure your recitation instructors
will be very happy

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00:01:45,540 --> 00:01:49,070
to help out in any way possible,
but there are other

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00:01:49,070 --> 00:01:52,150
options, not the least
of which is a tutor.

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00:01:52,150 --> 00:01:55,590
And so if you think you need one
and you need to be kind of

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00:01:55,590 --> 00:01:59,560
ruthless about examining
yourself--

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00:01:59,560 --> 00:02:02,990
if you think you need one, go
down and see Hilary and there

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00:02:02,990 --> 00:02:08,430
are tutors which are available
for individual instruction.

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00:02:08,430 --> 00:02:12,350
So I think it's a great time to
take it take advantage of

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00:02:12,350 --> 00:02:15,200
that because I can guarantee you
that test number two will

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00:02:15,200 --> 00:02:16,660
not be any easier.

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00:02:16,660 --> 00:02:20,980
In fact, it'll be considerably
harder because it'll be pretty

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00:02:20,980 --> 00:02:23,010
much new material.

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00:02:23,010 --> 00:02:23,380
OK.

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00:02:23,380 --> 00:02:28,790
So that's enough for that.

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00:02:28,790 --> 00:02:31,980
Last day, we were--

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00:02:31,980 --> 00:02:32,530
I wasn't here.

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00:02:32,530 --> 00:02:34,920
I was in Washington.

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00:02:34,920 --> 00:02:36,860
They're actually trying
to build what's

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00:02:36,860 --> 00:02:39,970
called an exoflop computer.

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00:02:39,970 --> 00:02:42,250
Does anybody know
what exo means?

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10 to the 18th.

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00:02:44,190 --> 00:02:49,090
10 to the 18th floating point
operations per second.

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00:02:49,090 --> 00:02:50,830
Why do they need that?

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00:02:50,830 --> 00:02:54,070
Because when you go beyond 3091
then starting modeling

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these atoms--

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00:02:55,470 --> 00:02:58,430
especially F-block atoms-- you
need a supercomputer that

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large and to do one run on a
petaflop machine takes 100,000

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CPUs 10 hours for one atom.

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00:03:12,100 --> 00:03:15,540
So solving the Schrodinger
equation's a bit tricky.

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OK.

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00:03:16,820 --> 00:03:23,210
Remember last time, we talked
about metallic bonding and

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we're sort of sneaking
up on it.

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Remember, Paul Drude--

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well, let's look up here.

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These are the characteristics
of metallic solids.

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They have high electrical
conductivity.

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They have high thermal
conductivity.

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They shine and they
have ductility.

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So we're going to deal with
the first three today, and

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later on in the course, we'll
talk about the ductility part.

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00:03:48,150 --> 00:03:54,610
But recall that Paul Drude
modeled the solid as a series

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of cations, which amounted to
the nucleus plus the inner

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core electrons and then allowed
the electrons--

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the remaining, the outer shell
electrons, the valence

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00:04:13,690 --> 00:04:20,290
electrons, to float around,
called it a free electron gas.

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And that model explained the
temperature dependence of heat

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capacity, but it was not
so good when it came to

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electrical conductivity.

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It explained the fact that you
get electrical conductivity,

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but not the fact that some
materials are conductors and

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some materials are insulators.

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So we need to deal with that and
for that, we need to talk

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to two sets of folks.

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00:04:46,620 --> 00:04:58,040
The first one is Felix Bloch
and he was a 1928--

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he was a--

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00:04:59,220 --> 00:05:02,080
he got his PhD under
Heisenberg.

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00:05:02,080 --> 00:05:04,290
Boy, it would've been nice back
in those days, working

91
00:05:04,290 --> 00:05:06,140
for those great folks.

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00:05:06,140 --> 00:05:12,680
And he applied quantum
mechanics to solids.

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He said, OK, let's consider that
in a solid, the atoms are

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arranged in an array.

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What's an array?

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00:05:33,650 --> 00:05:35,970
Well, it's actually
called a crystal.

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00:05:40,640 --> 00:05:43,650
It's an ordered array of atoms.
We're going to say a

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00:05:43,650 --> 00:05:48,040
lot more about that as
we go along, but--

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00:05:48,040 --> 00:06:06,350
and then he said, well, then
let's apply the Schrodinger

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00:06:06,350 --> 00:06:08,120
equation to this system.

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00:06:08,120 --> 00:06:10,600
Now it's a big difference
between the Schrodinger

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00:06:10,600 --> 00:06:14,390
equation for a single
atom in a gas and

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00:06:14,390 --> 00:06:16,306
multiple atoms in a solid.

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It's a different set of boundary
conditions, different

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00:06:19,270 --> 00:06:23,890
set of conditions
all together.

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00:06:23,890 --> 00:06:30,160
And when you do that, you get
a set of solutions for the

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00:06:30,160 --> 00:06:38,670
valence electrons which
is, as you might

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00:06:38,670 --> 00:06:40,035
expect, it's periodic.

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00:06:42,820 --> 00:06:57,340
It's periodic and it invokes
wave-like properties of the

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00:06:57,340 --> 00:07:05,890
electron and you end up with
a set of values of the

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00:07:05,890 --> 00:07:11,130
wavelengths for the electron
that are such that it allows

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00:07:11,130 --> 00:07:16,930
mobility, which is, after
all, what we're after.

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00:07:16,930 --> 00:07:19,220
These electrons got to move
through the solid if we're

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00:07:19,220 --> 00:07:23,540
going to have conductivity.

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00:07:23,540 --> 00:07:37,280
And this is an example where
classical physics wouldn't

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00:07:37,280 --> 00:07:38,900
allow that.

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00:07:38,900 --> 00:07:43,790
So you can't get this
kind of behavior

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00:07:43,790 --> 00:07:45,810
with classical physics.

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So that's one piece.

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00:07:48,050 --> 00:07:54,360
And the second group,
two guys.

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00:07:54,360 --> 00:08:06,380
Walter Heitler and
Fritz London.

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00:08:06,380 --> 00:08:11,510
We know Fritz London from London
dispersion force--

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00:08:11,510 --> 00:08:12,850
the same guy.

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00:08:12,850 --> 00:08:16,430
These guys were very,
very productive.

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00:08:16,430 --> 00:08:19,290
And he did a post-doc--

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00:08:22,260 --> 00:08:24,650
that's another word for slave
labor, by the way.

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00:08:27,180 --> 00:08:29,070
Folks will know that here.

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00:08:29,070 --> 00:08:30,060
For guess who?

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00:08:30,060 --> 00:08:31,440
Well, he did it for
Schrodinger.

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00:08:39,920 --> 00:08:41,930
Interesting story, I guess.

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00:08:41,930 --> 00:08:46,380
These guys showed up for their
slave labor at Schrodinger's

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00:08:46,380 --> 00:08:50,190
lab, only to discover that
Schrodinger had taken a

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00:08:50,190 --> 00:08:52,330
position at a different
university.

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00:08:52,330 --> 00:08:56,720
So these guys showed up
and he said, goodbye.

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00:08:56,720 --> 00:09:00,060
Anyway, that's a bummer.

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00:09:00,060 --> 00:09:00,960
OK.

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00:09:00,960 --> 00:09:03,220
And they sat down and
they said, well, OK.

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00:09:03,220 --> 00:09:08,270
Let's see if we can go at this
from an energy point of view

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00:09:08,270 --> 00:09:11,980
as opposed from the quantum
mechanical point of view and

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00:09:11,980 --> 00:09:17,560
let's see if we can
apply LCAOMO--

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00:09:20,420 --> 00:09:22,810
now don't break out in hives
because of the test--

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00:09:26,120 --> 00:09:33,070
to a solid, to large
aggregates.

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00:09:33,070 --> 00:09:34,320
Large what?

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00:09:37,480 --> 00:09:40,860
Of atoms. How big is large?

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00:09:40,860 --> 00:09:42,880
Well, I don't know.

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00:09:42,880 --> 00:09:46,670
Dream up a number-- say,
10 to the 23rd.

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00:09:46,670 --> 00:09:50,190
Lots of atoms. And let's
see what happens.

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00:09:50,190 --> 00:09:54,860
Well, we've already done a
little of this in the past. We

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00:09:54,860 --> 00:10:01,020
looked at the energetics of the
stability of hydrogen or

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00:10:01,020 --> 00:10:02,130
the stability of helium.

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00:10:02,130 --> 00:10:05,710
So we can take that and we can
kind of add up and we'll see

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00:10:05,710 --> 00:10:06,940
what happens.

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00:10:06,940 --> 00:10:13,360
Well, remember, we had atom A
and now let's only deal with

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00:10:13,360 --> 00:10:17,550
the valence electrons.

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00:10:17,550 --> 00:10:21,985
And so this would be 0 and
there's another atom A--

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00:10:24,880 --> 00:10:25,620
0--

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00:10:25,620 --> 00:10:30,830
and this would be A2 and we've
been through this before.

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00:10:30,830 --> 00:10:31,810
Let's just take--

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00:10:31,810 --> 00:10:37,940
we know that we get splitting
and we get a sigma bonding

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00:10:37,940 --> 00:10:42,820
orbital and a sigma star
anti-bonding orbital.

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00:10:42,820 --> 00:10:48,990
Well, let's start adding some
atoms here, additional atoms.

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00:10:48,990 --> 00:10:50,230
What do we get?

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00:10:50,230 --> 00:10:54,680
Well, let's just try
for A sub N--

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00:10:54,680 --> 00:10:56,436
lots of atoms. What do we get?

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00:11:02,160 --> 00:11:07,640
We end up with lots of states.

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00:11:07,640 --> 00:11:09,460
Remember, we have to have
conservation of states.

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00:11:09,460 --> 00:11:11,840
So for every atom we add--

168
00:11:11,840 --> 00:11:16,410
let's say this is copper,
for example, which

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00:11:16,410 --> 00:11:19,960
has an s1, one s.

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00:11:19,960 --> 00:11:21,880
It's an odd number
of electrons.

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00:11:21,880 --> 00:11:26,990
So every time I add a copper to
this, I add extra states.

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00:11:26,990 --> 00:11:27,870
And then what do I do?

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00:11:27,870 --> 00:11:33,510
I start filling them using
Aufbau, just like we've done

174
00:11:33,510 --> 00:11:40,140
in the past. Well, if we keep
going, and by the way, not to

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00:11:40,140 --> 00:11:49,030
scale, it starts looking like
a whole bunch of states.

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00:11:49,030 --> 00:11:52,370
And this energy level here,
these energies, what?

177
00:11:52,370 --> 00:11:54,180
We know for hydrogen,
this is what?

178
00:11:54,180 --> 00:11:58,560
Minus 13.6 electron volts.

179
00:11:58,560 --> 00:12:02,110
So what are we dealing with
here in terms of state

180
00:12:02,110 --> 00:12:03,330
differences?

181
00:12:03,330 --> 00:12:09,550
Well, let's take 10 to the 23rd
atoms and let's see if we

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00:12:09,550 --> 00:12:10,800
can calculate energy.

183
00:12:10,800 --> 00:12:12,910
Well, let's take for copper--

184
00:12:12,910 --> 00:12:16,110
the molar volume of
copper is what?

185
00:12:16,110 --> 00:12:22,220
7.11 centimeter cube for mole.

186
00:12:22,220 --> 00:12:22,790
All right.

187
00:12:22,790 --> 00:12:25,510
And that's N to the 23rd--

188
00:12:25,510 --> 00:12:32,310
actually, 6.02 times 10
to the 23rd atoms.

189
00:12:32,310 --> 00:12:36,930
And let's just ask ourselves,
what's the sort of range here?

190
00:12:36,930 --> 00:12:39,720
Well, we know it's 13.6 here.

191
00:12:39,720 --> 00:12:42,470
We know that's 0.

192
00:12:42,470 --> 00:12:43,820
We're all friends.

193
00:12:43,820 --> 00:12:47,880
So let's call it 10 ev,
just for grins.

194
00:12:47,880 --> 00:12:50,240
Not a bad number.

195
00:12:50,240 --> 00:12:54,600
And let's ask ourselves, well,
if we've got 10 to the 23rd

196
00:12:54,600 --> 00:13:01,340
atoms and 10 ev-- let's take 10
ev over 10 to the 23rd and

197
00:13:01,340 --> 00:13:02,000
you get what?

198
00:13:02,000 --> 00:13:14,940
Well, 10 to the minus
22 ev per state.

199
00:13:14,940 --> 00:13:16,370
That's small.

200
00:13:16,370 --> 00:13:20,120
That's really, really, really,
really small and if you

201
00:13:20,120 --> 00:13:23,800
convert that to joules,
you end up with 10 to

202
00:13:23,800 --> 00:13:27,690
the minus 41 joules.

203
00:13:27,690 --> 00:13:29,990
That's really small.

204
00:13:29,990 --> 00:13:31,160
So what are we saying?

205
00:13:31,160 --> 00:13:37,310
We're saying that this
organization here--

206
00:13:37,310 --> 00:13:41,850
when we and put a lot of atoms
in there, we end up with what

207
00:13:41,850 --> 00:13:45,060
amounts to a band.

208
00:13:48,380 --> 00:13:49,925
A band of states.

209
00:13:52,540 --> 00:13:54,150
And what do we do?

210
00:13:58,170 --> 00:14:02,790
We populate this band just like
we did using the Aufbau

211
00:14:02,790 --> 00:14:07,910
principle, but what does
it really look like?

212
00:14:07,910 --> 00:14:12,550
Well, in the case of copper,
you remember,

213
00:14:12,550 --> 00:14:19,810
copper has a 1s electron.

214
00:14:19,810 --> 00:14:28,660
Copper is 3d10s1.

215
00:14:28,660 --> 00:14:35,490
If we start filling start this
band, we're going to get--

216
00:14:39,860 --> 00:14:47,900
and so we start filling and we
get up here and we find that

217
00:14:47,900 --> 00:14:53,890
we end up with a half-filled
band, because there are states

218
00:14:53,890 --> 00:14:55,916
that are not occupied.

219
00:14:58,540 --> 00:15:03,290
But remember, the distance
between this guy and this guy,

220
00:15:03,290 --> 00:15:06,680
an occupied and unoccupied
state, is only 10 to

221
00:15:06,680 --> 00:15:09,020
the minus 41 joules.

222
00:15:09,020 --> 00:15:12,650
So that's pretty small.

223
00:15:12,650 --> 00:15:15,980
10 to the minus 22
electron volts.

224
00:15:15,980 --> 00:15:21,530
To give you an example, 0.025
electron volts, which is, if

225
00:15:21,530 --> 00:15:25,120
you want to convert that to
temperature, that's about 300

226
00:15:25,120 --> 00:15:27,160
degrees Kelvin.

227
00:15:27,160 --> 00:15:30,350
So very, very small energy.

228
00:15:30,350 --> 00:15:35,640
So that means if I were to take
and if I were to apply a

229
00:15:35,640 --> 00:15:39,750
potential here, then
what happens?

230
00:15:39,750 --> 00:15:41,960
Well, I add a little energy--
and I don't

231
00:15:41,960 --> 00:15:43,250
have to add much energy--

232
00:15:43,250 --> 00:15:48,120
and it's very easy for me to
promote one or more of these

233
00:15:48,120 --> 00:15:51,600
electrons up into the
above here and

234
00:15:51,600 --> 00:15:55,560
then I can get migration.

235
00:15:55,560 --> 00:16:00,200
So the endpoint is that if we
apply a potential, we end up

236
00:16:00,200 --> 00:16:09,830
with conductivity, which
is what we were after.

237
00:16:09,830 --> 00:16:14,100
Moreover, we can say
a few more things.

238
00:16:14,100 --> 00:16:16,590
If I shine--

239
00:16:16,590 --> 00:16:18,560
now this is a sort of
mixed metaphor here.

240
00:16:18,560 --> 00:16:21,180
This is an energy diagram and
this some plates on an

241
00:16:21,180 --> 00:16:24,270
electrode so be a little
bit careful.

242
00:16:24,270 --> 00:16:26,370
We shine photons
on this thing.

243
00:16:26,370 --> 00:16:27,130
What happens?

244
00:16:27,130 --> 00:16:29,560
What's the energy of the
photons, of light?

245
00:16:29,560 --> 00:16:33,190
Between 200 or 400 and
700 nanometers.

246
00:16:33,190 --> 00:16:35,330
It's about one electron volt.

247
00:16:35,330 --> 00:16:37,890
So there's plenty of electron
volts here.

248
00:16:37,890 --> 00:16:40,500
I'm going to-- with a metal,
not only will I have

249
00:16:40,500 --> 00:16:44,270
conductivity, but there'll be
enough energy here to promote

250
00:16:44,270 --> 00:16:50,010
electrons and those electrons
will move around and we'll end

251
00:16:50,010 --> 00:16:54,710
up with re-emission and we
end up with opaqueness.

252
00:16:54,710 --> 00:16:59,660
In other words, we absorb light
and readmit it and so we

253
00:16:59,660 --> 00:17:05,930
end up with, in the case
of a metal, luster.

254
00:17:05,930 --> 00:17:07,400
So there's a couple of things.

255
00:17:07,400 --> 00:17:10,530
So if we recall back here--

256
00:17:10,530 --> 00:17:12,680
we're talking about high
electrical conductivity.

257
00:17:12,680 --> 00:17:14,250
We had-- we need to say
a lot more about that,

258
00:17:14,250 --> 00:17:15,500
but we're OK here.

259
00:17:15,500 --> 00:17:17,940
But Drude, it was OK as well.

260
00:17:17,940 --> 00:17:21,000
High thermal conductivity,
Drude did that.

261
00:17:21,000 --> 00:17:22,100
That was fine.

262
00:17:22,100 --> 00:17:23,100
Luster.

263
00:17:23,100 --> 00:17:28,590
OK, So it works for copper,
seems to be OK.

264
00:17:28,590 --> 00:17:31,180
But what about another one?

265
00:17:31,180 --> 00:17:34,830
Like, say, beryllium.

266
00:17:34,830 --> 00:17:35,850
What's with beryllium?

267
00:17:35,850 --> 00:17:37,900
Well, beryllium is 2s2s2.

268
00:17:40,940 --> 00:17:46,270
So now let's draw the
thing for beryllium.

269
00:17:46,270 --> 00:17:47,290
We have beryllium.

270
00:17:47,290 --> 00:17:56,900
We have-- must be a 2s and now
it's 2p and we populate this.

271
00:17:56,900 --> 00:18:01,040
And now we want to
add a beryllium--

272
00:18:01,040 --> 00:18:03,530
n beryllium atoms, all right?

273
00:18:03,530 --> 00:18:04,980
What's happening?

274
00:18:04,980 --> 00:18:06,550
well, it'll be a little bit.

275
00:18:06,550 --> 00:18:11,270
We got this band that we've
talked about earlier.

276
00:18:11,270 --> 00:18:13,680
Now we go to fill it.

277
00:18:13,680 --> 00:18:17,390
So we're filling these guys
and we fill it, and lo and

278
00:18:17,390 --> 00:18:20,740
behold, we find out that we fill
it all the way to the top

279
00:18:20,740 --> 00:18:24,220
and so we're screwed.

280
00:18:24,220 --> 00:18:25,470
We have no conductivity.

281
00:18:28,530 --> 00:18:31,540
What I can imagine now is
there's 100 computers in here.

282
00:18:31,540 --> 00:18:33,910
50 of them have Skype.

283
00:18:33,910 --> 00:18:34,750
Guess what's going to happen?

284
00:18:34,750 --> 00:18:38,570
By the end of the
day, there'll be

285
00:18:38,570 --> 00:18:41,410
50 things up there.

286
00:18:41,410 --> 00:18:44,910
So we know beryllium's metal
and it has conductivity.

287
00:18:44,910 --> 00:18:46,410
So what's the deal?

288
00:18:46,410 --> 00:18:52,560
Well, it turns out that while
beryllium has the 2s band

289
00:18:52,560 --> 00:18:57,280
full, the 2p orbitals
still are there.

290
00:18:57,280 --> 00:18:58,745
They're still there and
so there's going

291
00:18:58,745 --> 00:19:06,410
to be a band unfilled.

292
00:19:06,410 --> 00:19:11,210
There's going to be a band
for the 2p orbitals.

293
00:19:11,210 --> 00:19:13,690
Well, guess what?

294
00:19:13,690 --> 00:19:24,650
It turns out that the way I've
drawn it, the 2p band overlaps

295
00:19:24,650 --> 00:19:26,180
the 2s band.

296
00:19:26,180 --> 00:19:33,110
And so what that means is that I
can promote into the 2p band

297
00:19:33,110 --> 00:19:36,940
and I can achieve
my conductivity.

298
00:19:36,940 --> 00:19:41,850
So that's another-- so we solved
the problem of the

299
00:19:41,850 --> 00:19:44,940
filled s-orbitals,
and we've got

300
00:19:44,940 --> 00:19:47,800
conductivity in both cases.

301
00:19:47,800 --> 00:19:55,760
So we're OK so far, but Drude
wasn't far behind.

302
00:20:05,500 --> 00:20:06,750
What can we say about
insulators?

303
00:20:15,630 --> 00:20:18,170
It looks like we
have a problem.

304
00:20:18,170 --> 00:20:21,210
Well, let's take a look
at another example.

305
00:20:21,210 --> 00:20:22,650
And let's try carbon.

306
00:20:26,290 --> 00:20:28,170
Well, we know carbon is what?

307
00:20:28,170 --> 00:20:29,420
2s2p2.

308
00:20:32,870 --> 00:20:34,650
And so we can go--

309
00:20:34,650 --> 00:20:38,470
and we know, by the way, that
most of the time carbon will

310
00:20:38,470 --> 00:20:42,100
hybridize and so we'll
end up with 2sp3.

311
00:20:45,360 --> 00:20:49,940
So n equals 2sp3 hybridized.

312
00:20:49,940 --> 00:20:51,820
So we see that happen.

313
00:20:51,820 --> 00:20:57,440
And we also know that carbon's
not a metal and that we have

314
00:20:57,440 --> 00:21:01,470
strong bonds.

315
00:21:04,040 --> 00:21:05,720
In the structure that we're
going to talk about, they're

316
00:21:05,720 --> 00:21:09,440
covalent bonds and so they're
very strong bonds.

317
00:21:09,440 --> 00:21:10,690
So let's do this.

318
00:21:10,690 --> 00:21:14,720
Carbon in the gas phase--

319
00:21:14,720 --> 00:21:21,160
we have 2s and 2p.

320
00:21:21,160 --> 00:21:25,540
We know that what happens is we
end up with hybridization

321
00:21:25,540 --> 00:21:29,030
and so we ends up and
we fill these guys.

322
00:21:33,940 --> 00:21:35,870
So that's what we get.

323
00:21:35,870 --> 00:21:46,620
Now this would be for diamond
in the gas phase.

324
00:21:49,550 --> 00:21:52,780
So with this hybridization,
we get bands.

325
00:21:52,780 --> 00:21:57,220
We start adding carbon atoms
to this and what do we get?

326
00:21:57,220 --> 00:22:04,280
Well, we get a band that's
the 2p band.

327
00:22:04,280 --> 00:22:08,820
The sp3 band is different
looking than the bands for

328
00:22:08,820 --> 00:22:14,430
magnesium or copper or beryllium
in that there's a

329
00:22:14,430 --> 00:22:19,080
separation between the sigma
and the sigma-star

330
00:22:19,080 --> 00:22:20,500
anti-bonding orbitals.

331
00:22:23,420 --> 00:22:31,860
So we start doing these guys
up using Aufbau, and we

332
00:22:31,860 --> 00:22:40,650
discover that there's an energy
gap e sub g between the

333
00:22:40,650 --> 00:22:45,180
sigma bonding orbital
part of the band and

334
00:22:45,180 --> 00:22:48,030
the sigma-star band.

335
00:22:48,030 --> 00:22:49,150
So what's happening?

336
00:22:49,150 --> 00:22:52,480
Well, that's actually
pretty good sized.

337
00:22:52,480 --> 00:22:58,220
It's about 5.4 electron volts.

338
00:22:58,220 --> 00:23:00,020
Now compare that with what?

339
00:23:00,020 --> 00:23:07,250
Visible light is around
one electron volt.

340
00:23:07,250 --> 00:23:12,110
So now we have a very, very
different situation and

341
00:23:12,110 --> 00:23:15,010
there's some terminology
we need to have here.

342
00:23:15,010 --> 00:23:18,870
This is the so-called conduction
band and this is

343
00:23:18,870 --> 00:23:23,530
the so-called valence.

344
00:23:23,530 --> 00:23:26,210
band.

345
00:23:26,210 --> 00:23:28,210
Valence band and conduction
band.

346
00:23:28,210 --> 00:23:33,820
So in order for us to get
electrical conductivity, we

347
00:23:33,820 --> 00:23:39,500
have to somehow promote an
electron across the 5.4

348
00:23:39,500 --> 00:23:43,090
electron-volt band gap.

349
00:23:43,090 --> 00:23:50,500
This is the so-called
band gap.

350
00:23:50,500 --> 00:23:54,540
Now we know that visible light
is about 1 electron volt so we

351
00:23:54,540 --> 00:23:56,910
know that's not going
to do it.

352
00:23:56,910 --> 00:24:00,870
And in fact, we might expect
that even a diamond is what?

353
00:24:00,870 --> 00:24:02,480
Transparent to visible light.

354
00:24:02,480 --> 00:24:05,710
So if the photons come in, if
there's no promotion, there's

355
00:24:05,710 --> 00:24:10,870
no mission, transparency
to visible light.

356
00:24:10,870 --> 00:24:15,390
So that's a big number.

357
00:24:15,390 --> 00:24:17,740
Let's try another one.

358
00:24:17,740 --> 00:24:19,710
Let's try silicon.

359
00:24:22,520 --> 00:24:30,970
Now I'm going down group four,
where silicon is going to be

360
00:24:30,970 --> 00:24:35,690
also sp3 hybridization.

361
00:24:35,690 --> 00:24:38,450
So we can do that, only
this time over

362
00:24:38,450 --> 00:24:41,800
here, carbon is what?

363
00:24:41,800 --> 00:24:46,040
n equals 2.

364
00:24:46,040 --> 00:24:53,980
For silicon, n equals 3 and so
we can do the same thing.

365
00:24:53,980 --> 00:24:55,950
Here's the 3s.

366
00:24:55,950 --> 00:24:57,200
Here's the 3p.

367
00:24:59,560 --> 00:25:06,270
And we hybridize and we end up
with before and then we end up

368
00:25:06,270 --> 00:25:12,300
with a band, same kind of band
structure where this is a

369
00:25:12,300 --> 00:25:20,980
sigma-star, star, this is e
sub g, this is the valence

370
00:25:20,980 --> 00:25:24,200
band, conduction band.

371
00:25:24,200 --> 00:25:28,270
Now we have states up
here, but in this

372
00:25:28,270 --> 00:25:29,930
case, what do you figure?

373
00:25:29,930 --> 00:25:32,040
n equals 3.

374
00:25:32,040 --> 00:25:36,290
So those valence electrons are
hanging out further away from

375
00:25:36,290 --> 00:25:37,860
the nucleus.

376
00:25:37,860 --> 00:25:42,300
And we know generally that the
energy drops off, the valence

377
00:25:42,300 --> 00:25:44,840
electron energy drops off
as we get further

378
00:25:44,840 --> 00:25:46,760
away from the nucleus.

379
00:25:46,760 --> 00:25:51,040
So you might expect that the
energy of this gap would be a

380
00:25:51,040 --> 00:25:53,360
little bit smaller and indeed.

381
00:25:53,360 --> 00:25:53,760
it is.

382
00:25:53,760 --> 00:25:58,090
Very fortunate for us, it's
1.1 electron volts.

383
00:25:58,090 --> 00:25:59,340
Now we're getting close.

384
00:26:04,010 --> 00:26:15,830
And so this is 1/4 or even 1/5
of that for carbon and

385
00:26:15,830 --> 00:26:20,850
remember, visible light
is on the order of

386
00:26:20,850 --> 00:26:21,700
one electron volt.

387
00:26:21,700 --> 00:26:24,700
So one, one and half
electron volts.

388
00:26:24,700 --> 00:26:26,190
So what happens?

389
00:26:26,190 --> 00:26:32,560
This is close enough so that
we get semi-conduction.

390
00:26:42,210 --> 00:26:47,410
It's called a semiconductor and
we'll make a definition.

391
00:26:47,410 --> 00:26:55,030
If the band gap is greater than
3 electron volts, we call

392
00:26:55,030 --> 00:27:00,160
it an insulator.

393
00:27:00,160 --> 00:27:05,976
If the band gap is less than--
well, let's give it a range.

394
00:27:16,140 --> 00:27:24,880
1 to 3 electron volts, we call
it a semiconductor and of

395
00:27:24,880 --> 00:27:28,280
course, if the band
gap is equal to 0,

396
00:27:28,280 --> 00:27:32,340
we call it a metal.

397
00:27:32,340 --> 00:27:39,040
So that's a distinction, which
is a little bit arbitrary, but

398
00:27:39,040 --> 00:27:41,450
pretty good.

399
00:27:41,450 --> 00:27:44,830
So now, if I take a look at
silicon, what do I see?

400
00:27:44,830 --> 00:27:48,340
Well, if I had a piece of
silicon here as opposed to

401
00:27:48,340 --> 00:27:51,200
diamond and I looked at
it, it would be gray.

402
00:27:51,200 --> 00:27:54,680
We would have color and the
reason it would have color is

403
00:27:54,680 --> 00:27:59,210
because I get some promotion
here and I get re-emission and

404
00:27:59,210 --> 00:28:00,730
so now I get color.

405
00:28:00,730 --> 00:28:04,835
So it's not transparent
to visible light.

406
00:28:16,640 --> 00:28:17,100
OK.

407
00:28:17,100 --> 00:28:21,520
Let's take a look in general
at what we--

408
00:28:21,520 --> 00:28:23,230
what we're talking about
is photoexcitation.

409
00:28:31,760 --> 00:28:35,120
Now this is a diagram
which is--

410
00:28:35,120 --> 00:28:36,710
you should have in
your aid sheet.

411
00:28:36,710 --> 00:28:39,680
Sooner or later, you should
have it in your aid sheet.

412
00:28:39,680 --> 00:28:40,110
OK.

413
00:28:40,110 --> 00:28:43,180
So let's draw a general band.

414
00:28:46,340 --> 00:28:47,410
Here's our two bands.

415
00:28:47,410 --> 00:28:49,500
This is the valence band.

416
00:28:49,500 --> 00:28:56,630
This is the conduction band
and we have a band gap.

417
00:28:59,530 --> 00:29:07,480
And now what happens if
I were a photon here?

418
00:29:07,480 --> 00:29:09,910
Well, I guess it depends.

419
00:29:09,910 --> 00:29:11,380
If the photon--

420
00:29:11,380 --> 00:29:17,740
if e photon greater than e band
gap, then what happens?

421
00:29:17,740 --> 00:29:24,570
I get promotion of an electron
up from the valence band to

422
00:29:24,570 --> 00:29:26,630
the conduction band.

423
00:29:26,630 --> 00:29:27,940
OK.

424
00:29:27,940 --> 00:29:29,210
So then what happens?

425
00:29:29,210 --> 00:29:32,865
Well, the photon is quantized.

426
00:29:32,865 --> 00:29:34,610
It's one shot.

427
00:29:34,610 --> 00:29:35,570
The photon's gone.

428
00:29:35,570 --> 00:29:38,070
Now I guess we need to settle
one little thing.

429
00:29:38,070 --> 00:29:40,520
What happens if the photon
is really a lot greater

430
00:29:40,520 --> 00:29:41,460
than the band gap?

431
00:29:41,460 --> 00:29:45,030
In another words, let's say it's
a million electron volts

432
00:29:45,030 --> 00:29:46,010
or something like that.

433
00:29:46,010 --> 00:29:50,260
Well, for purposes of 3.091,
what we're going to assume is

434
00:29:50,260 --> 00:29:58,820
that any excess energy
goes to heat.

435
00:29:58,820 --> 00:30:03,290
Let's not worry about what
happens for other things.

436
00:30:03,290 --> 00:30:07,850
In fact, that's not far off.

437
00:30:07,850 --> 00:30:11,990
Some of these LEDs that you
see, they get warm.

438
00:30:11,990 --> 00:30:14,600
So there is some heat.

439
00:30:14,600 --> 00:30:16,500
So the photon--

440
00:30:16,500 --> 00:30:18,450
once it goes away, I get--

441
00:30:20,960 --> 00:30:22,890
the electron falls back down.

442
00:30:22,890 --> 00:30:27,410
Well, if the electron falls back
down, then what do I get?

443
00:30:27,410 --> 00:30:32,250
I get another photon out, but
now I've basically built

444
00:30:32,250 --> 00:30:35,900
myself a diode or some
kind of device.

445
00:30:35,900 --> 00:30:37,150
That photon--

446
00:30:41,090 --> 00:30:44,610
the energy of the photon
is equal to what?

447
00:30:44,610 --> 00:30:47,320
It's equal to the band
gap, which is

448
00:30:47,320 --> 00:30:50,160
equal to HC over lambda.

449
00:30:50,160 --> 00:30:55,780
So I can adjust the wavelength
here if I can

450
00:30:55,780 --> 00:30:57,790
adjust the band gap.

451
00:31:00,350 --> 00:31:03,720
See where we're going
with this?

452
00:31:03,720 --> 00:31:06,510
Well, what happens if I--

453
00:31:06,510 --> 00:31:18,700
let's say I hook this up to a
resistor and I draw a current.

454
00:31:18,700 --> 00:31:22,230
Well, as long as I keep the
light shining on here,

455
00:31:22,230 --> 00:31:26,650
photons, then I can keep
promoting these guys, and I

456
00:31:26,650 --> 00:31:28,820
can keep drawing current.

457
00:31:28,820 --> 00:31:31,020
So what do I have?

458
00:31:31,020 --> 00:31:34,190
I have something that
I can generate

459
00:31:34,190 --> 00:31:39,500
electricity with light.

460
00:31:39,500 --> 00:31:42,600
And so that's sort
of solar-powered

461
00:31:42,600 --> 00:31:43,390
something, isn't it?

462
00:31:43,390 --> 00:31:44,760
We can generate current.

463
00:31:44,760 --> 00:31:48,850
What happens if I take--

464
00:31:48,850 --> 00:31:52,320
and now instead of doing that,
I hook up a battery to this

465
00:31:52,320 --> 00:31:57,070
thing and now I pump
current in here?

466
00:31:57,070 --> 00:31:57,980
I pump current in here.

467
00:31:57,980 --> 00:32:03,520
In that case, I can force
the electrons up here.

468
00:32:03,520 --> 00:32:10,480
So I can force electrons to go
in the reverse and I could

469
00:32:10,480 --> 00:32:15,410
make a photosensor or I could
force the electrons up here

470
00:32:15,410 --> 00:32:19,530
and let them come back down
and I know this wavelength

471
00:32:19,530 --> 00:32:24,350
here, I can make a
light-emitting diode.

472
00:32:24,350 --> 00:32:28,470
So just this one little concept
here, which is very

473
00:32:28,470 --> 00:32:38,830
simplified, gives us the basis
for photovoltaics.

474
00:32:41,360 --> 00:32:46,000
And that's exactly
the way it works.

475
00:32:48,980 --> 00:32:49,950
OK.

476
00:32:49,950 --> 00:32:52,120
Let's put this in another way.

477
00:32:55,810 --> 00:33:01,380
Let's plot the percent
absorption.

478
00:33:01,380 --> 00:33:03,490
In other words, if the energy's

479
00:33:03,490 --> 00:33:05,870
high enough, I absorb--

480
00:33:05,870 --> 00:33:12,730
versus wavelength this way and
since energy is inversely

481
00:33:12,730 --> 00:33:17,840
proportional to wavelength, we
have energy going this way.

482
00:33:21,420 --> 00:33:24,570
Let's put some numbers
in here.

483
00:33:24,570 --> 00:33:30,370
Let's say this is 400, this is
700 and this is Professor

484
00:33:30,370 --> 00:33:31,620
Sadoway's dreaded nanometers.

485
00:33:34,480 --> 00:33:42,970
So this is visible light and
let's put carbon on there.

486
00:33:42,970 --> 00:33:46,500
Well, if you do the calculation,
convert iy, it

487
00:33:46,500 --> 00:33:53,860
turns out that for carbon, with
this band gap, you end up

488
00:33:53,860 --> 00:33:58,160
with behavior where if
the energy is above

489
00:33:58,160 --> 00:34:00,480
the band gap, I get--

490
00:34:00,480 --> 00:34:02,800
well, let's call this 100.

491
00:34:02,800 --> 00:34:04,430
That's 0, right?

492
00:34:04,430 --> 00:34:07,110
I get 100% absorption.

493
00:34:07,110 --> 00:34:09,320
When I get to the band
gap, below the

494
00:34:09,320 --> 00:34:10,420
band gap, what happens?

495
00:34:10,420 --> 00:34:14,380
Well, I drop off and
it goes like that.

496
00:34:14,380 --> 00:34:18,960
In the case of carbon, this
wavelength, right, which is,

497
00:34:18,960 --> 00:34:25,565
by the way, called the
absorption edge--

498
00:34:28,200 --> 00:34:35,910
that number comes out
to be about 229.

499
00:34:35,910 --> 00:34:47,210
If I try it with silicon,
that number--

500
00:34:47,210 --> 00:34:53,930
so this would be carbon, this
would be silicon and carbon--

501
00:34:57,520 --> 00:34:59,660
1125.

502
00:34:59,660 --> 00:35:00,470
All right.

503
00:35:00,470 --> 00:35:05,740
So the absorption edge for
silicon is 1125, which means

504
00:35:05,740 --> 00:35:10,930
it absorbs in the visible range
and so that's the way we

505
00:35:10,930 --> 00:35:12,960
get the luster.

506
00:35:12,960 --> 00:35:14,470
And this would be in the what?

507
00:35:14,470 --> 00:35:15,720
Infrared.

508
00:35:18,380 --> 00:35:23,320
And this would be in the UV
region, if you wanted to--

509
00:35:23,320 --> 00:35:28,780
which would be far hard UV and
this would be far infrared.

510
00:35:33,840 --> 00:35:34,110
OK.

511
00:35:34,110 --> 00:35:37,840
This is the paper--

512
00:35:37,840 --> 00:35:39,440
Heitler and London's paper.

513
00:35:39,440 --> 00:35:44,720
It's in German and you
can see in Zurich.

514
00:35:44,720 --> 00:35:46,010
And this is their
original paper.

515
00:35:46,010 --> 00:35:49,620
You can go down to the library
and you can get this original

516
00:35:49,620 --> 00:35:52,790
paper and if you know how
to read German, it's--

517
00:35:52,790 --> 00:35:55,040
we have it.

518
00:35:55,040 --> 00:35:56,470
This is some of the
original paper.

519
00:35:56,470 --> 00:36:00,180
You notice the Schrodinger
equation up there.

520
00:36:00,180 --> 00:36:01,130
Nasty--

521
00:36:01,130 --> 00:36:03,950
really nasty, but this
is the calculations.

522
00:36:03,950 --> 00:36:04,700
This is radius.

523
00:36:04,700 --> 00:36:09,500
This is energy and you can see
a point here where you get an

524
00:36:09,500 --> 00:36:13,520
energy minimum and that's
where the bands operate.

525
00:36:13,520 --> 00:36:15,870
This is another way
to look at it.

526
00:36:19,510 --> 00:36:22,580
This would be the bottom of the
bonding orbital or the top

527
00:36:22,580 --> 00:36:27,160
of the anti-bonding orbitals.

528
00:36:27,160 --> 00:36:32,020
This is another way to look at
what we've drawn so far.

529
00:36:32,020 --> 00:36:34,060
Somebody is talking.

530
00:36:34,060 --> 00:36:36,070
Something you guys ought
to know, this room is

531
00:36:36,070 --> 00:36:38,350
acoustically perfect.

532
00:36:38,350 --> 00:36:43,470
If you pass gas in the back
row, I'll hear it, OK?

533
00:36:43,470 --> 00:36:47,070
So if you're talking up
there, I'll hear it.

534
00:36:47,070 --> 00:36:47,870
OK.

535
00:36:47,870 --> 00:36:49,790
So you can see what's
going on here.

536
00:36:49,790 --> 00:36:53,780
We've drawn that and this
another way to look at it.

537
00:36:53,780 --> 00:36:56,380
By the way, there's a mistake
in your book that

538
00:36:56,380 --> 00:36:57,320
doesn't make any sense.

539
00:36:57,320 --> 00:36:58,570
2s3p--

540
00:37:01,070 --> 00:37:04,770
it's 2p in the description
for beryllium.

541
00:37:04,770 --> 00:37:09,350
OK, this is another
way to look at it.

542
00:37:09,350 --> 00:37:10,650
This is in the archival notes.

543
00:37:10,650 --> 00:37:12,640
It's one of the few pieces of
the archival notes which I

544
00:37:12,640 --> 00:37:14,930
don't understand.

545
00:37:14,930 --> 00:37:17,200
So don't worry about that.

546
00:37:17,200 --> 00:37:18,370
OK.

547
00:37:18,370 --> 00:37:21,280
Here's what happens when you--

548
00:37:21,280 --> 00:37:23,940
where we illustrated this where
you apply a potential.

549
00:37:23,940 --> 00:37:27,200
What happens is you depopulate
the bonding orbitals, and you

550
00:37:27,200 --> 00:37:30,520
populate the antibonding
orbitals rules, and you get

551
00:37:30,520 --> 00:37:33,320
conduction.

552
00:37:33,320 --> 00:37:34,500
This is another--

553
00:37:34,500 --> 00:37:35,750
this is the right way
to look at it.

554
00:37:38,320 --> 00:37:40,370
This sort of illustrates the
things we've gone through the

555
00:37:40,370 --> 00:37:41,270
whole time.

556
00:37:41,270 --> 00:37:45,680
A metal has no band gap.

557
00:37:45,680 --> 00:37:51,150
That no band gap is achieved
either by half-filled set of

558
00:37:51,150 --> 00:37:55,190
orbitals or overlap
between one or

559
00:37:55,190 --> 00:37:56,920
between different levels.

560
00:37:56,920 --> 00:38:02,950
An insulator has a large band
gap and a semiconductor has a

561
00:38:02,950 --> 00:38:06,360
sort of intermediate band gap.

562
00:38:06,360 --> 00:38:08,930
Let's get a little--

563
00:38:08,930 --> 00:38:12,010
sort of wet your whistle for
your reading for next Tuesday.

564
00:38:12,010 --> 00:38:15,560
I think we have Monday
lecture on Tuesday.

565
00:38:15,560 --> 00:38:18,570
If you go over to
the reactor--

566
00:38:18,570 --> 00:38:21,130
they have a reactor
here at MIT--

567
00:38:21,130 --> 00:38:26,650
once a week, a truck backs up
and it's full of silicon logs.

568
00:38:26,650 --> 00:38:28,780
These things are about 12 inches
in diameter and they're

569
00:38:28,780 --> 00:38:34,140
about this tall and they bring
them into the reactor and

570
00:38:34,140 --> 00:38:36,460
they're irradiated
with neutrons.

571
00:38:36,460 --> 00:38:37,390
Well, what do you
think happens?

572
00:38:37,390 --> 00:38:46,250
Since everybody in here knows
the Periodic Table by heart,

573
00:38:46,250 --> 00:38:48,130
what's the next atom--
what's the next

574
00:38:48,130 --> 00:38:51,030
element over from silicon?

575
00:38:51,030 --> 00:38:52,160
Phosphorus.

576
00:38:52,160 --> 00:38:52,670
OK.

577
00:38:52,670 --> 00:38:53,860
So guess what?

578
00:38:53,860 --> 00:38:56,850
You take and you irradiate
the silicon.

579
00:38:56,850 --> 00:38:58,440
You absorb a neutron.

580
00:38:58,440 --> 00:39:00,690
It adds one to z, doesn't it?

581
00:39:00,690 --> 00:39:02,890
And it becomes phosphorus.

582
00:39:02,890 --> 00:39:09,560
Well, phosphorus has one more
electron than silicon.

583
00:39:09,560 --> 00:39:17,630
So I have implanted phosphorus
into silicon by transmutation.

584
00:39:17,630 --> 00:39:19,860
And there's one more electron
that's in there.

585
00:39:19,860 --> 00:39:20,610
Now where's it come from?

586
00:39:20,610 --> 00:39:21,350
I don't know.

587
00:39:21,350 --> 00:39:23,170
The electron bank, right?

588
00:39:23,170 --> 00:39:27,000
But what do you figure the
energy of that guy is?

589
00:39:27,000 --> 00:39:29,550
Well, it's a lot higher than
the electrons in silicon.

590
00:39:32,400 --> 00:39:33,600
And so guess what?

591
00:39:33,600 --> 00:39:38,000
That electron, we'll find out,
doesn't reside down here.

592
00:39:38,000 --> 00:39:42,880
It resides up here or
very close to that.

593
00:39:42,880 --> 00:39:45,830
So that's what's called--

594
00:39:45,830 --> 00:39:47,780
and we'll talk about it next
time-- it's called doping,

595
00:39:47,780 --> 00:39:52,850
only now we're doping it in
a special kind of way.

596
00:39:52,850 --> 00:39:53,510
OK.

597
00:39:53,510 --> 00:39:54,870
We've got-- let's keep going.

598
00:40:04,160 --> 00:40:07,800
I want to get this
one up there.

599
00:40:07,800 --> 00:40:09,050
There we go.

600
00:40:12,740 --> 00:40:13,990
OK.

601
00:40:17,050 --> 00:40:19,900
Now-- so far we've talked
about photons.

602
00:40:19,900 --> 00:40:22,050
They're a one shot deal.

603
00:40:22,050 --> 00:40:33,430
What about thermal excitation?

604
00:40:33,430 --> 00:40:36,700
Well, we can make our-- the same
drawing we have in the

605
00:40:36,700 --> 00:40:41,850
past. We got our material here
where we have a valence band,

606
00:40:41,850 --> 00:40:46,140
conduction band, and
now we put--

607
00:40:49,410 --> 00:40:54,780
we add thermal energy.

608
00:40:54,780 --> 00:40:58,340
By the way, what's the one
electron volt in temperature?

609
00:40:58,340 --> 00:41:00,040
Just to give you a feel--

610
00:41:00,040 --> 00:41:04,060
one electron volt is 11,600
degrees Kelvin if you convert

611
00:41:04,060 --> 00:41:05,420
that to temperature.

612
00:41:05,420 --> 00:41:08,650
So one electron volt seems like
a small number, but in

613
00:41:08,650 --> 00:41:10,830
temperature, is pretty warm.

614
00:41:10,830 --> 00:41:11,460
OK.

615
00:41:11,460 --> 00:41:19,480
So now the thermal
energy is what?

616
00:41:19,480 --> 00:41:20,730
It's constant.

617
00:41:24,040 --> 00:41:27,950
Unlike the photons, which
are one off, right?

618
00:41:27,950 --> 00:41:28,980
So it's constant.

619
00:41:28,980 --> 00:41:30,530
So what happens?

620
00:41:30,530 --> 00:41:39,762
Now I take an electron from the
valence band and I promote

621
00:41:39,762 --> 00:41:44,010
it up here.

622
00:41:44,010 --> 00:41:46,020
So it looks sort of like--

623
00:41:46,020 --> 00:41:48,360
so far up there with photons.

624
00:41:48,360 --> 00:41:51,080
But there's one critical
difference.

625
00:41:51,080 --> 00:41:53,730
It stays up there.

626
00:41:53,730 --> 00:41:57,290
It stays up there because
the energy is constant.

627
00:41:57,290 --> 00:41:59,290
So what does that mean?

628
00:41:59,290 --> 00:42:03,225
Well, it leaves behind
a broken bond.

629
00:42:10,080 --> 00:42:16,240
And that broken bond has a lot
of energy, and in fact, it

630
00:42:16,240 --> 00:42:17,900
doesn't like to stick around.

631
00:42:17,900 --> 00:42:19,500
So given a chance, it'll move.

632
00:42:19,500 --> 00:42:22,850
It's like a hot potato
and so that broken

633
00:42:22,850 --> 00:42:27,040
bond is called a hole.

634
00:42:31,050 --> 00:42:32,170
We're not too imaginative.

635
00:42:32,170 --> 00:42:34,610
It's a hole in the lattice.

636
00:42:34,610 --> 00:42:37,200
But it has high energy.

637
00:42:37,200 --> 00:42:38,770
So what's the deal
with this hole?

638
00:42:38,770 --> 00:42:42,050
Well, this is--

639
00:42:42,050 --> 00:42:51,580
a hole is a 0 in a
land of minus 1.

640
00:42:51,580 --> 00:42:52,380
So what does it mean?

641
00:42:52,380 --> 00:42:55,915
It's actually net positive.

642
00:42:58,860 --> 00:43:03,570
So now in the case of thermal
excitation, I end up with an

643
00:43:03,570 --> 00:43:09,070
electron in the conduction
band and a hole

644
00:43:09,070 --> 00:43:10,200
in the valence band.

645
00:43:10,200 --> 00:43:16,160
So I end up with an electron in
the conduction band and a

646
00:43:16,160 --> 00:43:21,800
hole and the electrical
engineers call this p.

647
00:43:21,800 --> 00:43:25,550
They're not very imaginative
either-- positive in the

648
00:43:25,550 --> 00:43:26,590
valence band.

649
00:43:26,590 --> 00:43:30,720
So we get 241.

650
00:43:30,720 --> 00:43:34,940
We get two charge carriers
for every event.

651
00:43:34,940 --> 00:43:36,420
That, we get one.

652
00:43:36,420 --> 00:43:40,035
This, we get two charge carriers
for every event.

653
00:43:45,260 --> 00:43:49,770
So now we have what?

654
00:43:49,770 --> 00:43:52,770
Let's ask ourselves,
what's the--

655
00:43:55,420 --> 00:43:57,340
can we do a little
math on this?

656
00:43:57,340 --> 00:44:03,940
And the broken bond, by the
way, is a hole and so the

657
00:44:03,940 --> 00:44:13,660
number of electrons is also
equal to the number of holes

658
00:44:13,660 --> 00:44:17,210
because it's a one for one,
and in the electrical

659
00:44:17,210 --> 00:44:20,060
engineering world, they
say n equals p.

660
00:44:23,930 --> 00:44:27,000
And so we can now go back and
say something about this

661
00:44:27,000 --> 00:44:27,830
conductivity.

662
00:44:27,830 --> 00:44:36,570
We can do some calculations here
and we can calculate the

663
00:44:36,570 --> 00:44:42,730
conductivity due to the
electrical connectivity, and

664
00:44:42,730 --> 00:44:47,920
it's really the sum over i of
n of i, which would be the

665
00:44:47,920 --> 00:45:00,430
number of the population
of carriers times--

666
00:45:00,430 --> 00:45:04,510
that's the value of the charge
on the carrier--

667
00:45:04,510 --> 00:45:07,110
times something called
the mobility.

668
00:45:14,210 --> 00:45:16,570
OK, so what's the mobility?

669
00:45:16,570 --> 00:45:22,510
Well, you could imagine that
these electrons have to move

670
00:45:22,510 --> 00:45:25,500
back and forth in the lattice
and in a metal versus a

671
00:45:25,500 --> 00:45:27,500
covalence solid or something
like that, it might be a

672
00:45:27,500 --> 00:45:29,350
little bit different.

673
00:45:29,350 --> 00:45:31,340
The resistance might be
different and so--

674
00:45:31,340 --> 00:45:32,890
in fact, it is.

675
00:45:32,890 --> 00:45:40,660
mu i is equal to the velocity of
the charge carrier divided

676
00:45:40,660 --> 00:45:43,440
by the electric field.

677
00:45:46,870 --> 00:45:47,840
OK.

678
00:45:47,840 --> 00:45:49,090
So we're almost there.

679
00:45:54,540 --> 00:45:59,880
Now we need to-- and we can
simplify this because of the n

680
00:45:59,880 --> 00:46:04,590
equals p business, and we can
say that the electrical

681
00:46:04,590 --> 00:46:06,790
conductivity is equal to what?

682
00:46:06,790 --> 00:46:12,760
It's equal to n sub e times e,
which is the electronic charge

683
00:46:12,760 --> 00:46:20,760
times mu sub e plus n sub h,
which would be the holes, the

684
00:46:20,760 --> 00:46:24,690
electronic charge,
times mu sub h.

685
00:46:24,690 --> 00:46:30,610
But since n is equal to p, we
end up with n sub e times the

686
00:46:30,610 --> 00:46:38,870
electronic charge times
mu sub e plus u sub h.

687
00:46:38,870 --> 00:46:40,490
OK.

688
00:46:40,490 --> 00:46:43,600
And so that-- what we really
need to get is this.

689
00:46:43,600 --> 00:46:47,450
Well, we don't have time to go
through that, but from a

690
00:46:47,450 --> 00:46:50,930
quantum mechanical calculation,
we can get that.

691
00:46:50,930 --> 00:46:52,740
n sub e is equal to what?

692
00:46:52,740 --> 00:46:58,700
It's equal to some constant
times T to 3/2 times the

693
00:46:58,700 --> 00:47:10,070
exponent of minus E sub g
over 2k sub B times T.

694
00:47:10,070 --> 00:47:11,650
So what is all this stuff?

695
00:47:11,650 --> 00:47:12,790
Well, this is a constant.

696
00:47:12,790 --> 00:47:15,370
This is the temperature.

697
00:47:15,370 --> 00:47:16,370
This is the band gap.

698
00:47:16,370 --> 00:47:20,340
So it's a representation
of the binding.

699
00:47:26,020 --> 00:47:27,090
What's down here?

700
00:47:27,090 --> 00:47:29,840
Well, k sub B is Boltzmann's
constant.

701
00:47:29,840 --> 00:47:36,020
This is absolute temperature
and so this represents the

702
00:47:36,020 --> 00:47:40,895
disruptive force.

703
00:47:44,800 --> 00:47:49,860
So it's a balance between how
tightly they're bound and how

704
00:47:49,860 --> 00:47:52,810
much energy I've
got to do this.

705
00:47:52,810 --> 00:47:54,115
Well, let's--

706
00:47:54,115 --> 00:47:56,000
we've got one minute.

707
00:47:56,000 --> 00:48:00,090
Let's do a quick calculations
for silicon, just to

708
00:48:00,090 --> 00:48:01,960
close the loop here.

709
00:48:01,960 --> 00:48:08,540
For silicon at room temperature,
that number comes

710
00:48:08,540 --> 00:48:15,560
out 1.3 times 10 to the 10th
per centimeter cubed.

711
00:48:15,560 --> 00:48:17,310
Say well, that's billions.

712
00:48:17,310 --> 00:48:19,260
That's a big deal.

713
00:48:19,260 --> 00:48:23,980
What about copper at
room temperature?

714
00:48:23,980 --> 00:48:31,800
Well, that number comes out
about 8.5 times 10 to the 22.

715
00:48:31,800 --> 00:48:33,950
Now we're talking big numbers.

716
00:48:33,950 --> 00:48:38,190
So there's a 10 to the 12th
difference between these two

717
00:48:38,190 --> 00:48:42,630
Well, let's take a quick look
before we finish up.

718
00:48:42,630 --> 00:48:42,790
OK.

719
00:48:42,790 --> 00:48:45,580
This is the band gap as a
function of position in the

720
00:48:45,580 --> 00:48:46,120
Periodic Table.

721
00:48:46,120 --> 00:48:49,690
Now you guys ought to be able
to rationalize this.

722
00:48:49,690 --> 00:48:52,460
Lead is a metal, bigger
atoms you can see.

723
00:48:52,460 --> 00:48:54,690
10 actually comes
in two flavors.

724
00:48:54,690 --> 00:48:56,320
Gray and white and
one of them--

725
00:48:56,320 --> 00:48:57,550
I think it's white--

726
00:48:57,550 --> 00:49:01,250
actually forms covalent
bonds and they use

727
00:49:01,250 --> 00:49:03,880
tin for night vision.

728
00:49:03,880 --> 00:49:07,860
Think about where that
band gap is.

729
00:49:07,860 --> 00:49:09,980
But here's the punch line.

730
00:49:09,980 --> 00:49:12,390
We're trying to rationalize
this large difference in

731
00:49:12,390 --> 00:49:13,420
conductivity.

732
00:49:13,420 --> 00:49:16,630
Well, there's copper up there
at 10 to the 7th, there

733
00:49:16,630 --> 00:49:20,820
silicon at 10 to the minus 4 and
ten to the minus 4, 10 to

734
00:49:20,820 --> 00:49:23,060
the minus-- about 10 to the
12th or thereabouts--

735
00:49:23,060 --> 00:49:26,490
and so, lo and behold, this--

736
00:49:26,490 --> 00:49:30,660
we were able to rationalize
with these fairly simple

737
00:49:30,660 --> 00:49:33,880
models, the range of
conductivities that go all the

738
00:49:33,880 --> 00:49:36,060
way from metals to

739
00:49:36,060 --> 00:49:38,150
semiconductors and even diamond.

740
00:49:38,150 --> 00:49:38,730
Look at diamond--

741
00:49:38,730 --> 00:49:40,630
10 to the minus 11.

742
00:49:40,630 --> 00:49:42,660
You can rationalize that
the band gap--

743
00:49:42,660 --> 00:49:43,620
where's the band gap?

744
00:49:43,620 --> 00:49:46,050
5.4 electron volts.

745
00:49:46,050 --> 00:49:48,550
OK, we're out of time.