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OK we're going to do problem 3
now on exam 2 from the fall

00:00:27.140 --> 00:00:29.840
2009 class.

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Let's talk a little bit about
what the problem concept is.

00:00:33.720 --> 00:00:35.170
This is doping.

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We're going to talk all about
doping semiconductors.

00:00:37.230 --> 00:00:41.220
As we say chemistry, where
doping is legal.

00:00:41.220 --> 00:00:44.620
So we're going to look at the
things we should probably know

00:00:44.620 --> 00:00:46.810
before attempting the problem.

00:00:46.810 --> 00:00:48.930
You want to review your
doping principles.

00:00:48.930 --> 00:00:49.770
How does doping works.

00:00:49.770 --> 00:00:52.730
What are the mechanisms, your
conduction mechanisms?

00:00:52.730 --> 00:00:54.680
So why does the material
conduct?

00:00:54.680 --> 00:00:56.590
What's actually happening?

00:00:56.590 --> 00:00:58.800
Your donor and acceptor levels,

00:00:58.800 --> 00:01:00.590
understanding which is which.

00:01:00.590 --> 00:01:03.130
And your p versus your
n type doping.

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What those mean.

00:01:04.510 --> 00:01:07.960
So look at those real quick
and do the problem.

00:01:07.960 --> 00:01:09.720
Let's go on.

00:01:09.720 --> 00:01:10.960
I wrote down the information
that we're

00:01:10.960 --> 00:01:13.300
given in the problem.

00:01:13.300 --> 00:01:19.330
The problem part a asks us to
find specifically how much

00:01:19.330 --> 00:01:24.070
gallium is needed to reach a
certain carrier concentration

00:01:24.070 --> 00:01:25.060
in our germanium.

00:01:25.060 --> 00:01:28.490
So we're doping gallium
into germanium.

00:01:28.490 --> 00:01:32.670
We're given the fact that the
germanium band gap is 0.7

00:01:32.670 --> 00:01:34.160
electron volts.

00:01:34.160 --> 00:01:37.280
We know that we want to
achieve a carrier

00:01:37.280 --> 00:01:41.670
concentration of 3.091 times
10 to the 17 carriers per

00:01:41.670 --> 00:01:43.920
centimeter cubed.

00:01:43.920 --> 00:01:46.640
And we're working with 1
kilogram of germanium.

00:01:46.640 --> 00:01:48.900
So we need to achieve this
density or this carrier

00:01:48.900 --> 00:01:52.640
concentration in one kilogram
of germanium.

00:01:52.640 --> 00:01:55.080
I've drawn schematically-- now
remember the germanium

00:01:55.080 --> 00:01:58.550
crystals are in 3-D so the bonds
don't actually look 90

00:01:58.550 --> 00:02:02.250
degrees like this-- but I've
drawn just for visual a

00:02:02.250 --> 00:02:03.055
germanium crystal.

00:02:03.055 --> 00:02:04.630
So this is what a
pure germanium

00:02:04.630 --> 00:02:05.810
crystal would look like.

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I'm going to draw the band
structure for the pure

00:02:07.840 --> 00:02:10.060
germanium crystal now as well.

00:02:10.060 --> 00:02:13.520
When you see a problem that
gives you your band gap and it

00:02:13.520 --> 00:02:15.790
tells you this is about doping,
the first thing you

00:02:15.790 --> 00:02:17.540
want to do is just
get some points.

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Put some stuff on the paper
that you know to be true.

00:02:19.630 --> 00:02:20.880
So let's draw the
band structure.

00:02:25.770 --> 00:02:28.290
I'm going to abbreviate
conduction band with cb and

00:02:28.290 --> 00:02:30.410
valence band with vb.

00:02:30.410 --> 00:02:34.970
So here's my conduction band,
here's my valence band.

00:02:34.970 --> 00:02:39.480
We're told that this is here.

00:02:39.480 --> 00:02:42.810
We know our band gap
energy is 0.7.

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OK and I'm going to use
this blue to show

00:02:49.580 --> 00:02:50.870
where electrons are.

00:02:50.870 --> 00:02:53.080
This just shows that there's
electrons in the valence band

00:02:53.080 --> 00:02:54.930
going all the way up to the
top of the valence band.

00:02:54.930 --> 00:02:58.090
That's how the valence band
level is defined.

00:02:58.090 --> 00:03:00.630
So this easy points.

00:03:00.630 --> 00:03:03.350
You've got this on the paper,
we're good to go.

00:03:03.350 --> 00:03:05.460
Now what we're talking
about is putting

00:03:05.460 --> 00:03:07.630
gallium into germanium.

00:03:07.630 --> 00:03:08.880
So let's do that.

00:03:14.960 --> 00:03:17.800
Let's take out this germanium.

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And let's put a gallium
in its place.

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We'll put it in red.

00:03:24.560 --> 00:03:27.380
OK so this isn't exactly
correct yet.

00:03:27.380 --> 00:03:28.660
Germanium makes 4 bonds.

00:03:28.660 --> 00:03:30.710
If you look at the periodic
table you'll see that it has 4

00:03:30.710 --> 00:03:32.110
valence electrons
to make bonds.

00:03:32.110 --> 00:03:33.200
But gallium does not.

00:03:33.200 --> 00:03:34.462
Gallium only has 3.

00:03:34.462 --> 00:03:38.430
So what that means is that one
of these bonds can't exist

00:03:38.430 --> 00:03:40.570
like this anymore.

00:03:40.570 --> 00:03:43.750
So the way I like to draw it,
is we still have an electron

00:03:43.750 --> 00:03:47.720
from this germanium but we're
missing one for this gallium.

00:03:47.720 --> 00:03:50.160
And this is what a hole
basically is,

00:03:50.160 --> 00:03:52.930
schematically, in doping.

00:03:52.930 --> 00:03:55.820
So we're going to write
this as hole plus.

00:03:55.820 --> 00:03:57.860
And the reason it has a positive
charge associated

00:03:57.860 --> 00:04:00.360
with it is because in our
neutral crystal with no

00:04:00.360 --> 00:04:02.750
charges you having an
electron there.

00:04:02.750 --> 00:04:04.750
And you've just removed an
electron and now it's

00:04:04.750 --> 00:04:05.780
positively charged.

00:04:05.780 --> 00:04:07.980
You have a positive charge in
this region of the crystal,

00:04:07.980 --> 00:04:11.000
which corresponds to
a missing electron.

00:04:11.000 --> 00:04:12.770
So we just created a hole.

00:04:12.770 --> 00:04:14.860
We have a hole here and
then it's going to

00:04:14.860 --> 00:04:16.840
result in what we call--

00:04:16.840 --> 00:04:19.350
I'll use red again--

00:04:19.350 --> 00:04:20.600
an acceptor level.

00:04:23.690 --> 00:04:28.530
And remember this band diagram
is an analogy for, these are

00:04:28.530 --> 00:04:32.330
the energy levels where your
electrons can exist. So we

00:04:32.330 --> 00:04:35.010
have these energy levels and the
valence band and we've got

00:04:35.010 --> 00:04:36.440
energy levels up in the
conduction band.

00:04:36.440 --> 00:04:39.580
What's just happened is that
this dopant has created an

00:04:39.580 --> 00:04:43.070
energy level slightly above
the valence band.

00:04:43.070 --> 00:04:46.180
If you have a donor level from
a different type of doping--

00:04:46.180 --> 00:04:47.490
which we'll talk about
in a second--

00:04:47.490 --> 00:04:52.780
you'll create a level right
below the conduction bands.

00:04:52.780 --> 00:04:54.040
So we've got some points.

00:04:54.040 --> 00:04:56.190
We understand the system now.

00:04:56.190 --> 00:04:56.880
It's just going well.

00:04:56.880 --> 00:04:58.370
So let's try to do a.

00:05:01.430 --> 00:05:04.440
So a, as I said before is asking
us to figure out the

00:05:04.440 --> 00:05:05.650
actual amount.

00:05:05.650 --> 00:05:09.130
We're looking for grams. This
is what we're looking for.

00:05:09.130 --> 00:05:10.540
Grams of gallium.

00:05:10.540 --> 00:05:14.040
That we need to put into a
kilogram of germanium to

00:05:14.040 --> 00:05:18.670
create a carrier concentration
of 3.091 times 10 to the 17

00:05:18.670 --> 00:05:21.010
carriers per centimeter cubed.

00:05:21.010 --> 00:05:23.400
Not too bad of a problem.

00:05:23.400 --> 00:05:25.500
This is basically just
stoichiometry.

00:05:25.500 --> 00:05:27.350
Dimensional analysis.

00:05:27.350 --> 00:05:30.540
Here's how I did it and many
people did it this way.

00:05:30.540 --> 00:05:31.790
I start off.

00:05:35.000 --> 00:05:37.380
times 10 to the 17.

00:05:37.380 --> 00:05:38.830
And I always keep my units.

00:05:38.830 --> 00:05:40.130
That's really important.

00:05:40.130 --> 00:05:43.620
So we're going to write
this as carriers

00:05:43.620 --> 00:05:44.870
per centimeter cubed.

00:05:49.490 --> 00:05:50.910
Now we're also told in the
problem, we have the

00:05:50.910 --> 00:05:54.230
additional information that the
temperature is high enough

00:05:54.230 --> 00:05:57.030
that all of the sites
are ionized.

00:05:57.030 --> 00:05:58.820
What that means is that--
let's take a look

00:05:58.820 --> 00:06:01.150
at this band diagram--

00:06:01.150 --> 00:06:03.780
we have electrons existing
in the valence

00:06:03.780 --> 00:06:06.190
bands up to that level.

00:06:06.190 --> 00:06:08.190
We've doped and now the
temperature's high enough that

00:06:08.190 --> 00:06:11.730
these electrons can be excited,
one of them in this

00:06:11.730 --> 00:06:16.520
case can be excited to this
level here, the acceptor

00:06:16.520 --> 00:06:20.570
level, creating, of course, a
hole in the valence band.

00:06:23.350 --> 00:06:25.690
That's what it means that
it can be fully ionized.

00:06:25.690 --> 00:06:28.470
So basically every gallium
atom that we put into our

00:06:28.470 --> 00:06:31.310
material creates a carrier.

00:06:31.310 --> 00:06:32.540
And why do I say that?

00:06:32.540 --> 00:06:37.770
Because conduction is either,
the movement of electrons in

00:06:37.770 --> 00:06:40.590
the conduction bands, which
we don't have. Or it's the

00:06:40.590 --> 00:06:43.790
movement of holes in the valence
band, which we now

00:06:43.790 --> 00:06:46.040
have. So we're talking
about conduction.

00:06:46.040 --> 00:06:51.670
And so for every gallium atom
we put in, we're creating an

00:06:51.670 --> 00:06:55.440
acceptor level, which takes an
electron up, which creates

00:06:55.440 --> 00:06:57.970
some conduction in
the valence band.

00:06:57.970 --> 00:07:00.610
Now if we add lots and lots
of gallium atoms--

00:07:00.610 --> 00:07:02.670
there's a lot more gallium
atoms in here--

00:07:02.670 --> 00:07:06.370
we're going to actually see
many more of these levels

00:07:06.370 --> 00:07:08.090
showing up.

00:07:08.090 --> 00:07:11.610
And you're going to get what
almost looks like very thin

00:07:11.610 --> 00:07:15.070
bands, an acceptor band or
acceptor level there.

00:07:15.070 --> 00:07:16.850
So we start off like this.

00:07:16.850 --> 00:07:18.510
And I went into that's
digression because now I'm

00:07:18.510 --> 00:07:22.760
just going to say that
for every atom we

00:07:22.760 --> 00:07:24.445
put in we get 1 carrier.

00:07:29.020 --> 00:07:30.270
And then we're going to say--

00:07:38.305 --> 00:07:40.230
I want to be sure I
get this right--

00:07:48.590 --> 00:08:03.440
we have 6.02 times 10 to
the 23 atoms per mole.

00:08:03.440 --> 00:08:04.540
That's right.

00:08:04.540 --> 00:08:07.730
And then we have 1 mole.

00:08:07.730 --> 00:08:11.060
And notice how I'm being very
careful about the dimensional

00:08:11.060 --> 00:08:11.600
analysis here.

00:08:11.600 --> 00:08:14.550
Because if you put something
in the wrong top or bottom

00:08:14.550 --> 00:08:18.620
you're off by 46 powers.

00:08:18.620 --> 00:08:20.235
So don't make that mistake.

00:08:20.235 --> 00:08:22.030
We saw that a lot on the exam.

00:08:30.320 --> 00:08:31.360
So we're good here.

00:08:31.360 --> 00:08:32.540
Let's do our dimensional
analysis.

00:08:32.540 --> 00:08:34.900
We start off, we're looking
for this particular

00:08:34.900 --> 00:08:37.630
concentration carriers
per centimeter cubed.

00:08:37.630 --> 00:08:43.370
We have 1 atom creates
1 carrier.

00:08:43.370 --> 00:08:46.740
1 mole has this many atoms.
And one mole of-- we're

00:08:46.740 --> 00:08:48.830
talking about in this case--

00:08:48.830 --> 00:08:50.080
gallium.

00:08:52.650 --> 00:08:56.380
I'll put Gallium here
to be clear.

00:08:56.380 --> 00:09:00.120
1 mole of gallium has
this much mass.

00:09:00.120 --> 00:09:02.350
And you're left with something
like this.

00:09:02.350 --> 00:09:12.740
You're left with 3.58 times 10
to the negative 5 grams per

00:09:12.740 --> 00:09:13.270
centimeter.

00:09:13.270 --> 00:09:16.560
Grams gallium per centimeter
cubed.

00:09:16.560 --> 00:09:18.880
So we're looking good.

00:09:18.880 --> 00:09:20.960
We're pretty close to the answer
but we don't actually

00:09:20.960 --> 00:09:21.630
have the answer yet.

00:09:21.630 --> 00:09:24.680
Remember we're looking for
total grams of gallium.

00:09:24.680 --> 00:09:27.520
Not how many grams per
centimeter cubed.

00:09:27.520 --> 00:09:29.830
That's pretty easy because
we're told the we have 1

00:09:29.830 --> 00:09:32.820
kilogram of germanium and we
know the density of germanium

00:09:32.820 --> 00:09:34.400
from our periodic table.

00:09:34.400 --> 00:09:37.540
So looking at our periodic
table we can look up

00:09:37.540 --> 00:09:41.280
germanium's density and we can
then back out how many

00:09:41.280 --> 00:09:44.460
centimeters cubed of germanium
we have. We'll

00:09:44.460 --> 00:09:46.140
do that right here.

00:09:46.140 --> 00:09:50.830
So 1 kilogram of germanium
is 1,000 grams, times--

00:09:50.830 --> 00:09:56.250
we have the density, which is
going to be times 1 over the

00:09:56.250 --> 00:09:58.120
density, rather--

00:09:58.120 --> 00:10:00.326
grams per centimeter cubed.

00:10:00.326 --> 00:10:08.500
And that's going to give us
187 centimeters cubed.

00:10:08.500 --> 00:10:09.290
And now we're good.

00:10:09.290 --> 00:10:15.240
Because we know here we have
3.58 times 10 to the negative

00:10:15.240 --> 00:10:18.900
5 grams of gallium per
centimeter cubed of germanium.

00:10:18.900 --> 00:10:22.400
We have this many centimeters
cubed of germanium.

00:10:22.400 --> 00:10:29.370
Multiply them together and you
get the answer, which is 6.69

00:10:29.370 --> 00:10:34.975
times 10 to the negative
3 grams of gallium.

00:10:34.975 --> 00:10:36.860
So that's part a.

00:10:36.860 --> 00:10:38.820
Just dimensional analysis
and stoichiometry.

00:10:38.820 --> 00:10:41.910
But I stress, be careful about
the way these things are.

00:10:41.910 --> 00:10:43.790
Even I pause to make sure
they're correct because if you

00:10:43.790 --> 00:10:45.730
get this wrong, the whole
problem's wrong.

00:10:45.730 --> 00:10:48.650
You're off orders of 46.

00:10:48.650 --> 00:10:51.905
You're off by orders of 1,000
here, so just be careful.

00:10:54.680 --> 00:10:56.310
Part b.

00:10:56.310 --> 00:10:58.740
We've actually already answered
when we drew it up,

00:10:58.740 --> 00:11:00.270
we threw down the
things we knew.

00:11:00.270 --> 00:11:02.550
We knew that we were
creating a hole.

00:11:02.550 --> 00:11:05.150
And a hole corresponds
to p type doping.

00:11:05.150 --> 00:11:06.480
How do I remember p and n?

00:11:06.480 --> 00:11:08.790
It's easy. p means positive.

00:11:08.790 --> 00:11:11.420
We've created a hole, which
has a positive charge.

00:11:11.420 --> 00:11:13.300
n, I think of as negative.

00:11:13.300 --> 00:11:16.830
So if you had put something else
in there like arsenic,

00:11:16.830 --> 00:11:19.160
arsenic would've had an extra
electron compared to

00:11:19.160 --> 00:11:21.590
germanium, which means you
have a negative charge.

00:11:21.590 --> 00:11:23.190
So n negative.

00:11:23.190 --> 00:11:24.410
So we have p type doping.

00:11:24.410 --> 00:11:25.380
We're done with part b.

00:11:25.380 --> 00:11:26.330
Easy.

00:11:26.330 --> 00:11:28.170
Part c.

00:11:28.170 --> 00:11:29.760
I'm just going to erase some of
this stuff here and we're

00:11:29.760 --> 00:11:47.580
going to draw a couple more
of these band diagrams. So

00:11:47.580 --> 00:11:50.490
basically what we're asked to do
now is to think about, what

00:11:50.490 --> 00:11:52.520
does this band diagram look
like at different

00:11:52.520 --> 00:11:53.690
temperatures?

00:11:53.690 --> 00:11:55.420
Because it actually looks
slightly different.

00:11:55.420 --> 00:11:58.600
I've drawn it here
schematically.

00:11:58.600 --> 00:11:59.840
But let's actually think
about what it looks

00:11:59.840 --> 00:12:01.730
like in real life.

00:12:01.730 --> 00:12:07.080
So let's do 2 more of these.

00:12:07.080 --> 00:12:10.440
And we'll use that one
as well for part c.

00:12:10.440 --> 00:12:12.540
OK so I'm drawing my
conduction bands.

00:12:12.540 --> 00:12:13.790
These are my conduction bands.

00:12:18.060 --> 00:12:19.310
These are my valence bands.

00:12:21.720 --> 00:12:23.570
I have the same band gap
for all of them.

00:12:23.570 --> 00:12:25.780
So you know band gap here,
here's the band gap.

00:12:29.084 --> 00:12:30.630
It's always worth
putting down.

00:12:30.630 --> 00:12:32.840
If you know it's true,
put it down.

00:12:32.840 --> 00:12:34.840
And we know that
in both cases--

00:12:34.840 --> 00:12:36.790
let me just get rid of this
thing here; we're going to

00:12:36.790 --> 00:12:41.600
start from the beginning;
put our electron back--

00:12:41.600 --> 00:12:46.480
we've created all these
acceptor levels.

00:12:46.480 --> 00:12:48.700
Because we've doped with more
than one gallium atom.

00:12:48.700 --> 00:12:53.150
We have many, many, 10 to the 17
gallium atoms. Which sounds

00:12:53.150 --> 00:12:57.364
like a lot, but in a mole we
have 10 to the 23 spots in a

00:12:57.364 --> 00:12:58.070
mole of material.

00:12:58.070 --> 00:13:02.270
So it's 6 orders of
magnitude less.

00:13:02.270 --> 00:13:05.120
So we have these systems and
we're asked to do them at--

00:13:05.120 --> 00:13:08.130
I'm going to keep going
back and forth--

00:13:08.130 --> 00:13:14.745
300 k, 4.2 k and 1200 k.

00:13:14.745 --> 00:13:15.995
That's Kelvin.

00:13:18.490 --> 00:13:21.590
Let's go with the extremes
first. And we'll do the middle

00:13:21.590 --> 00:13:24.700
one, 300 k, once we have an
idea of what's happening.

00:13:24.700 --> 00:13:28.400
So basically, in the very
beginning when we to dope in a

00:13:28.400 --> 00:13:39.330
material, time t equals 0 and no
electrons have had a chance

00:13:39.330 --> 00:13:40.780
to move around.

00:13:40.780 --> 00:13:43.040
You have all your electrons in
the valence band, you have

00:13:43.040 --> 00:13:45.670
these open holes in your
acceptor levels.

00:13:50.600 --> 00:13:53.660
And the reason that electrons
would move between levels is

00:13:53.660 --> 00:13:55.730
if they have some energy
associated with them.

00:13:55.730 --> 00:13:58.020
Now why would something have
energy in a crystal?

00:13:58.020 --> 00:14:00.100
Well that's because of
thermal vibrations.

00:14:00.100 --> 00:14:02.660
It's a thermal energy they have.
So it's completely based

00:14:02.660 --> 00:14:04.580
on the temperature at which
the crystal exists.

00:14:04.580 --> 00:14:06.105
So at a very low temperature--

00:14:08.690 --> 00:14:11.320
let me write that up
there for you, this

00:14:11.320 --> 00:14:13.370
is our basic equation--

00:14:13.370 --> 00:14:15.330
at a very low temperature we
have a very low thermal

00:14:15.330 --> 00:14:18.020
energy. kBT: this is the
Boltzman's Constant.

00:14:18.020 --> 00:14:19.800
At a very high temperature, we
have a very high thermal

00:14:19.800 --> 00:14:22.640
energy, which means that these
electrons have the ability to

00:14:22.640 --> 00:14:24.750
move between levels
more easily.

00:14:24.750 --> 00:14:28.390
So here's our very
low temperature.

00:14:28.390 --> 00:14:30.710
At a very low temperature
we can actually

00:14:30.710 --> 00:14:32.100
calculate the energy.

00:14:32.100 --> 00:14:36.030
We'll find that the energy
here is about--

00:14:36.030 --> 00:14:37.550
just so you have a scale--

00:14:37.550 --> 00:14:44.050
it's about 0.00036
electron volts.

00:14:44.050 --> 00:14:47.180
Now you say to yourself, wow
that is a lot less than 0.7

00:14:47.180 --> 00:14:51.670
electron volts, which is
the energy of this gap.

00:14:51.670 --> 00:14:54.120
So there's no way these
electrons here can even make

00:14:54.120 --> 00:14:55.980
it up to this acceptor level.

00:14:55.980 --> 00:14:58.550
That's not exactly true.

00:14:58.550 --> 00:15:03.400
This is best thought of as an
average thermal energy that an

00:15:03.400 --> 00:15:05.380
electron will have. It's
based off of a

00:15:05.380 --> 00:15:07.140
distribution, if you will.

00:15:07.140 --> 00:15:10.650
So most electrons will have
around this energy.

00:15:10.650 --> 00:15:12.500
But some will have a little bit
more and some will have a

00:15:12.500 --> 00:15:13.530
little bit less.

00:15:13.530 --> 00:15:16.250
And very, very, very few at the
tail of that distribution

00:15:16.250 --> 00:15:18.740
will have enough energy to
actually make it up to one of

00:15:18.740 --> 00:15:19.690
these levels.

00:15:19.690 --> 00:15:22.640
So the way to do this problem,
to be actually fully correct,

00:15:22.640 --> 00:15:24.330
is to say that and explain it.

00:15:24.330 --> 00:15:27.530
I actually, when I did this
problem on the answer key, I

00:15:27.530 --> 00:15:31.160
have an electron, one electron
going up into one of these

00:15:31.160 --> 00:15:34.770
spots and the rest
are all empty.

00:15:34.770 --> 00:15:37.610
I denote that with a little
bit of blue here.

00:15:37.610 --> 00:15:39.970
But everything else is empty.

00:15:39.970 --> 00:15:41.630
We've got a hole here.

00:15:41.630 --> 00:15:44.520
So there is a finite, very
small, amount of conduction.

00:15:44.520 --> 00:15:46.760
But it's extremely small.

00:15:46.760 --> 00:15:49.760
And it's extremely unlikely to
have electrons moving around

00:15:49.760 --> 00:15:52.060
but probabilistically
it will happen.

00:15:52.060 --> 00:15:53.430
That's 4.2 Kelvin.

00:15:53.430 --> 00:15:55.670
Very, very low.

00:15:55.670 --> 00:15:58.280
Let's go to very, very high.

00:15:58.280 --> 00:16:00.030
Starting at the beginning again,
we know all of our

00:16:00.030 --> 00:16:02.150
electrons are in the
valence bands.

00:16:02.150 --> 00:16:11.010
At 1,200 we have an energy
of about 0.1 eV.

00:16:11.010 --> 00:16:13.060
Still less than 0.7.

00:16:13.060 --> 00:16:17.700
We have a significantly larger
proportion electrons in that

00:16:17.700 --> 00:16:21.040
distribution, which
are at 0.7.

00:16:21.040 --> 00:16:23.810
So we actually do have electrons
that will move up

00:16:23.810 --> 00:16:24.910
into the spots.

00:16:24.910 --> 00:16:29.410
And even many that'll move
up here as well.

00:16:29.410 --> 00:16:32.310
Because they can overcome
this 0.7 eV.

00:16:32.310 --> 00:16:35.510
So we've got some electrons,
they're going to move here,

00:16:35.510 --> 00:16:37.780
they're going to fill
up most of these.

00:16:37.780 --> 00:16:41.250
Because this delta here, the
difference between our

00:16:41.250 --> 00:16:44.320
acceptor level and our valence
band, is actually quite small.

00:16:44.320 --> 00:16:46.310
It's extremely small.

00:16:46.310 --> 00:16:47.880
That's another reason why
we have an electron

00:16:47.880 --> 00:16:49.872
moving up at 4.2.

00:16:49.872 --> 00:16:51.880
I should have mentioned that.

00:16:51.880 --> 00:16:52.540
This is very small.

00:16:52.540 --> 00:16:55.110
This gets pretty much
completely filled.

00:16:55.110 --> 00:16:59.990
And I'll denote that with
a blue line here.

00:16:59.990 --> 00:17:03.160
And we have some electrons,
even going up into here.

00:17:06.510 --> 00:17:09.210
What that means, that that has
to correspond to electrons

00:17:09.210 --> 00:17:14.160
being depleted out of
the valence band.

00:17:14.160 --> 00:17:15.600
This is the way you would
draw this picture.

00:17:20.850 --> 00:17:23.290
So we lose these electrons
from the valence band.

00:17:23.290 --> 00:17:27.240
Some jump up to the acceptor
levels and the rest will go up

00:17:27.240 --> 00:17:29.430
to the conduction band.

00:17:29.430 --> 00:17:30.980
So this is 1,200.

00:17:30.980 --> 00:17:33.200
We have more than enough energy
to reach this acceptor

00:17:33.200 --> 00:17:35.670
level and we have
probabilistically some

00:17:35.670 --> 00:17:39.350
electrons will make it up
to the conduction bands.

00:17:39.350 --> 00:17:40.790
That's the best way
to think about it.

00:17:40.790 --> 00:17:42.655
Now let's go back to our
middle temperature.

00:17:45.360 --> 00:17:47.940
I think the best way to do
this one is to just go

00:17:47.940 --> 00:17:49.200
somewhere in the middle.

00:17:49.200 --> 00:17:50.630
That's the safest play, right?

00:17:50.630 --> 00:17:52.200
So we're at a temperature
which corresponds

00:17:52.200 --> 00:17:59.280
to about 0.025 eV.

00:17:59.280 --> 00:18:01.850
Now that is obviously smaller
than the gap.

00:18:01.850 --> 00:18:04.690
Probabilistically we'll still
get some electrons in the gap.

00:18:04.690 --> 00:18:06.060
Diminishingly small.

00:18:06.060 --> 00:18:07.500
But we'll put one up there.

00:18:07.500 --> 00:18:09.420
OK maybe one goes up there.

00:18:09.420 --> 00:18:15.160
And it's still much bigger than
the delta here between

00:18:15.160 --> 00:18:18.440
the acceptor level and
the valence band top.

00:18:18.440 --> 00:18:22.680
So these electrons will still
pretty easily make their way

00:18:22.680 --> 00:18:24.980
into the acceptor level.

00:18:24.980 --> 00:18:27.020
Now I'll put a little
bit here.

00:18:27.020 --> 00:18:32.445
We're going to lose electrons
very slightly.

00:18:37.750 --> 00:18:38.990
That's how I would have
done that problem.

00:18:38.990 --> 00:18:41.070
It sort of looks like that
on the answer key.

00:18:41.070 --> 00:18:42.990
Now I want to emphasize that,
what is what's the

00:18:42.990 --> 00:18:44.390
importance of this?

00:18:44.390 --> 00:18:47.050
Well when you dope, you're
creating conduction.

00:18:47.050 --> 00:18:47.660
Why is that?

00:18:47.660 --> 00:18:51.080
Because the more we dope, the
more holes we have that can be

00:18:51.080 --> 00:18:51.810
played around with.

00:18:51.810 --> 00:18:54.770
So we have more and more
of these acceptor

00:18:54.770 --> 00:18:56.570
level energy levels.

00:18:56.570 --> 00:18:58.590
And what happens is these
electrons at finite

00:18:58.590 --> 00:18:59.270
temperatures--

00:18:59.270 --> 00:19:02.230
temperatures above 0 Kelvin--
will move into those levels.

00:19:02.230 --> 00:19:05.660
And they will cause conduction
in the valence band.

00:19:05.660 --> 00:19:08.600
And you know at high
temperatures, back over here,

00:19:08.600 --> 00:19:10.730
we have electrons moving to the
conduction band, which is

00:19:10.730 --> 00:19:12.680
traditionally what we think of
when we think of conduction,

00:19:12.680 --> 00:19:14.400
electrons moving around.

00:19:14.400 --> 00:19:16.740
So we have in this case
conduction in the conductor

00:19:16.740 --> 00:19:19.830
band as well as in
the valence band.

00:19:19.830 --> 00:19:21.440
So that's this problem.

00:19:21.440 --> 00:19:23.210
This problem was generally
pretty easy; many

00:19:23.210 --> 00:19:24.550
students got it right.

00:19:24.550 --> 00:19:26.350
The learning goals and
objectives we had from this

00:19:26.350 --> 00:19:31.700
problem were, number 1, to
understand doping principles.

00:19:31.700 --> 00:19:34.100
What it means to n
and p type dope.

00:19:34.100 --> 00:19:36.150
Holes versus electrons
and how you get them.

00:19:36.150 --> 00:19:38.990
So if you have germanium or
silicon, those are very common

00:19:38.990 --> 00:19:41.720
examples and you dope
things into them.

00:19:41.720 --> 00:19:47.000
So gallium or arsenic or
aluminum, for example.

00:19:47.000 --> 00:19:48.850
We talked about conduction
mechanisms--

00:19:48.850 --> 00:19:50.090
just like here--

00:19:50.090 --> 00:19:53.520
and we also talked about the
donor and acceptor levels.

00:19:53.520 --> 00:19:57.120
So the donor levels are just
slightly below the conduction

00:19:57.120 --> 00:19:58.840
band and are full
of electrons.

00:19:58.840 --> 00:20:01.190
And the acceptor levels are
just slightly above the

00:20:01.190 --> 00:20:04.010
valence band and initially
holes.

00:20:04.010 --> 00:20:08.480
So that's probablem 3 and I hope
you had good luck at It.