0:00:00.000,0:00:02.070
- [Teacher] To figure out[br]how we use semiconductors

0:00:02.070,0:00:04.530
to build all these[br]awesome computing devices,

0:00:04.530,0:00:06.210
we're going to start from scratch,

0:00:06.210,0:00:08.620
all the way down to even understanding

0:00:08.620,0:00:11.520
why semiconductors are semiconductors.

0:00:11.520,0:00:13.070
I mean, why is it that certain materials

0:00:13.070,0:00:13.990
behave like conductors,

0:00:13.990,0:00:16.530
which are very good at passing electricity

0:00:16.530,0:00:18.870
through them while others are not?

0:00:18.870,0:00:23.570
To understand this, we need[br]to look at the atomic level.

0:00:23.570,0:00:26.490
Now we might have some[br]intuition about these atoms,

0:00:26.490,0:00:27.323
but guess what?

0:00:27.323,0:00:28.420
Turns out that our knowledge

0:00:28.420,0:00:30.900
of the atomic structure is not enough.

0:00:30.900,0:00:32.850
And so in this video, we're[br]just gonna recapitulate

0:00:32.850,0:00:34.650
all the stuff that we might already know

0:00:34.650,0:00:35.830
from the previous videos.

0:00:35.830,0:00:38.620
And we'll see why the current knowledge

0:00:38.620,0:00:39.830
or the current theory of the atoms

0:00:39.830,0:00:44.000
is not sufficient to talk[br]about solids in general,

0:00:44.000,0:00:45.450
which we'll be interested in.

0:00:46.620,0:00:48.890
For starters, you may[br]already have some intuition.

0:00:48.890,0:00:53.160
For example, you may know that[br]all matter is made of atoms.

0:00:53.160,0:00:56.900
And if you were to pick any[br]one of them and zoom in,

0:00:56.900,0:00:59.100
then you might know that[br]the atoms themselves

0:00:59.100,0:01:01.110
are made of even smaller things.

0:01:01.110,0:01:03.370
At the center, we have this[br]thing called as the nucleus,

0:01:03.370,0:01:05.000
which have a positive charge,

0:01:05.000,0:01:07.660
and the electrons which[br]are negatively charged

0:01:07.660,0:01:08.990
are attracted by the nucleus

0:01:08.990,0:01:12.210
and end up going around the[br]nucleus in different orbits

0:01:12.210,0:01:13.620
just like the solar system

0:01:13.620,0:01:15.460
and how the planets go around the sun.

0:01:15.460,0:01:17.290
Now this is not a very accurate model,

0:01:17.290,0:01:18.850
we'll get back to that.

0:01:18.850,0:01:20.650
But as of now, let's use this model.

0:01:20.650,0:01:23.490
But the important thing is[br]there are some electrons

0:01:23.490,0:01:26.690
like these, which are[br]tightly bound to the nucleus.

0:01:26.690,0:01:28.603
We call them as bound electrons.

0:01:29.620,0:01:31.750
Bound electrons, and[br]these are not responsible

0:01:31.750,0:01:33.070
for conduction.

0:01:33.070,0:01:35.300
Whereas there are other electrons

0:01:35.300,0:01:37.740
which are not strongly[br]attracted by the nucleus

0:01:37.740,0:01:41.210
and they are free, as[br]in, they're free to move

0:01:41.210,0:01:43.280
from one atom to another.

0:01:43.280,0:01:45.800
And it's these electrons which we call

0:01:45.800,0:01:47.580
as conduction electrons or free electrons,

0:01:47.580,0:01:50.590
which are really[br]responsible for conduction.

0:01:50.590,0:01:51.710
And in some materials,

0:01:51.710,0:01:54.640
it's very easy to get[br]these free electrons.

0:01:54.640,0:01:56.840
And so they end up having a lot of them,

0:01:56.840,0:01:59.440
and we call these materials[br]as good conductors

0:01:59.440,0:02:00.610
or conductors.

0:02:00.610,0:02:02.140
On the other hand, some materials,

0:02:02.140,0:02:04.690
well, it's extremely difficult[br]to get these free electrons.

0:02:04.690,0:02:07.900
And as a result, you have[br]extremely negligible amount.

0:02:07.900,0:02:11.340
And as a result, they are[br]bad conductors or insulators.

0:02:11.340,0:02:13.150
And of course we have[br]the intermediate ones

0:02:13.150,0:02:15.280
which we end up calling semiconductors.

0:02:15.280,0:02:16.600
So I think the most important question

0:02:16.600,0:02:18.540
that we have to ask ourselves over here,

0:02:18.540,0:02:21.060
is how does an electron become free?

0:02:21.060,0:02:23.330
I mean, what makes it free[br]and what does that depend on?

0:02:23.330,0:02:25.120
That's the thing that[br]we need to figure out.

0:02:25.120,0:02:27.800
And we have to look at,[br]look at this whole thing

0:02:27.800,0:02:31.610
for a solid, because our[br]semiconductors are solids.

0:02:31.610,0:02:33.650
So we need to find out,[br]or we need to figure out

0:02:33.650,0:02:37.080
what makes an electron free in solids.

0:02:37.080,0:02:39.850
And to do that, we need to get past this

0:02:39.850,0:02:43.110
solar system model of the[br]atom, as I mentioned before,

0:02:43.110,0:02:44.300
it's not very accurate.

0:02:44.300,0:02:47.280
And we need to look at[br]a more accurate model

0:02:47.280,0:02:49.510
of the atomic structure.

0:02:49.510,0:02:50.970
So let's do that.

0:02:50.970,0:02:53.680
Now, you may have already[br]learned about this in chemistry.

0:02:53.680,0:02:55.380
It turns out that instead of thinking

0:02:55.380,0:02:58.440
of where the electrons are and what orbits

0:02:58.440,0:02:59.850
or what path they take,

0:02:59.850,0:03:03.340
it's much better to think about[br]them in terms of energies.

0:03:03.340,0:03:05.450
It's better think about[br]what are the energies

0:03:05.450,0:03:07.000
that the electrons can take up.

0:03:07.000,0:03:09.280
And you may have already[br]studied in chemistry

0:03:09.280,0:03:11.200
that the inside of any atoms,

0:03:11.200,0:03:14.940
so if I draw over here energies,

0:03:14.940,0:03:18.140
inside any atom, electrons[br]can have only some

0:03:18.140,0:03:20.095
specific energy values,

0:03:20.095,0:03:22.880
only some specific energy values.

0:03:22.880,0:03:24.720
And so maybe the lowest energy

0:03:24.720,0:03:26.970
that electron can have[br]maybe somewhere over here.

0:03:26.970,0:03:29.310
We're not gonna write down[br]the numbers over here.

0:03:29.310,0:03:30.960
We're not gonna look at[br]it very quantitatively,

0:03:30.960,0:03:32.010
don't worry about it.

0:03:32.010,0:03:33.450
So maybe this is the lowest energy

0:03:33.450,0:03:35.000
that an electron can possess.

0:03:35.000,0:03:36.730
The next higher energy[br]an electron can possess

0:03:36.730,0:03:38.450
might be somewhere over here,

0:03:38.450,0:03:41.240
and maybe next higher might[br]be somewhere over here,

0:03:41.240,0:03:42.290
and so on and so forth.

0:03:42.290,0:03:44.550
And we give names to these energy levels.

0:03:44.550,0:03:48.570
We call the lowest one[br]as the 1S energy level.

0:03:48.570,0:03:50.120
The next higher one becomes 2S,

0:03:51.170,0:03:54.230
the one that comes above that would be 2P.

0:03:54.230,0:03:58.984
Then we have 3S and 3P[br]and so on and so forth.

0:03:58.984,0:04:01.780
And again, if this looks very new to you

0:04:01.780,0:04:03.800
and you have no idea what S and P are,

0:04:03.800,0:04:06.650
it would be a great idea[br]to pause this over here,

0:04:06.650,0:04:09.360
go back and watch the[br]electron configuration videos

0:04:09.360,0:04:13.180
on chemistry, and then[br]come back over here.

0:04:13.180,0:04:15.760
But anyways, it turns out[br]electrons cannot take up

0:04:15.760,0:04:17.700
these energy levels randomly.

0:04:17.700,0:04:20.340
There's a particular rule[br]using which electrons

0:04:20.340,0:04:23.310
sort of fill up these energy levels.

0:04:23.310,0:04:25.540
And that rule, again, you[br]may have studied about them.

0:04:25.540,0:04:28.980
We call that as the Pauli's[br]exclusion principle.

0:04:28.980,0:04:31.683
Pauli's exclusion,

0:04:33.380,0:04:35.930
exclusion principle, or rule.

0:04:35.930,0:04:39.150
And it simply says that no two electrons,

0:04:39.150,0:04:41.210
no two electrons

0:04:42.190,0:04:44.870
can have identical,

0:04:44.870,0:04:48.950
can have identical energies.

0:04:48.950,0:04:51.670
Now, again, this is not the[br]accurate statement of Pauli,

0:04:51.670,0:04:54.320
but this will help us,[br]this is enough for us.

0:04:54.320,0:04:56.230
So let's take a concrete example.

0:04:56.230,0:04:59.590
Suppose we take, say, a sodium atom,

0:04:59.590,0:05:03.600
then it has, it has 11[br]electrons inside it.

0:05:03.600,0:05:05.393
There are 11 electrons.

0:05:07.040,0:05:08.850
And now these 11 electrons

0:05:08.850,0:05:11.480
can only have these[br]specific energy levels.

0:05:11.480,0:05:13.560
And the way these electrons

0:05:13.560,0:05:15.200
are going to fill up the energy levels

0:05:15.200,0:05:17.700
will be using the exclusion principle.

0:05:17.700,0:05:21.250
So the first electron, well, remember,

0:05:21.250,0:05:23.580
electrons always want to take[br]the lowest energy possible.

0:05:23.580,0:05:26.960
So the first electron would[br]go over here, over here,

0:05:26.960,0:05:28.610
and then you might think,[br]well, the next electron

0:05:28.610,0:05:31.050
can't go over here because[br]that's what Pauli's telling us.

0:05:31.050,0:05:32.410
No arguing with Pauli.

0:05:32.410,0:05:34.110
Second electron, if it comes over here,

0:05:34.110,0:05:37.260
it might have identical[br]energy, but not really,

0:05:37.260,0:05:40.700
because it turns out[br]that electrons can have

0:05:40.700,0:05:42.380
up spin and down spins.

0:05:42.380,0:05:45.360
So if the first electron[br]goes into the 1S tier,

0:05:45.360,0:05:47.920
and suppose it takes up the up spin,

0:05:47.920,0:05:50.370
then another electron can actually take up

0:05:50.370,0:05:53.590
the same energy level and now be down spin

0:05:53.590,0:05:54.950
because turns out these two spins

0:05:54.950,0:05:57.100
have slightly different energy.

0:05:57.100,0:05:59.240
So these two electrons[br]are strictly speaking,

0:05:59.240,0:06:02.140
still being Pauli, because[br]they're not exactly identical

0:06:02.140,0:06:03.740
because of their spins.

0:06:03.740,0:06:05.640
But the next electron, the third electron,

0:06:05.640,0:06:08.650
well, it cannot take up the[br]1S energy level anymore,

0:06:08.650,0:06:10.640
because if it does and then up spin,

0:06:10.640,0:06:11.880
then it'll be identical to this one.

0:06:11.880,0:06:13.120
If it does with a down spin,

0:06:13.120,0:06:15.100
then it'll be identical to this one.

0:06:15.100,0:06:16.680
So it can't take the that up anywhere.

0:06:16.680,0:06:18.150
So it has to take up now

0:06:18.150,0:06:20.850
the next higher energy level[br]available that's over here.

0:06:20.850,0:06:22.730
It can take up anywhere[br]in between as well.

0:06:22.730,0:06:24.960
The energy levels in[br]between are inaccessible

0:06:24.960,0:06:25.793
to these electrons.

0:06:25.793,0:06:28.280
So the next energy it[br]will take up would be 2S,

0:06:28.280,0:06:30.300
again, it might take up with an up spin.

0:06:30.300,0:06:33.580
The fourth electron might[br]go over with a down spin.

0:06:33.580,0:06:36.910
The next electron will[br]take up over here, up spin,

0:06:36.910,0:06:38.763
and the next one will be down spin.

0:06:39.700,0:06:40.850
Now here's the thing.

0:06:40.850,0:06:44.060
It turns out that in P, in P energy level,

0:06:44.060,0:06:46.630
there are three ways in which electrons

0:06:46.630,0:06:48.420
can occupy that energy level.

0:06:48.420,0:06:50.830
We call them as orbitals, right?

0:06:50.830,0:06:52.960
It turns out that in the S energy levels,

0:06:52.960,0:06:53.920
there's only one way.

0:06:53.920,0:06:55.710
So there's only one orbital,

0:06:55.710,0:06:57.900
but in P there are three orbitals.

0:06:57.900,0:07:01.761
So another electron can[br]take up the 2P energy level

0:07:01.761,0:07:04.450
by being in a different orbital.

0:07:04.450,0:07:05.910
So this electron and this electron

0:07:05.910,0:07:07.660
will be in different orbitals,

0:07:07.660,0:07:09.450
or different configuration, we could say,

0:07:09.450,0:07:10.970
don't have to worry about it too much.

0:07:10.970,0:07:12.930
And so they'll still not be identical.

0:07:12.930,0:07:15.320
And so another electron can[br]take up that same orbital

0:07:15.320,0:07:16.750
with a down spin.

0:07:16.750,0:07:21.170
Another electron, the third[br]orbital of P with an up spin,

0:07:21.170,0:07:22.880
and then down spin.

0:07:22.880,0:07:25.040
And now the 2P is completely filled.

0:07:25.040,0:07:28.170
There are no more orbitals available.

0:07:28.170,0:07:29.190
And so the last electron,

0:07:29.190,0:07:31.120
we're down to one, two,[br]three, four, five, six, seven,

0:07:31.120,0:07:35.090
eight, nine, 10, the last[br]electron will be over here

0:07:35.090,0:07:37.810
in the 3S up spin.

0:07:37.810,0:07:41.540
But this is for a single atom of sodium.

0:07:41.540,0:07:44.970
What if we have say, two atoms of sodium,

0:07:44.970,0:07:47.413
very close to each[br]other, what happens then?

0:07:49.090,0:07:49.923
Somewhat like this,

0:07:49.923,0:07:52.060
what if they form some kind of a molecule?

0:07:52.060,0:07:54.990
How would the electrons of this molecule

0:07:54.990,0:07:56.310
fill up the energy levels?

0:07:56.310,0:07:59.600
Can we say that now each atom[br]will have something like this.

0:07:59.600,0:08:03.610
Each atom will have electrons[br]filled up accordingly.

0:08:03.610,0:08:06.160
Well, that won't work,[br]that can't be possible.

0:08:06.160,0:08:07.290
And the way we can think about it,

0:08:07.290,0:08:09.370
is we can say that, if you do it this way,

0:08:09.370,0:08:11.360
Pauli's rule will be violated.

0:08:11.360,0:08:13.850
Remember, Pauli says no two electrons,

0:08:13.850,0:08:15.490
and when we say no two electrons,

0:08:15.490,0:08:17.740
it can be no two electrons inside an atom,

0:08:17.740,0:08:20.370
or no two electrons inside a molecule,

0:08:20.370,0:08:23.960
or maybe no two electrons[br]inside an entire solid.

0:08:23.960,0:08:26.490
No two electrons can[br]have identical energies.

0:08:26.490,0:08:30.040
So if the two atoms have[br]these electron configurations

0:08:30.040,0:08:32.390
then I hope you can see that this electron

0:08:32.390,0:08:35.430
and this electron will,[br]they will be identical.

0:08:35.430,0:08:38.720
This one, and this one will[br]be absolutely identical.

0:08:38.720,0:08:40.960
And so all of them will[br]have identical pairs

0:08:40.960,0:08:45.360
and Pauli will be very, very[br]sad, so that can't be possible.

0:08:45.360,0:08:48.080
And if we have an entire solid,

0:08:48.080,0:08:51.710
which is made of sodium, where[br]we have like 10 to the 23

0:08:51.710,0:08:53.870
atoms packed very close to each other,

0:08:53.870,0:08:57.520
and if we used this model for each atom,

0:08:57.520,0:09:00.835
then there would be about 10[br]to the 23 identical copies

0:09:00.835,0:09:03.340
of electrons in each level.

0:09:03.340,0:09:08.020
And that would make Pauli[br]extremely sad, extremely sad.

0:09:08.020,0:09:11.370
So the key takeaway is that this structure

0:09:11.370,0:09:15.400
that we have learned for a[br]single atom cannot be extended

0:09:15.400,0:09:16.830
when we go all the way to the solids.

0:09:16.830,0:09:19.700
We require a new theory to[br]understand what's going on

0:09:19.700,0:09:22.233
and how electrons are arranged[br]or how to think about them

0:09:22.233,0:09:24.040
when it comes to solids.

0:09:24.040,0:09:26.583
And we'll explore them[br]in the future videos.