OK, let's talk a little bit about semiconductors--
semiconductors.
And of course, the classic example is silicon.
And as you no doubt know or you could look up,
silicon has an atomic number of 14.
And so it's got this electron configuration 1s2 2s2 2p6.
So we've got 10 electrons there.
And then we're going to move to the n equals 3 shell, 3s2 3p2.
OK, so it actually looks very much like carbon,
except for n equals 3 instead of n equals 2.
And that makes sense.
It's just one below carbon.
So this is good.
The electron configuration is, in fact,
dictating properties, which is what I always promise people.
So that's fantastic.
These core ones look like neon.
So those are the core electrons tightly bound,
and these are the valence ones.
And then these become sp3 hybridised.
Three states in 3p blended with that s.
And we treat them all the same.
And you end up with this octahedral-- correction,
tetrahedral arrangement in space of those four identical bonds.
Anyway, all that leads us to-- what do we have?
We could then look at the band structure,
band diagram for silicon.
And we've got all those hybridised orbitals there.
So this is the filled valence band.
And then we have this band gap.
We got this valence band, and we have a conduction band.
And in order to get conduction, we
need to promote an electron from the valence band
across the band gap into the conduction band.
All right, good.
OK.
So that's a good look at the band structure.
What about if we look at cartoon sketch of the crystal.
I think it'll be a little bit easier perhaps to visualise.
But we'll show the same event, that promotion of an electron
up like this to give conductivity.
So if this is silicon here, each of these little circles
is meant to be silicon.
And each silicon brings to the table those four
valence electrons.
So it's kind of four valence electrons like this.
And of course it shares those covalently
with the adjacent silicons.
And we get something that we could sketch like this.
And this is a two dimensional representation of course.
But not bad.
I mean, this is good enough for our purposes.
This is what we're talking about,
just these sp3 hybridised electrons.
That's kind of what it looks like.
It's again, two dimensions, but it's good for our purposes.
And so then what happens is when we promote
an electron from the valence band to the conduction band,
we go like this.
So we promote it up.
And we can think of that especially as freeing it up,
or in the model that we had from sea of electrons in a metal,
we're moving that electron into the conduction
band where it's free of nuclei.
So it's left behind a missing electron.
Missing electron.
OK, so this missing electron is in a place
where there would have been a negatively charged electron.
Now remember, this electron is negatively charged.
So this is the absence of an electron.
The absence of something you could call a hole.
And in fact, that's often what we do call this, a hole.
And so the interesting thing is we've promoted
an electron up into conduction.
It's free to move.
So now it can conduct through this semiconductor.
In fact, this model's not bad.
You can see this electron moving.
It might hit a nuclei.
It might get some thermal vibrations there.
There could be a green band, or any kind of scattering event
that would interfere with the conductivity of that electron.
But if the electron's moving this way,
say towards a positive electrode, the hole which is--
the hole appears--
--to be positive.
It appears as if it's positive.
And that's a little bit bizarre to think about this hole
as being something that you might see moving.
But we could, with a little stretch of our imagination,
imagine that that hole is something that's moving.
So it's as if the hole is moving the other way, say,
towards the negative electrode.
And so we get actually two--
We call them charge carriers.
Two things that are carrying charge.
This is carrying a positive charge,
and this is carrying a negative charge.
The electron is carrying a negative charge.
So there's actually, in this example
here, where we've promoted an electron up
and left behind a hole, we actually
have two charge carriers we say.
There's two charge carriers.
And this is actually called intrinsic semiconduction.
Intrinsic.
Intrinsic semiconduction.
And it's intrinsic because this is just the properties
of the silicon on its own.
We have its own electron promoted up.
There's nothing external to this.
So internal, or we say intrinsic to this material.
And I'll differentiate that from what we'll cover in a moment
where we add some other impurities to this.
We dope it, it's called.
But right now this is intrinsic semiconduction.
It's just the behaviour of the material.
In this case, silicon on it's own
has got two charge carriers.
So in fact the conductivity-- if we
were to calculate the conductivity,
it would have to be calculated in terms of the two charge
carriers.
And the conductivity is given the symbol sigma.
And it's going to be--
You can kind of imagine it should
be a function of the number of electrons times
whatever charge that electron is carrying--
and I'm giving it the absolute value of the charge
here-- times how easily the electron can move.
And so we have this symbol here for the-- this
is nu sub e for the mobility of the electron.
So how quickly is the electron moving?
What charge is it carrying?
And how many are there?
But that's only for the electron.
We need to also consider-- you can say that's n sub e.
We also need to consider the number of these holes,
or the positive charges.
In fact, actually-- sorry, let me.
I'm going to leave this n for negative.
And we're going to put p for positive.
So that would be the number of positive charges
carriers times their charge.
But they're carrying this.
The absolute value of their charge is the same.
And then times the mobility of those charge carriers.
And I put subscript h because these are holes.
So that's the mobility of a hole.
And p is the number of holes.
And of course, number of electrons promoted
is going to be actually the same as the number of holes.
So we could actually simplify this equation.
Which I'll do.
We could simplify this.
We could say that the conductivity
of an intrinsic semiconductor is going
to be equal to the number of intrinsic charge
carriers times the fundamental charge-- that's
the absolute value of the charge on electron--
times the sum of the electron mobility
and the whole mobility.
So there we go.
That's our equation for the conductivity.
And I'll just give you the units here.
This is a-- correction-- this is--
This is number per volume, per cubic metre.
This fundamental charge of course has units of coulombs.
And mobility is going to have units
of metres squared-- where did the metre go--
metre squared per volt second.
And remember, a volt is a joule per coulomb.
All right.
So that's an intrinsic semiconductor.
Let's consider, as I hinted, what if we added something
to it to change the properties?
And so what we're going to do is we're
going to make what we call an extrinsic semiconductor.
So we need to add something to it
so that the properties are dominated by that something
that we add in.
OK.
And so what we're going to do is we're
going to say let's add a tiny little amount of something
that's got a different number of electrons.
So say we'll add some phosphorus.
OK.
Well phosphorus has an atomic number or proton number of 15,
right?
So it's going to have that same electron configuration
that we had for silicon right up here, 3s2 3p2, except plus one
extra.
So it's going to be 3s2 3p3.
All right, so that's going to be neon 3s2 3p3.
It brings this extra electron, if you will.
Let me just say extra, because it's in quotes.
Extra relative to silicon.
But it brings this extra electron to the table.
And so what's going to happen is-- let's see.
I'm just going to copy this for you.
OK, I'm going to copy that.
Bring it down here.
Now we can use our-- we can start with our silicon here.
And what we're going to do is then
we're going to say, OK, let's actually
just replace one of these.
We're going to make it a little point defect here.
So we're going to actually replace
one of these silicons with phosphorus.
So not that there's any significance to the colour,
but I'm going to make that phosphorus.
And remember, phosphorus has five valence electrons.
So it would have contributed, say, these ones here
for the bonds.
But then it's still got one extra.
And that one extra, it's shielded
by these core electrons.
It's really weakly attracted.
It's weakly bound.
Or another way of looking at that
is in terms of band diagram.
This is the valence band.
This is the conduction band.
This extra electron is really close to being free.
So it's got an energy.
It's kind of already pretty close to the conduction band.
That is, you need very small amount of energy
to promote that electron and make it free.
And remember, what is this?
This is phosphorus donating an electron.
So we call that the donor level.
That's the donor level.
And what's it-- lever, no, no.
Not lever, level-- donor level.
That's the donor energy level, because phosphorus
is donating electrons.
And it's very close to the conduction band.
So it can quite easy do it.
And in fact, that means that there's
going to be far more of these contributed or donated
charge carriers than the intrinsic ones.
And so the conductivity then-- correction,
I don't know why I used-- OK, so it's supposed to be sigma.
The extrinsic conductivity will be
now just a-- it won't be influenced
very much by the intrinsic properties that contributed
or donated electrons.
They're going to dominate.
And so we can actually eliminate the contribution
from the holes.
Because there's very few holes.
The holes are just the intrinsically generated holes.
But we've got mostly the extrinsically contributed
electrons.
So our equation for connectivity would just now
involve the electron mobility.
And similarly, we could dope with-- oh,
and so actually one last thing is the charge carrier
is the electron.
And the electron is negative.
So we call this an n type semiconductor-- n type.
But you could imagine in fact, if we
had doped with something-- doped just means we're adding to it.
So what if we dope with boron?
Well boron has, in fact, one less one valence electron.
It's got atomic number of five.
So its electron configuration is going to be at 1s2 2s2 2p1.
It brings one less electron to the table.
So boron would look like this if I wanted to add it
to this picture up here.
What would boron do?
I'll use the white colour for boron.
So if we dope with boron, well boron
would only bring three electrons to the table or to the bond.
Brings less to the relationship here, right?
And so it leaves behind-- essentially,
what does it contribute?
It contributes a hole.
And so in that case, the charge carrier
is going to be the hole.
It's as if the hole is the one that's moving that exists.
So the charge carrier is the hole.
And in that case, we call that, because the hole is positive,
we call it a p type semiconductor.