This lecture is a part of Unit 1,

but it's really a different --

it's a supplemental part of Unit 1.

What we're assuming in this course is

that you have a basic understanding

of semiconductor physics.

If you have that basic understanding, you'll be able

to follow the course and, I think, learn some new

and interesting things about nano devices

and nano transistors in particular.

What I'd like to do in this special lecture is to quickly go

through some highlights of semiconductor physics.

Now, this is material that it takes me five or six weeks to go

through when I teach my introductory

semiconductor course.

So it's not going to be a lecture

that can teach semiconductor physics.

My intent is just to quickly review some quick --

some key concepts that we'll be using throughout the course.

If you've seen those before or if there are one or two

that you think, well, maybe I need to refresh my memory

and review that a little more, then you're in good shape.

If the material that I present

in this quick summary is completely brand new to you,

then you probably don't have the background that you're going

to need to be successful in this course.

[Slide 2] So let's take a quick look at some key concepts

in semiconductor physics.

These are the seven topics that I'd like to go over.

And I'm going to do them very quickly.

We're not teaching this material.

We're just quickly reviewing what some of the key points are.

[Slide 3] All right.

Let's begin at a very basic level; silicon atoms.

Silicon is the most common semiconductor used

for electronic devices.

You'll remember from your freshman chemistry course

that atoms have energy levels.

We label them like 1S, 2S, 2P, 3S, 3P,

etc. Silicon has Atomic Number 14,

which means it has 14 electrons that have to be accommodated

in those energy levels.

And you might remember from your freshman chemistry

that S orbitals can hold two electrons.

So each of these N equal 1

and N equals 2 orbitals hold two electrons.

In P orbitals we have a Px, a Py, and a Pz orbital.

Each one of those can hold two electrons,

spin up and spin down.

So the P orbitals can hold six electrons.

And we just go through and we fill up all the energy levels

until all 14 electrons are accounted for.

And if we do that, we'll find that we fill up the 3S level

and we put two electrons in the 3P level.

So we have four valence electrons.

But if you look at those uppermost energy levels,

the N equals 3 states, there are eight states there; two S states

and there are six P states.

And we've used four of those eight states.

The lower states here, lower energy states,

we call these the core levels.

There's not much that we can do to interact with them.

They're shielded from the outside world.

The chemistry in semiconductor physics all has to do

with the valence electrons, so that's what we focus on.

[Slide 4] Now, we're going to take a crystal chunk of silicon

where we have a large number of atoms

that are covalently bonded together.

So we're going to be talking

about a very large number of atoms.

The density of silicon is about 5 times 10

to the 22nd per cubic centimeter.

This is the crystal structure.

We call this a diamond crystal structure

because diamond also crystallizes in this structure.

And the key point is that each atom forms covalent bonds

to four nearest neighbors, with those four valence electrons

that it shares with its four nearest neighbors.

So that's the crystal structure.

Only the valence electrons are going to be --

in the valence states are going to be important to us.

We have eight states for every atom.

And if we have N atoms, 5 times 10

to the 22nd per cubic centimeter, then we're going

to have 8 times N atoms states in this solid that are going

to be of concern to us.

But when we put these atoms very closely together

and form these covalent bonds,

the electron wave functions overlap and things change.

The energy levels change.

[Slide 5] Energy levels become energy bands.

So if we just look at those valence electrons,

the four electrons in the eight states, if we put them

in a silicon crystal the energy levels are going to broaden

and smear out into a range of energy bands.

And what we'll find if we do the quantum mechanics properly is

that half of the states lower in energy

and form those covalent bonds.

We call that the valence band of energies.

So all of the energies within that range,

half of the states are there and they're all filled

with the four electrons from each of the silicon atoms.

Now, the other four states that were empty,

they go to higher ranges of energies.

And we create a band of energies we call the conduction band.

And at T equals 0, 0 temperature, they're all empty.

In between the valence band and the conduction band,

there is a region where there are no states

for electrons to reside.

That's called the "forbidden gap."

We can't have electrons there.

So this is the situation at 0 Kelvin.

All the electron -- valence electrons are

in the valence band.

The conduction band is completely empty.

[Slide 6] Now, if we go to room temperature, 300 Kelvin,

there is a small amount of thermal energy,

say, .026 electron volts.

You know, this forbidden gap is about 1 electron volt.

But there is a small probability

that there is enough thermal energy

to kick us some small fraction of the electrons

from the valence band and move them into the conduction band.

When we do that, we're left behind a hole

in the valance band; you know, a state that is now empty

in the valance band, and an electron in the conduction band.

We've now moved it up in energy into the conduction band.

We'll find that those holes are mobile and they behave

like positive charge carriers.

We'll use those for P channel transistors.

And the electrons are mobile.

They behave as charged carriers, and we'll use those

for N channel devices.

[Slide 7] So we're going to be talking a lot in this course

about energy band diagrams.

An energy band diagram is a plot of energy versus position.

Remember, only the top of the valence band is of interest

to us because deep down below that, all the states are filled.

Only the bottom of the conduction band is of interest

to that because way above the bottom all

of the states are empty.

But very near the bottom

of the conduction band we can have a few electrons.

Very near the top of the valence band we can have a few empty

states or holes.

So that's what we focus on.

If this is silicon,

the forbidden gap is 1.1 electron volts wide.

So room temperature we have some thermal energy due

to the jiggling of all of the atoms due

to the random thermal motion.

It's relatively small compared to the band gap.

But there is an exponentially small probability that some

of these bonds will be broken and an electron can be moved

from the valence band to the conduction band.

And that small probability times a large number of states

that there are there means that we're going

to have some small probability of creating electron hole pairs

in pure silicon at room temperature.

It turns out that the number in silicon is almost exactly 10

to the 10th electrons and holes per cubic centimeter

at room temperature.

Now, that may seem like a large number.

But remember, there are 5 times 10

to the 22nd atoms per cubic centimeter, and there are 10

to the 10th of these electron hole pairs.

So it's really a very small concentration.

[Slide 8] Now, there's another way that we like to look at this

and another picture that we like to draw.

It's a little complicated

to draw these three-dimensional diagrams

of how the crystal structure actually looks

and how the four nearest neighbors

of silicon arrange themselves in these tetrahedral bonds.

So frequently we'll draw a 2-D picture which is just meant

to represent the fact that each atom is surrounded

by four nearest neighbors

and that each one has four valence electrons.

It shares those four valence electrons

with its four nearest neighbors, completes its valence show

of states, and that forms covalent bonds.

Now, in this picture, if we look

at room temperature there is some small probability that one

of those bonds can be broken.

And if one of those bonds is broken,

we're left behind an empty state.

Now, if there's an empty state there, then an electron

from a nearby bond can hop into that

and the empty state can move.

And then an electron

from another nearby state can hop into that hole.

And what we find is that the hole then can move

about the crystal lattice much like a charge carrier.

It's an absence of a negative charge;

it behaves like a positive charge carrier.

Now, when we broke the bond we also released an electron

that used to be bound in the conduction band.

Now it's in the valence band.

That electron is free to wander around and carry current.

So that thermal energy creates a --

breaks a small number of bonds

and creates these electron hole pairs

which create mobile charge carriers

that are positive and negative.

[Slide 9] Now, a MOSFET, the basic material is a semiconductor.

It also makes uses of insulators and metals.

So we should just remind you briefly what an insulator,

a metal, and a semiconductor is.

Insulators don't conduct electricity very well.

They usually don't conduct heat very well either.

Metals conduct electricity very well.

And they usually conduct heat very well also.

Semiconductors aren't good metals

and they aren't good semiconductors,

but they have a very important feature.

You can control their properties.

We can make them reasonably metallic,

we can make them reasonably insulating, and we can do

that by adding a small number of impurities to the pure silicon.

That's what makes them so useful.

[Slide 10] That's why we use semiconductors to build electronic devices.

Now, on energy band diagrams, insulators, metals,

and semiconductors look something like this.

The key feature for an insulator is

that the band gap is very, very wide.

So if I look at silicon dioxide or glass, this is a material

that is commonly used in integrated circuits.

It has a very wide band gap.

It's very hard to create these electron hole pairs

and to create carriers.

Now, metals -- so it turns out in metals that when you fill

up all of the energy levels and account for all

of the electrons, the top-most energy level is

in the middle of a band.

That means we're not -- in an insulator or a semiconductor,

you fill it up -- you fill up all the states below a band,

and then the next state above that is completely empty.

In a metal, you simply fill up a band half way.

That means that if I apply a field it's very easy now

for these electrons to move because there's a state

for them to move up in energy.