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  • >> [Slide 1] So hello.

  • 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.

  • So this is an energy band diagram for a metal.

  • Now, in a semiconductor, it looks just like an insulator,

  • but the semiconductor is smaller.

  • Significantly smaller so that we can create some electron

  • hole pairs.

  • We can create charge carriers by other means as well.

  • [Slide 11] Okay. Now, I've been talking about silicon.

  • Silicon is a Column IV semiconductor.

  • The IV means there are four valence electrons.

  • You can see there's germanium below silicon.

  • That's also Column IV.

  • Germanium is also a semiconductor.