Lecture 14: Intrinsic and Extrinsic Semiconductors, Doping, Compound Semiconductors

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Wireless Fantasy by Vladimir Ussachevsky. It's one of the first pieces of computer-generated music. It was done at Columbia University in 1960. It was commissioned by a group of fans of Lee de Forest, and it was in honor of de Forest's contribution to wireless broadcast.

And one of the first broadcasts de Forest ever sent over the radio was the piece that you are hearing. It's Parsifal. It is from the Wagner Opera. And so what Ussachevsky has done in the piece is to process it to make it sound really distanct as though it is coming over a shortwave radio.

And then he has Morse Code, and there is various Morse Code messages going through the piece. Wireless Fantasy, from 1960, done long-hand, by the way. It was really done with Morse Code in a mainframe computer and giant reel-to-reel decks.

Nothing like what you have on your desktop today. OK, so announcements. Tomorrow will be the exceptional Thursday, quiz five based on homework five. Last day we talked about the band theory of solids.

And, in the band theory, we were able to distinguish metals from insulators from semi-conductors. And you can see up here, the metal has a very, very tiny energy gap between the top of the filled orbitals and the bottom of the unfilled orbitals.

So it is effortless to move the electron up into this zone and give it mobility. In an insulator, there is a substantial energy required to move from the filled orbitals to the unfilled orbitals, which we neatly refer to as the valence band and conduction band.

And, arbitrarily, we have chosen three electron volts. Typically the insulators are up four, five, six and so on electron volts. And then there is this class of material semiconductors for which the band gap is on the order of three electron volts.

And why is three such a magic number? Because three electrons volts is the threshold of visible light. Materials that have energy gaps below three electron volts will respond to visible light, and we are going to talk about such matters presently.

And just the last point to make is that the valence band is constructed of the splitting of orbitals that are associated with bonding. Valence band is valence electrons in bonding orbitals, and the conduction band was generated from antibonding orbitals.

And then we looked at photoexcitation. If we have incident photons that have enough energy to break the bond, electrons will be promoted up into the conduction band. And it is a momentary transit.

And they will subsequently cascade back down. And, when they do so, a photon will be reemitted. When the electron cascades down, a photon will be emitted. And the emission will be pegged at the band gap energy.

If we go into hc over lambda, lambda becomes a critical value that is associated with this particular material. And so we can plot percent absorption. Percent absorption of what? Percent absorption of incident light as a function of the energy of that incident light.

High wavelength, low energy light will pass through. It will be transmitted, and the material will appear transparent. High energy, that is to say low wavelength incident radiation will have enough energy to promote electrons.

And so, therefore, those incident photons will be absorbed, the excess energy will be dissipated up here as heat, and then we will get reemission of photons. And so, over here, the material is an absorber.

And so we have a sharp jump here at a critical wavelength which we termed the "absorption edge." And then, towards the end of the lecture, we talked about another type of excitation. This was photoexcitation.

We are going to talk about thermal excitation, where the thermal energy in the environment is enough to cause the breaking of the bonds and the promotion of the electron from the valence band to the conduction band.

But, in this case, we discovered that pair of carriers was generated. Not a single carrier. In the case of photoexcitation, the electron moves up, falls back down. Here we have pair excitation. What happens is this electron is permanently sustainably sitting up in the valence band leaving in its place a broken bond which consists of a single electron and a missing electron which is termed a "hole."

It is zero in a land of minus one, so it appears to be plus one. And this is minus one in a land of zero, so it appears to be minus one. You see charge conservation. The population of electrons in the conduction band due to thermal excitation is equal to the population of holes in the valence band.

And electrical engineers like to just refer to the nature of the charge, regardless of the carrier. Whether it is a positive ion or a positive hole, as far as they are concerned it is a positive. The electrical engineers write this relationship n equals p.

The number of negative charges in the conduction band equals the number of positive charges in the valence band. And then I left you with this mystery at the end of the lecture. I said, well, we observe thermal excitation in semiconductors but the thermal energy is roughly related to the product of the Boltzmann constant times the temperature.

And, in electron volts, this amounts to about one-fortieth of an electron volt at room temperature. But the band gap energy in semiconductors is on the order of several electron volts. In the case of silicon, it is 1.1 electron volts.

How can we justify any kind of thermal excitation given that the thermal energy is so much lower than that of the band gap energy? Well, I have good news. The answer is that the energy in this room is distributed amongst all of the entities in the room so that if you look at the gas, for example, let's go back to the 1850s and peer into the mind of James Clark Maxwell who also gave us Maxwell's equations.

He was a polymath like so many of the other people that we have been talking about in 3.091. He didn't just focus on electromagnetism. He was a renaissance scholar. And one of his areas of interest was physical chemistry, and he studied gases.

He reasoned that the gases have a distribution of velocities. All of the gas molecules in this room are not behaving as though they are at room temperature. A substantial number are, and that is how we establish temperature, but what Maxwell reasoned was that some gas molecules are moving around as though the temperature of the room is 500 Kelvin, and some are moving around as though it is only 100 Kelvin, but a large number of them are moving around as though it is roughly 300 Kelvin.

He gave us a mathematical formulation of the distribution of energies. And then, about 25 years later, Boltzmann came along and said I am going to going to generalize the idea. Forget about just gas molecules and velocity.

Let's talk about all molecules and say the reason the gas molecules are moving mainly at 300 Kelvin and that some are moving at 500 Kelvin is -- And this was a big leap for Boltzmann. He said I am going to propose that temperature is distributed as well.

That the reason some gas molecules are moving as though they have the velocity of 500 Kelvin is that I am going to propose that they have the energy of 500 Kelvin. What is local energy? That is temperature.

Maxwell and Boltzmann, we put the two of them together and we come up with the notion of a distribution of temperature, distribution of energy. And this is what that distribution looks like. What we do is we plot the number of particles in a particular ensemble that have a particular energy as a function of energy.

And then we will normalize it over the total number of particles in the system. Before I do that, why don't I just do an analogy? We had the test a few weeks ago. Let's do a distribution of grades, and then we will relate it.

For example, what I could do is plot grade on this axis and I could put the number of people who have a particular grade and then normalize it. Divide it by the total number of students in the class.

If it's a big class, as this one is, and we have some kind of reasonable test, we expect to see this kind of a distribution. A bell-shaped curve. A Gaussian distribution. What does this tell us? It tells us that some people had greater than the average value.

Some people had less than the average value, but the average value is given here. It is a symmetric distribution. And so we can call this the average. This is the average grade, g with a bar over it.

And you get the inflection point here. This is where the second derivative shifts from positive to negative. That is how you get the standard deviation. This is g bar plus standard deviation. This is g bar minus standard deviation.

You can have a lot of fun with this. And the area under this line, if I use normalized values, must equal one. Area equals one when I normalize from zero to infinity. Let's do the same thing here, only - this is Gaussian.

But that's not the way molecules are distributed or energies are distributed in ensemble. It is asymmetrical. It looks a little bit like this. It has a sharp rise and a long asymptotic tail. And so the average is not at the maximum in this case.

This is Maxwell-Boltzmann. We have a distribution of energies. And the energy average, E with a macron over it, is somewhere a little bit to the right of the maximum. And so what I am doing is taking the energy of a particle, the number of particles of a given energy divided by the total number of particles.

Also the area under this curve must equal one. This is the value at T1. And what I want to do is focus down here. Suppose up here this is 1.1 eV. Well, the average value is here. And I said that this was one-fortieth of an electron volt.

That is not the problem. The problem is not that the average is one-fortieth of an electron volt. The good news is that there is some tiny fraction of the distribution that has energy above 1.1 eV.

If I knew what that fraction was then I could guess how much I could expect in the wave promotion here. You can see it is non-zero. It is not a sharp cutoff. There is a tiny value out here. And the nature of this curve is that the fraction of the distribution out here, if I want to integrate, say, from 1.1 eV out to infinity, that is the area under this line, what am I integrating? I am integrating the fraction times dE.

This equals e to the minus energy gap divided by k Boltzmann temperature, this exponential. That is what gives us the fraction underneath this line. Now let's see what happens when temperature rises.

When temperature rises this line shifts to the right. And, as you would expect, the average shifts to the right as well. This now is E average at T2. Let's say I raise the temperature. Let's look at silicon.

Let's say T1 is equal to room temperature 300 Kelvin, and T2 will be the melting point of silicon. T2 is the melting point of silicon. Not to make liquid silicon. It is solid silicon at the melting point.

It would be like ice at zero degrees C. Melting point of silicon is 1414 degrees C. Add 273 to it and you get about 1700 Kelvin. What is the ratio? T2 to T1 is on the order of about six. This thing shifts by a factor of six.

Let's look at what happens in here. I am going to blow this up. What we are really looking at is what's the difference between the area here at room temperature? What we are going to do is not to scale.

Then we are going to look at the area under the green curve. And when we use this relationship, E to the minus energy gap energy over kT, band gap energy over kT, we find that the fraction at T2 divided by the fraction at T1 comes out to be 10 to the 15th.

Changing temperature changes the excitation population through the shift in the high end of the curve. And it is only through that that we end up seeing decent levels of population in the conduction band.

Actually, the number at room temperature is vanishingly small. At room temperature the fraction in the conduction band is about 10 to the minus 19th. There are so few of them you can give each of them a name.

There is almost no conduction. Silicon at room temperature is an insulator. If we want to get some conductivity are we going to heat our computers up to such a high temperature? I don't think so. We need some other way of populating the conduction band.

And we are going to do one other mode of promotion. We've looked at photoexcitation, thermal excitation, and the third mode is chemoexcitation. What we are going to do is get carrier injection by introducing impurities.

And I know you are sitting there thinking he is crazy. We just spent all of this time and money making silicon six-nines purity, and now we are going to start throwing impurities into it. Well, there are two kinds of impurities in this world.

There are good impurities and bad impurities. The good impurities are called dopants. These are the ones that are there desirably. Dopants are good guys. And then there are other ones that are called contaminants, and these are undesirable impurities.

We don't want contaminants. We are going to look at dopants. And this is a really important lesson right now that I am teaching you. What I am showing you, for the first time in 3.091, is how we can use chemistry to alter the performance of a material.

I am going to take plain high-purity silicon, which is an insulator at room temperature. And, by operating on its chemical composition, give it properties that it cannot possess otherwise. This is a paradigm for solid state chemistry.

You want something that has a higher yield strength? We will change its composition. You want something that has a higher connectivity? We will change its composition. That is different. This is an engineered material.

And how is it engineered? What we are getting is via chemical change, purposeful chemical change. We are getting, if you would like, tailored composition to give targeted properties. And this is what underlies material science.

If you don't see what you like, make it. And how do you make it? By understanding the relationship between electronic structure, bonding and ultimately properties. Here is what the gambit is. I am going to talk only about elemental semiconductors.

In the case of silicon and germanium, I am just going to restrict today to silicon and germanium. That is not such a bad restriction since we are in the silicon age. All of your micro devices contain silicon.

This is pretty good. Here is the gambit. You introduce aliovalent impurities. What do I mean by aliovalent? Alio is the same as the Latin world for alias, other. We are going to introduce impurities that have a difference valence from silicon and germanium.

Silicon and germanium are Group IV, or Group 14 if you want to use IUPAC notation. What I am going to do is introduce something else, and I will give you an example. And the purpose of introducing aliovalent impurities is to cause electron donation or electron consumption.

And how is that going to work? Well, you will see it best in action. Here is a simple example. Let's put phosphorus in silicon. Phosphorus, as you know, is Group 15 or Group V, so it has five valence electrons.

And let's first look at the Cartesian world. Here is silicon. It is sp3 hybridized. And it forms a diamond-like solid. It is crystalline, it is regular arrays, silicons at all of the corners of the tetrahedron, and on and on it goes.

I will give about three of these. Now what happens if I introduce phosphorus? If I introduce phosphorus, the phosphorus actually goes in and substitutes for silicon. The phosphorus substitutes. It does not go and sit in some void space.

It actually substitutes for silicon. Now, if it is going to substitute for silicon it has to form bonds. You cannot just sit there. There is no passive observer here. If you want to play you have got to bond.

Phosphorus comes in with five valence electrons. It goes one, two, three, four. There are four of its valence electrons bonding to the four adjacent silicons. What happens to the fifth valence electron of phosphorus? There is no empty orbital in which that fifth electron can sit.

That fifth electron is sitting here kind of tapping its foot wondering what it's going to do. Let's go over to the energy level diagram. Here is the energy level diagram. This is elemental silicon.

Downstairs is valence band. Upstairs is conduction band. When we put the phosphorus into the silicon in energy space, where is the only place that fifth electron can go? There is no room at the inn down here.

All of the valence orbitals are filled, so the only place it can go is up here in the conduction band. Here is the electron that came from phosphorus. It was donated from phosphorus. We call phosphorus a donor.

This is a donor electron. And can you see that every time I throw a phosphorus in I am going to get an extra electron in the conduction band? If I want to increase the conductivity of silicon, just keep adding phosphorus one for one.

Am I making holes down here? No, I am not breaking any bonds. In fact, I am forming bonds here. There is an extra electron. Everything is fine. Now I have got a lever. I can dial in how much conductivity I want.

You want to raise the conductivity to a certain value? I can tell you how much phosphorus to add to get to that level of conductivity. And this electron is not in a valence band. It is not bound so it can move.

This goes back to Paul Drude. These electrons are free to roam because they are not bound. I am going to show you something really cool. How far can that electron roam? Think about it. Phosphorus is five valent so it has an extra proton, too.

This phosphorus is a five plus in a land of four plus. The phosphorus you can think of as locally plus. And this electron that did not go into any of the valence band orbitals, it is locally minus.

Duh, an electron is locally minus, that is deep. I have the phosphorus that is locally plus and I have the electron that is locally minus. Do you know of a model that might describe the motion of an anchored positive charge with an electron that is free to roam? Do you know of a model that might talk about such things? Bohr.

Let's do something really whacked. Suppose we took this electron and said let's ask the question, if we applied the Bohr model to this pair what would we come up with? It is going to give us energies.

It is going to give us radii. It is going to give us velocities. Do you think there might be a relationship to velocity and mobility and conductivity? Well, let's see where it goes. What I am going to do is say recall in atomic hydrogen the ground state energy, this is the electron at the bottom, is minus k, what we have been calling k, which has this full-blown formula of me to the 4th over eight epsilon zero squared h squared.

Plug in all the numbers and you get minus 13.6 electron volts. Now, let's think about this. We are going to have to make a few changes. Epsilon zero, that is the permittivity of vacuum. But if you are an electron, you are looking down at the phosphorus, it is not just vacuum between you and the central phosphorus.

There is all this stuff. There are bonds. There is silicon nuclei. I have got to modify this. I have got to change this. What I am going to do is take epsilon zero, which is what we have for vacuum, and I am going to replace it with epsilon of silicon.

Silicon is the host crystal. What does this capture? It captures all the bonds, all of the silicon, all of the stuff. That is the dielectric constant of the host crystal. And there is one other thing.

This is some esoteric physics. I am just going to put it up here without proof. When you are in this situation, you don't use the rest mass. There is an effective mass, and that invokes a slight correction.

The effective mass of the electron at the bottom of the conduction band. This is a minor correction. The main correction is getting the dielectric constant. The second one is there for completeness.

Some of you are going to look back fondly at these notes and say we got it, this was good. Otherwise, you will say Sadoway left out the effective mass. You cannot say that now. Here are the values.

For silicon the dielectric constant is 11.7 and the effective mass at the bottom of the conduction band is one-fifth of the rest mass. I am going to plug these values into this equation. And what this gives me is then that the ground state energy of the donor electron is minus K, as we had before, and it is going to be multiplied by 0.2 on the top, and then I am going to have an 11.7 squared on the bottom.

And that gives me minus 0.02 electron volts. Two one-hundredths of electron volt. This quantity has been measured. The measured value compare with c.f. 0.045 eV measured. You might say that is more than double that.

And I will say wait a minute, we started at 13.6 and I took it down to 0.02. And you are telling me but the real value is 0.04. And I say you don't appreciate good work, that is what. This is fantastic, with a simple primitive Bohr model and two minor corrections to zoom into condensed matter and give this value.

Where is that going to be? 0.02 south of what? It is going to be here. This is where that lies. This distance here is the 0.02 electron volt difference. You're 0.02 electron volts below the conduction band.

You are not down here. This is valence. You are up top. And the electron is sitting in there because that's the ground state. And now you are saying, well, that is really great, Sadoway. Now you have an electron sitting in an orbital.

How are you going to get it up to here? I have an answer for that. But first look at this. I couldn't resist this derivation. I said what about the radius of the orbit? How far is that electron away from the phosphorus? Is it in tight? Is it moving around like this or is it way, way out here? Doesn't that intrigue you? It sure intrigues me.

Here is what I did. I said the r1, the radius of this ground state was going to be given by the Bohr radius times the modified dielectric constant divided by the modified mass. And when you plug in the numbers you get 30 angstroms.

We say I don't know what the silicon-silicon distance is. Well, what do you think it is? You know it has to be on the order of a couple of angstroms. If you compare that, the silicon-silicon distance is 2.35 angstroms.

This electron is way, way zooming around. Fantastic what we have learned here. Now let's look at this. We have an electron sitting in this energy level down below. Now what happens? How do I get this thing to move out? What am I going to do to make it move out? What do I have? I know that the energy is 0.02.

But how do I compare this energy with the thermal energy? E thermal is on the order of 0.025, one-fortieth of an eV. The thermal energy is so high at room temperature that it is able to promote these.

And, by the way, if the Bohr model works for ground state, what would happen if I were to blow this up? Can you imagine, if this is the conduction band, I get all of the energy levels. I get the whole Bohr energy state here.

I get ground state n equals two, n equals three all the way up. And now I have enough energy, from thermal energy, to take all of these electrons, because each one of these comes in because it is a separate phosphorus and they are far enough apart, they are separate states.

All of these can get promoted. What do we call this action? If I take a ground state electron in hydrogen and I get it right out of all of this set of energy levels, what do we call that process, we take that electron and we throw it out of the system? Ionization.

That is exactly what the electrical engineers call this process. They call the thermal excitation of the donor electrons ionization. For all intents and purposes, because E thermal is on the order of this E of the donor electron, we can assume complete -- And I am going to use the electrical engineering term here because I think I am still teaching at an engineering school, complete ionization of donor electrons.

This is fantastic. They are all ionized. Now, last day I said that the total number of electrons in the conduction band would equal the number of electrons from the host silicon due to thermal excitation.

Plus it is going to be the number of electrons from the impurity phosphorus. And we know this requires Eg on the order of about 1.1 eV. So very few of these are contributed. There is almost no promotion of electrons from the valence band to the conduction band to leave holes.

This is vanishingly small at room temperature in silicon. Whereas, here, I am going to put in quotation marks, the ionization energy is on the order of the thermal energy, we get all the electrons from here.

And so in such a material we say that the electrical properties are essentially those from the impurities. We send this to zero and say that such a material exhibits "extrinsic behavior." Why is it extrinsic? Because the electrical behavior of the silicon is governed by the impurities that we introduced into the silicon.

Extrinsic behavior. Or, let's call it dopant. I am going to use the word dopant and impurity interchangeably. It is dopant-dependent. And this, of course, depends on how much we put in. But the typical levels that we put in are great enough that they swamp the value that you get from thermal excitation.

In doped silicon, you neglect thermal excitation and you calculate the carrier population in the conduction band based on how much phosphorus you put in. Every phosphorus gives you a contribution. And, just to complete the definition, the undoped material, that is to say highly pure silicon exhibits intrinsic behavior.

In other words, it behaves as pure silicon should behave. An intrinsic semiconductor is one that has impurity levels so low that they do not manifest themselves. An extrinsic semiconductor has impurity levels high enough that we can perceive the action of those impurity levels.

We can say, in this material, that n that are generated from the impurity or the dopant are greater by far than the n from the host material itself. Or, if you like, the number of electrons from the dopant are much greater than the number of electrons from thermal excitation.

It all comes out to say then that the number of electrons that are up in the conduction band are much greater than the number of holes in the valence band. Because, if the impurity levels are dominating what comes out of the host, then that means if there is hardly any of the electrons that came from thermal excitation there are hardly any holes.

Now the number of electrons far exceeds the number of holes, so this material is not net neutral. We do not say that n equals p because the number of electrons in the conduction band is far greater than the number of holes.

And so we call this material, it is extrinsic, and electrical engineers refer to the type of carrier that is dominating its electrons. And electrons, when I went to school, were negative, so this is an n-type semiconductor.

Extrinsic n-type. We altered the electrical properties of silicon by introducing high level of supervalent. In other words, phosphorus, five is greater than four, so supervalent dopant leads to n-type semiconduction.

And now we can do it all over again. What can we do? I'm not going to drag you through it. This is something you can do at home or wherever you like to work. Repeat with subvalent impurity or subvalent dopant.

For example, boron. What would happen if we were to introduce boron here? Boron goes into the space and substitutes, but boron is Group 13 or Group III. Boron only has three valence electrons, so it fills one, two, three.

Boron is electropositive. It is sitting there. It wants to form the bond. How do we handle this situation? What do we do in order to balance the fact that this is lacking one electron? Where is the electron inventory in this crystal? Where is the electron store? If I go shopping for electrons, where is the only place I can find them? They are here.

They are in the bonds. That is to say, they are in the valence band. What will happen is we will rip an electron out of the valence band and move it over to here. And, when we do that, what happens if I take an electron out of here? What is left behind? A hole.

Let's generate a hole. Every time I introduce a subvalent impurity, I call for an electron out of the valence band and generate a hole. And where is that hole going to lie? We can go through the same analogy and we will find that the energy level of that hole is sitting just above the valence band.

But the electrons are sitting in the valence band, so how do I get the electrons out of the valence band up into this level? Thermal excitation. And guess what this energy difference is. It is on the order of the thermal energy, and so I get thermal ionization of the valence electrons up into this level.

This level is a place where electrons go. It accepts electrons. It is called the acceptor level. So now we have this configuration. Conduction band, valence band, subvalent impurity. This is not to scale, of course.

This is on the order of 0.02 eV. And this is called the acceptor level. We get thermal excitation leaving holes behind. Thermal excitation promotes the electrons up to here and leaves behind holes.

Every time I put in a subvalent impurity the result is a hole, so I can control the hole population. And the same thing will happen, if you go through this analogy what will happen? N will no longer equal p.

Instead, the number of positives is going to exceed the number of negatives. Now ne will be much less than nh. N will be less than p. And so this material will be rendered a positive conductor. It is going to be dominantly hole conduction.

So this is now an extrinsic p-type semiconductor. What is the template here? Subvalent dopant calls for electrons, generates holes and makes a p-type semiconductor. That is amazing. Now I can take these and make a sandwich out of these things.

I can do this. This is all silicon. I could dope this side with phosphorus. Let's say the right is phosphorus doped and the left side is boron doped. That means the left side will be p-type, the right side will be n-type.

And what do I have here? I have a p-n junction. I have a solid state rectifier. If I put an AC signal in here, I get rectification. This is the solid state. It is fantastic. I have been talking about elemental semiconductors, but these are found not only in elements.

This is just leftover from last day. We saw this last day. You can have compounds that are semiconductors. So far we talked about just Group IV. We talked about silicon and germanium. Tin is very, very mildly semiconducting, but these are the two workhorses.

And, in fact, it is dominantly silicon. But now, look, you can take Group III and Group V and make covalent compounds. And they, too, have band gaps on this interval. We have an entire palette here that we can paint on.

For example, let's look at this homologous series with aluminum antimonide 1.52 electron volts band gap. Aluminum nitride 6.3. Aluminum nitride is an insulator. It is a very strong material. We use it in my lab as a refractory.

It resists high temperature corrosion. Now, what is going on? The difference in electronegativity. These are covalent bonds, greater difference in electronegativity, higher bond energy. And that occurs in all of these columns as you go up.

So an increase in electronegativity difference is an increase in bond strength, and an increase in bond strength means an increase in band gap energy. And some of these are really interesting. Indium antimonide has a band gap of about two-tenths of an electron volt, which means that its absorption edge is 7 times 10 to the minus 67 micrometers, which puts it in the IR.

And this is one of the materials that would be used as a sensor for night vision. Because what are you really sensing when you are looking at night? You are sensing heat. You don't see the human body.

You see the heat coming from the human body. If everything is cold then there is no delta T and you don't see anything. Over here, cadmium sulfide is 5 times 10 to the minus 7. That is right smack dab in the middle of the visible.

When I was a child my father had a 35 millimeter camera. It had a cadmium sulfide light meter, and we would match the needle with the incoming radiation and cadmium sulfide. Well, I never understood why it was cadmium sulfide until I understood band gap.

And, obviously, there it is. You can also think about what happens if you are photographing something that is dominantly red and your light meter is parked in the middle of the yellow? You wonder why your photographs are overexposed.

Think about that some time. Now, the last thing I want to tell you is that not only do you have solid semiconductors, you have liquid semiconductors. And when silicon melts, it is not a semiconductor.

Silicon melts, the band gap collapses and molten silicon behaves as a liquid metal. But, for example, something like cadmium telluride, which is useful in night vision, as a solid has a band gap on the order of 1.45 electron volts.

As a liquid, it still has a band gap. It is about 0.3 electron volts. It is parked down in the infrared. And the transition metal oxides also do this. Liquid titania is dominantly an electronic conductor.

Not an ionic conductor because its band gap is parked there. And this is of interest to some of the work in my lab where we are looking at trying to set the stage for lunar colonization where you would want to get oxygen out of the surface of the moon.

The surface of the moon is not made out of green cheese, I am sorry to tell you. It is made dominantly of iron oxide and titanium oxide. That is why it is so brilliantly white. It is titania. It is 50% oxygen but tightly bound.

And, if you want to electrolyze the moon, you have to somehow repress this liquid semiconduction. That is a topic of research. This is probably a good place to stay. And what we are going to do next day is we are going to start onto the treatment of solids and crystal.

But I don't want a lot of moving. It is 11:47 and we still have a few minutes. Let's see. What do we want to talk about? We will move past this. We will get to this next day. And what I wanted to talk about today was this image here.

This image is an image of the first rectifying solid state diode. This was done at Bell Labs in Murray Hill, New Jersey in December of 1947. What you are looking at here is a piece of single crystal germanium and the various leads and so on.

And this was able to perform the function of a diode. Now, if I told you that someday there would be 16 million of those on a piece of real estate about the size of your fingernail you would say that I was crazy.

So what has happened from that day to this day? Do you think I could get the document camera on, please? I am going to show you where we have gone. Let's see. Oh, look at this. Let's look at Pentium.

There is Pentium. We have a gazillion of these things underneath the gold here. Everything is covered in gold because electrical engineers are very superstitious. They get nervous exposing wires so they plate everything with gold because they heard somewhere that gold is chemically inert.

Underneath there is, well, here you can see that there is the unit. It is sitting there. All of this. And here is the suspension. All of this spider web is being able to address all of the various devices.

It started with that first one. And here is sort of the intermediate. This is taking the silicon that I showed you last day. These are individual devices that have been put on the silicon through photolithography.

What are we doing? We are making masks and we are conducting these doping operations to set up the various devices. And we can make many of them and then break them up and eventually put them into something like this and so on.

That is the result of a long history of understanding the processing of devices based upon the chemistry that started with what? What started all of this? The search for octet stability. Never forget that.

That is what started this, the search for octet stability. OK. We will see you on Friday.

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