Video: Pure Semiconductors

In this lesson, we will learn how to describe the electrical bonds in pure semiconductor materials.


Video Transcript

In this video, our topic is pure semiconductors. We’re going to learn what semiconductors are and how electrons move about within them. Semiconductors form the basis of much of modern electronics. And in this lesson, we’re going to learn how they work.

We can begin here by thinking about electrical conductivity. We know that when it comes to this, there are two types of materials. First, there are insulators, such as glass or plastic or wood, which do not easily allow electricity to flow through them. And then, on the other end of the spectrum, there are conductors. Any sort of metal is a good example of a conductor. And we see this in the fact that wires in an electrical circuit are typically made of some metal. So, if a material is very effective at conducting electricity, it’s a conductor, and if it does this very ineffectively, it’s an insulator.

Our discussion here is about a class of materials that sits in between these two extremes. Semiconductors are neither great conductors nor great insulators. And this property is actually very helpful for the ways that we use them. Now, semiconductors can be made from combining certain atomic elements, but there are also several elements which, by themselves, have semiconductor properties. These include, for example, silicon, germanium, and tin.

Of these specific elements, the most common by far used for semiconductors is silicon. Partly this is because silicon is such a readily available element. It’s the second most abundant element in Earth’s crust, and it’s the eighth most abundant element in the universe overall. Silicon is part of the compound that makes up materials like sand or glass. And when we’re able to isolate it, we can use it to create a semiconductor. Keeping in mind that silicon isn’t the only semiconductor material, for the rest of our lesson, we’re going to use it consistently as an example of such a material.

Now, the usefulness of silicon as a semiconductor comes from its atomic structure. If we had a neutral atom of silicon, and say that this was the nucleus of that atom, then this nucleus would have three layers or levels of electronic states around it. The lowest of these energy levels has two electrons in it. Then, the next highest level has one, two, three, four, five, six, seven, eight electrons. And the highest electron energy level still bound to the silicon atom possesses one, two, three, four electrons in this shell called its valence shell.

Now, when it comes to the ways that atoms interact with other atoms, one of the biggest influences is the number of electrons a given atom has in its valence shell. For that reason, when we make a sketch of a particular atom, it’s not uncommon to only depict that outermost shell and all the electrons in it and leave the rest of the energy levels undrawn.

So, the current version of our sketch of a silicon atom shows us that it has four electrons in its valence level. And we can recall that in many cases, though not all, for an atom to be chemically stable, that is, for it to be unlikely to lose any electrons to its environment or take any electrons from the environment, it’s best for that outermost energy level to be populated with eight electrons. This is what is often called a full valence shell.

Silicon, we see, with four valence electrons is neither very close to having eight nor is it close to getting rid of this energy level entirely by losing all of these electrons. All this to say if we considered silicon atoms in isolation all by themselves, they wouldn’t make very good semiconductors. But in reality, we don’t work with individual atoms, but rather many of them arranged in what’s called an atomic lattice.

To get a sense for this, let’s say that our particular silicon atom we’re considering is surrounded by eight others. By the way, one reason we use the word lattice is to describe just how orderly this arrangement of atoms is. What we’ve drawn here is just a tiny, tiny part of what would be an overall atomic lattice. But nonetheless, it will help us start to understand the larger dynamics that take place in the lattice overall.

Now, as things stand, we’ve only drawn in the valence electrons for our central silicon atom. But of course, each of these atoms has its own four valence electrons. And what ends up happening when the atoms are arranged in this lattice formation is that what are called covalent bonds develop between them. This means that a pair of electrons are shared between two atoms in a common bond. To show this on our sketch, we’re going to relocate the valence electrons to the locations where these valence energy levels overlap.

So, for example, for these two silicon atoms, instead of separately possessing these two valence electrons right here, they would share them via a covalent bond. And we can show that by relocating the electrons to the overlaps between these energy states. So now we see that this electron here and this one here are shared, we can say, between these two silicon atoms. This sharing, that is, these covalent bonds, develop between all the adjacent silicon atoms in this lattice. And we can sketch that in like this.

Now, we can say that any particular shared electron, say this one right here, is equally possessed by both this silicon atom and this one. It can be counted as one of the valence electrons for both these atoms. Knowing that, let’s go back to our original silicon atom, the one that’s now at the center, and count the number of valence electrons it now possesses. Looking at them, we count one, two, three, four, five, six, seven, eight electrons, which means that now that this atom is surrounded by other identical silicon atoms, instead of only having four electrons in its valence shell, it has eight, a complete set.

It’s important to realize that throughout this sharing process, the overall electric charge of any of these atoms hasn’t changed. If we assume each one started out electrically neutral, then so far they maintain that neutrality. So, going back to our central silicon atom in our sketch, this atom is electrically neutral, and it has a full valence shell. This, we could say, is the starting point for the lattice overall to start to behave as a semiconductor.

We mentioned earlier that any realistic semiconductor lattice would be much greater in size than the one we’ve drawn here. When that’s true, when there are many more atoms making up this lattice, then there are many more silicon atoms that we can consider to be interior to the lattice, that is, fully surrounded by other silicon atoms. In that case, the majority of atoms in the lattice are like this one here that we see in the center. It shares four electrons with its surrounding atoms and itself has a full valence shell.

Now, if the temperature of our lattice were zero kelvin, that is, absolute zero, then the sketch we’ve drawn would be accurate for all time. It wouldn’t change over time. But as soon as the temperature of our lattice increases above this minimum, that means that thermal energy is available to be input to the lattice. And this energy, when absorbed, can cause some of the bound electrons to break free from their bonds. So, considering the eight electrons around our central silicon atom, say that, through energy being added to our system, this electron here broke free out of its bond. An electron liberated like this is called a free electron, and it leaves behind it a vacancy called a hole.

Now, this is where the overall electric charge of this silicon atom comes in. We said earlier that this atom is neutral, so it has the same number of positive charges as negative charges. But that was before it gave up this now-free electron. This central silicon atom then, having lost one negative charge, has an overall effective positive charge to it. More specifically, we can say that the charge of an electron hole, that is, a spot where an electron used to be before it was liberated, is effectively positive one. As we mentioned, that’s because it’s recently lost a negative charge and, therefore, on balance has a positive charge to it.

Now interestingly, in the case of semiconductors, even though this central silicon atom now has an overall positive charge, it’s typical not to call this atom an ion, that is, a charged particle. The reason for this is as follows. Recall we said that in any real atomic lattice, there are many, many interior silicon atoms, far more than the one that we’ve shown here. Well, as thermal energy is added to the lattice overall, all of those interior atoms are candidates for losing an electron. Each one could potentially lose an electron to the rest of the lattice, which would then leave behind a positively charged electron hole. This means that in practice, at any one time, there isn’t just one free electron and one electron hole, but many of them.

So, considering the electron hole we can see here, it’s likely that a free electron liberated from somewhere else in the lattice will find it, so to speak, and occupy it. And likewise, this free electron here is likely to end up in a vacancy, a hole, created in some other silicon atom in the lattice. For a lattice of silicon then or any other pure semiconductor material, when the semiconductor is at room temperature, many of the bonds holding electrons in place in valence energy levels are being broken, releasing free electrons into the lattice, which move from atom to atom throughout the lattice, filling vacancies, and then perhaps even being liberated again.

The important thing to see here is that since each free electron leaves a vacancy or a hole behind it, at any given moment, the number of free electrons in the atomic lattice will be equal to the number of holes in that lattice. They always go together, a free electron with a vacancy or a hole. And the higher the temperature of our semiconductor gets, the more free electrons are generated per unit time and therefore the more holes are created and then filled by other free electrons. Knowing all this about silicon as a pure semiconductor material, let’s get some practice with these ideas through an example exercise.

An atom of silicon is part of an object made of silicon atoms, as shown in the diagram. Only the electrons in the outermost shells of the atom are individually represented. How many of the electrons in the outermost shell of an atom in the object form covalent bonds with adjacent atoms?

Okay, so we’re told that in this diagram, all of the atoms represented are silicon atoms. And we can think of these red circles as the nuclei of these silicon atoms. And then the smaller blue dots around them represent valence electrons. That is, they’re electrons in the outermost shells of the respective atoms. Our question asks, how many of these electrons in the outermost shell, that is, these valence electrons, of an atom that is in the object form covalent bonds with adjacent atoms? To answer this question, there’s something important we’ll need to know about silicon.

When we have a neutral silicon atom, say that this is the nucleus of that atom, then that silicon atom possesses four electrons in its outermost shell. And we might represent that like this. This is the natural state of a neutral silicon atom when it’s all by itself. We see in our sketch though that we have many silicon atoms represented here. They’re all arranged in this orderly formation called a lattice. We can see that lattice in the even rows and columns of all these silicon atoms.

When they’re arranged this way, adjacent silicon atoms, that is, atoms that are right next to one another in the lattice, are actually capable of sharing electrons between them. So, for example, if we had a second silicon atom right here that also had its own four valence electrons, then the two electrons in this outermost energy level here and here, right between the adjacent atoms, could be shared by a bond called a covalent bond. Through this sharing, we could say that both of these silicon atoms possess both of these electrons. And this would mean that for each of these atoms individually, whereas it used to have four electrons in its outermost shell, now it has five.

If we take this idea of electron sharing and apply it to the silicon atoms in our object, specifically for the interior silicon atoms, that is, the ones in the object, like, for example, this one right here, we can see that even more electron sharing goes on. That’s because this particular silicon atom is adjacent to this atom and this atom and this one and this one. It shares a side, we could say, with four other identical silicon atoms. And therefore, rather than one instance of electron sharing, like we saw here with our two adjacent atoms, there are now four opportunities for that to happen for our interior silicon atom. And we see the result of this for this highlighted interior atom right here.

Notice that it has one, two, three, four, five, six, seven, eight electrons in its outermost shell. That has happened, we can say, because the four original electrons in this individual silicon atom’s outermost shell now have four other electrons added to their total, one each, thanks to sharing between this silicon atom and the four adjacent to it. That is, this atom here shares one electron with this silicon atom, as does this atom here, as does this one, and this one. It’s through the sharing process that an interior silicon atom, such as this one, is able to populate a full or a complete outermost shell with eight electrons.

So then, we’ve taken the four original valence electrons, and through the formation of covalent bonds, we’ve added four more to them. This is true for all of the atoms inside this object, that is, in its interior.

Let’s take a moment now to summarize what we’ve learned about pure semiconductors. In this lesson, we saw that semiconductors are a class of material that exists between electrical insulators and electrical conductors. Basically, semiconductors neither conduct nor insulate very strongly. We saw further that silicon is the most common semiconductor material and that a neutral atom of silicon has four valence electrons or four electrons in its outermost shell.

This means that when many silicon atoms are arranged together in an orderly pattern called an atomic lattice, electron sharing takes place through the formation of what are called covalent bonds between adjacent silicon atoms. In this way, interior atoms end up with a fully populated valence shell. But then, as the temperature of this atomic lattice goes up, energy is provided for the electrons in these covalent bonds to break that bond and become liberated, creating in the process a pair of objects. One object is the free electron, the liberated electron from the silicon atom, and the other is the vacancy, also called an electron hole, left behind.

We saw that while the effective charge of an electron is minus one, the effective charge of an electron hole is positive one. And lastly, in normal room temperature operation of a semiconductor material, we saw that many free electrons and therefore corresponding electron holes are created in an ongoing fashion. A hole is likely to be filled by a free electron from somewhere else in the lattice, while the free electron that created that hole is likely to find a hole somewhere else to fill. In this way, there are always the same number of free electrons and holes in a semiconductor material.

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