Electrons and Holes

So far when we’ve talked about electronic properties of materials, we have emphasized electrons as the carriers of charge through the material. As we know, in atoms, nuclei are big and mostly immobile, whereas electrons are small and exist in a probability cloud around the nuclei. Thus the mobility and number of electrons, plus the available energy states, are what determine how easily electrons can flow through a material. And this decides whether something is an insulator, a metal, or most interestingly a semiconductor.

But consider a material that has many, many electrons, one in which the band of electron states is nearly full with only a few vacancies. Even with an applied electric field, very few electrons will be able to go anywhere if there are not many available states to move into. A material like this would be nearly an insulator. But we may see one electron move over into an empty state, then a second electron move into the state vacated by the first, then a third electron move into the state vacated into the second, and so on. The motion of the electrons is causing a net charge flow, but no individual electron is able to get very far because of the dearth of available states. From a distance it might almost appear as if the empty space without an electron is what’s moving.

This is similar to a very common occurrence, in fizzy beverages such as soda or beer. Bubbles form, and once they detach from the sides of the container, they rise up through the liquid. But the force causing this motion is gravity, which doesn’t affect the gas in the bubbles as much as it affects the relatively dense liquid around them. In order for the liquid to fall, the bubble must rise. Or, imagine a row of seats, with a middle seat unoccupied but all the other seats full, in a narrow space that makes it difficult to get past occupied seats. A person next to the empty seat could move over, and then the person next to them can move over, and so on. It is the people that are doing the moving, but if we wanted to describe the motion it would almost be simpler to say that the empty seat moves to the edge of the row. There are lots of other examples of the same phenomenon, shown in the diagram below using marbles.

Thus, for the materials whose electron states are crowded but not quite full, the empty states are called ‘electron holes’ or just ‘holes’. Holes are quasiparticles, meaning we can treat them as individual particles even though they are really a collection of behavior exhibited by many particles. Conduction of charge still occurs via the movement of electrons, but conceptually and mathematically it is easier to describe the movement of holes in the system. So one can calculate the charge of a hole, which is the opposite of the charge of an electron, or the mass of a hole in various materials, or the hole mobility which describes how easy it is for a hole to traverse any given material. A material with holes as the charge carrier is called p-type, and a material with electrons as the charge carrier is called n-type,  because of the positive and negative charges of holes and electrons.

Practically, this is an important distinction between different types of semiconductor, and you’ll see how it comes into play in technology when we talk about p-n junctions and finally get to the transistor. But conceptually, I find it really cool that the emergent behavior of a bunch of electrons can be described as a quasiparticle, with its own mass, charge, and electronic properties. It’s elegant and weird, as nature often is.

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6 responses to “Electrons and Holes

  1. Reblogged this on Vijana wetu and commented:
    Electronic properties of materials

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