Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice. It is different from the positron, which is an actual particle of antimatter, whereas the hole is just a fiction, used for modeling convenience.
The electron hole was introduced into calculations for the following two situations:
- If an electron is excited into a higher state it leaves a hole in its old state. This meaning is used in Auger electron spectroscopy (and other x-ray techniques), in computational chemistry, and to explain the low electron-electron scattering-rate in crystals (metals, semiconductors).
- In crystals, band structure calculations lead to an effective mass for the charge carriers, which can be negative. Inspired by the Hall effect, Newton's law is used to attach the negative sign onto the charge.
Solid state physics
In solid state physics, an electron hole (usually referred to simply as a hole) is the absence of an electron from an otherwise full electron shell. A hole is essentially a way to conceptualise the interactions of the electrons within a nearly full system, which is missing just a few electrons. In some ways, the behaviour of a hole within a semiconductor crystal lattice is comparable to that of the bubble in an otherwise full bottle of water.[1]
Hole conduction in a valence band can be explained by the following analogy. Imagine a row of people seated in an auditorium, where there are no spare chairs. Someone in the middle of the row wants to leave, so he jumps over the back of the seat into an empty row, and walks out. The empty row is analogous to the conduction band, and the person walking out is analogous to a free electron.
Now imagine someone else comes along and wants to sit down. The empty row has a poor view; so he does not want to sit there. Instead, a person in the crowded row moves into the empty seat the first person left behind. The empty seat moves one spot closer to the edge and the person waiting to sit down. The next person follows, and the next, etcetera. One could say that the empty seat moves towards the edge of the row. Once the empty seat reaches the edge, the new person can sit down.
In the process everyone in the row has moved along. If those people were negatively charged (like electrons), this movement would constitute conduction. If the seats themselves were positively charged, then only the vacant seat would be positive. This is a very simple model of how hole conduction works.
In reality, due to the crystal structure properties, the hole is not localized to a single position as described in the previous example. Rather, the hole spans an area in the crystal lattice covering many hundreds of unit cells. This is equivalent to being unable to tell which broken bond corresponds to the "missing" electron.
Instead of analyzing the movement of an empty state in the valence band as the movement of billions of separate electrons, a single equivalent imaginary particle called a "hole" is considered. In an applied electric field, the electrons move in one direction, corresponding to the hole moving in the other. If a hole associates itself with a neutral atom, that atom loses an electron and becomes positive. Therefore the hole is taken to have positive charge of +e, precisely the opposite of the electron charge.
Coulomb's law allows the force on the "hole" due to an electric field to be calculated. An effective mass can then be derived which relates the (imaginary) force on the (imaginary) hole to the acceleration of that hole. In some semiconductors, such as silicon, the hole's effective mass is dependent on direction (anisotropic), however a value averaged over all directions can be used for some macroscopic calculations.
In most semiconductors, the effective mass of a hole is much larger than that of an electron. This results in lower mobility for holes under the influence of an electric field and this may slow down the speed of the electronic device made of that semiconductor. This is one major reason for adopting electrons as the primary charge carriers, whenever possible in semiconductor devices, instead of holes.
Holes in quantum chemistry
An alternate meaning for the term electron hole is used in computational chemistry. In coupled cluster methods, the ground (or lowest energy) state of a molecule is interpreted as the "vacuum state"—conceptually, in this state there are no electrons. In this scheme, the absence of an electron from a normally-filled state is called a "hole" and is treated as a particle, and the presence of an electron in a normally-empty state is simply called an "electron". This terminology is almost identical to that used in solid-state physics.
See also
References
- ^ Weller, Paul F. (1967). "An analogy for elementary band theory concepts in solids". J. Chem. Educ. 44 (7): 391. Bibcode:1967JChEd..44..391W. doi:10.1021/ed044p391.