In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or crystal lattice the negative charge of the electrons is balanced by the positive charge of the atomic nuclei, the absence of an electron leaves a net positive charge at the hole's location. Holes in a metal or semiconductor crystal lattice can move through the lattice as electrons can, and act similarly to positively-charged particles. They play an important role in the operation of semiconductor devices such as transistors, diodes and integrated circuits. However they are not actually particles, but rather quasiparticles; they are different from the positron, which is the antiparticle of the electron. (See also Dirac Sea.) 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, electronic band structure calculations lead to an effective mass for the electrons, which typically is negative at the top of a band. The negative mass is an unintuitive concept,For these negative mass electrons, momentum is opposite to velocity, so forces acting on these electrons cause their velocity to change in the 'wrong' direction. As these electrons gain energy (moving towards the top of the band), they slow down. and in these situations a more familiar picture is found by considering a positive charge with a positive mass.
Solid-state physicsIn solid-state physics, an electron hole (usually referred to simply as a hole) is the absence of an electron from a full valence band. A hole is essentially a way to conceptualize the interactions of the electrons within a nearly full system, which is missing just a few electrons. In some ways, the behavior of a hole within a semiconductor crystal lattice is comparable to that of the bubble in a full bottle of water.
Simplified analogy: Empty seat in an auditoriumHole 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, et cetera. 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. Instead of analyzing the movement of an empty state in the valence band as the movement of many 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. In reality, due to the uncertainty principle of quantum mechanics, combined with the energy levels available in the crystal, the hole is not localizable to a single position as described in the previous example. Rather, the positive charge which represents 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. Conduction band electrons are similarly delocalized.
Detailed picture: A hole is the absence of a negative-mass electron(right) includes the dispersion relation of each band, i.e. the energy of an electron E as a function of the electron's wavevector k. The "unfilled band" is the semiconductor's conduction band; it curves upward indicating positive effective mass. The "filled band" is the semiconductor's valence band; it curves downward indicating negative effective mass.]] The analogy above is quite simplified, and cannot explain why holes create an opposite effect to electrons in the Hall effect and Seebeck effect. A more precise and detailed explanation follows.Kittel, Introduction to Solid State Physics, 8th edition, pp. 194–196.
- The dispersion relation determines how electrons respond to forces (via the concept of effective mass).
- Positively-charged holes as a shortcut for calculating the total current of an almost-full band.
- A hole near the top of the valence band moves the same way as an electron near the top of the valence band would move (which is in the opposite direction compared to conduction-band electrons experiencing the same force.)
- Conclusion: Hole is a positive-charge, positive-mass quasiparticle.
Role in semiconductor technologyIn 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, rather than holes. Also, why NMOS logic is faster than PMOS logic. However, in many semiconductor devices, both electrons and holes play an essential role. Examples include p–n diodes, bipolar transistors, and CMOS logic.
Holes in quantum chemistryAn 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.
- Band gap
- Carrier generation and recombination
- Effective mass
- Electrical resistivity and conductivity
- Hole formalism