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[1] 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. 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). Although they act like elementary particles, holes are not actually particles, but rather quasiparticles; they are different from the positron, which is the antiparticle of the electron. (See also Dirac sea.)
In crystals, electronic band structure calculations lead to an effective mass for the electrons, which is typically negative at the top of a band. The negative mass is an unintuitive concept,[2] and in these situations, a more familiar picture is found by considering a positive charge with a positive mass.
Detailed picture: A hole is the absence of a negative-mass electron[edit]
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.[4]
- The dispersion relation determines how electrons respond to forces (via the concept of effective mass).[4]
A dispersion relation is the relationship between wavevector (k-vector) and energy in a band, part of the electronic band structure. In quantum mechanics, the electrons are waves, and energy is the wave frequency. A localized electron is a wavepacket, and the motion of an electron is given by the formula for the group velocity of a wave. An electric field affects an electron by gradually shifting all the wavevectors in the wavepacket, and the electron accelerates when its wave group velocity changes. Therefore, again, the way an electron responds to forces is entirely determined by its dispersion relation. An electron floating in space has the dispersion relation E=ℏ2k2/(2m), where m is the (real) electron mass and ℏ is reduced Planck constant. Near the bottom of the conduction band of a semiconductor, the dispersion relation is instead E=ℏ2k2/(2m*) (m* is the effective mass), so a conduction-band electron responds to forces as if it had the mass m*.
- Electrons near the top of the valence band behave as if they have negative mass.[4]
The dispersion relation near the top of the valence band is E=ℏ2k2/(2m*) with negative effective mass. So electrons near the top of the valence band behave like they have negative mass. When a force pulls the electrons to the right, these electrons actually move left. This is solely due to the shape of the valence band and is unrelated to whether the band is full or empty. If you could somehow empty out the valence band and just put one electron near the valence band maximum (an unstable situation), this electron would move the "wrong way" in response to forces.
- Positively-charged holes as a shortcut for calculating the total current of an almost-full band.[4]
A perfectly full band always has zero current. One way to think about this fact is that the electron states near the top of the band have negative effective mass, and those near the bottom of the band have positive effective mass, so the net motion is exactly zero. If an otherwise-almost-full valence band has a state without an electron in it, we say that this state is occupied by a hole. There is a mathematical shortcut for calculating the current due to every electron in the whole valence band: Start with zero current (the total if the band were full), and subtract the current due to the electrons that would be in each hole state if it wasn't a hole. Since subtracting the current caused by a negative charge in motion is the same as adding the current caused by a positive charge moving on the same path, the mathematical shortcut is to pretend that each hole state is carrying a positive charge, while ignoring every other electron state in the valence 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[4] (which is in the opposite direction compared to conduction-band electrons experiencing the same force.)
This fact follows from the discussion and definition above. This is an example where the auditorium analogy above is misleading. When a person moves left in a full auditorium, an empty seat moves right. But in this section we are imagining how electrons move through k-space, not real space, and the effect of a force is to move all the electrons through k-space in the same direction at the same time. In this context, a better analogy is a bubble underwater in a river: The bubble moves the same direction as the water, not the opposite.
Since force = mass × acceleration, a negative-effective-mass electron near the top of the valence band would move the opposite direction as a positive-effective-mass electron near the bottom of the conduction band, in response to a given electric or magnetic force. Therefore, a hole moves this way as well.
- Conclusion: Hole is a positive-charge, positive-mass quasiparticle.
From the above, a hole (1) carries a positive charge, and (2) responds to electric and magnetic fields as if it had a positive charge and positive mass. (The latter is because a particle with positive charge and positive mass respond to electric and magnetic fields in the same way as a particle with a negative charge and negative mass.) That explains why holes can be treated in all situations as ordinary positively charged quasiparticles.
Role in semiconductor technology[edit]
In some semiconductors, such as silicon, the hole's effective mass is dependent on a 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 chemistry[edit]
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[edit]
- Band gap
- Carrier generation and recombination
- Effective mass
- Electrical resistivity and conductivity
- Hole formalism
https://en.wikipedia.org/wiki/Electron_hole
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