Electron hole

In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle denoting 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 (including light-emitting 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 and semiconductors). Although they act like elementary particles, holes are 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 show that electrons have a negative effective mass at the top of a band. Although negative mass is unintuitive, a more familiar and intuitive picture emerges by considering a hole, which has a positive charge and a positive mass, instead.

In semiconductors, 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 valence band of a crystal lattice, which is missing a small fraction of its 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.

More generally, a hole is defined as the absence of an electron relative to the system's ground state. This concept applies not only to semiconductors but also to metals with partially filled bands and other electronic systems. A hole with wavevector ${\displaystyle k}$ and spin ${\displaystyle \uparrow }$ is created by removing an electron with a wavevector ${\displaystyle -k}$ and spin ${\displaystyle \downarrow }$.

The hole concept was pioneered in 1929 by Rudolf Peierls, who analyzed the Hall effect using Bloch's theorem, and demonstrated that a nearly full and a nearly empty Brillouin zones give the opposite Hall voltages.

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 another row, and walks out. The empty row is analogous to the conduction band, and the person walking out is analogous to a conduction electron.