thumb|When an electron leaves a [[helium atom, it leaves an electron hole in its place. This causes the helium atom to become positively charged.]]
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.
Definition
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 <math>k</math> and spin <math>\uparrow</math> is created by removing an electron with a wavevector <math>-k</math> and spin <math>\downarrow</math>.
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.
The dispersion relation determines how electrons respond to forces (via the concept of effective mass). In both cases, the system is described as a filled sea of negative-energy or valence states, and the removal of an electron leads to a positively charged entity that can carry current. The analogy extends to their electromagnetic behavior: both holes and positrons have a charge that is equal and opposite to that of an electron. When an electron and positron collide, they annihilate each other and the energy is emitted as photons or other radiation. An analogous process, recombination, happens in semiconductors, and can be described as an electron falling to the empty hole state and filling it, emitting radiation.
However, there are also limitations to this analogy. Due to the symmetries of Dirac's theory, positron and electron have exactly the same mass, while holes and electrons in crystals generally have different masses. The positron is a real particle with positive inertial mass and rest energy, while the hole is a quasiparticle whose inertial mass is negative. For this reason the responses differ in non-inertial frames: in an accelerating crystal lattice, a positron lags behind, whereas a hole moves forward with the lattice. These differences also appear in composite systems; for example, excitons (electron–hole pairs) move rigidly with the lattice and carry no net momentum, unlike positronium atoms (electron–positron pairs), which gain momentum and energy relative to an accelerating frame.
See also
- Band gap
- Effective mass (solid-state physics)
- Electrical resistivity and conductivity