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A semiconductor is a solid material that has electrical conductivity in between a conductor and an insulator; it can vary over that wide range either permanently or dynamically.

Semiconductors are important in electronic technology. Semiconductor devices, electronic components made of semiconductor materials, are essential in modern consumer electronics, including computers, mobile phones, and digital audio players. Silicon is used to create most semiconductors commercially, but dozens of other materials are used as well.

Band structure

Image:HAtomOrbitals.png| In a single H-atom an electron resides in well known orbits. Note that the orbits are called s,p,d in order of increasing circular current. Image:CovalentBond.png| Putting two atoms together leads to delocalized orbits across two atoms, a so called covalent bond. Due to Paulis principle in every state there is max one electron. Image:Bändermodell-Potentialtöpfe.png| This can be continued with more atoms. Note: This picture unfortunately shows a metal. Image:Benz4.png| Using 6 carbon atoms one can create molecular orbits which allow for circular current. Filling the states following Pauli's principle leads to zero net current. Current due to uneven filling needs an energy investment. Image:Ressauts et terrasses.png| Proceeding in a regular fashion and create a crystal, which may after creation be cut into a tape and fused together at the ends allow for circular currents. Image:Si-band-schematics.PNG| For this regular solid the band structure can be calculated or measured. Image:Electronic_band_diagram.svg| Integrating over the k axis gives the bands of a semiconductor showing a full valence band and an empty conduction band. Generally stopping at the vacuum level is dumb, because some people want to calculate: photoemission, inverse photoemission Image:Wave packet (no dispersion).gif| After the band structure is determined states can be combined to generate wave packets. As this is analogous to wave packages in free space, the results are similar. Image:Diffusion rayleigh et diffraction.png| An alternative description, which does not really appreciate the strong Coulomb interaction, shoots free electrons into the crystal and looks at the scattering. Image:Semiconduttore intrinseco.png| A third alternative description uses strongly localized unpaired electrons in chemical bonds, which looks almost like a Mott insulator.

Explaining semiconductor energy bands

There are three popular ways to describe the electronic structure of a crystal.

Energy level splitting due to electron energy level Pauli exclusion

The first starts from single atoms. An atom has discrete energy levels. When two atoms come close each energy level splits into an upper and a lower level, whereby they delocalize across the two atoms. With more atoms the number of levels increases, and groups of levels form bands. Semiconductors contain many bands. If there is a large distance between the highest occupied state and the lowest unoccupied space, then a gap will likely remain between occupied and unoccupied bands even after band formation.