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# Band gap

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In solid state physics (and related applied fields), the band gap is the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is often spelt "bandgap".

See electrical conduction and semiconductor for a more detailed description of band structure.

The band gap of a semiconductor is important for a number of reasons. An intrinsic (pure) semiconductor's conductivity is strongly dependent on the band gap. This is because the only available carriers for conduction are the electrons which manage to get enough thermal energy to be excited from the valence band into the conduction band. From Fermi-Dirac statistics, the probability of these excitations occurring is proportional to:

$\exp\left(\frac{-E_g}{kT}\right)$

where:

exp is the exponential function
Eg is the band gap energy
k is Boltzmann's constant
T is temperature

In many devices this kind of conductivity is undesirable, and larger bandgap materials give better performance. In infrared photodiodes, a small band gap semiconductor is used to allow detection of low-energy photons. The ability to tailor the bandgap of a device is possible in semiconductor alloys (such as GaAlAs, InGaAs, InAlAs, etc...), and is sometimes referred to as bandgap engineering. This is exploited in the design of heterojunction bipolar transistors[?] (HBTs) and laser diodes.

The difference between semiconductors and insulators is rather ambiguous. Indeed, according to one definition, a semiconductor is a type of insulator. In general, a material with a sufficiently large band gap will be an insulator. The figure of 3 eV is sometimes given. Mobility also plays a role in determining a material's informal classification.

Band gap decreases with increasing temperature, in a process related to thermal expansion[?]. Bandgaps can be either direct or indirect bandgaps.

Band gaps of some common materials at room temperature:

 Si 1.11 eV Ge 0.67 eV GaAs 1.43 eV InP[?] 1.34 eV AlAs[?] 2.16 eV GaN[?] 3.37 eV Diamond 5.46 - 6.4 eV AlGaAs 1.42 - 2.16 eV

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