Band gap

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In solid state physics and related applied fields, the band gap (or energy 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 spelled "bandgap".

Image:Semiconductor_band_structure_(lots_of_bands).png
Semiconductor band structure
See electrical conduction and semiconductor for a more detailed description of band structure.

An intrinsic (pure) semiconductor's conductivity is strongly dependent on the band gap. The only available carriers for conduction are the electrons which have enough thermal energy to be excited across the band gap, which is defined as the energy level difference between the conduction band and the valence band. The probability that a state of energy, E0, will be occupied by an electron is derived from Fermi-Dirac statistics. An approximation, called the Boltzmann approximation, is valid if the energy of the state E0 > > EF, where EF is the Fermi energy. The Boltzman approximation is given by:

e^{\left(\frac{-E_g}{kT}\right)}

where:

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

Conductivity is undesirable, and larger band gap materials give better performance. In infrared photodiodes, a small band gap semiconductor is used to allow detection of low-energy photons.


Band gaps
Common materials at room temperature
InSb 0.17 eV
Ge 0.67 eV
InN 0.7 eV
HgCdTe 0.0 - 1.5 eV
InGaAs 0.4 - 1.4 eV
Silicon 1.14 eV(InD)
InP 1.34 eV(D)
GaAs 1.42 eV(D)
CdTe 1.56 eV(D)
AlGaAs 1.42 - 2.16 eV
InGaP2 1.8 eV
GaAsP 1.42-2.26eV(In/D)
InGaN 0.7 - 3.4 eV(D)
AlAs 2.16 eV
GaP 2.26 eV(InD)
AlGaInP 1.91 - 2.52 eV
ZnSe 2.7 eV
SiC 6H 3.03 eV
SiC 4H 3.28 eV
GaN 3.37 eV
Diamond 5.46 - 6.4 eV

Band gap engineering is the process of controlling or altering the band gap of a material by controlling the composition of certain semiconductor alloys, such as GaAlAs, InGaAs, and InAlAs. It is also possible to construct layered materials with alternating compositions by techniques like molecular beam epitaxy. These methods are exploited in the design of heterojunction bipolar transistors (HBTs), laser diodes and solar cells.

The distinction between semiconductors and insulators is a matter of convention. One approach is to consider semiconductors a type of insulator with a low band gap. Insulators with a higher band gap, usually greater than 3 eV, are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical conditions. 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. Special purpose integrated circuits such as the DS1621 exploit this property to perform accurate temperature measurements. Band gap also depends on pressure. Bandgaps can be either direct or indirect bandgaps, depending on the band structure.

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