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Concept
Anderson's rule
Résumé
Anderson's rule is used for the construction of energy band diagrams of the heterojunction between two semiconductor materials. Anderson's rule states that when constructing an energy band diagram, the vacuum levels of the two semiconductors on either side of the heterojunction should be aligned (at the same energy).
It is also referred to as the electron affinity rule, and is closely related to the Schottky–Mott rule for metal–semiconductor junctions.
Anderson's rule was first described by R. L. Anderson in 1960.
Once the vacuum levels are aligned it is possible to use the electron affinity and band gap values for each semiconductor to calculate the conduction band and valence band offsets. The electron affinity (usually given by the symbol in solid state physics) gives the energy difference between the lower edge of the conduction band and the vacuum level of the semiconductor. The band gap (usually given the symbol ) gives the energy difference between the lower edge of the conduction band and the upper edge of the valence band. Each semiconductor has different electron affinity and band gap values. For semiconductor alloys it may be necessary to use Vegard's law to calculate these values.
Once the relative positions of the conduction and valence bands for both semiconductors are known, Anderson's rule allows the calculation of the band offsets of both the valence band () and the conduction band ().
After applying Anderson's rule and discovering the bands' alignment at the junction, Poisson’s equation can then be used to calculate the shape of the band bending in the two semiconductors.
Consider a heterojunction between semiconductor 1 and semiconductor 2. Suppose the conduction band of semiconductor 2 is closer to the vacuum level than that of semiconductor 1. The conduction band offset would then be given by the difference in electron affinity (energy from upper conducting band to vacuum level) of the two semiconductors:
Next, suppose that the band gap of semiconductor 2 is large enough that the valence band of semiconductor 1 lies at a higher energy than that of semiconductor 2.
Source officielle
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