Anderson's rule 4567548 126872104 2007-04-29T15:28:39Z Jrf 351176 /* Using Anderson's rule to construct energy band diagrams */ '''Anderson's rule''' is used for the construction of [[Electronic band structure|energy band]] diagrams of the [[heterojunction]] between two [[semiconductor]] materials. It is also referred to as the [[electron affinity]] rule. Anderson's rule was first described by R. L. Anderson in [[1960]] (Anderson, 1960). 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) (Borisenko and Ossicini, 2004). ==Using Anderson's rule to construct energy band diagrams== 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 (Davies, 1997). The electron affinity (usually given the symbol <math>\chi</math> 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 <math>E_{g}</math>) 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 offset]]s of both the valence band (<math>\Delta E_{v}</math>) and the conduction band (<math>\Delta E_{c}</math>). Consider a heterojunction between semiconductor A and semiconductor B. Suppose the conduction band of semiconductor A lies at a higher energy than that of semiconductor B. The conduction band offset would then be given by: <math>\Delta E_{c} = \chi_{B} - \chi_{A}\,</math> Then suppose that the band gap of semiconductor A is large enough that the valence band of semiconductor B lies at a higher energy than that of semiconductor A, then the valence band offset is given by: <math>\Delta E_{v} = (\chi_{A} + E_{gA}) - (\chi_{B} + E_{gB})\,</math> [[Poisson equation|Poisson’s equation]] can then be used to calculate the [[band bending]] between the two semiconductors. ==References== Anderson, R. L., (1960). Germanium-gallium arsenide heterojunction, ''IBM J. Res. Dev.'' '''4'''(3), pp. 283-287 Borisenko, V. E. and Ossicini, S. (2004). ''What is What in the Nanoworld: A Handbook on Nanoscience and Nanotechnology''. Germany: Wiley-VCH. Davies, J. H., (1997). ''The Physics of Low-Dimensional Semiconductors''. UK: [[Cambridge University Press]]. [[Category:Semiconductors]] [[ja:アンダーソンの法則]]