Anderson's rule is used for the construction of 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). In solid state physics, the electronic band structure (or simply band structure) of a solid describes ranges of energy that an electron is forbidden or allowed to have. ... A heterojunction is a semiconductor diode junction which is composed of alternating layers of semiconductor material. ... A semiconductor is a solid whose electrical conductivity can be controlled over a wide range, either permanently or dynamically. ... The electron affinity, Eea, of an atom or molecule is the energy required to detach an electron from a singly charged negative ion, that is the energy change for the process X- → X + e- An equivalent definition is the energy released (Einitial âˆ’ Efinal) when an electron is attached to a... 1960 (MCMLX) was a leap year starting on Friday (the link is to a full 1960 calendar). ...

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). Look up Vacuum in Wiktionary, the free dictionary. ...

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 χ 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 E_g) 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. 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. ... In semiconductors and insulators, the conduction band is the range of electron energy, higher than that of the valence band, sufficient to make the electrons free to accelerate under the influence of an applied electric field and thus constitute an electric current. ... In solids, the valence band is the highest range of electron energies where electrons are normally present at zero temperature. ... Solid-state physics, the largest branch of condensed matter physics, is the study of rigid matter, or solids. ... An alloy is a combination, either in solution or compound, of two or more elements, at least one of which is a metal, and where the resultant material has metallic properties. ...

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 (ΔE_v) and the conduction band (ΔE_c).

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:

Then suppose that the band gap of semiconductor A is large enough that the valence band of semiconductor B lies at a higher energy that than of semiconductor A, then the valence band offset is given by:

Poisson’s equation can then be used to calculate the band bending between the two semiconductors. Poissons equation is the partial differential equation: Or alternately: or i. ... Band bending refers to the local change in energy of electrons at a semiconductor junction due to space charge effects. ...

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. The headquarters of the Cambridge University Press, in Trumpington Street, Cambridge. ...