Anderson's rule
Encyclopedia
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).
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).
The term is also used in the field of computer security
for a principle formulated by Ross J. Anderson: by their nature large database
s will never be free of abuse by breaches of security. If a large system is designed for ease of access it becomes insecure; if made watertight it becomes impossible to use.
values for each semiconductor to calculate the conduction band
and valence band
offsets (Davies, 1997). The electron affinity (usually given 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 offset
s of both the valence band (
) and the conduction band (
).
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 than that 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.
Electronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
diagrams of the heterojunction
Heterojunction
A heterojunction is the interface that occurs between two layers or regions of dissimilar crystalline semiconductors. These semiconducting materials have unequal band gaps as opposed to a homojunction...
between two semiconductor materials. It is also referred to as the electron affinity
Electron affinity
The Electron affinity of an atom or molecule is defined as the amount of energy released when an electron is added to a neutral atom or molecule to form a negative ion....
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
Vacuum level
In physics, the vacuum level refers to the energy of a free stationary electron that is outside of any material .It may be taken as infinitely far away from a solid or modified to be defined near a surface...
of the two semiconductors on either side of the heterojunction should be aligned (at the same energy) (Borisenko and Ossicini, 2004).
The term is also used in the field of computer security
Computer security
Computer security is a branch of computer technology known as information security as applied to computers and networks. The objective of computer security includes protection of information and property from theft, corruption, or natural disaster, while allowing the information and property to...
for a principle formulated by Ross J. Anderson: by their nature large database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
s will never be free of abuse by breaches of security. If a large system is designed for ease of access it becomes insecure; if made watertight it becomes impossible to use.
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 gapBand gap
In solid state physics, a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference between the top of the valence band and the...
values for each semiconductor to calculate the conduction band
Conduction band
In the solid-state physics field of semiconductors and insulators, the conduction band is the range of electron energies, higher than that of the valence band, sufficient to free an electron from binding with its individual atom and allow it to move freely within the atomic lattice of the material...
and valence band
Valence band
In solids, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature....
offsets (Davies, 1997). The electron affinity (usually given the symbol
in solid state physics) gives the energy difference between the lower edge of the conduction band and the vacuum levelVacuum level
In physics, the vacuum level refers to the energy of a free stationary electron that is outside of any material .It may be taken as infinitely far away from a solid or modified to be defined near a surface...
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 lawVegard's law
In metallurgy, Vegard's law is an approximate empirical rule which holds that a linear relation exists, at constant temperature, between the crystal lattice parameter of an alloy and the concentrations of the constituent elements....
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
Band offset
Band offset describes the relative alignment of the energy bands at a semiconductor heterojunction.-References:Franciosi A.; Van de Walle C.G: Heterojunction band offset engineering, Surface Science Reports, Volume 25, Number 1, October 1996 , pp. 5-140...
s of both the valence band (
) and the conduction band ().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 than that of semiconductor A, then the valence band offset is given by:
Poisson’s equation can then be used to calculate the band bending
Band bending
Band bending refers to the local change in energy of electrons at a semiconductor junction due to space charge effects. Because the common way to visualize the electron energy states and Fermi level in a material is to draw bands on an energy vs...
between the two semiconductors.