Editing Heterojunction (section)

== Energy band alignment ==

[[Image:Heterojunction types.png|430px|thumb|right|The three types of semiconductor heterojunctions organized by band alignment.]]
[[File:Straddling gap heterojunction band diagram.svg|thumb|[[Band diagram]] for straddling gap, ''n''-''n'' semiconductor heterojunction at equilibrium.]]

The behaviour of a semiconductor junction depends crucially on the alignment of the [[energy band]]s at the interface.
Semiconductor interfaces can be organized into three types of heterojunctions: straddling gap (type I), staggered gap (type II) or broken gap (type III) as seen in the figure.<ref>{{Cite book|title=Semiconductor Nanostructures Quantum States and Electronic Transport|url=https://archive.org/details/semiconductornan00ihnt|url-access=limited|last=Ihn|first=Thomas|publisher=Oxford University Press|year=2010|isbn=9780199534432|location=United States of America|pages=[https://archive.org/details/semiconductornan00ihnt/page/n82 66]|chapter=ch. 5.1 Band engineering}}</ref> Away from the junction, the [[band bending]] can be computed based on the usual procedure of solving [[Poisson's equation]].

Various models exist to predict the band alignment.
* The simplest (and least accurate) model is [[Anderson's rule]], which predicts the band alignment based on the properties of vacuum-semiconductor interfaces (in particular the vacuum [[electron affinity]]). The main limitation is its neglect of chemical bonding.
* A ''common anion rule'' was proposed which guesses that since the valence band is related to anionic states, materials with the same anions should have very small valence band offsets. This however did not explain the data but is related to the trend that two materials with different anions tend to have larger [[valence band]] offsets than [[conduction band]] offsets. 
* Tersoff<ref>{{cite journal|author=J. Tersoff|doi=10.1103/PhysRevB.30.4874|title=Theory of semiconductor heterojunctions: The role of quantum dipoles|year=1984|journal=Physical Review B|volume=30|issue=8|pages=4874–4877|bibcode = 1984PhRvB..30.4874T }}</ref> proposed a ''gap state'' model based on more familiar [[metal–semiconductor junction]]s where the conduction band offset is given by the difference in [[Schottky barrier]] height. This model includes a [[dipole]] layer at the interface between the two semiconductors which arises from [[electron tunneling]] from the conduction band of one material into the gap of the other (analogous to [[metal-induced gap states]]). This model agrees well with systems where both materials are closely lattice matched<ref name="pallab">Pallab, Bhattacharya (1997), Semiconductor Optoelectronic Devices, Prentice Hall, {{ISBN|0-13-495656-7}}</ref> such as [[GaAs]]/[[AlGaAs]].
* The ''60:40 rule'' is a heuristic for the specific case of junctions between the semiconductor GaAs and the alloy semiconductor Al<sub>''x''</sub>Ga<sub>1−''x''</sub>As. As the ''x'' in the Al<sub>''x''</sub>Ga<sub>1−''x''</sub>As side is varied from 0 to 1, the ratio <math>\Delta E_C/\Delta E_V</math> tends to maintain the value 60/40. For comparison, Anderson's rule predicts <math>\Delta E_C / \Delta E_V = 0.73/0.27</math> for a GaAs/AlAs junction (''x''=1).<ref>{{cite book|isbn=9780852965580|url=https://books.google.com/books?id=s7icD_5b67oC|title=Properties of Aluminium Gallium Arsenide|last1=Adachi|first1=Sadao|date=1993-01-01}}</ref><ref name="Debbar">{{cite journal|doi=10.1103/PhysRevB.40.1058|title=Conduction-band offsets in pseudomorphic InxGa1-xAs/Al0.2Ga0.8As quantum wells (0.07≤x≤0.18) measured by deep-level transient spectroscopy|year=1989|last1=Debbar|first1=N.|last2=Biswas|first2=Dipankar|last3=Bhattacharya|first3=Pallab|journal=Physical Review B|volume=40|issue=2|pages=1058–1063|pmid=9991928|bibcode = 1989PhRvB..40.1058D }}</ref>

The typical method for measuring band offsets is by calculating them from measuring [[exciton]] energies in the [[luminescence]] spectra.<ref name="Debbar" />