In 2000, the Nobel Prize was awarded with one half jointly to Herbert Kroemer (University of California at Santa Barbara, California, USA) and Zhores I. Alferov (A.F. Ioffe Physico-Technical Institute, St. Petersburg, Russia) for "developing semiconductor heterostructures used in high-speed- and opto-electronics"
Calculating energy band offsets for an ideal heterojunction is straightforward given these material properties using the Anderson's rule. The conduction band offset depends only on the electron affinity difference between the two semiconductors:
Then using the change in band gap:
The valence band offset is simply given by:
Which confirms the trivial relationship between band offsets and band gap difference:
In Anderson's idealized model these material parameters are unchanged when the materials are brought together to form an interface, so it ignores the quantum size effect, defect states and other perturbations which may or may not be the result of imperfect crystal lattice matches (more on lattice considerations below). When two materials are brought together and allowed to reach chemical/thermal equilibrium the fermi level in each material aligns and is constant throughout the system. To the extent that they are able, electrons in the materials leave some regions (depletion) and build up in others (accumulation) in order to find equilibrium. When this occurs a certain amount of band bending occurs near the interface. This total band bending can be quantified with the built in potential given by:
In most cases where the materials are undoped, these terms are just half the band gap. Otherwise, can be calculated with typical solid state device calculations and depends on dopant concentrations and temperature. The built in potential gives the degree to which band bending occurs but tells us nothing about how this happens spatially. In order to know over what distance the bending occurs in which materials, we must know the density of states and state occupation given by the Fermi-Dirac distribution.
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.
Tersoff2 proposed a model based on more familiar metal-semiconductor junctions where the conduction band offset is given by the difference in Schottky barrier height. This model includes a dipole later 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. This model agrees well with systems where both materials are closely lattice matched1 such as GaAs/AlGaAs.
Anderson's rule overestimates the offset in the conduction band of the commercially important type two offset GaAs/AlAs system with from the data above. It has been shown3 that for the actual ratio is closer . This is known as the 60:40 rule and applies to heterojunctions of GaAs with all compositions of AlGaAs. The typical method for measuring band offsets is by calculating them from measuring exciton energies in the luminescence spectra3.
It has been shown5 that the driving force for charge transfer between conduction bands in these structures is the conduction band offset. By decreasing the size of CdSe nanocrystals grown on Robel et. al5 found that electrons transferred faster from the higher CdSe conduction band into . In CdSe the quantum size effect is much more pronounced in the conduction band due to the smaller effective mass than in the valence band and this is the case with most semiconductors. Consequently, engineering the conduction band offset is typically much easier with nanoscale heterojunctions. For staggered (type II) offset nanoscale heterojunctions, photo-induced charge separation can occur since there the lowest energy state for holes may be on one side of the junction where as the lowest energy for electrons is on the opposite side. It has been suggested5 that anisotropic staggered gap (type II) nanoscale heterojunctions may be used for photo catalysis, specifically for water splitting with solar energy.
Semiconductor diode lasers used in CD & DVD players and fiber optic transceivers are manufactured using alternating layers of various III-V and II-VI compound semiconductors to form lasing heterostructures.
When a heterojunction is used as the base-emitter junction of a bipolar junction transistor, extremely high forward gain and low reverse gain result. This translates into very good high frequency operation (values in tens to hundreds of GHz) and low leakage currents. This device is called a heterojunction bipolar transistor (HBT).
Heterojunctions are used in high electron mobility transistors (HEMT) which can operate at significantly higher frequencies (over 500 GHz). The proper doping profile and band alignment gives rise to extremely high electron mobilities by creating a two dimensional electron gas within a dopant free region where very little scattering can occur.
 , ISBN 0134956567
 J. Tersoff, Physical Review, B30, 4874, 1984
 N. Debbar et al., Physical Review, B40, 1058, 1989
 Sergei A. Ivanov, Andrei Piryatinski, Jagjit Nanda, Sergei Tretiak, Kevin R. Zavadil, William O. Wallace, Don Werder and Victor I. Klimov, J. Am. Chem. Soc., 129, 11708-11719, 2007
 Istvan Robel, Masaru Kuno and Prashant V. Kamat, J. Am. Chem. Soc., 129, 4136-4137, 2007
 H. Kroemer, Proceedings of the IEEE, Vol. 51, pp. 1782-1783, 1963