This alignment is caused by the discontinuous band structures of the semiconductors when compared to each other and the interaction of the two surfaces at the interface.
Depending on the type of the interface, the offsets can be very accurately considered intrinsic, or be able to be modified by manipulating the interfacial structure.
[2] The band offsets, especially those at heterovalent heterojunctions depend significantly on the distribution of interface charge.
The built-in potential is caused by the bands which bend close at the interface due to a charge imbalance between the two semiconductors, and can be described by Poisson's equation.
These older techniques were used to extract the built-in potential by assuming a square-root dependence for the capacitance C on
This square root dependence corresponds to an ideally abrupt transition at the interface and it may or may not be a good approximation of the real junction behaviour.
Band offset values are usually estimated using the optical response as a function of certain geometrical parameters or the intensity of an applied magnetic field.
It states that during the construction of an energy band diagram, the vacuum levels of the semiconductors on either side of the heterojunction should be equal.
Anderson's rule states that when we construct the heterojunction, we need to have both semiconductors on an equal vacuum energy level.
By having the same reference point for both semiconductors, ΔEc becomes equal to the built-in potential, Vbi = Φ1 - Φ2, and the behaviour of the bands at the interface can be predicted as can be seen at the picture above.
However predictions made by linear response theory coincide exactly with those of self-consistent first principle calculations.
Here is showcased the different types of heterojunctions in semiconductors. In type I, the conduction band of the second semiconductor is lower than that of the first, whilst its valence band is higher than that of the first. As a consequence the band gap of the first semiconductor is larger than the band gap of the second semiconductor. In type II the conduction band and valence band of the second semiconductor are both lower than the bands of the first semiconductor. In this staggered gap, the band gap of the second semiconductor is no longer restricted to being smaller than the first semiconductor, although the band gap of the second semiconductor is still partially contained in the first semiconductor. In type III however, the conduction band of the second semiconductor overlaps with the valence band of the first semiconductor. Due to this overlap, there are no forbidden energies at the interface, and the band gap of the second semiconductor is no longer contained by the band gap of the first.
In this heterojunction of type I alignment, one can clearly see the built-in potential Φbi = Φ(A) + Φ(B). The band gap difference ΔEg = Eg(A) - Eg(B) is distributed between the two discontinuities,ΔEv, and ΔEc$. In alignments, it is generally the case that the conduction band which has the higher energy minimum will bend upward, whilst the valence band which has the lower energy maximum will bend upward. In this type of alignment, this means that both of the bands of semiconductor A will bend upwards, whilst both of the bands of semiconductor B will bend downwards. The band bending, caused by the built-in potential, is determined by the interface position of the Fermi level, and predicting or measuring this level is related to the Schottky barrier height in metal-semiconductor interfaces. Depending on the doping of the bulk material, the band bending can be into the thousands of angstroms, or just fifty, depending on the doping. The discontinuities on the other hand, are primarily due to the electrostatic potential gradients of the abrupt interface, working on a length scale of ideally a single atomic interplanar spacing, and is almost independent of any doping used.
