A **heterostructure** is a crystal composed of multiple semiconductors of different types. Generally these are in the form of more or less thin layers aligned one after the other in a direction called the growth direction. The interface between one layer and the next is called a heterojunction.

## Fabrication

It is possible to realize very refined heterostructures, with transitions from one semiconductor to another with atomic precision, by means of epitaxial growth techniques such as molecular beam epitaxy (MBE) or MOCVD (Metal-Organic Chemical Vapor Deposition). These techniques allow to deposit the materials with such accuracy to provide a range of possibilities extremely wide to the realization of heterostructures.

In particular, through the alternation of materials of different forbidden band, they offer the possibility to develop systems in which the charge carriers are confined in spaces with reduced dimensionality. In this way, more optically efficient materials or materials with higher carrier mobility can be obtained. For this reason, most of the semiconductor devices currently produced are made of etho-structures: these are the fundamental elements of high-performance optical sources and detectors and of digital and analog devices that require high operating frequencies.

From a mathematical point of view, heterostructures and their properties can be studied with varying degrees of precision: from the most idealized methods, suitable for modeling particularly pure crystals, to those able to take into account crystal impurities or doping of various kinds.

## Ideal heterostructures

In an idealized heterostructure model, perfect lattice fit is achieved when the various semiconductors are characterized by crystals of the same symmetry (e.g., that of zincblende) and with lattice steps of the same size. Elastic deformation effects that could lead to changes in the band structure of the crystal are therefore neglected. In such a model, it is also assumed that the crystal retains total homogeneity and isotropy in directions orthogonal to the growth direction, taken along a cubic axis.

In such conditions, the translational symmetry of the crystal in the direction of growth is lost: it is no longer possible to speak of Bloch eigenfunctions and therefore of band theory in that direction. Instead we can continue to speak of bands for the directions orthogonal to that of growth and the approximation of perfect lattice matching makes that in the various layers the band structure has the same symmetries and the various bands refer to different energies. Nevertheless, one finds in all semiconductors of the heterostructure the same point in the bands.

A subsequent approximation, called the flat band approximation, neglects all the charge transport effects that can occur at the interfaces of the various semiconductors and that can give rise to electric fields. Given all of these approximations, graphing a point of the bands as a function of the direction of growth yields a constant function at intervals.

Among the heterostructure models we recognize the quantum dot, the quantum wire the quantum well, the super lattice and the multiple quantum well. Each structure exhibits particular quantum effects generated by the discreteness of energy states in certain spatial directions.