Superlattice
Superlattices were discovered early in 1925 by Johansson and Linde[1] after the studies on gold–copper and palladium–copper systems through their special X-ray diffraction patterns.
Further experimental observations and theoretical modifications on the field were done by Bradley and Jay,[2] Gorsky,[3] Borelius,[4] Dehlinger and Graf,[5] Bragg and Williams[6] and Bethe.
Koehler theoretically predicted[8] that by using alternate (nano-)layers of materials with high and low elastic constants, shearing resistance is improved by up to 100 times as the Frank–Read source of dislocations cannot operate in the nanolayers.
If the superlattice is made of two semiconductor materials with different band gaps, each quantum well sets up new selection rules that affect the conditions for charges to flow through the structure.
The two different semiconductor materials are deposited alternately on each other to form a periodic structure in the growth direction.
Since the 1970 proposal of synthetic superlattices by Esaki and Tsu,[11] advances in the physics of such ultra-fine semiconductors, presently called quantum structures, have been made.
For type I the bottom of the conduction band and the top of the valence subband are formed in the same semiconductor layer.
In type II the conduction and valence subbands are staggered in both real and reciprocal space, so that electrons and holes are confined in different layers.
Semiconductor materials, which are used to fabricate the superlattice structures, may be divided by the element groups, IV, III-V and II-VI.
It describes a bi-layer of 20Å of Iron (Fe) and 30Å of Vanadium (V) repeated 20 times, thus yielding a total thickness of 1000Å or 100 nm.
In addition to the MBE technology, metal-organic chemical vapor deposition (MO-CVD) has contributed to the development of superconductor superlattices, which are composed of quaternary III-V compound semiconductors like InGaAsP alloys.
For a large barrier thickness, tunneling is a weak perturbation with regard to the uncoupled dispersionless states, which are fully confined as well.
by virtue of the Bloch theorem, is fully sinusoidal: and the effective mass changes sign for
The condition for observing single miniband transport is the absence of interminiband transfer by any process.
For an ideal superlattice a complete set of eigenstates states can be constructed by products of plane waves
This may provide difficulties if electric fields are applied or effects due to the superlattice's finite length are considered.
Nevertheless, such a choice has a severe shortcoming: the corresponding states are solutions of two different Hamiltonians, each neglecting the presence of the other well.
Applying an electric field F to the superlattice structure causes the Hamiltonian to exhibit an additional scalar potential eφ(z) = −eFz that destroys the translational invariance.
If an external bias is applied to a conductor, such as a metal or a semiconductor, typically an electric current is generated.
The magnitude of this current is determined by the band structure of the material, scattering processes, the applied field strength and the equilibrium carrier distribution of the conductor.
A particular case of superlattices called superstripes are made of superconducting units separated by spacers.
Recently, Felix and Pereira investigated the thermal transport by phonons in periodic[13] and quasiperiodic[14][15][16] superlattices of graphene-hBN according to the Fibonacci sequence.
They reported that the contribution of coherent thermal transport (phonons like-wave) was suppressed as quasiperiodicity increased.
Soon after two-dimensional electron gases (2DEG) had become commonly available for experiments, research groups attempted to create structures[17] that could be called 2D artificial crystals.
The idea is to subject the electrons confined to an interface between two semiconductors (i.e. along z-direction) to an additional modulation potential V(x,y).
Contrary to the classical superlattices (1D/3D, that is 1D modulation of electrons in 3D bulk) described above, this is typically achieved by treating the heterostructure surface: depositing a suitably patterned metallic gate or etching.
Lattice constants of atomic crystals are of the order of 1Å while those of superlattices (a) are several hundreds or thousands larger as dictated by technological limits (e.g. electron-beam lithography used for the patterning of the heterostructure surface).
), phenomena like commensurability oscillations or fractal energy spectra (Hofstadter butterfly) occur.
The superlattice of palladium-copper system is used in high performance alloys to enable a higher electrical conductivity, which is favored by the ordered structure.
Further alloying elements like silver, rhenium, rhodium and ruthenium are added for better mechanical strength and high temperature stability.
