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Concept in quantum mechanics

A quantum well is a potential well with only discrete energy values. The classic model used to demonstrate a quantum well is to confine particles, which were initially free to move in three dimensions, to two dimensions, by forcing them to occupy a planar region. The effects of quantum confinement take place when the quantum well thickness becomes comparable to the de Broglie wavelength of the carriers (generally electrons and holes), leading to energy levels called "energy subbands", i. e., the carriers can only have discrete energy values. The concept of quantum well was proposed in 1963 independently by Herbert Kroemer and by Zhores Alferov and R. F. Kazarinov.

The semiconductor quantum well was developed in 1970 by Esaki and Tsu, who also invented synthetic superlattices. They suggested that a heterostructure made up of alternating thin layers of semiconductors with different band gaps should exhibit interesting and useful properties. Since then, much effort and research has gone into studying the physics of quantum well systems as well as developing quantum well devices. The development of quantum well devices is greatly attributed to the advancements in crystal growth techniques. This is because quantum well devices require structures that are of high purity with few defects. Therefore, having great control over the growth of these heterostructures allows for the development of semiconductor devices that can have very fine tuned properties. The theory surrounding quantum well devices has led to significant advancements in the production and efficiency of many modern components such as light emitting diodes, transistors for example. Today, such devices are ubiquitous in modern cell phones, computers, and many other computing devices.

Quantum wells are formed in semiconductors by having a material, like gallium arsenide, sandwiched between two layers of a material with a wider bandgap, like aluminum arsenide. (Other examples: a layer of indium gallium nitride sandwiched between two layers of gallium nitride.) These structures can be grown by molecular beam epitaxy or chemical vapor deposition with control of the layer thickness down to monolayers. Thin metal films can also support quantum well states, in particular, thin metallic overlayers grown in metal and semiconductor surfaces. The vacuum metal interface confines the electron (or hole) on one side, and in general, by an absolute gap with semiconductor substrates, or by a projected band gap with metal substrates. There are 3 main approaches to growing a QW material system: lattice matched, strain balanced, and strained. Lattice matched system: In a lattice matched system, the well and the barrier have a similar lattice constant as the underlying substrate material. A defining property of superlattices is that the barriers between wells are thin enough for adjacent wells to couple. Periodic structures made of repeated quantum wells that have barriers that are too thick for adjacent wave functions to couple, are called multiple quantum well (MQW) structures.

Quantum wells have shown promise for energy harvesting as thermoelectric devices. They are claimed to be easier to fabricate and offer the potential to operate at room temperature. The wells connect a central cavity to two electronic reservoirs. The central cavity is kept at a hotter temperature than the reservoirs. The wells act as filters that allow electrons of certain energies to pass through. In general, greater temperature differences between the cavity and the reservoirs increases electron flow and output power. An experimental device delivered output power of about 0.18 W/cm2 for a temperature difference of 1 K, nearly double the power of a quantum dot energy harvester. The extra degrees of freedom allowed larger currents. Its efficiency is slightly lower than the quantum dot energy harvesters. Quantum wells transmit electrons of any energy above a certain level, while quantum dots pass only electrons of a specific energy. Photons of energy within the well depth are absorbed in the wells and generate electron hole pairs. In room temperature conditions, these photo generated carriers have sufficient thermal energy to escape the well faster than the recombination rate. Elaborate multi junction quantum well solar cells can be fabricated using layer by layer deposition techniques such as molecular beam epitaxy or chemical vapor deposition. It has also been shown that metal or dielectric nanoparticles added above the cell lead to further increases in photo absorption by scattering incident light into lateral propagation paths confined within the multiple quantum well intrinsic layer.

With conventional single junction photovoltaic solar cells, the power it generates is the product of the photocurrent and voltage across the diode. As semiconductors only absorb photons with energies higher than their bandgap, smaller bandgap material absorbs more of the sun's radiative spectrum resulting in a larger current. The highest open circuit voltage achievable is the built in bandgap of the material. The maximum theoretical limit of efficiency for conventional solar cells is determined to be only 31%, with the best silicon devices achieving an optimal limit of 25%. Researchers infer that the resulting increase indicates that the generation of new carriers and photocurrent due to the inclusion of lower energies in the absorption spectrum outweighs the drop in terminal voltage resulting from the recombination of carriers trapped in the quantum wells. Further studies have been able to conclude that the photocurrent increase is directly related to the redshift of the absorption spectrum. Second, due to the strain, there is a splitting of heavy hole and light hole degeneracy. In a heavily compressed material, the heavy holes (hh) move to a higher energy state. In tensile material, light holes (lh) move to a higher energy state. One can calculate the difference in energy due to the splitting of hh and lh from the shear deformation potential, , strain, , and elastic stiffness coefficients, and and Anderson's rule is applied to estimate the conduction band and valence band offsets in energy.