Quantum well

A quantum well is a potential well wherein the energy spectrum of charge carriers is discrete. As opposed to a bulk region, wherein the carriers are free to move in three spatial directions, their motion is free only in two (planar) directions in a quantum well. The quantum size effects take place when the size of a region in at least one of the directions (the direction of growth in the case of semiconductor heterostructure quantum wells - the transverse direction) becomes comparable to the de Broglie wavelength of the carriers (electrons and holes in a semiconductor), resulting in a discrete energy spectrum for them. Semiconductor quantum wells can be realized in double heterostructures. The double heterostructure concept was proposed in 1963 independently by Herbert Kroemer and by Zhores Alferov and Rudolf Kazarinov.

History In 1970, Leo Esaki and Raphael Tsu invented synthetic superlattices. They also 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. Semiconductor materials and devices, and particularly those based on quantum wells, have been a hot topic in the physics research. The development of high-speed and optoelectronic devices based on semiconductor heterostructures has been recognized in the Nobel Prize in Physics for Zhores Alferov and Herbert Kroemer in 2000. 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.

Fabrication 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 three 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. With this method, the bandgap difference there is minimal dislocation but also a minimal shift in the absorption spectrum. Strain-balanced system: In a strain-balanced system, the well and barrier are grown so that the increase in lattice constant of one of the layers is compensated by the decrease in lattice constant in the next compared to the substrate material. The choice of thickness and composition of the layers affect bandgap requirements and carrier transport limitations. This approach provides the most flexibility in design, offering a high number of periodic QWs with minimal strain relaxation. Strained system: A strained system is grown with wells and barriers that are not similar in lattice constant. A strained system compresses the whole structure. As a result, the structure is only able to accommodate a few quantum wells.

Description and overview One of the simplest quantum well systems can be constructed by inserting a thin layer of one type of semiconductor material between two layers of another with a different band-gap. Consider, as an example, two layers of AlGaAs with a large bandgap surrounding a thin layer of GaAs with a smaller band-gap. Let's assume that the change in material occurs along the z-direction and therefore the potential well is along the z-direction (no confinement in the x–y plane.). Since the bandgap of the contained material is lower than the surrounding AlGaAs, a quantum well (Potential well) is created in the GaAs region. This change in band energy across the structure can be seen as the change in the potential that a carrier would feel, therefore low energy carriers can be trapped in these wells. Within the quantum well, there are discrete energy eigenstates that carriers can have. For example, an electron in the conduction band can have lower energy within the well than it could have in the AlGaAs region of this structure. Consequently, an electron in the conduction band with low energy can be trapped within the quantum well. Similarly, holes in the valence band can also be trapped in the top of potential wells created in the valence band. The states that confined carriers can be in are particle-in-a-box-like states.

Physics Quantum wells and quantum well devices are a subfield of solid-state physics that is still extensively studied and researched today. The theory used to describe such systems uses important results from the fields of quantum physics, statistical physics, and electrodynamics.

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