400px|thumb|Schematic of a semiconductor heterostructure quantum well. The shaded (well) region should be narrow enough (L should be typically less than 30 nm) for quantum effects to be manifested, in particular, for a discrete energy spectrum of charge carriers to be sufficiently resolved at room temperature.

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.

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. 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.

Thermoelectrics

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&nbsp;W/cm<sup>2</sup> for a temperature difference of 1&nbsp;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.

Single-junction solar cells

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.

: <math>\Delta E=-2a\left(\frac{C_{11}-C_{12{C_{11\right)\epsilon</math>

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, <math>b</math>, strain, <math>\epsilon</math>, and elastic stiffness coefficients, <math>C_{11}</math> and <math>C_{12}</math>. and Anderson's rule is applied to estimate the conduction band and valence band offsets in energy.

thumb|Top: Thermionic Escape of Charge Carriers, Bottom: Tunneling of Charge Carriers

Carrier capture and lifetime

With the effective use of carriers in the QWs, researchers can increase the efficiency of quantum well solar cells (QWSCs). Within QWs in the intrinsic region of the p-i-n solar cells, optically generated carriers are either collected by the built-in field or lost due to carrier recombination.

: <math>\frac{1}{\tau_\text{tun. = \frac{n \pi \hbar}{2t_\text{w}^2m_\text{w}^*} e^{\frac{-2}{\hbar}\int_{0}^{t_\text{b \sqrt{2m_\text{b}^* (E_\text{b} - E(z)z)}\,dz}

</math>

: <math>\frac{1}{\tau_\text{therm. = \frac{1}{t_\text{w\sqrt{\frac{kT}{2\pi m_\text{w}^* e^{-\frac{E_\text{b{kT</math>,

where <math>m_\text{b}^*</math> and <math>m_\text{w}^*</math> are effective masses of charge carriers in the barrier and well, <math>E_\text{b}</math> is the effective barrier height, and <math>E(z)</math> is the electric field.

Then one can calculate the escape lifetime by the following: to a 100-period In<sub>0.30</sub>Ga<sub>0.70</sub>As(3.5&nbsp;nm)/GaAs(2.7&nbsp;nm)/ GaAs<sub>0.60</sub>P<sub>0.40</sub>(3.0&nbsp;nm) QWSC by Fuji et al. The bulk material shows higher EQE values than those of QWs in the 880-900&nbsp;nm region, whereas the QWs have higher EQE values in the 400-600&nbsp;nm range. and InGaAsP by Jain et al. are compared by Sayed Like the 1.1–1.3&nbsp;eV range, the EQE of the bulk material is higher in the longer wavelength region of the spectrum, but QWs are advantageous in the sense that they absorb a broader region in the spectrum. Furthermore, they can be grown in lower temperatures preventing thermal degradation.