Quantum well

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 originally 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.

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 aluminium arsenide. (Other example: 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, metallic thin overlayers grown in metal and semiconductor surfaces. The electron (or hole) is confined by the vacuum-metal interface in one side, and in general, by an absolute gap with semiconductor substrates, or by a projected band gap with metal substrates.

Applications

Because of their quasi-two dimensional nature, electrons in quantum wells have a density of states as a function of energy that has distinct steps, versus a smooth square root dependence that is found in bulk materials. Additionally, the effective mass of holes in the valence band is changed to more closely match that of electrons in the conduction band. These two factors, together with the reduced amount of active material in quantum wells, leads to better performance in optical devices such as laser diodes. As a result quantum wells are in wide use in diode lasers, including red lasers for DVDs and laser pointers, infra-red lasers in fiber optic transmitters, or in blue lasers. They are also used to make HEMTs (High Electron Mobility Transistors), which are used in low-noise electronics. Quantum well infrared photodetectors are also based on quantum wells, and are used for infrared imaging.

By doping either the well itself, or preferably, the barrier of a quantum well with donor impurities, a two-dimensional electron gas (2DEG) may be formed. Such a structure forms the conducting channel of a HEMT, and has interesting properties at low temperature. One such property is the quantum Hall effect, seen at high magnetic fields. Acceptor dopants can also lead to a two-dimensional hole gas (2DHG).

Saturable absorber

A quantum well can be fabricated as a saturable absorber utilizing its saturable absorption property. Saturable absorbers are widely used in passively mode locking lasers. Semiconductor saturable absorbers (SESAMs) were used for laser mode-locking as early as 1974 when p-type germanium was used to mode lock a CO₂ laser which generated pulses ~500 ps. Modern SESAMs are III-V semiconductor single quantum well (SQW) or multiple quantum wells (MQW) grown on semiconductor distributed Bragg reflectors (DBRs). They were initially used in a Resonant Pulse Modelocking (RPM) scheme as starting mechanisms for Ti:sapphire lasers which employed KLM as a fast saturable absorber. RPM is another coupled-cavity mode-locking technique. Different from APM lasers which employ non-resonant Kerr-type phase nonlinearity for pulse shortening, RPM employs the amplitude nonlinearity provided by the resonant band filling effects of semiconductors. SESAMs were soon developed into intracavity saturable absorber devices because of more inherent simplicity with this structure. Since then, the use of SESAMs has enabled the pulse durations, average powers, pulse energies and repetition rates of ultrafast solid-state lasers to be improved by several orders of magnitude. Average power of 60 W and repetition rate up to 160 GHz were obtained. By using SESAM-assisted KLM, sub-6 fs pulses directly from a Ti:sapphire oscillator was achieved. A major advantage SESAMs have over other saturable absorber techniques is that absorber parameters can be easily controlled over a wide range of values. For example, saturation fluence can be controlled by varying the reflectivity of the top reflector while modulation depth and recovery time can be tailored by changing the low temperature growing conditions for the absorber layers. This freedom of design has further extended the application of SESAMs into modelocking of fibre lasers where a relatively high modulation depth is needed to ensure self-starting and operation stability. Fibre lasers working at ~1 μm and 1.5 μm were successfully demonstrated.^[1]

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.^[2][3]

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 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.^[2]

One possible application is to convert waste heat from electric circuits, e.g. in computer chips, back into electricity, reducing the need for cooling and energy to power the chip.^[2]

Solar cells

Quantum wells have been proposed to increase the efficiency of solar cells. The theoretical maximum efficiency of traditional single-junction cells is about 34%, due in large part to their inability to capture many different wavelengths of light. Multi-junction solar cells, which consist of multiple p-n junctions of different bandgaps connected in series, increase the theoretical efficiency by broadening the range of absorbed wavelengths, but their complexity and manufacturing cost limit their use to niche applications. On the other hand, cells consisting of a p-i-n junction in which the intrinsic region contains one or more quantum wells, lead to an increased photocurrent over dark current, resulting in a net efficiency increase over conventional p-n cells.^[4] 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.^[5] 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.^[6]

See also

• Particle in a box
• Quantum wire, carriers confined in two dimensions.
• Quantum dot, carriers confined in all three dimensions.
• Quantum well laser
• Modulating retro-reflector

References

General

• Thomas Engel, Philip Reid Quantum Chemistry and Spectroscopy. ISBN 0-8053-3843-8. Pearson Education, 2006. Pages 73–75.