Quantum well

A quantum well is the realization of the potential hole that confines particles, forcing their localization. A quantum well is used to confine electrons to specific energy levels. The effects of quantum confinement take place when the thickness of the well becomes comparable to the coherence length of the carriers (usually electrons and gaps); as a result, the particles confined in the well can occupy a discrete number of energy levels, forming a nearly two-dimensional gas.

The concept of a quantum well was proposed in 1963 independently by Herbert Kroemer and Zhores Alferov and R.F. Kazarinov. Herbert Dingle made the first experimental observations of the phenomenon in 1974, a decade after its theoretical prediction.

Quantum wells are called “wells” not only because of their behavior in trapping electrons like a well would trap water, but also because of their appearance when represented graphically. When quantum wells are represented on energy vs position graphs, they look like deep valleys, or wells, often rectangular in shape. A quantum well is a type of potential well, which means that there is a potential for the production of a minimal, fixed amount of energy.

Grown, rather than created, a quantum well is usually made of material such as gallium arsenide surrounded by aluminum arsenide. Wells are grown, most often, by a process called molecular beam epitaxy, which uses an effusion cell to fire molecules of the substance at a base substance. This method creates a single atomic layer of the well material with each firing of the cell.

Structure

Planar semiconductor heterostructure, grown by epitaxial techniques, consisting of a layer enclosed between two semiconductors (the barriers) different from the one of which the well is made. The semiconductors making up the well and the barriers are chosen so that the discontinuity between their conduction (or valence) bands gives rise along the direction of growth to a potential hole in which the electrons (or holes) are confined and which limits their translational motion to the two dimensions parallel to the plane of the quantum well.

In the most common quantum wells (type I) the energy gap between valence band and conduction band of the semiconductor constituting the well is less than that of the semiconductors constituting the barriers and the alignment between the valence band in the well and in the barriers (the valence-band offset) is such that both electrons and holes are confined within the quantum well. The confinement potential (of the order of 100 meV) determines for each type of free carriers (negative electrons and positive holes) one or more bound states inside the well corresponding to the quantization of their motion along the growth direction and to the localization of their wave function which decreases exponentially penetrating the barriers.

To achieve such quantum confinement, the thickness of the well (typically on the order of 10 nm) is required to be less than the quantum coherence length of the wavefunction (limited by diffusion processes due to lattice imperfections or vibrations), and this implies the nanoscopic character of a quantum well and other heterostructures related to it, such as coupled quantum wells.

The two-dimensional confinement of electrons and/or holes in a quantum well implies large modifications of their electronic and optical properties. In particular, it allows very high mobility values to be achieved by doping modulation, as well as engineering the energy levels and oscillator forces responsible for optical transitions. This has led to the study of fundamental physical phenomena, such as the integer and fractional quantum Hall effect, as well as to the realization of optoelectronic devices, such as lasers or quantum well electro-optic modulators, and transistors with high electronic mobility.

Leave a Comment