## Parabolic And Triangular Quantum Wells 441 Parabolic well

The case of the parabolic well is well known in solid state physics since the vibrations of the atoms in a crystal lattice, whose quantification gives rise to phonons, are described in a first approximation by harmonic oscillators. In addition, a magnetic field applied to a two-dimensional electron system gives rise to a parabolic potential, and the electrons oscillate at the so-called cyclotron frequency. Parabolic quantum well profiles can also be produced by the MBE growth technique. In this...

## Square Quantum Well Of Finite Depth

The quantum wells for electrons and holes in GaAs nanostructures surrounded by higher gap AlGaAs, studied in the previous section, are not of infinite height, as was assumed in order to derive closed expressions for the energy and wave functions in Section 4.2. In fact, the value of the height of the potential for electrons should coincide with the discontinuity AEc that appears at the interface in the conduction bands of AlGaAs and GaAs, which for the above system is of the order of some...

## 1

Before we study the effects of reduced size and dimensionality on the properties of solids, we review in this chapter those concepts of solid state physics which are essential for the understanding of the behaviour of quantum nanostructures. For instance, the behaviour of electrons in a quantum well is very different to the case of bulk solids if their motion is across the potential barriers confining the quantum well, but is very similar if the motion is parallel to the interfaces. In Section...

## Band Structure In Quantum Wells

In order to interpret correctly the optical absorption experiments in quantum wells, we need to know the band structure. Figure 8.2 of Chapter 8 shows the absorption spectra of a 40 period multiple quantum well (MQW) GaAs-AlGaAs, in which the barriers have a width of 7.6nm 3 . Observe that the spectrum follows in general the steps of the DOS curve in 2D semiconductors (Section 4.2). At the edge of each step there is a sharp maximum that, as will be shown in the next section, is attributed to...

## Lattice Vibrations

In this section we pretend to give a short review of vibrations in periodic systems such as crystals. The adiabatic approximation in solid state physics allows the separate study of those properties of materials, attributed to electrons, like the electrical conductivity, and those which depend on the vibrations of the atoms, such as the thermal properties. Suppose a mechanical wave, or a sound wave, travelling through a solid. If its wavelength X is much larger than the lattice constant of the...

## Quantum Transport In Nanostructures

Next we are going to deal with quantum transport, which is produced when nanostructures are connected to an external current by means of leads or contacts. This transport is also called mesoscopic transport. As we explained in Section 1.3, the term mesoscopic refers to systems with a range of sizes between the macroscopic world and the microscopic or atomic one, and which have to be explained by quantum mechanics. These systems in electronics are also known as submicron or nanoscale devices....

## Perpendicular Transport

In this section, we study the motion of the carriers perpendicularly to the planes of the potential barriers separating quantum heterostructures. This kind of transport is often associated to quantum transmission or tunnelling, since the carriers do not need to have enough energy to surmount the barriers. When a particle goes through a potential barrier, the wave function and its derivative in the perpendicular direction must be continuous, which leads to transmitted and reflected wave...

## Mosfet Structures

The main contribution to present technology in general, and microelectronics in particular, is probably the metal-oxide-semiconductor field-effect-transistor MOSFET . This device is the basic unit of present ultra-large-scale-integration ULSI microelectronics industry. It is estimated that MOSFET-based electronic devices now constitute close to 90 of the semiconductor device market. The MOSFET is formed by a MOS structure and two p-n junctions in which the n material is heavily doped Figure 5.1...