Imagine a piece of pure semiconductor. Electrons in this bulk are free to move around, in three dimensions. In solid state physics, these electrons are sometimes referred to as an electron gas.
It is possible to constrain the movement of the electrons by disallowing one dimension -- that is, by reducing one degree of freedom. The electrons can then move freely in only two dimensions. A system of electrons confined to a plane is called a two-dimensional electron gas, or 2DEG.
Quantum wires have only 1 degree of freedom, and quantum dots have 0 degrees of freedom.
It is important to note that confinement is not perfect. A quantum dot is often defined as confinement to a very small volume of space, such as a sphere that has a diameter on the order of the material's Exciton Bohr Radius. At this size the energy bands of the semiconductor are no longer continuous, which results in the confinement.
Quantum confinement gives rise to many interesting effects, and these effects can be exploited to develop new semiconductor devices. One such type of device are mesoscopic devices, such as single-electron transistors.
Aman Ahuja, Physics Ugrad Student, WPI
'The strength and weakness of physicists is that we believe in what we can measure. And if we can't measure it, then we say it probably doesn't exist. And that closes us off to an enormous amount of phenomena that we may not be able to measure because they only happened once. For example, the Big Bang. ... That's one reason why they scoffed at higher dimensions for so many years. Now we realize that there's no alternative... '