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.