The Fermi Energy is a useful quantity for determining the
characteristics of a system. The Fermi Energy, which is synonymous
with the electron chemical potential at T=0,
represents the energy level that the next electron into the system
must have, to be at the lowest possible freely-available state.
In solids, a related characteristic of the material is the
Fermi Surface. The Fermi Surface represents the 3-D
distribution in reciprocal space of where the Fermi energy lies.
For a free-electron gas in 3 dimensions, the energy is proportional
to k2, and the system is isotropic. Hence, the
Fermi surface is a sphere of radius kF.
In real materials, there is almost always a directional dependence
of the energy. For example, in copper, as shown above, the
energy depends on not just the distance from the k-space origin,
but also whether one is traveling along the line of atoms or
not. (Ie, whether the Miller index is some perturbation
of (100) or not).
