ABSTRACT
V π where the density of states was obtained from Eq.(40.8). In other words, since each allowed band is associated with a Brillouin zone, the number of electron states in each energy band, including spin, is 2N. If there is one valence electron per atom, the N electrons will fill only half of the states available in the band, as in Figure 42.1. Since nearly-free electrons can be accelerated by an applied electric field, conduction will take place, in this case, as if the electrons were free. The material will exhibit metallic behaviour with an electrical conductivity defined by Eq.(40.50). Note that, if there are two valence electrons per atom, overlap between adjacent bands is predicted by the weak-binding approximation. The Fermi energy
( )kN
Fε is such that the first band is partially empty and the second band is partially filled, and hence, the nearly-free electrons behave much as if they were free electrons, and the solid is also a metal.
