2.5. METALS AND INSULATORS 43
Figure 2.8: Schematic of the Fermi function for electrons and other fermions. In general the
position ofEFis dependent on temperature. The occupation probability is at 0.5 at the Fermi
energy.
Thus, even though Pauli exclusion principle would allow two (or more) electrons to reside on
the state, the repulsion would not. In such cases the occupation function can be shown to be
f(E)=1
1
gdexp(
E−EF
kBT)
+1
(2.4.4)
In figure 2.8 we show a schematic of the Fermi function for electrons and its dependence on
temperature. It is important to note that atE=EF,f(E)=0. 5 regardless of the temperature.
At zero temperature, the Fermi function becomes a step function withf(E<EF)=1. 0 and
f(E)>EF=0. 0.
2.5 METALS AND INSULATORS
Band theory shows that the allowed energy states of electrons in a crystalline material are de-
scribed by a series of allowed bands separated by forbidden bandgaps. Two important situations