How to calculate the Fermi Energy: One possibility to calculate the fermi energy of a certain
material is to construct it straightforward out of the density of states. To get the density of states we
first need the dispersion relationship. By calculating the energy for everyk-value we can look how
many states there are at a certain energy. The curve we get, when we integrate this density of states
gives us the total number of states over the energy. Assuming that you know how many electrons
belong to the material you can read the fermi energy out of that curve.
An example is given in fig. 51 for the transition metal Osmium. The energy, where the curve for the
total number of states reaches the number of electrons determines the fermi energy for Osmium.
Figure 51: Density of states of the transition metal Osmium plus its integrated signal