The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.

At absolute zero temperature, electrons fill all energy states up to the Fermi level, leaving upper states empty. As the temperature rises, the energy of electrons increases and they become capable of occupying the vacant states above the Fermi level.

In intrinsic semiconductors, where the concentration of electrons and holes is equal, the Fermi level is situated in the middle of the band gap. This is altered when impurities are added to create either n-type or p-type semiconductors. In n-type semiconductors, with an excess of electrons, the Fermi level shifts closer to the conduction band. Conversely, in p-type semiconductors, where there is a higher concentration of holes, the Fermi level moves closer to the valence band.

The rise in temperature leads to more numbers of electrons making the leap from the valence band to the conduction band, nudging the Fermi level towards the conduction band in the process. This shift affects the conductivity of the semiconductor.

When materials with differing Fermi levels come into contact, electrons flow from the region of higher Fermi levels to the lower one. The movement of electrons aligns the Fermi levels at the junction, establishing an equilibrium. This concept plays a crucial role in the operation of numerous electronic components, enabling the regulation and adjustment of electrical conductivity and the performance of electronic devices.