Fermi level is deﬁned as the energy level separating the ﬁlled states from the empty states at 0 K. It is also the highest ﬁlled energy level in a metal. This deﬁnition needs to be modiﬁed for a semiconductor since these have an energy gap between the ﬁlled states (valence band) and empty states (conduction band). The expression for the carrier concentration (n or p) in
In metals the Fermi level separates the ﬁlled and empty states. This is because metals have partially ﬁlled energy bands and the Fermi level lies within the band. This deﬁnition cannot be used for semiconductors. Another deﬁnition is that Fermi level deﬁnes the average energy required to remove an electron from the material. This is called the work function, denoted by φ, and is the energy diﬀerence between the Fermi level and the vacuum level. This deﬁnition can also used for semiconductors, with the realization that electrons in the CB and the holes in the VB are linked. So the Fermi level, deﬁnes the average potential energy per electron for electrical work. If an external electric ﬁeld is applied the Fermi level in the material will no longer be uniform. This will be important when considering junctions formed between diﬀerent semiconductors and between semiconductors and metals.