The Fermi Level

Abstract

The Fermi level is the maximum energy of the electrons in a material. Effectively there is a Fermi equation: EF = E max. This chapter examines the discrete electron energy levels in individual atoms as a consequence of the Pauli exclusion principle, the corresponding energy bands in a material composed of many atoms or molecules, and the way in which conductor, insulator and semiconductor materials depend on the position of the Fermi level relative to the energy bands. It explains: the concepts of electron mobility, mean free path and conductivity; the dielectric effect and capacitance; p-type, n-type, intrinsic and extrinsic semiconductors; and the behaviour of some simple microelectronic devices. Enrico Fermi was the son of a minor railway official in Rome. He had a meteoric scientific career in Italy, developing Fermi-Dirac statistics for the energies of fundamental fermion particles (such as electrons and protons), discovering the neutrino, and explaining the behaviour of different materials under bombardment from fast and slow neutrons. After initially joining Mussolini’s Fascist Party, he became unhappy at the level of anti-Semitism (his wife was Jewish) and left suddenly for America, immediately after receiving the Nobel Prize in Sweden. At Columbia and Chicago Universities and at Los Alamos National Labs, he played a key scientific role in developing controlled fission in an atomic pile, leading to the development of the atomic bomb towards the end of the Second World War, and the nuclear energy industry after the war.