Page 305 - Instant notes

Strong solid phase interactions 291

Fermi level, E f (Fig. 2). The Fermi energy is more precisely defined as the energy where
the probability of it being occupied by an electron is ½. Above zero Kelvin, electrons are
thermally excited to higher levels. The assumptions used to obtain the Boltzmann
distribution for atomic and molecular energy distributions (Topic G8) do not apply to
electrons in solids. With the limitations of the band structure, the Pauli exclusion
principle, and the indistinguishability of electrons, the thermal excitation is best described
by Fermi-Dirac statistics. The probability f(E) of occupation for an electron at an energy
E at a temperature, T is given by:

The resulting form of the electron distribution is illustrated for an idealized band in Fig.
3.

Fig. 3. Fermi-Dirac distribution of
electrons in an idealized band.

Metals, insulators and semiconductors
In real solids, a number of different bands are formed from the interaction of a number of
atomic orbitals. The relative energy of these bands and the number of electrons which
occupy them dictate the electrical properties of the solid.
The conductivity of a solid is proportional to the number and mobility of the charge
carriers. In a metal, or a metallic conductor, one or more of the bands is only partially