The Fermi level

Key point: The Fermi level is the highest occupied energy level in a solid at T=0. At T=0, electrons occupy the individual molecular orbitals of the bands in accordance with the building-up principle. If each atom supplies one’s electron, then at T=0 the lowest N orbitals are occupied. The highest occupied orbital at T=0 is called the Fermi level; it lies near the centre of the band (Fig. 3.67). When the band is not completely full, the electrons close to the Fermi level can easily be promoted to nearby empty levels. As a result, they are mobile and can move relatively freely through the solid, and the substance is an electrical conductor. The solid is in fact a metallic conductor. We have seen that the criterion of metallic conduction is the decrease of electrical conductivity with increasing temperature. This behaviour is the opposite of what we might expect if the conductivity were governed by thermal promotion of electrons above the Fermi level. The competing effect can be identified once we recognize that the ability of an electron to travel smoothly through the solid in a conduction band depends on the uniformity of the arrangement of the atoms. An atom vibrating vigorously at a site is equivalent to an impurity that disrupts the orderliness of the orbitals. This decrease in uniformity reduces the ability of the electron to travel from one edge of the solid to the other, so the conductivity of the solid is less than at T=0. If we think of the electron as moving through the solid, then we would say that it was ‘scattered’ by the atomic vibration. This carrier scattering increases with increasing temperature as the lattice vibrations increase, and the increase accounts for the observed inverse tempera ture dependence of the conductivity of metals.

Fig. 3.67 If each of the N atoms supplies one’s electron, then at T=0 the lower ½N orbitals are occupied and the Fermi level lies near the centre of the band.

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مواضيع ذات صلة

Densities of states

Band formation by orbital overlap

The conductivities of inorganic solids

Nonstoichiometry

Intrinsic point defects

Solubility

Thermal stabilities of ionic solids

The Born–Mayer equation

Structure maps

The radius ratio

Ionic radii

Characteristic structures of ionic solids