Fermi level in the context of Chemical potential

A metal (from Ancient Greek μέταλλον (métallon) 'mine, quarry, metal') is a material that, when polished or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. These properties are all associated with having electrons available at the Fermi level, as opposed to nonmetallic materials which do not. Metals are typically ductile (can be drawn into a wire) and malleable (can be shaped via hammering or pressing).

A metal may be a chemical element such as iron; an alloy such as stainless steel; or a molecular compound such as polymeric sulfur nitride. The general science of metals is called metallurgy, a subtopic of materials science; aspects of the electronic and thermal properties are also within the scope of condensed matter physics and solid-state chemistry, it is a multidisciplinary topic. In colloquial use materials such as steel alloys are referred to as metals, while others such as polymers, wood or ceramics are nonmetallic materials.

A semimetal is a material with a small energy overlap between the bottom of the conduction band and the top of the valence band, but they do not overlap in momentum space. According to electronic band theory, solids can be classified as insulators, semiconductors, semimetals, or metals. In insulators and semiconductors the filled valence band is separated from an empty conduction band by a band gap. For insulators, the magnitude of the band gap is larger (e.g., > 4 eV) than that of a semiconductor (e.g., < 4 eV). Because of the slight overlap between the conduction and valence bands, semimetals have no band gap and a small density of states at the Fermi level. A metal, by contrast, has an appreciable density of states at the Fermi level because the conduction band is partially filled.

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.

The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi level (also called electrochemical potential).There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article:

In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a semiconducting material, the valence band is located below the Fermi level, while the conduction band is located above it.

The distinction between the valence and conduction bands is meaningless in metals, because conduction occurs in one or more partially filled bands that take on the properties of both the valence and conduction bands.