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This diagram illustrates a direct semiconductor (A), an indirect semiconductor (B), and a semimetal (C).

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. Metals have a partially filled conduction band. A semimetal is a material with a small overlap in the energy of the conduction band and valence bands.^[1]

Insulators, semiconductors, and semimetals differ from metals in that their electrical conductivity increases with temperature rather than decreasing. Insulators such as diamond have larger band gaps than semiconductors. To classify semiconductors and semimetals, the energies of their filled and empty bands must be plotted against the crystal momentum of conduction electrons. According to the Bloch theorem the conduction of electrons depends on the periodicity of the crystal lattice in different directions.

In a semimetal, the bottom of the conduction band is typically situated in a different part of momentum space (at a different k-vector) than the top of the valence band. One could say that a semimetal is a semiconductor with a negative indirect bandgap, although they are seldom described in those terms.

Schematically, the figure shows

A) a semiconductor with a direct gap (like e.g. CuInSe₂),

B) a semiconductor with an indirect gap (like Si) and

C) a semimetal (like Sn or graphite).

The figure is schematic, showing only the lowest-energy conduction band and the highest-energy valence band in one dimension of momentum space (or k-space). In typical solids, k-space is three dimensional, and there are an infinite number of bands.

Unlike a regular metal, semimetals have charge carriers of both types (holes and electrons), so that one could also argue that they should be called 'double-metals' rather than semimetals. However, the charge carriers typically occur in much smaller numbers than in a real metal. In this respect they resemble degenerate semiconductors more closely. This explains why the electrical properties of semimetals are partway between those of metals and semiconductors.

As semimetals have fewer charge carriers than metals, they typically have lower electrical and thermal conductivities. They also have small effective masses for both holes and electrons because the overlap in energy is usually the result of the fact that both energy bands are broad. In addition they typically show high diamagnetic susceptibilities and high lattice dielectric constants.

The classic semimetallic elements are arsenic, antimony, and bismuth. These are also considered metalloids but the concepts are not synonymous. Semimetals, in contrast to metalloids, can also be compounds, such as HgTe^[2], and tin and graphite are typically not considered metalloids.^[3]

[edit] See also

• Solid-state physics
• Charge transfer insulators
• Mott insulators
• Hubbard model

[edit] References