Band structure of insulators, semiconductors and metals

Solid materials can be divided into three classes insulators, which do not readily conduct electricity metals, which easily conduct electricity and semiconductors, which in the presence of an external stimulus such a Hght or a voltage will conduct electricity. Whether or not a material conducts electricity depends on the energy structure of its highest energy electrons. 

In an insulator, the forbidden energy gap between the valence and conduction bands is so large that the thermal energy, kT, per electron is too small to elevate electrons to the upper level, and the solid is an insulator at all temperatures. 

In a metal, the valence and conduction bands overlap (in the ideal case the upper band is half filled). Thus a metal is a conductor, regardless of the magnitude of the thermal energy. In a metal, the electron is not bound to any particular atom so is able to diffuse around the lattice. 

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