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Solid-State Band Theory

Introduction

Because of the very large number of atoms that interact in a solid material, the energy levels are so closely spaced that they form bands. The highest energy filled band, which is analogous to the highest occupied molecular orbital in a molecule (HOMO), is called the valence band. The next higher band, which is analogous to the lowest unoccupied molecular orbital (LUMO) in a molecule, is called the conduction band. The energy separation between these bands is called the energy gap, Eg.

Idealized representation of energy bands and gaps

The filling of these bands and the size of the energy gap determine if a material is a conductor (a metal), a semiconductor, or an insulator. In metals there is no energy gap between filled and unfilled energy levels. A significant number of electrons are thermally excited into empty levels, creating holes in the filled band. The electrons in a conduction band and the holes in a valence band can move throughout the material, allowing it to easily conduct electricity. In semiconductors Eg is small, but large enough so that a fairly small number of electrons are in the conduction band due to thermal energy, and these materials conduct poorly. In insulators Eg is large so that electrons are not promoted to the conduction band due to thermal energy, and these materials do not conduct electricity.


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