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, E_g.

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 E_g 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 E_g 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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