Band Theory

Band theory models how electrons behave in solids by extending molecular orbital theory. When many atoms combine in a solid, their atomic orbitals overlap to form an enormous number of closely spaced molecular orbitals. These orbitals group together into continuous energy ranges called bands, separated by energy gaps. This framework explains why different solids conduct electricity differently based on their band structure and electron distribution.

In conductors such as copper, valence electrons occupy a band containing many empty orbitals. Electrons can readily move between these orbitals with minimal energy, allowing them to flow freely through the solid. These mobile valence electrons are responsible for the excellent electrical conductivity observed in metallic conductors, making them ideal for transmitting electrical current.

The valence band is the highest-energy band containing electrons in the ground state, with few to no empty orbitals. The conduction band sits just above it and contains empty orbitals. Electrons must cross the energy gap between these bands to move freely through the solid. The size of this band gap determines whether a material conducts electricity easily or poorly.

Insulators have a large band gap between valence and conduction bands, making it extremely difficult for electrons to jump across and conduct electricity, resulting in poor conductivity. Semiconductors have a smaller band gap, allowing valence electrons to reach the conduction band when moderate energy is supplied. This makes semiconductors more conductive than insulators but less conductive than metals.

When valence electrons in semiconductors are excited to the conduction band, they can move freely between empty orbitals there. Additionally, the empty orbitals they leave behind in the valence band facilitate electron movement within that band. This dual effect increases the overall electrical conductivity of the semiconductor, enabling it to conduct electricity under appropriate energy conditions.

As the number of atoms in a solid increases, the number of molecular orbitals increases proportionally. In solids with an exceedingly large number of atoms, these orbitals become so closely spaced that they form continuous energy ranges called bands rather than discrete energy levels. This transformation from discrete molecular orbitals to continuous bands is fundamental to understanding electronic properties of bulk solids.

Glass and other insulators have a large energy gap, or band gap, between the valence and conduction bands. This wide gap prevents valence electrons from easily crossing to the conduction band where they could move freely. Without accessible empty orbitals in the conduction band, electrons remain localized and cannot flow through the material, resulting in poor electrical conductivity.