Energy Bands in Solids

Energy levels split due to the Pauli exclusion principle, which states that no two electrons can occupy the same energy state simultaneously. When atoms approach each other, their electron orbitals overlap, forcing electrons into different energy states. As more atoms combine, splitting becomes so fine that discrete levels merge into continuous energy bands.

The valence band contains energy levels filled with electrons at absolute zero temperature, while the conduction band sits above it with vacant energy levels. The energy gap between these two bands is called the band gap. This gap determines how easily electrons can be excited into the conduction band for electrical conduction.

The band gap size is crucial because it determines how easily electrons transition into the conduction band. In semiconductors, the band gap is small enough that thermal energy or light can excite electrons across the gap, resulting in electrical conduction. This property distinguishes semiconductors from insulators and conductors.

Silicon has four valence electrons in its 3s and 3p subshells that determine its chemical and electrical properties. These electrons form bands when silicon atoms create a crystal lattice. The valence band contains 4N states and the conduction band contains 4N states, where N is the number of silicon atoms.

In semiconductors like silicon, the valence band and conduction band each contain 4N energy states, where N represents the number of atoms in the crystal. This large number of states creates the continuous band structure. At equilibrium interatomic spacing, these bands form from overlapping 3s and 3p subshells.

Silicon's inner 10 electrons occupy deep-lying energy levels that remain filled and do not participate in bonding or conduction. Only the four valence electrons in the 3s and 3p subshells contribute to the material's electrical properties. These valence electrons form the bands responsible for carrier generation and recombination in semiconductor devices.

As more atoms combine, the number of discrete energy levels increases exponentially, and the splitting between them becomes so fine that individual levels merge into continuous energy bands. At equilibrium interatomic distance, these bands separate into the valence band and conduction band. This band formation is fundamental to understanding semiconductor behavior.