Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as E_n. Higher quantum numbers 'n' yield less negative, closer electron energy levels.

Band Formation:

When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states that no two electrons can simultaneously occupy the same quantum state. As more atoms are combined, the number of discrete energy levels increases, and the splitting becomes so fine that it forms a continuous energy band. At a certain point, known as the equilibrium interatomic distance, these bands become the valence band, filled with electrons, and the conduction band, which is empty at absolute zero temperature.

Energy Bands in Semiconductors:

The energy band structure is more complex in semiconductors like silicon, which has 14 electrons. The inner 10 electrons occupy the deep-lying energy levels and do not contribute to the bonding. The remaining four valence electrons, which are in the 3s and 3p subshells, determine the chemical and electrical properties of the material. As silicon atoms form a crystal lattice, the 3s, and 3p subshells overlap and form bands. At the equilibrium distance in the crystal, these bands contain 4N states for the valence band, and 4N states for the conduction band, where N is the number of silicon atoms.

The bandgap size is crucial because it determines how easily electrons can be excited into the conduction band. This bandgap is small enough for semiconductors that thermal energy or light can excite electrons across the gap, resulting in electrical conduction.