Bandgap

A bandgap, in solid state physics, is the energy difference between the top of the valence band and the bottom of the conduction band in a crystalline material. This gap determines whether a material behaves as a conductor, semiconductor, or insulator at a given temperature. Electrons must acquire energy at least equal to the bandgap to transition from a bound state in the valence band to a conducting state in the conduction band. The band structure of a material can feature a direct bandgap or an indirect bandgap: in a direct gap, the conduction-band minimum and valence-band maximum occur at the same crystal momentum, allowing efficient radiative transitions; in an indirect gap, a phonon is required to conserve momentum, making light emission less efficient.

The bandgap strongly influences optical and electronic properties. Absorption of photons with energies above the bandgap initiates electronic excitation, setting the absorption edge and the spectral response of devices such as photodetectors and solar cells. The intrinsic carrier concentration depends exponentially on the bandgap, with ni ~ sqrt(NcNv) exp(-Eg/(2kT)). Temperature generally reduces the bandgap in most materials, a behavior described by empirical models like the Varshni equation.

Common bandgap values at room temperature provide a sense of material classes: silicon about 1.12 eV, gallium arsenide about 1.42 eV, gallium nitride around 3.4 eV, zinc oxide around 3.3 eV, and silicon carbide ranging roughly 2.3–3.3 eV depending on polytype. Direct-gap semiconductors (e.g., GaAs, GaN) are preferred for light emission, while indirect-gap materials (e.g., silicon) excel in electronics but emit light inefficiently.

Bandgap engineering uses alloying, quantum confinement, and heterostructures to tailor Eg and its temperature dependence for specific applications in electronics, optoelectronics, and photovoltaics.