bandgaps

In solid state physics, a bandgap or energy gap is the energy difference between the top of the valence band and the bottom of the conduction band in a crystalline material. In a perfect crystal, allowed energy levels form bands separated by gaps. The size and nature of the bandgap determine a material’s electrical behavior: metals have overlapping bands, insulators have large gaps, and semiconductors have moderate gaps that can be tuned by temperature, doping, or quantum effects.

Direct vs indirect bandgaps: If the conduction-band minimum and valence-band maximum occur at the same crystal momentum, the material has a direct bandgap, enabling efficient radiative transitions and light emission. Indirect bandgaps require phonons to conserve momentum, reducing optical efficiency and making such materials better suited to electronic applications.

Bandgaps vary with temperature and pressure and can be engineered by alloying or quantum confinement. In nanoscale structures such as quantum wells, wires, and dots, confinement raises the effective bandgap and shifts optical properties, enabling size-tuned devices.

Examples include silicon, an indirect bandgap semiconductor of about 1.1 eV at room temperature; gallium arsenide, a direct bandgap semiconductor of about 1.42 eV; and diamond, with a wide gap near 5.5 eV. Some materials, such as graphene, lack a conventional bandgap, while many metals have partially filled bands.

Band structure theory, arising from solving the Schrödinger equation for electrons in a periodic lattice, yields E(k) relations plotted in the Brillouin zone. Bandgaps influence a wide range of devices, including diodes, transistors, LEDs, and solar cells.