the band gap
The band gap is the height of the forbidden step between the filled valence band and the empty conduction band — the energy an electron must gain in one leap to go from bound to free. No electron is allowed to have an energy inside the gap, so it is all-or-nothing: an electron either stays down in the valence band or makes the full jump up into the conduction band. Measured in electron-volts (eV), the band gap is the single number that most cleanly separates conductors, semiconductors, and insulators.
The rule is simple and worth memorizing. No gap (or overlapping bands): metal, always conducting. Small gap, up to roughly 2 eV: semiconductor, where room-temperature heat can push a useful number of electrons across. Large gap, above roughly 3 eV: insulator, where the jump is so high almost nothing makes it. Silicon's gap is 1.1 eV, germanium's 0.67 eV, gallium arsenide's 1.42 eV — all semiconductors. Diamond's is 5.5 eV and quartz's near 9 eV — insulators. The link between gap and conduction is exponential: the number of thermally excited carriers goes roughly as e^(-Eg / 2kT), so even a modest increase in the gap slashes the conductivity dramatically.
The band gap is not just a sorting label; it is a design knob. It sets the color of light an LED emits and the color a solar cell can absorb (photon energy must exceed Eg to be captured). It sets how hot a device can run before heat alone floods it with carriers and it stops switching — which is why wide-gap materials like silicon carbide (3.3 eV) and gallium nitride are prized for high-power, high-temperature electronics. Choosing a semiconductor is, to a large degree, choosing a band gap.
The band gap sets an LED's color directly. A material with a gap near 1.9 eV emits red light, one near 2.5 eV emits green, and a wide-gap material near 2.7 eV or more emits blue — the hard-won blue LED that unlocked white lighting needed a wide-gap semiconductor (gallium nitride) that engineers struggled for decades to make.
No gap = metal; small gap = semiconductor; large gap = insulator. The gap also sets LED and solar-cell color.
The 2-to-3 eV boundary between semiconductor and insulator is a soft convention, not a law of nature — the same material can act as a leaky insulator or a poor semiconductor depending on temperature and purpose. Also, band gaps shrink slightly as a material heats up.