Conductors, Insulators and Semiconductors: A Band-Theory Classification

Conductors ($E_g \approx 0$, bands overlapping). In a typical metal (copper, silver, aluminium), the valence and conduction bands OVERLAP -- there is effectively no forbidden gap between them at all. A huge number of electrons therefore sit right at the boundary between the two bands, and even the smallest applied electric field can promote them into available nearby states and set them moving -- explaining why a metal conducts electricity so freely, at any temperature, including very close to absolute zero.

Insulators ($E_g$ large, typically $> 3\ \text{eV}$). In a material such as diamond or glass, the forbidden gap between a completely full valence band and a completely empty conduction band is very WIDE. Ordinary thermal energy at room temperature (of order $k_BT \approx 0.026\ \text{eV}$) is utterly inadequate to promote any appreciable number of electrons across so large a gap, so the conduction band stays essentially empty and the material conducts electricity extremely poorly -- an insulator. …