Fermi energy
/ FAIR-mee EN-er-jee /
Electrons in a metal are forced to occupy separate energy levels, filling up from the lowest available rung. At absolute zero, when everything has cooled as far as it can, the electrons settle into the lowest slots they can — but since no two can share a slot, they pile up to a definite height. The energy of that topmost filled rung is the Fermi energy.
Think of it as the water line in a tank that has been filled to the brim with the cheapest seats. Everything below is occupied; everything above is empty. Crucially, this top level is not zero energy — the highest electrons are moving very fast, simply because the only seats left for them are high-energy ones.
It matters because almost everything interesting in a metal happens near the Fermi energy: only electrons close to that top can absorb a bit of heat, carry current, or jump to empty levels. A common misconception is that all the electrons share the action — in fact the deep ones are locked in place, and only the lucky few at the top get to move.
In copper the Fermi energy is about 7 electron-volts — so even at the temperature of liquid helium, the topmost electrons are racing at over a thousand kilometres per second, never able to slow down because all the calmer states beneath them are already full.
Copper's Fermi energy (~7 eV) keeps its top electrons racing even near absolute zero.
Strictly, "Fermi energy" means the top filled level at absolute zero. At ordinary temperatures the sharp edge softens a little and people often say "Fermi level" instead; the two are nearly the same in metals, but the distinction matters in semiconductors.