a semiconductor

A semiconductor sits in the middle between conductor and insulator — hence the name, 'half-conductor'. It conducts, but poorly and reluctantly, and the exciting part is that its conduction can be switched, tuned, and controlled. Silicon is the star; germanium, gallium arsenide, and silicon carbide are others. This controllability is what makes every chip, solar cell, LED, and transistor possible, so semiconductors are arguably the most important material class of the modern age.

The band-theory picture is the same as an insulator but with a SMALL band gap — for silicon only about 1.1 eV, for germanium 0.67 eV. That gap is small enough that at room temperature a modest number of electrons have enough thermal energy to jump from the valence band up into the conduction band. Each electron that leaves also frees up a positive 'hole' behind it, and both the electron above and the hole below can carry current. So a pure semiconductor conducts a little, and here is the honest inversion from metals: HEAT IT and it conducts BETTER, because warmth frees more carriers across the small gap. Resistivity falls with temperature, the exact opposite of a conductor. Pure silicon's conductivity sits around 10^-3 to 10^-4 S/m, halfway (on a log scale) between copper and quartz.

The real magic is doping. Adding just a few foreign atoms per million — phosphorus to donate electrons, boron to accept them — changes the conductivity by many orders of magnitude and decides whether the carriers are mostly negative electrons (n-type) or positive holes (p-type). Join a piece of n-type to a piece of p-type and you get a p-n junction, the one-way valve at the heart of every diode and transistor. So the whole edifice of electronics is built by deliberately, precisely dirtying an otherwise mediocre conductor.