an intrinsic semiconductor

An intrinsic semiconductor is a semiconductor in its pure, undoped state — the conduction comes only from the material itself, with no foreign atoms added. Pure silicon or pure germanium at room temperature are the textbook cases. Its conduction is entirely 'intrinsic', built in, arising from electrons that thermal energy happens to knock across the band gap.

Here is the mechanism, in plain steps. At absolute zero the valence band is completely full and the conduction band is empty, so pure silicon is an insulator. Warm it up, and now and then a bit of thermal energy is enough to boot a valence electron across the 1.1 eV gap into the conduction band. Two carriers are created at once: the electron up in the conduction band, and the hole it leaves behind in the valence band. So a defining rule of the intrinsic state is that electrons and holes are created in exactly equal numbers, n = p. Both drift under a field, both carry current, and the conductivity is small but real — this is why the number of intrinsic carriers rises steeply with temperature, following that e^(-Eg / 2kT) law.

The intrinsic case is the honest baseline against which everything else is measured, but it is rarely useful on its own — its conductivity is both feeble and wildly temperature-sensitive, exactly what you do NOT want in a stable device. The whole art of the semiconductor industry is to overwhelm this trickle of intrinsic carriers with a controlled flood of extrinsic ones by doping, so the material's behavior is set by the engineer, not by the weather. Even so, understanding the intrinsic state is essential: it sets the leakage, the temperature limit, and the carrier balance that doping then tips one way or the other.