# How should semiconductors be understood? [duplicate]

In the chemistry setting, a doped semiconductor is a crystal lattice with holes/extra electrons in it.

In the band/quantum mechanical picture, these holes/extra electrons can be seen as the amount of missing/excess charges from a full band of energy states.

Therefore, in a pure silicon crystal, with full covalent bonds and thus no holes or extra electrons, the valence band is completely full, and the conducting band is completely empty.

Which means that Silicon is an insulator, since the Fermi level lies above the valence and below the conducting band. What are the holes in my reasoning?

## marked as duplicate by Brandon Enright, Ali, Kyle Kanos, Qmechanic♦Aug 4 '14 at 10:25

Your reasoning is fine and indeed the band gap of silicon is $1.12$ eV, which is $43kT$ at room temperature, so thermal promotion of electrons from the valence to the conduction bands at room temperature should be negligable. The trouble is that it's exceedingly hard to get silicon so pure that there are no gap states, and while the conductivity of (relatively) pure silicon is about ten orders of magnitude lower than copper, it's still a lot higher than good insulators like glass.