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This question already has an answer here:

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?

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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ possible duplicate of What are "electron holes" in semiconductors? $\endgroup$ – Phonon Aug 2 '14 at 21:04
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    $\begingroup$ For a perfect undoped Si crystal at T=0K you are correct. For imperfect doped Si at any temperature above zero you need to do more figuring... $\endgroup$ – Jon Custer Aug 2 '14 at 23:13
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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.

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It's not only a question of purity. For example in the case of III-V materials, also antisite defects (e.g. As on a Ga site) can create doping, although the crystal would still not contain any contamination.

In fact, when you buy semi-insulating GaAs or InP, this means that there are purposely deep traps introduced to capture excess electrons.

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