There is no official rule which decides whether the band gap is small enough to be called an intrinsic semiconductor, or large enough to be called an insulator. It is something you can judge for yourself depending on the situtation.
An extrinsic semiconductor is an insulator which has been doped with impurities. These impurities have their own bands:
Doping to produce extrinsic semiconductors requires remarkably low levels of impurities, such as a one in a billion atoms. There are two types of extrinsic semiconductors:
N-type: These have an electron-filled donor band close in energy to the conductance band of the insulator. Heat promotes electrons to the conductance band which can then move freely, turning the insulator into a semiconductor.
P-type: These have an empty acceptor band close to the filled valance band of the insulator. Heat promotes electrons into the acceptor band. The holes left over in the valance band are then able to move freely, turning the insulator into a semiconductor.
The trick to remember these is that negative electrons carry charge in the n-type semiconductor, while positive hole carry charge in the p-type semiconductor.
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