Intrinsic carrier concentration in doped semiconductors For an intrinsic semiconductor, due to thermal energy we get some charge carriers whose concentration is known as intrinsic carrier concentration.
Now if we dope the material we'll have carriers both due to donation and due to thermal energy generation.
In this case is the intrinsic carrier concentration still defined to be equal to the thermally generated carriers?
And in what way might this doping affect the number of intrinsic carrier concentration?
 A: In heavily-doped semiconductors, acceptor and donor energy levels (which are close to the valence and conduction band edges, respectively) form energy bands, effectively moving the valence and conduction band edges toward the middle of the band gap, and hence effectively reducing the band gap. This is called band gap narrowing. Since the intrinsic carrier concentration is related to band gap, i.e.
$$ n_i = \sqrt{N_CN_V}\exp\left(\frac{-E_g}{2k_BT}\right),$$
heavy doping can increase the intrinsic carrier concentration, in the sense that in a semiconductor compensated by large and equal concentrations of acceptors and donors, the electron and hole densities will be greater than $n_i$ of a pure sample.
A: Intrinsic carrier concentration is the concentration of electrons or holes in a pure, undoped, semiconductor. Doping a semiconductor changes the concentration of electrons and holes but it doesnt change the intrinsic concentration. It just stops being an example of an intrinsic semiconductor. Its the same as heating water above 0 C doesnt change the freezing point of water. You just no longer have ice.
