Understanding Freeze-Out in Semiconductors at Low Temperatures

[dreamldw]

Studying the semiconductor in equilibrium, i found a sentence which i don't understand.

"At the very low temperature, freeze-out occurs; the Boltzmann approximation is no longer valid."

I know that freeze-out occurs at the very low temperature, but why is it that the Boltzmann approximation is no longer valid?

 

[f95toli]

Because the Boltzmann distribution comes from a classical theory. At low temperatures "quantum effects" start to become noticeble and you have to use the Fermi-Dirac distribution (for Fermions) or the Bose-Einstein distribution (for bosons).