# Conductivity of a semiconductor at high temperatures

I understand that increasing the temperature of a semiconductor excites electrons in the valence band into the conduction band. Hence, the resistivity of a semiconductor decreases with temperature.

Is there a high enough temperature where the conduction band would be saturated from electron with the valence band and the resistance of the semiconductor would start to increase like a regular metal?

Assuming the seminconductor couldn't melt, as temperature got aribtrarily high would the seminconductor's resistance get arbitrarily low?

• There is not only one conduction band, but infinite numbers - so you generally do not saturate it/them. – Greg Aug 22 '16 at 6:46
• Still, I guess at some point the resistance would start to increase, unless the semiconductor would melt before that. – Ivan Neretin Aug 22 '16 at 8:37

First, the carrier concentration does increase steeply, although for Si at its melt temperature it is still only about 10$^{20}$/$cm^{3}$, much lower than a metal.
Finally, the phonon population increases with temperature, which will increase scattering, decreasing the conductivity (just like a metal). This can be seen from a graph of carrier mobility (also in Sze) with temperature. The mobility drops roughly as T$^{-2.2}$ or so.