# 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

## 1 Answer

A number of different things are going on in this scenario.

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.

In addition, the band gap is decreasing with temperature (not from carriers, but from changes to the lattice spacing). From a graph in Sze's Physics of Semiconductor Physics, Si goes from 1.12eV at room temperature to a little under 0.9eV at 900K. Extrapolation (probably a bad idea) means that somewhere above 2700K there will be little to no band gap. However, this assumes the physics extrapolates linearly, which it doesn't. (Well, liquid silicon is metallic. However, there is still a large increase in conductivity at the melt point).

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.

Getting the balance of all of these just right under extreme extrapolation, well, that is hard. It is actually easier to point to papers on the electrical characteristics of undercooled liquid silicon (since that has been measured), than to superheated solid silicon (which has not been observed). - for ev

• Surely once the band gap has decreased to zero the semiconductor would start to behave more like a normal metal (vibration of metal cations increases resistance more than the increasing overlap of the conduction and valence bands). – Honwang Aug 30 '16 at 21:47
• @Honwang - that would be my take as well. Just not sure how to extrapolate to where that occurs. – Jon Custer Aug 30 '16 at 22:06