# Can a semiconductor become more conductive than a conductor with heat?

I am looking for a good idea for a science fair project for PA Junior Academy of Science (PJAS). An interesting idea that I have stumbled across is making semiconductors more conductive with heat. I already know that conductors obtain a higher resistivity when heated up and vise-versa when they are cooled down. Theoretically, with the formulas that I have found online, a semiconductor will begin to conduct better than a conductor at a great enough temperature. The formula is in here:

Is this correct for both Conductors and semiconductors? And if so, is it actually possible to do this? Please elaborate on how if true and what temperature is needed.

• For any reasonable dopant, they are already essentially fully ionized at room temperature. Increasing the temperature of a semiconductor increases the intrinsic carrier density, which is exponential with temperature. Silicon at room temperature has $n_{i} \approx 10^{10}$, but at around 1100C this approaches $10^{19}$. Note that a metal will have a carrier density closer to $10^{22}$. This is one reason you have to keep semiconductor devices relatively cool - if the intrinsic concentration exceeds the dopant concentration you don't have a device any more... – Jon Custer Nov 30 '18 at 21:27