# 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.

## 1 Answer

For usual circumstances, it’s impossible to make a semiconductor more conductive than a conductor. This is because the semiconductor is generally affected by the same process that governs the conductor’s decrease in conductivity with temperature: phonon scattering of the conducting electrons. The difference is that with a semiconductor, increasing the temperature also increases the number of conducting electrons, by thermally exciting the dopants. But this increase of carrier density can only take you up to the complete ionization of dopants, which probably won’t get you as much conductivity as a good metal (unless the semiconductor mobility is absurdly good) since the metal gets ~1 or 2 free electrons from every atom.

All of this, of course, isn’t to say that there’s no interesting project for you in this. You could measure the resistance of some semiconductors vs temperature and see how well they match your formula (which is an approximation for small temperature changes only). You can also look up some data about this too, so try searching around!

• 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
• @JonCuster indeed, we’re talking about two different temperature regimes. But thank you for commenting; I didn’t have the enthusiasm to bring up the intrinsic population, especially not to compute/estimate the density vs temp for a given semiconductor. The larger point, I guess, is just that the ~1 eV band gaps of common semiconductors limits the intrinsic concentration to orders of magnitude smaller than metal, and then the mobility can’t make up the difference. – Gilbert Nov 30 '18 at 22:04