Question

On increasing temperature of a semiconductor, what will be effect on its conductivity?

Hint:

Use \( \sigma = n e \mu \): heating breaks covalent bonds and creates many more electron-hole pairs, so the carrier number wins over the drop in mobility.

Answer 1

Step 1 (Band picture): In a semiconductor a small forbidden energy gap (\(E_g \approx 1\) eV) separates the filled valence band from the empty conduction band. Conduction needs electrons in the conduction band.

Step 2 (Thermal excitation): Raising the temperature supplies thermal energy \(kT\) to the electrons. The number of electrons able to jump across the gap follows \(n \propto e^{-E_g/2kT}\), so \(n\) grows quickly as \(T\) increases, leaving behind an equal number of holes in the valence band.

Step 3 (Conclusion): More carriers in both bands mean more current for the same field, so the material conducts better at higher temperature. This is opposite to a metal, whose resistance rises on heating.

\[\boxed{\sigma \uparrow \ \text{with temperature; semiconductor becomes a better conductor.}}\]