JEE Main 2023 · 31 January · morning · Single correct · +4 / −1
The effect of increase in temperature on the number of electrons in conduction band (nₑ) and resistance of a semiconductor will be as:
- (a) nₑ decreases, resistance increases
- (b) Both nₑ and resistance increase
- (c) nₑ increases, resistance decreases
- (d) Both nₑ and resistance decrease
Answer and solution
Answer (c) nₑ increases, resistance decreases
Solution
Physics sir · 4 steps
Heat breaks more bonds, so more electrons jump the gap; more carriers means less resistance.
- Small band gap. In a semiconductor the gap between the valence band and the conduction band is small, about 1 eV. Thermal energy alone can push some electrons across it.
- Raise the temperature. At a higher temperature more electrons gain enough energy to cross the gap. So nₑ rises sharply, roughly as e^(-E_g/2kT), and each electron that crosses also leaves a hole behind.
σ = e(nₑ μₑ + nₕ μₕ), R = (ρ L)/A = L/(σ A)
- Effect on resistance. Mobility does fall a little with temperature, but the rise in carrier number is far larger. So conductivity σ increases and resistance decreases. A semiconductor has a negative temperature coefficient of resistance.
- So. nₑ increases and resistance decreases, which is option (c).
The idea to keep. For semiconductors, think carriers first: heat creates more electron-hole pairs, so resistance falls. Metals are the opposite, because their carrier count is fixed and only collisions increase.
Answer from the NTA final answer key. Solution by PrepWiser.