The resistivity (ρ) of semiconductor varies with temperature. Which of the following curve represents the correct behaviour :

Solution

Physics sir · 4 steps

Heat frees more charge carriers, so a semiconductor's resistivity falls, and it falls exponentially.

1. More carriers. In a semiconductor the band gap is small. As temperature rises, more electrons jump from the valence band to the conduction band, and each one leaves a hole behind. So the number of carriers grows very fast with T.
2. Resistivity. Resistivity is ρ = 1/(n e μ). The carrier density n grows exponentially with T, which is far stronger than the slow drop in mobility μ. So ρ goes down, roughly as below.

   ρ ∝ e^(E_g/2k_BT)

3. Shape of curve. This function is very large at low T, drops steeply, and then flattens out towards a small positive value. It never becomes a straight line and never touches zero.
4. So. The graph that falls steeply and then levels off is (d). Semiconductors have a negative temperature coefficient of resistivity.

The idea to keep. Metals: resistivity rises with temperature because carriers collide more. Semiconductors: resistivity falls with temperature because heat creates more carriers, and that effect wins.

Answer from the NTA final answer key. Solution by PrepWiser.