JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Semiconductors

In a semiconductor the number density $n$ of charge carriers rises steeply with temperature as electrons are thermally excited across the band gap. Since $\rho =\frac{m}{n{e}^2\tau }$ and $n$ grows much faster than the relaxation time $\tau$ falls, the resistivity decreases as temperature increases. The fall is rapid at low temperatures and becomes gentler at higher temperatures, so the $\rho$–$T$ graph is a decreasing, concave-up curve.