Physics - Semiconductors Question with Solution | TestHub

The resistivity of a semiconductor is given by the relation:

$\rho ={\rho }_0{e}^{\frac{E_g}{2k_{B}T}}$

where $E_g$ is the band gap energy, $k_B$ is the Boltzmann constant, and $T$ is the absolute temperature.

As the temperature $T$ increases, the number of charge carriers (electrons and holes) increases exponentially. Consequently, the resistivity $\rho$ decreases exponentially with an increase in temperature.

Graph (C) correctly represents this non-linear (exponential) decrease of resistivity with temperature.

Answer: C