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 density of charge carriers (electrons and holes) increases exponentially because more electrons gain enough thermal energy to jump from the valence band to the conduction band. Consequently, the resistivity $\rho$ decreases exponentially with an increase in temperature.

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

Answer: B