Which of the following graph represents the temperature (T) dependence of resistivity ( ) of a semiconductor?

Step-by-step solution

The resistivity of a semiconductor is given by the relation: = ₀ e^ 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 decreases exponentially with an increase in temperature. Graph (B) correctly represents thi