The conductivity of a semiconductor increases with increase in temperature because A) number density of free current carriers increases B) relaxation time increases C) both number density of carriers and relaxation time increase D) number density of current carriers increases, relaxation time decreases but effect of decrease in relaxation time is much less than increase in number density

Step-by-step solution

The conductivity of a semiconductor is given by the relation = e(n_e _e + n_h _h) , where n_e and n_h are the number densities of electrons and holes, and _e and _h are their respective mobilities. As temperature increases, the thermal energy provided to the valence electrons allows them to jump across the band gap into the conduction band, leading to an exponential increase in the number density of charge carriers ( n_e and n_h ). The mobility is related to the relaxation time by = e m . With an increase in temper