Question

Show, on a plot, variation of resistivity of (i) a conductor, and (ii) a typical semiconductor as a function of temperature. 

Using the expression for the resistivity in terms of number density and relaxation time between the collisions, explain how resistivity in the case of a conductor increases while it decreases in a semiconductor, with the rise of temperature.

Answer 1

For conductors 

For semiconductors

1. Conductors : For conductors, the number density n of free electrons is almost independent of temperature. As temperature increases, the thermal speed of free electrons increases and also the amplitude of vibration of the metal ions increases. Consequently, the free electrons collide more frequently with the metal ions. The mean collision time τ decreases. Hence the resistivity of a metal (p∝ 1/τ) increases and the conductivity decreases with the increases in temperature.

2. Semiconductors : In case of insulators and semiconductors, the relaxation time τ does not change with temperature but the number density of free electrons increases exponentially with the increase in temperature. Consequently, the conductivity increases or resistivity decreases exponentially with the increase in temperature.