Question

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

Hint:

In semiconductors, the increase in conductivity with temperature is mainly due to the increase in the number density of charge carriers, while the effect of relaxation time is secondary.

Answer 1

The Correct Option is B

In a semiconductor, conductivity is given by: \[ \sigma = n e \tau \] Where: - \( n \) is the number density of free charge carriers, - \( e \) is the charge of the electron, - \( \tau \) is the relaxation time. As the temperature increases, the number density of free carriers \( n \) increases due to the increased excitation of electrons from the valence band to the conduction band. 
However, the relaxation time \( \tau \) typically decreases as temperature increases because higher temperatures cause more collisions of charge carriers, leading to more scattering. The net effect is that the increase in number density dominates, causing an overall increase in conductivity. 
Thus, the correct answer is that the relaxation time increases with temperature, but the increase in number density is the primary reason for the increase in conductivity.