Q. 13.7( 4 Votes )

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.

Answer :

In a semiconductor material, the electrons are distributed in two energy bands, called the valence band and the conduction band. These two are separated by an energy gap. The electrons, which, at a certain temperature, have the required energy to cross the gap are in the conduction band are responsible for conduction. When the temperature increases the covalent bonds increase and the number of electrons having sufficient energy to enter the conduction band increases leading to increase in both holes and electrons and therefore the number density of free current carriers increase.

Also, since the charge carriers have increased at higher temperature, the frequency of collisions increase, which results in a decrease in the relaxation time of the carries due to decrease in the drift velocity as the frequent collisions don’t allow them to gain velocity. However, the effect of decrease in relaxation time is much less than the increase in number density.

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