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Explain mathematically, why the resistance of metals increases while that of semiconductor decreases with the rise in temperature. Plot Resistance versus Temperature for Cu and for Silicon.

Explain mathematically, why the resistance of metals increases while that of semiconductor decreases with the rise in temperature. Plot Resistance versus Temperature for Cu and for Silicon.

Grade:Upto college level

1 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
10 months ago
Dear student

The conductivity of a material depends on two factors
Factor 1: no ofelectrons in the conductionband
Factor 2: Collisionof conductionelectron withcoreatom. Factor 1 increases conductivity and Factor 2 decreases.

An increase in temperature causes bothfactorsto increases. For conductor factor 2 dominates over factor 1 because conduction and valence band overlap so all the electrons of valence band are already in conduction band hence there is no increase in conduction electron with temperature but collision rate of conduction electron with core atom increases resistance. For semiconductor factor 1 dominates over factor 2. As temperature increases electrons from the valanceband jump to the conductionband. Hence, no. ofelectrons in conduction band increases, and conductivity increases.

Regards

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