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The conductivity of a semiconductor increases with increases in temperature because:

$\begin{array}{1 1} \text{number density of free current carries increase } \\ \text{both number density of carries and relaxation time increases } \\ \text{relaxation time increases } \\ \text{Number density of current carries increases , relaxation time decreases , but effect of decrease in relaxation time is much less than increase in number density } \end{array} $

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