Answer:
The resistivity of a semiconductor is given by \[\rho =\frac{1}{\sigma }=\frac{1}{e({{n}_{e}}{{\mu }_{e}}+{{n}_{h}}{{\mu }_{h}})}\] As the temperature increases, the mobilities \[{{\mu }_{e}}\]and \[{{\mu }_{h}}\] of electrons and holes decrease due to the increase in their collision frequency. But due to the small energy gap of semiconductors, more and more electrons \[(n\propto {{e}^{-{{E}_{g}}/{{k}_{B}}T}})\] from the valence band cross over to the conduction band. The increase in carrier concentrations, \[{{n}_{e}}\] and \[{{n}_{h}}\] is so large that decrease in the values of \[{{\mu }_{e}}\] g and \[{{\mu }_{h}}\] has no influence. The overall effect is that conductivity increases or resistivity decreases with the increase of temperature.
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