Explain the variation of resistivity with temperature in pure-sem… - Vidyadip

Question

Explain the variation of resistivity with temperature in pure-semiconductors.

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Answer

The resistivity of a semiconductor is given by
$\rho=\frac{1}{\sigma}=\frac{1}{e\left(n_e \mu_e+n_h \mu_h\right)}$
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 $\mu_e$ 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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