The resistivity (rho) of a semiconductor vari | vedclass

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(B) The resistivity of a material is given by the formula $ho = \frac{m}{ne^2	au}$,where $m$ is the mass of the electron,$n$ is the number density

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(B) The resistivity of a material is given by the formula $ho = \frac{m}{ne^2	au}$,where $m$ is the mass of the electron,$n$ is the number density of charge carriers,$e$ is the electronic charge,and $	au$ is the relaxation time.In semiconductors,as the temperature $(T)$ increases,the number density $(n)$ of electrons and holes increases exponentially due to the thermal excitation of charge carriers across the band gap.Since $m$ and $e$ are constants,and the increase in $n$ dominates over the slight decrease in $	au$ at higher temperatures,the resistivity $ho$ decreases significantly as temperature $T$ increases.This relationship is represented by an exponential decay curve,which is a non-linear decrease. Therefore,the curve in option $B$ correctly represents the behavior of resistivity with temperature for a semiconductor.

The resistivity $(\rho)$ of a semiconductor varies with temperature. Which of the following curves represents the correct behavior?

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