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(B) In a semiconductor, the number of charge carriers (electrons and holes) increases exponentially with an increase in temperature $(T)$.This increas

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(B) In a semiconductor, the number of charge carriers (electrons and holes) increases exponentially with an increase in temperature $(T)$.This increase in the number of charge carriers dominates over the effect of increased scattering of charge carriers.As a result, the resistivity $(\rho)$ of a semiconductor decreases as the temperature increases.The relationship is given by $\rho = \rho_0 e^{E_g / 2kT}$, where $E_g$ is the energy band gap, $k$ is the Boltzmann constant, and $T$ is the absolute temperature.This represents an exponential decay curve.Therefore, graph $B$ correctly represents the temperature dependence of resistivity for a semiconductor.

Which of the following graphs represents the temperature $(T)$ dependence of resistivity $(\rho)$ of a semiconductor?

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