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(D) In a semiconductor,the intrinsic carrier concentration $n_i$ is given by the relation:$n_i = A T^{3/2} \exp\left(-\frac{E_g}{2kT}\right)$where $A$

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$n \propto T^{3/2}$

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(D) In a semiconductor,the intrinsic carrier concentration $n_i$ is given by the relation:$n_i = A T^{3/2} \exp\left(-\frac{E_g}{2kT}\right)$where $A$ is a constant,$E_g$ is the band gap energy,and $k$ is the Boltzmann constant.For a given semiconductor,the temperature dependence is dominated by the $T^{3/2}$ factor in the pre-exponential term.Therefore,the number density of free electrons $n$ is proportional to $T^{3/2}$.

What is the relationship between the number density of free electrons $(n)$ and temperature $(T)$ in a semiconductor?

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