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(A) The probability $P(E)$ of an electron being found in the conduction band of an intrinsic semiconductor is given by the Fermi-Dirac distribution fu

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Decreases exponentially with increasing band gap

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(A) The probability $P(E)$ of an electron being found in the conduction band of an intrinsic semiconductor is given by the Fermi-Dirac distribution function: $P(E) = \frac{1}{1 + e^{(E - E_F) / kT}}$.Here,$E$ is the energy level in the conduction band,$E_F$ is the Fermi level,$k$ is the Boltzmann constant,and $T$ is the absolute temperature.For the conduction band,$E - E_F$ is approximately $E_g / 2$,where $E_g$ is the band gap.Since $E - E_F \gg kT$,the term $e^{(E - E_F) / kT}$ is much greater than $1$.Therefore,$P(E) \approx e^{-(E - E_F) / kT} = e^{-E_g / 2kT}$.This shows that the probability decreases exponentially as the band gap $E_g$ increases.

The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature

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