A) decreases exponentially with increasing band gap
B) increases exponentially with increasing band gap
C) decreases with increasing temperature
D) is independent of the temperature and the band gap
Correct Answer: A
Solution :
The fermi function \[f(E)\] gives the probability that a given available electron energy state will be occupied at a given temperature. The fermi function comes from Fermi-Dirac statistics and has the form \[f(E)=\frac{1}{{{E}^{(E-{{E}_{F}})/kT}}+1}\] The basic nature of this function dictates that at ordinary temperatures, most of the levels up to the fermi level are filled. At higher temperature, a larger fraction of the electrons can bridge this gap and participate in electrical conduction. Hence, at finite temperature, the probability decreases exponentially with increasing band gap.
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