Question

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

• 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

Answer 1

Answer: (A)

decreases exponentially with increasing band gap

Answer 2

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 $f(E)=\frac{1}{E^{\left(E-E_{F}\right) / k T}+1}$ 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.