(a) What is the probability of an electron state being filled if it is located a

Question

(a) What is the probability of an electron state being filled if it is located at the Fermi level?

(b) If the probability that a state is filled at the conduction band edge (Ec) is precisely equal to the probability that a state is empty at the valence band edge (Ev), where is the Fermi level located?

(c) The Maxwell-Boltzmann distribution is often used to approximate the Fermi-Dirac distribution function. On the same set of axes, sketch both distributions as a function of (E- Ef)/kT. Consider only positive values of E- Ef. For what range of (E- Ef)/kT is the Maxwell- Boltzmann approximation accurate to within 10%?

Explanation / Answer

(a)
Assuing that the material we are talking about is intrinsic in that case the probability will be of 50 % or say0.5

(b)
The Fermi level represents the highest energy level that is filled at 0 Kelvin, or the energy level that has a 50% probability of being filled. Note though that in a semiconductor without defect levels in the band gap, there exist no states to fill near the Fermi level. For an intrinsic semiconductor, the Fermi level is at the midgap.

(c):

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