Question

The probability that a state is filled at the conduction edge \((E_c)\) is precisely equal to the probability that a state is empty at the valence band edge \((E_v)\). The Fermi level is located at:

• A. \(E_F = E_c + E_v\)
• B. \(E_F = \frac{E_c + E_v}{2}\)
• C. \(E_F = E_c - E_v\)
• D. \(E_F = E_c + 2E_v\)

Hint:

For intrinsic semiconductors, always locate the Fermi level as the midpoint of the energy gap Eg = Ec − Ev.

Answer 1

The Correct Option is A

At thermal equilibrium, the Fermi level is defined as the point where the probability of an electron being at the conduction edge equals the probability of a hole being at the valence edge. This occurs at:
\[E_F = \frac{E_c + E_v}{2}\]
This relation ensures that the Fermi level lies symmetrically between the conduction and valence bands.