For a heavily doped n-type semiconductor, Fermi level lies:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A little below the conduction band
The Fermi level marks the energy around which the states are half filled. In an intrinsic semiconductor it lies near the middle of the gap, because there are as many electrons as holes.
In an n-type semiconductor the donor impurities supply many extra electrons at a level just below the conduction band, so the electrons far outnumber the holes. The Fermi level is pushed up from the middle of the gap towards the conduction band, and the heavier the doping the closer it gets to the bottom of the conduction band, staying a little below it.
Why the other options are incorrect
Option (1) A little above the valence band — Incorrect. This is where the Fermi level goes in a heavily doped p-type semiconductor, where holes are in excess.
Option (3) At the center or middle of valence and conduction band — Incorrect. This is the position for an intrinsic (undoped) semiconductor.
Option (4) A little above the conduction band — Incorrect. The Fermi level of an n-type semiconductor approaches the bottom of the conduction band as the doping increases but is placed just below it.