Concept:Donor dopants add free electrons to the conduction band, increasing the electron occupation probability and shifting the Fermi level closer to the conduction band.
Formula:$$E_F - E_i = k_B T \ln\left(\frac{N_D}{n_i}\right) > 0$$
Solution:- Doping with donor atoms increases the electron concentration (\( n \approx N_D \gg n_i \)).
- To reflect the increased probability of finding electrons in the conduction band, the Fermi level (\( E_F \)) shifts upward toward the conduction band edge \( E_c \).
Why other options are incorrect:- Option B: A downward shift toward the valence band occurs in P-type semiconductors.
- Option C: The Fermi level sits at the midpoint only in undoped intrinsic semiconductors.
- Option D: Shifting below the valence band corresponds to degenerate P-type doping.
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.