For a heavily doped n-type semiconductor (Ge), the ionisation energy required to set the electrons free to move in conduction band is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \sim 0.01 \) eV
In an n-type semiconductor each pentavalent donor atom uses four electrons in covalent bonds; the fifth is only loosely bound. Its energy level lies just below the conduction band, and the energy needed to free it (the donor ionisation energy) is about 0.01 eV in germanium and about 0.05 eV in silicon. This is less than \( kT \approx 0.026\,\mathrm{eV} \) at room temperature, so nearly all donors are ionised. With very heavy doping the donor levels spread into a band and the energy becomes even smaller, so \( \sim 0.01 \) eV is the only option of the right order for Ge.
Why the other options are incorrect
Option (1) \( \sim 0.05 \) eV — Incorrect. About 0.05 eV is the donor ionisation energy for silicon, not germanium.
Option (2) \( \sim 0.7 \) eV — Incorrect. About 0.7 eV is the band gap of germanium, the energy needed to free an electron from the valence band.
Option (3) \( \sim 0.5 \) eV — Incorrect. 0.5 eV is far larger than a donor ionisation energy; the donor level lies very close to the conduction band.
NCERT (2026-27):
Extrinsic Semiconductor – “… As a result the ionisation energy required to set this electron free is very small and even at room temperature it will be free to move in the lattice of the semiconductor. For example, the energy required is ~ 0.01 eV for germanium, and 0.05 eV for silicon, to separate this electron from its atom. This is in contrast to the energy required to jump the forbidden band (about 0.72 eV for germanium and about 1.1 eV for silicon) at room temperature in the intrinsic semiconductor.”