When a semiconductor is doped with a donor impurity

The correct answer is Option (4) → electron concentration increases and hole concentration decreases

A donor impurity (a pentavalent atom such as P or As) gives its fifth valence electron to the crystal, so the electron concentration increases. At the same time, the extra electrons recombine with holes, so the number of holes falls below its intrinsic value. In thermal equilibrium the product of the two concentrations stays fixed (law of mass action):

    \( n_e\,n_h = n_i^{2} \)

If \( n_e \) goes up, \( n_h \) must go down.

Option (1) electron concentration decreases and hole concentration remains the same — Incorrect. A donor adds electrons, so the electron concentration increases, not decreases.

Option (2) hole concentration decreases and electron concentration remains the same — Incorrect. The electron concentration does not stay the same; the donor atoms add free electrons.

Option (3) electron concentration increases and hole concentration remains the same — Incorrect. The hole concentration does not stay the same; since \( n_e n_h = n_i^2 \), a rise in \( n_e \) lowers \( n_h \).

Option (4) electron concentration increases and hole concentration decreases — Correct. Electrons increase because of the donors, and holes decrease because of recombination.

NCERT (2026-27):
n-type Semiconductor – “… In a doped semiconductor the total number of conduction electrons n_e is due to the electrons contributed by donors and those generated intrinsically, while the total number of holes n_h is only due to the holes from the intrinsic source. But the rate of recombination of holes would increase due to the increase in the number of electrons. As a result, the number of holes would get reduced further.”