AIIMS 2019 Physics Doping MCQ Question

In a pure semiconductor, the electron concentration $n_e$ equals the hole concentration $n_h$, which is given as $10^{16} \, \text{m}^{-3}$. When gallium is introduced as a p-type dopant, it significantly increases the hole concentration to $n_h = 5 \times 10^{22} \, \text{m}^{-3}$. Since the semiconductor remains charge neutral, the relationship $n_e \cdot n_h = n_i^2$ (where $n_i$ is the intrinsic carrier concentration) must hold. Given the large increase in $n_h$, the electron concentration $n_e$ decreases to $2 \times 10^9 \, \text{m}^{-3}$ to maintain charge neutrality, making option D correct.

Options A and C are incorrect because they suggest electron concentrations that are too low compared to the required balance for charge neutrality, while option B does not account for the significant increase in hole concentration due to doping.