GATE EC 2022 Set 1 — Question 47

Statement (A) is correct: In an intrinsic semiconductor at thermal equilibrium, the concentration of electrons ($n$) is equal to the concentration of holes ($p$), i.e., $n = p = n_i$. This is a fundamental property of intrinsic materials.Statement (B) is incorrect: In a standard BJT, the doping levels are typically $N_E > N_B > N_C$. The emitter is the most heavily doped to ensure high injection efficiency, and the base is generally more heavily doped than the collector to reduce base resistance and prevent punch-through.Statement (C) is correct: Under steady-state conditions ($\frac{\partial \rho}{\partial t} = 0$), the continuity equation $\nabla \cdot \vec{J} + \frac{\partial \rho}{\partial t} = 0$ implies $\nabla \cdot \vec{J} = 0$. For a two-terminal device, this means the total current density $\vec{J}$ must be spatially constant throughout the device to satisfy charge conservation.Statement (D) is incorrect: For temperatures above 300 K, lattice scattering is the dominant mechanism limiting carrier mobility. The mobility $\mu$ is proportional to $T^{-m}$ (where $m \approx 1.5$ to $2.5$), meaning mobility decreases as temperature increases.