GATE EC 2022 Set 1 — Question 57

Let's analyze each statement:(A) Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.
In an intrinsic semiconductor, the number of electrons in the conduction band is equal to the number of holes in the valence band, as electron-hole pairs are generated in equal numbers. Thus, at equilibrium, the electron concentration ($n$) equals the hole concentration ($p$), and both are equal to the intrinsic carrier concentration ($n_i$). So, $n = p = n_i$. This statement is CORRECT.(B) Collector region is generally more heavily doped than Base region in a BJT.
In a Bipolar Junction Transistor (BJT), the doping concentrations are typically ordered as: Emitter (most heavily doped) > Collector (moderately doped) > Base (lightly doped). This doping profile is chosen to optimize current gain and breakdown voltage. Therefore, the collector region is indeed generally more heavily doped than the base region. This statement is CORRECT.(C) Total current is spatially constant in a two terminal electronic device in dark under steady state condition.
According to the principle of current continuity, in a steady-state condition (where charge accumulation is zero, i.e., $\frac{\partial \rho}{\partial t} = 0$) and in the absence of generation (like in the dark), the total current density (and thus total current) must be constant throughout the device. This means that the sum of drift and diffusion currents remains constant at every cross-section of the device. This statement is CORRECT.(D) Mobility of electrons always increases with temperature in Silicon beyond 300 K.
In semiconductors like Silicon, carrier mobility is primarily limited by two scattering mechanisms: lattice scattering (phonon scattering) and impurity scattering. Lattice scattering increases with temperature, causing mobility to decrease. Impurity scattering decreases with temperature. At temperatures above 300 K, lattice scattering dominates, leading to a decrease in carrier mobility (both electron and hole mobility) as temperature increases. This statement is INCORRECT.Therefore, the correct statements are (A), (B), and (C).