Select the CORRECT statement(s) regarding semiconductor devices.
Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.
Collector region is generally more heavily doped than Base region in a BJT.
Total current is spatially constant in a two terminal electronic device in dark under steady state condition.
Mobility of electrons always increases with temperature in Silicon beyond 300 K.
ANSWER
The correct statements are (A) and (C).
Official answer: A, CSource: Official answer key, GATE 2022 EC (IIT Kharagpur)
Statement (A): By definition of an intrinsic semiconductor at thermal equilibrium, — electron and hole densities are equal by symmetry (no dopants). TRUE.
Statement (B): The standard BJT doping hierarchy is : the emitter is doped heaviest for high injection efficiency, while the collector is kept lightly doped (relative to the base) so it can support the reverse-biased collector–base junction with a high breakdown voltage and good Early voltage. So the collector is NOT more heavily doped than the base. FALSE.
Statement (C): In steady state the continuity equation gives everywhere, and a two-terminal device has only one current path, so by Kirchhoff's current law the total current (drift + diffusion, electrons + holes summed) must be identical at every cross-section of the device — spatially constant. TRUE.
Statement (D): Above the impurity-scattering-dominated low-temperature regime, electron mobility in Silicon is limited by lattice (phonon) scattering, whose rate increases with temperature; consequently decreases with (roughly ) for well above 300 K. Mobility does NOT always increase with temperature. FALSE.
Hence the correct statements are (A) and (C).
KEY IDEA
Apply the four separate physical facts: intrinsic carrier symmetry, standard BJT doping hierarchy (emitter heaviest, collector lightest), KCL/continuity in steady state, and phonon-scattering-limited mobility above ~300 K in Si.
WATCH OUT FOR
Assuming the collector must be more heavily doped than the base because it is physically larger, or assuming mobility keeps rising with temperature by analogy with intrinsic carrier concentration (which does rise with T) — mobility and carrier concentration have opposite temperature dependences above ~300 K in Si.
From the GATE 2022 EC paper. Every question of this paper · Download the full paper · All 9 Carrier transport questions, with notes
