GATE EC 2021 Question Paper (07-Feb-2021) (Shift 2)

A bar of silicon is doped with a boron concentration of 10¹⁶ cm⁻³ and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of 10²⁰ cm⁻³s⁻¹. If the recombination lifetime is 100 μs, the intrinsic carrier concentration of silicon is 10¹⁰ cm⁻³ and assuming 100% ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is

The energy band diagram of a p-type semiconductor bar of length L under equilibrium condition (i.e., the Fermi energy level E${}_F$ is constant) is shown in the figure. The valance band E${}_V$ is sloped since doping is non-uniform along the bar. The difference between the energy levels of the valence band at the two edges of the bar is Δ.



If the charge of an electron is q, then the magnitude of the electric field developed inside this semiconductor bar is

In a circuit shown in the figure, the transistors M₁ and M₂ are operating in saturation. The channel length modulation coefficients of both the transistors are non-zero. The transconductance of the MOSFETs M1 and M2 are g${}_{m1}$ and g${}_{m2}$, respectively, and the internal resistance of the MOSFETs M1 and M2 are r₀₁ and r₀₂, respectively.



Ignoring the body effect, the ac small-signal voltage gain (∂Vₒᵤₜ / ∂Vᵢₙ) of the circuit is:

For the circuit with an ideal OPAMP shown in the figure. V${}_{REF}$ is fixed.



If V${}_{OUT}$ = 1 for V${}_{IN}$ = 0.1 volt and V${}_{OUT}$ = 6 volt for V${}_{IN}$ = 1 volt, where V${}_{OUT}$ is measured across R${}_L$ connected at the output of this OPAMP, the value of R${}_F$ / R${}_{IN}$ is

Consider the circuit with and ideal OPAMP shown in the figure.



Assuming |V${}_{IN}$ | << |V${}_{CC}$ | and |V${}_{REF}$ | << |V${}_{CC}$ |, the condition at which V${}_{OUT}$ equals to zero is