GATE EC 2017 Question Paper (05-Feb-2017) (Shift 1)

The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of n = 1 × 10¹⁶ cm${}^{\text{–}3}$ and electronic charge q = 1.6 × 10${}^{\text{–}19}$ C. If a bias of 5 V is applied across a 1 μm region of this semiconductor, the resulting current density in this region, in kA/cm², is ________.

As shown, a uniformly doped Silicon (Si) bar of length L = 0.1 μm with a donor concentration N${}_D$ = 10¹⁶ cm${}^{\text{–}3}$ is illuminated at x = 0 such that electron and hole pairs are generated at the rate of G${}_L$ = $G_{L0}\left(1-\frac{x}{L}\right),0\le x\le L$, where G${}_{L0}$ = 10¹⁷ cm${}^{\text{–}3}$ s${}^{\text{–}1}$.

Hole lifetime is 10${}^{\text{–}4}$ s, electronic charge q = 1.6 × 10${}^{\text{–}19}$ C, hole diffusion coefficient Dₚ = 100 cm²/s and low level injection condition prevails.

Assuming a linearly decaying steady sate excess hole concentration that goes to 0 at x = L, the magnitude of the diffusion current density at x = L/2, in A/cm², is ________.

As shown, two Silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentrations of N${}_{D1}$ = 10¹⁴ cm${}^{\text{–}3}$ and N${}_{D2}$ = 10¹⁶ cm${}^{\text{–}3}$ in the n-regions of the diodes, and uniform acceptor doping concentrations of N${}_{A1}$ = 10¹⁴ cm${}^{\text{–}3}$ and N${}_{A2}$ = 10¹⁶ cm${}^{\text{–}3}$ in the p-regions of the diodes, respectively. Assuming that the reverse bias voltage is ≫ built-in potentials of the diodes, the ratio C₂/C₁ of their reverse bias capacitances for the same applied reverse bias, is ________.

In the figure shown, the npn transistor acts as a switch



For the input Vᵢₙ(t) as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to-emitter voltage at saturation V${}_{CE(sat)}$ = 0.2V and base-to-emitter voltage V${}_{BE}$ = 0.7V. The minimum value of the common-base current gain (α) of the transistor for the switching should be ________.

For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage Vₜₙ = 1 V and its transconductance parameter ${\mu }_n{C}_{ox}\left(\frac{W}{L}\right)=1mA/V^2.$ Neglect channel length modulation and body bias effects. Under these conditions, the drain current I${}_D$ in mA is ________.