GATE EC 2016 Question Paper (30-Jan-2016) (Shift 1)

Consider a silicon p-n junction with a uniform acceptor doping concentration of 10¹⁷ cm${}^{-3}$ on the p side and a uniform donor doping concentration of 10¹⁶ cm−3 on the n-side. No external voltage is applied to the diode. Given: kT/${}_q$ = 26 mV, nᵢ =1.5 ×10¹⁰ cm⁻³, ε${}_{Si}$ = 12ε₀, ε₀ = 8.85 × 10⁻¹⁴ F/m, and q = 1.6 ×10⁻¹⁹ C. The charge per unit junction area (nC cm⁻²) in the depletion region on the p-side is ___________.

Consider an n-channel metal-oxide-semiconductor field-effect transistor (MOSFET) with a gate-to-source voltage of 1.8 V. Assume that $\frac{W}{L}=4$, μₙCₒₓ = 70 × 10⁻⁶ AV⁻², the threshold voltage is 0.3 V, and the channel length modulation parameter is 0.09 V⁻¹. In the saturation region, the drain conductance (in micro seimens) is ________.

The figure below shows the doping distribution in a p-type semiconductor in log scale.



The magnitude of the electric field (in kV/cm) in the semiconductor due to non-uniform

doping is _________.

Consider a silicon sample at T = 300 K, with a uniform donor density 𝑁${}_{\text{d}}$ = 5 × 10¹⁶

cm⁻³, illuminated uniformly such that the optical generation rate is 𝐺${}_{\text{opt}}$ = 1.5 × 10²⁰cm⁻³𝑠⁻¹ throughout the sample. The incident radiation is turned off at 𝑡 = 0. Assume low-level injection to be valid and ignore surface effects. The carrier lifetimes are 𝜏${}_{\text{p}0}$ = 0.1 μs and 𝜏${}_{\text{n}0}$ = 0.5 μs.



The hole concentration at 𝑡 = 0 and the hole concentration at 𝑡 = 0.3 μs, respectively, are

An ideal opamp has voltage sources V₁, V₃, V₅, …, V${}_{N-1}$ connected to the non-inverting input and V₂, V₄, V₆, …, V${}_N$ connected to the inverting input as shown in the figure below (+V${}_{CC}$ = 15 volt, −V${}_{CC}$ = −15 volt). The voltages V₁, V₂, V₃, V₄, V₅, V₆,… are 1, − 1/2, 1/3, −1/4, 1/5, −1/6, … volt, respectively. As N approaches infinity, the output voltage (in volt) is ___________