Figures $${\rm I}$$ and $${\rm I}{\rm I}$$ show two MOS capacitor of unit area. The capacitor in Figure I has insulator materials X (of thickness t₁ = 1 nm and dielectric constant $${\varepsilon _1}$$ = 4) and Y (of thickness t₂ =3 nm and dielectric constant $${\varepsilon _2}$$ = 200). The capacitor in Figure $${\rm I}{\rm I}$$ has only insulator material X of thickness t_eq. If the capacitors are of equal capacitance, then the value of t_eq (in nm) is ______

In the circuit shown, both the enhancement mode NMOS transistors have the following characteristics: k_n = $${\mu _n}{C_{ox}}(W/L) = 1m{\rm A}/{V^2}$$ ; V_TN = 1V. Asuume that the channel length modulation parameter $$\lambda $$ is zero and body is shorted to source. The minimum supply voltage V_DD (in volts) needed to ensure that transistor M₁ operates in saturation mode of operation is _____

The current in an enhancement mode NMOS transistor biased in saturation mode was measured to be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain to source saturation voltage is much smaller than the applied drain-source voltage. The channel length modulation p[arameter $$\lambda $$ (in V^-1) is _______

In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness is 100 nm. The permittivities of the semiconductor and the oxide layer are $${\varepsilon _s}$$ and $${\varepsilon _{os}}$$ respectively. Asuuming $${\varepsilon _s}/{\varepsilon _{ox}} = 3$$ , the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is________