A MOS capacitor is fabricated on p-type Si (silicon) where the metal work function is 4.1 eV and electron affinity of Si is 4.0 eV, E_c - E_F = 0.9 eV; where E_c and E_F are conduction band minimum and the Fermi energy levels of Si, respectively. Oxide$${\varepsilon _r} = \,\,3.9,\,\,\,{\varepsilon _{0\,\,}}=\,8.85 \times {10^{ - 14}}$$ F/cm, oxide thickness $${t_{ox}} = 0.1\,\mu m$$ and electronic charge q = $$1.6 \times {10^{ - 19}}$$ C. If the measured flat band voltage of the capacitor is –1V, then the magnitude of the fixed charge at the oxide semiconductor interface, in nC/cm², is __________.

For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage V_tn = 1 V and its trans-conductance parameter $${\mu _n}{C_{ox}}\left( {{W \over L}} \right) = 1m{\rm A}/{V^2}.$$ Neglect channel length modulation and body bias effects. Under these conditions the drain current I_D in mA is______.

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 in the figure, the channel length modulation of all transistors is non-zero $$\left( {\lambda \ne 0} \right)$$. Also all transistors operate in saturation and have negligible body effect. The ac small signal voltage gain $$\left( {{V_0}/{V_{in}}} \right)$$ of the circuit is