A voltage V_G is applied across a MOS capacitor with metal gate and p-type silicon substrate at T=300 K. The inversion carrier density (in number of carriers per unit area) for V_G = 0.8 V is $$2\,\, \times \,\,{10^{11}}\,\,\,\,\,\,c{m^{ - 2}}$$ . For $${V_G}\,\, = \,\,1.3\,\,V,$$ the inversion carrier density is $$4\,\,\, \times \,\,\,{10^{11}}\,\,\,\,c{m^{ - 2}}.$$ What is the value of the inversion carrier density for V_G = 1.8 V?

Consider a long-channel NMOS transistor with source and body connected together. Assume that the electron mobility is independent of V_GS and V_DS. Given,
g_m = 0.5$$\mu {\rm A}/V$$ for V_DS = 50 m V and V_GS = 2V,
g_d = $$8\mu {\rm A}/V$$ for V_GS = 2 V and V_DS = 0 V,
Where g_m =$${{\partial {{\rm I}_D}} \over {\partial {V_{GS}}}}\,\,and\,\,{g_d}\,\, = \,{{\partial {{\rm I}_D}} \over {\partial {V_{DS}}}}$$

The threshold voltage (in volts) of the transistor is

Consider an n-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-to-source voltage of 1.8 V. Assume that $${W \over L} = 4,{\mu _{\rm N}}{C_{ox}} = 70 \times {10^{ - 6}}{\rm A}{V^{ - 2}}$$ , the threshold voltage is 0.3V, and the channel length modulation parameter is 0.09 V^-1, In the saturation region, the drain conductance (in micro siemens) 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 ______