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 __________.

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__________.