(Solved): Problem 3: (Points: \( 5 \times 7=35 \) ) The silicon based nMOS transistor is shown below which is ...

Problem 3: (Points: \( 5 \times 7=35 \) ) The silicon based nMOS transistor is shown below which is operated at \( 27^{\circ} \mathrm{C} \) and silicon's intrinsic carrier concentration is \( n_{i}=1 \times 10^{10} \mathrm{~cm}^{-3} \). It has channel length \( \mathrm{L}=45 \mathrm{~nm} \), width \( \mathrm{W}=1 \mu \mathrm{m} \), channel mobility is \( \mu_{n}=200 \mathrm{~cm}^{2} V^{-1} \mathrm{~s}^{-1} \), p-well doping \( N_{A}=1 \times 10^{17} \mathrm{~cm}^{-3} \), and channel length modulation \( \lambda=0 \). The gate oxide's relative permittivity and thickness are \( \varepsilon_{r}=3.9 \) and \( t_{e x}=30 \mathrm{~nm} \). Solve the following problems. (a) Calculate oxide capacitance \( C_{\mathrm{ef}} \) in \( \mathrm{F} / \mathrm{cm}^{2} \). (b) Calculate the threshold voltage \( V_{r} \) if \( \phi_{m i}=0.6 \mathrm{~V} \), and \( Q_{s}=Q_{s s}=Q_{t}=0 \) and body effect coefficient \( y=0 \). (c) Calculate the current \( I_{D} \) when \( V_{\theta}=0 \mathrm{~V} \), and \( V_{D}=3 \mathrm{~V} \). (d) Calculate the current \( I_{D} \) when \( V_{G}=3 \mathrm{~V} \), and \( V_{D}=1 \mathrm{~V} \). (e) Calculate the current \( I_{D} \) when \( V_{G}=3 \mathrm{~V} \), and \( V_{D}=4 \mathrm{~V} \).