Question 6.2: For an n-channel MOSFET with a gate oxide thickness of 10 ...
For an n-channel MOSFET with a gate oxide thickness of 10 nm,V_{T} =0.6V, and Z = 25 µm, L = 1 µ m. Calculate the drain current at V_{G} =5VandV_{D} =0.1V. Repeat forV_{G} =3Vand V_{D} =5V. Discuss what happens forV_{D} =7V. Assume an electron channel mobility of \bar{\mu }_{n} =200 {cm^{2} }/{V-s}.
C_{i}=\frac{\epsilon _{i} }{d} =\frac{\left(3.9\right)\left(8.85\times 10^{-14} \right) }{10^{-6}} =3.45\times 10^{-7}{F}/{cm^{2} }
forV_{G} =5VandV_{D} =0.1Vand V_{T} =0.6V, V_{D}\lt \left(V_{G}-V_{T}\right), we are in the linear region. Thus,
I_{D}=\frac{Z}{L} \bar{\mu }_{n}C_{i}\left[\left(V_{G}-V_{T}\right)V_{D}-\frac{1}{2} V^{2}_{D} \right]
=\frac{25}{1}\left(200\right) \left(3.45\times 10^{-7} \right) \left[\left(5-0.6\right)\times 0.1 -\frac{1}{2}\left(0.1\right)^{2} \right] =7.51\times 10^{-4} A
forV_{G} =3Vand V_{D} =5V,V_{D} \left(sat.\right) =V_{G}-V_{T}=3-0.6=2.4V
I_{D} =\frac{Z}{L} \bar{u}_{n}[_{i}\left[\left(V_{G} – V_{T} \right)V_{D}(sat.)-\frac{1}{2}V^{2}_{D}\left(sat.\right) \right ]
=\frac{25}{1}\left(200\right)\left(3.45\times 10^{-7} \right) \left[\left(2.4 \right)^{2}-\frac{1}{2} \left(2.4 \right)^{2} \right] =4.97\times 10^{-3} A
For V_{D} =7V,I_{D} will not increase, because we are in the saturation region.
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