An n-channel MOSFET is doped to Na = 3×1016 cm−3 and has an oxide thickness of tox = 20 nm. The diffused junction radius is rj = 0.30 μm. Determine the minimum channel length such that the threshold voltage shift due to short channel effects is limited to ΔVT = −0.15 V.
![For an ideal n-channel MOSFET, the drain current equation (ID) is given as below. ID = WμnCox 2L[2(VGS − VT)VDS − VDS2] (0 ≤ VDS ≤ VDS(sat)) (a) Derive the saturation drain voltage (VDS(sat)) as a function of (VGS − VT). (b) Derive the saturation drain current (ID(sat)) as a function of (VGS − VT). (c) For very small VDS, describe how to experimentally determine both parameters, i. e. , (i) electron mobility (μn) and (ii) threshold voltage (VT). (d) Derive the transconductance (gm) at the saturation point as a function of VDS. (e) Assume that this n-channel MOSFET has the following parameters: channel length (L) = 1.25×10−4 cm, electron mobility (μn) = 650 cm2 /V−s, gate oxide (SiO2) capacitance (Cox) = 6.9×10−8 F/cm2, and threshold voltage (VT) = 0.65 V. Determine the channel width (W) such that ID (sat) is 4×10−3 A when VGS = 5 V.](https://www.doubtrix.com/uploads/editor/7329276601GxBbwPuntf.png)
