Q3. Imperfect MOSFET As is often the case, 'real' MOSFETS are generally not ideal. One non-ideality that we saw in the lectures is the channel length modulation, where the effective length of the channel is shortened which Vps exceeds Vps (sat). The geometry of such a situation, for an nMOS is shown in Fig. 2, where the change to the channel length is AL. O VGs Inversion S charge O Vps n* AL p type Vps(sat) = VGs Vr*AVps * Vps - Vps(sat) Figure 2: Channel length modulation for an nMOS. (a) Recall that the width of the space charge region width at the drain is, 26 Xp = (fp + Vps), eNa which is equal to zero when Vps = Vps (sat). Begin by writing the voltage drop at points A and B, for the scenario shown in Fig. 2. (b) To first order, we can write the change in channel length AL as the difference between the space charge region width of the whole channel (B) and that at the point of inversion (A). What is this expression for AL? (c) We wish to design an enhancement mode nMOS out of Si doped at Na = 1017 cm-3 that has a threshold voltage VTN = 0.5 V, a channel length L = 1 m, and which at an applied VGS = 1 V and Vps = 2.5 V has a saturation current of Ip = 5 mA. Assume also that the oxide layer is15 nm Si) as in Q2. In the ideal case, what width should the nMOS channel be (Fig. 3 may be helpful)? (d) Now, lets account for the modulation of the channel length using our results in part (b). How should we change the channel width to recover our desired I-V relation?. (e) How would the width change, in both the ideal and non-ideal situations, if we want the same operation but with a channel that is only 500 nm long? 104 103 Si 10 1014 10'5 1016 1017 Impurity concentration (cm-3) 1018 1019 Figure 3: Mobility in silicon as a function of impurity concentration. Mobility (cm/V-s)