A certain n-channel MOSFET has a channel length of 2 microns, a gate oxide thickness of 40 nm, and a channel mobility for electrons of 600 cm2/V s. The threshold voltage is 1 V.
(a) What is the transit time of the electrons through this channel when VGS is 3 V?
(b) What is wT for this transistor at the same bias?
(c) How do your answers in parts a and b change if the channel length is reduced to 1 pm and the gate oxide thickness is reduced to 30 nm? Assume that when the gate oxide thickness is reduced, the mobility also decreases to 400 cm2/V·s.
(d) Calculate the minimum transit times for these two channels assuming $sat is 107 cmls. Calculate also what value of gate-to-source voltage VGS this transit time would correspond to if velocity saturation is not a factor (or if the saturation model of Eq. (10.77) is used); that is, find VGS in (VGS - VT) = Lssat/μe.
(e) What limits us from biasing any MOSFETs to the point that the carrier velocity is saturated in the channel?