Why doesn't body effect place limit on number of series transistors in CMOS network?

Question

My textbook (Weste and Harris) asks the following:

Does the body effect of a process limit the number of transistors that can be placed in series in a CMOS gate at low frequencies?

It answers with the following:

No. Any number of transistors may be placed in series, although the delay increases with the square of the number of series transistors.

Now I'm not at a point where I've studied delay so I'll take that for granted, but why on Earth is the answer "No" in the first place? Consider, let's say, a PDN which is trying to discharge the capacitance on the output node of a custom CMOS logic gate. If I stack enough transistors in series, won't the high source voltages (and thus high threshold voltages) of the transistors "higher up"/closer to the high voltage output node utterly restrict (and perhaps completely cut off, neglecting subthreshold effects?) this discharge?

Answer 1

I think my problem was with not understanding what was meant by "limit" in the problem statement.

In terms of the setup of the problem, we are to imagine the setup for the problem as that we have a series stack PDN of NMOS transistors and that all transistors on the stack go from having 0 on their gates to 1 on their gates at the same instant, or that all were previously 1 except the bottom transistor which switches to 1 (and I guess based on leakage arguments or by assumption it would follow that these intermediate nodes are variously charged at some voltage between \$V_{DD}\$ down to \$GND\$) -- that is, basically the situation outlined in Figure 4.23 of the text:

I will call the NMOS nearest \$GND\$ as M1 and that nearest the output node as MN. It follows that the discharge begins with M1 and potentially some other Mi with source voltages not too high so that they can turn on as discharging, and that this propagates up the chain until eventually MN turns on. From this, it would seem to follow that the body effect \emph{does} matter, because it for a given source voltage on Mi, there will be less current draw from Mi because of the higher threshold voltage of Mi. This slows down the discharge of the PDN.

But by "limit" I think we mean "will the PDN eventually discharge completely", in which case I agree that the answer is "yes, and so the body effect has no difference." If this is the case, the allusion to "low frequencies" basically refers to low clock frequencies, so that we can "imagine the PDN has as much time as it needs to discharge".