In the Pao-Sah charge model of the MOSFET the diffusion term cancels out. This should not be a huge surprise because there is no dissimilar semiconductor junction. Current is constant along the channel so let's treat it like a resistor while again ignoring any gate structure.
The old fashioned formula for conductance.
Translate that into MOSFET terminology using the following:
where Q is charge density which we will choose to be charge density at the source to agree with the Pao Sah model.
Sneak an h (height) subscript onto W to remind that W is really an area. Using these we get
Although this method is different and much shorter and intuitive than the standard book derivation for this formula it agrees with the Pao Sah model. See page 40 of CMOS Analog Design Using All Region MOSFET Modeling: equation 2.1.51
Notes
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The Professor likes big mosfets. Fist-sized barrels of silicon with a few terminals.
I saw this pine cone the other day that looked like a pineapple. And by pineapple, you know what I mean. That would be an interesting disguise.
Nostrand leaves no man behind in a cloud of misunderstanding or fog of darkness. Want to know what to do whe you think it's butter but it's not? Then call The Professor as he tells it like it is. Profess, Professor, profess! Word. Testify.
(sumbuddy got attuned ta'nite)
Oh man Prof Nasalhar….that is funny schtuff!