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Hi, I think it is only true for long channel devices (length>10um). Under this length you will get other parameters which modify the equation. And Cgs depends on the operation region, bottom formula is true when your transistor is in saturation:
Cgs changes with gate potential (see C-V curves).
Your channel capacitance under the gate only gets
"hooked up" once the channel inverts. Before this
it has a varying series depletion capacitance ("off"
transitioning to a very-resistive oxide capacitance,
to a well connected one. Besides this you have the
fringing and overlap capacitances which at short
channels can be very significant. This all ought to
be characterized by the foundry modeling folks as
it's not really tractable by simple methods.
There is also the difference between optical Tox
and electrical Tox, which seem to be diverging
more as technologies advance. You'd use the
electrical, in calculations, but may only be given
the optical value.
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