It is useful to follow this derivation along with following
Fig. 3.24.b. in the book (p. 141). In the figure, MOS is biased in
inversion. It means that the gate voltage is a bit higher than
threshold voltage 
, but lets assume one is at threshold. One
can then sum the voltages, 
, necessary to bias the device
in inversion using flatband voltage 
as a
reference. Therefore, 
. On the other hand, one
can sum the potential drops from gate material to the silicon bulk,
therefore obtaining 
. One can then
equate the two , and obtain
. But in inversion 
,
so from now on write 
as 
. Further, one knows that
, and that 
,
resulting in 
. Also
, where 
is an inversion charge,
and 
is the depletion charge. At the onset of inversion, there is
no inversion charge, so 
. 
, where
. Collecting all
the terms, one obtains the equation
or
or
and lastly
