I
am working with 90 nm CMOS at the moment and have some difficulty with the hand
calculations. I am trying to
hand calculate
values, similar to what's seen in Table 9.2, using short-channel
equations.
You
can't use MOSFET current-voltage (IV) equations to get small-signal parameters
for hand calculations in
nanometer CMOS since
there aren't any equations that are accurate. If there were the SPICE models
would be much
simpler.
You
have to use experimental data to get small-signal parameters (gm, ro, etc.) for hand calculations. The experimental
data is easiest to
use in plot form from SPICE simulations or from the electrical information you
get from the foundry.
All
SPICE models nowadays are determined experimentally so the simulations give you
the experimental data (see, for
example, pages 298 and
299 in the book). The parameters of the SPICE model are "curve fit"
to match the experimental
data. The designer
can then take the model and generate plots, using SPICE, for specific operating
conditions and
thus hand
calculations.
So,
why didn't (or can't) we use, for example, Eqs. (9.56) and
(9.57) to do hand calculations? Many reasons.
In
Eq.
(9.56) vsat, for example, isn't a constant but a
function of device size, VDS,
and VGS. VTHN and VDS,sat also
aren't constant values
and change drastically with changes in the voltage across the devices. The
equations are
useful to see the
reduction in gm or ID in short-channel
processes; however, they aren't useful for hand calculations
since they can't be
used for good modeling of the devices.
Note
that I assumed you weren't talking about using long-channel (square-law)
equations, page 271, for nanometer
CMOS
since that is fundamentally wrong as discussed in the book.