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
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.