  This paper addresses the question of whether a ``rigid molecule'' (one which
does not deform in an external field) used as the conducting channel in a
standard three-terminal MOSFET configuration can offer any performance
advantage relative to a standard silicon MOSFET. A self-consistent solution of
coupled quantum transport and Poisson's equations shows that even for extremely
small channel lengths (about 1 nm), a ``well-tempered'' molecular FET demands
much the same electrostatic considerations as a ``well-tempered'' conventional
MOSFET. In other words, we show that just as in a conventional MOSFET, the gate
oxide thickness needs to be much smaller than the channel length (length of the
molecule) for the gate control to be effective. Furthermore, we show that a
rigid molecule with metallic source and drain contacts has a temperature
independent subthreshold slope much larger than 60 mV/decade, because the
metal-induced gap states in the channel prevent it from turning off abruptly.
However, this disadvantage can be overcome by using semiconductor contacts
because of their band-limited nature.
