  A general solution for the electrostatic potential in an atomic-thin-body
(ATB) field-effect transistor geometry is presented. The effective
electrostatic scaling length, {\lambda}eff, is extracted from the analytical
model, which cannot be approximated by the lowest order eigenmode as
traditionally done in SOI-MOSFETs. An empirical equation for the scaling length
that depends on the geometry parameters is proposed. It is shown that even for
a thick SiO2 back oxide {\lambda}eff can be improved efficiently by thinner top
oxide thickness, and to some extent, with high-k dielectrics. The model is then
applied to self-consistent simulation of graphene nanoribbon (GNR)
Schottky-barrier field-effect transistors (SB-FETs) at the ballistic limit. In
the case of GNR SB-FETs, for large {\lambda}eff, the scaling is limited by the
conventional electrostatic short channel effects (SCEs). On the other hand, for
small {\lambda}eff, the scaling is limited by direct source-to-drain tunneling.
A subthreshold swing below 100mV/dec is still possible with a sub-10nm gate
length in GNR SB-FETs.
