  We present a simple tight-binding model for the two-dimensional energy bands
of polyacene field-effect transistors and for the coupling of these bands to
lattice vibrations of their host molecular crystal. We argue that the strongest
electron-phonon interactions in these systems originate from the dependence of
inter-molecule hopping amplitudes on collective molecular motion, and introduce
a generalized Su-Schrieffer-Heeger model that accounts for all vibrations and
is parameter-free once the band mass has been specified. We compute the
electron-phonon spectral function $\alpha^2F(\omega)$ as a function of
two-dimensional hole density, and are able to explain the onset of
superconductivity near 2D carrier density $n_{2D} \sim 10^{14} cm^{-2}$,
discovered in recent experiments by Sch\"on {\it et al.} \onlinecite{Batlogg}.
