  A model describing the low density carrier state in an organic single crystal
FET with high-$\kappa$ gate dielectrics is studied. The interplay between
charge carrier coupling with inter-molecular vibrations in the bulk of the
organic material and the long-range interaction induced at the interface with a
polar dielectric is investigated. This interplay is responsible for the
stabilization of a polaronic state with an internal structure extending on few
lattice sites, at much lower coupling strengths than expected from the polar
interaction alone. This effect could give rise to polaron self-trapping in
high-$\kappa$ organic FET's without invoking unphysically large values of the
carrier interface interaction.
