  In this letter we describe electronic measurements of a conjugated polymer of
phenylenevinylene (PPV) with electrode spacings down to 20 nm; all measurements
are made in a gated transistor geometry. With rectangular electrodes we find
that the current is fit by an exponential in the applied electric field for
spacings between 50 nm and 2um. Based on this finding we conclude that the
current is not injection limited, and is concentrated in a very small region;
we also discuss possible transport mechanisms. The calculated mobility appears
exponential in the electric field rather than in the square root of field. We
also show fabricated triangular electrodes with spacings down to 5 nm, and
discuss measurements with spacings down to 20 nm in which a single chain of
polymer may dominate the conductance.
