  The electrostatic potential across a short ballistic molecular conductor
depends sensitively on the geometry of its environment, and can affect its
conduction significantly by influencing its energy levels and wave functions.
We illustrate some of the issues involved by evaluating the potential profiles
for a conducting gold wire and an aromatic phenyl dithiol molecule in various
geometries. The potential profile is obtained by solving Poisson's equation
with boundary conditions set by the contact electrochemical potentials and
coupling the result self-consistently with a nonequilibrium Green's function
(NEGF) formulation of transport. The overall shape of the potential profile
(ramp vs. flat) depends on the feasibility of transverse screening of electric
fields. Accordingly, the screening is better for a thick wire, a multiwalled
nanotube or a close-packed self-assembled monolayer (SAM), in comparison to a
thin wire, a single-walled nanotube or an isolated molecular conductor. The
electrostatic potential further governs the alignment or misalignment of
intramolecular levels, which can strongly influence the molecular I-V
characteristic. An external gate voltage can modify the overall potential
profile, changing the current-voltage (I-V) characteristic from a resonant
conducting to a saturating one. The degree of saturation and gate modulation
depends on the metal-induced-gap states (MIGS) and on the electrostatic gate
control parameter set by the ratio of the gate oxide thickness to the channel
length.
