  Self-assembled-monolayer (SAM) molecular junctions (MJs) constitute a
promising building block candidate for future molecular electronic devices.
Transport properties of SAM-MJs are usually calculate using either the
phenomenological Simmons model, or a fully-coherent transport theory, employing
the SAMs periodicity. We suggest that dephasing plays an important role in
determining the transport properties of SAM-MJs. We present an approach for
calculating the transport properties of SAM-MJs that inherently takes into
account in-plane dephasing in the electron motion as it traverses the SAM
plane. The calculation is based on the non-equilibrium Green's function
formalism, with a local dynamics approximation that describes incoherent motion
along the SAM plane. Our approach describes well the two hallmarks of transport
through SAM-MJs, namely the exponential decay of current with molecular chain
length and the reduction of the current per molecule as compared to
single-molecule junctions. Specifically, we show that dephasing leads to an
exponential decay of the current as a function of molecular length, even for
resonant tunneling, where the fully coherent calculation shows little or no
length-dependence of the current. The dephasing is also shown to lead to a
substantial reduction of the current in a SAM-MJ as compared to the single
molecule junction, in a realistic parameter regime, where the coherent
calculation shows only a very small reduction of the current. Finally, we
discuss the effect of dephasing on more subtle transport phenomena such as the
conductance even-odd effect and negative differential resistance.
