  Electron transfer processes at molecule-semiconductor interfaces involve a
complex mixture of thermionic, tunneling and hopping events. Traditionally
these processes have been modeled in a piece-meal fashion, relying on
phenomenological treatments such as Simmons and Richardson equations that are
not vetted in atomistic systems and do not flow seamlessly into each other. We
present a unified modeling approach, based on the Non-equilibrium Greens
function (NEGF) formalism that allows us to integrate diverse transport regimes
and establish a comprehensive quantitative theory. By comparing our simulations
with experiments on a metal-molecule-semiconductor junction (varying molecular
lengths ~1-3nm), we identify the role of molecular monolayers in tuning the
semiconductor band-bending, and thereby overall device conductivity. We find
that the principal role of molecules is to act as a voltage divider, altering
the Schottky barriers, thereby modulating current levels, voltage-asymmetries
and crossover from Schottky to tunneling transport. While this provides an
appealingly simple explanation for our observed experimental trends, the
calculated shifts in crossover voltages are insufficient to explain the
experiments quantitatively. Quantitative correspondence with experiments
requires invocation of an additional voltage divider arising from molecular
dipoles that further tunes semiconductor band-bending. The extracted dipole
moments are rationalized using ab-initio calculations for each molecule,
along-with a dilution of packing fraction for the shortest molecular lengths.
The methodology described herein can be used to better understand and predict
transport characteristics of such junctions.
