  Molecular electronics on silicon has distinct advantages over its metallic
counterpart. We describe a theoretical formalism for transport through
semiconductor-molecule heterostructures, combining a semi-empirical treatment
of the bulk silicon bandstructure with a first-principles description of the
molecular chemistry and its bonding with silicon. Using this method, we
demonstrate that the presence of a semiconducting band-edge can lead to a novel
molecular resonant tunneling diode (RTD) that shows negative differential
resistance (NDR) when the molecular levels are driven by an STM potential into
the semiconducting band-gap. The peaks appear for positive bias on a p-doped
and negative for an n-doped substrate. Charging in these devices is compromised
by the RTD action, allowing possible identification of several molecular
highest occupied (HOMO) and lowest unoccupied (LUMO) levels. Recent experiments
by Hersam et al. [1] support our theoretical predictions.
