Semi-microscopic Theory for the Current Rectification Phenomenon in Nanogap Molecular Devices

A semi-microscopic theory is developed for heterogeneous electron transfer (HET) kinetics based on the energy level alignment approach at self-assembled monolayer (SAM) covered metal electrodes. Theory provides the electronic and molecular property-dependent equations for the HET rate constant (k⁰) and the transfer coefficient (α) for potential. k⁰ is formulated using the activation free energy as a product of the SAM covered metal work function (WF) and fractional electronic charge exchanged at the transition state (attained through the alignment of the frontier molecular orbital (FMO) energy level of the electroactive group with the WF of metal). k⁰ is a function of the metal jellium electronic screening length and dielectric and of the molecular self-assembly (through its dipole moment, size, and packing density) and the FMO energies of electroactive groups. The operative potential at the transition state is governed by α, which is a function of molecular spacer length and characteristic electronic-dipolar coupling length. The current rectification phenomenon in nanogap molecular devices is theoretically analyzed using equations for k⁰ and α for SAM covered source and drain electrodes. Theory unravels the LUMO or HOMO dichotomy for a given metal: (i) for the HOMO assisted ET, the metal with a high WF has a high current rectification ratio (RR), while (ii) for the LUMO assisted ET, the metal with a low WF has a high current RR in asymmetrical devices. Theory predicts the reversal in current rectification by altering the dipole moment of the anchoring molecule, the HOMO/LUMO energy of the electroactive groups, and the nature of the metal. Finally, theory shows qualitative and quantitative coherence with the reported experimental current-potential response of molecular device.