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

Abstract

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 (k 0) and the transfer coefficient (α) for potential. k 0 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). k 0 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 k 0 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.

Theory for Outer Sphere Electron Transfer Coupled with Ion Transfer Kinetics on Atomically Stepped Metal

“…The effective applied potential at X ‡ is characterized through the transfer coefficient (α) or screening factor for the applied potential in eq of ET kinetics. Earlier we showed that for the nanogap molecular device, the transfer coefficient depends on the reaction coordinate at the transition state and a characteristic electronic-dipolar coupling length l e d . Using X ‡ = (2 l TF + r i )/2 in potential drop factor, we obtain a special case without spacer in nanogap molecular device for the transfer coefficient as α = exp ( − X ⧧ l e d ) ≈ exp ( − l T F + r i / 2 l e d ) The potential drop or screening factor in eq is useful to formulate the applied potential dependent reaction current and exchange current in HET.…”

“…Earlier we showed that for the nanogap molecular device, the transfer coefficient depends on the reaction coordinate at the transition state and a characteristic electronic-dipolar coupling length l e d . Using X ‡ = (2 l TF + r i )/2 in potential drop factor, we obtain a special case without spacer in nanogap molecular device for the transfer coefficient as α = exp ( − X ⧧ l e d ) ≈ exp ( − l T F + r i / 2 l e d ) The potential drop or screening factor in eq is useful to formulate the applied potential dependent reaction current and exchange current in HET. The operative potential at the transition state has a reduced value depending on the solvent dipole size ( r d ) and the separation of electroactive groups from the metal jellium surface.…”

“…Our earlier theories did not account for FMO energy level fluctuation induced facilitated OS-HET kinetics and therefore underpredicted the standard rate constant or demanded higher Fermi energy. (vii) The theory for the electron transport in nanogap molecular devices with rectification phenomenon is developed using conceptual modeling similar to that for OS-HET kinetics . Molecular device problems do not require inclusion of fluctuations in the FMO energy level.…”

“…The theory explains the current–potential response in quasi-tunneling and the activation control regimes. Earlier theories − ignored the contributions of (i) the solvent reorganization induced fluctuations in FMO levels of electroactive species, causing higher estimation of the Fermi energy for a quantitative agreement with experimental data, and (ii) the root-mean-square (rms) width of nanocorrugation in formulation of the step density. Earlier models did not account for an additional anomaly arising out of ion transfer kinetics to the OHP through the electric double layer (EDL), which is essential for quantitative prediction of the standard rate constant, particularly in facile or barrierless kinetics.…”

A universal platform of molecular orbital energy level prediction and molecular design for organic materials

“…Tao J. team reduced the HOMO to -5.3 eV and the LUMO to -2.8 eV in 1,6-DTEP of OPDs cuts the dark current and heightens sensitivity beyond 10 6 A/W [20][21][22]. An optimal bandgap of the electroactive groups is vital for superior OPD performance, broader spectral response, and improved photocurrent and responsivity [23]. Overall, accurately tuning HOMO and LUMO not only boosts the performance of these organic optoelectronic devices but also broadens their application scope, which is key to high-performance organic optoelectronic devices and propels the advancement of organic materials in optoelectronics.…”