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The splitting of quasi-Fermi levels (QFLs) represents a key concept utilized to describe finite-bias operations of semiconductor devices, but its atomic-scale characterization remains a significant challenge. Herein, the non-equilibrium QFL or electrochemical potential profiles within single-molecule junctions obtained from the newly developed first-principles multi-space constrained-search density functional formalism are presented. Benchmarking the standard non-equilibrium Green's function calculation results, it is first established that algorithmically the notion of separate electrode-originated nonlocal QFLs should be maintained within the channel region during self-consistent finite-bias electronic structure calculations. For the insulating hexandithiolate junction, the QFL profiles exhibit discontinuities at the left and right electrode interfaces and across the molecule the accompanying electrostatic potential drops linearly and Landauer residual-resistivity dipoles are uniformly distributed. For the conducting hexatrienedithiolate junction, on the other hand, the electrode QFLs penetrate into the channel region and produce split QFLs. With the highest occupied molecular orbital entering the bias window and becoming a good transport channel, the split QFLs are also accompanied by the nonlinear electrostatic potential drop and asymmetric Landauer residua-resistivity dipole formation. Our findings underscore the importance of the first-principles extraction of QFLs in nanoscale junctions and point to a new direction for the computational design of next-generation electronic, optoelectronic, and electrochemical devices.