There is at present a great deal of interest in the current-voltage (I-V) characteristics of different molecular conductors sandwiched between two metallic contacts. The objective of this paper is to (i) illustrate the similarities and differences between a metal-molecule heterostructure and conventional semiconductor heterostructures; (ii) show that as in conventional heterostructures, the energy level line-up is crucial in determining the I-V characteristics, and (iii) describe a rigorous but practical parameter-free model that can be used to calculate the I-V characteristics of arbitrary metal-molecule heterostructures. Specifically, we will illustrate our method with two example molecules: (1) Au6, a short six atom chain of gold, and (2) a phenyl dithiol (PDT) molecule chemisorbed onto two FCC (111) gold contacts.
We simplify our computation by partitioning the conducting system into a molecular device and two contacts. The coupling of the contacts with the device is given by self-energy matrices which are computed by a recursive Green's function technique, incorporating the full FCC symmetry of gold. We thereafter self-consistently couple a nonequilibrium Green's function formalism (NEGF) describing transport in an open system under bias, with a evaluation of the molecular Hamiltonian, making use of the sophisticated computational power of a standard quantum chemical package (Gaussian '98). We use this method to study the effects of charging in molecular conductors, which self-consistently generates voltage screening and yields a parameter-free I-V characteristic.
We start by calculating the density of states (DOS) for Au6 bonded to two FCC gold contacts. Coupling with the contacts broadens the wire DOS from discrete atomic levels into a continuous metallic band. One can define a charge neutrality level (CNL) for the wire, such that filling the DOS up to the CNL keeps the wire neutral. The energy line-up diagram allows us to understand the process of equilibriation in the system through charge transfer. The Fermi energy of FCC gold is higher than the CNL of the wire, so electrons are transferred from the contacts to the wire. The consequent capacitative charging of the molecule floats all the levels up till the wire and the contacts are in equilibrium.
Fig. 1 shows the parameter-free I-V characteristics for an Au6 molecule. The ballistic Au6 molecular wire exhibits an ohmic I-V with a quantized conductance Go = 2e2/h 77µS, describing thus the behavior of a quantum point contact from a molecular viewpoint. Reducing the couplings with the contacts gives quasi-discrete levels as in isolated molecules, leading to a conductance gap in the I-V. Such a conductance gap is also observed in PDT, describing resonant transmission through its molecular levels. The size of the conductance gap is determined by the proximity of the metal Fermi energy with respect to the HOMO level, as well as the strength of the coupling with the contacts.
Avik W Ghosh
Purdue University, School of Electrical and Computer Engineering
1285 EE Building, West Lafayette, IN 47907-1285 USA