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Landauer FormulaWe consider the transport of electrons through a molecular system by modeling it as a one electron elastic scattering problem. The molecule acts as a defect between two metallic reservoirs of electrons. An electron incident from the source lead with an energy E, has a transmission probability T(E)to scatter through the molecule into the drain lead. A schematic of the model system is shown in Fig. 2.1. By determining the transmission probability for a range of energies around the Fermi energy of the source lead, the finite temperature, finite voltage, Landauer formula can be used to calculate the transmitted current I as a function of the bias voltage, V, applied between the source (left lead) and drain (right lead)The two electrochemical potentials and , refer to the source and drain, respectively. They are defined to be, and . The differential conductance is then given by the derivative of the current with respect to voltage.

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