Tunneling through molecular wires: a comparison of the Franz two‐band model with exact results

Abstract

AbstractThis report concerns finding the tunneling exponential factor exp [–2κ (E) d ], on the basis of electronic band structure of organic oligomers, which are d ‐long molecular wires. It is shown that energy dependence κ (E) given by the Franz two‐band model agrees remarkably well with exact model calculations, provided that the quadratic dispersion parameter is calculated from the real (non‐parabolic) band structure of organic oligomers. For narrow and moderate band gaps (with respect to the band width), the approximate dependence is practically indistinguishable from that which is obtained from these exact calculations. The divergence (particularly, in the mid of the band gap) becomes appreciable and increases with an increase of the band‐gap/band‐width ratio. The apparent effective mass (as it is estimated from κ (E) measured at the Fermi energy E = EF) is defined in terms of the inherent parameters of the wire. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)