ABSTRACT
Transition voltage (Vt) spectroscopy (TVS) represents an appealing tool of molecular electronics. It aims at determining the relative energetic alignment 0 of the frontier molecular orbitals by using Vt , the voltage at the minimum of the so-called Fowler-Nordheim plot. A series of theoretical aspects related to TVS will be addressed here. It will be shown that many experimental TVS data can be very accurately described by means of the Newns-Anderson model, which also allows to deduce analytical expressions that can easily be used by experimentalists for processing transport data. The transition voltage can be considered as a molecular signature, because, unlike the ohmic conductance, it is less affected, e.g., by stochastic fluctuations or electron correlations brought about by
Coulomb interactions at the contacts. Contrary to the initial claim, Vt is not related to a “transition” in a conventional sense; rather, the “transition” is from a linear response regime to a significant nonlinear regime. A critical aspect considered here is the applicability of the so-called Simmons model-the reason why this model is inappropriate for molecular transport will be presented. 11.1 Introduction
In the continuous efforts for miniaturization, using single molecules as active components for future nanoelectronics (Choi et al., 2008; Hybertsen et al., 2008; Lindsay and Ratner, 2007; Reed et al., 1997; Nitzan and Ratner, 2003; Tao, 2006; Song et al., 2009; Song et al., 2011; Venkataraman et al., 2006; Xu and Tao, 2003) appears at present as the only conceivable alternative, which escapes the fundamental limitations of complementary metal-oxide semiconductor (CMOS) technologies.In nanoelectronic devices, charge transfer between the source and drain electrodes across a nanogap (spatial width d of a few nanometers) can occur via through-bond and through-space processes. An important nanotransport mechanism, to which we will restrict ourselves below, is the coherent electron tunneling.Currents through vacuum nanojunctions are due to electron tunneling across an energy barrier whose height is basically determined by the metallic work functions. If molecules are inserted into the nanogap and contacted to the electrodes to form molecular junctions, they influence the charge transfer in different ways depending on the molecular properties. If none of the molecular orbitals is sufficiently close to the Fermi energy EF of the electrodes, one could still consider electrons tunnel through an energy barrier. However, this barrier is different from that in vacuum; the molecules in the nanogap modify the barrier height via polarization effects (dielectric constant κr > 1) and renormalize the electron mass (effective free mass different from free electron mass, m ≠ m0). The transport in this case resembles (but is not iden-tical to) the transport through thin metal-semiconductor-metal junctions in traditional electronics. Early attempts made in semi-
conductor physics (Gundlach, 1966; Simmons, 1963) recognized that the direct determination the barrier height from the measured current-voltage (I-V ) characteristics is an important and, at the same time, nontrivial task. The transport mechanism based on the barrier picture is referred to as direct tunneling by some authors, although this term is also employed in a different sense (see below).In most cases, due to the charge neutrality condition, the electrodes’ Fermi level lies between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In such situations, electrons travel from one electrode to another via nonresonant (superexchange (McConnell, 1961; Ratner, 1990; Skourtis and Beratan, 1999)) tunneling, through the tails of the density of states of the molecular orbital (MO), which is closest to the Fermi level. The latter acquires a finite width due to the molecule-electrode couplings. The energetic alignment 0 EMO − EF of the frontier molecular orbitals (HOMO or LUMO) relative to the electrode Fermi energy EF plays a role similar to the barrier height mentioned above and represents a key parameter of molecular electronic devices.Transition voltage spectroscopy (TVS) is an appealing method proposed recently (Beebe et al., 2006), which aims at the determination of 0. Due to its simplicity, it is becoming increasingly popular among experimentalists working in molecular electronics (Beebe et al., 2008; Chiu and Roth, 2008; Coll et al., 2009; Coll et al., 2011; Fracasso et al., 2013; Guo et al., 2011; Guo et al., 2013a; Guo et al., 2013b; Kim et al., 2011; Lee and Reddy, 2011; Lennartz et al., 2011; Malen et al., 2009; Ricoeur et al., 2012; Song et al., 2009; Song et al., 2011; Smaali et al., 2012; Tan et al., 2010; Trouwborst et al., 2011; Tran et al., 2013; Wang et al., 2011; Yu et al., 2008; Zangmeister et al., 2008.
