Improving Transition Voltage Spectroscopy of Molecular Junctions

Transition voltage spectroscopy (TVS) is a promising spectroscopic tool for molecular junctions. The principles in TVS is to find the minimum on a Fowler-Nordheim plot where $\ln(I/V^2)$ is plotted against $1/V$ and relate the voltage at the minimum, $V_{\rm min}$, to the closest molecular level. Importantly, $V_{\rm min}$, is approximately half the voltage required to see a peak in the $dI/dV$ curve. Information about the molecular level position can thus be obtained at relatively low voltages. In this work we show that the molecular level position can be determined at even lower voltages, $V_{\rm min}^{(\alpha)}$ by finding the minimum of $\ln(I/V^\alpha)$ with $\alpha<2$. On the basis of a simple Lorentzian transmission model we analyze theoretical {\it ab initio} as well as experimental $I-V$ curves and show that the voltage required to determine the molecular levels can be reduced by $\sim 30%$ as compared to conventional TVS. As for conventional TVS, the symmetry/asymmetry of the molecular junction needs to be taken into account in order to gain quantitative information. We show that the degree of asymmetry may be estimated from a plot of $V_{\rm min}^{(\alpha)}$ vs. $\alpha$.