Motivated in part by this recent paper and ensuing conversation here, I thought it might be useful to say a few words about inelastic electron tunneling spectroscopy (IETS). Mysterious kinks in the current as a function of voltage were first observed over 40 years ago in oxide tunnel junctions between superconductors. As the voltage passed certain threshold values, the conductance (slope of I vs. V) increased suddenly. A kink in I vs. V could also be plotted as a step in dI/dV vs. V, or as a peak in d2I/dV2 vs. V. When plotted this way, and converting V into units of energy, Jaklevic and Lamb realized that what they saw looked remarkably like an infrared or Raman spectrum of some organic compound. They were right - using inelastic electron tunneling, they had measured the vibrational spectrum of organic compounds that had been trapped in their tunnel barrier during the fabrication process. IETS has undergone a major resurgence in the last decade, in part because of Wilson Ho's group's beautiful demonstration that one can see these effects at the single molecule level, and because it's a way of confirming that fabricated molecular junctions actually contain what they're supposed to.
In IETS, current flows via a second-order tunneling process, in which an electron tunnels on to the vibrational ground state of a molecule, and in the same coherent process tunnels of the vibrationally excited state of that molecule, leaving behind a vibrational quantum of energy. This can only happen of the voltage applied is large enough to supply the necessary energy; hence the thresholds seen in experiment. The voltage positions of the features correspond directly with the energies of the modes being excited. (In the single-electron transistor world, this process would be called "inelastic cotunneling" via vibrationally excited states.) The requirement that there be a nonzero amplitude for this process gives rise to selection rules, so that not every mode can be pumped this way. More recently, it's been realized that IETS may not necessarily always lead to simple peaks in d2I/dV2 vs. V, because the IETS process can interfere coherently with other tunneling processes. This is supported by data in the paper mentioned at the top of this post.
IETS is pretty amazing, when you think about it. Even though the tunneling electrons never "really" occupy the molecule (such a state is classically forbidden due to energy conservation), nonetheless the molecule "feels" the effects of the electrons as they tunnel past.