Inelastic Electron Tunneling via Molecular Vibrations in Single-Molecule Transistors

In single-molecule transistors, we observe inelastic cotunneling features that correspond energetically to vibrational excitations of the molecule, as determined by Raman and infrared spectroscopy. This is a form of inelastic electron tunneling spectroscopy of single molecules, with the transistor geometry allowing in situ tuning of the electronic states via a gate electrode. The vibrational features shift and change shape as the electronic levels are tuned near resonance, indicating significant modification of the vibrational states. When the molecule contains an unpaired electron, we also observe vibrational satellite features around the Kondo resonance.

Figure 1

(a) Energetics of single-electron transistor, with $\Delta \equiv \mathrm{\text{single-particle}}$ level spacing, $E_c\equiv \mathrm{\text{charging energy}}$. Dashed levels indicate manifold of vibrational excitations in molecular devices. (b) Map of $\partial I_D/\partial V_{SD}$ (brightness) of such an SET, vs source-drain bias $V_{SD}$ and gate voltage $V_G$, showing one Coulomb transition from $n$ to $n+1$ electrons on the island. Numbered points refer to the transport regimes shown in (c). (c) Relevant conduction processes in (b): $1=\mathrm{\text{elastic cotunneling}}$; $2=\mathrm{\text{inelastic cotunneling}}$; $3=\mathrm{\text{resonant conduction}}$; $4=\mathrm{\text{resonant inelastic conduction}}$; $5=\mathrm{\text{Kondo resonant conduction}}$.

Figure 2

(a) Diagram of typical single-molecule transistor fabricated by electromigration. (b) structure of $\mathbf{1}$, the compound of interest. (c) Cyclic voltammograms showing reversible change in Co ion charge state [26]. (d) Differential conductance of a transistor containing $\mathbf{1}$, at $5\mathrm{K}$. White corresponds to $\partial I_D/\partial V_{SD}=3\times {10}^{-6}S$. The zero-bias peak in the right-hand charge state is characteristic of Kondo resonant conduction.

Figure 3

Maps of ${\partial }^2{I}_D/\partial V_{SD}^2$ as a function of $V_{SD}$ and $V_G$ at 5 K for two devices. Smoothing window in $V_{SD}$ is 5 mV. Brightness scales are $-8\times {10}^{-5}\mathrm{A}/{\mathrm{V}}^2$ (black) to $3\times {10}^{-5}\mathrm{A}/{\mathrm{V}}^2$ (white), and $-2\times {10}^{-5}\mathrm{A}/{\mathrm{V}}^2$ (black) to $2\times {10}^{-5}\mathrm{A}/{\mathrm{V}}^2$, respectively. The zero-bias features correspond to Kondo peaks in $\partial I_D/\partial V_{SD}$. Prominent inelastic features are indicated by black arrows. In both devices, when the inelastic features approach the boundaries of the Coulomb blockade region, these levels shift and alter line shape (white arrows). Black dashed line in left map traces an inelastic feature across the Coulomb blockade region boundary and into the Kondo regime.

Figure 4

(top) Histogram of $|V_{SD}|$ positions of 43 features in $\partial I_D^2/\partial V_{SD}^2$ that are persistent at constant $V_{SD}$ over at least a 10 V gate voltage range, for the 12 samples discussed. Bin size is 1 meV. Width of actual features is at least 5 meV, with position indicating feature center. (bottom) Raman (black) and IR (gray) peak positions taken of $\mathbf{1}$ in the solid state at room temperature. The indicated Raman peak near $28\mathrm{m}\mathrm{e}\mathrm{V}$ is only present in films of $\mathbf{1}$ self-assembled on Au electrodes.