Determining the molecular Huang-Rhys factor via scanning-tunneling- microscopy–induced luminescence

Scanning-tunneling-microscopy–induced luminescence can be used to probe the optical and electronic properties of molecules. Concerning the vibronic coupling, we model the molecule as a two-level system with vibrational degrees of freedom. Based on Bardeen's theory, we express the inelastic tunneling current in terms of the Huang-Rhys factor within the inelastic electron scattering mechanism. We find that the differential conductance, varying with the bias voltage, exhibits a distinct step structure with various vibronic coupling strengths. The second derivative of the inelastic tunneling current with respect to the bias voltage shows the characteristics of a vibrational-level structure with the Franck-Condon factor. Consequently, we propose a method to determine the Huang-Rhys factor of molecules, holding promising potential within the realm of solid-state physics.

Figure 1

(a) The inelastic tunneling current and (b) the differential conductance as a function of the bias voltage. The red (upper) curve, the yellow (middle) curve, and the blue (lower) curve correspond to vibronic coupling strengths with $S=0.5, S=5$, and $S=10$, respectively. We have chosen parameters as $R=0.5\mathrm{nm}, d=0.5\mathrm{nm}, \vec{a}=(0,0,d+R), E_{eg}=2\mathrm{eV}$, and ${\mu }_0=-4.64\mathrm{eV}$. The characteristic frequency of the molecular vibration is fixed at $0.1\mathrm{eV}$.

Figure 2

The second derivative of the inelastic tunneling current with respect to the bias voltage (solid red line) and the Frank-Condon factor (blue asterisks) as a function of the bias voltage. (a)–(d) correspond to cases of $S=0.5, S=1, S=5$, and $S=10$, respectively. Parameters are the same as before.

Figure 3

The comparison of the estimated value of $S$ from Eq. (28) with the true value of $S$. The red line is linear and represents the true value of $S$. The blue circles are the estimated values from the left-hand side of Eq. (28), corresponding to cases of $S=0.1, S=0.5, S=1, S=5$, and $S=10$, respectively.