Scanning Tunneling Spectroscopy of Cl Vacancies in NaCl Films: Strong Electron-Phonon Coupling in Double-Barrier Tunneling Junctions

Broad Gaussian line shapes are observed in scanning tunneling spectroscopy of single, localized electronic states induced by Cl vacancies in ultrathin NaCl films on Cu surfaces. Using a simple inelastic resonance tunneling model, we show that the observed broad line shapes are caused by a strong coupling between the localized state and the optical phonons in the film. The parameters for the model are obtained from density functional calculations, in which the occupation of the vacancy state temporarily taking place in the experiment has also been accounted for.

Figure 1

Experimental (a), (b) and simulated STM images (c) of an individual Cl vacancy in the top layer of a bilayer of NaCl on Cu(111) (a), (b) and Cu(100) (c). Whereas the low-bias image (a), (c) shows a missing protrusion, the image at high bias voltage (b) shows a large protrusion of 4.5 Å in height. (d) $dI/dV$ spectra at a Cl vacancy in a bilayer of NaCl on Cu(311), Cu(100), and Cu(111). The calculated peak positions are shown as vertical lines for NaCl bilayer on Cu(311) and Cu(100). In the case of $\mathrm{NaCl}/\mathrm{Cu}(111)$, there is an additional peak at $-0.26\mathrm{V}$ that can be resolved only when taking a spectrum with the tip being about $\Delta z\simeq -7\AA$ closer to the surface. In the inset a sphere model of the vacancy geometry is shown.

Figure 2

$dI/dV$ spectrum of the VS in a bilayer of NaCl on Cu(111) fitted to Lorentzian and Gaussian line shapes. The slight deviation from the Gaussian (shaded area) is in agreement with the tunneling barrier being modified by the applied voltage [33]. Inset: VS peak position for varying tip-surface distances. The best fit to a 1D capacitor model [4] is indicated by a solid line. $\Delta z=0$ refers to a current of 1.5 pA.

Figure 3

$dI/dV$ spectrum of the ISL in a bilayer of NaCl on Cu(111) fitted to Lorentzian and Gaussian line shapes. The slight deviation from the Lorentzian (shaded area) is due to the remnants of the interface-state band. For comparison, the position of the onset of the interface-state band for the defect-free surface is indicated by an arrow. Inset: STM image acquired at $V=58\mathrm{mV}$ showing the scattering of the interface state at the vacancies.

Figure 4

Illustration of the broadening mechanism.