Physics Department, University of Wisconsin, Madison, WI, USA (1999)
The normalization problem described in the previous section can be averted if we utilize thin films, where the tunneling current I remains finite inside the band gap. The states of the silicon substrate decay exponentially through the CaF_{2} film, leaving a finite density of states at the CaF_{2} surface available for tunneling.
Fig. 2 Tunneling spectra of CaF_{1}/Si(111)
and CaF_{2}/CaF_{1}/Si(111).
Two sharp onsets in the (dI/dV) spectra characterize the respective
conduction band minima and provide chemical selectivity. The normalized
(dI/dV)/(I/V) spectra exhibit resonances at the CBM. Different
line types represent different tip-sample separations.
The experimental^{5} (dI/dV)/(I/V) tunneling spectra obtained from CaF_{2}/Si(111) and CaF_{1}/Si(111) interfaces are presented in Fig. 2. The conduction band edges correspond to onsets in the (dI/dV) curves. In the normalized spectra well-defined peaks are observed at the CBM. The peak is three times as high as the continuum above it for CaF_{2} and five times as high for CaF_{1}. In search of an explanation for this phenomenon several options can be considered^{5}. Here a model for tunneling through a thin insulator film is developed, based on established approaches for planar tunneling^{6}. The outcome produces the observed resonances and even their absolute height, suggesting that the most important physical effects are indeed captured in the model with a simple barrier structure. Some possible extensions of this approach for more realistic barrier potentials will be discussed as well.