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 CaF₂ film, leaving a finite density of states at the CaF₂ surface available for tunneling.

Fig. 2 Tunneling spectra of CaF1/Si(111) and CaF2/CaF1/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 experimental⁵ (dI/dV)/(I/V) tunneling spectra obtained from CaF₂/Si(111) and CaF₁/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 CaF₂ and five times as high for CaF₁. In search of an explanation for this phenomenon several options can be considered⁵. Here a model for tunneling through a thin insulator film is developed, based on established approaches for planar tunneling⁶. 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.