Ex situ determination of the tip DOS

In general, the tip DOS does not resemble that of a free-electron metal. To have meaningful STS measurements, the tip DOS must be determined independently. A well-established experimental method for determining the energy spectmm a sharp metal tip is field emission spectroscopy (FES), which was described in Section 4.4. For free-electron metal tips, the FES is described by the Young formula, Eq. (4.20). A deviation from the Young formula indicates a deviation from a free-electron metal behavior. 

In Section 13.3.4, a method of generating sharp tips ended with single atom was described (Binh and Garcia, 1991, 1992). Such tips are necessary for 

The spectra of the single-atom tips are composed solely of well-separated peaks. An example is shown in Fig. 14.8(a). Here, three peaks are observed. The actual position and intensity of the peaks depends on the details of the atomic structure near the apex atom. For comparison, with a macroscopic tip, only one peak is observed right below the Fermi level, see Fig. 14.8(b). 

Although the FES of the macroscopic tip fits well with the Young formula, Eq. (4.20), none of the peaks in the FES of the single-atom tip fits it. 

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