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Field-Emission Resonances in Thin Metallic Films: Nonexponential Decrease of the Tunneling Current as a Function of the Sample-to-Tip Distance
Field-emission resonances (FERs) for two-dimensional Pb(111) islands grown on Si(111)7x7 surfaces were studied by low-temperature scanning tunneling microscopy and spectroscopy (STM/STS) in a broad range of tunneling conditions with both active and disabled feedback loop. These FERs exist at quantized sample-to-tip distances Z_n above the sample surface, where n is the serial number of the FER state. By recording the trajectory of the STM tip during ramping of the bias voltage U (while keeping the tunneling current I fixed), we obtain the set of the Z_n values corresponding to local maxima in the derived dZ/dU(U) spectra. This way, the continuous evolution of Z_n as a function of U for all FERs was investigated by STS experiments with active feedback loop for different I. Complementing these measurements by current--distance spectroscopy at a fixed U, we could construct a 4-dimensional I-U-Z-dZ/dU diagram, that allows us to investigate the geometric localization of the FERs above the surface. We demonstrate that (i) the difference \delta Z_n=Z_(n+1)-Z_n between neighboring FER lines in the Z-U diagram is independent of n for higher resonances, (ii) the \delta Z_n value decreases as U increases; (iii) the quantized FER states lead to the periodic variations of ln I as a function of Z with periodicity \delta Z; (iv) the periodic variations in the ln I – Z spectra allows to estimate the absolute height of the tip above the sample surface. Our findings contribute to a deeper understanding on how the FER states affect various types of tunneling spectroscopy experiments and how they lead to a non-exponential decay of the tunneling current as a function of Z at high bias voltages in the regime of quantized electron emission.