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In chapter 1.3.2
we considered that it is possible to estimate average electron
work-function of electrodes using current-distance experimental curves.
However, these measurements give work-function values only in small
region where one electrode is located over another. In STM there is
another method which is able to measure distribution of work-function
along all investigated sample surface.
The work function distribution measurement is performed in parallel with surface topography imaging in the 
mode. In this case, the Z-axis piezo tube motion is determined not only
by the feedback signal but also by application of an alternating signal
producing motion law  . Accordingly, the tip-sample separation is  , where parameter being  ,  – tip-sample separation held constant through the feedback,  – Z-axis piezo tube resonant frequency (Fig. 1).
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| Fig. 1. Diagram of MIM system when tip-sample distance is modulated as . |
If voltage applied between tip and sample is small  , then according to designations introduced, expression (2) from chapter 1.2.2 can be transformed to the following
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(1) |
where  .
Thus, total current flowing through the tunneling gap in this case is equal to  , where  – alternating tunneling current. Because 
is held constant during the scan, the alternating tunneling current
amplitude is proportional to the square root of the tip and the sample
work function half-sum. Assuming that tip work function is constant
during scanning, the amplitude will depend only on the studied surface work function.
The frequency ,
as mentioned above, should be much more than the reciprocal feedback
integrator time constant and be limited by maximum permissible scan
frequency.
Summary.
- Modulation of tip-sample distance results in oscillations of tunneling current
 .
- Using this method it is possible to measure the distribution of work-function along all investigated sample surface.
References.
- G. Binnig., H. Rohrer. Scanning tunneling microscopy. Helv. Phys. Acta. - 1982, - V. 55 726.
- A. Burshtein, S. Lundquist. Tunneling phenomena in solid bodies. Mir, 1973 (in Russian).
- E. Wolf. Electron tunneling spectroscopy principles. Kiev: "Naukova Dumka", 1990, 454 p. (in Russian).
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