# 1.3.4 Work-Function Distribution Study

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)**.

**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

(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).