# 1.3.1 Current-Voltage Characteristic

Measurement of relation between tunneling current and probe-sample voltage is carried out in
spectroscopy mode. The
spectroscopy is based on the dependence of tunneling current on number of electron states
, forming a tunneling contact of conductors, in the energy range from the Fermi level
to
**(Fig. 1)**, which at
gives (see (7) in **chapter 1.2.1**)

(1)

Thus the tunneling current dependence
at constant tip-sample separation
represents an allocation of torn bonds as well as other electron states corresponding different energies, i.e. energy band structure of either tip or surface. Function
, which was introduced in (6) of **chapter 1.2.1**, depends on electron state density of phase space plane which is normal to tunneling direction at given
.

**Fig. 1. Model of MIM system with an arbitrary shape potential barrier.
Positive potential is applied to the right metal.**

Using expression (1) and curve at constant tip-sample separation , it is possible to compute the density of electronic states:

(2)

Thus, inspection of
and its derivative
curves allows to investigate energy levels distribution with atomic resolution. It is possible to determine a conductivity type, in particular for semiconductors – to detect the valence band, conductivity band and impurity band [**1-3**].

According to (2) and (3) from **chapter 1.2.2** tunneling conductivity
does not depend on applied voltage
in case

(3)

at relation between and is parabolic

(4)

On Fig. 2, 3 experimental dependences , , which were measured for Pt and HOPG samples and Pt-Ro probe using STM Solver P47, is shown. Experimental data are in good agreement with the theoretical predictions (1)–(4).

**Fig. 1a. Experimental (points) and theoretical (solid line)
dependences
for Pt**

**Fig. 1b. Experimental dependence
for Pt**

**Fig. 2a. Experimental (points) and theoretical (solid line)
dependences
for HOPG**

**Fig. 2b. Experimental dependence
for HOPG**

## Summary.

- Tunneling current-voltage characteristic represents number of electron states and their distribution in energy spectrum of electrodes which creates tunneling contact.
- Differential conduction is proportional an electron state density. For metals at low voltages does not depend on applied voltage (3). At intermediate voltages the relation between and applied voltage is parabolic (4).
- Experimantal current-voltage and differential characteristic are in good agreement with theory.

## 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).