Second and third derivative of a tunnel junction characteristic application to the observation of electronic excitations

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Abstract
Tunneling spectroscopy at high bias has proved to be useful as a tool for studying electronic excitations in junctions although one major difficulty encountered is the huge background in the second derivative of the tunneling characteristics I(V). This background however depends on which second derivative is used. We compare the sensitivity of the functions d 2V/dI2, d2I/dV 2 and 1/σ.dσ/dV to inelastic phenomena and conclude that the last one is rather better adapted. We describe a system for obtaining this function at the output of a lock-in detector. The use of higher derivatives to show up very weak, but rather abrupt, peaks in thé curves is discussed and we propose a circuit to plot a third derivative characteristic of tunnel junctions. In order to illustrate the possibilities of this equipment, we re-examine a situation where a peak due to an inelastic phenomenon was expected but not yet observed because of a large base-line and where the use of the third derivative technique enabled us to see it very distinctly

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