Structure in the current-voltage characteristics of heavily doped p-n junctions and superconductor junctions is more clearly revealed if the current is differentiated with respect to the voltage and is still more clearly revealed if a second differentiation is performed to obtain d2I/dV2. This paper describes a working system for automatically measuring and continuously plotting these derivatives as a function of voltage. Traces of current-voltage characteristics of heavily doped degenerate p-n junctions and the first and second derivatives of these characteristics obtained by the techniques described are given. A series of first derivative curves for an Al-Al2O3-Pb tunnel junction is also included to illustrate the speed of the method.
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Thomas et al. (1963) studied this question.