Analysis of an inhomogeneous bulk "S-shaped" negative differential conductivity element in a circuit containing reactive elements

This paper analyzes the time and space evolution of the current density distribution in an inhomogeneous bulk "S-shaped" negative differential conductivity (SNDC) element and the response of the surrounding lumped element circuit. The SNDC element, in series with a package inductance, is in parallel with a package capacitance, the loop being in series with a load resistance and a battery. First the presence of isothermal current density filamentation in SNDC elements is demonstrated. By approximating the SNDC element as an appropriate conductive voltage curve in series with an appropriate intrinsic inductance, it is next shown that various modes of behavior (switching, relaxation oscillations, and a bias induced transition between the two) can all occur in the same SNDC element for appropriate values of the circuit parameters. A major aspect of the circuit theory is that it transforms directly between S and N shaped NDC elements when the important reactive components are identified in each case (duals). The techniques used are applicable to all SNDC elements, such as p-n-p-n and p-i-n diodes, and Ovonic threshold switches; emphasis is placed on the latter.