Analytic solution of a simple model for negative differential resistance

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Abstract
Current-controlled negative differential resistance under the constraint of uniform current flow has been shown previously to result from the incorporation of the thermal conductance of the substrate in solving for the steady-state electrical and thermal behaviour of a Joule heated semiconducting thin film mounted on a substrate. Herein are derived expressions which yield the current density-voltage characteristic in the commonly applicable limit of small temperature variation in the film. An analytic expression for the voltage at the onset of negative differential resistance is induced from the expressions in the above limit and in the isothermal limit, and is demonstrated to be an approximate solution of the model for all values of substrate thermal conductance. The predictions of this model are discussed, and are shown to be consistent with experimental measurements of the threshold voltage as a function of film thickness and of ambient temperature.

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