Abstract
Current-controlled negative differential resistance under the constraint of uniform current flow is shown to result from the incorporation of realistic boundary conditions in solving for the steady-state electrical and thermal behavior of a Joule heated semiconducting thin film mounted on a substrate. The thermal conductance of the substrate, which is a necessary feature of the experimental situation, is shown to influence significantly the measured properties of the film-substrate combination. An analytic expression is induced for the voltage at the onset of negative differential resistance (the turnover voltage), and is demonstrated to be an approximate solution of the model for all values of substrate thermal conductance. The predictions of this model 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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