We derived analytical formulas to estimate the effective thermal resistance of a metallic cylinder subjected to Joule heating, surrounded by an insulator and bounded by two constant temperature planes in order to estimate the temperature of the hottest point of the system. These solutions are especially relevant for modeling unipolar resistive switches (or memristive devices), and they provide insight into the performance tradeoffs for a thermally driven reset transition. In particular, our results indicate that a minimum current of 1 μA is required to successfully reset a unipolar switch, even under the most favorable conditions.
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