Threshold switches, which typically exhibit an abrupt increase in current at an onset voltage, have been used as selector devices to suppress leakage current in crosspoint arrays of two-terminal resistive switching memory devices. One of the most important metrics for selector devices is the leakage or low-voltage current, which limits the maximum achievable size of the crosspoint memory array. Here, we show that for self-heating-triggered threshold switches, there is an intrinsic lower limit to the leakage current resulting from the need to avoid an electric field-induced breakdown of the active material. We provide a quantitative theoretical estimate of this limit for NbOx threshold switches, one of the most widely studied selectors, and provide a plausible explanation for the experimentally observed leakage currents in NbOx. Our results provide some guidelines for achieving minimum leakage currents in threshold switches.

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