Intrinsic limits of leakage current in self-heating-triggered threshold switches

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 NbO_x threshold switches, one of the most widely studied selectors, and provide a plausible explanation for the experimentally observed leakage currents in NbO_x. Our results provide some guidelines for achieving minimum leakage currents in threshold switches.