We show that Joule heating causes current-controlled negative differential resistance (CC-NDR) in TiO2 by constructing an analytical model of the voltage-current V(I) characteristic based on polaronic transport for Ohms Law and Newtons Law of Cooling, and fitting this model to experimental data. This threshold switching is the soft breakdown observed during electroforming of TiO2 and other transition-metal-oxide based memristors, as well as a precursor to ON or SET switching of unipolar memristors from their high to their low resistance states. The shape of the V(I) curve is a sensitive indicator of the nature of the polaronic conduction.
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