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.
