Modeling of the Hysteretic $I{-}V$ Characteristics of ${\rm TiO}_{2}$ -Based Resistive Switches

An equivalent circuit representation for the conduction characteristics of TiO₂-based resistive switches based on the generalized diode equation is reported. The proposed model consists of two antiparallel diodes with series and parallel resistances representing the filamentary current pathway spanning the oxide layer and the possible parasitic conduction effects. The model accounts for the pulse-induced hysteretic behavior exhibited by the I-V characteristic after electroforming. Three different approaches, each one of them with increased complexity, are assessed: 1) constant; 2) nanowire-like; and 3) sigmoidal diode amplitude. In all cases, the logarithmic conductance of the diodes is modeled using a logistic-type threshold function.