I. Introduction
Despite the major technological advances achieved in the last years in the fabrication of metal-insulator-metal (MIM) information storage cells for nonvolatile memory devices [1], a simple and flexible analytic model able to represent the wide variety of quasi-static current-voltage characteristics exhibited by resistive switching (RS) devices is still lacking. On the other hand, several models have been proposed to account for the switching dynamics using physics- and/or circuit-based approaches [2]–[8]. Physically, the RS effect in MIM devices has been ascribed to the alternate formation (low resistance state, LRS) and dissolution (high resistance state, HRS) of a filamentary current path spanning the oxide film following a redox process [1]. The filament is initiated by the so-called electroforming process, which is statistically consistent with the percolation theory of oxide breakdown [9]. Interestingly, no clear dependence of both LRS and HRS on the dielectric thickness has been found yet, which is an indication that the current is presumably driven by the narrowest section of the filament regardless of its specific location (bulk or interface). This limitation for the electron flux is often modeled by a material [7], [8], [10]–[12] or virtual [13], [14] potential barrier. In this letter, we modeled the characteristics of -based MIM resistive switches using an extension of Szot's equivalent electrical circuit for the transition [15] [see Fig. 1(a)]. Starting out from the generalized diode equation [16], three different approaches for the hysteretic curves are assessed. The connection with the physics of filamentary conduction is also discussed.
(a) Szot's model for the RS mechanism [15]. The two antiparallel diodes and the resistance represent the HRS and LRS states, respectively. (b) Schematic of the potential barrier with height sandwiched between metal electrodes with electrochemical potentials and . (c) Equivalent electrical circuit model including series and parallel ( and ) resistances.