The rules of the resistive switching operation parameters based on Ta/Ta$_{2}$O$_{5}$ RRAM device*

The resistive switching (RS) of the TaO$_{x}$ based RRAM has been widely studied due to its excellent endurance and thermal stability. The RS mechanism is generally understood as the formation and dissolution of nanometer-size conductive filament (CF) formed in set and reset process, respectively. However the exact process of dielectric break down remains unknown. In this work we studied the RS of the Ta/Ta$_{2}$O$_{5}$ based RRAM devices from the dependences of operation parameters V$_{set}$, I$_{CC}$, V$_{reset}$, and I$_{reset}$ on device resistance. From statistical analysis of variation in the threshold parameters, we found that the set process is mainly determined by the voltage stress on the device, instead of current. The first forming process is different from the following set process. The forming voltage exponentially depends on the pristine resistance. The forming process gives a smallest low resistance (R$_{LRS})$ for each device. As a result change in compliance current (I$_{CC})$ has no obvious effects on this low resistance state.