An Empirical Model for RRAM Resistance in Low- and High-Resistance State

We present a simple empirical expression describing hafnium-based RRAM resistance at different reset voltages and current compliances. The model that we propose describes filament resistance measured at low (∼0.1 V) reading voltage in both low-resistance state (LRS) and high-resistance state (HRS). The proposed description confirms that conduction in LRS is ohmic (after forming with a sufficiently high current compliance) and is consistent with the earlier description of HRS resistance as controlled by a trap-assisted electron transfer via traps in the oxidized portion of the filament. The length of the nonohmic part of the filament is found to be directly proportional to reset voltage. Moreover, low-frequency noise measurements at different reset voltages evidence a tradeoff between HRS resistance and noise in reading conditions.