Comprehensive physics-based RRAM compact model including the effect of variability and multi-level random telegraph noise

Resistive Random Access Memory (RRAM) technologies are a promising candidate for the development of more energy efficient circuits, for computing, security, and storage applications. However, such devices show stochastic behaviours that not only originate from variations introduced during fabrication, but that are intrinsic to their operation. Specifically, cycle-to-cycle variations cause the programmed resistive state to be randomly distributed, while Random Telegraph Noise (RTN) introduces random current fluctuations over time. These phenomena can easily affect the reliability and performance of RRAM-based circuits. Therefore, designing such circuits requires accurate compact models. Although several RRAM compact models have been proposed in the literature, these are rarely implemented following the programming best-practice for improving the simulator convergence, and a compact model that is able to reproduce the device characteristic including thermal effects, RTN, and variability in multiple operating conditions using a single set of parameters is still missing. Also, only a few works in the literature describe the procedure to calibrate such compact models, and even fewer address the calibration of the variability on experimental data. In this work, we extend the UniMORE RRAM physics-based compact model by developing and validating two variability models, (i) a comprehensive variability model which can reproduce the effect of cycle-to-cycle variability in multiple operating conditions, and (ii) a simplified version that requires fewer calibration data and enables to reproduce cycle-to-cycle variations in specific operating conditions. The model is implemented following Verilog-A programming best-practices and validated on data from three RRAM technologies from the literature and experimentally on TiN/Ti/HfOx/TiN devices, and the relation between experimental data and the variability model parameters is described.