Analysis and modeling of resistive switching statistics
Authors: Long Shibing , Cagli Carlo , Ielmini Daniele , Liu Ming , Suñé Jordi 
Published: April 2012

The resistive random access memory (RRAM), based on the reversible switching between different resistance states, is a promising candidate for next-generation nonvolatile memories. One of the most important challenges to foster the practical application of RRAM is the control of the statistical variation of switching parameters to gain low variability and high reliability. In this work, starting from the well-known percolation model of dielectric breakdown (BD), we establish a framework of analysis and modeling of the resistive switching statistics in RRAM devices, which are based on the formation and disconnection of a conducting filament (CF). One key aspect of our proposal is the relation between the CF resistance and the switching statistics. Hence, establishing the correlation between SET and RESET switching variables and the initial resistance of the device in the OFF and ON states, respectively, is a fundamental issue. Our modeling approach to the switching statistics is fully analytical and contains two main elements: (i) a geometrical cell-based description of the CF and (ii) a deterministic model for the switching dynamics. Both ingredients might be slightly different for the SET and RESET processes, for the type of switching (bipolar or unipolar), and for the kind of considered resistive structure (oxide-based, conductive bridge, etc.). However, the basic structure of our approach is thought to be useful for all the cases and should provide a framework for the physics-based understanding of the switching mechanisms and the associated statistics, for the trustful estimation of RRAM performance, and for the successful forecast of reliability. As a first application example, we start by considering the case of the RESET statistics of NiO-based RRAM structures. In particular, we statistically analyze the RESET transitions of a statistically significant number of switching cycles of Pt/NiO/W devices. In the RESET transition, the ON-state resistance (RON) is a key parameter to describe the initial state of the CF. Hence, we subdivide the statistical samples (obtained mainly in a single device) in several RON ranges so as to study the switching statistics as a function of RON. In this regard, we have found that the experimental data can be nicely fit to a Weibull model in all the resistance ranges. Moreover, the distributions significantly change with RON. This change might be even more significant than the device-to-device related variations and, hence, mostly determine the overall statistics of switching parameters. In particular, we have found that the Weibull slopes of both VRESET, IRESET, and PRESET cumulative distributions increase linearly with 1/RON, i.e., they increase with the area of the CF. On the other hand, while the scale factor of the VRESET distribution (V63%) is roughly independent of RON, the scale factor of the distribution of IRESET and PRESET (I63% and P63%) linearly increases with 1/RON. Upon a direct analogy with the cell-based analytical percolation model of oxide BD, two simple geometrical cell-based models, the single path model with variable width and the multiple parallel path model, are proposed to address the RESET statistics. In the limit where these two geometrical models coincide, we incorporate a deterministic model for the RESET switching dynamics based on the self-accelerated thermal dissolution of the CF. With these two ingredients, the complete physics-based model for the RESET statistics is constructed. This analytical model is shown to nicely account for the experimental results with remarkable agreement.