Advanced temperature dependent statistical analysis of forming voltage distributions for three different HfO2-based RRAM technologies

Abstract

In this work, voltage distributions of forming operations are analyzed by using an advanced statistical approach based on phase-type distributions (PHD). The experimental data were collected from batches of 128 HfO2-based RRAM devices integrated in 4-kbit arrays. Three different switching oxides, namely, polycrystalline HfO2, amorphous HfO2, and Al-doped HfO2, were tested in the temperature range from −40 to 150 °C. The variability of forming voltages has been usually studied by using the Weibull distribution (WD). However, the performance of the PHD analysis demonstrated its ability to better model this crucial operation. The capacity of the PHD to reproduce the experimental data has been validated by means of the Kolmogorov-Smirnov test, while the WD failed in many of the cases studied. In addition, PHD allows to extract information about intermediate probabilistic states that occur in the forming process and the transition probabilities between them; in this manner, we can deepen on the conductive filament formation physics. In particular, the number of intermediate states can be related to the device variability.