A Physical Model for the Statistics of the Set Switching Time of Resistive RAM Measured With the Width-Adjusting Pulse Operation Method

Abstract

The correlation between the set time ( $t_{\mathrm {\mathrm {set}}}$ ) and the initial off-state resistance ( $R_{\mathrm{\scriptscriptstyle OFF}}$ ) statistics for a Ti/ZrO2/Pt bipolar resistive random access memory device was investigated. The width-adjusting pulse operation method, which can significantly improve the switching uniformity, was used to accurately measure $t_{\mathrm {\mathrm {set}}}$ , and the gathered statistical data were analyzed using Weibull distributions. Both the Weibull slope ( $\beta _{t}$ ) and the scale factor ( $t_{\mathrm {\mathrm {set63\%}}}$ ) of $t_{\mathrm {\mathrm {set}}}$ distributions were found to increase logarithmically with $R_{\mathrm{\scriptscriptstyle OFF}}$ . The observed $t_{\mathrm {\mathrm {set}}}-R_{\mathrm{\scriptscriptstyle OFF}}$ interdependence provides a guideline in improving the switching uniformity and optimizing the tradeoff between set speed and disturb immunity. An analytical cell-based model was developed to explain the $R_{\mathrm{\scriptscriptstyle OFF}}$ -dependent $t_{\mathrm{\scriptscriptstyle SET}}$ statistics, which can be implemented in statistical compact models and circuit simulators for improving RRAM cell design and memory performances.