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

The correlation between the set time (
$t_{\mathrm {\mathrm {set}}}$
) and the initial off-state resistance (
$R_{\mathrm{\scriptscriptstyle OFF}}$
) statistics for a Ti/ZrO
₂
/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.