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 ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{\mathrm {\mathrm {set}}}$ </tex-math></inline-formula> ) and the initial off-state resistance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm{\scriptscriptstyle OFF}}$ </tex-math></inline-formula> ) statistics for a Ti/ZrO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{\mathrm {\mathrm {set}}}$ </tex-math></inline-formula> , and the gathered statistical data were analyzed using Weibull distributions. Both the Weibull slope ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta _{t}$ </tex-math></inline-formula> ) and the scale factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{\mathrm {\mathrm {set63\%}}}$ </tex-math></inline-formula> ) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{\mathrm {\mathrm {set}}}$ </tex-math></inline-formula> distributions were found to increase logarithmically with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm{\scriptscriptstyle OFF}}$ </tex-math></inline-formula> . The observed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{\mathrm {\mathrm {set}}}-R_{\mathrm{\scriptscriptstyle OFF}}$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm{\scriptscriptstyle OFF}}$ </tex-math></inline-formula> -dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{\mathrm{\scriptscriptstyle SET}}$ </tex-math></inline-formula> statistics, which can be implemented in statistical compact models and circuit simulators for improving RRAM cell design and memory performances.