Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices

Abstract The choice of the right statistical model to describe the distribution of switching parameters (forming, SET and RESET voltages) is a critical requirement for RRAM, as it is used to analyze the worst case scenarios of operation that have to be accounted for while designing the cross-bar array structures, so as to ensure a robust design of the circuit and reliable data storage unit. Several models have been proposed in the recent past to characterize the voltage variations in V FORM , V SET and V RESET using the percolation framework. However, most of these models assume defect generation to be a Poisson process and apply the standard Weibull distribution for parameter extraction and lifetime extrapolation. Recent dielectric breakdown studies both at the front-end as well as back-end have shown that the Weibull statistics does not describe the stochastic trends well enough, more so in downscaled structures at the low and high percentile regions given the possibility of defect clustering which is either physics-driven or process quality-driven. This phenomenon of defect clustering is all the more applicable in the context of resistive random access memory (RRAM) devices, as switching occurs repeatedly at ruptured filament locations where defect clusters pre-exist. This study examines the validity of the clustering model for RRAM switching parameter statistics (time/voltage to FORM, SET and RESET) and presents a physical picture to explain the origin of clustering in RRAM. A large set of data from various published studies has been used here to test the suitability and need for a clustering model based reliability assessment. Dependence of the clustering factor on temperature, voltage, device area, dielectric microstructure and resistance state has also been examined.

[1]  S. Wenham,et al.  Point-Contacting by Localized Dielectric Breakdown With Breakdown Fields Described by the Weibull Distribution , 2015, IEEE Transactions on Electron Devices.

[2]  S. Yokogawa.  Statistical characteristics of lifetime distribution based on defect clustering for time-dependent dielectric breakdown in middle- and back-end-of-line , 2015 .

[3]  O. Richard,et al.  10×10nm2 Hf/HfOx crossbar resistive RAM with excellent performance, reliability and low-energy operation , 2011, 2011 International Electron Devices Meeting.

[4]  J. Sune,et al.  Analytical Cell-Based Model for the Breakdown Statistics of Multilayer Insulator Stacks , 2009, IEEE Electron Device Letters.

[5]  R. Waser,et al.  On the stochastic nature of resistive switching in Cu doped Ge0.3Se0.7 based memory devices , 2011 .

[6]  James H. Stathis,et al.  Modeling of time-dependent non-uniform dielectric breakdown using a clustering statistical approach , 2013 .

[7]  M. Porti,et al.  Grain boundary-driven leakage path formation in HfO2 dielectrics , 2011, 2010 Proceedings of the European Solid State Device Research Conference.

[8]  R. Degraeve,et al.  Low Weibull slope of breakdown distributions in high-k layers , 2002, IEEE Electron Device Letters.

[9]  Jordi Suñé,et al.  Investigation on the RESET switching mechanism of bipolar Cu/HfO2/Pt RRAM devices with a statistical methodology , 2013 .

[10]  G. Bersuker,et al.  Electron-Injection-Assisted Generation of Oxygen Vacancies in Monoclinic HfO2 , 2015 .

[11]  Shibing Long,et al.  A Model for the Set Statistics of RRAM Inspired in the Percolation Model of Oxide Breakdown , 2013, IEEE Electron Device Letters.

[12]  H. Aono,et al.  A new aspect of time-dependent clustering model for non-uniform dielectric TDDB , 2016, 2016 IEEE International Reliability Physics Symposium (IRPS).

[13]  D. Ielmini,et al.  Impact of correlated generation of oxide defects on SILC and breakdown distributions , 2004, IEEE Transactions on Electron Devices.

[14]  Alexander L. Shluger,et al.  The interaction of oxygen vacancies with grain boundaries in monoclinic HfO2 , 2009 .

[15]  C. H. Stapper,et al.  On yield, fault distributions, and clustering of particles , 1986 .

[16]  J. Stathis.  Percolation models for gate oxide breakdown , 1999 .

[17]  D. Ielmini,et al.  Reset Statistics of NiO-Based Resistive Switching Memories , 2011, IEEE Electron Device Letters.

[18]  Yoshifumi Nishi,et al.  Weibull analysis of the kinetics of resistive switches based on tantalum oxide thin films , 2013, 2013 Proceedings of the European Solid-State Device Research Conference (ESSDERC).

[19]  J. Stathis,et al.  Time-dependent clustering model versus combination-based approach for BEOL/MOL and FEOL non-uniform dielectric breakdown: Similarities and disparities , 2014, 2014 IEEE International Reliability Physics Symposium.

[20]  Way Kuo,et al.  An overview of manufacturing yield and reliability modeling for semiconductor products , 1999, Proc. IEEE.

[21]  D. Ielmini,et al.  Analysis and modeling of resistive switching statistics , 2012 .

[22]  J. Sune,et al.  New physics-based analytic approach to the thin-oxide breakdown statistics , 2001, IEEE Electron Device Letters.

[23]  G. Bersuker,et al.  Modelling of oxygen vacancy aggregates in monoclinic HfO2: can they contribute to conductive filament formation? , 2015, Journal of physics. Condensed matter : an Institute of Physics journal.