Time series statistical analyses (TSSA) have been employed to evaluate the variability of resistive switching memories and to model the set and reset voltages for modeling purposes. The conventional procedures behind time series theory have been used to obtain autocorrelation and partial autocorrelation functions and determine the simplest analytical models to forecast the set and reset voltages in a long series of resistive switching processes. To do so, and for the sake of generality in our study, a wide range of devices have been fabricated and measured. Different oxides and electrodes have been employed, including bilayer dielectrics in devices such as Ni/HfO2/Si-n+, Cu/HfO2/Si-n+, and Au/Ti/TiO2/SiOx/Si-n+. The TSSA models obtained allowed one to forecast the reset and set voltages in a series if previous values were known. The study of autocorrelation data between different cycles in the series allows estimating the inertia between cycles in long resistive switching series. Overall, TSSA seems to be a very promising method to evaluate the intrinsic variability of resistive switching memories.
References
1.
F.
Pan
, S.
Gao
, C.
Chen
, C.
Song
, and F.
Zeng
, “Recent progress in resistive random access memories: Materials, switching mechanisms and performance
,” Mater. Sci. Eng.
83
, 1
–59
(2014
). 2.
D.
Ielmini
and R.
Waser
, “Resistive Switching: From Fundamentals of Nanoionic Redox Processes to Memristive Device Applications”
(Wiley-VCH
, 2015
).3.
R.
Waser
and M.
Aono
, “Nanoionics-based resistive switching
,” Nat. Mater.
6
, 833
–840
(2007
). 4.
M.
Lanza
, G.
Bersuker
, M.
Porti
, E.
Miranda
, M.
Nafría
, and X.
Aymerich
, “Resistive switching in hafnium dioxide layers: Local phenomenon at grain boundaries
,” Appl. Phys. Lett.
101
, 193502
(2012
). 5.
M.
Lanza
, H.-S. P.
Wong
, E.
Pop
, D.
Ielmini
, D.
Strukov
, B. C.
Regan
, L.
Larcher
, M. A.
Villena
, J. J.
Yang
, L.
Goux
, A.
Belmonte
, Y.
Yang
, F. M.
Puglisi
, J.
Kang
, B.
Magyari-Köpe
, E.
Yalon
, A.
Kenyon
, M.
Buckwell
, A.
Mehonic
, A.
Shluger
, H.
Li
, T.-H.
Hou
, B.
Hudec
, D.
Akinwande
, R.
Ge
, S.
Ambrogio
, J. B.
Roldan
, E.
Miranda
, J.
Suñe
, K. L.
Pey
, X.
Wu
, N.
Raghavan
, E.
Wu
, W. D.
Lu
, G.
Navarro
, W.
Zhang
, H.
Wu
, R.
Li
, A.
Holleitner
, U.
Wurstbauer
, M.
Lemme
, M.
Liu
, S.
Long
, Q.
Liu
, H.
Lv
, A.
Padovani
, P.
Pavan
, I.
Valov
, X.
Jing
, T.
Han
et al., “Recommended methods to study resistive switching devices
,” Adv. Electron. Mater.
5, 1800143
(2018
). 6.
7.
M. A.
Villena
, J. B.
Roldán
, F.
Jiménez-Molinos
, E.
Miranda
, J.
Suñé
, and M.
Lanza
, “SIM2RRAM: A physical model for RRAM devices simulation
,” J. Comput. Electron.
16
, 1095
(2017
). 8.
R.
Degraeve
, A.
Fantini
, N.
Raghavan
, L.
Goux
, S.
Clima
, B.
Govoreanu
, A.
Belmonte
, D.
Linten
, and M.
Jurczak
, “Causes and consequences of the stochastic aspect of filamentary RRAM
,” Microelectron. Eng.
147
, 171
–175
(2015
). 9.
F. M.
Puglisi
, N.
Zagni
, L.
Larcher
, and P.
Pavan
, “Random telegraph noise in resistive random access memories: Compact modeling and advanced circuit design
,” IEEE Trans. Electron Devices
65
, 2964
–2972
(2018
). 10.
S.
Menzel
, P.
Kaupmann
, and R.
Waser
, “Understanding filamentary growth in electrochemical metallization memory cells using kinetic Monte Carlo simulations
,” Nanoscale
7
, 12673
(2015
). 11.
S.
Long
, X.
Lian
, T.
Ye
, C.
Cagli
, L.
Perniola
, E.
Miranda
, M.
Liu
, and J.
Suñé
, “Cycle-to-cycle intrinsic RESET statistics in HfO2-based unipolar RRAM devices
,” IEEE Electron Device Lett.
34
(5
), 623
–625
(2013
). 12.
W. C.
Luo
, J. C.
Liu
, H. T.
Feng
, Y. C.
Lin
, J. J.
Huang
, K. L.
Lin
, and T. H.
Hou
, “RRAM SET speed-disturb dilemma and rapid statistical prediction methodology
,” in International Electron Device Meeting
(IEEE
, 2012
), p. 951
.13.
J. W.
McPherson
, Reliability Physics and Engineering. Time-to-Failure Modeling
, 2nd ed. (Springer
, 2013
).14.
E. Y.
Wu
, B.
Li
, and J. H.
Stathis
, “Modeling of time-dependent non-uniform dielectric breakdown using a clustering statistical approach
,” Appl. Phys. Lett.
103
, 152907
(2013
). 15.
E. Y.
Wu
, E. J.
Nowak
, R.
Vollertsen
, and L. K.
Han
, “Weibull breakdown characteristics and oxide thickness uniformity
,” IEEE Trans. Electron Device
47
, 2301
–2309
(2000
). 16.
C.
Acal
, J. E.
Ruiz-Castro
, A. M.
Aguilera
, F.
Jiménez-Molinos
, and J. B.
Roldán
, “Phase-type distributions for studying variability in resistive memories
,” J. Comput. Appl. Math.
345
, 23
–32
(2019
). 17.
H.
Tian
, X.-F.
Wang
, M. A.
Mohammad
, G.-Y.
Gou
, F.
Wu
, Y.
Yang
, and T.-L.
Ren
, “A hardware Markov chain algorithm realized in a single device for machine learning
,” Nat. Commun.
9
, 4305
(2018
). 18.
F. M.
Puglisi
and P.
Pavan
, “RTN analysis with FHMM as a tool for multi-trap characterization in HfOX RRAM
,” in 2013 IEEE International Conference of Electron Devices and Solid-State Circuits
(IEEE
, 2013
).19.
F.
Pan
, S.
Yin
, and V.
Subramanian
, “A detailed study of the forming stage of an electrochemical resistive switching memory by KMC simulation
,” IEEE Electron Device Lett.
32
, 949
–951
(2011
). 20.
X.
Guan
, S.
Yu
, and H. S.
Philip Wong
, “On the switching parameter variation of metal-oxide RRAM—Part I: Physical modeling and simulation methodology
,” IEEE Trans. Electron Devices
59
, 1172
–1182
(2012
). 21.
L.
Larcher
, A.
Padovani
, O.
Pirrotta
, L.
Vandelli
, and G.
Bersuker
, “Microscopic understanding and modeling of HfO2 RRAM device physics
,” in Proceedings of the IEEE International Electron Devices Meeting
(IEEE
, 2012
), pp. 20.1.1
–20.1.4
.22.
J.
Guy
, G.
Molas
, P.
Blaise
, M.
Bernard
, A.
Roule
, G.
Le Carval
, V.
Delaye
, A.
Toffoli
, G.
Ghibaudo
, F.
Clermidy
, B.
De Salvo
, and L.
Perniola
, “Investigation of forming, SET, and data retention of conductive-bridge random-access memory for stack optimization
,” IEEE Trans. Electron Devices
62
(11
), 3482
–3489
(2015
). 23.
S.
Aldana
, P.
García-Fernández
, A.
Rodríguez-Fernández
, R.
Romero-Zaliz
, M. B.
González
, F.
Jiménez-Molinos
, F.
Campabadal
, F.
Gómez-Campos
, and J. B.
Roldán
, “A 3D kinetic Monte Carlo simulation study of resistive switching processes in Ni/HfO2/Si-n+-based RRAMs
,” J. Phys. D Appl. Phys.
50
, 335103
(2017
). 24.
S.
Aldana
, J. B.
Roldán
, P.
García-Fernández
, J.
Suñe
, R.
Romero-Zaliz
, F.
Jiménez-Molinos
, S.
Long
, F.
Gómez-Campos
, and M.
Liu
, “An in-depth description of bipolar resistive switching in Cu/HfOx/Pt devices, a 3D kinetic Monte Carlo simulation approach
,” J. Appl. Phys.
123
, 154501
(2018
). 25.
M.
Schie
, S.
Menzel
, J.
Robertson
, R.
Waser
, and R. A.
De Souza
, “Field-enhanced route to generating anti-Frenkel pairs in HfO2
,” Phys. Rev. Mater.
2
, 035002
(2018
). 26.
M.
Xie
and S. L.
Ho
, “Analysis of repairable system failure data using time series models
,” J. Qual. Maint. Eng.
5
(1)
, 50
–61
(1999
). 27.
K. L.
Lee
and S. A.
Billings
, “Time series prediction using support vector machines, the orthogonal and the regularized orthogonal least-squares algorithms
,” Int. J. Syst. Sci.
33
(10
), 811
–821
(2002
). 28.
M. B.
González
, J. M.
Rafí
, O.
Beldarrain
, M.
Zabala
, and F.
Campabadal
, “Analysis of the switching variability in Ni/HfO2-based RRAM devices
,” IEEE Trans. Device Mater. Reliab.
14
(2
), 769
–771
(2014
). 29.
N.
Xiao
, M. A.
Villena
, B.
Yuan
, S.
Chen
, B.
Wang
, M.
Elias
, Y.
Shi
, F.
Hui
, X.
Jing
, A.
Sheuermann
, K.
Tang
, P. C.
McIntyre
, and M.
Lanza
, “Resistive random access memory cells with a bilayer TiO2/SiOX insulating stack for simultaneous filamentary and distributed resistive switching
,” Adv. Funct. Mater.
27
, 1700384
(2017
). 30.
P. J.
Brockwell
and R. A.
Davis
, Introduction to Time Series and Forecasting
, 2nd ed. (Springer
, 2002
).31.
S.
Bisgaard
and M.
Kulahci
, Time Series Analysis and Forecasting by Example
(Wiley
, 2011
).32.
G. U.
Yule
, “On a method of investigating periodicities in disturbed series, with reference to Wolfer’s sunspot numbers
,” Philos. Trans. R. Soc. London A
226
, 267
–298
(1927
). 33.
D. C.
Montgomery
, C. L.
Jennings
, and M.
Kulahci
, Introduction to Time Series Analysis and Forecasting
, Wiley Series in Probability and Statistics (Wiley
, 2015
).34.
M. A.
Villena
, J. B.
Roldán
, F.
Jiménez-Molinos
, J.
Suñé
, S.
Long
, E.
Miranda
, and M.
Liu
, “A comprehensive analysis on progressive reset transitions in RRAMs
,” J. Phys. D Appl. Phys.
7
, 205102
(2014
). 35.
A.
Coghlan
, “A little book of R for time series,” Release 0.2, 2018, see https://media.readthedocs.org/pdf/a-little-book-of-r-for-time-series/latest/a-little-book-of-r-for-time-series.pdf.36.
Y.
Yang
et al., “Electrochemical dynamics of nanoscale metallic inclusions in dielectrics
,” Nat. Commun.
5
, 4232
(2014
). 37.
Y.
Shi
, X.
Liang
, B.
Yuan
, V.
Chen
, H.
Li
, F.
Hui
, Z.
Yu
, F.
Yuan
, E.
Pop
, H.-S.
Philip Wong
, and M.
Lanza
, “Electronic synapses made of layered two-dimensional materials
,” Nat. Electron.
1
, 458
–465
(2018
). 38.
U.
Celano
, L.
Goux
, R.
Degraeve
, A.
Fantini
, O.
Richard
, H.
Bender
, M.
Jurczak
, and W.
Vandervorst
, “Three-dimensional observation of the conductive filament in nanoscaled resistive memory devices
,” Nanoletters
14
, 2401
–2406
(2014
). 39.
S.
Kim
, C.
Du
, P.
Sheridan
, W.
Ma
, S.
Choi
, and W. D.
Lu
, “Experimental demonstration of a second-order memristor and its ability to biorealistically implement synaptic plasticity
,” Nanoletters
15
, 2203
(2015
). 40.
See https://nano.stanford.edu/stanford-rram-model for the Stanford-PKU RRAM model is SPICE-compatible and describes the switching performance for bipolar metal oxide RRAMs.
41.
X.
Guan
, S.
Yu
, and H.-S. P.
Wong
, “A SPICE compact model of metal oxide resistive switching memory with variations
,” IEEE Electron Device Lett.
33
, 1405
–1407
(2012
). © 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.
