Variability in Resistive Memories

This research was supported by project B-TIC-624-UGR20 funded by the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain) and the FEDER program. F.J.A. acknowledges grant PGC2018-098860-B-I00 and PID2021-128077NB-I00 financed by MCIN/ AEI/10.13039/501100011033/FEDER and A-FQM-66-UGR20 financed by the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain) and the FEDER program. M.B.G. acknowledges the Ramón y Cajal Grant No. RYC2020-030150-I. M.L. and M.A.V. acknowl- edge generous support from the King Abdullah University of Science and Technology. A.N.M., N.V.A., A.A.D., M.N.K. and B.S. acknowledge the Government of the Russian Federation under Megagrant Program (agreement no. 074-02-2018-330 (2)) and the Ministry of Science and Higher Education of the Russian Federation under “Priority-2030” Academic Excellence Program of the Lobachevsky State University of Nizhny Novgorod (N-466-99_2021-2023). The authors thank D.O. Filatov, A.S. Novikov, and V.A. Shishmakova for their help in studying the dependence of MFPT on external voltage (Section 4). The devices in Section 4 were designed in the frame of the scientific program of the National Center for Physics and Mathematics (project “Artificial intel- ligence and big data in technical, industrial, natural and social systems”) and fabricated at the facilities of Laboratory of memristor nanoelectronics (state assignment for the creation of new laboratories for electronics industry). E.M. acknowledges the support provided by the European proj- ect MEMQuD, code 20FUN06, which has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme.Resistive memories are outstanding electron devices that have displayed a large potential in a plethora of applications such as nonvolatile data storage, neuro- morphic computing, hardware cryptography, etc. Their fabrication control and performance have been notably improved in the last few years to cope with the requirements of massive industrial production. However, the most important hurdle to progress in their development is the so-called cycle-to-cycle variability, which is inherently rooted in the resistive switching mechanism behind the operational principle of these devices. In order to achieve the whole picture, variability must be assessed from different viewpoints going from the experi- mental characterization to the adequation of modeling and simulation techni- ques. Herein, special emphasis is put on the modeling part because the accurate representation of the phenomenon is critical for circuit designers. In this respect, a number of approaches are used to the date: stochastic, behavioral, meso- scopic..., each of them covering particular aspects of the electron and ion transport mechanisms occurring within the switching material. These subjects are dealt with in this review, with the aim of presenting the most recent advancements in the treatment of variability in resistive memories.Junta de Andalucía B-TIC-624-UGR20 PID2021-128077NB-I00European CommissionMCIN/AEI/FEDER A-FQM-66-UGR20 PGC2018-098860-B-I00Spanish Government RYC2020-030150-IKing Abdullah University of Science & TechnologyGovernment of the Russian Federation under Megagrant Program 074-02-2018-330 (2)Ministry of Science and Higher Education of the Russian Federation under "Priority-2030" Academic Excellence Program of the Lobachevsky State University of Nizhny Novgorod N-466-99_2021-2023European project MEMQuD 20FUN06EMPIR programmeEuropean Union's Horizon 2020 research and innovation programm

A Statistical Study of Resistive Switching Parameters in Au/Ta/ZrO2(Y)/Ta2O5/TiN/Ti Memristive Devices

Variability is an inherent property of memristive devices based on the switching of resistance in a simple metal–oxide–metal structure compatible with the standard complementary metal–oxide–semiconductor fabrication process. For each specific structure, the variability should be measured and assessed as both the negative and positive factors for different applications of memristive devices. In this report, it is shown how this variability can be extracted and analyzed for such main parameters of resistive switching as the set and reset voltages/currents and how it depends on the methodology used and experimental conditions. The obtained results should be taken into account in the design and predictive simulation of memristive devices and circuits.Junta de AndaluciaEuropean Commission A-TIC-117-UGR18 B-TIC-624-UGR20 IE2017-5414Government of the Russian Federation 074-02-2018-330 (2)Ministry of Science and Higher Education of the Russian Federation N-466-99_2021-202

Thermal Characterization of Conductive Filaments in Unipolar Resistive Memories

A methodology to estimate the device temperature in resistive random access memories (RRAMs) is presented. Unipolar devices, which are known to be highly influenced by thermal effects in their resistive switching operation, are employed to develop the technique. A 3D RRAM simulator is used to fit experimental data and obtain the maximum and average temperatures of the conductive filaments (CFs) that are responsible for the switching behavior. It is found that the experimental CFs temperature corresponds to the maximum simulated temperatures obtained at the narrowest sections of the CFs. These temperature values can be used to improve compact models for circuit simulation purposesConsejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain)FEDER B-TIC-624-UGR20. M.B.GRamón y Cajal RYC2020-030150-

Variability and power enhancement of current controlled resistive switching devices

characterized using both current and voltage sweeps, with the device resistance and its cycle-to-cycle variability being analysed in each case. Experimental measurements indicate a clear improvement on resistance states stability when using current sweeps to induce both set and reset processes. Moreover, it has been found that using current to induce these transitions is more efficient than using voltage sweeps, as seen when analysing the device power consumption. The same results are obtained for devices with a Ni top electrode and a bilayer or pentalayer of HfO2/Al2O3 as dielectric. Finally, kinetic Monte Carlo and compact modelling simulation studies are performed to shed light on the experimental resultsConsejería de Conocimiento, Investigaci´on y Universidad, Junta de Andalucía (Spain)FEDER program for the project B-TIC-624-UGR20Spanish Consejo Superior de Investigaciones Científicas (CSIC) for the intramural project 20225AT012Ramón y Cajal grant No. RYC2020-030150-I

Optimization of Multi-Level Operation in RRAM Arrays for In-Memory Computing

Accomplishing multi-level programming in resistive random access memory (RRAM) arrays with truly discrete and linearly spaced conductive levels is crucial in order to implement synaptic weights in hardware-based neuromorphic systems. In this paper, we implemented this feature on 4-kbit 1T1R RRAM arrays by tuning the programming parameters of the multi-level incremental step pulse with verify algorithm (M-ISPVA). The optimized set of parameters was assessed by comparing its results with a non-optimized one. The optimized set of parameters proved to be an effective way to define non-overlapped conductive levels due to the strong reduction of the device-to-device variability as well as of the cycle-to-cycle variability, assessed by inter-levels switching tests and during 1k reset-set cycles. In order to evaluate this improvement in real scenarios, the experimental characteristics of the RRAM devices were captured by means of a behavioral model, which was used to simulate two different neuromorphic systems: an 8×8 vector-matrixmultiplication (VMM) accelerator and a 4-layer feedforward neural network for MNIST database recognition. The results clearly showed that the optimization of the programming parameters improved both the precision of VMM results as well as the recognition accuracy of the neural network in about 6% compared with the use of non-optimized parameters.German Research Foundation (DFG) - FOR2093Government of Andalusia (Spain) and the FEDER program in the frame of the project A.TIC.117.UGR18Open Access Fund of the Leibniz Associatio

Toward Reliable Compact Modeling of Multilevel 1T-1R RRAM Devices for Neuromorphic Systems

The authors would like to thank the financial support by Deutsche Forschungsgemeinschaft (German Research Foundation) with Project-ID SFB1461 and by the Federal Ministry of Education and Research of Germany under grant numbers 16ES1002, 16FMD01K, 16FMD02 and 16FMD03. The authors also gratefully acknowledge the support of the Spanish Ministry of Science, Innovation and Universities and the FEDER program through project TEC2017-84321-C4-3-R and project A.TIC.117.UGR18 funded by the government of Andalusia (Spain) and the FEDER program. The publication of this article was funded by the Open Access Fund of the Leibniz Association.The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.In this work, three different RRAM compact models implemented in Verilog-A are analyzed and evaluated in order to reproduce the multilevel approach based on the switching capability of experimental devices. These models are integrated in 1T-1R cells to control their analog behavior by means of the compliance current imposed by the NMOS select transistor. Four different resistance levels are simulated and assessed with experimental verification to account for their multilevel capability. Further, an Artificial Neural Network study is carried out to evaluate in a real scenario the viability of the multilevel approach under study.German Research Foundation (DFG) SFB1461Federal Ministry of Education & Research (BMBF) 16ES1002 16FMD01K 16FMD02 16FMD03Spanish Ministry of Science, Innovation and UniversitiesEuropean Commission TEC2017-84321-C4-3-Rgovernment of Andalusia (Spain) A.TIC.117.UGR18Leibniz Associatio

A thorough investigation of the switching dynamics of TiN/Ti/10 nm-HfO2/W resistive memories

The switching dynamics of TiN/Ti/HfO2/W-based resistive memories is investigated. The analysis consisted in the systematic application of voltage sweeps with different ramp rates and temperatures. The obtained results give clear insight into the role played by transient and thermal effects on the device operation. Both kinetic Monte Carlo simulations and a compact modeling approach based on the Dynamic Memdiode Model are considered in this work with the aim of assessing, in terms of their respective scopes, the nature of the physical processes that characterize the formation and rupture of the filamentary conducting channel spanning the oxide film. As a result of this study, a better understanding of the different facets of the resistive switching dynamics is achieved. It is shown that the temperature and, mainly, the applied electric field, control the switching mechanism of our devices. The Dynamic Memdiode Model, being a behavioral analytic approach, is shown to be particularly suitable for reproducing the conduction characteristics of our devices using a single set of parameters for the different operation regimesFEDER program [PID2022-139586NB-C41, PID2022- 139586NB-C42PID2022-139586NB-C43PID2022-139586NB-C44]The Consejería de Conocimiento, Investigaci´on y UniversidadJunta de Andalucía (Spain) [B-TIC-624-UGR20]Spanish Consejo Superior de Investigaciones Científicas (CSIC) [20225AT012]FEDER fundsRamón y Cajal grant number RYC2020-030150-IEuropean project MEMQuD, code 20FUN06EMPIR programme co-financed by the Participating StatesEuropean Union’s Horizon 2020 research and innovation programm

TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing: from synaptic plasticity to stochastic resonance

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fnins.2023. 1271956/full#supplementary-materialFunding The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. The authors thank the support of the Consejeria de Conocimiento, Investigacion y Universidad, Junta de Andalucia (Spain), and the FEDER program through project B-TIC-624-UGR20. They also thank the support of the Federal Ministry of Education and Research of Germany under Grant 16ME0092.We characterize TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing. We analyze different features that allow the devices to mimic biological synapses and present the models to reproduce analytically some of the data measured. In particular, we have measured the spike timing dependent plasticity behavior in our devices and later on we have modeled it. The spike timing dependent plasticity model was implemented as the learning rule of a spiking neural network that was trained to recognize the MNIST dataset. Variability is implemented and its influence on the network recognition accuracy is considered accounting for the number of neurons in the network and the number of training epochs. Finally, stochastic resonance is studied as another synaptic feature. It is shown that this effect is important and greatly depends on the noise statistical characteristics.Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain), and the FEDER program through project B-TIC-624-UGR20Federal Ministry of Education and Research of Germany under Grant 16ME009

Parameter extraction techniques for the analysis and modeling of resistive memories

A revision of the different numerical techniques employed to extract resistive switching (RS) and modeling parameters is presented. The set and reset voltages, commonly used for variability estimation, are calculated for different resistive memory technologies. The methodologies to extract the series resistance and the parameters linked to the charge-flux memristive modeling approach are also described. It is found that the obtained cycle-to-cycle (C2C) variability depends on the numerical technique used. This result is important, and it implies that when analyzing C2C variability, the extraction technique should be described to perform fair comparisons between different resistive memory technologies. In addition to the use of extensive experimental data for different types of resistive memories, we have also included kinetic Monte Carlo (kMC) simulations to study the formation and rupture events of the percolation paths that constitute the conductive filaments (CF) that allow resistive switching operation in filamentary unipolar and bipolar devices.Consejería de Conocimiento, Investigaci ́on y Universidad, Junta de Andalucía (Spain) and the FEDER program for the projects A.TIC.117.UGR18, B-TIC-624-UGR20 and IE2017-5414Ramón y Cajal grant No. RYC2020-030150-IFunding for open access charge: Universidad de Granada/CBU

A Statistical Study of Resistive Switching Parameters in Au/Ta/ZrO2(Y)/Ta2O5/TiN/Ti Memristive Devices

The authors acknowledge the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain), European Regional Development Fund (ERDF) under projects A-TIC-117-UGR18, B-TIC-624-UGR20, and IE2017-5414. Support from the Government of the Russian Federation under Megagrant Program (agreement no. 074-02-2018-330 (2)) and the Ministry of Science and Higher Education of the Russian Federation under “Priority-2030” Academic Excellence Program of the Lobachevsky State University of Nizhny Novgorod (N-466-99_2021- 2023) is also acknowledged. Memristive devices were designed in the frame of the scientific program of the National Center for Physics and Mathematics (project “Artificial intelligence and big data in technical, industrial, natural and social systems”).Variability is an inherent property of memristive devices based on the switching of resistance in a simple metal–oxide–metal structure compatible with the standard complementary metal–oxide–semiconductor fabrication process. For each specific structure, the variability should be measured and assessed as both the negative and positive factors for different applications of memristive devices. In this report, it is shown how this variability can be extracted and analyzed for such main parameters of resistive switching as the set and reset voltages/cur- rents and how it depends on the methodology used and experimental conditions. The obtained results should be taken into account in the design and predictive simulation of memristive devices and circuits.Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain), European Regional Development Fund (ERDF) under projects A-TIC-117-UGR18, B-TIC-624-UGR20, and IE2017-5414Government of the Russian Federation under Megagrant Program (agreement no. 074-02-2018-330 (2))Ministry of Science and Higher Education of the Russian Federation under “Priority-2030” Academic Excellence Program of the Lobachevsky State University of Nizhny Novgorod (N-466-99_2021- 2023