Hybrid 2D–CMOS microchips for memristive applications

Ministry of Science and Technology of China (grant nos. 2019YFE0124200 and 2018YFE0100800)National Natural Science Foundation of China (grant no. 61874075)Baseline funding scheme of the King Abdullah University of Science and Technolog

Hardware implementation of a true random number generator integrating a hexagonal boron nitride memristor with a commercial microcontroller

The development of the internet-of-things requires cheap, light, small and reliable true random number generator (TRNG) circuits to encrypt the data—generated by objects or humans—before transmitting them. However, all current solutions consume too much power and require a relatively large battery, hindering the integration of TRNG circuits on most objects. Here we fabricated a TRNG circuit by exploiting stable random telegraph noise (RTN) current signals produced by memristors made of two-dimensional (2D) multi-layered hexagonal boron nitride (h-BN) grown by chemical vapor deposition and coupled with inkjet-printed Ag electrodes. When biased at small constant voltages (≤70 mV), the Ag/h-BN/Ag memristors exhibit RTN signals with very low power consumption (∼5.25 nW) and a relatively high current on/off ratio (∼2) for long periods (>1 hour). We constructed TRNG circuits connecting an h-BN memristor to a small, light and cheap commercial microcontroller, producing a highly-stochastic, high-throughput signal (up to 7.8 Mbit s−1) even if the RTN at the input gets interrupted for long times up to 20 s, and if the stochasticity of the RTN signal is reduced. Our study presents the first full hardware implementation of 2Dmaterial- based TRNGs, enabled by the unique stability and figures of merit of the RTN signals in h-BN based memristors.Ministry of Science and Technology, China 2019YFE0124200 2018YFE0100800National Natural Science Foundation of China (NSFC) 61874075Collaborative Innovation Centre of Suzhou Nano Science and TechnologyPriority Academic Program Development of Jiangsu Higher Education Institutions111 Project from the State Administration of Foreign Experts Affairs of ChinaKing Abdullah University of Science & TechnologyMinisterio de Ciencia, Tecnologia e Innovacion (MINCyT) PICT 2016/0579 PME 2015-0196 PICTE 2018-0192 UTN-FRBA CCUTIBA4764TC MATUNBA4936 CCUTNBA5182 CCUTNBA661

Closed-Form and Explicit Analytical Model for Crosstalk in CMOS Photodiodes

A closed-form and explicit 2-D analytical model for crosstalk(CTK) effects in p-n + CMOS photodiodes for pixel design optimization has been developed in this paper. This model complements and extends a previous development describing the photocurrent because of the active area illumination along with the lateral depletion region and lateral components owing to the diffused photocarriers from the surroundings of the junction. The model has very few fitting parameters because it is physically based. Similarly, it can be of great use for CMOS image sensors designers, especially to fulfill high resolution and small area requirements by pixel size reduction. The model was validated extensively through device simulations with ATLAS and experimental data, and describes the CTK dependencies on light conditions and physical, geometrical, and process parametersThis work has been partially supported by the Spanish Government under projects TEC2009-12686 and TEC2012-38921-C02-02 (co-funded by the European Region Development Fund, ERDF/FEDER), by the Xunta de Galicia under project 10PXIB206037PR, by the Junta de Andalucía under project P08-TIC-3580 and by AE CITIUS under the project CN2012/151 of the Xunta de Galicia (ERDF/FEDER)S

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

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

Analytical Model for Crosstalk in p-nwellPhotodiodes

The response and crosstalk (CTK) of the p-n well photodiode were studied through device simulations performed with ATLAS and experimental data. As a result, a closed-form and explicit 2-D analytical model for its photoresponse and CTK was developed. The model has very few fitting parameters since it is physically based and describes the CTK dependencies on light conditions and physical, geometrical, and process parameters. This is of great interest for pixel design optimization to fulfill high resolution and small area requirements driven by pixel size reduction. As this model extends a previous one focused on p-n + devices, the behavior of both the structures was also comparedThis work has been partially supported by the Spanish Government under projects TEC2009-12686 and TEC2012-38921-C02-02 (co-funded by the European Region Development Fund, ERDF/FEDER), by the Xunta de Galicia under project 10PXIB206037PR, by the Junta de Andalucía under project P08-TIC-3580 and by AE CITIUS under the project CN2012/151 of the Xunta de Galicia (ERDF/FEDER)S

Stochastic resonance in 2D materials based memristors

Stochastic resonance is an essential phenomenon in neurobiology, it is connected to the constructive role of noise in the signals that take place in neuronal tissues, facilitating information communication, memory, etc. Memristive devices are known to be the cornerstone of hardware neuromorphic applications since they correctly mimic biological synapses in many different facets, such as short/long-term plasticity, spike-timing-dependent plasticity, pair-pulse facilitation, etc. Different types of neural networks can be built with circuit architectures based on memristive devices (mostly spiking neural networks and artificial neural networks). In this context, stochastic resonance is a critical issue to analyze in the memristive devices that will allow the fabrication of neuromorphic circuits. We do so here with h-BN based memristive devices from different perspectives. It is found that the devices we have fabricated and measured clearly show stochastic resonance behaviour. Consequently, neuromorphic applications can be developed to account for this effect, that describes a key issue in neurobiology with strong computational implications

One Cut‐Point Phase‐Type Distributions in Reliability. An Application to Resistive Random Access Memories

A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non‐homogeneous phase‐type distribution. It is built by considering one cut‐point in the non‐negative semi‐line of a phase‐type distribution. The density function is defined and the main measures associated, such as the reliability function, hazard rate, cumulative hazard rate and the characteristic function, are also worked out. This new class of dis‐ tributions enables us to decrease the number of parameters in the estimate when inference is con‐ sidered. Additionally, the likelihood distribution is built to estimate the model parameters by maximum likelihood. Several applications considering Resistive Random Access Memories com‐ pare the adjustment when phase type distributions and one cut‐point phase‐type distributions are considered. The developed methodology has been computationally implemented in R‐cran.This paper is partially supported by the project FQM‐307 of the Government of Andalu‐ sia (Spain), by the project PID2020‐113961GB‐I00 of the Spanish Ministry of Science and Innovation (also supported by the European Regional Development Fund program, ERDF) and by the project PPJIB2020‐01 of the University of Granada. Additionally, the first and second authors acknowledge financial support by the IMAG–María de Maeztu grant CEX2020‐001105‐M/AEI/10.13039/501100011033. They also acknowledge the financial support of the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain) and the FEDER programme for projects A.TIC.117.UGR18, IE2017‐5414, B.TIC.624.UGR20 and A‐FQM‐66‐UGR20

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-

Modeling the variability of Au/ Ti/h BN/Au memris t ive devices

The variability of memristive devices using multilayer hexagonal boron nitride (h-BN) coupled with Ti and Au electrodes (i.e., Au/Ti/h-BN/Au) is analyzed in depth using different numerical techniques. We extract the reset voltage using three different methods, quantified its cycle-to-cycle variability, calculated the charge and flux that allows to minimize the effects of electric noise and the inherent stochasticity of resistive switching, described the device variability using time series analyses to assess the “memory” effect, and employed a circuit breaker simulator to understand the formation and rupture of the percolation paths that produce the switching. We conclude that the cycle-to-cycle variability of the Au/Ti/h-BN/Au devices presented here is higher than that previously observed in Au/h-BN/Au devices, and hence they may be useful for data encryption.Ministry of Science and Technology of China (2019YFE0124200, 2018YFE0100800)National Natural Science Foundation of China (61874075)Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain) and European Regional Development Fund (ERDF) under projects A-TIC-117-UGR18, A-FQM-66-UGR20, A-FQM-345- UGR18, B-TIC-624-UGR20 and IE2017-5414Grant PGC2018-098860-B-I00 supported by MCIU/AEI/FEDERMaria de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCIN/AEI/10.13039/501100011033King Abdullah University of Science and Technolog