Dissolution Of Conductive Filament Research Articles

Three-Dimensional Integrated Synaptic Devices Based on a Silver-Cluster Conduction Mechanism with High Thermostability.

During the operation of synaptic devices based on traditional conductive filament (CF) models, the formation and dissolution of CFs are usually uncertain. Moreover, when the device is operated for a long time, the CFs may dissolve due to both the Joule heat generated by the device itself and the thermal coupling between the devices. These problems seriously reduce the reliability and stability of the synaptic device. Here, an artificial synapse device based on polyimide-molybdenum disulfide quantum dot (MoS2 QD) nanocomposites is presented. Research has shown that MoS2 QDs doped into the active layer can effectively induce the reduction of Ag ions into Ag atoms, leading to the formation of Ag clusters and thereby achieving control over the growth of the CFs. Therefore, the device is capable of stably realizing various basic synaptic functions. Moreover, the long-term potentiation/long-term depression (LTP/LTD) of this device shows good linearity. In addition, due to the change in the shape of the CFs, the highly integrated devices with a three-dimensional (3D) stacked structure can operate normally even in a high-temperature environment of 110 °C. Finally, the synaptic characteristics of the devices on learning and inference tests show that their recognition rates are approximately 90.75% (room temperature) and 90.63% (110 °C).

Observing resistive switching behaviors in single Ta2O5 nanotube-based memristive devices

Recently, one-dimensional (1D) metal oxide nanostructured materials have attracted considerable attention owing to their appealing properties and functionalities. In previous studies, 1D metal oxide materials have been widely applied to electronic components; among them, resistive switching memristive devices are one of the most promising applications. The resistive switching mechanism in thin-film dielectric layers is widely explored, but understanding of that in 1D materials is insufficient. Moreover, a direct evidence regarding the switching behavior resulting from the formation and dissolution of conductive filaments is still lacking. In this study, a single Ta2O5 nanotube (NT) was fabricated as an Ag/Ta2O5 NT/Ag device, and its electrical properties were examined, which demonstrated a stable resistance state with a large memory window of approximately 107. The in-situ transmission electron microscopy (TEM), high-resolution TEM, energy dispersive spectroscopy techniques and electron energy loss spectroscopy (EELS) were used to establish a unique resistive switching mechanism in such devices for the first time. In addition, the crystallinity of the Ta2O5 NTs was well-controlled through rapid thermal annealing and furnace. The relationship between crystallinity and electrical properties was investigated. Oxygen vacancies play a crucial role in resistance switching, and thus, their amounts were determined using EELS. Therefore, the established mechanism revealed the dynamic behavior of Ta2O5 NTs in memristive devices, which allows the exploration of a wide range of NT materials for memory applications.

Statistical Simulation of the Switching Mechanism in ZnO-Based RRAM Devices

Resistive random access memory (RRAM) has two distinct processes, the SET and RESET processes, that control the formation and dissolution of conductive filament, respectively. The laws of thermodynamics state that these processes correspond to the lowest possible level of free energy. In an RRAM device, a high operating voltage causes device degradation, such as bends, cracks, or bubble-like patterns. In this work, we developed a statistical simulation of the switching mechanism in a ZnO-based RRAM. The model used field-driven ion migration and temperature effects to design a ZnO-based RRAM dynamic SET and RESET resistance transition process. We observed that heat transport within the conducting filament generated a great deal of heat energy due to the carrier transport of the constituent dielectric material. The model was implemented using the built-in COMSOL Multiphysics software to address heat transfer, electrostatic, and yield RRAM energy. The heat energy increased with the increase in the operating power. Hence, the reliability of a device with high power consumption cannot be assured. We obtained various carrier heat analyses in 2D images and concluded that developing RRAM devices with low operating currents through material and structure optimization is crucial.

Atomistic Insights on the Full Operation Cycle of a HfO2-Based Resistive Random Access Memory Cell from Molecular Dynamics.

We characterize the atomic processes that underlie forming, reset, and set in HfO2-based resistive random access memory (RRAM) cells through molecular dynamics (MD) simulations, using an extended charge equilibration method to describe external electric fields. By tracking the migration of oxygen ions and the change in coordination of Hf atoms in the dielectric, we characterize the formation and dissolution of conductive filaments (CFs) during the operation of the device with atomic detail. Simulations of the forming process show that the CFs form through an oxygen exchange mechanism, induced by a cascade of oxygen displacements from the oxide to the active electrode, as opposed to aggregation of pre-existing oxygen vacancies. However, the filament breakup is dominated by lateral, rather than vertical (along the filament), motion of vacancies. In addition, depending on the temperature of the system, the reset can be achieved through a redox effect (bipolar switch), where oxygen diffusion is governed by the applied bias, or by a thermochemical process (unipolar switch), where the diffusion is driven by temperature. Unlike forming and similar to reset, the set process involves lateral oxygen atoms as well. This is driven by field localization associated with conductive paths.

Uniform switching behavior of HfOx-based memory with gradual-grown filaments by interface modulation

HfOx/Cu/HfOx structures with Ti electrodes were fabricated to investigate the resistive switching characteristics. Stable and uniform switching behaviors can be observed for HfOx/Cu/HfOx sample except the few cycles at the beginning. XPS depth profile of the structure was carried out to explore the role of interface layer on chemical composition of HfOx film and the defects in the films were analyzed. In addition, the resistance in LRS was insensitive to device area. The processes of growth and dissolution of conductive filaments in HfOx film during switching cycles were investigated. The undissolved filaments in the bottom part of HfOx film promoted the growth of filaments in the subsequent set process. As the fixed Vos filaments and stable residual Cu filaments which can act as a precursor in upper and bottom part of the sample were formed, excellently uniform distribution of switching parameters can be obtained. Meanwhile, good endurance and retention properties can be observed for HfOx/Cu/HfOx sample. The migration of Vos and diffusion of Cu atoms under electric field were both responsible for the resistive switching behavior for HfOx/Cu/HfOx sample, and the underlying physical model of conductive filaments was proposed to illustrate the switching mechanism of HfOx/Cu/HfOx sample.

The role of oxygen vacancies in the high cycling endurance and quantum conductance in BiVO4‐based resistive switching memory

AbstractResistive random access memory (RRAM) has emerged as a new discipline promoting the development of new materials and devices toward a broad range of electronic and energy applications. Here, we realized a memristive device with weak dependence on the top electrodes and demonstrated the quantized conductance (QC) nature in BiVO4 matrix. The electronic properties have been investigated by the measurements of I‐V curves, where the resistive switching (RS) phenomenon with stable switching ratio and excellent long‐term retention capabilities are identified. Two more inert materials, TiN and Pd, are applied as the top electrodes to exclude the influence of electrodes on the RS states and QC behavior. The X‐ray photoelectron spectroscopy results and transport measurements reveal that the conductive filament (CF) is composed by elemental bismuth. The naturally existed oxygen vacancies in BiVO4 matrix plays as the role of catalyst in the formation and dissolution of CF in BiVO4‐based RRAM device, which is the primary cause for the observed weak dependence of switching performance in this device on the type of top electrodes. Our results clearly illustrate that BiVO4 could be a new idea platform to realize the high scalability, high cycling endurance, and multilevel storage RRAM devices.image

Stimulated Ionic Telegraph Noise in Filamentary Memristive Devices

Random telegraph noise is a widely investigated phenomenon affecting the reliability of the reading operation of the class of memristive devices whose operation relies on formation and dissolution of conductive filaments. The trap and the release of electrons into and from defects surrounding the filament produce current fluctuations at low read voltages. In this work, telegraphic resistance variations are intentionally stimulated through pulse trains in HfO2-based memristive devices. The stimulated noise results from the re-arrangement of ionic defects constituting the filament responsible for the switching. Therefore, the stimulated noise has an ionic origin in contrast to the electronic nature of conventional telegraph noise. The stimulated noise is interpreted as raising from a dynamic equilibrium establishing from the tendencies of ionic drift and diffusion acting on the edges of conductive filament. We present a model that accounts for the observed increase of noise amplitude with the average device resistance. This work provides the demonstration and the physical foundation for the intentional stimulation of ionic telegraph noise which, on one hand, affects the programming operations performed with trains of identical pulses, as for neuromorphic computing, and on the other hand, it can open opportunities for applications relying on stochastic processes in nanoscaled devices.

(Invited) Analog Hfox-Rram Switches for Neural Networks

Memristive systems represent today a disruptive technology for the semiconductor industry with high potential for a wide range of applications ranging from non-volatile memories and non-volatile logic, to analog circuits, biomimetic devices, and neuromorphic computing paradigms. Among the general class of memristive systems, our work focus on oxide filamentary resistive random access memories (oxide RRAM) that base their operation on redox reactions and electrochemical phenomena that allow the formation and dissolution of conductive filaments, shorting the two electrodes of a metal/oxide/metal stack [1]. RRAMs have already demonstrated their great potential for non-volatile memory applications because of low power consumption, fast switching times, scalability down to nm scale [2] or atomic level, and CMOS compatibility. In parallel, significant efforts to redirect the device engineering towards neuromorphic computing [3] and neural networks have been devoted by a large community in the last years. Indeed, the RRAM technology can localize memory and computation in one single device, thus allowing a conceptual realization of non-Von Neumann paradigms that dramatically reduce the power-cost in computing architectures and data communication. This research finds its main application in the development of intelligent and adaptive systems towards the ‘Internet of Things’ concept. It is a highly interdisciplinary research field which merges, on one hand, materials development, nanodevice fabrication, modelling, electrical testing aimed at building artificial synapses with memristive devices. On the other hand, it studies the implementation of neuron functions into VLSI electronics that has to match memristive behavior and electrical features for a functional and physical integration of artificial neuronal and synaptic units. In our work we are focusing on switching dynamics in relation to material properties of HfOx-based RRAM devices [4-7] in order to reach the switching characteristics that fit biologically plausible behaviors. Here we present analog memristive behavior for use in two different approaches, named (i) 1 RRAM-1 synapse and (ii) 1T-1 RRAM–synapse for subthreshold CMOS circuits. In approach (i), a single RRAM device plays the role of a synapse by itself. The analog behavior allows realizing a Spike Timing Dependent-Plasticity (STDP) learning rule (Fig1a), which translates the timing of two superimposing spikes with specific shapes sent to the two device terminals into a causality relation among events [6-9]. The experimental STDP learning rule has been employed in a simulated neuromorphic network able to recognize vowels after an unsupervised training (Fig.1b). While conceptually simple and allowing for a highly compact design, the previous approach is very challenging in practice. The 1T-1 RRAM synapse for subthreshold CMOS circuits, despite being less compact, is more feasible and allows some biological plausibility even within a network utilizing short simply shaped spikes. The use of subthreshold transistor in the analog regime refers back to the original definition of neuromorphic system as given by Carver Mead [9] and is used to generate the biorealistic temporal dynamics of post synaptic spikes [10]. We will demonstrate that RRAM devices can be interfaced with such synaptic circuits including subthreshold transistors to obtain a non-volatile control of synaptic weights. [1] Brivio, G. Tallarida, E. Cianci and S. Spiga, Formation and disruption of conductive filaments in a HfO2/TiN structure, Nanotechnology 25, 385705 (2014) [2] J. Frascaroli , S. Brivio, F. F. Lupi , G. Seguini , L. Boarino , M. Perego, and S. Spiga , Resistive Switching in High-Density Nanodevices Fabricated by Block Copolymer Self-Assembly, ACS Nano 9, 2518 (2015) [3] G. Indiveri, S.-C. Liu, Memory and information processing in neuromorphic systems, In Proceedings of the IEEE, IEEE, volume 103, 2015. [4] J. Frascaroli, F. G. Volpe, S. Brivio, and S. Spiga, Effect of Al doping on the retention behavior of HfO2 resistive switching memories, Microelectronic Engineering 147, 104 (2015) [5] S. Brivio, J. Frascaroli, and S. Spiga, Role of metal-oxide interfaces in the multiple resistance switching regimes of Pt/HfO2/TiN devices, Applied Physics Letters 107, 023504 (2015) [6]E. Covi, S. Brivio, M. Fanciulli, and S. Spiga, Synaptic potentiation and depression in Al:HfO2-based memristor , Microelectronic Engineering 147, 41-44 (2015) [7] S. Brivio, E. Covi, A. Serb, T. Prodromakis, M. Fanciulli, and S. Spiga, Gradual set dynamics in HfO2-based memristor driven by sub-threshold voltage pulses, in Memristive Syst. MEMRISYS 2015 IEEE Int. Conf. On (2015), pp. 1–2. [8] E. Covi, S. Brivio, A. Serb, T. Prodromakis, M. Fanciulli, and S. Spiga, HfO2-based Memristors for Neuromorphic Applications, Proceedings of 2016 IEEE International Symposium on Circuits and Systems (ISCAS) [9] C. Mead, Analog VLSI and neural systems. Reading, MA: Addison-Wesley (1989) [10] Bartolozzi et al., Neural Computation 19 (2007) 2581. Figure 1

Statistical characteristics of reset switching in Cu/HfO2/Pt resistive switching memory.

A major challenge of resistive switching memory (resistive random access memory (RRAM)) for future application is how to reduce the fluctuation of the resistive switching parameters. In this letter, with a statistical methodology, we have systematically analyzed the reset statistics of the conductive bridge random access memory (CBRAM) with a Cu/HfO2/Pt structure which displays bipolar switching property. The experimental observations show that the distributions of the reset voltage (Vreset) and reset current (Ireset) are greatly influenced by the initial on-state resistance (Ron) which is closely related to the size of the conductive filament (CF) before the reset process. The reset voltage increases and the current decreases with the on-state resistance, respectively, according to the scatter plots of the experimental data. Using resistance screening method, the statistical data of the reset voltage and current are decomposed into several ranges and the distributions of them in each range are analyzed by the Weibull model. Both the Weibull slopes of the reset voltage and current are demonstrated to be independent of the on-state resistance which indicates that no CF dissolution occurs before the reset point. The scale factor of the reset voltage increases with on-state resistance while that of the reset current decreases with it. These behaviors are fully in consistency with the thermal dissolution model, which gives an insight on the physical mechanism of the reset switching. Our work has provided an inspiration on effectively reducing the variation of the switching parameters of RRAM devices.

Direct Observation of Conversion Between Threshold Switching and Memory Switching Induced by Conductive Filament Morphology

Volatile threshold switching (TS) and non‐volatile memory switching (MS) are two typical resistive switching (RS) phenomena in oxides, which could form the basis for memory, analog circuits, and neuromorphic applications. Interestingly, TS and MS can be coexistent and converted in a single device under the suitable external excitation. However, the origin of the transition from TS to MS is still unclear due to the lack of direct experimental evidence. Here, conversion between TS and MS induced by conductive filament (CF) morphology in Ag/SiO2/Pt device is directly observed using scanning electron microscopy and high‐resolution transmission electron microscopy. The MS mechanism is related to the formation and dissolution of CF consisting of continuous Ag nanocrystals. The TS originates from discontinuous CF with isolated Ag nanocrystals. The results of current–voltage fitting and Kelvin probe force microscopy further indicate that the TS mechanism is related to the modulation of the tunneling barrier between Ag nanocrystals in CF. This work provides clearly experimental evidence to deepen understanding of the mechanism for RS in oxide‐electrolyte‐based resistive switching memory, contributing to better control of the two RS behaviors to establish high‐performance emerging devices.

High ON/OFF Ratio and Quantized Conductance in Resistive Switching of ${\rm TiO}_{2}$ on Silicon

TiO2 has been investigated extensively as an active resistive switching (RS) material for resistive random access memory. In this letter, single-crystal anatase- TiO2 thin films fabricated on silicon by atomic layer deposition are used to realize highly stable and clean bipolar RS behavior with a record high ON/OFF ratio (~107) and low leakage current in the high-resistance state. The switching characteristics resemble those of electrochemical memories via formation and dissolution of conductive filaments (CFs) composed of oxygen vacancies, and small numbers of quantized channels are reproducibly observed in the low-resistance state, consistent with quantized conductance (QC) found in conventional electrolytic systems and indicating its potential for forming ultrathin CF amenable to device scaling. A detailed analysis of QC and contact resistance is presented. The emergence of QC is believed to be related to the single-crystal nature of the TiO2 thin films.

Cycle-to-Cycle Intrinsic RESET Statistics in ${\rm HfO}_{2}$-Based Unipolar RRAM Devices

The statistics of the RESET voltage ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> ) and the RESET current ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> ) of Pt/HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Pt resistive random access memory (RRAM) devices operated under unipolar mode are analyzed. The experimental results show that both the distributions of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> are strongly influenced by the distribution of initial resistance in the ON state ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> ), which is related to the size of the conductive filament (CF) before RESET. By screening the statistical data into different resistance ranges, both the distributions of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> are shown to be compatible with a Weibull model. Contrary to previous reports for NiO-based RRAM, the Weibull slopes of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> are demonstrated to be independent of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> . This is an indication that the RESET point, defined in this letter as the point of maximum current, corresponds to the initial phase of CF dissolution. On the other hand, given that the scale factor of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> distribution ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET63%</sub> ) is roughly independent of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> , the scale factor of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET</sub> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RESET63%</sub> ) is inversely proportional to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> . This is analogous to what was found in NiO-based RRAM and it is consistent with the thermal dissolution model of RESET. Our results highlight the intrinsic link between the SET and RESET statistics and the need for controlling the variation of ON-state resistance to reduce the variability of the RESET voltage and current.

Response to “Comment on Real‐Time Observation on Dynamic Growth/Dissolution of Conductive Filaments in Oxide‐Electrolyte‐Based ReRAM”

In our recently published paper, [ 1 ] we achieved direct visualization of the dynamic growth and dissolution of conductive fi laments (CFs) in Ag (or Cu)/ZrO 2 /Pt systems based on in situ transmission electron microscope (TEM) observations. Furthermore, continuous TEM images clearly showed that the CFs start to grow at the Cu/ZrO 2 (or Ag/ZrO 2 ) interface and begin to dissolve at the ZrO 2 /Pt interface, which is in contrast to the prediction from the electrochemical metallization (ECM) theory developed for the solid-electrolyte-based ReRAM (also referred to a the ECM cell). [ 2 , 3 ] The same direction of CF growth/dissolution had been demonstrated in other ECM cells, including Ag/ α -Si/Pt, [ 4 ] Cu/ZnO/Pt, [ 5 ] and Cu/P3HT:PCBM/ ITO devices. [ 6 ] In our paper, [ 1 ] we suggested that the differences in cation solubility and diffusion coeffi cient between traditional solid-electrolyte and oxide-electrolyte materials accounts for this discrepancy, and based on our suggestion, the metal ions would be reduced and crystallized inside the ZrO 2 -electrolyte system in order to explain the observed results. Valov and Waser made a comment to dispute our explanation based on the following arguments. (1) The EDX analysis presented in our paper cannot identify the chemical valence of Ag (Cu) species inside the CF region. They suggested that the resistive switching (RS) behavior in our device cannot rule out valence change memory (VCM) effects due to oxide materials like ZrO 2 , TiO 2 , HfO 2 , and Ta 2 O 5 which are often used for ECM and VCM cells. (2) The large amount of electrons in the solid materials is not a suffi cient condition to reduce the incoming metal ions inside the solid electrolyte materials. (3) Considering the electric potential distribution, the Cu or Ag CFs should not start to grow at the Cu/ZrO 2 (or Ag/ZrO 2 ) interface and begin to dissolve at the ZrO 2 /Pt interface. At the end of their comment, they presented a hypothesis in which the growth and dissolution of CF in ZrO 2 result from the metal ion doping/

A Monte Carlo study of the low resistance state retention of HfOx based resistive switching memory

A Monte Carlo simulator is developed to investigate the low resistance state (LRS) retention of HfOx based resistive switching memory. The simulator tracks the evolution of oxygen ions and oxygen vacancies by choosing the occurrence of the generation/recombination/migration processes based on their corresponding probability at each simulation step. The current through the resulting conductive filament (CF) configuration is then calculated by a trap-assisted-tunneling solver. The simulation results are corroborated with experimental data. The LRS retention is found to be CF size dependent, and its variability is suggested to be intrinsic due to the stochastic nature of the CF dissolution. The tail bits of the failure time distribution become a limiting factor of the device reliability in a large memory array.