The Art and Science of Constructing a Memristor Model: Updated

Kumar, Suhas; Gibson, Gary A. P.; Graves, Catherine E.; Pickett, Matthew D.; Strachan, John Paul; Williams, R. Stanley

doi:10.1007/978-3-319-76375-0_9

Cited by 4 publications

(5 citation statements)

References 61 publications

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“…Equation (6) shows that ( ) eff crit C T is thus dependent on the bias temperature, the electrical and thermal conductances, the thermal capacitance, and the nonlinearity parameter Γ − (T) at that bias. The necessary condition of EOC is built into Equation (6), i.e., a physical critical capacitance C 0…”

Section: Local Activity Theory: Ndr Nonlinearity and Oscillationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Without answers to these questions, crucial design decisions like what material should be used, what processing can optimize its electrical transport in what way, and what level of device or circuit performance can be expected, become equally matters of art as well as science. [6] The first difficulty of modeling networks of nonlinear dynamical devices has been addressed using compact modeling, which aims to capture the behavior of individual devices across the full range of relevant physical conditions within a small set of lumped model parameters. [7] Such modeling is accomplished through a careful compromise of just-sufficient fidelity with physics-based intuition; compact models are neither expensive high-fidelity molecular dynamics simulations nor naïve empirical fits of current-voltage curves that change for each new data set.…”

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confidence: 99%

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Electro‐Thermal Characterization of Dynamical VO₂ Memristors via Local Activity Modeling

et al. 2022

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Translating the surging interest in neuromorphic electronic components, such as those based on nonlinearities near Mott transitions, into large‐scale commercial deployment faces steep challenges in the current lack of means to identify and design key material parameters. These issues are exemplified by the difficulties in connecting measurable material properties to device behavior via circuit element models. Here, the principle of local activity is used to build a model of VO2/SiN Mott threshold switches by sequentially accounting for constraints from a minimal set of quasistatic and dynamic electrical and high‐spatial‐resolution thermal data obtained via in situ thermoreflectance mapping. By combining independent data sets for devices with varying dimensions, the model is distilled to measurable material properties, and device scaling laws are established. The model can accurately predict electrical and thermal conductivities and capacitances and locally active dynamics (especially persistent spiking self‐oscillations). The systematic procedure by which this model is developed has been a missing link in predictively connecting neuromorphic device behavior with their underlying material properties, and should enable rapid screening of material candidates before employing expensive manufacturing processes and testing procedures.

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Section: Local Activity Theory: Ndr Nonlinearity and Oscillationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Electro‐Thermal Characterization of Dynamical VO₂ Memristors via Local Activity Modeling

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“…On the other hand, analytical models are formulated as mathematical equations, which match the device's experimentally-observed behaviour. The physical principles approach and analytical approach are two extremes, and in reality, a model for RRAM is a compromise between these two extremes [19]. Analytical approaches can be further classified as being either physicsbased or black-box.…”

Section: Introductionmentioning

confidence: 99%

“…Examples of these would be [21] and [22] that specifically model Valence Change Mechanism (VCM) and Electrochemical Metallization (ECM) devices, respectively. More details on RRAM models and their classifications can be found in [13], [17], [19], [23]- [26]. Since the focus of this work is variability modeling, we discuss a few models which have the capability to reproduce variability (in section V) to make our contribution clear.…”

Section: Introductionmentioning

confidence: 99%

Incorporating Variability of Resistive RAM in Circuit Simulations Using the Stanford–PKU Model

Reuben

Biglari

Fey

2020

IEEE Trans. Nanotechnology

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Intrinsic variability observed in resistive-switching devices (cycle-to-cycle and device-to-device) is widely recognised as a major hurdle for widespread adoption of Resistive RAM technology. While physics-based models have been developed to accurately reproduce the resistive-switching behaviour, reproducing the observed variability behavior of a specific RRAM has not been studied. Without a properly fitted variability in the model, the simulation error introduced at the device-level propagates through circuit-level to system-level simulations in an unpredictable manner. In this work, we propose an algorithm to fit a certain amount of variability to an existing physicsbased analytical model (Stanford-PKU model). The extent of variability exhibited by the device is fitted to the model in a manner agnostic to the cause of variability. Further, the model is modified to better reproduce the variations observed in a device. The model, fitted with variability can well reproduce cycle-tocycle, as well as device-to-device variations. The significance of integrating variability into RRAM models is underscored using a sensing example. Index Terms-Resistive RAM (RRAM), physics-based models, cycle-to-cycle variability, device-to-device variability, Stanford model, memristor, sense amplifier, resistive-switching, 1T-1R there cannot be a proper assessment of the functionality and yield of RRAM-based ICs, which will result in a series of expensive trial-and-errors. Pessimistic design approaches which allocate huge safety margins to accommodate variability are not recommended since they sacrifice design properties like energy, delay, and area. Consequently, there is an exigent RRAM models FEM DFT KMC Simulation speed Stanford-PKU model Classification based on abstraction levels Computational cost Physical detail Circuit µm 2-mm 2 Devicẽ 10 3 nm 3 Material few nm 3 Compact model Classification based on modeling approach Physical model (from first principles) Analytical Physics-based Black-box (measurement) Stanford-PKU model

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Physics-based compact modeling of electro-thermal memristors: Negative differential resistance, local activity, and non-local dynamical bifurcations

Brown

Kumar

Williams

2022

Applied Physics Reviews

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Leon Chua's Local Activity theory quantitatively relates the compact model of an isolated nonlinear circuit element, such as a memristor, to its potential for desired dynamical behaviors when externally coupled to passive elements in a circuit. However, the theory's use has often been limited to potentially unphysical toy models and analyses of small-signal linear circuits containing pseudo-elements (resistors, capacitors, and inductors), which provide little insight into required physical, material, and device properties. Furthermore, the Local Activity concept relies on a local analysis and must be complemented by examining dynamical behavior far away from the steady-states of a circuit. In this work, we review and study a class of generic and extended one-dimensional electro-thermal memristors (i.e., temperature is the sole state variable), re-framing the analysis in terms of physically motivated definitions and visualizations to derive intuitive compact models and simulate their dynamical behavior in terms of experimentally measurable properties, such as electrical and thermal conductance and capacitance and their derivatives with respect to voltage and temperature. Within this unified framework, we connect steady-state phenomena, such as negative differential resistance, and dynamical behaviors, such as instability, oscillations, and bifurcations, through a set of dimensionless nonlinearity parameters. In particular, we reveal that the reactance associated with electro-thermal memristors is the result of a phase shift between oscillating current and voltage induced by the dynamical delay and coupling between the electrical and thermal variables. We thus, demonstrate both the utility and limitations of local analyses to understand non-local dynamical behavior. Critically for future experimentation, the analyses show that external coupling of a memristor to impedances within modern sourcing and measurement instruments can dominate the response of the total circuit, making it impossible to characterize the response of an uncoupled circuit element for which a compact model is desired. However, these effects can be minimized by proper understanding of the Local Activity theory to design and utilize purpose-built instruments.

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The Art and Science of Constructing a Memristor Model: Updated

Cited by 4 publications

References 61 publications

Electro‐Thermal Characterization of Dynamical VO₂ Memristors via Local Activity Modeling

Electro‐Thermal Characterization of Dynamical VO₂ Memristors via Local Activity Modeling

Incorporating Variability of Resistive RAM in Circuit Simulations Using the Stanford–PKU Model

Physics-based compact modeling of electro-thermal memristors: Negative differential resistance, local activity, and non-local dynamical bifurcations

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The Art and Science of Constructing a Memristor Model: Updated

Cited by 4 publications

References 61 publications

Electro‐Thermal Characterization of Dynamical VO2 Memristors via Local Activity Modeling

Electro‐Thermal Characterization of Dynamical VO2 Memristors via Local Activity Modeling

Incorporating Variability of Resistive RAM in Circuit Simulations Using the Stanford–PKU Model

Physics-based compact modeling of electro-thermal memristors: Negative differential resistance, local activity, and non-local dynamical bifurcations

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Electro‐Thermal Characterization of Dynamical VO₂ Memristors via Local Activity Modeling

Electro‐Thermal Characterization of Dynamical VO₂ Memristors via Local Activity Modeling