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

Abstract

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.

Spontaneous Symmetry‐Breaking of Nonequilibrium Steady–States Caused by Nonlinear Electrical Transport

“…This expression is the same as the criterion derived for edge of chaos (EOC) and negative differential resistance (NDR) properties in a constrained system in which the thermal conductance is constant, showing the interdependence and simultaneous appearance of EOC with electrothermal localizations. [10] To provide insight into the thermodynamic driving forces behind temperature and current density localizations in thermallyactivated material systems, we used the conductor-based model to verify whether the electro-thermal localizations shown throughout this work are consistent with the principle of minimum entropy production. [6] This principle states that the most stable configuration of a steady-state system has the lowest rate of entropy production to be as close as possible to the equilibrium state, which by definition has an entropy production rate of Ṡeq = 0.…”

“…Devices operated in a region of NDR are locally active, meaning that they are capable of utilizing DC power to couple to external circuitry and thereby amplify small fluctuations in their internal state variable or external electrical biasing, which can be used in circuits to implement amplifiers, oscillators, signal multiplexers and other useful functions. [8,[10][11][12][13] NDR can manifest from a variety of nonlinear physical mechanisms and associated state variables, including temperature in thermally-activated transport, tunneling distance in ion electro-migration, and reaction coordinate in phase transitions and chemical reactions, and each may either cause or result from current density localization in the device (Figure 1a). [14][15][16][17][18][19][20] In this work, we restrict our analysis to current-controlled, or S-type, NDR resulting from the feedback between thermallyactivated nonlinear electrical conductivity, internal Joule heating, and heat dissipation via Newton's law of cooling, such as that observed in VO x , NbO x , or TaO x .…”

Abisko: Deep codesign of an architecture for spiking neural networks using novel neuromorphic materials

“…By contrast, semiconductors in ideal circumstances exhibit no memory effects. Although a fairly large number of devices that exhibit both nonlinearity and memory have been demonstrated, the descriptive and predictive understanding of the enabling phenomena is not on the same mature level of semiconductor physics (Nili et al, 2020b; Brown et al, 2022). Given that codesign of modern semiconductor circuitry presently occurs across all contributing length scales (i.e., from atoms to architectures (Stettler et al, 2021)), the argument in favor of fundamental understanding of material mechanism that can best implement specific neuromorphic functions is very compelling.…”

“…However, the intrinsic challenge is that both nonlinear and memory functions imply that the desired properties originate from non-equilibrium behavior (generally transient, metastable, and temporal), so that many trusted methodologies for materials design will, at best, have limited applicability to the neuromorphic paradigm. Some of the specific challenges that arise from incomplete understanding of nonlinear device mechanisms include the limited level of reproducibility and predictability over resistive switching devices, the challenge of long-term retention of their programmed characteristics, and even well-defined, physics-based compact models that abstract the device properties for further integration with computing architectures (Gao et al, 2021; Dao and Koch 2020; Hamdioui et al, 2017; Brown et al, 2022).…”

Controllable branching of robust response patterns in nonlinear mechanical resonators

“…Systems with robust, yet flexible, dynamics have been proposed as models for a wide variety of complex responses ranging from weather patterns to neural circuits and decision-making [1][2][3][4][5][6][7] . Such long-term robust complex response sequences can be described by models from nonlinear dynamical systems in terms of global structures in phase space involving saddle points (or their higher dimensional generalizations) linked by robust dynamics segments 1,8,9 .…”