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Biological plausibility and stochasticity in scalable VO2 active memristor neurons

Wei Yi, Kenneth K. Tsang, Stephen K. Lam, Xiwei Bai, Jack A. Crowell, Elias A. Flores

arXiv:1809.07867v1cs.ETphysics.app-ph

TL;DR

Existing memristor neurons lacked evidence of biological competitiveness and rich neuronal dynamics. This paper develops VO2 active-memristor neuron circuits and shows biologically competitive energy efficiency and area scaling.

  • Problem

    Biologically competitive memristor neurons require energy efficiency above 10^13 spikes/J.

  • Method

    The paper combines experimental VO2 active-memristor neurons with circuit models derived from coupled first-order ODEs and action-potential generation mechanisms.

  • Results

    VO2 neurons can surpass the estimated human-brain energy efficiency of 1.8x10^14 spike/J at neuron sizes below 3 μm2.

  • Takeaways & Limitations

    The results show that VO2 neurons can achieve biologically competitive energy efficiency and area.

  • Takeaways & Limitations

    At low firing rates, static power may dominate total power consumption because VO2 standby current remains constant.

Abstract

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Neuromorphic networks of artificial neurons and synapses can solve computational hard problems with energy efficiencies unattainable for von Neumann architectures. For image processing, silicon neuromorphic processors outperform graphic processing units (GPUs) in energy efficiency by a large margin, but they deliver much lower chip-scale throughput. The performance-efficiency dilemma for silicon processors may not be overcome by Moore's law scaling of complementary metal-oxide-semiconductor (CMOS) field-effect transistors. Scalable and biomimetic active memristor neurons and passive memristor synapses form a self-sufficient basis for a transistorless neural network. However, previous demonstrations of memristor neurons only showed simple integrate-and-fire (I&F) behaviors and did not reveal the rich dynamics and computational complexity of biological neurons. Here we show that neurons built with nanoscale vanadium dioxide active memristors possess all three classes of excitability and most of the known biological neuronal dynamics, and are intrinsically stochastic. With the favorable size and power scaling, there is a path toward an all-memristor neuromorphic cortical computer.

Locally-active memristors

Locally-active memristors operate in a hysteretic negative differential-resistance regime, enabling signal gain and oscillations for scalable information processing. Electroform-free VO2 devices combine high yield, low variability, endurance, rich biological spiking dynamics, stochastic firing, and favorable energy-area scaling.

  • Locally-active memristors: A memristor becomes locally active when its operating point lies in the hysteretic negative differential-resistance regime, enabling a.c. signal gain and oscillations.These properties make active memristors scalable gain elements for information processing.
  • Device technology: Electroform-free VO2 active memristors on CMOS-compatible substrates achieved typical yield >98 % and <13 % coefficient of variation in switching threshold voltage.The devices had critical dimensions from 50-600 nm.
  • Device technology: >26.6 million cycles were sustained without discernible change in device I-V characteristics, while simulated Mott transition in VO2 was 100 times faster than in NbO2.VO2 consumed about one-sixth (16 %) of the energy of NbO2 in the simulated transition.
  • Neuronal dynamics: VO2 neurons experimentally demonstrated 23 types of known biological neuron spiking behaviors, spanning tonic, phasic, and mixed-mode dynamics.Observed behaviors included all-or-nothing firing, refractory periods, adaptation, latency, three excitability classes, bursting, resonance, rebound responses, and accommodation.
  • Stochasticity: VO2 memristor neurons exhibit input-noise-sensitive, stochastically phase-locked firing, with a fundamental ISI median of 29.3 µs that remains robust against noise.Increasing noise produces drop-outs and irregular spiking, while missed firings retain subthreshold sawtooth oscillations.

Supplementary Tables

The supplementary tables quantify VO2 transition energy, specify material and structural parameters for SPICE simulations, and report experimental circuit conditions for neuron spiking tests.

  • Energy cost: At the same volume, NbO2’s Mott phase-transition free energy cost is 6.1 times that of VO2.A VO2 nano-crossbar with channel radius r = 10 nm and length L = 10 nm has a total volumetric enthalpy change of 1.15 fJ.
  • SPICE model: The SPICE simulations use published VO2 material properties and a cylindrical VO2 conduction channel of 56 nm.The Mott physics-based analytical compact model can reproduce experimental device switching dynamics and neuron spiking behaviors in most cases.
  • Experimental parameters: Experimental spiking tests use randomly selected VO2 nano-crossbar devices X1 and X2 with the same nominal size of 100 u 100 nm2 and film thickness of 100 nm.Simulation setup adds stray capacitances, typically ~1 nF, to the discrete capacitor values C1 and C2.

Supplementary Notes · Supplementary Note 1: VO2 active memristor relaxation oscillator

The VO2 active memristor relaxation oscillator exploits Joule-heating-driven Mott switching, volatile hysteresis, and negative differential resistance. VO2 is suitable for electronic applications because its transition temperature is near room temperature, unlike NbO2, whose much higher transition temperature increases operating demands.

  • Supplementary Note 1: VO2 active memristor relaxation oscillator: VO2 undergoes a first-order Mott insulator-to-metal transition near 67 °C.The transition is thermodynamically driven and has critical temperature TC near 67 °C.
  • Supplementary Note 1: VO2 active memristor relaxation oscillator: Joule heating in metal/VO2/metal devices produces volatile hysteretic resistive switching and a negative differential resistance regime.These effects arise from the Mott transition induced by electrical current.
  • Supplementary Note 1: VO2 active memristor relaxation oscillator: The switching and negative differential resistance enable construction of oscillators, amplifiers, impulse circuits, and neurons.Mott memristors based on the Mott transition provide the active-device basis for these circuits.
  • Supplementary Note 1: VO2 active memristor relaxation oscillator: Many transition-metal oxides have Mott transition temperatures below 300 K, limiting their suitability for room-temperature electronics.Materials with TC > 300 K, including VO2, Ti2O3, Ti3O5, NbO2, SmNiO3, and LaCoO3, are identified as more suitable.
  • Supplementary Note 1: VO2 active memristor relaxation oscillator: VO2 is among the Mott insulators with TC > 300 K considered suitable for electronic applications.The passage lists VO2 alongside Ti2O3, Ti3O5, NbO2, SmNiO3, and LaCoO3.
  • Supplementary Note 1: VO2 active memristor relaxation oscillator: NbO2 has been demonstrated for spiking neurons but requires a TC of 1080 K.Operating NbO2 requires a large local temperature rise of 800 K, negatively affecting power consumption and device longevity.

Supplementary Note 2: Action potential generation in a VO2 active memristor neuron

The supplement outlines experimental and simulated action-potential generation in a VO2 active memristor neuron, using analogous biological processes for explanation. It defines hyperpolarization and depolarization and describes the resting state as closed, insulating Na+ and K+ channels.

  • Action potential generation: Experimental and simulated action-potential generation follows basic operational steps illustrated alongside analogous biological processes.These processes are shown in Supplementary Fig. 10 for pedagogical comparison.
  • Action potential generation: Hyperpolarization drives membrane potential toward negative values, whereas depolarization drives it in the opposite direction.These definitions follow neuroscience convention.
  • Action potential generation: In the resting, or quiescent, state, both Na+ and K+ channels are closed and represented by insulating X1 and X2.The passage identifies X1 and X2 as the insulating channel states.

Supplementary Note 3: Device modeling of VO2 active memristors

The VO2 active-memristor model uses analytical equations in which a normalized metallic-channel radius is the single state variable driving device dynamics. A corresponding SPICE compact model was implemented and simulated with LTspice IV.

  • Model formulation: The model uses analytical equations previously developed for VO2 active-memristor dynamics, with parameters summarized in Supplementary Table 2.The main equations are relisted in the supplementary note.
  • Model formulation: The normalized metallic-channel radius u ≜ r_met/r_ch is the single state variable determining the VO2 channel resistance R_ch(u).The conducting channel is heated above the TC of the Mott transition.
  • Model formulation: The first-order differential equation drives state dynamics, while auxiliary functions define state-dependent resistance, thermal conductance, and enthalpy change.These functions are given by Eqs. (S3)–(S5).
  • SPICE implementation: The SPICE compact model was constructed similarly to the supplementary model of Ref. 16, and simulations used LTspice IV on a personal computer.The implementation follows the modeling approach outlined for the reference device model.

Supplementary Note 4: Dynamics equations of an active memristor neuron circuit

The tonic active memristor neuron circuit is modeled by four coupled first-order ODEs derived from the device equations using Kirchhoff’s voltage and current laws. The formulation uses four state variables and supports recasting the dynamics in experimentally probeable Na+ and K+ membrane potentials.

  • Circuit dynamics: Four coupled first-order ODEs drive the tonic active memristor neuron circuit’s dynamics.They solve for the four state variables u1, v1, u2, and v2.
  • Circuit dynamics: The equations are derived from the active memristor device model by applying Kirchhoff’s voltage law and Kirchhoff’s current law.The external input current is expressed as I = IC1 + i1 + IC2 + i2 through KCL.
  • Equation formulation: The model defines auxiliary functions for differential enthalpy change, heat flux, and channel resistance to simplify the active-memristor equations.The two active memristors’ model equations are rewritten using ℋ(u), Q(u), and Rch(u).
  • Experimental variables: The state equations can be recast using experimentally probeable Na+ and K+ channel membrane potentials, VNa = v1 − E1 and VK = v2 + E2.This substitution replaces v1 and v2 in the previously grouped dynamics equations.
  • Nonlinear dynamics: Unlike hard switching between preset Ron and Roff values, the continuous state equations retain nonlinear dynamics relevant to VNa-VK nullcline analysis.The simplified hard-switching approach omits aspects of the nonlinear dynamics in the full equations.

Supplementary Note 5: Dynamic and static power scaling of VO2 neurons

SPICE simulations show that VO2 neuron dynamic spiking energy scales nearly linearly with membrane capacitance, while static standby power can dominate at low firing rates. Smaller capacitors and higher firing rates therefore improve energy efficiency under the described scaling behavior.

  • Dynamic power scaling: Dynamic spiking energy scales almost linearly with membrane capacitance, with fitted slopes of 0.96 and 0.924 for r/L = 10/10 nm and 36/50 nm, respectively.Neuron area also scales linearly with membrane capacitance because capacitor elements dominate circuit area.
  • Dynamic power scaling: <0.1 pJ/spike is achievable at a total capacitor area of ~1 μm2 using 20 fF membrane capacitors for r/L = 36/50 nm.The passage relates this estimate to integrated high-κ MIM capacitors with a record-high capacitance density of 43 fF/µm2.
  • Static power scaling: Static power arises from standby current through d.c.-biased VO2 devices because the insulating phase has finite resistivity of ~1 ٘cm.At low firing rates, this static consumption may dominate total power.
  • Static power scaling: Dynamic power increases with firing rate, whereas static power remains constant, so static power constitutes a smaller percentage of total power at higher firing rates.The simulations estimate lower and higher static-power bounds using d.c. biases of Vth and Vth/2.
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