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SPICE model of memristive devices with threshold
Y. V. Pershin, M. Di Ventra
TL;DR
Many SPICE models of memristive devices omit voltage-threshold behavior, although threshold switching is common and important for storage and logic. The paper presents a SPICE implementation of a voltage-controlled threshold memristor, with models for two simulators. The authors report testing the model and describe its potential generalization and inclusion in NGSPICE.
Problem
Available SPICE models of memristive devices typically omit thresholds, although threshold switching is common and important for non-volatile storage and logic.
Source: §1 · p. 1Method
Results
The authors developed and tested the model, and report that the NGSPICE implementation was included in the latest NGSPICE distribution.
Source: §4 · p. 3Takeaways & Limitations
The model is based on one internal state variable but can be generalized to more complex physical models with several state variables.
Source: §4 · p. 3
Abstract
from arXiv · showhide
Although memristive devices with threshold voltages are the norm rather than the exception in experimentally realizable systems, their SPICE programming is not yet common. Here, we show how to implement such systems in the SPICE environment. Specifically, we present SPICE models of a popular voltage-controlled memristive system specified by five different parameters for PSPICE and NGSPICE circuit simulators. We expect this implementation to find widespread use in circuits design and testing.
1. Introduction
Existing SPICE models of memristive systems typically omit threshold behavior, even though threshold switching is common and important for information storage and logic. This paper introduces a SPICE model for a voltage-threshold memristive device previously used in several circuit demonstrations.
1. Introduction
- Existing SPICE models of memristive devices typically rely on physical models without a threshold.The introduction notes that several models for memcapacitive and meminductive elements are also available.Source: §1 · p. 1
- Threshold switching is common in memristive devices and supports non-volatile storage and logic operations.The authors also expect it to be common in memcapacitive and meminductive elements because of physical constraints.Source: §1 · p. 1
- Atomic migration in many important experimental systems is induced by applied electric field rather than current flow, favoring voltage-threshold models on physical grounds.The paper contrasts these models with models using a current threshold.Source: §1 · p. 1
- The paper introduces a SPICE implementation of a voltage-threshold memristive model previously proposed by the authors.That model had been used in learning, neural-network, logic, analog, and memristive-to-memcapacitive or meminductive circuits.Source: §1 · p. 1
2. SPICE model
The paper formulates a voltage-controlled memristive device with threshold and implements it in SPICE. The model constrains memristance between limiting values and provides simulator-specific implementations for NGSPICE and PSPICE.
2. SPICE model
- The device model defines current through memristance and evolves its internal state according to the applied voltage.The general voltage-controlled formulation uses internal state variables, device voltage, and current; memristance is a scalar.Source: §2 · pp. 1–2
- The threshold model uses Vt, Ron, and Roff to set the switching threshold and bound memristance, while α and β set state-change rates below and above threshold.With α = 0, the state changes only when |VM| > Vt.Source: §2 · p. 2
- The NGSPICE implementation combines a behavioral resistor, current source, and capacitor, using ternary functions to keep memristance between Ron and Roff.The capacitor voltage sets the behavioral resistor value, and the implementation uses the function f from the model.Source: §2 · p. 2
- The PSPICE implementation replaces the behavioral resistor with an additional current source and smooths f to avoid convergence problems.The authors report identical simulation results for both SPICE versions and compatibility of the PSPICE code with LTspice.Source: §2 · p. 2
3. Example
The example compares soft- and hard-threshold devices under sinusoidal voltage and examines their time dynamics and frequency-dependent hysteresis. The two cases differ in when memristance changes and how loop span varies with frequency.
3. Example
- Table 1 presents an NGSPICE implementation of Eqs. (3)–(5), while Table 2 presents their PSPICE implementation for α = 0.The PSPICE caption notes separate positive and negative threshold inputs, Vtp and Vtm.Source: Table 1 · p. 3, Table 2 · p. 3
- For soft thresholds (α < β), memristance changes at any nonzero voltage; for hard thresholds (α = 0), it changes only when |V| > Vt.The hard-threshold case is described as closer to the behavior of many experimentally realizable systems.Source: §3 · p. 3
- At ν = 0.05 GHz, hard-threshold memristance changes only above Vt, while soft-threshold memristance switches between Ron and Roff and begins changing when voltage polarity reverses.The plotted current is not a simple sine wave, and the hard-threshold memristance steps are shifted relative to the soft-threshold steps.Source: §3 · p. 3
- The lowest-frequency loop span is smallest for soft thresholds but largest for hard thresholds.The authors relate this difference to soft-threshold memristance changing at lower voltages; the hard-threshold inset changes only above Vt = 4.6 V.Source: §3 · p. 3
4. Conclusions
The authors report a tested SPICE model for threshold-voltage memristive devices, with memristance limits implemented using ternary functions. They describe its scope, simulator availability, and related simulation issues for future work.
4. Conclusions
- The authors developed and tested a SPICE model of threshold-voltage memristive devices, using ternary functions for memristance limits instead of the previously suggested window-function approach.The authors say this implementation adheres more closely to the physical situation.Source: §4 · p. 3
- The model uses one internal state variable, but the authors say it can be generalized to models with several state variables.They also report that their NGSPICE model was included in the latest NGSPICE distribution.Source: §4 · p. 3
- The authors leave convergence and simulation issues for SPICE memelements to future work and note that threshold memcapacitive and meminductive models can be implemented similarly.The figure parameters include V0 = 5 V, ν = 0.05 GHz, Ron = 1 kΩ, Roff = 10 kΩ, and Vt = 4.6 V.Source: §4 · pp. 3–4
- The illustrated hard-threshold case changes memristance only when the applied-voltage magnitude exceeds Vt = 4.6 V.The Fig. 4 caption identifies voltage, current, and memristance over time for soft- and hard-threshold devices; Fig. 5 identifies frequency-dependent hysteresis loops for both cases.Source: §4 · p. 4, Figure 4 · p. 4, Figure 5 · p. 4
About Authors. . .
The paper provides biographical information about its two authors and their research interests.
About Authors. . .
- Yuriy V. Pershin received a Ph.D. in theoretical physics from the University of Konstanz in 2002; his interests include semiconductor nanodevices, spintronics, and biophysics.The biography notes that he was born in Russia.Source: About Authors · p. 5
- Massimiliano Di Ventra received a Ph.D. in theoretical physics from EPFL in 1997; his interests include nanoscale electronic and transport properties, non-equilibrium statistical mechanics, nanopores, unconventional computing, and biophysics.The biography notes that he was born in Italy.Source: About Authors · p. 5