[Paper Review] Which Memristor Theory is Best for Relating Devices Properties to Memristive Function?

Ella Gale, Ben de Lacy Costello+1 more|arXiv (Cornell University)|Dec 16, 2013

Advanced Memory and Neural Computing27 references3 citations

TL;DR

This paper experimentally tests three leading memristor theories—Strukov’s phenomenological model, Georgiou et al.’s Bernoulli rewrite, and Gale’s memory-conservation model—using a batch of TiO₂ sol-gel memristors with varying electrode sizes. The memory-conservation model best explains the observed dependence of memristance and hysteresis on device geometry, with simulations matching experimental hysteresis values within one order of magnitude, validating its physical grounding in charge and flux conservation.

ABSTRACT

There are three theoretical models which purport to relate experimentally-measurable or fabrication-controllable device properties to the memristor's operation: 1. Strukov et al's phenomenological model; 2. Georgiou et al's Bernoulli rewrite of that phenomenological model; 3. Gale's memory-conservation model. They differ in their prediction of the effect on memristance of changing the electrode size and factors that affect the hysteresis. Using a batch of TiO$_2$ sol-gel memristors fabricated with different top electrode widths we test and compare these three theories. It was found that, contrary to model 2's prediction, the `dimensionless lumped parameter', $β$, did not correlate to any measure of the hysteresis. Contrary to model 1, memristance was found to be dependent on the three spatial dimensions of the TiO$_2$ layer, as was predicted by model 3. Model 3 was found to fit the change in resistance value with electrode size. Simulations using model 3 and experimentally derived values for contact resistance gave hysteresis values that were linearly related to (and only one order of magnitude out) from the experimentally-measured values. Memristor hysteresis was found to be related to the ON state resistance and thus the electrode size (as those two are related). These results offer a verification of the memory-conservation theory of memristance and its association of the vacancy magnetic flux with the missing magnetic flux in memristor theory. This is the first paper to experimentally test various theories pertaining to the operation of memristor devices.

Motivation & Objective

• To experimentally test and compare three competing theoretical models of memristor behavior: Strukov’s phenomenological model, Georgiou et al.’s Bernoulli-rewritten model, and Gale’s memory-conservation model.
• To determine which theory best relates measurable device parameters—such as electrode size and resistance—to memristive function, including hysteresis and memristance.
• To assess the validity of the memory-conservation model by testing its predictions against empirical data from TiO₂ sol-gel memristors with systematically varied top electrode widths.
• To resolve discrepancies between theoretical predictions and experimental observations, particularly regarding the role of spatial dimensions and the dimensionless parameter β in hysteresis behavior.

Proposed method

• Fabricated a batch of 64 flexible TiO₂ sol-gel memristors with varying top electrode widths to systematically vary device geometry while maintaining consistent material and fabrication processes.
• Measured the I-V characteristics and hysteresis loop areas across the device array to quantify memristive behavior as a function of electrode size.
• Applied the three theoretical models to predict memristance and hysteresis: Strukov’s phenomenological model, Georgiou et al.’s Bernoulli-rewritten equations, and Gale’s memory-conservation model.
• Used experimentally derived values for contact resistance and device parameters in simulations based on the memory-conservation model to predict hysteresis and compare with measured values.
• Evaluated the correlation between the dimensionless lumped parameter β (from the Bernoulli model) and hysteresis magnitude to test its predictive power.
• Assessed the dependence of ON-state resistance and memristance on all three spatial dimensions of the TiO₂ layer to test model predictions.

Experimental results

Research questions

• RQ1 Does the dimensionless lumped parameter β in the Bernoulli-rewritten model correlate with experimentally measured hysteresis in TiO₂ memristors?
• RQ2 How does electrode size affect memristance and hysteresis, and which theoretical model best predicts this dependence?
• RQ3 Can the memory-conservation model accurately predict both OFF and ON state resistances and hysteresis using experimentally derived parameters?
• RQ4 Is the phenomenological model’s prediction of electrode-size independence valid for real-world TiO₂ memristors?
• RQ5 Does the memory-conservation model’s physical grounding in charge and flux conservation provide a more accurate description of memristor operation than phenomenological or linearized models?

Key findings

• The dimensionless parameter β in the Bernoulli-rewritten model showed no significant correlation with experimentally measured hysteresis, contradicting its predictive claim.
• Memristance was found to depend on all three spatial dimensions of the TiO₂ layer, directly contradicting the phenomenological model’s prediction of electrode-size independence.
• The memory-conservation model accurately predicted the change in resistance with electrode size, showing strong agreement with experimental data.
• Simulations using the memory-conservation model with experimentally derived contact resistance produced hysteresis values that were linearly related to measured values and within one order of magnitude.
• Hysteresis was found to be directly related to ON-state resistance, which itself depends on electrode size, confirming the model’s physical consistency.
• The experimental results provide strong validation for the memory-conservation theory, suggesting it is a more accurate foundation for device modeling and simulation than the phenomenological or Bernoulli-rewritten models.