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There are three theoretical models which purport to relateexperimentally-measurable or fabrication-controllable device properties to thememristor's operation: 1. Strukov et al's phenomenological model; 2. Georgiouet al's Bernoulli rewrite of that phenomenological model; 3. Gale'smemory-conservation model. They differ in their prediction of the effect onmemristance of changing the electrode size and factors that affect thehysteresis. Using a batch of TiO$_2$ sol-gel memristors fabricated withdifferent top electrode widths we test and compare these three theories. It wasfound that, contrary to model 2's prediction, the `dimensionless lumpedparameter', $\beta$, did not correlate to any measure of the hysteresis.Contrary to model 1, memristance was found to be dependent on the three spatialdimensions of the TiO$_2$ layer, as was predicted by model 3. Model 3 was foundto fit the change in resistance value with electrode size. Simulations usingmodel 3 and experimentally derived values for contact resistance gavehysteresis values that were linearly related to (and only one order ofmagnitude out) from the experimentally-measured values. Memristor hysteresiswas 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 thememory-conservation theory of memristance and its association of the vacancymagnetic flux with the missing magnetic flux in memristor theory. This is thefirst paper to experimentally test various theories pertaining to the operationof memristor devices.

Which Memristor Theory is Best for Relating Devices Properties to Memristive Function?