A superstatistics approach to the modelling of memristor current-voltage responses

Memristors are expected to form a major cornerstone in the upcoming renaissance of analog computing, owing to their very small spatial footprint and low power consumption. Due to the nature of their structure and operation, the response of a memristor is intrinsically tied to local variabilities in the device. This characteristic is amplified by currently employed semiconductor fabrication processes, which introduce spatial inhomogeneities into the structural fabric that makes up the layers of memristors. In this work, we propose a novel q-deformed current-voltage model for memristors based on the superstatistics framework, which allows the description of system-level responses while taking local variabilities into account. Applied on a Ag-Cu based synaptic memory cell, we demonstrate that our model has a 4-14% lower error than currently used models. Additionally, we show how the resulting q-parameter can be used to make statements about the internal makeup of the memristor, giving insights to spatial inhomogeneities and quality control.