Accuracy enhancement of pickett tunnelling barrier memristor model

Titanium dioxide (TiO₂) memristors exhibit complex conduction mechanism. Several models of different complexity have been developed in order to mimic the experimental results for physical behaviors observed in memristor devices. Pickett´s tunneling barrier model describes the TiO₂ memristors, and utilizes complex derivative of tunnel barrier width. It attains a large error in the ON switching region. Variety of research consider it as the reference model for the TiO₂ memristors. In this paper, we first analyze the theory of operation of the memristor and discuss Pickett´s model. Then, we propose a modification to its derivative functions to provide a lower error and closer agreement with physical behavior. This modification is represented by two additional fitting parameters to damp or accelerate the tunnel width derivative. Also, we incorporate a hard limiter term to limit the tunnel width to its physical extremes 1 nm and 2 nm. We run simulations to test the model modifications and we compare the results to the experimental and original Pickett´s model results. The modified model more closely resembles the experimental behavior of TiO₂ memristors and potentially enables the memristor to be used as a multilevel memory.