  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.
