A Zeno Paradox: Some Well-known Nonlinear Dopant Drift Memristor Models Have Infinite Resistive Switching Time

Abstract

There are nonlinear drift memristor models utilizing window functions in the literature. The resistive memories can also be modeled using memristors. If the memristor’s resistance switches from its minimum value to its maximum value or from its maximum value to its minimum value, the transition phenomenon is called resistive or memristive switching. The value of the time required for this transition is especially important for resistive computer memory applications. The switching time is measured by experiments and should be calculatable from the parameters of the memristor model used. In the literature, to the best of our knowledge, the resistive switching times have not been calculated except for the HP memristor model and a piecewise linear memristor model. In this study, the memristive switching times of some of the well-known memristor models using a window function are calculated and found to be infinite. This is not feasible according to the experiments in which a finite memristive switching time is reported. Inspired by these results, a new memristor window function that results in a finite switching time is proposed. The results of this study and the criteria given here can be used to make more realistic memristor models in the future.