Logistic Function based Nonlinear Modeling and Circuit Analysis of the Bipolar Vacancy Migration Memristor

Memristor is an acronym for memory resistor. Memristors promise to be building blocks for high density memory and analog computation. Hewlett Packard’s announcement in 2008 of having fabricated a memristor on an integrated circuit scale has created a tangible excitement in this field. Understanding and exploiting the full potential of these devices requires good compact models. Symbolic modeling provides a balance between achieving accurate empirical fit and generating closed form expressions. This dissertation simplifies the transport equation into a variable coefficient advection equation, very similar to a Burgers’ equation traditionally used in fluid dynamics. The Burgers’-like model reveals the dual variable resistance initially proposed by HP that has served as a gold standard to date. The Burgers’ model also shows the emergence of an active phenomenon within the device as some researchers have suspected. Results from this model are compared favorably with independent experimental data. The insight obtained from this computational ion transport model is the motivation for proposing a simpler computational logistic function based memory resistance model. The logistic model is a solution to the well-known logistic equation and map. This relationship between functions and maps opens the door to understanding how the memristor can exhibit sensitivity to initial conditions as claimed by some researchers. The logistic model is validated by fitting to experimental data. The usability of the model in practical circuit design is demonstrated with a relaxation oscillator implemented in LTSpice. The oscillator implemented is power and reliability aware. A formal method to estimate the frequency of such a nonlinear circuit is presented. Computationally estimated frequency is validated against results from LTSpice. A variant of the oscillator is shown to function as a simple offset voltage detector. Unlike numerical methods, the symbolic, closed form approach in this dissertation provides an unparalleled perspective into the inner workings of the memristor. The peer reviewed, published findings of this research invalidate the claim that the memristor is a passive fundamental circuit element; an issue associated with the device since its inception