Simulation Study of the Pulse Shaping Effects on the Power, Energy, and Programming Time Requirements of Filamentary-Type Memristors

As with any memory device, programming a memristor involves trade-offs between power, energy, and time. In this letter, we investigate in detail how these factors are interrelated under different programming conditions. We show that, under time constraints, lower energy consumption can be achieved using faster programming pulses at the cost of increased power dissipation. Conversely, when limiting the maximum power is the priority, longer programming times are required to minimize energy consumption. These trade-offs ultimately stem from the physical response time of ions and vacancies involved in the formation and dissolution of the conductive filament within the oxide layer of a metal-insulator-metal (MIM) structure. We begin by analytically examining the effect of applying a single trapezoidal pulse to the device. Next, we extend the analysis to multiple pulses, using a compact recursive approach to model both potentiation and depression. Finally, we perform SPICE simulations under unconstrained programming conditions. Modeling and simulations are based on the Dynamic Memdiode Model, combined with the Method of Elementary Solvers. Given the variability of device parameters and experimental conditions, we provide the complete SPICE schematic to allow interested readers to explore different scenarios and tailor the analysis to their specific use cases.