A Massively Parallel Time Domain Phase Field Model for Multi-domain Ferroelectric Device Simulation

摘要

In this work, we report a massively parallel and time domain implementationof the 3D phase field model that can reach beyond micron scale and consider forarbitrary electrical and mechanical boundary conditions. The first part of thepaper describes the theory and the numerical implementation of the model. Amixed-mode approach of finite difference and finite element grid has been usedfor calculating the nonlocal electrostatic and elastic interactionsrespectively. All the local and non-local interactions are shown to scalelinearly up to thousands of processors. This massive parallelization allows usto directly compare our results with multiple experiments at the same sizescale. The second part of the paper presents results of ferroelectric switchingin devices based on the multi-ferroic BiFeO$_{3}$. We have particularlyemphasized the importance of charge driven domain growth and the effect ofelectrical boundary conditions that explain the temporal evolution offerroelectric domains observed in recent experiments. We also predict amechanism of controlling domain size in the multi-domain ferroelectricswitching that could be useful for practical applications.