Control systems analysis of a multiscale simulation code for copper electrodeposition

Multiscale systems involve phenomena that span several orders of magnitude in time and length scales, from the molecular to the macroscopic. To account for the multiscale character of these processes, many papers have adopted a simulation architecture that employs coupled simulation codes, in which each code simulates the physicochemical phenomena for a different range of length scales. A key issue in dynamically coupling simulation codes is that it is possible for the codes that solve the individual continuum or non-continuum models to be numerically stable, while the dynamic linkage of the individual codes is numerically unstable. This paper uses control systems analysis to gain insight into these numerical instabilities as well as to design numerical linkage algorithms that modify the dynamic information passed between the individual codes to numerically stabilize their coupling, and to increase the numerical accuracy of the simulation results. The approach is applied to a coupled KMC-FD code for simulating copper electrodeposition in sub-micron trenches.