Coupled Mesoscale—Continuum Simulations of Copper Electrodeposition in a Trench

Copper electrodeposition in submicron trenches involves phenomena that span many orders of magnitude in time and length scales. In the present work, two codes that simulate electrochemical phenomena on different time and length scales were externally linked. A Monte Carlo code simulated surface phenomena in order to resolve surface roughness evolution and trench in-fill. A 2-D finite difference code simulated transport phenomena in the diffusion boundary layer outside the trench. The continuum code passed fluxes to the Monte Carlo code, which passed back a concentration to the continuum code. A numerical instability that arises in the multiscale linked code was suppressed by filtering the concentration data passed from the Monte Carlo code to the finite difference code. The resulting simulation results were self-consistent for a sufficiently small amount of filtering. © 2004 American Institute of Chemical Engineers AIChE J, 50: 226–240, 2004