An ALE Model for Prediction and Control of the Microvia Fill Process with Two Additives

A computational model for examining the microvia fill process as encountered in the multilayered printed circuit board industry is presented. The model includes mass transfer of both copper and the additive species present. The additives' mass balance is considered between both the solution and the surface-adsorbed layer of additives, as well as on the shape-changing cathode surface where the mass balance of adsorbed additives is affected by the surface shape change and diffusive mass transfer along the surface. The model is implemented as a finite element model applying the arbitrary Lagrange–Eulerian (ALE) method for boundary tracking, and a weak formulation of the mass-balance equations is given to aid numerical solution of the model. Model stability and fitting against experimental data is examined over a range of relevant parameters.