A method for microvia-fill process modeling in a cu plating system with additives

A microvia-fill model is formulated for control-design purposes of the via-fill process in 100 mu m scale. The formulas required to model a Cu-Cu-electrode electroplating system with generic additive-type chemicals in both single-directional and bidirectional processes are given in detail. The model relies on principles familiar from a submicrometer-scale via-filling model known as the curvature-enhanced accelerator accumulation model. Additive coverage is modeled based on a simplified method based on local surface-area computation and an analytical formula for surfactant coverage is given. A galvanostatic control law that does not require computing cell voltage is derived. The model also considers the Cu (II)-ion activity vs Cu (II)-ion concentration. A finite element method-based implementation, applying the arbitrary Lagrange-Eulerian method to compute geometry changes, is tested and compared to via-fill experiment results. (c) 2007 The Electrochemical Society.