A microvia-fill model is formulated for control-design purposes of the via-fill process in scale. The formulas required to model a -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 -ion activity vs -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.
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Pohjoranta et al. (2007) studied this question.
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