Spatial-Temporal Modeling of Extreme Bottom-up Filling of Through-Silicon-Vias

Extreme bottom-up superfilling of annular through-silicon-vias (TSV) during copper electrodeposition has been reported wherein metal deposits on the bottom surface of the TSV with negligible deposition on its sidewalls or the field around it. The growth mode derives from a suppressor species that generates critical behavior manifesting as a negative differential resistance that, when coupled with a resistive electrolyte, yields bottom-up filling of recessed surface features. This paper models the observed phenomenon, the predictions capturing the full dynamics of the bottom-up filling process. The model considers the impact of the potential drop in the resistive electrolyte between the reference electrode and workpiece and the gradients of metal ion and rate-suppressing additive that accompany TSV filling. The predictions provide insight into the temporal and spatial variations of concentrations and overpotential that drive the bottom-up metal deposition process.