Parameter Correlation and Computational Modeling for the Flow of Encapsulant in Through-Silicon-Via Underfill Dispensing

Abstract

This paper introduces a through-silicon-via (TSV) dispensing approach to accomplish the underfill process without a conventional reservoir. The vias function as entrances for dispensing or paths for fluid flow. Typically, the inflows of dispensing can be free droplets or a constant flow rate. The underfill flow in the gap includes two flowing stages: 1) the initial bidirectional flow and 2) the subsequent flow along chip edges. To find the factors affecting the filling time in TSV underfill, an analytical model is first built for the initial bidirectional underfill flow. The bidirectional flow is approximately modeled as a laminar and quasi-steady creeping flow between two parallel plates. The filling time in the initial stage is closely related to the flow radius, the inlet boundary, the material properties, the gap geometry, and the bump pattern. Afterward, the subsequent flow along the chip edges is investigated using a computational multiphase model. The governing equations of the computational model consist of mass conversation, momentum conversation, and element volume conservation. The computational results show that the chip length–width ratio also has a significant impact on the filling time if the inflow is free droplets.