Direct silicon bonding dynamics: A coupled fluid/structure analysis

Abstract

During direct bonding, a thin gas film is trapped in-between the two wafers, leading to an interactive fluid/structure dynamics. A model of bonding dynamics is formulated using the plate approximation, Reynolds equation, and adhesion forces as the boundary condition at the bonding front. The transient equation is solved numerically in a one dimensional cylindrical case. The entire process, including initiation and propagation of the front, is modelled. The model is supported by experimental data from an original setup involving non-contact optical sensors to measure the vertical movement of the wafer during the bonding sequence.