Bond front velocity in lubrication-mediated bonding of flexible substrates

Abstract

Bonding and assembly processes have started to take the centre-stage in semiconductor manufacturing as they enable three-dimensional (3D) stacking and heterogeneous integration for novel interconnect architectures of integrated circuits. The progression of a bond front hinges on balance of adhesion and dissipation forces. Here, a lubrication–elasticity model is reported, to elucidate near-field dynamics of the process while staying within continuum limits, excluding adhesion mechanisms. When governed by lubrication flow in the gap, and linear elasticity in the substrates, the unbonded part of the substrates assumes a power-law shape as a function of the distance from the bond front. Furthermore, an entirely self-consistent formulation for the bond front velocity is derived. The formulation presented here crucially relies on a re-parameterization of the problem in terms of a ‘high viscous dissipation region’ ahead of the bond front, which travels along with the adhesion front. This approach for expressing the bond front velocity allows for its acceleration as the unbonded region shrinks, for example with bond front approaching the edge of a finite substrate. Finally, unifying velocity and length scales are proposed, incorporating a lateral adhesion front length scale that effectively captures velocity variations in the limit of vanishing viscous dissipation, bridging continuum and molecular scales. This framework provides scalable insights for better understanding and process control in applications with wafer and die bonding.