An imec researcher has published a model that describes the motion of a bond front in lubrication-mediated bonding of flexible substrates. The paper focuses on the near-field mechanics of wafer and die bonding and explains why the bond front can accelerate as the remaining unbonded area becomes smaller.
The model treats the problem as a balance between lubrication flow in the gap and linear elasticity in the substrates, while staying within continuum limits and excluding adhesion mechanisms. Under these assumptions, the unbonded part of the substrates follows a power-law shape as a function of distance from the bond front. The paper also derives a self-consistent expression for bond-front velocity.
A key step in the formulation is the introduction of a re-parameterization based on a high viscous dissipation region ahead of the bond front, which travels together with the adhesion front. This makes it possible to express the velocity in a way that naturally captures acceleration when the unbonded region shrinks, for example as the bond front approaches the edge of a finite substrate.
The paper also proposes unified velocity and length scales, including a lateral adhesion-front length scale that captures velocity changes in the limit of vanishing viscous dissipation. According to the author, this bridges continuum and molecular-scale descriptions and provides a framework for better understanding and process control in wafer and die bonding.