Surface Roughness Modeling for Silicon Direct Bonding

The surface roughness in silicon direct bonding is investigated based on the contact theory of a flat plate. Two silicon wafers with the same surface roughness in a Gaussian distribution are modeled as two different surfaces in contact. One surface is a rigid flat surface, and the other is a surface having a combined Gaussian-distributed roughness. The relations among the elastic stress due to surface deformation, the adhesive force due to surface activation, and the distance due to surface separation are developed to describe silicon direct bonding. The impact of separation distance on bonding force is explained in detail. A practical surface roughness criterion considering the influence of surface activation quality on silicon bonding is proposed. The model indicates that the bonding ability of silicon depends on the surface roughness and the quality of surface activation. It explains the threshold of surface roughness for silicon direct bonding and describes the experimental data well. Thus, the model can provide a helpful basis for the optimization of the silicon direct bonding process.