Mathematical model of low-temperature wafer bonding under medium vacuum and its application

Low-temperature direct wafer bonding was successfully performed under medium vacuum level. A mathematical model was developed based on the qualitative understanding of the bonding mechanisms. The model combined the diffusion-reaction model of water in SiO₂ and the diffusion theory in porous media. It is found that the model agrees well with the experimental data. This model can be applied to predict the effects of annealing time, annealing temperature, ambient vacuum, wafer orientation, and wafer dimension on the bond strength.