Nonuniform Load Mechanical Modeling for Direct Wafer Bonding Incorporating the Pressure Distribution

Considering the non-uniform bonding pressure due to the downward push of the indenter, this study proposes a mechanical model to analyze the interfacial contact behavior during direct wafer bonding. The model includes a pressure location coefficient and a pressure distribution coefficient to define the distribution of the bonding pressure. Expression of wafer deflection and strain energy is derived by the thin-plate theory. The wafer bonding process with different pressure distributions is analyzed and the bonding results are predicted. The results show that the extreme value of the contact radius occurs when the pressure location coefficient is about 0.9, and the contact radius is positively correlated with the pressure distribution coefficient. In comparison to uniform pressure, alterations in contact radius at non-uniform pressures exhibit considerable discrepancies. Finally, the correctness of the proposed model is verified by finite element simulation. This study can provide a reference for the design of wafer bonding pressure distribution in industrial applications.