A mechanical model for direct wafer bonding by strain energy under normal pressure

Direct wafer bonding is widely applied in the fabrication of microelectromechanical systems. In this study, a mathematical model is proposed to analyze the interface contact behavior during direct wafer bonding. The model describes the wafer bonding process before the bonding pressure is released and takes into account the curvature of the both wafers. The wafer bonding process is analyzed for different wafer curvatures and thicknesses, and the bonding results are predicted. Results show that the critical contact radius, deflections and strain energy increase nonlinearly with the increase of bonding pressure. It is also observed that the smaller the curvature and thickness of the wafer, the easier it is to bond successfully. Due to the assumption that κ1 > κ2, the curvature and thickness of the lower wafer have less influence on the bonding result than the upper wafer, but still cannot be neglected. Finally, the correctness of the proposed model is verified by finite element simulation. This study can provide a reference for the design of bonding pressure and initial geometry of wafers in industrial applications.