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
,
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.
Keywords
direct wafer bonding, mathematical model, contact
mechanics, strain energy