A deterministic mechanic model for predicting the strain energy across the wafer bonding process coupling the effects of normal pressure and wafer geometry. (1st April 2023) - Jiang, Jiahao; Sun, Yunyun
Graphical abstract: Highlights: A deterministic mechanic model to evaluate the strain energy under an arbitrary pressure for wafer bonding is proposed. The gap between external conditions and evolutions of contact area, wafer deflection as well as strain energy across the bonding process is filled. Analytical expression of strain energy coupling the effects of bonding pressure and wafer bow is derived. Predictions of strain energy agree with FE simulations and the previous classical model. Abstract: Direct wafer bonding is widely employed in the fabrication of micro-electromechanical systems. Wafer deflection and strain energy can be used to evaluate the bonding quality. Since the complexity of the mechanic process of contact interface, researches mainly concentrate on the final state of wafer bonding. The gap between external conditions (include normal pressure and flatness deviation) and evolutions of key variables (include contact area, wafer deflection and strain energy) across the bonding process remains unfilled. In this paper, the bridge between external conditions and bonding variables is established analytically. A mechanic deterministic model across the bonding process is proposed and the dependence of contact radius on the bonding pressure is obtained. Considering the coupling effects of bonding pressure and wafer geometry, analytical expressions for the contact area, deflection and strain energy are derived. Accordingly, the effects of both external conditions and internal geometry on the wafer deflection as well as strain energy are revealed. Results demonstrate that the wafer curvature and thickness jointly determine the deflection of the wafer at a given pressure. Wafer deflection and strain energy vary with critical contact position nonlinearly. The proposed model of wafer bonding is verified by the finite element simulations. The current work may provide a reference for the bonding pressure selection in industrial applications.