Modeling of direct wafer bonding: Effect of wafer bow and etch patterns

Direct wafer bonding is an important technology for the manufacture of silicon-on-insulator substrates and microelectromechanical systems. As devices become more complex and require the bonding of multiple patterned wafers, there is a need to understand the mechanics of the bonding process. A general bonding criterion based on the competition between the strain energy accumulated in the wafers and the surface energy that is dissipated as the bond front advances is developed. The bonding criterion is used to examine the case of bonding bowed wafers. An analytical expression for the strain energy accumulation rate, which is the quantity that controls bonding, and the final curvature of a bonded stack is developed. It is demonstrated that the thickness of the wafers plays a large role and bonding success is independent of wafer diameter. The analytical results are verified through a finite element model and a general method for implementing the bonding criterion numerically is presented. The bonding criterion developed permits the effect of etched features to be assessed. Shallow etched patterns are shown to make bonding more difficult, while it is demonstrated that deep etched features can facilitate bonding. Model results and their process design implications are discussed in detail.