Direct wafer bonding has been identified as an en-abling technology for microelectromechanical systems (MEMS). As the complexity of devices increase and the bonding of multiple patterned wafers is required, there is a need to understand the factors that lead to bonding failure. Bonding relies on short-ranged surface forces, thus flatness deviations of the wafers may prevent bonding. Bonding success is determined by whether or not the surface forces are sufficient to overcome the flatness deviations and deform the wafers to a common shape. A general bonding criterion based on this fact is developed by comparing the strain energy required to deform the wafers to the surface energy that is dissipated as the bond is formed. The bonding criterion is used to examine the case of bonding bowed wafers with etch patterns on the bonding surface. An analytical expression for the bonding criterion is developed using plate theory for the case of bowed wafers. Then, the criterion is implemented using finite element analysis, to demonstrate its use and to validate the analytical model. The results indicate that wafer thickness and curvature are important in determining bonding success and that the bonding criterion is independent of wafer diameter. Results also demonstrate that shallow etched patterns can make bonding more difficult while deep features, which penetrate through an appreciable thickness of the wafer, may facilitate bonding. Design implications of the model results are discussed in detail. Preliminary results from experiments designed to validate the model, agree with the trends seen in the model, but further work is required to achieve quantitative correlation.
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