Influence of the bonding front propagation on the wafer stack curvature

The influence of the dynamics of the direct wafer bonding process on the curvature of the final wafer stack is investigated. An analytical model for the final curvature of the bonded wafers is developed, as a function of the different load components acting during the bonding front propagation, using thin plate theory and considering a strain discontinuity locked at the bonding interface. Experimental profiles are measured for different bonding conditions and wafer thicknesses. A very good agreement with the model prediction is obtained and the influence of the thin air layer trapped in-between the two wafers is demonstrated. The proposed model contributes to further improvement of the bonding process, in particular, for the stacking of layers of electronic devices, which requires a high accuracy of wafer-to-wafer alignment and a very low distortion level.