Mechanical modeling and analysis of direct wafer bonding technology considering the effect of impurity particles

Direct wafer bonding technology has been widely used in the manufacturing of microelectromechanical systems (MEMS). The chip deflection and strain energy can be used to evaluate the bonding quality. Current research assumes that the wafer surface is perfectly clean and neglects the influence of impurities, lacking an analytical model to characterize the effects of external conditions (normal pressure, planarity deviation, impurity particle counts) on key mechanical variables (wafer deflection and strain energy) during the bonding process. In this paper, an analytical method is used to establish a bridge between external conditions and bonding variables. A mechanical model of the adhesive process is established, and the relationship between impurity particle count and strain energy is obtained. By considering the bonding pressure, chip geometry, and impurity particle count, analytical expressions for deflection and strain energy are derived, revealing the influence of external conditions and internal geometry on wafer deflection and strain energy. The results show that under certain pressure, the curvature and thickness of the wafer, as well as the impurity particle count, jointly determine the wafer deflection. The wafer deflection and strain energy exhibit nonlinear variations with changes in particle position. The correctness of the proposed model is verified through finite element simulation. This work provides a reference for judging wafer bonding with impurity particles in industrial applications.