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

• Analytical Method for Wafer Bonding Quality Assessment: The paper introduces an analytical method that connects external conditions such as normal pressure, planarity deviation, and impurity particle counts with key mechanical variables like wafer deflection and strain energy during the direct wafer bonding process. This is a significant advancement as previous research did not account for the impact of impurities on bonding quality. • Influence of Impurities on Bonding Process: The study establishes a mechanical model of the adhesive process that elucidates the relationship between impurity particle count and strain energy. It reveals how impurities affect wafer deflection and strain energy, showing nonlinear variations with changes in particle position. The results indicate that wafer curvature, thickness, and impurity count are critical factors determining deflection under specific pressures. • Theoretical Guidance for Practical Bonding: The proposed mechanical model, verified through finite element simulation, offers theoretical guidance for selecting adhesive materials and evaluating the feasibility of wafer bonding in industrial applications. It provides insights into the effects of initial wafer geometry, adhesive energy, and particle positions on successful bonding outcomes under applied external pressures. 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. [ABSTRACT FROM AUTHOR]