晶圆对晶圆键合：第一部分 -- 耦合物理问题与二维有限元实现
摘要
晶圆对晶圆（WxW）键合是实现三维集成的关键技术，包括用于细距Cu-Cu互连的混合键合。键合过程中，晶圆变形与晶圆之间夹住的气体通过强耦合、时变的流体-结构相互作用（FSI）相互作用，可能产生非直观的键合动力学和工艺灵敏性。本文通过从三维线性弹性导出Kirchhoff-Love薄板方程来描述晶圆弯曲，并将其耦合到晶圆间气膜的Reynolds lubrication方程，开发了一种针对WxW键合的数学一致的简化模型。 resulting nonlinear plate-Reynolds system is discretized and solved monolithically in the high-performance FEniCSx framework using a interior-penalty formulation for the fourth-order plate operator, standard continuous Galerkin discretization for the pressure field, implicit time integration, and a Newton solver with automatic differentiation. Simulations reproduce experimentally reported probe-displacement histories for multiple initial gaps and verify force equilibrium at the bond front, where the Reynolds pressure acts as an effective contact reaction. Parametric studies reveal nonlinear, and in some cases non-monotonic, sensitivities of bonding-front kinetics to the initial gap, air viscosity, and interfacial energy, providing actionable trends for process optimization.
引用
@article{arxiv.2603.22827,
title = {Wafer-to-Wafer Bonding: Part: I -- The Coupled Physics Problem and the 2D Finite Element Implementation},
author = {Kamalendu Ghosh and Bhavesh Shrimali and Subin Jeong},
journal= {arXiv preprint arXiv:2603.22827},
year = {2026}
}