Dynamics of Contact Wave in Silicon Wafer Direct Bonding

A quantitative description of the dynamics of silicon wafer direct bonding is proposed, and the contact wave for bonding front propagation is modeled as a function of time. The changes in exhaust gas power, accumulated deformation power and wafer surface energy during bond processing have been studied systematically, and the governing differential equation of the contact wave position is deduced from the law of conservation of energy. The relationship of wave front position to the height of gas gap between bonded wafers is derived. Moreover, the functional dependence of contact wave position and bonding wave velocity on time is investigated, and the average wave velocity is obtained. The model describes well the experimental data available from literatures, and provides a basis for silicon wafer direct bonding process optimization.