(Invited) Water Transport Along Si/Si Direct Wafer Bonding Interfaces

The transport of water in a highly confined gap made by the direct bonding of low roughness silicon hydrophilic wafers is studied. We derive the equation for the transport of water from chemical potential gradients, using Stokes and conservation equations. The transport equation is found to be a Porous Medium Equation with exponent 2. A solution for this equation with stepwise boundary conditions is given. The model is tested against different initial conditions for inward and outward flow, and different temperatures and humidity levels.