Low‐Knudsen‐number transport and deposition

We present our model for transport and deposition in features for situations in which intermolecular collisions dominate the species transport. Species transport in this ‘‘low’’‐Knudsen‐number regime is modeled using continuum diffusion. Our model allows both homogeneous reactions and heterogeneous (surface) reactions. We use the Galerkin finite element method to estimate reactant species concentration profiles for infinite trenches with arbitrary cross section, for which two‐dimensional profile evolution is appropriate. We simulate deposition processes using a solution domain which includes the trench as well as a specified region above the surface of the wafer. As an example application, we present results for the deposition of tungsten using the hydrogen reduction of tungsten hexafluoride in trenches of rectangular cross section with initial aspect ratio 4. The model predicts that step coverage increases with decreasing temperature and increasing tungsten hexafluoride partial pressure, while keeping hydrogen partial pressure and the height of the solution domain constant. These trends are in agreement with experimental observations for tungsten deposition processes. Trends in film conformality with deposition conditions are explained in terms of the ‘‘step coverage modulus’’ and reactant concentration ratios for given initial trench dimensions. The step coverage modulus is the ratio of a characteristic deposition rate to a characteristic transport rate.