Two deterministic approaches to topography evolution

We discuss two deterministic approaches to model free-molecular transport and reaction inside features on patterned wafers during thermal deposition processes. One approach that has been widely used to model chemical vapor deposition processes, which are largely steady state at the equipment scale, is based upon the ballistic transport and reaction model (BTRM). The major computational burden in BTRM based codes is usually computing the geometry-defined matrix of transmission probabilities; each element of which is used to determine what fraction of material leaving one point on the surface goes to each other point. This computation scales quadratically in the size of the discretizations, but is done in parallel. The second approach to modeling transport and reaction in the free-molecular flow regime is based on the kinetic transport and reaction model (KTRM). The KTRM starts from the Boltzmann equation and is particularly appropriate for processes operated under transient conditions at the reactor scale; e.g., atomic layer deposition. The KTRM is computationally expensive; models in three spatial dimensions require the discretization of the three spatial dimensions, three velocity dimensions, and time for transient studies. The spatial mesh scales with the third power of the system size, for the same resolution. The KTRM is implemented in parallel.