It is obvious that the assumption of homogeneous boundary conditions is not correct when applying wafer scale to consider variations in heat distribution, gas flow and gas concentrations. In general, inhomogeneous thermal distributions and flow conditions within the reactor lead to strong variations in overall film thickness, film composition, profile evolution, and step coverage across the wafer.
It is beyond the scope of the presented approach to address also simulation and modeling on reactor scale. Reactor scale simulators dealing with different types of mass transport on non-moving grids such as FLUENT1are commercially available. As an example Fig. 7.8 shows the distribution of the concentration across the wafer for a reactor scale simulation of tungsten CVD with reduction. Nevertheless, the feature scale model allows the integration of the results from such equipment level simulations. Dirichlet boundaries at the top of the simulation domain can be set according to the concentration resulting from the equipment simulation. Together with the heat variations they account also for changes in the species effective diffusivities which influence the profile evolution by determining the balance between diffusion velocity and reaction rate. Variations in growth rate and overall film thickness varying across the wafer can also be covered by adjusting the local deposition rate. By these means of integrating results from reactor scale simulation our CVD model represents a link to the final prediction of the feature scale profile evolution in an integrated back-end process simulation.