Comparison of LPCVD Film Conformalities Predicted by Ballistic Transport‐Reaction and Continuum Diffusion‐Reaction Models

Abstract

Two models used for predicting film profile evolution during low pressure chemical vapor deposition in features on patterned substrates are compared; (i) a ballistic transport‐reaction model (BTRM) in which transport between surfaces in a feature is "line of sight" and (ii) a diffusion‐reaction model (DRM) in which gas‐phase transport is expressed in terms of concentration gradients and Knudsen diffusion. In order to compare the qualitative and quantitative predictions of the two models we use blanket tungsten deposition by the hydrogen reduction of tungsten hexafluoride in long (two‐dimensional) rectangular trenches as an example. The two models are based on the same underlying assumptions: however, they differ in their treatment of molecular transport in features. For both models, film deposition occurs through heterogeneous gas‐solid reactions, and profile evolution is two dimensional. The BTRM is formulated in terms of three‐dimensional fluxes to the evolving film surface. These fluxes are expressed in terms of fluxes from all other points on the surface of the feature and from the source volume and are therefore "nonlocal." In the DRM, fluxes to the local surface are expressed in terms of local gas‐phase concentrations. Because of the assumptions used to compute Knudsen diffusivity in the DRM, the transport occurs in one dimension. "Rules of thumb" relating qualitative changes in film conformality to changes in process conditions, derived using the governing equations of the two models, are the same and agree well with observed trends. Using a "relative reactant depletion criterion," both models predict the same ratio of partial pressures of reactants which maximizes film conformality. Quantitative step coverage predictions obtained from the BTRM simulations are consistently higher than those of the DRM.