A Mathematical Model for Chemical Vapor Deposition Processes Influenced by Surface Reaction Kinetics: Application to Low‐Pressure Deposition of Tungsten

Abstract

A model for the simultaneous reaction kinetics and transport processes in chemical vapor deposition (CVD) reactors has been extended to treat deposition of materials that have a broad range of surface characteristics, e.g., sites with multiple dangling bonds and adsorbates with multiple bonding configurations. The model uses the nature of the surface to determine the elementary processes that can take place during growth. Rate constants for these processes are calculated from first principles using statistical thermodynamics, transition state theory, and bond dissociation enthalpies. In this way, deposition rates are determined without either assuming the reaction mechanism or arbitrarily choosing any kinetic parameter values. The utility of the approach is illustrated by modeling low‐pressure CVD of tungsten from tungsten hexafluoride and hydrogen. The treatment considers 14 species and eight reactions in the gas together with 21 species and 65 processes at the surface. The calculations indicate that, for the range of operating conditions considered, the process is controlled by surface reaction kinetics and that gas‐phase reactions are unimportant. Deposition rates and surface fluxes predicted by the model show quantitative agreement with available experimental data. In addition, the major reaction pathways and rate‐limiting steps are identified. This information is used to develop simplified rate expressions (still without using any fitted rate constants) that give reasonable predictions for the growth rate. Sensitivity studies are performed to assess the impact of uncertainties in species properties and rate constants on the theoretical results.