Multiscale modeling of chemical vapor deposition

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Abstract
An integrated method for modeling chemical vapor deposition on length scales ranging from microns to meters has been developed. The macroscale problem of flow and transport in a single wafer, low pressure chemical vapor deposition reactor is solved using the finite element method. However, on the feature scale, continuum models of flow and transport are not valid and discrete particle transport models must be employed. The two transport regimes, continuum and discrete particle, are linked by an effective reactivity function ε which includes both effects of multiscale surface heterogeneity and microscale transport resistance. A hybrid ballistic transport, Monte Carlo method, is developed permitting calculation of ε for any set of reaction pathways occurring over microelectronic device features of any geometry. Surface topography, that is, feature scale calculations, are combined to yield an effective reactivity map over the surface of the substrate. This map is subsequently used to formulate a flux boundary condition on the macroscopic model. Iteration between macroscopic and microscopic models is used to assure a consistent set of conditions at the macro–micro interface. The resulting linked models are used for investigation of local and reactor wide loading effects. Matched macroscopic solutions provide inputs for profile evolution calculations during fill of trenches and vias.