Multiscale modeling in chemical vapor deposition processes: Coupling reactor scale with feature scale computations

Abstract

A methodology for coupling multiple length scales in chemical vapor deposition processes is presented. A reactor scale model (RSM), used for the description of the macro-scale in the bulk, is coupled with a feature scale model (FSM), used for the description of the topography evolution of the micro-scale features (e.g. trenches or holes) on the wafer. The RSM is implemented with a commercial package and the FSM is implemented by combining a ballistic model for the transport and a profile evolution algorithm based on the level set method. The coupling of the RSM with the FSM is performed through the correction of the boundary condition for the species consumption along the wafer. Essentially, the pre-exponential factor of the Arrhenius expression for the surface reaction(s) is locally corrected along the wafer and this correction allows taking into account the micro-topography on the wafer without including it in the computational domain of the RSM. The coupling methodology implements flow of information in both directions, i.e. from the RSM to the FSM and backwards. Tungsten deposition from tungsten hexafluoride and hydrogen is the case studied. The reactor is axisymmetric and the wafer includes a series of trenches with dimensions at the micro-scale. The effect of the deposition time and the density (number) of trenches on the wafer on (a) the species’ consumption on the wafer and (b) the trench profile evolution is investigated. The loading phenomenon, i.e. the depletion of reactants due to their increased consumption on the micro-topography on the wafer surface is predicted. The importance of the feedback from the micro-scale (to the macro-scale) is demonstrated by comparing trench profiles produced with and without feedback.