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7.1.5 Time-Step Control

A very important task is the time-step control, especially when the process conditions lead to the formation of voids. In general the CVD model uses a constant time-step $\Delta t$ for the surface propagation. It is assumed that the change in the steady state equilibrium for the competition between diffusion and surface reaction is not influenced by the differential change in the geometry during one time-step. Therefore $\Delta t$ has to be set in a way that the maximum distance in the surface propagation for each time-step does not exceed a certain limit which guarantees the fulfilling of the steady state assumption.

Depending on the ratio between diffusion velocities and reaction rates a depletion of the reactants at the bottom of the feature may be observed which in consequence leads to strong variations of the local deposition rates, to characteristic overhang structures, and finally to the formation of voids. To avoid the underestimation of the size of such a void by choosing a too large time-step when the void is closed the topography simulator checks for voids. When void formation is observed, the time-step is reduced until the first closure of the void is detected. Within the cellular material representation a region of vacuum cells not connected with the gas domain above the surface can be detected easily and used for the control of void closure.

Prev: 7.1.4 Surface Propagation