3.4 Timings

Table 2 summarizes the times necessary for lithography development simulation [21] as well as for different etching and deposition models and compares them with timings for a level set method taken from [12].

The simulations with the cellular algorithm were performed on a DEC 600/333 workstation. The numbers in parentheses in Table 2 are taken from [12] for level set simulations on a Sparc Ultra.

**Table 2:** CPU time [s] for different etching and deposition models per time step. Numbers in parentheses are for level set.
$\begin{tabular}{\vert\vert l\vert\vert c\vert c\vert\vert c\vert c\vert\vert}\hl... ...putter deposition} & (0.065) & (0.3) & (24) & (756) \hline\hline \end{tabular}$

There are a few things to note about this comparison: Since the number of cells used for the simulation was the only information we could extract from the reference we made the comparison with the same number of cells. Of course the level set method has a higher accuracy when taking the same number of cells. But again, as already explained in Section 2, there is a trade-off for the level set method when converting the surface to a polygonal representation, requiring mesh refinement at sharp corners. The cellular approach represents sharp corners quite accurately, again with the drawback, that they might be shifted in location by $\pm$ half of the cell resolution.

Regarding this drawback it has to be mentioned, that the figures for our cellular approach were obtained by timing a full simulation run including all necessary file reading and writing steps, geometry and material initialization, rate calculations and surface propagation. The figures in the table were derived by dividing the resulting final CPU times by the number of time steps which were set to either one or two. In this way these figures represent an upper limit for the core operations of the topography algorithm and include a considerable margin in CPU time for a even higher accuracy. The figures taken from the reference seem to account only for the surface propagation, with the time for all additional operations already subtracted.

Finally the comparison for sputter deposition contains only a fitting model for redeposition on the cellular side, less physically based than the corresponding model used for the level set method. But there is still enough CPU time left for a more sophisticated treatment of redeposition in our cellular model.