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3.3 Sputter Deposition

Another acceleration with the linear structuring element algorithm is gained for sputter deposition where the growth direction is given by the vector integration of a given particle distribution function over the solid angle visible at a specific surface position. In this case the interpolation can be performed between the rate vectors of two neighboring cells. In general there is only a small difference in the directions and only a few interpolation steps are necessary.

We approximate the sputter reactor flux by using an exponential function which is fitted to the angular distributions resulting from Monte-Carlo simulations of sputtering particle transport [18]. The detailed model for the sputter deposition including derivation of visibility conditions, particle distributions and simulations at arbitrary wafer positions is described in [19].

Fig. 9 shows a cross-section of calculated deposition rates for a three-dimensional simulation of TiN magnetron sputter deposition into a circular via. The dark area at the topmost corner shows the interpolation of the rates similar to the interpolation for the isotropic simulation.

Figure 9: Magnetron sputter deposition: linear structuring elements resulting from flux integration.
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Fig. 10 shows how the procedure described above is used for the three-dimensional simulation of sputter deposition. The figure shows a via located close to the edge of the wafer. The view angle of the sputter target center is about 12$^\circ$, therefore the main incidence direction of particles is tilted resulting in the asymmetrical profile evolution. Fig. 11 shows the application of this model to the simulation of TiN magnetron sputter deposition. A special thing to note is the formation of overhangs at the topmost convex corner of the structure. The simulation clearly reveals the bulge formation observed in the experimental SEM pictures. This is only possible with a special treatment of the convex corners already presented in detail in [20].

Figure 10: Sputter deposition for an off-center position on the wafer.
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Figure 11: Deposition of TiN into a 1.0 $\mu\mathrm m$ diameter and 1.3 $\mu\mathrm m$ deep contact hole structure in the center and at a peripheral position on the wafer.
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W. Pyka, R. Martins, and S. Selberherr: Optimized Algorithms for Three-Dimensional Cellular Topography Simulation