11.3 A Three-Dimensional Example

Figure 11.4: A front view of the sample Monte Carlo ion implantation after smoothing using the new algorithm. The unstructured destination grid with 78651 points is shown as well.

Figure 11.5: A front view of the sample Monte Carlo implantation after smoothing using the new algorithm.

Figure 11.6: A front view of the sample Monte Carlo ion implantation after extracting values using least squares fits of multivariate polynomials of degree two.

Figure 11.7: A cut parallel to the front side of the sample Monte Carlo ion implantation after smoothing using the new algorithm.

Figure 11.8: A back view of the sample Monte Carlo ion implantation after smoothing using the new algorithm.

The example is a three-dimensional CMOS structure as shown in Figure 11.2 and Figure 11.3, which consists of poly-silicon in the upper part, of silicon dioxide in the middle part, and silicon in the lower part. A boron dose of $10^{13}\,\mathrm{cm^{-2}}$ with an energy of $15\,\mathrm{keV}$ was implanted in a Monte Carlo simulation [52,50,51] using an isotropic homogeneous grid. The resulting concentration of boron interstitial atoms in $[\mathrm{cm^{-3}}]$ is shown in Figures 11.4, 11.5, 11.6, 11.7, and 11.8. The new anisotropic inhomogeneous grid with 78651 grid points is additionally shown in Figure 11.4. In Figures 11.4, 11.5, 11.7, and 11.8 the new algorithm was applied on $5\cdot5$ grids, whereas in Figure 11.6 least squares fits of polynomials of degree two on grids of the same size were performed.

Obviously the result in Figure 11.6 is inferior to the result yielded by the algorithm described in the previous section. The new algorithm provides very good smoothing and yields concentration values at the grid points that can serve as input to subsequent simulation steps without problems.