5.5 Example for the Potential Method and the Electrode Placement

The structure given in Figure 5.15 should be meshed by the original potential method. On the basis of this structure an electrode placement, different than selecting the physical top plane as the upper electrode is shown. As an interactive description of placing the electrodes is quite complicated, this artificial geometry with some simple and flat surfaces is selected.

The top electrode will not surround the whole top of the structure; it is rather placed along the hole in the middle of the structure. The whole bottom side of the structure is selected as its opposite electrode. In sum, all six electrodes must cover the entire surface. The chosen electrode placement can be seen in Figure 5.15 where opposite electrodes are shown in the same color.

Figure 5.15: Three-dimensional structure with the placed electrodes.

Figure 5.16: Three-dimensional structure with a potential distribution and shown base grid, on which the potential evaluation is performed.

Figure 5.17: Final grid, developed by the potential method with shown potential distribution, contacts at left and right.

Figure 5.18: Final grid, a quarter of the device is cut away for illustration purposes.

A relatively crude grid with low demands on the quality is generated by the Delaunay grid generator DeLink [12] for evaluating the potential distributions. This initial grid has about 4000 grid points. The resulting potential distribution, derived by this grid is presented in Figure 5.16.

After calculating the three different potential distributions, the grid points are placed along the equipotential surfaces. A potential distribution with the resulting equipotential surfaces of all three potentials is shown in Figure 5.17.

Along the upper electrode surface, the distances of the potential values will be equidistant. The selected potential ticks start with a dense spacing at the upper electrode and grow monotonically to the lower electrode. The final grid can be seen in Figure 5.18. To illustrate the anisotropy of the generated grid, a quarter of the structure is cut away. Under the top surface, the dense grid spacing can be seen, while in lateral direction the density is lower.