# Hints, Tips and Solutions

Q: What Types of 3D Delaunay Shape Refinement can be used in Victory Process?

A. The Victory Process cell mode Delaunay 3D device meshing algorithm already includes various TCAD-based local refinement algorithms to ensure accurate and robust device simulation. These include junction and interface distance refinement. One benefit of these approaches is that complex refinement behavior can be specified via a simple deck interface, but a limitation is that the results can only vary according to the small number of parameters of the schemes. In some cases, such as particle path refinement, it can be useful to have finer, more local control over the mesh and the shape distance refinement schemes have been produced to support this.

The new shape refinement algorithms plug into the existing framework for distance-based refinement based on a scalar sizing field. All of the distance-based refinement schemes share a subset of deck syntax which controls the size of the mesh elements on or inside the particular focus geometry and the distance over which the size of the elements increases to the uniform, background refinement size. The shape refinement algorithms have additional syntax which controls the parameters of the shape, such as the center of a sphere and its radius.

Examples

Syntax:

export victory(delaunay) \

structure=”delaunay_final_uniform.str” \
max.size=0.1

Figure 1 shows a simple reference cube with elements of similar, uniform size. The right-hand image shows a cutaway view where the interior of the mesh can be seen. This example provides the basis for the further refinement produced by the shape distance algorithms.

 Figure 1. Uniform Refinement with cutaway.

Syntax:

export victory(delaunay) \

structure=”delaunay_final_box.str” \
max.size=0.1 \
box.min=”0.616, 0.616, 0” \
box.max=”0.716, 0.716, 1” \
max.box.size=0.01 \
max.box.distance=0.5

Figure 2 shows the results of the box distance refinement algorithm. In this case, the axis-aligned box is defined by a pair of diagonally-opposite points which are on the boundary of the mesh. The plane defining the cutaway view passes through the center of the box. The elements on the interior of the box have a maximum size of 0.01 microns and the mesh is graded to the background size over a distance of 0.5 microns from the box.

 Figure 2. Box refinement with cutaway.

Syntax:

export victory(delaunay) \

structure=”delaunay_final_sphere.str” \
max.size=0.1 \
sphere.center=”0.666, 0.666, 0.666” \
max.sphere.size=0.01 \
max.sphere.distance=0.5

Figure 3 shows an example of the sphere refinement algorithm. The plane used to define the cutaway view passes through the center of the sphere which has a radius of 0.1 microns. The maximum element size within the sphere is 0.01 microns and the size of the elements increases to the uniform size over 0.5 microns distance to the sphere.

 Figure 3. Sphere refinement with cutaway.

Syntax:

export victory(delaunay) \

structure=”delaunay_final_cylinder.str” \
max.size=0.1 \
cylinder.start=”1, 0.5, 0.5” \
cylinder.end=”0, 1, 1” \
max.cylinder.size=0.01 \
max.cylinder.distance=0.5

Figure 4 shows an example of the cylinder refinement algorithm. In this case, the center of the cylinder passes through a corner of the cube and the middle of an opposite face. The maximum size of the element inside the cylinder and the distance over which the mesh is graded has been chosen to match Figures 2 and 3.

 Figure 4. Cylinder refinement with cutaway.

Syntax:

export victory(delaunay) \

structure=”delaunay_final_cone.str” \
max.size=0.1 \
cone.start=”1, 0.5, 0.5” \
cone.end=”0, 1, 1” \