3.3.1 Segment Grids

Segments represent local areas within a device. Each segment is assigned a grid which is the corresponding part of the device grid. Grid points at the interface to other segments are doubled. To handle this, segment grid points are implemented as references to the device grid points. Within the segment grid these references are treated as grid points of the segment. All other information stored for segment grids refer to these imaginary grid points.

The segment grid structure contains an array of indices of those grid point coordinates in the device coordinate array which belong to the segment. A simple example of a small device with three segments is shown in Fig. 3.1. The indices stored in the array for segment A are 0, $1$, $2$, $6$, $7$, $8$, $12$, $13$, $14$ shown in Fig. 3.1(c). This approach allows to determine the coordinates of each segment very quickly. The indices which are used by subsequent segment grid information are shown in Fig. 3.1(d).

(a)  A device which contains three segments.

(b)  The indices of the coordinates.

(c) The indices stored in ref for each segment.

(d)  The inherent segment indices.

Figure 3.1: The indices of the grid points stored in the segment arrays.

Another list stores the box volumes for every grid point of the segment in the same order. The box volumes refer to the points denoted by the elements of the array.

The point connectivity list which represents the grid lines is stored for each segment. As an example Fig. 3.2 shows the connectivity list for the grid of segment A. The connectivity list consists of $12$ lines. The lines start at the grid point ${P}_{i}$ and end in ${P}_{j}$. The lines must be unique and need not be sorted. The direction can be chosen at random. For each line the distance ${d}_{{i}{j}}$ of the points ${P}_{i}$ and ${P}_{j}$ is stored. Furthermore, the fraction of the area ${A}_{{i}{j}}$ between the two Voronoi boxes ${V}_{i}$ and ${V}_{j}$ and the distance of the points ${A}_{{i}{j}}/ {d}_{{i}{j}}$ is stored which is required by the box integration method.

${P}_{i}$		${P}_{j}$
0	$\longrightarrow$	$3$
0	$\longrightarrow$	$1$
$1$	$\longrightarrow$	$4$
$1$	$\longrightarrow$	$2$
$2$	$\longrightarrow$	$5$
$3$	$\longrightarrow$	$6$
$3$	$\longrightarrow$	$4$
$4$	$\longrightarrow$	$7$
$4$	$\longrightarrow$	$5$
$5$	$\longrightarrow$	$8$
$6$	$\longrightarrow$	$7$
$7$	$\longrightarrow$	$8$

Figure 3.2: The connectivity list for segment A in Fig. 3.1(d).