Page 227 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Transport Theory
In order to solve equations (6.85)–(6.87b) we use the box integration
method. The idea is to discretize the simulation domain in terms of boxes
surrounding each discretization node this way that the whole simulation
domain is completely covered by the box subdomains. These subdomains
do not overlap. A schematic view is given in Figure 6.8.

Figure 6.8. Schematic view of a
two–dimensional triangular grid
with the boxes (shaded) defined by
the normal bisectors the sides
emanating from a given node.

We rewrite equations (6.85)–(6.87b) as follows using Gauss’ theorem

∫ Ds S = ∫ ρ V (6.90a)
d
d
S V
∫ j s Sd = ∫ qR V (6.90b)
d
n
S V
∫ j s Sd = – ∫ qR V (6.90c)
d
p
S V
which is more suitable to explain the idea behind the box integration
method. and denote the volume and the boundary of a box and is
s
S
V
the normal vector on the boundary of the box, shown in Figure 6.9.

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