is the
diffusion current of the dopant and 
denotes an algebraic dopant
generation/recombination rate and t the simulation time.
Let us assume 
to be the two-dimensional simulation domain covered
by a grid consisting of N grid points. We extend this planar grid into the
third dimension so that 
represents the Voronoi box volume around point
i (see Fig. 4.1-8). If the given simulation grid is
appropriate for the box integration method, the relation (4.1-2) must
hold.
Figure 4.1-8: Volume
discretization for the box integration method. The divergence operator is
calculated for the shaded area .
To discretize the diffusion equation for point i, we integrate
(4.1-1) over the box volume to obtain (4.1-3).
By applying the Gauß theorem
which transforms a volume integral into a closed line integral, we get the
discretized continuity equation for a given grid node i as given by
(4.1-4), where the 
denotes the diffusion current, 
the diffusion flux across the box interface area 
in 
direction and 
is the distance between the grid point pair.
The flux is the projection 
and is
assumed to be constant between the grid points ij. The sum 
can be seen as diffusion current balance in the
integration box. The flux is now determined by the applied
diffusion current model.
