We use a fully adaptive tensor product grid for the ion implantation module.
The design of the initial grid depends on the geometry and the expected
profile characteristics. First, we determine all characteristic points of
the geometry (see points 
and 
in Figure 2.3-7),
and characteristic lengths 
, 
and
from (2.3-17), (2.3-18) and (2.3-19).
The regions where significant changes in the profile can be expected are estimated from the characteristic points, the characteristic lengths considering possible overlaps and the boundaries. The available grid lines are equidistributed in these regions (Figure 2.3-7).
For all points of the initial grid the concentration is calculated using
(2.3-14). Remember that the geometry has been rotated by the
negative tilt angle and, therefore, also the coordinates of a certain grid
point (
, 
) have to be rotated using (2.3-8).
Thereon, the grid is adapted to the concentration profile. At all new (inserted) grid points the concentration is calculated again using (2.3-14). This adaption loop continues until no further grid update is necessary or a maximum number of grid adaptions has been exceeded.
The adaption of the spatial grid is based on two criteria, the dose conservation criterion and the gradient criterion. The dose conservation criterion equidistributes the local dose error and consequently inserts grid lines in the close vicinity to the maximum of the concentration. The gradient criterion inserts lines mainly at larger gradients of the profiles to resolve the slopes properly. For a detailed explanation of these two criteria see Section 3.6.2.
The overall program structure of the Analytical Ion Implantation
Module is quite simple (see Program 2.3-1). First, the
geometry, the material information, the implantation parameters (dose,
energy, tilt angle, ...) are read from a PIF input file
[Fas91]. The different parts of the program have
already been explained in this section.
The range statistic parameters (moments, etc.) are calculated according to
the selected range statistic model. The geometry is extended at all
boundaries which have the attribute "artificial". For tilt angles 
the geometry is rotated by 
so that the ions incident direction is
vertical. Here, we also check if one-dimensional computation is possible
where only the vertical ion distribution has to be calculated and no lateral
convolution is necessary. The selected distribution functions have to be
initialized, i.e. their parameters are calculated for each target
material from the moments. The geometry is cut in thin slices and for each
of these slices the 
's and 
's are calculated.
An initial grid is designed according to the expected profiles. A concentration update-grid adaption is performed successively until the grid sufficiently resolves all details of the concentration profile. Finally the concentration profile is limited to a physically relevant value range.
