With immobile impurity clusters composed of 
impurity atoms (
) and
electrons (
), the kinetic equation for the clustering process is
given by (3.2-11). The coefficients 
and 
are the
clustering and declustering rates, respectively. Note, that one impurity
cluster 
contains clustered impurity atoms (
).
The model DIFDCL takes into consideration the dynamic clustering
of arsenic [Tsa80]. For arsenic predominant clusters consist of three
arsenic atoms and one electron [Gue82] which are active at the
diffusion temperature and electrically neutral at room temperature
[Tsa80], giving 
and 
. All dopants
except arsenic are assumed active and mobile (3.2-12). Although
attempts for kinetic modeling of boron cluster formation exist
(e.g. [Cow90], [Sol90]), the models and parameters are not
well-established.
We solve equation (3.2-13) for all impurities other than arsenic, and equations (3.2-14) and (3.2-15) for mobile arsenic and clustered arsenic, respectively.
According to the charge state of the impurities (
for singly
charged acceptors, 
for singly charged donors) and for an
arsenic atom in a cluster (
) the net active
concentration 
(at diffusion temperature), the electron
concentration and the electric field are given by (3.2-16),
(3.2-17) and (3.2-18), respectively.
Neumann boundary conditions (zero flux 
) are
used for all impurities at all boundaries.
