This model can handle clustering of boron, phosphorus, arsenic and antimony.
Due to the lack of experimental data for phosphorus and antimony the
respective clustering is switched off. When the cluster formation
process (3.2-10) attains equilibrium, the clustered
concentration is related to the active concentration
by (3.2-19), and the total concentration amounts
to (3.2-20). There, 
is the equilibrium rate constant
which corresponds to the ratio 
in the case of dynamic
clustering.
In practically all cases there is only one impurity which forms clusters at
a given point in the device. We can use this fact to simplify the system of
PDEs by approximating 
in (3.2-19) by the
following expression which only involves the charge contribution of the
clusters of that impurity (3.2-21).
In consistency with the dynamic model an arsenic cluster is formed by three
arsenic atoms (
) and one electron (
), and
in accordance with the model used in ICECREM [Pic90], a boron
cluster consists of six boron atoms (
) and six
electrons (
) which means that boron clusters are neutral.
The total boron and arsenic concentrations amount to (3.2-22)
and (3.2-23), respectively.
We model the active concentration similar to the relation used in
ICECREM (3.2-24) for all dopants 
. To guarantee the
correct exponents in (3.2-22) and (3.2-23) we substitute the
original values of 
by artificial values 
in
(3.2-24).These artificial values are 
for arsenic and 
for boron. We retain the original
values of and 
for calculating the charge contribution of a
clustered dopant (
). Then, the net concentration
is given by (3.2-25). In (3.2-24) the solid solubility
limit 
is a fit parameter.
The clustered part of the impurities is immobile (
)
and therefore we get (3.2-26) for the flux with the field
term (3.2-27).
Neumann boundary conditions (zero flux 
) are
used for all impurities at all boundaries.
