In presence of an electric field, the dopants 
are driven by two forces,
the concentration gradients, and the electric field which acts on all
charged particles (intrinsic point defects, ionized dopants, ...).
Assuming that the point defects do not deviate from their value under
inert and intrinsic conditions and all dopants are ionized and mobile, the
flux 
of the dopants is modeled by (3.2-1)
[Hu68]. 
denotes the diffusion coefficient, 
is the charge
state of the dopant (
for singly charged acceptors, 
for singly
charged donors) and 
is the thermal voltage. Since no generation
or recombination mechanisms occur, the dopant's conservation reads as given
by (3.2-2).
The electrostatic potential 
is calculated by assuming Boltzmann
statistics for the electron concentration 
and hole concentration 
(
, 
) and local
charge neutrality (
). The error induced by the local
charge neutrality approximation is sufficiently small as long as the
impurity diffusion length is big compared to the Debye length [Hu72].
With 
the dopants' concentrations and 
their charge state, the net
electrically active concentration reads (3.2-3). The flux of
dopant is then given by (3.2-5).
The first line in (3.2-5) accounts for the dopant's self induced flux including the field enhancement and the second line accounts for the flux induced by other dopant gradients. Under inert conditions zero flux boundary conditions are generally accepted for all dopants (3.2-6).
The dopant conservation laws (3.2-2), together with the dopant fluxes (3.2-5) and the boundary conditions (3.2-6) represent the system of PDEs which is solved by the PROMIS library diffusion model DIFC.
