The generalized boundary condition is the constitutive relation for the contact potential
and reads
where QC is the contact charge and
IC = InC + IpC + QC/
t
the contact current. It should be noted that all these quantities are
solution variables, which simplifies the formulation of the contact models.
For the special case of a traditional voltage controlled contact
= 1,
=
= 0, and
= V0 and (5.20) degenerates
to
f![]() ![]() |
(5.21) |
Modeling a series contact resistance using
= RC one gets
f![]() ![]() |
(5.22) |
For a current controlled contact
= 1,
=
= 0, and
= I0 and (5.20) degenerates
to
For a charge controlled contact
=
= 0,
= 1, and
= Q0 and (5.20) degenerates
to
Using different units for the coefficients ,
,
, and
(5.20) can be interpreted in different ways.
These include a parallel conductance and capacitance to ground for a current
controlled contact, and a series resistance and parallel capacitance
to ground for a voltage controlled contact.
As (5.20) is normally not diagonal-dominant it is pre-eliminated.
In (5.23) the main-diagonal entry is zero, therefore fIC
must be eliminated first in order to get the derivatives with respect to .