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 = - V0 = 0||(5.21)|
Modeling a series contact resistance using = RC one gets
|f = + RC . IC - V0 = 0||(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 .