Charge Transport at Dielectric Interfaces
Charge transport at dielectric interface is critical in many applications. Electric charges can accumulate at the interface, for example, by corona discharge. Space charges at the interface can also drift along the interface surface due to the surface electric field, drift into adjacent conducting domains.
Charge Conservation
At the interface of two insulator domains, surface charge can modify the electric field through the boundary condition
Current Conservation
At the interface of two conductor domains, surface conduction can be taken into account through
where nup and ndown are the outward normal vector from the upside and downside domains, respectively; σs is the surface conductivity; and Es is the surface electric field computed as the negative of the tangential potential gradient.
Charge Accumulation
At the interface of a charge transport domain and another charge transport domain or an insulator domain, charge accumulates at the interface. For electrostatics, the surface charge is considered through
where ρs is the solution to the following transport equation at the interface:
where the right-hand side of the equation considers charge transport from bulk materials.
Charge Accumulation and Current Conservation
At the interface of a conductor domain and a charge transport domain or an insulator domain, charge can both accumulate at the interface and move to the conductor domain. This general charge transport dynamics can be modeled by enforcing current conservation at the interface: