Potential Jump Condition¶
The potential jump condition defines a discontinuous electric potential \(\phi\) with a given step across the boundary between two contacting regions:
\[
\left. \phi \right|_{\partial\Omega_0} - \left. \phi \right|_{\partial\Omega_1}
= \phi_0,
\]
where \(\partial\Omega_0\) and \(\partial\Omega_1\) are the touching boundaries of the two regions and \(\phi_0\) is the prescribed potential jump.
Both bodies need their own boundary markers on the shared interface. Then the two sides carry independent DOFs, and \(\phi_0\) can offset them.
When to use this¶
- Contact potential / work-function differences at metal-metal or metal-semiconductor junctions.
- Surface-charge double layers that produce a known potential step (electrochemical, biological membranes).
- Idealised thin-film batteries with a prescribed open-circuit voltage modelled as a jump across the cell.