Hi @ghost
For the “continuous” interface, the bulk equations are added together into the same row of the simulation matrix. This works with your equation 3-211 above, since the surface normals \hat{n} are actually pointing in opposite directions away from the interface.
I am not sure what you mean about having subtraction. Are you saying that opposite signed sheet charges are being placed at each side of the interface?
Would the thermionic emission model take care of the existence of the sheet charge, or is the charge actually specified?
Please see these posts where I try to explain the different modes:
Interface equation for tunneling current
Could the more information can be offered about fluxterm in interface_equation
If it turns out neither of these interface options work for you, there is also the capability to create custom matrix entries that get added to the simulation.
How to use the function custom_equation/
My suggestion is to keep the Potential equation as “continuous”, since the voltage should be continuous across the interface.
For the thermionic emission, have both electrons and holes use the “fluxterm” condition.
If charge still needs to be added, use the custom equation to add it.