At the interface between:

1) conductor/conductor

2) conductor/semiconductor (or dielectric)

3) semiconductor/semiconductor (or dielectric/dielectric)

What quantity should be continuous?

Is it the electrochemical potential, only the chemical potential or is it the electric potential?

Since they are all connected by Vec=Vc+Ve, if two of them are continuous then all of them are continuous, but I think this situations cannot be true.

However, I know that the Fermi energy is continuous (which I think is the chemical potential but I'm not sure since there's a lot of misleading information). And also the electric potential should be continuous, otherwise the electric field (defined by E=-grad(Ve)) would be infinity.

This question refer both for equilibrium and for an applied voltage (steady currents).

I couldn't find any information on this matter. All books on semiconductors or electrostatic/dynamic does not mention it and does not get to much deep into such physics.

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