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.
The electric potential must be continuous at the interface of the two different materials, as the electrostatic potential has a single value at any position.
The electrochemical potential at equilibrium which is equal to the Fermi level is constant among materials in thermal equilibrium.
Best wishes
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