why there is band bending in semiconductor QDs but there is no in metal (at metal- semiconductor interface)?
Band bending is due to surfaces or interfaces states in the gap of the semiconductors that pins the chemical potential at surfaces or interfaces. As the chemical potential is at equilibrium the same everywhere bending occurs. In the case of metals, The chemical potential of the metal is essentially unchanged at surfaces or interfaces
since the number of available electrons in the bulk metal is very large compared to the
necessary number of electrons to fill the surface states.
I have a different model. Band bendings also occur in metals. But the bending is very strong because of the super-high density of "carriers"; the thickness of the band bending area is very thin, possibly only one atomic layer or less, so it is negligible. I think this model give easier understanding especially about metal--metal boundaries.
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