Is a 'neutral' metal-semiconductor junction possible?

Hello,

While reviewing literature on metal-semiconductor junctions, I came
across a definition for a "neutral contact", which was described as the
junction that is formed when two materials with identical work
functions are joined, so that no band bending occurs. This makes sense
for two identical materials, but if for example, an n-type
semiconductor with a wide forbidden band gap and a metal somehow had
the same work functions and were joined, I appreciate that there would
be no built-in potential barrier, but wouldn't a Schottky barrier be
formed due to the position of the conduction band edge over the common
Fermi level? Would electrons still not have to overcome this barrier if
the metal was biased negative wrt the semiconductor? Is it that metal
electrons simply tunnel into the forbidden gap, where they are swept to
the conduction band under the influence of the external bias? If so,
wouldn't there not be a minimum bias required to achieve this, which
would be proportional to the size of the energy gap between the
Fermi-level and the conduction band? Sorry for all the questions, but I
would be glad if someone could help me to clarify my understanding.

Thanks,
John.

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