So why does not happen this shift for ohmic contact under bias?
Refer to new attachment
The figures shown by Khalil Eslami (for Schottky Barrier (SB) and Ohmic Contact (OC) ) reveals the essence of the difference between the two meta-semiconductor contacts.
1) In SB the contacts (just at the contact between the Metal and the Semiconductor) supports the most part of the voltage drop applied to the structure. Certain drop also appears across the semiconductor just as the figure of the OC shows (gradual change in the Fermi level in the semiconductor - series resistance at high current level in the forward region). The voltage drop appears as the change in the Fermi energy at the contact we see an abrupt change of the Fermi energy revealing that there is a voltage drop just at the contact.
2) In OC there is no barrier and the contact does not support any voltage drop (no change in Fermi energy at the contact). The whole applied voltage drops gradually across the distributed resistive semiconductor material. In fact there should be a very small drop at the contact because of the contact resistance Rc.
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