Your drawing is missing 2 juntions. One between the p-type and the wire, and another between the n-type and the wire. The voltage drop on these 2 juntions will compensate V_depletion. See Feynamn section 14-4 for a similar discussion

Your drawing is missing 2 junctions. One between the p-type and the wire, and another between the n-type and the wire.

The voltage drop on these 2 junctions will compensate V_depletion and the wire will be no need potential across it. 

See Feynman section 14-4 for a similar discussion