Why there is a sharp cut off of the charged region outside the depletion region, like on this image?
For example why don't electrons on the conduction band in the n-type side rush towards the positively charged area making the whole piece positively charged somewhat, not just at the area near the depletion region?
The source of the confusion is that I know if you charge up a regular conductors the internal currents will uniformly distribute the charge along the whole piece, while insulators are only locally charged up, since they cannot carry current. Semiconductors here seem to act like insulators, but diodes do carry current when used. How?