I apologise in advance for not finding the answer myself. I spent some time googling, but was only able to find a few related questions but no direct answer to my one. I also have to add that I'm not a student and study semiconductors in my free time.
I wonder why the majority carriers in a semiconductor have such a freedom of movement and not stay in the vicinity of the dopant atoms?
I'll provide a specific example: a Silicon crystal doped with Phosphorus. Phosphorous does indeed have an extra electron that can serve as a majority carrier, however, it also contains one proton more which attracts the electron.
Doesn't that mean that even if an electron manages to escape far enough for the electrostatic forces to be negligible, the extra proton not moving anywhere would constitute a local positive charge that would attract other passing by majority carriers and eventually trap one of them?
I would also imagine that the electrostatic force attracting electrons to the Phosphorus ion should be much greater in its direct proximity than any reasonable bias voltage applied to the far-away terminals.