Check out https://en.wikipedia.org/wiki/Hot-carrier_injection hot carrier degredation, it’s in the vicinity of electron mobility but in a semiconductor setting. Key link is it’s electrons with momentum doing the work. In this case electrons (much hotter than in electron mobility, which are limited by the saturation velocity) smash into the gate dielectric, making it a worse dielectric. Hot carrier injection doesn’t have to end in damage to the dielectric, but when it does it’s hot carrier degredation. There’s a lot going on though, semiconductors are really complex - like electron tunneling also exists.

Electromigration in ICs typically occurs in metal interconnect, so there are no dopants there to move. Dopants are added to the silicon substrate.