We describe a novel state of electrons and phonons arising in semiconductor superlattices (SSL) due to strong electron-phonon interactions. These states are characterized by a localization of phonons and a self-trapping or locking of electrons in one or several quantum wells due to an additional, deformational potential arising around these locking wells in SSL. The effect is enhanced in a longitudinal magnetic field. Using the tight-binding and adiabatic approximations the whole energy

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... of the self-trapped states is found and accurate, analytic expressions are included for strong electron-phonon coupling. Finally, we discuss possible experiments which may detect these predicted self-trapped states.